text
stringlengths 165
245k
β | summary
stringlengths 67
14.4k
| prompt
stringlengths 860
246k
|
|---|---|---|
in recent years , significant advances have been achieved in the development of topical glaucoma medications ( camras et al 1996 ; silver 1998 ; brubaker et al 2000 ) , and options for combination therapy have increased . because a significant proportion of glaucoma patients eventually need more than one agent for adequate control of intraocular pressure ( iop ) ( kobelt - nguyen et al 1998 ) , it is important to reduce adverse ocular or systemic events in those treated with combination therapy . using prostaglandin analogs as first - line treatment has given rise to numerous studies in search for the most effective and best - tolerated combination , from both a local and a systemic perspective .
iop reduction rates with various agents have been reported as follows : timolol 0.5% monotherapy , approximately 23.4% ( schenker et al 1999 ) ; topical carbonic anhydrase inhibitors ( cais ) such as brinzolamide , 13.2%16.7% ( sall 2000 ) ; and dorzolamide , 19.4% ( arici et al 1998 ) .
meta - analysis of the iop - lowering effects of several glaucoma medications demonstrated similar results ( van der valk 2005 ) , with iop reduction rates being highest with beta - blockers . the combination of a prostaglandin analog plus a beta - blocker has been extensively studied and is probably the most commonly used combination ( alm et al 1995 ; larsson 2001 ; higginbotham et al 2002 ) .
it is noteworthy that the addition of a topical beta - blocker to latanoprost provides a slight additional iop reduction ( bucci 1999 ; oconnor et al 2002 ) . the efficacy of combination therapy using a topical cai and latanoprost
has not been studied to the same extent as that of latanoprost in combination with a beta - blocker ; however , dorzolamide and brinzolamide have been reported to lower iop at least as effectively as a beta - blocker when added to latanoprost ( oconnor et al 2002 ; shoji 2005 ) .
this option of latanoprost and topical cai combination therapy may confer advantages for glaucoma patients as both drugs present an excellent systemic safety profile .
brinzolamide ( 1% ophthalmic solution ) is a topical cai that , like dorzolamide , is known to lower iop by inhibiting the production of aqueous humor ( silver 1998 ; schenker et al 1999 ; brubaker et al 2000 ; desantis 2000 ; march and ochsner 2000 ; michaud and friren 2001 ) .
the iop - lowering effect of brinzolamide 1.0% is reported to be equivalent to that of dorzolamide 2% , both as monotherapy ( barnebey and kwok 2000 ; sall 2000 ) and in combination therapy with timolol ( michaud and friren 2001 ) .
furthermore , when brinzolamide is substituted for dorzolamide , iop is further decreased ( barnebey and kwok 2000 ) or is equal to iop before substitution ( kobayashi et al 2004 ; kubota et al 2004 ) . in evaluations of ocular adverse events ,
dorzolamide has reportedly caused more intense ocular irritation than brinzolamide ( barnebey and kwok 2000 ; sall 2000 ; silver 2000 ; michaud and friren 2001 ; seong et al 2001 ; kobayashi et al 2004 ; stewart et al 2004 ; tsukamoto et al 2005 ) .
the incidence of ocular discomfort or blurred vision for brinzolamide is significantly higher than that of dorzolamide in one study ( silver 2000 ) , but not statistically significant in other studies ( sall 2000 ; michaud and friren 2001 ; stewart et al 2004 ; tsukamoto et al 2005 ) .
the objective of this study was to evaluate the effects of a change in therapeutic regimen from combination therapy with timolol / latanoprost to combination therapy with brinzolamide / latanoprost in terms of : iop , the cardiovascular functions of blood pressure ( bp ) and pulse rate ( pr ) , and ocular adverse events .
a 12-week , open - label , non - randomized , prospective , comparative study was conducted in japanese patients with primary open - angle glaucoma ( poag ) ( 17 patients ) or ocular hypertension ( oh ) ( 3 patients ) at ryukyu university hospital and yamagata university hospital .
poag was defined as glaucomatous optic neuropathy with repeatable visual field defects , and open angle .
enrolled patients had been under treatment with both latanoprost ( once daily , at 8 pm ) and timolol 0.5% ( twice a day , at 8 am and 8 pm ) for 3 months or longer and had not used any topical cai prior to this study .
inclusion criteria for the study were : ( 1 ) patients with primary open - angle glaucoma or ocular hypertension , ( 2 ) patients who had been treated with both latanoprost 0.005% once daily and timolol 0.5% twice daily for more than 3 months , ( 3 ) patients with iop on latanoprost and timolol treatment 16 mmhg , ( 4 ) patients aged 20 years or over .
the following patients were excluded from the study : ( 1 ) patients with a history of chronic or recurrent inflammatory eye disease , ocular trauma , or ocular infection within the past 3 months , ( 2 ) those with corneal abnormalities preventing reliable applanation tonometry , ( 3 ) those who had had intraocular surgery , ( 4 ) those who had had laser surgery within the past 3 months , ( 5 ) those with severe , unstable , or uncontrolled cardiovascular or pulmonary disease that would preclude use of an ophthalmic beta - blocker , ( 6 ) those currently using any ophthalmic , dermatologic , or systemic corticosteroid or oral cais , ( 7 ) those with a history of severe hypersensitivity to oral cais , sulfonamide drugs , or any components of these medications , ( 8) those with dementia , and ( 9 ) those whom the investigator determined ineligible to participate in this study . because enrolled patients were eligible for latanoprost and timolol combination therapy , those with hypersensitivity or allergy to either of these agents were excluded prior to the study .
all patients were given a thorough explanation of the aims , protocol , and all procedures of the study before enrollment , and informed consent was then obtained .
binzolamide 1% twice daily ( at 8 am and 8 pm ) was given to each patient in place of timolol 0.5% twice daily to compare the efficacy and side effects from this change in therapeutic regimen .
the prescription of brinzolamide 1% twice a day is common practice and is based on the label approved by the government in japan .
if both eyes were eligible for inclusion , the eye with higher baseline iop was selected as the study eye . when iop was the same in both eyes , the right eye was selected .
iop was measured at the baseline visit and at 4 , 8 , and 12 weeks after enrollment using goldmann applanation tonometry .
the time of day at which iop was measured during the study was the same as that at baseline .
resting bp ( systolic and diastolic ) and pr were also measured at the baseline and at 12 weeks .
subjective ocular discomfort ( mild irritation , blurred vision , and conjunctival hyperemia ) and subjective ocular adverse events ( stinging / intense irritation ) after instillation of eye drops were investigated by patient interview . during clinic visits
patients were asked whether they had a sense of ocular discomfort at the time of instillation and how long the ocular discomfort persisted after instillation .
if a patient complained of any sense of irritation and/or blurred vision at least once during the follow - up period , the patient was regarded as having ocular discomfort .
the wilcoxon signed rank test was used for statistical analysis , and the difference was considered significant when the p value was less than 0.05 .
of the 20 patients ( 11 males and 9 females ) enrolled , no patients dropped out during the course of the study , and therefore 20 patients were accepted for analysis of iop and local and systemic adverse events .
briefly , the mean age of the patients was 64.5 11.0 ( mean standard deviation ) years old .
seventeen patients ( 17 eyes ) had poag , and 3 patients ( 3 eyes ) had oh . all had been treated with a combination of latanoprost 0.005% and timolol 0.5% for more than 3 months .
mean iop at baseline , 4 , 8 , and 12 weeks after enrollment were 18.6 2.1 mmhg , 17.8 2.6 mmhg , 17.4 2.5 mmhg , and 17.3 3.5 mmhg , respectively .
significant reductions in mean iop were observed at the 4-week and 8-week time points ( p < 0.05 ) ( figure 2 ) .
mean iop reduction from baseline was 0.8 mmhg ( 4.3% reduction ) after 4 weeks , 1.2 mmhg ( 6.5% reduction ) after 8 weeks , and 1.3 mmhg ( 7.0% reduction ) after 12 weeks .
mean systolic and diastolic bps were 139 20 mmhg and 80 12 mmhg at baseline , and 135 24 mmhg and 81 13 mmhg at the 12-week point .
thus the substitution of brinzolamide had little effect on systolic and diastolic bp ( p > 0.05 ) ( figure 3 ) .
in contrast , mean pr was 68 9 bpm at baseline , with a significant increase to 78 13 bpm at the 12-week point ( p < 0.01 ) ( figure 4 ) .
after therapeutic substitution , ocular adverse events were observed in 4 cases ( 2 blurred vision , 1 mild irritation , and 1 mild hyperemia ) ( table 2 ) .
in this study , we compared the efficacy and safety of brinzolamide 1% twice daily as a second - line medication when substituted for timolol 0.5% in combination therapy with latanoprost in japanese patients with poag or oh . we concluded that substitution of brinzolamide for timolol significantly lowered iop with significant improvement of pr without systemic or serious local adverse reactions .
two recently developed topical cais , dorzolamide and brinzolamide , are now usually used as an adjunctive therapy to other anti - glaucoma eye drops .
the iop - lowering effect of brinzolamide 1% ( twice daily ) was equivalent to dorzolamide 2% ( 3 times daily ) when added to timolol 0.5% ( michaud and friren 2001 ) .
the effect of topical cais as a second - line medication has been reported ( arici et al 1998 ; shin 2000 ; michaud and friren 2001 ; oconnor et al 2002 ; martinez - de - la - casa et al 2004 ; shoji et al 2005 ; tsukamoto et al 2005 ) . brinzolamide was reported to show an additional iop reduction of 5.3 mmhg ( 23.5% ) when added to latanoprost ( shoji et al 2005 ) .
it has also been reported that the addition of dorzolamide to latanoprost decreased iop by 3.9 mmhg ( 19.7% ) compared with beta - blocker ( 2.5 mmhg ; 12.3% ) ( oconner et al 2002 ) .
brinzolamide showed similar efficacy to timolol maleate when added to travoprost ( hollo et al 2006 ) . in our study , iop reductions from baseline at 4 , 8 , and 12 weeks after the substitution of brinzolamide 1% for timolol 0.5% were 0.8 , 1.2 , and 1.3 mmhg , respectively .
the patients who enrolled in this study had already undergone treatment with latanoprost 0.005% and timolol 0.5% . nevertheless , the substitution of brinzolamide for timolol 0.5% further significantly decreased iop .
this result was similar to the iop reduction observed by oconner et al ( 2002 ) .
the early manifest glaucoma trial group reported that on follow - up , each mmhg reduction in iop decreased the risk of disease progression by approximately 10% ( heijl et al 2002 ) . therefore , even though the reduction in iop after the substitution of brinzolamide for timolol was small ( < 2 mmhg ) , this iop reduction could be considered clinically significant .
brinzolamide is a white suspension . in our study , brinzolamide caused blurred vision ( 2 cases ) , and mild irritation and mild hyperemia ( 1 case ) after switching from timolol . as with earlier studies , adverse events related to brinzolamide treatment generally occurred on instillation ,
were usually mild , resolved without treatment , and generally did not interrupt therapy continuation ( silver 1998 ; barnebey and kwok 2000 ; martinez - de - la - casa et al 2004 ) ( ie , no patient was discontinued from the current study due to adverse events ) .
it has also been reported that in comparisons of brinzolamide and timolol monotherapy ( march and ochsner 2000 ) , brinzolamide produced fewer ( 3.3% ) ocular adverse events ( burning / stinging ) than timolol ( 8.0% ) .
the ocular discomfort of blurred vision was generally mild , and the medication was well tolerated .
therefore , evidence suggests that substituting brinzolamide for timolol may produce very few ocular adverse events in combination therapy with latanoprost .
non - selective and selective beta - blockers may have significant side effects on cardiovascular and respiratory organs , especially in elderly populations ( nelson et al 1986 ) .
when assessing a drug like timolol , which is used by a predominantly elderly population that is a priori at risk for cardiovascular and respiratory disease , it is often difficult to determine whether the suspect event is a consequence of the drug , the patients age , an underlying medical condition , or a combination of factors . in agreement with a previous study ,
no clinically significant adverse effect on pr and bp occurred with brinzolamide ( silver 1998 ) and no systemic side effects were noted .
topical beta - blockers can cause nocturnal hypotension in glaucoma patients ( heyreh et al 1999 ) .
the most effective medications for long - term therapy are those that are efficacious , well tolerated , and show few side effects . in those patients in whom beta - blockers are contraindicated , brinzolamide offers an effective alternative .
two recently developed topical cais , dorzolamide and brinzolamide , are now usually used as an adjunctive therapy to other anti - glaucoma eye drops .
the iop - lowering effect of brinzolamide 1% ( twice daily ) was equivalent to dorzolamide 2% ( 3 times daily ) when added to timolol 0.5% ( michaud and friren 2001 ) .
the effect of topical cais as a second - line medication has been reported ( arici et al 1998 ; shin 2000 ; michaud and friren 2001 ; oconnor et al 2002 ; martinez - de - la - casa et al 2004 ; shoji et al 2005 ; tsukamoto et al 2005 ) .
brinzolamide was reported to show an additional iop reduction of 5.3 mmhg ( 23.5% ) when added to latanoprost ( shoji et al 2005 ) .
it has also been reported that the addition of dorzolamide to latanoprost decreased iop by 3.9 mmhg ( 19.7% ) compared with beta - blocker ( 2.5 mmhg ; 12.3% ) ( oconner et al 2002 ) .
brinzolamide showed similar efficacy to timolol maleate when added to travoprost ( hollo et al 2006 ) . in our study , iop reductions from baseline at 4 , 8 , and 12 weeks after the substitution of brinzolamide 1% for timolol 0.5% were 0.8 , 1.2 , and 1.3 mmhg , respectively .
the patients who enrolled in this study had already undergone treatment with latanoprost 0.005% and timolol 0.5% .
this result was similar to the iop reduction observed by oconner et al ( 2002 ) .
the early manifest glaucoma trial group reported that on follow - up , each mmhg reduction in iop decreased the risk of disease progression by approximately 10% ( heijl et al 2002 ) .
therefore , even though the reduction in iop after the substitution of brinzolamide for timolol was small ( < 2 mmhg ) , this iop reduction could be considered clinically significant .
brinzolamide is a white suspension . in our study , brinzolamide caused blurred vision ( 2 cases ) , and mild irritation and mild hyperemia ( 1 case ) after switching from timolol . as with earlier studies , adverse events related to
brinzolamide treatment generally occurred on instillation , were usually mild , resolved without treatment , and generally did not interrupt therapy continuation ( silver 1998 ; barnebey and kwok 2000 ; martinez - de - la - casa et al 2004 ) ( ie , no patient was discontinued from the current study due to adverse events ) .
it has also been reported that in comparisons of brinzolamide and timolol monotherapy ( march and ochsner 2000 ) , brinzolamide produced fewer ( 3.3% ) ocular adverse events ( burning / stinging ) than timolol ( 8.0% ) .
the ocular discomfort of blurred vision was generally mild , and the medication was well tolerated .
therefore , evidence suggests that substituting brinzolamide for timolol may produce very few ocular adverse events in combination therapy with latanoprost .
non - selective and selective beta - blockers may have significant side effects on cardiovascular and respiratory organs , especially in elderly populations ( nelson et al 1986 ) .
when assessing a drug like timolol , which is used by a predominantly elderly population that is a priori at risk for cardiovascular and respiratory disease , it is often difficult to determine whether the suspect event is a consequence of the drug , the patients age , an underlying medical condition , or a combination of factors . in agreement with a previous study , no clinically significant adverse effect on pr and bp occurred with brinzolamide ( silver 1998 ) and no systemic side effects were noted .
topical beta - blockers can cause nocturnal hypotension in glaucoma patients ( heyreh et al 1999 ) .
the most effective medications for long - term therapy are those that are efficacious , well tolerated , and show few side effects . in those patients in whom beta - blockers
the latanoprost / brinzolamide combination can have a significant additive effect on iop reduction compared with the latanoprost / timolol combination .
iop reduction has been established to be an effective means of treating glaucoma ( mao et al 1991 ; collaborative normal - tension glaucoma study group 1998 ; agis investigations 2000 ; heijl et al 2002 ; kass 2002 ; tsukamoto et al 2005 ) . to improve quality of life and vision , and to reduce the adverse events of glaucoma treatment , it is necessary to achieve a maximum iop reduction with a minimum but adequate number of instillations .
substitution of brinzolamide 1% for timolol 0.5% in combination therapy with latanoprost 0.005% demonstrated superior and significant iop reduction and improvement of pr .
the ocular discomforts of blurred vision in 2 cases , mild irritation in 1 case , and mild hyperemia in 1 case were transient and mild after regimen change , and all resolved without treatment .
the use of brinzolamide in place of timolol as a second - line medication in combination with latanoprost can be recommended for poag or oh patients for better iop control and fewer systemic side effects .
however , this open non - randomized study evaluated a limited number of the patients treated in the short term , so that additional randomized studies on long - term administration and diurnal iops need to be considered . | purposeto compare the efficacy of brinzolamide in japanese patients with primary open - angle glaucoma ( poag ) or ocular hypertension ( oh ) after a change from timolol in combination therapy with latanoprost.methodsa 12-week , prospective , open - label , comparative study was performed in 20 patients [ 11 males and 9 females , mean age of 64.5 11.0 ( sd)y ] with poag or oh treated with both latanoprost once daily and timolol 0.5% twice daily . during the study brinzolamide
was substituted for timolol . intraocular pressure ( iop )
was measured at baseline , 4 , 8 , and 12 weeks .
blood pressure ( bp ) , pulse rate ( pr ) , and adverse events were also recorded.resultsiops at baseline , 4 , 8 , and 12 weeks were 18.6 2.1 mmhg , 17.8 2.6 mmhg , 17.4 2.5 mmhg , and 17.3 3.5 mmhg , respectively .
iop reduction at 4 and 8 weeks was statistically significant ( p < 0.05 ) .
the pr was significantly increased at 12 weeks ( p < 0.01 ) , but bp was not significantly affected .
four ocular adverse events were noted , but all were mild and transient.conclusionssubstituting brinzolamide 1% for timolol 0.5% in combination therapy with latanoprost 0.005% demonstrated significant iop reduction with improvement in pr with poag or oh . combination therapy using latanoprost and brinzolamide may be recommended for better iop control with fewer systemic adverse events . | <s>[INST]in recent years , significant advances have been achieved in the development of topical glaucoma medications ( camras et al 1996 ; silver 1998 ; brubaker et al 2000 ) , and options for combination therapy have increased . because a significant proportion of glaucoma patients eventually need more than one agent for adequate control of intraocular pressure ( iop ) ( kobelt - nguyen et al 1998 ) , it is important to reduce adverse ocular or systemic events in those treated with combination therapy . using prostaglandin analogs as first - line treatment has given rise to numerous studies in search for the most effective and best - tolerated combination , from both a local and a systemic perspective .
iop reduction rates with various agents have been reported as follows : timolol 0.5% monotherapy , approximately 23.4% ( schenker et al 1999 ) ; topical carbonic anhydrase inhibitors ( cais ) such as brinzolamide , 13.2%16.7% ( sall 2000 ) ; and dorzolamide , 19.4% ( arici et al 1998 ) .
meta - analysis of the iop - lowering effects of several glaucoma medications demonstrated similar results ( van der valk 2005 ) , with iop reduction rates being highest with beta - blockers . the combination of a prostaglandin analog plus a beta - blocker has been extensively studied and is probably the most commonly used combination ( alm et al 1995 ; larsson 2001 ; higginbotham et al 2002 ) .
it is noteworthy that the addition of a topical beta - blocker to latanoprost provides a slight additional iop reduction ( bucci 1999 ; oconnor et al 2002 ) . the efficacy of combination therapy using a topical cai and latanoprost
has not been studied to the same extent as that of latanoprost in combination with a beta - blocker ; however , dorzolamide and brinzolamide have been reported to lower iop at least as effectively as a beta - blocker when added to latanoprost ( oconnor et al 2002 ; shoji 2005 ) .
this option of latanoprost and topical cai combination therapy may confer advantages for glaucoma patients as both drugs present an excellent systemic safety profile .
brinzolamide ( 1% ophthalmic solution ) is a topical cai that , like dorzolamide , is known to lower iop by inhibiting the production of aqueous humor ( silver 1998 ; schenker et al 1999 ; brubaker et al 2000 ; desantis 2000 ; march and ochsner 2000 ; michaud and friren 2001 ) .
the iop - lowering effect of brinzolamide 1.0% is reported to be equivalent to that of dorzolamide 2% , both as monotherapy ( barnebey and kwok 2000 ; sall 2000 ) and in combination therapy with timolol ( michaud and friren 2001 ) .
furthermore , when brinzolamide is substituted for dorzolamide , iop is further decreased ( barnebey and kwok 2000 ) or is equal to iop before substitution ( kobayashi et al 2004 ; kubota et al 2004 ) . in evaluations of ocular adverse events ,
dorzolamide has reportedly caused more intense ocular irritation than brinzolamide ( barnebey and kwok 2000 ; sall 2000 ; silver 2000 ; michaud and friren 2001 ; seong et al 2001 ; kobayashi et al 2004 ; stewart et al 2004 ; tsukamoto et al 2005 ) .
the incidence of ocular discomfort or blurred vision for brinzolamide is significantly higher than that of dorzolamide in one study ( silver 2000 ) , but not statistically significant in other studies ( sall 2000 ; michaud and friren 2001 ; stewart et al 2004 ; tsukamoto et al 2005 ) .
the objective of this study was to evaluate the effects of a change in therapeutic regimen from combination therapy with timolol / latanoprost to combination therapy with brinzolamide / latanoprost in terms of : iop , the cardiovascular functions of blood pressure ( bp ) and pulse rate ( pr ) , and ocular adverse events .
a 12-week , open - label , non - randomized , prospective , comparative study was conducted in japanese patients with primary open - angle glaucoma ( poag ) ( 17 patients ) or ocular hypertension ( oh ) ( 3 patients ) at ryukyu university hospital and yamagata university hospital .
poag was defined as glaucomatous optic neuropathy with repeatable visual field defects , and open angle .
enrolled patients had been under treatment with both latanoprost ( once daily , at 8 pm ) and timolol 0.5% ( twice a day , at 8 am and 8 pm ) for 3 months or longer and had not used any topical cai prior to this study .
inclusion criteria for the study were : ( 1 ) patients with primary open - angle glaucoma or ocular hypertension , ( 2 ) patients who had been treated with both latanoprost 0.005% once daily and timolol 0.5% twice daily for more than 3 months , ( 3 ) patients with iop on latanoprost and timolol treatment 16 mmhg , ( 4 ) patients aged 20 years or over .
the following patients were excluded from the study : ( 1 ) patients with a history of chronic or recurrent inflammatory eye disease , ocular trauma , or ocular infection within the past 3 months , ( 2 ) those with corneal abnormalities preventing reliable applanation tonometry , ( 3 ) those who had had intraocular surgery , ( 4 ) those who had had laser surgery within the past 3 months , ( 5 ) those with severe , unstable , or uncontrolled cardiovascular or pulmonary disease that would preclude use of an ophthalmic beta - blocker , ( 6 ) those currently using any ophthalmic , dermatologic , or systemic corticosteroid or oral cais , ( 7 ) those with a history of severe hypersensitivity to oral cais , sulfonamide drugs , or any components of these medications , ( 8) those with dementia , and ( 9 ) those whom the investigator determined ineligible to participate in this study . because enrolled patients were eligible for latanoprost and timolol combination therapy , those with hypersensitivity or allergy to either of these agents were excluded prior to the study .
all patients were given a thorough explanation of the aims , protocol , and all procedures of the study before enrollment , and informed consent was then obtained .
binzolamide 1% twice daily ( at 8 am and 8 pm ) was given to each patient in place of timolol 0.5% twice daily to compare the efficacy and side effects from this change in therapeutic regimen .
the prescription of brinzolamide 1% twice a day is common practice and is based on the label approved by the government in japan .
if both eyes were eligible for inclusion , the eye with higher baseline iop was selected as the study eye . when iop was the same in both eyes , the right eye was selected .
iop was measured at the baseline visit and at 4 , 8 , and 12 weeks after enrollment using goldmann applanation tonometry .
the time of day at which iop was measured during the study was the same as that at baseline .
resting bp ( systolic and diastolic ) and pr were also measured at the baseline and at 12 weeks .
subjective ocular discomfort ( mild irritation , blurred vision , and conjunctival hyperemia ) and subjective ocular adverse events ( stinging / intense irritation ) after instillation of eye drops were investigated by patient interview . during clinic visits
patients were asked whether they had a sense of ocular discomfort at the time of instillation and how long the ocular discomfort persisted after instillation .
if a patient complained of any sense of irritation and/or blurred vision at least once during the follow - up period , the patient was regarded as having ocular discomfort .
the wilcoxon signed rank test was used for statistical analysis , and the difference was considered significant when the p value was less than 0.05 .
of the 20 patients ( 11 males and 9 females ) enrolled , no patients dropped out during the course of the study , and therefore 20 patients were accepted for analysis of iop and local and systemic adverse events .
briefly , the mean age of the patients was 64.5 11.0 ( mean standard deviation ) years old .
seventeen patients ( 17 eyes ) had poag , and 3 patients ( 3 eyes ) had oh . all had been treated with a combination of latanoprost 0.005% and timolol 0.5% for more than 3 months .
mean iop at baseline , 4 , 8 , and 12 weeks after enrollment were 18.6 2.1 mmhg , 17.8 2.6 mmhg , 17.4 2.5 mmhg , and 17.3 3.5 mmhg , respectively .
significant reductions in mean iop were observed at the 4-week and 8-week time points ( p < 0.05 ) ( figure 2 ) .
mean iop reduction from baseline was 0.8 mmhg ( 4.3% reduction ) after 4 weeks , 1.2 mmhg ( 6.5% reduction ) after 8 weeks , and 1.3 mmhg ( 7.0% reduction ) after 12 weeks .
mean systolic and diastolic bps were 139 20 mmhg and 80 12 mmhg at baseline , and 135 24 mmhg and 81 13 mmhg at the 12-week point .
thus the substitution of brinzolamide had little effect on systolic and diastolic bp ( p > 0.05 ) ( figure 3 ) .
in contrast , mean pr was 68 9 bpm at baseline , with a significant increase to 78 13 bpm at the 12-week point ( p < 0.01 ) ( figure 4 ) .
after therapeutic substitution , ocular adverse events were observed in 4 cases ( 2 blurred vision , 1 mild irritation , and 1 mild hyperemia ) ( table 2 ) .
in this study , we compared the efficacy and safety of brinzolamide 1% twice daily as a second - line medication when substituted for timolol 0.5% in combination therapy with latanoprost in japanese patients with poag or oh . we concluded that substitution of brinzolamide for timolol significantly lowered iop with significant improvement of pr without systemic or serious local adverse reactions .
two recently developed topical cais , dorzolamide and brinzolamide , are now usually used as an adjunctive therapy to other anti - glaucoma eye drops .
the iop - lowering effect of brinzolamide 1% ( twice daily ) was equivalent to dorzolamide 2% ( 3 times daily ) when added to timolol 0.5% ( michaud and friren 2001 ) .
the effect of topical cais as a second - line medication has been reported ( arici et al 1998 ; shin 2000 ; michaud and friren 2001 ; oconnor et al 2002 ; martinez - de - la - casa et al 2004 ; shoji et al 2005 ; tsukamoto et al 2005 ) . brinzolamide was reported to show an additional iop reduction of 5.3 mmhg ( 23.5% ) when added to latanoprost ( shoji et al 2005 ) .
it has also been reported that the addition of dorzolamide to latanoprost decreased iop by 3.9 mmhg ( 19.7% ) compared with beta - blocker ( 2.5 mmhg ; 12.3% ) ( oconner et al 2002 ) .
brinzolamide showed similar efficacy to timolol maleate when added to travoprost ( hollo et al 2006 ) . in our study , iop reductions from baseline at 4 , 8 , and 12 weeks after the substitution of brinzolamide 1% for timolol 0.5% were 0.8 , 1.2 , and 1.3 mmhg , respectively .
the patients who enrolled in this study had already undergone treatment with latanoprost 0.005% and timolol 0.5% . nevertheless , the substitution of brinzolamide for timolol 0.5% further significantly decreased iop .
this result was similar to the iop reduction observed by oconner et al ( 2002 ) .
the early manifest glaucoma trial group reported that on follow - up , each mmhg reduction in iop decreased the risk of disease progression by approximately 10% ( heijl et al 2002 ) . therefore , even though the reduction in iop after the substitution of brinzolamide for timolol was small ( < 2 mmhg ) , this iop reduction could be considered clinically significant .
brinzolamide is a white suspension . in our study , brinzolamide caused blurred vision ( 2 cases ) , and mild irritation and mild hyperemia ( 1 case ) after switching from timolol . as with earlier studies , adverse events related to brinzolamide treatment generally occurred on instillation ,
were usually mild , resolved without treatment , and generally did not interrupt therapy continuation ( silver 1998 ; barnebey and kwok 2000 ; martinez - de - la - casa et al 2004 ) ( ie , no patient was discontinued from the current study due to adverse events ) .
it has also been reported that in comparisons of brinzolamide and timolol monotherapy ( march and ochsner 2000 ) , brinzolamide produced fewer ( 3.3% ) ocular adverse events ( burning / stinging ) than timolol ( 8.0% ) .
the ocular discomfort of blurred vision was generally mild , and the medication was well tolerated .
therefore , evidence suggests that substituting brinzolamide for timolol may produce very few ocular adverse events in combination therapy with latanoprost .
non - selective and selective beta - blockers may have significant side effects on cardiovascular and respiratory organs , especially in elderly populations ( nelson et al 1986 ) .
when assessing a drug like timolol , which is used by a predominantly elderly population that is a priori at risk for cardiovascular and respiratory disease , it is often difficult to determine whether the suspect event is a consequence of the drug , the patients age , an underlying medical condition , or a combination of factors . in agreement with a previous study ,
no clinically significant adverse effect on pr and bp occurred with brinzolamide ( silver 1998 ) and no systemic side effects were noted .
topical beta - blockers can cause nocturnal hypotension in glaucoma patients ( heyreh et al 1999 ) .
the most effective medications for long - term therapy are those that are efficacious , well tolerated , and show few side effects . in those patients in whom beta - blockers are contraindicated , brinzolamide offers an effective alternative .
two recently developed topical cais , dorzolamide and brinzolamide , are now usually used as an adjunctive therapy to other anti - glaucoma eye drops .
the iop - lowering effect of brinzolamide 1% ( twice daily ) was equivalent to dorzolamide 2% ( 3 times daily ) when added to timolol 0.5% ( michaud and friren 2001 ) .
the effect of topical cais as a second - line medication has been reported ( arici et al 1998 ; shin 2000 ; michaud and friren 2001 ; oconnor et al 2002 ; martinez - de - la - casa et al 2004 ; shoji et al 2005 ; tsukamoto et al 2005 ) .
brinzolamide was reported to show an additional iop reduction of 5.3 mmhg ( 23.5% ) when added to latanoprost ( shoji et al 2005 ) .
it has also been reported that the addition of dorzolamide to latanoprost decreased iop by 3.9 mmhg ( 19.7% ) compared with beta - blocker ( 2.5 mmhg ; 12.3% ) ( oconner et al 2002 ) .
brinzolamide showed similar efficacy to timolol maleate when added to travoprost ( hollo et al 2006 ) . in our study , iop reductions from baseline at 4 , 8 , and 12 weeks after the substitution of brinzolamide 1% for timolol 0.5% were 0.8 , 1.2 , and 1.3 mmhg , respectively .
the patients who enrolled in this study had already undergone treatment with latanoprost 0.005% and timolol 0.5% .
this result was similar to the iop reduction observed by oconner et al ( 2002 ) .
the early manifest glaucoma trial group reported that on follow - up , each mmhg reduction in iop decreased the risk of disease progression by approximately 10% ( heijl et al 2002 ) .
therefore , even though the reduction in iop after the substitution of brinzolamide for timolol was small ( < 2 mmhg ) , this iop reduction could be considered clinically significant .
brinzolamide is a white suspension . in our study , brinzolamide caused blurred vision ( 2 cases ) , and mild irritation and mild hyperemia ( 1 case ) after switching from timolol . as with earlier studies , adverse events related to
brinzolamide treatment generally occurred on instillation , were usually mild , resolved without treatment , and generally did not interrupt therapy continuation ( silver 1998 ; barnebey and kwok 2000 ; martinez - de - la - casa et al 2004 ) ( ie , no patient was discontinued from the current study due to adverse events ) .
it has also been reported that in comparisons of brinzolamide and timolol monotherapy ( march and ochsner 2000 ) , brinzolamide produced fewer ( 3.3% ) ocular adverse events ( burning / stinging ) than timolol ( 8.0% ) .
the ocular discomfort of blurred vision was generally mild , and the medication was well tolerated .
therefore , evidence suggests that substituting brinzolamide for timolol may produce very few ocular adverse events in combination therapy with latanoprost .
non - selective and selective beta - blockers may have significant side effects on cardiovascular and respiratory organs , especially in elderly populations ( nelson et al 1986 ) .
when assessing a drug like timolol , which is used by a predominantly elderly population that is a priori at risk for cardiovascular and respiratory disease , it is often difficult to determine whether the suspect event is a consequence of the drug , the patients age , an underlying medical condition , or a combination of factors . in agreement with a previous study , no clinically significant adverse effect on pr and bp occurred with brinzolamide ( silver 1998 ) and no systemic side effects were noted .
topical beta - blockers can cause nocturnal hypotension in glaucoma patients ( heyreh et al 1999 ) .
the most effective medications for long - term therapy are those that are efficacious , well tolerated , and show few side effects . in those patients in whom beta - blockers
the latanoprost / brinzolamide combination can have a significant additive effect on iop reduction compared with the latanoprost / timolol combination .
iop reduction has been established to be an effective means of treating glaucoma ( mao et al 1991 ; collaborative normal - tension glaucoma study group 1998 ; agis investigations 2000 ; heijl et al 2002 ; kass 2002 ; tsukamoto et al 2005 ) . to improve quality of life and vision , and to reduce the adverse events of glaucoma treatment , it is necessary to achieve a maximum iop reduction with a minimum but adequate number of instillations .
substitution of brinzolamide 1% for timolol 0.5% in combination therapy with latanoprost 0.005% demonstrated superior and significant iop reduction and improvement of pr .
the ocular discomforts of blurred vision in 2 cases , mild irritation in 1 case , and mild hyperemia in 1 case were transient and mild after regimen change , and all resolved without treatment .
the use of brinzolamide in place of timolol as a second - line medication in combination with latanoprost can be recommended for poag or oh patients for better iop control and fewer systemic side effects .
however , this open non - randomized study evaluated a limited number of the patients treated in the short term , so that additional randomized studies on long - term administration and diurnal iops need to be considered .[/INST]purposeto compare the efficacy of brinzolamide in japanese patients with primary open - angle glaucoma ( poag ) or ocular hypertension ( oh ) after a change from timolol in combination therapy with latanoprost.methodsa 12-week , prospective , open - label , comparative study was performed in 20 patients [ 11 males and 9 females , mean age of 64.5 11.0 ( sd)y ] with poag or oh treated with both latanoprost once daily and timolol 0.5% twice daily . during the study brinzolamide
was substituted for timolol . intraocular pressure ( iop )
was measured at baseline , 4 , 8 , and 12 weeks .
blood pressure ( bp ) , pulse rate ( pr ) , and adverse events were also recorded.resultsiops at baseline , 4 , 8 , and 12 weeks were 18.6 2.1 mmhg , 17.8 2.6 mmhg , 17.4 2.5 mmhg , and 17.3 3.5 mmhg , respectively .
iop reduction at 4 and 8 weeks was statistically significant ( p < 0.05 ) .
the pr was significantly increased at 12 weeks ( p < 0.01 ) , but bp was not significantly affected .
four ocular adverse events were noted , but all were mild and transient.conclusionssubstituting brinzolamide 1% for timolol 0.5% in combination therapy with latanoprost 0.005% demonstrated significant iop reduction with improvement in pr with poag or oh . combination therapy using latanoprost and brinzolamide may be recommended for better iop control with fewer systemic adverse events .</s> |
Add a location to your Tweets
When you tweet with a location, Twitter stores that location. You can switch location on/off before each Tweet and always have the option to delete your location history. Learn more ||||| This image from a NASA space shuttle mission shows the International Space Station in orbit. The space station is the size of a football field and home to six astronauts. Image taken: Feb. 10, 2010.
Astronauts on the International Space Station have discovered a leak of ammonia coolant on their orbiting habitat, and NASA is looking into the problem, though it poses no immediate danger to the crew, officials said today (May 9).
The space station uses chilled liquid ammonia to cool down the power systems on its eight giant solar array panels. A minor leak of this ammonia was first noticed in 2007, and NASA has been studying the issue ever since. In November 2012 two astronauts took a spacewalk to fix the problem, rewiring some coolant lines and installing a spare radiator due to fears the original radiator was damaged by a micrometeorite impact.
At the time, those measures appeared to fix the problem, but today astronauts on the football field-size space station noticed a steady stream of frozen ammonia flakes leaking from the area of the suspect coolant loop in the Photovoltaic Thermal Control System (PVTCS). [Gallery: Building the International Space Station]
"It is in the same area, but we don't know whether it's the same leak," NASA spokesman Kelly Humphries of the Johnson Space Center in Houston told SPACE.com. Humphries said the agency was taking the leak seriously because it affects an important system β if they lose the ability to cool that particular solar array, it won't be able to generate power for the station. In fact, the leak has worsened to the point that Mission Control expects that particular loop to shut down within the next 24 hours.
However, "the crew is in no danger," Humphries stressed. It's too soon to speculate on a possible spacewalk or other measure to deal with the issue, he added.
Mission Control has been discussing the problem with the astronauts on the station throughout the afternoon.
"What you guys have provided in the way of imagery and video has been just like gold to us on the ground," astronaut Doug Wheelock from Mission Control radioed to space station commander Chris Hadfield, a Canadian Space Agency astronaut. "We are fairly confident that it's coming from the vicinity of the TCS." However, flight contollers noted they were still unable to pinpoint the leak's exact location.
NASA engineers are reviewing plans to potentially move the station's robotic arm over to the area of the port truss, the scaffolding-like backbone of the station (the original leak was traced to the Port 6 truss).
"Tomorrow we'll plan to get the arm in the game to see if we can better pinpoint the location of the leak," Wheelock said.
Hadfield said he and his crewmates had noticed the rate of the leak varied depending on the orientation of the station with the sun, suggesting particular angles allowed the ammonia coolant to leak more quickly.
Hadfield is in charge of the station's Expedition 35 crew, which also includes NASA astronauts Tom Marshburn and Chris Cassidy, and Russian cosmonauts Roman Romanenko, Pavel Vinogradov, and Alexander Misurkin. He asked Mission Control to send the crew a summary of what they know about the problem, and the possible courses to take to address it, before their bedtime.
"It would just be good for the six of us to know," Hadfield said.
Today had otherwise been a relatively light day for the crew of the International Space Station, which had taken some time off to celebrate the Russian holiday Victory Day. Hadfield, Marshburn and Romanenko are due to depart the space station on Monday (May 13) to return to Earth after a roughly five-month stay. Three new crewmembers plan to launch on May 28 from Kazakhstan on a Russian spacecraft to take up residence on the orbiting outpost.
Hadfield asked Wheelock if the leak, and resulting power loss from that solar array, could delay his planned undocking.
"We don't see anything technically that we can't overcome with the undocking but we are still getting our arms fully around that issue," Wheelock responded, adding that they should have more information for the astronauts in the morning.
Follow Clara Moskowitz on Twitter and Google+. Follow us @Spacedotcom, Facebook and Google+. Original article on SPACE.com. ||||| If there's any phrase an astronaut never wants to mutter, it's "Houston, we have a problem." Calling from the International Space Station on Thursday evening, Commander Chris Hadfield did just that. Well, he didn't actually quote that excellent Tom Hanks movie, but he did make a distressing call down to mission control. The astronauts on board the ISS had noticed what they believe to be ammonium cooling fluid leaking from the hull. The fluid is used to cool the power systems that control the space station's eight solar array panels, meaning that a total failure would cripple the floating habitat's ability to generate power.
But don't worry. Everything's going to be okay. NASA and Hadfield both say that the leak isn't putting the astronauts on the ISS in any immediate danger. The minor leak is actually not a new problem but an old headache that dates back to 2007. The ISS limped along for five years before astronauts fixed the problem on a space walk β or at least they thought they'd fixed it. Over the radio, Hadfield described the leak as "a very steady stream of flakes or bits" coming from the hull. (You can listen to the audio here.) "It is a serious situation, but between crew and experts on the ground, it appears to have been stabilized," Hadfield tweeted (from space!). "Tomorrow we find out for certain."
So chill out, Earth. Commander Hadfield really doesn't want you to worry about him. About an hour after the scary radio call and subsequent scary tweets, Hadfield offered this, "A view to put the mind at ease."
Want to add to this story? Let us know in comments. You can share ideas for stories on the Open Wire.
Adam Clark Estes | β The International Space Station is leaking ammonia coolant used to maintain its solar-panel power gear, Space.com reports. NASA says astronauts are "in no danger," but the situation could affect the station's power capabilities. Crew members spotted the frozen ammonia leaking from from a coolant loop yesterday. A similar leak was observed in 2007, but a spacewalk last year was believed to have fixed it. The new leak "is in the same area, but we don't know whether it's the same leak," says a NASA rep. Experts are still trying to figure out the exact location of the leak. In the meantime, Commander Chris Hadfield has offered a somewhat reassuring tweet, picked up by the Atlantic Wire: "It is a serious situation, but between crew and experts on the ground, it appears to have been stabilized. Tomorrow we find out for certain." | <s>[INST]Add a location to your Tweets
When you tweet with a location, Twitter stores that location. You can switch location on/off before each Tweet and always have the option to delete your location history. Learn more ||||| This image from a NASA space shuttle mission shows the International Space Station in orbit. The space station is the size of a football field and home to six astronauts. Image taken: Feb. 10, 2010.
Astronauts on the International Space Station have discovered a leak of ammonia coolant on their orbiting habitat, and NASA is looking into the problem, though it poses no immediate danger to the crew, officials said today (May 9).
The space station uses chilled liquid ammonia to cool down the power systems on its eight giant solar array panels. A minor leak of this ammonia was first noticed in 2007, and NASA has been studying the issue ever since. In November 2012 two astronauts took a spacewalk to fix the problem, rewiring some coolant lines and installing a spare radiator due to fears the original radiator was damaged by a micrometeorite impact.
At the time, those measures appeared to fix the problem, but today astronauts on the football field-size space station noticed a steady stream of frozen ammonia flakes leaking from the area of the suspect coolant loop in the Photovoltaic Thermal Control System (PVTCS). [Gallery: Building the International Space Station]
"It is in the same area, but we don't know whether it's the same leak," NASA spokesman Kelly Humphries of the Johnson Space Center in Houston told SPACE.com. Humphries said the agency was taking the leak seriously because it affects an important system β if they lose the ability to cool that particular solar array, it won't be able to generate power for the station. In fact, the leak has worsened to the point that Mission Control expects that particular loop to shut down within the next 24 hours.
However, "the crew is in no danger," Humphries stressed. It's too soon to speculate on a possible spacewalk or other measure to deal with the issue, he added.
Mission Control has been discussing the problem with the astronauts on the station throughout the afternoon.
"What you guys have provided in the way of imagery and video has been just like gold to us on the ground," astronaut Doug Wheelock from Mission Control radioed to space station commander Chris Hadfield, a Canadian Space Agency astronaut. "We are fairly confident that it's coming from the vicinity of the TCS." However, flight contollers noted they were still unable to pinpoint the leak's exact location.
NASA engineers are reviewing plans to potentially move the station's robotic arm over to the area of the port truss, the scaffolding-like backbone of the station (the original leak was traced to the Port 6 truss).
"Tomorrow we'll plan to get the arm in the game to see if we can better pinpoint the location of the leak," Wheelock said.
Hadfield said he and his crewmates had noticed the rate of the leak varied depending on the orientation of the station with the sun, suggesting particular angles allowed the ammonia coolant to leak more quickly.
Hadfield is in charge of the station's Expedition 35 crew, which also includes NASA astronauts Tom Marshburn and Chris Cassidy, and Russian cosmonauts Roman Romanenko, Pavel Vinogradov, and Alexander Misurkin. He asked Mission Control to send the crew a summary of what they know about the problem, and the possible courses to take to address it, before their bedtime.
"It would just be good for the six of us to know," Hadfield said.
Today had otherwise been a relatively light day for the crew of the International Space Station, which had taken some time off to celebrate the Russian holiday Victory Day. Hadfield, Marshburn and Romanenko are due to depart the space station on Monday (May 13) to return to Earth after a roughly five-month stay. Three new crewmembers plan to launch on May 28 from Kazakhstan on a Russian spacecraft to take up residence on the orbiting outpost.
Hadfield asked Wheelock if the leak, and resulting power loss from that solar array, could delay his planned undocking.
"We don't see anything technically that we can't overcome with the undocking but we are still getting our arms fully around that issue," Wheelock responded, adding that they should have more information for the astronauts in the morning.
Follow Clara Moskowitz on Twitter and Google+. Follow us @Spacedotcom, Facebook and Google+. Original article on SPACE.com. ||||| If there's any phrase an astronaut never wants to mutter, it's "Houston, we have a problem." Calling from the International Space Station on Thursday evening, Commander Chris Hadfield did just that. Well, he didn't actually quote that excellent Tom Hanks movie, but he did make a distressing call down to mission control. The astronauts on board the ISS had noticed what they believe to be ammonium cooling fluid leaking from the hull. The fluid is used to cool the power systems that control the space station's eight solar array panels, meaning that a total failure would cripple the floating habitat's ability to generate power.
But don't worry. Everything's going to be okay. NASA and Hadfield both say that the leak isn't putting the astronauts on the ISS in any immediate danger. The minor leak is actually not a new problem but an old headache that dates back to 2007. The ISS limped along for five years before astronauts fixed the problem on a space walk β or at least they thought they'd fixed it. Over the radio, Hadfield described the leak as "a very steady stream of flakes or bits" coming from the hull. (You can listen to the audio here.) "It is a serious situation, but between crew and experts on the ground, it appears to have been stabilized," Hadfield tweeted (from space!). "Tomorrow we find out for certain."
So chill out, Earth. Commander Hadfield really doesn't want you to worry about him. About an hour after the scary radio call and subsequent scary tweets, Hadfield offered this, "A view to put the mind at ease."
Want to add to this story? Let us know in comments. You can share ideas for stories on the Open Wire.
Adam Clark Estes[/INST]β The International Space Station is leaking ammonia coolant used to maintain its solar-panel power gear, Space.com reports. NASA says astronauts are "in no danger," but the situation could affect the station's power capabilities. Crew members spotted the frozen ammonia leaking from from a coolant loop yesterday. A similar leak was observed in 2007, but a spacewalk last year was believed to have fixed it. The new leak "is in the same area, but we don't know whether it's the same leak," says a NASA rep. Experts are still trying to figure out the exact location of the leak. In the meantime, Commander Chris Hadfield has offered a somewhat reassuring tweet, picked up by the Atlantic Wire: "It is a serious situation, but between crew and experts on the ground, it appears to have been stabilized. Tomorrow we find out for certain."</s> |
actually , any quantum system interacting with the environment ( the bath ) can not be isolated from the environment completely .
@xcite in quantum information and quantum computation , @xcite the decay process of quantum system induced by quantum fluctuations of the bath is very important for the qubit . in quantum optics ,
@xcite the jaynes - cummings model has been one of the most important models , @xcite which describes the light - matter interaction of a two - level atom and a single mode of the quantized electromagnetic field .
@xcite among these light - matter interaction issues , @xcite the revivals and collapses of the atomic population inversion ( also named rabi oscillation ) has been studied in the literatures .
@xcite decay of rabi oscillation has also been used as a tool to characterize the decoherence in superconducting qubits ( charge qubit , phase qubit and flux qubit ) .
@xcite recently , in circuit qed system , @xcite the researchers have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field .
@xcite also in nanomechanical qed system , the integration of josephson junction qubit and nanomechanical resonators are attracting considerable attentions .
@xcite the dynamics of all these qubit - resonator systems could be described by the jaynes - cummings hamiltonian .
when intrinsic nonlinearity of nanomechanical resonator @xcite is considered in the coupled qubit - resonator system , superconducting qubit can be used to probe quantum fluctuations of nonlinear resonator . @xcite and
the nonlinearity can be used to create nonclassical states in mechanical systems @xcite and selectively address the nanomechanical qubit transitions in quantum information processing .
@xcite in previous studies , @xcite master equation approach has been used to deal with the issues in open quantum system . in this paper ,
considering the influence of the environment on this nanomechanical qed system , we can use microscopic master equation approach @xcite to solve time evolution of the density operator for the qubit - resonator system and study the temporal behavior of rabi oscillation .
the paper is structured as follows . in sec.ii ,
a nonlinear jaynes - cummings model @xcite is used to describe the dynamics of the coupled qubit - nanomechanical resonator system . in sec.iii , using microscopic master equation approach , we solve time evolution of density operator for the qubit - resonator system . the probability on excited state of the qubit is calculated to show the temporal process of rabi oscillation .
finally , the results are summarized .
in nanomechanical qed system , we can use a jaynes - cummings type hamiltonian to describes the dynamics of the qubit - resonator system consisting of a charge qubit and a nanomechanical resonator system , @xmath0 considering the nonlinearity of nanomechanical resonator , the hamiltonian for this qubit - resonator system writes @xcite @xmath1 here the rotating - wave approximation ( @xmath2 ) and @xmath3 is adopted .
corresponding to charge qubit and nanomechanical resonator , the lowering ( raising ) operator @xmath4 ( @xmath5 ) and the annihilation ( creation ) operator @xmath6 ( @xmath7 ) satisfy the commutation relation @xmath8=\sigma_{z}$ ] and @xmath9=1 $ ] .
the hamiltonian in eq .
( [ nonlinear jc ham ] ) describes the dynamics of a nonlinear jaynes - cummings model , @xcite and a quartic potential @xmath10 @xcite gives nonlinear part @xmath11 which leads to the phonon - phonon interaction in nanomechanical qed systems .
the @xmath12 is the coupling constant and the @xmath13 is the nonlinearity parameter ( @xmath14 ) . solving the hamiltonian @xmath15 , we get the ground state @xmath16 with energy @xmath17 and excited state doublets @xmath18 for @xmath19 with energy @xmath20 some parameters are defined , i.e. , @xmath21 and @xmath22 . with the loss of nanomechanical resonator , the total hamiltonian @xmath23 consists of three parts , i.e. , the system part @xmath15 , the interaction part @xmath24 and the bath part @xmath25 where @xmath26 and @xmath27 are bosonic annihilation and creation operators for the bath oscillators for the mode frequency @xmath28 ( @xmath29 ) . in this paper , we adopt microscopic master equation approach @xcite to solve time evolution of density operator ( @xmath30 ) for the qubit - resonator system , our master equation is @xmath31 where @xmath32 is a time - independent linear superoperator . using the microscopic master equation approach , @xcite
we obtain the eigen - equations @xmath33 the @xmath34 is a set of eigenoperators due to the superoperator @xmath32 with the eigenvalue @xmath35 for the index @xmath36 . given initial state of the qubit - resonator system , the initial reduced density operator @xmath37 is expanded in terms of @xmath38 , @xmath39 where the @xmath40s are time - independent coefficients .
the results in ref.@xcite tell us that time evolution of reduced density operator @xmath30 will be @xmath41 now only one excitation is interested , our truncated basis @xmath42 consists of the three lowest eigenstates due to the hamiltonian @xmath15 , now we can rewrite the master equation in eq .
( [ master equation-1 ] ) , @xmath43+\mathcal{l}_{+}\rho+\mathcal{l}_{-}\rho.\label{master equation}\ ] ] here the non - unitary parts of dissipative dynamics are described by @xmath44 and @xmath45 , @xmath46 the superoperator @xmath47describe the transitions between the higher excited state @xmath48 and the ground state @xmath49 induced by the environment . the corresponding decay rate @xmath50 ( @xmath51 ) describes the transition from the excited state @xmath52 ( @xmath53 ) to the ground state @xmath49 , these transitions are induced by the interaction between the system and the environment . with respect to the system hamiltonian @xmath15 in eq .
( [ nonlinear jc ham ] ) , the eigenoperators @xmath38s are obtained , @xmath54 the corresponding eigenvalues @xmath55s ( for @xmath56 ) are @xmath57 @xmath58 and @xmath59
in traditional cavity qed theory , @xcite the rabi oscillation means that there exists energy exchange of one photon between a two - level atom and a single mode quantized field in cavity .
considering the nonlinearity of nanomechanical resonator , we study the decay process of rabi oscillation in the nonlinear jaynes - cummings model described by the hamiltonian in eq .
( [ nonlinear jc ham ] ) . given the initial state of the qubit - resonator system @xmath60 , it means that the qubit is in excited state @xmath61 and the resonator is in vacuum state @xmath62 .
thus , the initial reduced density operator reads @xmath63 expanding @xmath37 into some eigenoperators @xmath38s , we obtain a set of coefficients @xmath40s , @xmath64 @xmath65 and @xmath66 according to eq.([time rho ] ) , the time evolution of density operator for the qubit - resonator system is calculated as @xmath67 here the probability of the qubit in the excited ( upper ) state @xmath68 is @xmath69^{2}\nonumber \\ & & + \sin^{2}\theta e^{-\frac{\gamma_{1+}+\gamma_{1-}}{4}t}\cos^{2}\left(\omega t\right).\label{probability of excited state}\end{aligned}\ ] ] it characterizes the temporal behavior of rabi oscillation in the qubit - resonator system , decay process of rabi oscillation owns the periodic structure of time oscillating . the nanomechanical resonator is assumed to be an ideal resonator ( @xmath70 ) , and ignoring the difference of decay rates ( @xmath71 ) , then the probability @xmath72 becomes @xmath73 it describes the well known rabi oscillation in jaynes - cummings model.@xcite comparing the results in eq .
( [ probability of excited state ] ) with eq .
( [ probability at excited state in rabi ] ) , we find that nonlinearity parameter @xmath13 and decay rates @xmath74 modify the periodic structure of time oscillating in rabi oscillation . to further clarify the dependence of nonlinearity parameter and decay rates on the probability @xmath72 clearly
, some figures are plotted with parameters @xmath75 . here ,
we take the frequency @xmath76 as the unit for all these parameters . in fig.@xmath77 , the probability @xmath72 versus time @xmath78 is plotted with parameters @xmath70 and @xmath79 .
figure 1 shows the well known rabi oscillation , it verifies the results in eq .
( [ probability at excited state in rabi ] ) . and
@xmath80.,title="fig:",width=302][rabi in jc model ] vs the time @xmath78 , where the excite states ( @xmath81 and @xmath82 ) own the different decay rate ( @xmath83 and @xmath84 ) and @xmath70.04.,title="fig:",width=302][different decay rate and nonlinearity ] in fig.@xmath85 , the probability @xmath72 versus time @xmath78 is plotted with parameters @xmath86 , @xmath84 and @xmath83 .
figure 2 shows that nonlinearity parameter @xmath13 and decay rates ( @xmath74 ) modify the periodic structure of time oscillating in rabi oscillation , which is obviously different from figure 1 .
based on those results in eq .
( [ probability of excited state],[probability at excited state in rabi ] ) , we find that nonlinearity parameter @xmath13 slows down the time - oscillating period of rabi oscillation @xmath87 . in the following , we will study how nonlinearity parameter @xmath13 and decay rates ( @xmath74 ) affect the temporal behavior in rabi oscillation solely .
firstly , assuming the same decay rates @xmath88 and nonlinearity parameter @xmath89 , the probability in eq .
( [ probability of excited state ] ) becomes @xmath90 the dependence of the probability @xmath72 on nonlinearity parameter @xmath13 is plotted in fig.@xmath91 .
when @xmath92 , the minimum of the probability @xmath93 decays exponentially , which is different from the well known rabi oscillation in fig.@xmath77 . secondly , assuming no nonlinearity @xmath70 and different decay rates ( @xmath74 ) , the probability in eq .
( [ probability of excited state ] ) becomes @xmath94 the dependence of the probability @xmath72 on different decay rates is plotted in fig.@xmath95 .
when @xmath96 , the minimum of the probability @xmath97 shows that the difference of decay rates between @xmath98 and @xmath99 does not affect the short - time behavior and long - time behavior of rabi oscillation obviously , which is seen in fig.@xmath95 .
vs the time @xmath78 , where the excite states ( @xmath81 and @xmath82 ) own the same decay rate ( @xmath100 ) and nonlinearity parameter @xmath86.,title="fig:",width=302][nonlinearity fig1 ] vs the time @xmath78 , the excite states ( @xmath81 and @xmath82 ) of the qubit - resonator system own the different decay rate ( @xmath83 and @xmath84 ) and nonlinearity parameter @xmath70.,title="fig:",width=302][pure jc with microscopic master ] analytically , we can study the short - time behavior of rabi oscillation , then the probability @xmath101 becomes @xmath102t\right\ } .\label{short - time probability}\ ] ] ignoring the nonlinearity of nanomechanical resonator or the difference of decay rates , i.e. , @xmath70 or @xmath103 , the probability @xmath101 becomes @xmath104 according to the results in eq .
( [ short - time probability ] ) and eq .
( [ short - time decay rate ] ) , we find that both nonlinearity parameter @xmath13 and the difference of decay rates ( @xmath74 ) affect dominate the short - time behavior of rabi oscillation jointly .
also , these two factors speed up the decay of rabi oscillation in short - time limit .
in summary , we have studied the dynamics of the nanomechanical qed system consisting of a charge qubit and a nanomechanical resonator .
the temporal behavior of rabi oscillations is analytically studied while the intrinsic nonlinearity of nanomechanical resonator is considered . with the loss of nanomechanical resonator
, microscopic master equation approach is used to calculate the excited - state probability of charge qubit in this nonlinear jaynes - cummings model .
these results show that nonlinearity parameter and decay rates can affect time - oscillating and decaying of rabi oscillation solely or jointly . | in nanomechanical qed system , consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity , we study the temporal behavior of rabi oscillation in the nonlinear jaynes - cummings model . using microscopic master equation approach ,
we solve time evolution of the density operator describing this model .
also , the probability of excited state of charge qubit is calculated .
these analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit - resonator system affect time - oscillating and decaying of rabi oscillation . | <s>[INST]actually , any quantum system interacting with the environment ( the bath ) can not be isolated from the environment completely .
@xcite in quantum information and quantum computation , @xcite the decay process of quantum system induced by quantum fluctuations of the bath is very important for the qubit . in quantum optics ,
@xcite the jaynes - cummings model has been one of the most important models , @xcite which describes the light - matter interaction of a two - level atom and a single mode of the quantized electromagnetic field .
@xcite among these light - matter interaction issues , @xcite the revivals and collapses of the atomic population inversion ( also named rabi oscillation ) has been studied in the literatures .
@xcite decay of rabi oscillation has also been used as a tool to characterize the decoherence in superconducting qubits ( charge qubit , phase qubit and flux qubit ) .
@xcite recently , in circuit qed system , @xcite the researchers have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field .
@xcite also in nanomechanical qed system , the integration of josephson junction qubit and nanomechanical resonators are attracting considerable attentions .
@xcite the dynamics of all these qubit - resonator systems could be described by the jaynes - cummings hamiltonian .
when intrinsic nonlinearity of nanomechanical resonator @xcite is considered in the coupled qubit - resonator system , superconducting qubit can be used to probe quantum fluctuations of nonlinear resonator . @xcite and
the nonlinearity can be used to create nonclassical states in mechanical systems @xcite and selectively address the nanomechanical qubit transitions in quantum information processing .
@xcite in previous studies , @xcite master equation approach has been used to deal with the issues in open quantum system . in this paper ,
considering the influence of the environment on this nanomechanical qed system , we can use microscopic master equation approach @xcite to solve time evolution of the density operator for the qubit - resonator system and study the temporal behavior of rabi oscillation .
the paper is structured as follows . in sec.ii ,
a nonlinear jaynes - cummings model @xcite is used to describe the dynamics of the coupled qubit - nanomechanical resonator system . in sec.iii , using microscopic master equation approach , we solve time evolution of density operator for the qubit - resonator system . the probability on excited state of the qubit is calculated to show the temporal process of rabi oscillation .
finally , the results are summarized .
in nanomechanical qed system , we can use a jaynes - cummings type hamiltonian to describes the dynamics of the qubit - resonator system consisting of a charge qubit and a nanomechanical resonator system , @xmath0 considering the nonlinearity of nanomechanical resonator , the hamiltonian for this qubit - resonator system writes @xcite @xmath1 here the rotating - wave approximation ( @xmath2 ) and @xmath3 is adopted .
corresponding to charge qubit and nanomechanical resonator , the lowering ( raising ) operator @xmath4 ( @xmath5 ) and the annihilation ( creation ) operator @xmath6 ( @xmath7 ) satisfy the commutation relation @xmath8=\sigma_{z}$ ] and @xmath9=1 $ ] .
the hamiltonian in eq .
( [ nonlinear jc ham ] ) describes the dynamics of a nonlinear jaynes - cummings model , @xcite and a quartic potential @xmath10 @xcite gives nonlinear part @xmath11 which leads to the phonon - phonon interaction in nanomechanical qed systems .
the @xmath12 is the coupling constant and the @xmath13 is the nonlinearity parameter ( @xmath14 ) . solving the hamiltonian @xmath15 , we get the ground state @xmath16 with energy @xmath17 and excited state doublets @xmath18 for @xmath19 with energy @xmath20 some parameters are defined , i.e. , @xmath21 and @xmath22 . with the loss of nanomechanical resonator , the total hamiltonian @xmath23 consists of three parts , i.e. , the system part @xmath15 , the interaction part @xmath24 and the bath part @xmath25 where @xmath26 and @xmath27 are bosonic annihilation and creation operators for the bath oscillators for the mode frequency @xmath28 ( @xmath29 ) . in this paper , we adopt microscopic master equation approach @xcite to solve time evolution of density operator ( @xmath30 ) for the qubit - resonator system , our master equation is @xmath31 where @xmath32 is a time - independent linear superoperator . using the microscopic master equation approach , @xcite
we obtain the eigen - equations @xmath33 the @xmath34 is a set of eigenoperators due to the superoperator @xmath32 with the eigenvalue @xmath35 for the index @xmath36 . given initial state of the qubit - resonator system , the initial reduced density operator @xmath37 is expanded in terms of @xmath38 , @xmath39 where the @xmath40s are time - independent coefficients .
the results in ref.@xcite tell us that time evolution of reduced density operator @xmath30 will be @xmath41 now only one excitation is interested , our truncated basis @xmath42 consists of the three lowest eigenstates due to the hamiltonian @xmath15 , now we can rewrite the master equation in eq .
( [ master equation-1 ] ) , @xmath43+\mathcal{l}_{+}\rho+\mathcal{l}_{-}\rho.\label{master equation}\ ] ] here the non - unitary parts of dissipative dynamics are described by @xmath44 and @xmath45 , @xmath46 the superoperator @xmath47describe the transitions between the higher excited state @xmath48 and the ground state @xmath49 induced by the environment . the corresponding decay rate @xmath50 ( @xmath51 ) describes the transition from the excited state @xmath52 ( @xmath53 ) to the ground state @xmath49 , these transitions are induced by the interaction between the system and the environment . with respect to the system hamiltonian @xmath15 in eq .
( [ nonlinear jc ham ] ) , the eigenoperators @xmath38s are obtained , @xmath54 the corresponding eigenvalues @xmath55s ( for @xmath56 ) are @xmath57 @xmath58 and @xmath59
in traditional cavity qed theory , @xcite the rabi oscillation means that there exists energy exchange of one photon between a two - level atom and a single mode quantized field in cavity .
considering the nonlinearity of nanomechanical resonator , we study the decay process of rabi oscillation in the nonlinear jaynes - cummings model described by the hamiltonian in eq .
( [ nonlinear jc ham ] ) . given the initial state of the qubit - resonator system @xmath60 , it means that the qubit is in excited state @xmath61 and the resonator is in vacuum state @xmath62 .
thus , the initial reduced density operator reads @xmath63 expanding @xmath37 into some eigenoperators @xmath38s , we obtain a set of coefficients @xmath40s , @xmath64 @xmath65 and @xmath66 according to eq.([time rho ] ) , the time evolution of density operator for the qubit - resonator system is calculated as @xmath67 here the probability of the qubit in the excited ( upper ) state @xmath68 is @xmath69^{2}\nonumber \\ & & + \sin^{2}\theta e^{-\frac{\gamma_{1+}+\gamma_{1-}}{4}t}\cos^{2}\left(\omega t\right).\label{probability of excited state}\end{aligned}\ ] ] it characterizes the temporal behavior of rabi oscillation in the qubit - resonator system , decay process of rabi oscillation owns the periodic structure of time oscillating . the nanomechanical resonator is assumed to be an ideal resonator ( @xmath70 ) , and ignoring the difference of decay rates ( @xmath71 ) , then the probability @xmath72 becomes @xmath73 it describes the well known rabi oscillation in jaynes - cummings model.@xcite comparing the results in eq .
( [ probability of excited state ] ) with eq .
( [ probability at excited state in rabi ] ) , we find that nonlinearity parameter @xmath13 and decay rates @xmath74 modify the periodic structure of time oscillating in rabi oscillation . to further clarify the dependence of nonlinearity parameter and decay rates on the probability @xmath72 clearly
, some figures are plotted with parameters @xmath75 . here ,
we take the frequency @xmath76 as the unit for all these parameters . in fig.@xmath77 , the probability @xmath72 versus time @xmath78 is plotted with parameters @xmath70 and @xmath79 .
figure 1 shows the well known rabi oscillation , it verifies the results in eq .
( [ probability at excited state in rabi ] ) . and
@xmath80.,title="fig:",width=302][rabi in jc model ] vs the time @xmath78 , where the excite states ( @xmath81 and @xmath82 ) own the different decay rate ( @xmath83 and @xmath84 ) and @xmath70.04.,title="fig:",width=302][different decay rate and nonlinearity ] in fig.@xmath85 , the probability @xmath72 versus time @xmath78 is plotted with parameters @xmath86 , @xmath84 and @xmath83 .
figure 2 shows that nonlinearity parameter @xmath13 and decay rates ( @xmath74 ) modify the periodic structure of time oscillating in rabi oscillation , which is obviously different from figure 1 .
based on those results in eq .
( [ probability of excited state],[probability at excited state in rabi ] ) , we find that nonlinearity parameter @xmath13 slows down the time - oscillating period of rabi oscillation @xmath87 . in the following , we will study how nonlinearity parameter @xmath13 and decay rates ( @xmath74 ) affect the temporal behavior in rabi oscillation solely .
firstly , assuming the same decay rates @xmath88 and nonlinearity parameter @xmath89 , the probability in eq .
( [ probability of excited state ] ) becomes @xmath90 the dependence of the probability @xmath72 on nonlinearity parameter @xmath13 is plotted in fig.@xmath91 .
when @xmath92 , the minimum of the probability @xmath93 decays exponentially , which is different from the well known rabi oscillation in fig.@xmath77 . secondly , assuming no nonlinearity @xmath70 and different decay rates ( @xmath74 ) , the probability in eq .
( [ probability of excited state ] ) becomes @xmath94 the dependence of the probability @xmath72 on different decay rates is plotted in fig.@xmath95 .
when @xmath96 , the minimum of the probability @xmath97 shows that the difference of decay rates between @xmath98 and @xmath99 does not affect the short - time behavior and long - time behavior of rabi oscillation obviously , which is seen in fig.@xmath95 .
vs the time @xmath78 , where the excite states ( @xmath81 and @xmath82 ) own the same decay rate ( @xmath100 ) and nonlinearity parameter @xmath86.,title="fig:",width=302][nonlinearity fig1 ] vs the time @xmath78 , the excite states ( @xmath81 and @xmath82 ) of the qubit - resonator system own the different decay rate ( @xmath83 and @xmath84 ) and nonlinearity parameter @xmath70.,title="fig:",width=302][pure jc with microscopic master ] analytically , we can study the short - time behavior of rabi oscillation , then the probability @xmath101 becomes @xmath102t\right\ } .\label{short - time probability}\ ] ] ignoring the nonlinearity of nanomechanical resonator or the difference of decay rates , i.e. , @xmath70 or @xmath103 , the probability @xmath101 becomes @xmath104 according to the results in eq .
( [ short - time probability ] ) and eq .
( [ short - time decay rate ] ) , we find that both nonlinearity parameter @xmath13 and the difference of decay rates ( @xmath74 ) affect dominate the short - time behavior of rabi oscillation jointly .
also , these two factors speed up the decay of rabi oscillation in short - time limit .
in summary , we have studied the dynamics of the nanomechanical qed system consisting of a charge qubit and a nanomechanical resonator .
the temporal behavior of rabi oscillations is analytically studied while the intrinsic nonlinearity of nanomechanical resonator is considered . with the loss of nanomechanical resonator
, microscopic master equation approach is used to calculate the excited - state probability of charge qubit in this nonlinear jaynes - cummings model .
these results show that nonlinearity parameter and decay rates can affect time - oscillating and decaying of rabi oscillation solely or jointly .[/INST] in nanomechanical qed system , consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity , we study the temporal behavior of rabi oscillation in the nonlinear jaynes - cummings model . using microscopic master equation approach ,
we solve time evolution of the density operator describing this model .
also , the probability of excited state of charge qubit is calculated .
these analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit - resonator system affect time - oscillating and decaying of rabi oscillation . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Corporate Accountability Tax Gap Act
of 2005''.
SEC. 2. AVAILABILITY OF CERTAIN TAX INFORMATION OF PUBLICLY TRADED
CORPORATIONS.
(a) In General.--Section 6103 of the Internal Revenue Code of 1986
is amended by redesignating subsection (q) as subsection (r) and by
inserting after subsection (p) the following new subsection:
``(q) Public Disclosure of Certain Corporate Tax Information.--
``(1) In general.--Each specified corporation shall, on the
date that it files its return of tax imposed by chapter 1 for
each taxable year, electronically file the information
described in paragraph (2) for such year. Not later than 30
days after receiving such information, the Secretary shall make
it electronically available to the public as a single document
and as part of a searchable database as provided in paragraph
(3).
``(2) Information.--The information described in this
paragraph with respect to a corporation for a taxable year are
the following items:
``(A) Net corporate income tax as shown on the
return for such year.
``(B) Amount shown as Federal income tax expense on
its annual statement (if any) filed with the Securities
and Exchange Commission.
``(C) Taxable income as shown on such return.
``(D) Adjusted book income.
``(E) The portion of the total difference between
taxable income and adjusted book income which is
attributable to each of the following:
``(i) Transactions disclosable under
section 6011.
``(ii) Depreciation differences.
``(iii) Stock options.
``(iv) Income from entities consolidated
for book income purposes but not for Federal
income tax purposes.
``(v) Income from pension funds or tax-
exempt bonds.
``(vi) Other items, pursuant to regulations
prescribed by the Secretary.
``(F) An explanation of the differences between
taxable income and adjusted book income that are
attributable to one or more of the following:
``(i) Transactions referred to in
subparagraph (E)(i).
``(ii) Other items specified in regulations
referred to in subparagraph (E)(vi).
``(iii) Any additional information that the
Secretary determines would be useful in
enforcing this title, including any information
which is an indicia of abusive tax avoidance
schemes.
``(3) Access.--The Secretary shall make the information
described in paragraph (2) accessible electronically by a
search which uses the following items:
``(A) Name of the corporation.
``(B) Headquarters location by postal zip code.
``(C) Each category of such information.
``(D) Taxable year or other time period to which
such information relates.
``(E) The CUSIP identification number under which
the corporation files reports with the Securities and
Exchange Commission.
``(4) Specified corporation.--For purposes of this
subsection, the term `specified corporation' means--
``(A) any corporation issuing any class of
securities required to be registered under section 12
of the Securities Exchange Act of 1934, and
``(B) any other domestic corporation which is a
member of an affiliated group (as defined in section
1504) which includes a corporation described in
subparagraph (A).
In the case of a corporation which is a member of an affiliated
group filing a consolidated return, the term `specified
corporation' means such group and not each member thereof.
``(5) Other definitions.--For purposes of this subsection--
``(A) Net corporate income tax.--The term `net
corporate income tax' means the sum of regular tax
liability (as defined by section 26(b)) and the tax
imposed by section 55, reduced by the credits allowable
under part IV of subchapter A of chapter 1.
``(B) Adjusted book income.--The term `adjusted
book income' means book income reported to the
Securities and Exchange Commission (or to shareholders)
without reduction for preferred stock dividends,
Federal income taxes, and income, war profits, or
excess profits taxes imposed by any foreign country or
possession of the United States.''.
(b) Effective Date.--The amendment made by subsection (a) shall
apply to taxable years ending after the date of the enactment of this
Act.
SEC. 3. STUDY OF TAX SHELTER ACTIVITY.
(a) Study.--The Secretary of the Treasury (or the Secretary's
delegate) shall, in coordination with the Joint Committee on Taxation,
Committee on Finance of the Senate, and the Committee on Ways and Means
of the House of Representatives, conduct a study of recent known
corporate tax shelter activity, including information gained from the
tax shelter amnesty announced in Internal Revenue Service Announcement
2002-02 and from the study of Enron tax returns by the Committee on
Finance of the Senate.
(b) Report.--Not later than 1 year after the date of the enactment
of this Act, the report of such study shall be submitted to the
Committee on Finance of the Senate and the Committee on Ways and Means
of the House of Representatives. Such report shall include
recommendations (if any) for--
(1) requiring additional information on the reconciliation
of book/tax accounting and publicly disclosing that additional
information under section 6103(q) of the Internal Revenue Code
of 1986, and
(2) publicly disclosing additional information from the
corporate income tax return.
Such report also shall include a description of the actions that such
Secretary has taken toward implementing any such recommendations. | Corporate Accountability Tax Gap Act of 2005 - Amends the Internal Revenue Code to provide for public disclosure of certain information of publicly traded corporations, including: (1) net corporate income tax and taxable income as shown on the corporation's current year tax return; (2) adjusted book income; and (3) differences between taxable income and adjusted book income due to certain transactions, depreciation differences, stock options, and other factors. Directs the Secretary of the Treasury to conduct a study of corporate tax shelter activity. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Corporate Accountability Tax Gap Act
of 2005''.
SEC. 2. AVAILABILITY OF CERTAIN TAX INFORMATION OF PUBLICLY TRADED
CORPORATIONS.
(a) In General.--Section 6103 of the Internal Revenue Code of 1986
is amended by redesignating subsection (q) as subsection (r) and by
inserting after subsection (p) the following new subsection:
``(q) Public Disclosure of Certain Corporate Tax Information.--
``(1) In general.--Each specified corporation shall, on the
date that it files its return of tax imposed by chapter 1 for
each taxable year, electronically file the information
described in paragraph (2) for such year. Not later than 30
days after receiving such information, the Secretary shall make
it electronically available to the public as a single document
and as part of a searchable database as provided in paragraph
(3).
``(2) Information.--The information described in this
paragraph with respect to a corporation for a taxable year are
the following items:
``(A) Net corporate income tax as shown on the
return for such year.
``(B) Amount shown as Federal income tax expense on
its annual statement (if any) filed with the Securities
and Exchange Commission.
``(C) Taxable income as shown on such return.
``(D) Adjusted book income.
``(E) The portion of the total difference between
taxable income and adjusted book income which is
attributable to each of the following:
``(i) Transactions disclosable under
section 6011.
``(ii) Depreciation differences.
``(iii) Stock options.
``(iv) Income from entities consolidated
for book income purposes but not for Federal
income tax purposes.
``(v) Income from pension funds or tax-
exempt bonds.
``(vi) Other items, pursuant to regulations
prescribed by the Secretary.
``(F) An explanation of the differences between
taxable income and adjusted book income that are
attributable to one or more of the following:
``(i) Transactions referred to in
subparagraph (E)(i).
``(ii) Other items specified in regulations
referred to in subparagraph (E)(vi).
``(iii) Any additional information that the
Secretary determines would be useful in
enforcing this title, including any information
which is an indicia of abusive tax avoidance
schemes.
``(3) Access.--The Secretary shall make the information
described in paragraph (2) accessible electronically by a
search which uses the following items:
``(A) Name of the corporation.
``(B) Headquarters location by postal zip code.
``(C) Each category of such information.
``(D) Taxable year or other time period to which
such information relates.
``(E) The CUSIP identification number under which
the corporation files reports with the Securities and
Exchange Commission.
``(4) Specified corporation.--For purposes of this
subsection, the term `specified corporation' means--
``(A) any corporation issuing any class of
securities required to be registered under section 12
of the Securities Exchange Act of 1934, and
``(B) any other domestic corporation which is a
member of an affiliated group (as defined in section
1504) which includes a corporation described in
subparagraph (A).
In the case of a corporation which is a member of an affiliated
group filing a consolidated return, the term `specified
corporation' means such group and not each member thereof.
``(5) Other definitions.--For purposes of this subsection--
``(A) Net corporate income tax.--The term `net
corporate income tax' means the sum of regular tax
liability (as defined by section 26(b)) and the tax
imposed by section 55, reduced by the credits allowable
under part IV of subchapter A of chapter 1.
``(B) Adjusted book income.--The term `adjusted
book income' means book income reported to the
Securities and Exchange Commission (or to shareholders)
without reduction for preferred stock dividends,
Federal income taxes, and income, war profits, or
excess profits taxes imposed by any foreign country or
possession of the United States.''.
(b) Effective Date.--The amendment made by subsection (a) shall
apply to taxable years ending after the date of the enactment of this
Act.
SEC. 3. STUDY OF TAX SHELTER ACTIVITY.
(a) Study.--The Secretary of the Treasury (or the Secretary's
delegate) shall, in coordination with the Joint Committee on Taxation,
Committee on Finance of the Senate, and the Committee on Ways and Means
of the House of Representatives, conduct a study of recent known
corporate tax shelter activity, including information gained from the
tax shelter amnesty announced in Internal Revenue Service Announcement
2002-02 and from the study of Enron tax returns by the Committee on
Finance of the Senate.
(b) Report.--Not later than 1 year after the date of the enactment
of this Act, the report of such study shall be submitted to the
Committee on Finance of the Senate and the Committee on Ways and Means
of the House of Representatives. Such report shall include
recommendations (if any) for--
(1) requiring additional information on the reconciliation
of book/tax accounting and publicly disclosing that additional
information under section 6103(q) of the Internal Revenue Code
of 1986, and
(2) publicly disclosing additional information from the
corporate income tax return.
Such report also shall include a description of the actions that such
Secretary has taken toward implementing any such recommendations.[/INST]Corporate Accountability Tax Gap Act of 2005 - Amends the Internal Revenue Code to provide for public disclosure of certain information of publicly traded corporations, including: (1) net corporate income tax and taxable income as shown on the corporation's current year tax return; (2) adjusted book income; and (3) differences between taxable income and adjusted book income due to certain transactions, depreciation differences, stock options, and other factors. Directs the Secretary of the Treasury to conduct a study of corporate tax shelter activity.</s> |
ERIN, Wis. (AP) β A blimp flying over the U.S. Open has gone down and the aircraft's operator says he doesn't know if the pilot is alive.
Justin Maynard is a sales manager for AirSign, the advertising company that operates the blimp.
Maynard says only the pilot was on board the craft. He says the company's operations team on the ground confirmed citizen video on social media showing the blimp going down.
Maynard says he is "not 100 percent" on the condition of the pilot but that believes he is alive. ||||| A blimp with a lone pilot on board plummeted from the sky on June 15 during the first round of the U.S. Open in Erin Hills, Wis. (Adam Johnson/Twitter)
An advertising blimp with a lone pilot on board plummeted from the sky on Thursday afternoon during the first round of the U.S. Open at Erin Hills in Wisconsin, according to multiple reports from the scene. The Milwaukee Journal-Sentinel says the blimp caught fire before it hit the ground in a field near the intersection of Highway 83 and Highway 167, just outside the course.
βIt started deflating, and then it started going down,β witness Bryan Rosine told the Journal-Sentinel. βThey were trying to give it some throttle and it didnβt go up. Then there was a bunch of kabooms and smoke clouds.β
AirSign, the company that operated the blimp, had an update on the pilotβs condition later Thursday.
Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be ok. No details on cause of crash β AirSign (@AirSign) June 15, 2017
Fox Sports has video of the explosion on the ground.
A manned blimp unaffiliated with FOX Sports or the #USOpen crashed near the course earlier today. pic.twitter.com/XXaj3n8j2H β FS1 (@FS1) June 15, 2017
According to the USGA, which runs the event, the blimp was unaffiliated with the tournament or with Fox Sports, which is broadcasting the event.
Just got to the #USOpen and the blimp caught fire and crashed. People parachuted out. pic.twitter.com/1lDi3VkXCu β madison seigworth (@msiggyy) June 15, 2017
[From the archives: The blimp pilots that fly over PGA Tour events have the best views, but they have solitary lives.]
WMTV in Madison, Wis., posted photos of the crash scene and had a helicopter circling the crash scene. Its live footage showed what appeared to be a good number of emergency workers tending to a single individual on the ground. The person was transported from the middle of a field in the back of a pickup truck and driven to the parking lot of what appeared to be a warehouse in the middle of a vast field. Workers loaded the gurney onto a waiting emergency helicopter, which then flew off to a nearby hospital.
ESPNβs Ian OβConnor reports that the pilot was the only person on board and that he was alert and conscious.
Paramedics moving apparent victim of blimp crash at US Open pic.twitter.com/qrdrsVXaAT β Ian O'Connor (@Ian_OConnor) June 15, 2017
Hereβs more footage:
#BREAKING: A blimp has crashed and caught on fire at the U.S. Open in Wisconsin pic.twitter.com/FmVbcxwTnG β WSVN 7 News (@wsvn) June 15, 2017
Pretty sure I just watched the blimp crash at the #USOPEN! Hope everybody is ok! pic.twitter.com/OSOCSBF46p β Adam Johnson (@Coach_Guy_AJ) June 15, 2017
The blimp was operated by AirSign, a national aerial advertising firm. The company had announced earlier Thursday that one of their blimps would be present.
Patrick Walsh, AirSignβs CEO, told CBS News that the cause of the crash was still under investigation. The pilot suffered burns, he said, and there were no injuries on the ground.
According to a National Transportation Safety Board database, AirSign aircraft have been involved in two incidents, both involving planes. In April 2010, the pilot was killed after a small propeller plane he was flying βwas substantially damaged when it impacted terrain after a loss of control during initial climbβ at Orlando North Airpark in Florida. The plane was involved in a βbanner towing job,β according to the NTSB, which cited the pilotβs failure to maintain airspeed after takeoff as the reason for the crash.
In March 2005, a Cessna registered to AirSign made an emergency crash landing on a road after the pilot reported a loss of engine power shortly after takeoff from Charlotte Douglas International Airport in North Carolina. The pilot suffered what the NTSB report described as minor injuries after colliding with a curb and a parked car, and the agency found that he failed to follow a preflight checklist.
But crashes involving blimps are βextremely rare,β Dan Coffee, owner of the Wisconsin airstrip from which the blimp took off Thursday, told the Journal-Sentinel, and a check of the NTSB database seems to back this up. The last blimp incident logged by the agency took place in 2006.
According to Terry Sater of WISN-TV in Milwaukee, the NTSB is gathering information about Thursdayβs blimp crash. ||||| 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 ||||| CLOSE A PenFed blimp deflated, burst into flames and crashed late Thursday morning near the U.S. Open at Erin Hills.
The damaged blimp falls to the ground near the U.S. Open at Erin Hills. (Photo: Associated Press)
TOWN of ERIN - Some of the biggest drama at the U.S. Open took place in the sky just east of the course Thursday morning when a blimp advertising for PenFed Credit Union deflated, burst into flames and crashed.
The blimp went down about 11:15 a.m. near Highways 83 and 167. The crash site was about a mile from the Erin Hills golf course where thousands of people gathered for the first morning of competition.
The pilot was flown by Flight for Life around noon to be treated for serious injuries, including burns, at Froedtert Hospital. The hospital identified him as Trevor Thompson and said he was in serious condition.
Thompson was coherent and stable enough to talk to officers, officials from the National Transportation Safety Board said at a news conference Thursday night. The NTSB is investigating the crash.
Officers reported that the aircraft had reached an altitude of about 1,000 feet before Thompson decided to land because of high winds. As he was descending, he heard panels rip off the air balloon and blimp hybrid that he was flying. He then turned the engines off, but residual fuel in the engines is what led to the fiery explosion that followed once the aircraft hit the ground.
Thompson was the only occupant of the aircraft, and no one on the ground was injured.
The blimp was operated by AirSign, an aerial advertising firm with operations across the country. The company website says it specializes in banner, blimps and sky writing.
FULL COVERAGE: 2017 U.S. Open at Erin Hills
Buy Photo Blimp pilot Trevor Thompson is transported by Flight for Life after the crash near the U.S. Open at Erin Hills on June 15, 2017. (Photo: Mark Hoffman / Milwaukee Journal Sentinel)
"He stayed with the blimp until it went down," a spokesman for AirSign said in a telephone interview from Florida. He said that a crew member on the ground pulled Thompson from the wreckage.
Fox 6 reported that Thompson had made forced landings in 2015 and 2016.
The aircraft, a Gefa-Flug Airship, was manufactured in 2004, registered in Great Britain and owned by Airsign Ltd. of Williston, Fla.
The Federal Aviation Administration had no record of the blimp being involved in any accidents before Thursday, according to Lynn Lunsford, a public affairs manager for the agency.
The company tweeted: "Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be OK. No details on cause of crash."
Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be ok. No details on cause of crash β AirSign (@AirSign) June 15, 2017
A close-up of the damaged blimp as it falls to the ground. (Photo: Associated Press)
"It started deflating, and then it started going down," said Bryan Rosine, who noticed the blimp while he was taking a tree down.
"They were trying to give it some throttle and it didn't go up. Then there was a bunch of kabooms and smoke clouds."
Another witness, Tim Guetzke and his 16-year-old son Hunter, an incoming junior at Hartford Union High School, were in the area and watching the blimp.
"The side started deflating," Tim Guetzke said. "One side was going in. As it headed toward the ground, it caught fire."
"It was doing fine for hours," he said. "Hunter could see it. He said, 'Dad, it's deflating. I think it's starting on fire.' When you realize someone is in there it makes you sad."
Golfer Jamie Lovemark said he saw the blimp while on the 5th hole.
"I was teeing off and I looked up and saw it on fire and I felt sick to my stomach," he said. "I had the shakes. I felt terrible for the people inside. I didn't know what was going on. It was a horrible sight."
The blimp landed in a farmer's field near a stand of trees and looked like a large deflated balloon. Videos show flames and explosions after the wreckage hit the ground.
The sign on the blimp advertised PenFed Credit Union, also known as the Pentagon Federal Credit Union. The nation's third-largest credit union with assets of about $22 billion, PenFed serves about 1.5 million people with connections to the military and has branches in 10 states.
Earlier Thursday morning, AirSign tweeted about the blimp's arrival and encouraged visitors to share photos.
The blimp took off from a small privately operated air field not far from the crash site, said Dan Coffey, owner of the Air Strip WN75.
"They were going to use it all week," Coffey said. "He was flying it for hours. I don't know if the wind caught up with him or what."
Coffey said that the accident was extremely unusual.
"These airships are FAA approved. They make sure that every one is inspected," he said. "This is an extremely rare accident."
Terry Williams, a spokesman for the National Transportation Safety Board, said the agency has launched an investigation into the incident and has dispatched an investigator to the scene.
A blimp unaffiliated with the #USOpen or @FOXSports has crashed near Erin Hills. Pilot was injured and first responders are on the scene. β U.S. Open (USGA) (@usopengolf) June 15, 2017
A statement distributed by the United States Golf Association said the blimp was not affiliated with the USGA or the U.S. Open.
"Our thoughts and prayers are with the pilot at this time," the USGA statement said.
Earlier Thursday morning, AirSign tweeted a picture: "The beautiful @penfed blimp is flying high over the US Open today!"
The company also tweeted a picture of the golf course taken from the blimp.
A manned blimp unaffiliated with FOX Sports or the #USOpen crashed near the course today. We will provide more details as they're available. pic.twitter.com/QEAk8tiU0K β FOX Sports (@FOXSports) June 15, 2017
Pretty sure I just watched the blimp crash at the #USOPEN! Hope everybody is ok! pic.twitter.com/OSOCSBF46p β Adam Johnson (@Coach_Guy_AJ) June 15, 2017
The blimp crash was far from the course but the smoke that rose above the trees afterwards was terrifying. β Mike Hall (@BTNMikeHall) June 15, 2017
#USOpen A blimp has caught fire flying over the @usopengolf and crashed in the woods near @ErinHillsGolf . pic.twitter.com/OlhebVlNky β Mr. Terrific β’ (@RealMrTerrific) June 15, 2017
Just got to the #USOpen and the blimp caught fire and crashed. People parachuted out. pic.twitter.com/1lDi3VkXCu β madison seigworth (@msiggyy) June 15, 2017
Joe Taschler, Kevin Crowe and Jordyn Noennig of the Journal Sentinel staff contributed to this report.
Read or Share this story: http://jsonl.in/2swQDP8 | β "It started deflating, and then it started going down," witness Bryan Rosine tells the Journal Sentinel. "Then there was a bunch of kabooms and smoke clouds." One person is reportedly injured after an advertising blimp crashed Thursday near the US Open at Erin Hills in Wisconsin. A witness says the blimp caught fire as it fell. Another says the pilot appeared to parachute from the blimp. One person was transported from the scene for medical attention; the person is presumed to be the pilot. The USGA says the blimp was not affiliated with the US Open, the Washington Post reports. The blimp, which bore an advertisement for PenFed Credit Union, is operated by AirSign, which tweeted a photo of it prior to the crash with the message "Share your blimp sighting pics!" Multiple witnesses tweeted videos of the crashing blimp. According to the AP, AirSign says the pilot was the only person on board the blimp. A sales manager for AirSign says he's "not 100%" on the pilot's condition but believes he's alive. | <s>[INST]ERIN, Wis. (AP) β A blimp flying over the U.S. Open has gone down and the aircraft's operator says he doesn't know if the pilot is alive.
Justin Maynard is a sales manager for AirSign, the advertising company that operates the blimp.
Maynard says only the pilot was on board the craft. He says the company's operations team on the ground confirmed citizen video on social media showing the blimp going down.
Maynard says he is "not 100 percent" on the condition of the pilot but that believes he is alive. ||||| A blimp with a lone pilot on board plummeted from the sky on June 15 during the first round of the U.S. Open in Erin Hills, Wis. (Adam Johnson/Twitter)
An advertising blimp with a lone pilot on board plummeted from the sky on Thursday afternoon during the first round of the U.S. Open at Erin Hills in Wisconsin, according to multiple reports from the scene. The Milwaukee Journal-Sentinel says the blimp caught fire before it hit the ground in a field near the intersection of Highway 83 and Highway 167, just outside the course.
βIt started deflating, and then it started going down,β witness Bryan Rosine told the Journal-Sentinel. βThey were trying to give it some throttle and it didnβt go up. Then there was a bunch of kabooms and smoke clouds.β
AirSign, the company that operated the blimp, had an update on the pilotβs condition later Thursday.
Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be ok. No details on cause of crash β AirSign (@AirSign) June 15, 2017
Fox Sports has video of the explosion on the ground.
A manned blimp unaffiliated with FOX Sports or the #USOpen crashed near the course earlier today. pic.twitter.com/XXaj3n8j2H β FS1 (@FS1) June 15, 2017
According to the USGA, which runs the event, the blimp was unaffiliated with the tournament or with Fox Sports, which is broadcasting the event.
Just got to the #USOpen and the blimp caught fire and crashed. People parachuted out. pic.twitter.com/1lDi3VkXCu β madison seigworth (@msiggyy) June 15, 2017
[From the archives: The blimp pilots that fly over PGA Tour events have the best views, but they have solitary lives.]
WMTV in Madison, Wis., posted photos of the crash scene and had a helicopter circling the crash scene. Its live footage showed what appeared to be a good number of emergency workers tending to a single individual on the ground. The person was transported from the middle of a field in the back of a pickup truck and driven to the parking lot of what appeared to be a warehouse in the middle of a vast field. Workers loaded the gurney onto a waiting emergency helicopter, which then flew off to a nearby hospital.
ESPNβs Ian OβConnor reports that the pilot was the only person on board and that he was alert and conscious.
Paramedics moving apparent victim of blimp crash at US Open pic.twitter.com/qrdrsVXaAT β Ian O'Connor (@Ian_OConnor) June 15, 2017
Hereβs more footage:
#BREAKING: A blimp has crashed and caught on fire at the U.S. Open in Wisconsin pic.twitter.com/FmVbcxwTnG β WSVN 7 News (@wsvn) June 15, 2017
Pretty sure I just watched the blimp crash at the #USOPEN! Hope everybody is ok! pic.twitter.com/OSOCSBF46p β Adam Johnson (@Coach_Guy_AJ) June 15, 2017
The blimp was operated by AirSign, a national aerial advertising firm. The company had announced earlier Thursday that one of their blimps would be present.
Patrick Walsh, AirSignβs CEO, told CBS News that the cause of the crash was still under investigation. The pilot suffered burns, he said, and there were no injuries on the ground.
According to a National Transportation Safety Board database, AirSign aircraft have been involved in two incidents, both involving planes. In April 2010, the pilot was killed after a small propeller plane he was flying βwas substantially damaged when it impacted terrain after a loss of control during initial climbβ at Orlando North Airpark in Florida. The plane was involved in a βbanner towing job,β according to the NTSB, which cited the pilotβs failure to maintain airspeed after takeoff as the reason for the crash.
In March 2005, a Cessna registered to AirSign made an emergency crash landing on a road after the pilot reported a loss of engine power shortly after takeoff from Charlotte Douglas International Airport in North Carolina. The pilot suffered what the NTSB report described as minor injuries after colliding with a curb and a parked car, and the agency found that he failed to follow a preflight checklist.
But crashes involving blimps are βextremely rare,β Dan Coffee, owner of the Wisconsin airstrip from which the blimp took off Thursday, told the Journal-Sentinel, and a check of the NTSB database seems to back this up. The last blimp incident logged by the agency took place in 2006.
According to Terry Sater of WISN-TV in Milwaukee, the NTSB is gathering information about Thursdayβs blimp crash. ||||| 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 ||||| CLOSE A PenFed blimp deflated, burst into flames and crashed late Thursday morning near the U.S. Open at Erin Hills.
The damaged blimp falls to the ground near the U.S. Open at Erin Hills. (Photo: Associated Press)
TOWN of ERIN - Some of the biggest drama at the U.S. Open took place in the sky just east of the course Thursday morning when a blimp advertising for PenFed Credit Union deflated, burst into flames and crashed.
The blimp went down about 11:15 a.m. near Highways 83 and 167. The crash site was about a mile from the Erin Hills golf course where thousands of people gathered for the first morning of competition.
The pilot was flown by Flight for Life around noon to be treated for serious injuries, including burns, at Froedtert Hospital. The hospital identified him as Trevor Thompson and said he was in serious condition.
Thompson was coherent and stable enough to talk to officers, officials from the National Transportation Safety Board said at a news conference Thursday night. The NTSB is investigating the crash.
Officers reported that the aircraft had reached an altitude of about 1,000 feet before Thompson decided to land because of high winds. As he was descending, he heard panels rip off the air balloon and blimp hybrid that he was flying. He then turned the engines off, but residual fuel in the engines is what led to the fiery explosion that followed once the aircraft hit the ground.
Thompson was the only occupant of the aircraft, and no one on the ground was injured.
The blimp was operated by AirSign, an aerial advertising firm with operations across the country. The company website says it specializes in banner, blimps and sky writing.
FULL COVERAGE: 2017 U.S. Open at Erin Hills
Buy Photo Blimp pilot Trevor Thompson is transported by Flight for Life after the crash near the U.S. Open at Erin Hills on June 15, 2017. (Photo: Mark Hoffman / Milwaukee Journal Sentinel)
"He stayed with the blimp until it went down," a spokesman for AirSign said in a telephone interview from Florida. He said that a crew member on the ground pulled Thompson from the wreckage.
Fox 6 reported that Thompson had made forced landings in 2015 and 2016.
The aircraft, a Gefa-Flug Airship, was manufactured in 2004, registered in Great Britain and owned by Airsign Ltd. of Williston, Fla.
The Federal Aviation Administration had no record of the blimp being involved in any accidents before Thursday, according to Lynn Lunsford, a public affairs manager for the agency.
The company tweeted: "Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be OK. No details on cause of crash."
Thanks to everyone for your concerns, the blimp pilot is being taken to the hospital but is expected to be ok. No details on cause of crash β AirSign (@AirSign) June 15, 2017
A close-up of the damaged blimp as it falls to the ground. (Photo: Associated Press)
"It started deflating, and then it started going down," said Bryan Rosine, who noticed the blimp while he was taking a tree down.
"They were trying to give it some throttle and it didn't go up. Then there was a bunch of kabooms and smoke clouds."
Another witness, Tim Guetzke and his 16-year-old son Hunter, an incoming junior at Hartford Union High School, were in the area and watching the blimp.
"The side started deflating," Tim Guetzke said. "One side was going in. As it headed toward the ground, it caught fire."
"It was doing fine for hours," he said. "Hunter could see it. He said, 'Dad, it's deflating. I think it's starting on fire.' When you realize someone is in there it makes you sad."
Golfer Jamie Lovemark said he saw the blimp while on the 5th hole.
"I was teeing off and I looked up and saw it on fire and I felt sick to my stomach," he said. "I had the shakes. I felt terrible for the people inside. I didn't know what was going on. It was a horrible sight."
The blimp landed in a farmer's field near a stand of trees and looked like a large deflated balloon. Videos show flames and explosions after the wreckage hit the ground.
The sign on the blimp advertised PenFed Credit Union, also known as the Pentagon Federal Credit Union. The nation's third-largest credit union with assets of about $22 billion, PenFed serves about 1.5 million people with connections to the military and has branches in 10 states.
Earlier Thursday morning, AirSign tweeted about the blimp's arrival and encouraged visitors to share photos.
The blimp took off from a small privately operated air field not far from the crash site, said Dan Coffey, owner of the Air Strip WN75.
"They were going to use it all week," Coffey said. "He was flying it for hours. I don't know if the wind caught up with him or what."
Coffey said that the accident was extremely unusual.
"These airships are FAA approved. They make sure that every one is inspected," he said. "This is an extremely rare accident."
Terry Williams, a spokesman for the National Transportation Safety Board, said the agency has launched an investigation into the incident and has dispatched an investigator to the scene.
A blimp unaffiliated with the #USOpen or @FOXSports has crashed near Erin Hills. Pilot was injured and first responders are on the scene. β U.S. Open (USGA) (@usopengolf) June 15, 2017
A statement distributed by the United States Golf Association said the blimp was not affiliated with the USGA or the U.S. Open.
"Our thoughts and prayers are with the pilot at this time," the USGA statement said.
Earlier Thursday morning, AirSign tweeted a picture: "The beautiful @penfed blimp is flying high over the US Open today!"
The company also tweeted a picture of the golf course taken from the blimp.
A manned blimp unaffiliated with FOX Sports or the #USOpen crashed near the course today. We will provide more details as they're available. pic.twitter.com/QEAk8tiU0K β FOX Sports (@FOXSports) June 15, 2017
Pretty sure I just watched the blimp crash at the #USOPEN! Hope everybody is ok! pic.twitter.com/OSOCSBF46p β Adam Johnson (@Coach_Guy_AJ) June 15, 2017
The blimp crash was far from the course but the smoke that rose above the trees afterwards was terrifying. β Mike Hall (@BTNMikeHall) June 15, 2017
#USOpen A blimp has caught fire flying over the @usopengolf and crashed in the woods near @ErinHillsGolf . pic.twitter.com/OlhebVlNky β Mr. Terrific β’ (@RealMrTerrific) June 15, 2017
Just got to the #USOpen and the blimp caught fire and crashed. People parachuted out. pic.twitter.com/1lDi3VkXCu β madison seigworth (@msiggyy) June 15, 2017
Joe Taschler, Kevin Crowe and Jordyn Noennig of the Journal Sentinel staff contributed to this report.
Read or Share this story: http://jsonl.in/2swQDP8[/INST]β "It started deflating, and then it started going down," witness Bryan Rosine tells the Journal Sentinel. "Then there was a bunch of kabooms and smoke clouds." One person is reportedly injured after an advertising blimp crashed Thursday near the US Open at Erin Hills in Wisconsin. A witness says the blimp caught fire as it fell. Another says the pilot appeared to parachute from the blimp. One person was transported from the scene for medical attention; the person is presumed to be the pilot. The USGA says the blimp was not affiliated with the US Open, the Washington Post reports. The blimp, which bore an advertisement for PenFed Credit Union, is operated by AirSign, which tweeted a photo of it prior to the crash with the message "Share your blimp sighting pics!" Multiple witnesses tweeted videos of the crashing blimp. According to the AP, AirSign says the pilot was the only person on board the blimp. A sales manager for AirSign says he's "not 100%" on the pilot's condition but believes he's alive.</s> |
gastrointestinal stromal tumours ( gists ) can arise from the gastrointestinal tract , with the highest incidence in the stomach ( 50 - 60% ) .
all gastric gists > 1 cm should be considered as potentially malignant , and the recommended procedure for non - metastatic forms includes the removal of the visible tumour without spillage and with macroscopic free margins of resection ( 1 - 2 cm ) . with comparable oncological results , the laparoscopic approach offers significant advantages in terms of post - operative pain and length of stay compared to open surgery and is increasingly adopted in many centres .
however , there is a controversy about the impact of tumour size on both the technical feasibility of laparoscopic resection for gastric gist and its oncological adequacy in terms of tumour rupture and resection margins .
while the size limit for laparoscopic gist resection is continuously being modified , larger tumours have generally been approached through an open approach and frequently involve more extensive resections .
the perceived advantages or equivalence of the laparoscopic approach when compared with the open approach may therefore be a result of this size selection bias , and improved outcomes associated with laparoscopy may be surrogates for less extensive resections .
therefore , the aim of the present study was to evaluate whether the laparoscopic approach jeopardised the short- and long - term outcomes of patients with large ( > 5 cm ) gastric gists when compared to smaller ones .
between january 2003 and september 2013 , all consecutive pathologically confirmed gastric gists operated on with a curative intent were selected .
preoperative investigations included complete blood function tests as well as routine oesophagogastroduodenoscopy , computed tomography ( ct ) scan and endoscopic ultrasonography .
initially , preoperative biopsy of the tumour was performed on a case - by - case basis but was carried out routinely during the final 5 years of the study . in accordance with privette et al .
, gists were divided according to site into type i ( greater curvature ) , type ii ( prepyloric and antrum ) , and type iii ( lesser curvature and near the gastro - oesophageal junction ) .
the choice between open or laparoscopic approach was made after careful examination of the previous medical and surgical history of each patient as well as the type and the site of the tumour . in the laparoscopic group ,
each patient was placed in the supine position with anti - trendelenburg of 15 and right tilt .
carbon dioxide was insufflated through the first port with a pressure setting of 12 mmhg .
a second and third 15 mm port were inserted in the right and left upper abdominal quadrants , respectively , under direct vision .
the gastric wedge resection was achieved using an endo - gia stapler , and the tumour specimen was extracted using an endocatch bag .
all intraoperative parameters including estimated blood loss with subsequent blood transfusion and duration of surgery were recorded .
mitotic rate was defined as the number of mitoses per 50 high - power fields ( hpf ) , and tumour size was defined as the maximal tumour dimension in the resected specimen .
large gist group. post - operative complications were stratified according to the clavien - dindo classification , which defines major complications by a score of 3 or higher . both complications and operative mortality
were considered as those occurring within 90 days of surgery or at any time during the post - operative hospital stay .
after discharge , patients were seen at the outpatient clinic for clinical examination , and morphological evaluation ( including mainly computed tomography ) 1 month after discharge , every 3 months for the first 2 years and every 6 months until the fifth postoperative year .
thereafter , patients were seen yearly , and follow - up was discontinued in the absence of recurrence after the 10 year . actuarial overall survival ( os ) and disease - free survival ( dfs )
patient baseline characteristics are expressed as median ( range ) for continuous data ( mean standard error of the mean are also indicated where appropriate ) , and as numbers with percentages for categorical data .
preoperative , operative and post - operative characteristics as well as long - term survival of patients were compared according to the tumour size ( vs < 5 cm ) .
fisher 's exact test or chi - square test was used to compare differences in categorical variables , and the mann - whitney test for continuous variables .
cumulative overall survival was determined using the kaplan - meier method and compared with the log - rank test .
statistical analyses were performed using spss version 18.0 for windows software ( ibm , armonk , new york , usa ) .
between january 2003 and september 2013 , all consecutive pathologically confirmed gastric gists operated on with a curative intent were selected .
preoperative investigations included complete blood function tests as well as routine oesophagogastroduodenoscopy , computed tomography ( ct ) scan and endoscopic ultrasonography .
initially , preoperative biopsy of the tumour was performed on a case - by - case basis but was carried out routinely during the final 5 years of the study . in accordance with privette et al .
, gists were divided according to site into type i ( greater curvature ) , type ii ( prepyloric and antrum ) , and type iii ( lesser curvature and near the gastro - oesophageal junction ) .
all resections for gastric gists were performed with curative intent . the choice between open or laparoscopic approach was made after careful examination of the previous medical and surgical history of each patient as well as the type and the site of the tumour . in the laparoscopic group ,
each patient was placed in the supine position with anti - trendelenburg of 15 and right tilt .
carbon dioxide was insufflated through the first port with a pressure setting of 12 mmhg .
a second and third 15 mm port were inserted in the right and left upper abdominal quadrants , respectively , under direct vision .
the gastric wedge resection was achieved using an endo - gia stapler , and the tumour specimen was extracted using an endocatch bag .
clinical and histopathologic data were obtained from patient medical records . all intraoperative parameters including estimated blood loss with subsequent blood transfusion and duration of surgery were recorded .
mitotic rate was defined as the number of mitoses per 50 high - power fields ( hpf ) , and tumour size was defined as the maximal tumour dimension in the resected specimen .
large gist group. post - operative complications were stratified according to the clavien - dindo classification , which defines major complications by a score of 3 or higher . both complications and operative mortality
were considered as those occurring within 90 days of surgery or at any time during the post - operative hospital stay .
after discharge , patients were seen at the outpatient clinic for clinical examination , and morphological evaluation ( including mainly computed tomography ) 1 month after discharge , every 3 months for the first 2 years and every 6 months until the fifth postoperative year .
thereafter , patients were seen yearly , and follow - up was discontinued in the absence of recurrence after the 10 year . actuarial overall survival ( os ) and disease - free survival ( dfs ) were calculated from the date of curative surgery to the first recurrence .
patient baseline characteristics are expressed as median ( range ) for continuous data ( mean standard error of the mean are also indicated where appropriate ) , and as numbers with percentages for categorical data .
preoperative , operative and post - operative characteristics as well as long - term survival of patients were compared according to the tumour size ( vs < 5 cm ) .
fisher 's exact test or chi - square test was used to compare differences in categorical variables , and the mann - whitney test for continuous variables .
cumulative overall survival was determined using the kaplan - meier method and compared with the log - rank test .
statistical analyses were performed using spss version 18.0 for windows software ( ibm , armonk , new york , usa ) .
fifty patients underwent gastrectomy for gist including 26 females ( 52% ) and 24 males ( 48% ) with a median age of 63 years ( range : 17 to 83 ) .
sixteen ( 32% ) gastric gist patients underwent open resection while the 34 ( 68% ) remaining were treated by laparoscopy [ table 1 ] .
the preoperative characteristics of the laparoscopic group are detailed in table 2 . among them , 12 ( 35% ) patients with tumours > 5 cm formed the
tumour was diagnosed incidentally in 12 ( 35% ) patients , whereas the most common symptoms were abdominal pain ( 50% ) , bleeding ( 23% ) and anaemia ( 18% ) .
the tumours were most frequently located in greater ( 29% ) and lesser curvatures ( 29% ) , and 19 ( 56% ) patients had preoperative biopsy .
one patient had received imatinib mesylate as neoadjuvant chemotherapy . demographic characteristics and preoperative data of patients undergoing open and laparoscopic gastric gist resection demographic and preoperative data of laparoscopic small gist and large gist groups in the selected population fifteen ( 44% ) patients had previous abdominal surgery without significant difference in the two groups ( 41% vs 50% , p = 0.72 ) .
gastric resection was atypical in 28 ( 82% ) patients without difference in the two groups .
although the median operative time was significantly longer in the large gist group ( 112 min vs 60 min , p = 0.001 ) , the median estimated blood loss ranged 5 - 1300 ml , without any difference in the two groups ( p = 0.86 ) .
all tumours in the large gist group were extracted through a pfannenstiel incision , the length of which varied according to the size of each tumour .
operative results , pathological data and perioperative outcomes of laparoscopic small gist and large gist groups in our patient population the mortality rate was nil and 3 ( 9% ) patients experienced post - operative complications , mainly pulmonary complications .
the overall median length of hospital stay in the laparoscopic group was 6 days ( range 3 - 16 days ) , and it was significantly higher in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
the overall mean tumour size in our study was 4.5 cm , 7.9 cm in the open resection group and 4.3 cm in the laparoscopic group ( p = 0.003 ) .
large gist group compared to the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) . on microscopic analysis
, 71% of tumours had a mitotic rate of fewer than 5 mitoses per 50 hpf , 12% had a mitotic rate between 5 and 10 mitoses per 50 hpf , and 18% had more than 10 mitoses per 50 hpf .
small gist groups regarding a mitotic rate higher than 10 mitoses per 50 hpf ( 41.7% vs 4.5% , p = 0.013 ) .
there was no statistically significant difference between the two groups regarding histologic type ( p = 0.14 ) [ table 3 ] .
the median follow - up in the laparoscopic group was 47 months ( range 6 - 124 months ) .
one ( 3% ) patient with large - gist recurrence developed recurrence with peritoneal carcinomatosis 6 months after laparoscopic resection and was subsequently treated by both laparoscopic resection and chemotherapy ; the patient is still alive 7 years after surgery .
actuarial 1-year , 5-year and 10-year os was 100% in both groups ; 1-year , 5-year and 10-year dfs was 95% , 95% and 95% , respectively .
fifty patients underwent gastrectomy for gist including 26 females ( 52% ) and 24 males ( 48% ) with a median age of 63 years ( range : 17 to 83 ) .
sixteen ( 32% ) gastric gist patients underwent open resection while the 34 ( 68% ) remaining were treated by laparoscopy [ table 1 ] .
the preoperative characteristics of the laparoscopic group are detailed in table 2 . among them , 12 ( 35% ) patients with tumours > 5 cm formed the
tumour was diagnosed incidentally in 12 ( 35% ) patients , whereas the most common symptoms were abdominal pain ( 50% ) , bleeding ( 23% ) and anaemia ( 18% ) .
the tumours were most frequently located in greater ( 29% ) and lesser curvatures ( 29% ) , and 19 ( 56% ) patients had preoperative biopsy .
one patient had received imatinib mesylate as neoadjuvant chemotherapy . demographic characteristics and preoperative data of patients undergoing open and laparoscopic gastric gist resection demographic and preoperative data of laparoscopic small gist and large gist groups in the selected population
fifteen ( 44% ) patients had previous abdominal surgery without significant difference in the two groups ( 41% vs 50% , p = 0.72 ) .
gastric resection was atypical in 28 ( 82% ) patients without difference in the two groups .
although the median operative time was significantly longer in the large gist group ( 112 min vs 60 min , p = 0.001 ) , the median estimated blood loss ranged 5 - 1300 ml , without any difference in the two groups ( p = 0.86 ) .
all tumours in the large gist group were extracted through a pfannenstiel incision , the length of which varied according to the size of each tumour .
operative results , pathological data and perioperative outcomes of laparoscopic small gist and large gist groups in our patient population the mortality rate was nil and 3 ( 9% ) patients experienced post - operative complications , mainly pulmonary complications .
the overall median length of hospital stay in the laparoscopic group was 6 days ( range 3 - 16 days ) , and it was significantly higher in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
the overall mean tumour size in our study was 4.5 cm , 7.9 cm in the open resection group and 4.3 cm in the laparoscopic group ( p = 0.003 ) .
large gist group compared to the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) . on microscopic analysis
, 71% of tumours had a mitotic rate of fewer than 5 mitoses per 50 hpf , 12% had a mitotic rate between 5 and 10 mitoses per 50 hpf , and 18% had more than 10 mitoses per 50 hpf .
small gist groups regarding a mitotic rate higher than 10 mitoses per 50 hpf ( 41.7% vs 4.5% , p = 0.013 ) .
there was no statistically significant difference between the two groups regarding histologic type ( p = 0.14 ) [ table 3 ] .
the median follow - up in the laparoscopic group was 47 months ( range 6 - 124 months ) .
one ( 3% ) patient with large - gist recurrence developed recurrence with peritoneal carcinomatosis 6 months after laparoscopic resection and was subsequently treated by both laparoscopic resection and chemotherapy ; the patient is still alive 7 years after surgery .
actuarial 1-year , 5-year and 10-year os was 100% in both groups ; 1-year , 5-year and 10-year dfs was 95% , 95% and 95% , respectively .
laparoscopic gastric resection has the potential advantage of requiring smaller incisions and less bowel manipulation compared with open surgery .
to our knowledge , this is the first comparison of laparoscopic gastric resection in large and small gastric gists .
our data demonstrate that laparoscopic resection is safe and technically feasible in large gists and does not negatively influence the oncologic course or oncological safety .
the absence of conversion to open surgery in the present series and a conversion rate of 4.7% in other large series confirms the feasibility of the laparoscopic approach for large lesions . despite the fact that the sample size of our study was small
, there was no significant difference in the incidence of overall or major complications between the large- and small - gist groups .
the few complications observed were essentially pulmonary complications mainly related to a high gastric localisation of the gist ( near the oesogastric junction or greater curvature ) .
all complications were promptly treated without endangering the patient 's life at any moment . however , in order to obtain similar results , the resection of such large lesions has to be performed by surgeons experienced in both laparoscopic and upper gastrointestinal tract surgery . at our department , surgeons are well trained in laparoscopic surgery , such as bariatric , hepatobiliary , and oesophageal / cardia cancer procedures .
finally , a prerequisite for performing gastric gist surgery is an advanced knowledge of intracorporeal suturing , which is often necessary in such procedures .
laparoscopic resection of large gastric gists appears to be a reasonable surgical technique for appropriately skilled surgeons performing minimally invasive gastric resections .
large gastric gists and tumours located in difficult locations , such as the oesogastric junction and posterior wall , are technically more difficult to resect , especially via the laparoscopic approach , with an increased risk of tumour spillage . in some difficult situations
for this reason , the guidelines for optimal management of patients with gist suggested that laparoscopic resection should be limited to tumours less than 2 cm .
however , the mean tumour size for laparoscopic gastrectomy ranged 2.7 - 6.0 cm in recent meta - analysis and was 8.4 cm in our large - gist group . given the low rate of both positive margins and local recurrence , it appears that this recommendation is not based on strong evidence . in the present series ,
the oncological safety of lr was confirmed , as shown by the comparable overall survival rates of the two groups .
hence , even though safe oncologic resection is the primary concern when considering lr for large gist , the present study suggests that a laparoscopic approach for gastric gist should not be limited to tumours smaller than 2 cm and could also be considered for tumours larger than 5 cm .
the present study has several important limitations , which should be taken into account when considering the results .
first , although the patients were entered into the database in a prospective fashion , some of the outcome data were gathered through a retrospective review of the medical records and are therefore subject to bias .
indeed , these patients were not randomly selected with regard to the surgical approach , and gastric gists were significantly larger in the open group compared to the laparoscopic group .
therefore , these results need to be confirmed by high - quality randomised controlled trials with larger sample sizes that compare gastric resection for gists smaller and larger than 5 cm .
in conclusion , this study suggests that laparoscopic resection for large gists is safe and technically feasible and does not negatively influence the oncologic course or oncological safety .
nevertheless , prospective randomised trials should be performed before incorporation of these new data into routine surgical care . | background : laparoscopic resection ( lr ) offers significant advantages compared to open resections for gastric gastrointestinal stromal tumours ( gists ) .
we aimed to evaluate whether lr outcomes jeopardised short and long - term outcomes of patients with large gists.patients and methods : among 50 patients undergoing surgery for gastric gists , 12 underwent lr for large gists ( > 5 cm ) .
their characteristics , perioperative results and survival were retrospectively compared to those of 22 patients who underwent lr for small gist.results:the two groups were similar regarding demographics , rate of wedge resection and mean blood loss .
no patient required transfusion or conversion .
operative time was significantly increased in the large gist group ( 160 min vs 112 min , p = 0.001 ) .
mean tumour size was significantly lower in the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) .
resection margins were negative .
the mortality rate was nil and the overall morbidity rates was similar in both groups .
median length of hospital stay was significantly increased in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
median follow - up was 47 months and one patient in the
small gist group developed recurrence and died during follow - up 11 years after surgery .
no patient died during follow-up.conclusions:lr for large gists is safe and technically feasible and does not negatively influence the oncologic course .
prospective randomised trials should be performed before using this approach in routine surgical care . | <s>[INST]gastrointestinal stromal tumours ( gists ) can arise from the gastrointestinal tract , with the highest incidence in the stomach ( 50 - 60% ) .
all gastric gists > 1 cm should be considered as potentially malignant , and the recommended procedure for non - metastatic forms includes the removal of the visible tumour without spillage and with macroscopic free margins of resection ( 1 - 2 cm ) . with comparable oncological results , the laparoscopic approach offers significant advantages in terms of post - operative pain and length of stay compared to open surgery and is increasingly adopted in many centres .
however , there is a controversy about the impact of tumour size on both the technical feasibility of laparoscopic resection for gastric gist and its oncological adequacy in terms of tumour rupture and resection margins .
while the size limit for laparoscopic gist resection is continuously being modified , larger tumours have generally been approached through an open approach and frequently involve more extensive resections .
the perceived advantages or equivalence of the laparoscopic approach when compared with the open approach may therefore be a result of this size selection bias , and improved outcomes associated with laparoscopy may be surrogates for less extensive resections .
therefore , the aim of the present study was to evaluate whether the laparoscopic approach jeopardised the short- and long - term outcomes of patients with large ( > 5 cm ) gastric gists when compared to smaller ones .
between january 2003 and september 2013 , all consecutive pathologically confirmed gastric gists operated on with a curative intent were selected .
preoperative investigations included complete blood function tests as well as routine oesophagogastroduodenoscopy , computed tomography ( ct ) scan and endoscopic ultrasonography .
initially , preoperative biopsy of the tumour was performed on a case - by - case basis but was carried out routinely during the final 5 years of the study . in accordance with privette et al .
, gists were divided according to site into type i ( greater curvature ) , type ii ( prepyloric and antrum ) , and type iii ( lesser curvature and near the gastro - oesophageal junction ) .
the choice between open or laparoscopic approach was made after careful examination of the previous medical and surgical history of each patient as well as the type and the site of the tumour . in the laparoscopic group ,
each patient was placed in the supine position with anti - trendelenburg of 15 and right tilt .
carbon dioxide was insufflated through the first port with a pressure setting of 12 mmhg .
a second and third 15 mm port were inserted in the right and left upper abdominal quadrants , respectively , under direct vision .
the gastric wedge resection was achieved using an endo - gia stapler , and the tumour specimen was extracted using an endocatch bag .
all intraoperative parameters including estimated blood loss with subsequent blood transfusion and duration of surgery were recorded .
mitotic rate was defined as the number of mitoses per 50 high - power fields ( hpf ) , and tumour size was defined as the maximal tumour dimension in the resected specimen .
large gist group. post - operative complications were stratified according to the clavien - dindo classification , which defines major complications by a score of 3 or higher . both complications and operative mortality
were considered as those occurring within 90 days of surgery or at any time during the post - operative hospital stay .
after discharge , patients were seen at the outpatient clinic for clinical examination , and morphological evaluation ( including mainly computed tomography ) 1 month after discharge , every 3 months for the first 2 years and every 6 months until the fifth postoperative year .
thereafter , patients were seen yearly , and follow - up was discontinued in the absence of recurrence after the 10 year . actuarial overall survival ( os ) and disease - free survival ( dfs )
patient baseline characteristics are expressed as median ( range ) for continuous data ( mean standard error of the mean are also indicated where appropriate ) , and as numbers with percentages for categorical data .
preoperative , operative and post - operative characteristics as well as long - term survival of patients were compared according to the tumour size ( vs < 5 cm ) .
fisher 's exact test or chi - square test was used to compare differences in categorical variables , and the mann - whitney test for continuous variables .
cumulative overall survival was determined using the kaplan - meier method and compared with the log - rank test .
statistical analyses were performed using spss version 18.0 for windows software ( ibm , armonk , new york , usa ) .
between january 2003 and september 2013 , all consecutive pathologically confirmed gastric gists operated on with a curative intent were selected .
preoperative investigations included complete blood function tests as well as routine oesophagogastroduodenoscopy , computed tomography ( ct ) scan and endoscopic ultrasonography .
initially , preoperative biopsy of the tumour was performed on a case - by - case basis but was carried out routinely during the final 5 years of the study . in accordance with privette et al .
, gists were divided according to site into type i ( greater curvature ) , type ii ( prepyloric and antrum ) , and type iii ( lesser curvature and near the gastro - oesophageal junction ) .
all resections for gastric gists were performed with curative intent . the choice between open or laparoscopic approach was made after careful examination of the previous medical and surgical history of each patient as well as the type and the site of the tumour . in the laparoscopic group ,
each patient was placed in the supine position with anti - trendelenburg of 15 and right tilt .
carbon dioxide was insufflated through the first port with a pressure setting of 12 mmhg .
a second and third 15 mm port were inserted in the right and left upper abdominal quadrants , respectively , under direct vision .
the gastric wedge resection was achieved using an endo - gia stapler , and the tumour specimen was extracted using an endocatch bag .
clinical and histopathologic data were obtained from patient medical records . all intraoperative parameters including estimated blood loss with subsequent blood transfusion and duration of surgery were recorded .
mitotic rate was defined as the number of mitoses per 50 high - power fields ( hpf ) , and tumour size was defined as the maximal tumour dimension in the resected specimen .
large gist group. post - operative complications were stratified according to the clavien - dindo classification , which defines major complications by a score of 3 or higher . both complications and operative mortality
were considered as those occurring within 90 days of surgery or at any time during the post - operative hospital stay .
after discharge , patients were seen at the outpatient clinic for clinical examination , and morphological evaluation ( including mainly computed tomography ) 1 month after discharge , every 3 months for the first 2 years and every 6 months until the fifth postoperative year .
thereafter , patients were seen yearly , and follow - up was discontinued in the absence of recurrence after the 10 year . actuarial overall survival ( os ) and disease - free survival ( dfs ) were calculated from the date of curative surgery to the first recurrence .
patient baseline characteristics are expressed as median ( range ) for continuous data ( mean standard error of the mean are also indicated where appropriate ) , and as numbers with percentages for categorical data .
preoperative , operative and post - operative characteristics as well as long - term survival of patients were compared according to the tumour size ( vs < 5 cm ) .
fisher 's exact test or chi - square test was used to compare differences in categorical variables , and the mann - whitney test for continuous variables .
cumulative overall survival was determined using the kaplan - meier method and compared with the log - rank test .
statistical analyses were performed using spss version 18.0 for windows software ( ibm , armonk , new york , usa ) .
fifty patients underwent gastrectomy for gist including 26 females ( 52% ) and 24 males ( 48% ) with a median age of 63 years ( range : 17 to 83 ) .
sixteen ( 32% ) gastric gist patients underwent open resection while the 34 ( 68% ) remaining were treated by laparoscopy [ table 1 ] .
the preoperative characteristics of the laparoscopic group are detailed in table 2 . among them , 12 ( 35% ) patients with tumours > 5 cm formed the
tumour was diagnosed incidentally in 12 ( 35% ) patients , whereas the most common symptoms were abdominal pain ( 50% ) , bleeding ( 23% ) and anaemia ( 18% ) .
the tumours were most frequently located in greater ( 29% ) and lesser curvatures ( 29% ) , and 19 ( 56% ) patients had preoperative biopsy .
one patient had received imatinib mesylate as neoadjuvant chemotherapy . demographic characteristics and preoperative data of patients undergoing open and laparoscopic gastric gist resection demographic and preoperative data of laparoscopic small gist and large gist groups in the selected population fifteen ( 44% ) patients had previous abdominal surgery without significant difference in the two groups ( 41% vs 50% , p = 0.72 ) .
gastric resection was atypical in 28 ( 82% ) patients without difference in the two groups .
although the median operative time was significantly longer in the large gist group ( 112 min vs 60 min , p = 0.001 ) , the median estimated blood loss ranged 5 - 1300 ml , without any difference in the two groups ( p = 0.86 ) .
all tumours in the large gist group were extracted through a pfannenstiel incision , the length of which varied according to the size of each tumour .
operative results , pathological data and perioperative outcomes of laparoscopic small gist and large gist groups in our patient population the mortality rate was nil and 3 ( 9% ) patients experienced post - operative complications , mainly pulmonary complications .
the overall median length of hospital stay in the laparoscopic group was 6 days ( range 3 - 16 days ) , and it was significantly higher in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
the overall mean tumour size in our study was 4.5 cm , 7.9 cm in the open resection group and 4.3 cm in the laparoscopic group ( p = 0.003 ) .
large gist group compared to the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) . on microscopic analysis
, 71% of tumours had a mitotic rate of fewer than 5 mitoses per 50 hpf , 12% had a mitotic rate between 5 and 10 mitoses per 50 hpf , and 18% had more than 10 mitoses per 50 hpf .
small gist groups regarding a mitotic rate higher than 10 mitoses per 50 hpf ( 41.7% vs 4.5% , p = 0.013 ) .
there was no statistically significant difference between the two groups regarding histologic type ( p = 0.14 ) [ table 3 ] .
the median follow - up in the laparoscopic group was 47 months ( range 6 - 124 months ) .
one ( 3% ) patient with large - gist recurrence developed recurrence with peritoneal carcinomatosis 6 months after laparoscopic resection and was subsequently treated by both laparoscopic resection and chemotherapy ; the patient is still alive 7 years after surgery .
actuarial 1-year , 5-year and 10-year os was 100% in both groups ; 1-year , 5-year and 10-year dfs was 95% , 95% and 95% , respectively .
fifty patients underwent gastrectomy for gist including 26 females ( 52% ) and 24 males ( 48% ) with a median age of 63 years ( range : 17 to 83 ) .
sixteen ( 32% ) gastric gist patients underwent open resection while the 34 ( 68% ) remaining were treated by laparoscopy [ table 1 ] .
the preoperative characteristics of the laparoscopic group are detailed in table 2 . among them , 12 ( 35% ) patients with tumours > 5 cm formed the
tumour was diagnosed incidentally in 12 ( 35% ) patients , whereas the most common symptoms were abdominal pain ( 50% ) , bleeding ( 23% ) and anaemia ( 18% ) .
the tumours were most frequently located in greater ( 29% ) and lesser curvatures ( 29% ) , and 19 ( 56% ) patients had preoperative biopsy .
one patient had received imatinib mesylate as neoadjuvant chemotherapy . demographic characteristics and preoperative data of patients undergoing open and laparoscopic gastric gist resection demographic and preoperative data of laparoscopic small gist and large gist groups in the selected population
fifteen ( 44% ) patients had previous abdominal surgery without significant difference in the two groups ( 41% vs 50% , p = 0.72 ) .
gastric resection was atypical in 28 ( 82% ) patients without difference in the two groups .
although the median operative time was significantly longer in the large gist group ( 112 min vs 60 min , p = 0.001 ) , the median estimated blood loss ranged 5 - 1300 ml , without any difference in the two groups ( p = 0.86 ) .
all tumours in the large gist group were extracted through a pfannenstiel incision , the length of which varied according to the size of each tumour .
operative results , pathological data and perioperative outcomes of laparoscopic small gist and large gist groups in our patient population the mortality rate was nil and 3 ( 9% ) patients experienced post - operative complications , mainly pulmonary complications .
the overall median length of hospital stay in the laparoscopic group was 6 days ( range 3 - 16 days ) , and it was significantly higher in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
the overall mean tumour size in our study was 4.5 cm , 7.9 cm in the open resection group and 4.3 cm in the laparoscopic group ( p = 0.003 ) .
large gist group compared to the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) . on microscopic analysis
, 71% of tumours had a mitotic rate of fewer than 5 mitoses per 50 hpf , 12% had a mitotic rate between 5 and 10 mitoses per 50 hpf , and 18% had more than 10 mitoses per 50 hpf .
small gist groups regarding a mitotic rate higher than 10 mitoses per 50 hpf ( 41.7% vs 4.5% , p = 0.013 ) .
there was no statistically significant difference between the two groups regarding histologic type ( p = 0.14 ) [ table 3 ] .
the median follow - up in the laparoscopic group was 47 months ( range 6 - 124 months ) .
one ( 3% ) patient with large - gist recurrence developed recurrence with peritoneal carcinomatosis 6 months after laparoscopic resection and was subsequently treated by both laparoscopic resection and chemotherapy ; the patient is still alive 7 years after surgery .
actuarial 1-year , 5-year and 10-year os was 100% in both groups ; 1-year , 5-year and 10-year dfs was 95% , 95% and 95% , respectively .
laparoscopic gastric resection has the potential advantage of requiring smaller incisions and less bowel manipulation compared with open surgery .
to our knowledge , this is the first comparison of laparoscopic gastric resection in large and small gastric gists .
our data demonstrate that laparoscopic resection is safe and technically feasible in large gists and does not negatively influence the oncologic course or oncological safety .
the absence of conversion to open surgery in the present series and a conversion rate of 4.7% in other large series confirms the feasibility of the laparoscopic approach for large lesions . despite the fact that the sample size of our study was small
, there was no significant difference in the incidence of overall or major complications between the large- and small - gist groups .
the few complications observed were essentially pulmonary complications mainly related to a high gastric localisation of the gist ( near the oesogastric junction or greater curvature ) .
all complications were promptly treated without endangering the patient 's life at any moment . however , in order to obtain similar results , the resection of such large lesions has to be performed by surgeons experienced in both laparoscopic and upper gastrointestinal tract surgery . at our department , surgeons are well trained in laparoscopic surgery , such as bariatric , hepatobiliary , and oesophageal / cardia cancer procedures .
finally , a prerequisite for performing gastric gist surgery is an advanced knowledge of intracorporeal suturing , which is often necessary in such procedures .
laparoscopic resection of large gastric gists appears to be a reasonable surgical technique for appropriately skilled surgeons performing minimally invasive gastric resections .
large gastric gists and tumours located in difficult locations , such as the oesogastric junction and posterior wall , are technically more difficult to resect , especially via the laparoscopic approach , with an increased risk of tumour spillage . in some difficult situations
for this reason , the guidelines for optimal management of patients with gist suggested that laparoscopic resection should be limited to tumours less than 2 cm .
however , the mean tumour size for laparoscopic gastrectomy ranged 2.7 - 6.0 cm in recent meta - analysis and was 8.4 cm in our large - gist group . given the low rate of both positive margins and local recurrence , it appears that this recommendation is not based on strong evidence . in the present series ,
the oncological safety of lr was confirmed , as shown by the comparable overall survival rates of the two groups .
hence , even though safe oncologic resection is the primary concern when considering lr for large gist , the present study suggests that a laparoscopic approach for gastric gist should not be limited to tumours smaller than 2 cm and could also be considered for tumours larger than 5 cm .
the present study has several important limitations , which should be taken into account when considering the results .
first , although the patients were entered into the database in a prospective fashion , some of the outcome data were gathered through a retrospective review of the medical records and are therefore subject to bias .
indeed , these patients were not randomly selected with regard to the surgical approach , and gastric gists were significantly larger in the open group compared to the laparoscopic group .
therefore , these results need to be confirmed by high - quality randomised controlled trials with larger sample sizes that compare gastric resection for gists smaller and larger than 5 cm .
in conclusion , this study suggests that laparoscopic resection for large gists is safe and technically feasible and does not negatively influence the oncologic course or oncological safety .
nevertheless , prospective randomised trials should be performed before incorporation of these new data into routine surgical care .[/INST]background : laparoscopic resection ( lr ) offers significant advantages compared to open resections for gastric gastrointestinal stromal tumours ( gists ) .
we aimed to evaluate whether lr outcomes jeopardised short and long - term outcomes of patients with large gists.patients and methods : among 50 patients undergoing surgery for gastric gists , 12 underwent lr for large gists ( > 5 cm ) .
their characteristics , perioperative results and survival were retrospectively compared to those of 22 patients who underwent lr for small gist.results:the two groups were similar regarding demographics , rate of wedge resection and mean blood loss .
no patient required transfusion or conversion .
operative time was significantly increased in the large gist group ( 160 min vs 112 min , p = 0.001 ) .
mean tumour size was significantly lower in the small gist group ( 8.4 cm vs 2.4 cm , p = 0.0001 ) .
resection margins were negative .
the mortality rate was nil and the overall morbidity rates was similar in both groups .
median length of hospital stay was significantly increased in the large gist group ( 7 days vs 5 days , p = 0.004 ) .
median follow - up was 47 months and one patient in the
small gist group developed recurrence and died during follow - up 11 years after surgery .
no patient died during follow-up.conclusions:lr for large gists is safe and technically feasible and does not negatively influence the oncologic course .
prospective randomised trials should be performed before using this approach in routine surgical care .</s> |
She was ill-tempered, moody, vain and insecure.
She berated her famous husband in public, went on shopping binges and made enemies. She was called βthe hell catβ by some of the staff at the White House.
First lady Mary Todd Lincoln, who also experienced the deaths of three of her children and the assassination of her husband, was a troubled figure in 19th-century American history. Later in life, she was temporarily institutionalized.
On Tuesday, a California cardiologist advanced what he said was a fresh theory to explain some of her behavior: She suffered from an ailment called βpernicious anemia,β which is related to a vitamin B-12 deficiency.
John G. Sotos, who has also studied the medical history of Abraham Lincoln, detailed his theory in the journal Perspectives in Biology and Medicine, published by the Johns Hopkins University Press.
Mary Todd Lincoln, wife of President Abraham Lincoln, wore this dress for his inauguration in 1861. (Library of Congress/Getty Images)
[Abraham Lincoln β beloved, scrutinized and exhumed]
Mary Lincolnβs litany of ailments and complaints was often thought to be, in part, those of a hypochondriac, Sotos wrote.
βA diagnosis of chronic multisystem pernicious anemia would clarify [her conduct] as First Lady and widow, and illuminate challenges faced by her husband,β he wrote.
The ailment begins with an autoimmune attack on the stomach, which then stops making the chemical that helps absorb Βdietary B-12, Sotos explained in an email.
βThe symptoms of deficiency appear months to years later, after the bodyβs storehouse of B12 is depleted, and over time, symptoms arise from more and more organs,β he said.
Itβs not clear how Mary Lincoln got it.
βIt is likely she was predisposed to it genetically,β Sotos said. βSome people have suspected that the same bacterium that causes ulcers . . . also triggers the autoimmune attack on the stomach, but the question is far from settled.β
Maryβs physical afflictions included fevers, headaches, fatigue, a rapid heart rate, progressive weakness, a sallow complexion and tingling of the skin, he wrote. All are consistent with vitamin B-12 deficiency.
And her irritability, delusions and hallucinations also are in line with such a deficiency, he argued.
βMary Todd Lincoln ranks among the most detested public women in American history,β Βbiographer Jean H. Baker wrote in 1987. βAnd Americans . . . have unshakable opinions about Mary Lincolnβs failings.β
But Sotos contended that βshe was simply a woman with a biochemically injured mind struggling in a complicated, Βrelentlessly demanding environment.β
A native of Lexington, Ky., Mary Todd and the budding politician and lawyer Abraham Lincoln were married in 1842 in Springfield, Ill., according to Bakerβs biography.
She and her family lived briefly in Washington after her husband was elected to his single term in Congress in 1846 and returned after he was elected president in 1860.
By then, one of her children had died in Springfield, and another would die in the White House in 1862.
It was while she was first lady that her questionable conduct emerged publicly.
She spent lavishly on White House furnishings, shelling out huge sums for china, wallpaper, carpets and furniture. She spent the governmentβs $20,000 four-year allowance for White House refurbishing in one year, Baker wrote.
She also spent heavily on clothing and jewelry, seeking to emulate European royalty, even as the United States was in the grip of the Civil War.
After her 11-year-old son, ΒWillie, died on Feb. 20, 1862, Mary took to her bed for three weeks, overcome with grief, ΒBaker wrote.
Later, she dabbled in spiritualism and attended seances in the White House to try to contact her departed son. She believed that he and his deceased brother, ΒEddie, appeared to her in her room at night.
Meanwhile, her jealousies tormented her.
Three weeks before her husband was assassinated, she attended an Army review with him in Virginia. Arriving late in a wagon, she became enraged that the wife of a prominent general was riding on horseback beside the president.
Mary confronted her husband and began to rail at him in front of Army officers, according to Baker.
βHe bore it as Christ might have done, with an expression of pain and sadness that cut one to the heart,β an officer wrote later. βHe pleaded with eyes and tones, till she turned on him like a tigress, and then he walked away.β
She demanded that the general be fired for his wifeβs offense. He wasnβt.
Calamity struck again when Lincoln was assassinated while sitting beside his wife in Fordβs Theatre on April 14, 1865, and she was unhinged anew.
Sotos wrote that although Mary Lincoln left few surviving medical records, he amassed a compendium of hundreds of letters and historical sources related to her health.
After the assassination, she moved to Chicago with her surviving sons, Robert and Tad, ΒSotos wrote. But in 1871, Tad Lincoln died there at the age of 18, further afflicting his mother.
In the years after that, Mary suffered from auditory hallucinations, paranoia and delusions.
In 1875, Robert, worried about her well-being, sought a warrant for her arrest on the grounds of insanity. After a court hearing, she was ruled insane and committed to an asylum outside Chicago, where she was confined for three months.
After her release, she went to France for four years, then moved in with her sister in Springfield. She died there on July 16, 1882, at the age of 63.
Doctors in those times knew almost nothing about pernicious anemia, and until the early 20th century it was frequently fatal, according to Sotos.
Nowadays it can be spotted early through routine blood tests, he said. It is treated with B-12 pills or shots.
Mary Lincolnβs misfortune βwas living before treatment was available,β Sotos wrote, βand before physicians could make a diagnosis that would have prevented 150 years of misunderstanding about her.β ||||| Mary Todd Lincoln had a lot of tragedy in her life. She lost two young children -- and, of course, was sitting next to President Lincoln when he was assassinated.
All of that contributed to years of depression, but now a medical expert believes there was a physical cause for her mental struggles.
History has not been kind to the wife of our 16th president. She was known to be a tempestuous, unpredictable force, and her son eventually had her committed. Sally Field's 2012 portrayal of Mary Todd showed a fierce and sharp-tongued first lady.
"You think I'm ignorant of what you're up to because you haven't discussed this scheme with me as you ought to have done," she said in one scene. "When have I ever been so easily bamboozled?"
But Dr. John Sotos, a physician and medical historian, says the famously fiery first lady was not only misunderstood - but misdiagnosed. Sotos puts forth a new theory about Mary Todd Lincoln -- her erratic behavior was caused by a condition called pernicious anemia.
"Pernicious anemia is an autoimmune disease that starts in the stomach and that impairs the body's ability to absorb food efficiently," Sotos said. "And as a result, the person becomes B12 deficient eventually, and that causes lots of problems in every organ of the body."
It was a fatal illness until treatment was discovered decades after her death. The disease can lead to many of the symptoms exhibited by Mary Todd Lincoln: a sore mouth, pale skin, difficulty walking and psychiatric problems. It can also cause swelling.
"The puffiness is not in a way that would occur with just an accumulation of fat," Sotos said.
Today, the disease can be picked up on a simple blood test and easily treated with B12 supplements.
"She had a sick brain and was doing the best that she could in a very complicated, relentlessly demanding environment," Sotos said. "And I think to have done as well as she did with the kind of handicaps that she had, I think that deserves admiration." ||||| Could pernicious anemia, a disease caused by a vitamin B12 deficiency, have explained the many strange behaviors of Mary Todd Lincoln?
She was not exactly a model first lady. Historians have had a field day describing her violent temper, wild shopping sprees (she owned 300 pairs of kid gloves), depressed moods and all-consuming fears of burglars, storms and poverty. Late in life, at her sonβs urging, she was committed to a mental hospital for several months.
Plenty of theories, none proven, have been floated. She was bipolar. She had syphilis or that well known cause of feminine madness, menstrual trouble. She was spoiled and narcissistic. She never recovered from a road accident in which her head hit a rock. She lost her mind grieving the deaths of three of her four sons and her husbandβs assassination.
The latest addition to the list of possible diagnoses comes from Dr. John G. Sotos, a cardiologist, technology executive at Intel and one of the medical consultants who helped dream up the mystery diseases that afflicted patients on the television show βHouse.β ||||| Abstract
To date, no single diagnosis has unified the psychiatric illness and the numerous poorly defined physical complaints that Mary Lincoln (nΓ©e Todd, 1818β1882) suffered in adulthood. Here, I show that her physical ailments spanned 30 years and included sore mouth, pallor, paresthesias, the Lhermitte symptom, fever, headaches, fatigue, resting tachycardia, edema, episodic weight loss, progressive weakness, ataxia, and visual impairment. Long thought hypochondriacal, these findings, plus their time course and her psychopathology (irritability, delusions, hallucinations, with preserved clarity), are all consistent with vitamin B12 deficiency. Pernicious anemia most probably caused this deficiency: she lacked risk factors for other causes, and her consanguineous parents both derived from a region of Scotland having a high incidence of pernicious anemia. A diagnosis of chronic multisystem pernicious anemia would clarify the conduct of Mary Lincoln as First Lady and widow, and illuminate challenges faced by her husband, President Abraham Lincoln. Her case highlights many forgotten features of the natural history of untreated pernicious anemia and is unique in the medical literature in demonstrating such a course extending over a lifetime. | β She's been described as perhaps the most troubled first lady to set foot in the White House, with fearsome moods, depression, and paranoia. Now a doctor says he may have uncovered the secret to Mary Todd Lincoln's behavior: a vitamin deficiency. Interestingly, this latest theory in Perspectives in Biology and Medicine comes from cardiologist John G. Sotos, who helped come up with all those strange diseases decoded on the TV show House, per the New York Times. In what might as well be a plot from the show, Sotos was researching Abraham Lincolnβwhom he suspects had a genetic syndrome that led to cancerβwhen he found an 1852 letter describing Mrs. Lincoln's sore mouth and set out to discover what ailed her. His theory? She suffered from pernicious anemia, an autoimmune disease "that impairs the body's ability to absorb food efficiently," says Sotos, per CBS News. Sufferers become B12-deficient, and a lack of B12 can cause a wide range of health problemsβincluding a sore tongue. It can wreak havoc on the entire body over time, reports the Washington Post. "You get a long list of symptoms," from headaches to irritability and hallucinations, Sotos says. "Mary had just about all of them." The first ladyβwho spent months in a mental hospital in later lifeβalso had "a wide face, wide jaw, and widely separated blue eyes," as do many with pernicious anemia, he writes. What's more, her ancestors came from an area of Scotland where the disease was once prevalent. One doctor calls Sotos' study "ingenious," though there's no proof he's correct. But Sotos simply hopes historians cut Mrs. Lincoln some slack. "To have done as well as she did with the kind of handicaps that she had, I think that deserves admiration." (Someone stole Abraham Lincoln's hand.) | <s>[INST]She was ill-tempered, moody, vain and insecure.
She berated her famous husband in public, went on shopping binges and made enemies. She was called βthe hell catβ by some of the staff at the White House.
First lady Mary Todd Lincoln, who also experienced the deaths of three of her children and the assassination of her husband, was a troubled figure in 19th-century American history. Later in life, she was temporarily institutionalized.
On Tuesday, a California cardiologist advanced what he said was a fresh theory to explain some of her behavior: She suffered from an ailment called βpernicious anemia,β which is related to a vitamin B-12 deficiency.
John G. Sotos, who has also studied the medical history of Abraham Lincoln, detailed his theory in the journal Perspectives in Biology and Medicine, published by the Johns Hopkins University Press.
Mary Todd Lincoln, wife of President Abraham Lincoln, wore this dress for his inauguration in 1861. (Library of Congress/Getty Images)
[Abraham Lincoln β beloved, scrutinized and exhumed]
Mary Lincolnβs litany of ailments and complaints was often thought to be, in part, those of a hypochondriac, Sotos wrote.
βA diagnosis of chronic multisystem pernicious anemia would clarify [her conduct] as First Lady and widow, and illuminate challenges faced by her husband,β he wrote.
The ailment begins with an autoimmune attack on the stomach, which then stops making the chemical that helps absorb Βdietary B-12, Sotos explained in an email.
βThe symptoms of deficiency appear months to years later, after the bodyβs storehouse of B12 is depleted, and over time, symptoms arise from more and more organs,β he said.
Itβs not clear how Mary Lincoln got it.
βIt is likely she was predisposed to it genetically,β Sotos said. βSome people have suspected that the same bacterium that causes ulcers . . . also triggers the autoimmune attack on the stomach, but the question is far from settled.β
Maryβs physical afflictions included fevers, headaches, fatigue, a rapid heart rate, progressive weakness, a sallow complexion and tingling of the skin, he wrote. All are consistent with vitamin B-12 deficiency.
And her irritability, delusions and hallucinations also are in line with such a deficiency, he argued.
βMary Todd Lincoln ranks among the most detested public women in American history,β Βbiographer Jean H. Baker wrote in 1987. βAnd Americans . . . have unshakable opinions about Mary Lincolnβs failings.β
But Sotos contended that βshe was simply a woman with a biochemically injured mind struggling in a complicated, Βrelentlessly demanding environment.β
A native of Lexington, Ky., Mary Todd and the budding politician and lawyer Abraham Lincoln were married in 1842 in Springfield, Ill., according to Bakerβs biography.
She and her family lived briefly in Washington after her husband was elected to his single term in Congress in 1846 and returned after he was elected president in 1860.
By then, one of her children had died in Springfield, and another would die in the White House in 1862.
It was while she was first lady that her questionable conduct emerged publicly.
She spent lavishly on White House furnishings, shelling out huge sums for china, wallpaper, carpets and furniture. She spent the governmentβs $20,000 four-year allowance for White House refurbishing in one year, Baker wrote.
She also spent heavily on clothing and jewelry, seeking to emulate European royalty, even as the United States was in the grip of the Civil War.
After her 11-year-old son, ΒWillie, died on Feb. 20, 1862, Mary took to her bed for three weeks, overcome with grief, ΒBaker wrote.
Later, she dabbled in spiritualism and attended seances in the White House to try to contact her departed son. She believed that he and his deceased brother, ΒEddie, appeared to her in her room at night.
Meanwhile, her jealousies tormented her.
Three weeks before her husband was assassinated, she attended an Army review with him in Virginia. Arriving late in a wagon, she became enraged that the wife of a prominent general was riding on horseback beside the president.
Mary confronted her husband and began to rail at him in front of Army officers, according to Baker.
βHe bore it as Christ might have done, with an expression of pain and sadness that cut one to the heart,β an officer wrote later. βHe pleaded with eyes and tones, till she turned on him like a tigress, and then he walked away.β
She demanded that the general be fired for his wifeβs offense. He wasnβt.
Calamity struck again when Lincoln was assassinated while sitting beside his wife in Fordβs Theatre on April 14, 1865, and she was unhinged anew.
Sotos wrote that although Mary Lincoln left few surviving medical records, he amassed a compendium of hundreds of letters and historical sources related to her health.
After the assassination, she moved to Chicago with her surviving sons, Robert and Tad, ΒSotos wrote. But in 1871, Tad Lincoln died there at the age of 18, further afflicting his mother.
In the years after that, Mary suffered from auditory hallucinations, paranoia and delusions.
In 1875, Robert, worried about her well-being, sought a warrant for her arrest on the grounds of insanity. After a court hearing, she was ruled insane and committed to an asylum outside Chicago, where she was confined for three months.
After her release, she went to France for four years, then moved in with her sister in Springfield. She died there on July 16, 1882, at the age of 63.
Doctors in those times knew almost nothing about pernicious anemia, and until the early 20th century it was frequently fatal, according to Sotos.
Nowadays it can be spotted early through routine blood tests, he said. It is treated with B-12 pills or shots.
Mary Lincolnβs misfortune βwas living before treatment was available,β Sotos wrote, βand before physicians could make a diagnosis that would have prevented 150 years of misunderstanding about her.β ||||| Mary Todd Lincoln had a lot of tragedy in her life. She lost two young children -- and, of course, was sitting next to President Lincoln when he was assassinated.
All of that contributed to years of depression, but now a medical expert believes there was a physical cause for her mental struggles.
History has not been kind to the wife of our 16th president. She was known to be a tempestuous, unpredictable force, and her son eventually had her committed. Sally Field's 2012 portrayal of Mary Todd showed a fierce and sharp-tongued first lady.
"You think I'm ignorant of what you're up to because you haven't discussed this scheme with me as you ought to have done," she said in one scene. "When have I ever been so easily bamboozled?"
But Dr. John Sotos, a physician and medical historian, says the famously fiery first lady was not only misunderstood - but misdiagnosed. Sotos puts forth a new theory about Mary Todd Lincoln -- her erratic behavior was caused by a condition called pernicious anemia.
"Pernicious anemia is an autoimmune disease that starts in the stomach and that impairs the body's ability to absorb food efficiently," Sotos said. "And as a result, the person becomes B12 deficient eventually, and that causes lots of problems in every organ of the body."
It was a fatal illness until treatment was discovered decades after her death. The disease can lead to many of the symptoms exhibited by Mary Todd Lincoln: a sore mouth, pale skin, difficulty walking and psychiatric problems. It can also cause swelling.
"The puffiness is not in a way that would occur with just an accumulation of fat," Sotos said.
Today, the disease can be picked up on a simple blood test and easily treated with B12 supplements.
"She had a sick brain and was doing the best that she could in a very complicated, relentlessly demanding environment," Sotos said. "And I think to have done as well as she did with the kind of handicaps that she had, I think that deserves admiration." ||||| Could pernicious anemia, a disease caused by a vitamin B12 deficiency, have explained the many strange behaviors of Mary Todd Lincoln?
She was not exactly a model first lady. Historians have had a field day describing her violent temper, wild shopping sprees (she owned 300 pairs of kid gloves), depressed moods and all-consuming fears of burglars, storms and poverty. Late in life, at her sonβs urging, she was committed to a mental hospital for several months.
Plenty of theories, none proven, have been floated. She was bipolar. She had syphilis or that well known cause of feminine madness, menstrual trouble. She was spoiled and narcissistic. She never recovered from a road accident in which her head hit a rock. She lost her mind grieving the deaths of three of her four sons and her husbandβs assassination.
The latest addition to the list of possible diagnoses comes from Dr. John G. Sotos, a cardiologist, technology executive at Intel and one of the medical consultants who helped dream up the mystery diseases that afflicted patients on the television show βHouse.β ||||| Abstract
To date, no single diagnosis has unified the psychiatric illness and the numerous poorly defined physical complaints that Mary Lincoln (nΓ©e Todd, 1818β1882) suffered in adulthood. Here, I show that her physical ailments spanned 30 years and included sore mouth, pallor, paresthesias, the Lhermitte symptom, fever, headaches, fatigue, resting tachycardia, edema, episodic weight loss, progressive weakness, ataxia, and visual impairment. Long thought hypochondriacal, these findings, plus their time course and her psychopathology (irritability, delusions, hallucinations, with preserved clarity), are all consistent with vitamin B12 deficiency. Pernicious anemia most probably caused this deficiency: she lacked risk factors for other causes, and her consanguineous parents both derived from a region of Scotland having a high incidence of pernicious anemia. A diagnosis of chronic multisystem pernicious anemia would clarify the conduct of Mary Lincoln as First Lady and widow, and illuminate challenges faced by her husband, President Abraham Lincoln. Her case highlights many forgotten features of the natural history of untreated pernicious anemia and is unique in the medical literature in demonstrating such a course extending over a lifetime.[/INST]β She's been described as perhaps the most troubled first lady to set foot in the White House, with fearsome moods, depression, and paranoia. Now a doctor says he may have uncovered the secret to Mary Todd Lincoln's behavior: a vitamin deficiency. Interestingly, this latest theory in Perspectives in Biology and Medicine comes from cardiologist John G. Sotos, who helped come up with all those strange diseases decoded on the TV show House, per the New York Times. In what might as well be a plot from the show, Sotos was researching Abraham Lincolnβwhom he suspects had a genetic syndrome that led to cancerβwhen he found an 1852 letter describing Mrs. Lincoln's sore mouth and set out to discover what ailed her. His theory? She suffered from pernicious anemia, an autoimmune disease "that impairs the body's ability to absorb food efficiently," says Sotos, per CBS News. Sufferers become B12-deficient, and a lack of B12 can cause a wide range of health problemsβincluding a sore tongue. It can wreak havoc on the entire body over time, reports the Washington Post. "You get a long list of symptoms," from headaches to irritability and hallucinations, Sotos says. "Mary had just about all of them." The first ladyβwho spent months in a mental hospital in later lifeβalso had "a wide face, wide jaw, and widely separated blue eyes," as do many with pernicious anemia, he writes. What's more, her ancestors came from an area of Scotland where the disease was once prevalent. One doctor calls Sotos' study "ingenious," though there's no proof he's correct. But Sotos simply hopes historians cut Mrs. Lincoln some slack. "To have done as well as she did with the kind of handicaps that she had, I think that deserves admiration." (Someone stole Abraham Lincoln's hand.)</s> |
consider the degree @xmath4 universal picard stack over @xmath6-pointed smooth curves of genus @xmath7 , @xmath8 , parametrizing families of @xmath6-pointed smooth curves of genus @xmath7 endowed with line bundles of relative degree @xmath4 over these curves .
@xmath8 is , of course , not complete . in the present paper we search for a compactification of @xmath8 over @xmath1 , the moduli stack of stable curves of genus @xmath7 . by this we mean an algebraic stack with a proper ( or at least universally closed ) map onto @xmath1 , containing @xmath8 as a dense open substack
the problem of compactifying the ( generalized ) jacobian of curves or of families of curves has been widely studied in the last decades , starting from the work of igusa @xcite and of mayer and mumford @xcite .
the first solution to this problem , in the case on irreducible curves , was due to dsouza in @xcite and since then , several other solutions where found , the more general one being probably simpson s construction of moduli spaces of coherent sheaves on projective schemes in @xcite ( see @xcite for an overview and comparison results on these constructions ) . on the other hand , the construction of the moduli space of stable curves with marked points was done by knudsen in @xcite , following ideas of mumford , with the scope of proving the projectivity of the moduli space of stable curves . since then , @xmath1 itself became the subject of great interest , because of its rich geometry , and because of several applications . in particular
, @xmath1 has a central role in gromov - witten theory and enumerative geometry .
in fact , in part motivated by witten s conjecture ( @xcite ) , the study of the cohomology ring of @xmath9 attracted the attention of several mathematicians in the last decades and led to very important results .
we recall , for instance , kontsevich s first proof of the witten conjecture in ( @xcite ) ; the interaction between geometry and physics leading to the development of quantum cohomoly and gromov - witten theory ( see e.g. @xcite ) ; the algebro - geometric inductive calculations on the cohomology ring of @xmath1 due to arbarello and cornalba in @xcite ; faber s conjectures on the structure of the tautological ring of @xmath10 and its pointed versions ( @xcite , @xcite ) , the elsv formulas relating intersection formulas in @xmath1 with hurwitz numbers ( @xcite , @xcite ) and the recent proof by faber , shadrin and zvonkine in @xcite of the generalized witten conjecture ( @xcite ) .
so , it is natural to search for a compactification of @xmath8 over @xmath1 and to study its applications .
nevertheless , at least to our knowledge , there was no construction of compactified picard varieties for curves with marked points until now .
the aim of the present paper is to construct an algebraic ( artin ) stack @xmath0 with a geometrically meaningful modular description , giving a solution for the above problem for @xmath2 .
let @xmath11 and consider pic@xmath12 , the
universal picard variety of degree @xmath4over @xmath13 parametrizing isomorphism classes of line bundles of degree @xmath4 over automorphism - free nonsingular curves .
the problem of compactifying @xmath14 over @xmath15 was addressed by caporaso in @xcite and later by pandharipande in @xcite ( the second author s construction holds also for bundles of higher rank ) .
both compactifications were done by means of git - quotients yielding projective varieties endowed with a proper map onto @xmath15 , extending the natural map @xmath16 .
even if the boundary objects used by the two authors have different modular interpretations , it turns out that the resulting varieties coincide .
we here focus on caporaso s original compactification , which works for @xmath2 ; denote it by @xmath17 and by @xmath18 its natural map onto @xmath15 .
given @xmath19\in { \overline}m_g$ ] , @xmath20 is a projective connected scheme with a finite number of components ( that can not exceed a certain numerical invariant of the curve ) and , if @xmath21 has trivial automorphism group , @xmath20 is reduced and its smooth locus is isomorphic to the disjoint union of a finite number of copies of the jacobian of @xmath21 , @xmath22 . later , on @xcite , the same author gives a stack - theoretical description of the above quotient for degrees @xmath4 such that @xmath23 , getting a modular compactification of @xmath24 over @xmath25 .
we considered the same problem in @xcite with no assumption on @xmath4 , getting an algebraic ( artin ) stack @xmath26 with a universally closed morphism @xmath27 onto @xmath25 parametrizing families of _ quasistable _ curves endowed with _ balanced _ line bundles of relative degree @xmath4 .
our stack @xmath0 coincides with @xmath26 for @xmath11 .
let @xmath28 , @xmath29 and @xmath2 .
we define @xmath0 to be the stack whose sections over a scheme @xmath30 are given by families of genus @xmath7 @xmath6-pointed quasistable curves over @xmath30 endowed with a relative degree @xmath4 balanced line bundle ( see definitions [ quasistabledef ] and [ balanced ] below ) .
morphisms between two such sections are given by cartesian diagrams of the families compatible with the sections plus an isomorphism between the line bundles ( see definition [ compstack ] ) .
the principal result of this paper consists in proving that @xmath0 is a smooth and irreducible algebraic ( artin ) stack of dimension @xmath3 , endowed with a universally closed morphism onto @xmath1 .
our interest in constructing such a space is also due to goulden , jackson and vakil s
generalized elsv formulaconjecturing a relation between the intersection theory of a @xmath31-dimensional space and certain double hurwitz numbers ( see @xcite and @xcite ) . according to these authors
, this space should be a suitable compactification of @xmath8 over @xmath1 supporting particular families of classes satisfying certain properties .
unfortunately , we do not know yet if our space supports such classes , except for what they call @xmath32-classes , which turn out to be the pullback of the @xmath32-classes in @xmath1 .
it is certainly interesting to consider this as a future research problem .
our construction of @xmath0 goes in the following way .
for @xmath11 , we define @xmath33 to be equal to @xmath26 .
then , for @xmath34 , along the lines of knudsen s construction of @xmath25 in @xcite , we show that there is an isomorphism between @xmath0 and the universal family over @xmath35 .
this isomorphism is built explicitly and it generalizes knudsen s notion of _ contraction _ and _ stabilization _ of @xmath6-pointed stable curves , in this more general context of quasistable curves endowed with balanced line bundles .
the stacks @xmath0 can never be deligne - mumford since there is an action of @xmath36 given by scalar product on the line bundles , leaving the curves and the sections fixed .
even the rigidification in the sense of @xcite of @xmath0 by this action of @xmath36 , denoted by @xmath37 is not deligne - mumford in general .
in fact , already for @xmath11 , it was proved by caporaso in @xcite that @xmath38 is deligne - mumford if and only if @xmath23 .
this holds in general for any @xmath29 . in order to make the contraction process work
, we also need to prove some technical properties for balanced line bundles over quasistable pointed curves .
in particular , we get general results concerning global and normal generation for line bundles on ( reducible ) nodal curves depending only on their multidegree ( see section [ technical ] ) . in section [ forgetful ]
we show that @xmath0 is endowed with a ( forgetful ) morphism @xmath39 onto @xmath9 .
we also study the fibres of @xmath39 .
finally , in section [ properties ] , we study further properties of @xmath0 . for example , we show that if @xmath4 and @xmath40 are such that @xmath41 divides @xmath42 , then @xmath0 is isomorphic to @xmath43 .
we also study the map form @xmath44 to @xmath0 and its sections and we show that these yield cartier divisors on @xmath44 with interesting intersection properties .
we would also like to observe that another possible approach to the construction of @xmath0 would be to use baldwin and swinarski s git construction of the moduli space of stable maps and , in particular , of @xmath45 , in @xcite , and then procede as caporaso in @xcite .
we will always consider schemes and algebraic stacks locally of finite type over an algebraically closed base field @xmath46 .
a curve @xmath21 will always be a connected projective curve over @xmath46 having at most nodes as singularities . given a curve @xmath21 , we will denote by @xmath47 its canonical or dualizing sheaf .
for each proper subcurve @xmath48 of @xmath21 ( which we always assume to be complete and connected ) , denote by @xmath49 and by @xmath50 its arithmetic genus . recall that , since @xmath48 is connected , the adjunction formula gives @xmath51 for @xmath52 its _ multidegree _ is @xmath53 and its ( total ) degree is @xmath54 , where @xmath55 are the irreducible components of @xmath21 .
given @xmath56 , we set @xmath57 and @xmath58 .
we have that @xmath59 , where @xmath60 .
let @xmath8 be the universal picard stack over the moduli space of smooth curves with @xmath6 marked points .
sections of @xmath8 over a scheme @xmath30 consist of flat and proper families @xmath61 of smooth curves of genus @xmath7 , with @xmath6 distinct sections @xmath62 and a line bundle @xmath63 of relative degree @xmath4 on @xmath64 .
morphisms between two such objects are given by cartesian diagrams @xmath65^{\pi } \ar[r]^{\beta_2 } & { c ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_{i ' } } } \ ] ] such that @xmath66 , @xmath67 , together with an isomorphism @xmath68 .
in the present paper we search for a compactification of @xmath8 over @xmath9 . by this
we mean to construct an algebraic stack @xmath0 with a map @xmath39 onto @xmath1 with the following properties . 1 . @xmath0 and @xmath39 fit in the following diagram ; @xmath69 \ar @{^{(}->}[r ] & { { \overline}{\mathcal p}_{d , g , n } } \ar[d]^{\psi_{d , g , n } } \\
{ \mathcal m_{g , n } } \ar @{^{(}->}[r ] & { { \overline}{\mathcal m}_{g , n } } } \ ] ] 2 .
@xmath39 is proper ( or , ate least , universally closed ) ; 3 .
@xmath8 has a geometrically meaningful modular description .
note that in order to complete @xmath8 over @xmath1 it is not enough to consider the stack of line bundles over families of @xmath6-pointed stable curves , since this is not complete as well .
so , it is necessary to enlarge the category either admitting more general sheaves than line bundles or a bigger class of curves .
our construction of @xmath0 will go as follows .
we will start by noticing that , for @xmath11 , this problem is already solved .
then , for @xmath34 , we will construct @xmath0 by induction on the number of marked points @xmath6 , following the lines of knudsen s construction of @xmath9 .
the problem of constructing compactifications of the picard varieties of singular curves has been widely studied and , in fact , there are several known compactifications .
we will focus on the one built by caporaso in @xcite , which we will now briefly describe .
consider the hilbert scheme @xmath70 of genus @xmath7 curves embedded in @xmath71 as nondegenerate curves of degree @xmath4 , where @xmath72 .
there is a natural action of @xmath73 in @xmath70 corresponding to the choice of the coordinates used to embed the curves .
for @xmath74 , define @xmath75 as the git - quotient of @xmath76 , the locus of git - semistable points for this action . by results of @xcite and @xcite , we know that points in @xmath76 correspond exactly to _
quasistable _ curves embedded by _ balanced _ line bundles ( of degree @xmath4 ) , where quasistable curves are semistable curves such that two exceptional components never meet and balanced is a combinatorial condition on the multidegree of the line bundle on the curve ( see definition [ balanced ] and ( [ giesekerbasic ] ) below ) . by construction , @xmath17 has a proper morphism @xmath77 such that @xmath78 is isomorphic to the
universal picard variety of degree @xmath4 , @xmath14 , which parametrizes isomorphism classes of line bundles of degree @xmath4 over automorphism - free nonsingular curves .
later , in @xcite , caporaso shows that , if @xmath74 and @xmath23 , the quotient stack associated to the git - quotient above , @xmath79 $ ] , is a smooth and irreducible deligne - mumford stack endowed with a proper and strongly representable map onto @xmath80 .
moreover , @xmath79 $ ] has the following modular description .
consider the stack @xmath26 ( over @xmath81 ) whose sections over a @xmath82scheme @xmath30 consist on families @xmath83 of genus @xmath7 quasistable curves over @xmath30 endowed with a balanced line bundle of relative degree @xmath4 over @xmath21 and whose morphisms consist on cartesian diagrams of the curves plus an isomorphism between the line bundles ( as in @xmath8 above , ignoring the sections ) .
there is a natural action of @xmath36 on @xmath84 given by fiberwise scalar multiplication on the line bundles . then @xmath79 $ ]
is the rigidification ( in the sense of @xcite ) of @xmath84 by the action of @xmath36 .
this result uses mainly the fact that the above git - quotient is geometric if and only if @xmath85 . in @xcite
we showed that , for @xmath74 , even if @xmath86 , @xmath84 is isomorphic to @xmath87 $ ] , where @xmath88 acts by projection on @xmath73 .
this implies that @xmath84 is a smooth and irreducible artin stack endowed with a universally closed map onto @xmath25 . since for @xmath4 and @xmath40 such that @xmath89 for some @xmath90
, @xmath26 is isomorphic to @xmath91 , we get that the same statement holds in general for any @xmath28 .
in the present section we will generalize the notions of quasistable curve and of balanced line bundle for curves with marked points .
our definitions will be done in such a way that , for @xmath11 , these coincide with the old notions introduced by gieseker and caporaso ( see definition 1.1 in @xcite ) , and that , for @xmath34 , @xmath6-pointed quasistable curve are the ones we get by applying the stabilization morphism defined by knudsen in @xcite ( see [ proof ] below ) to @xmath92-pointed quasistable curves endowed with an extra section without stability conditions . moreover , balanced line bundles on @xmath6-pointed quasistable curves correspond to balanced line bundles on the quasistable curves obtained by forgetting the points and by contracting the rational components that get _ quasidestabilized _ without the points ( see lemma [ balcorresp ] ) .
we start by recalling the definitions of ( semi)stable pointed curve and by introducing some notation .
[ pointedcurves ] an * @xmath6-pointed curve * is a connected , projective and reduced nodal curve @xmath21 together with @xmath6 distinct marked points @xmath93 such that @xmath21 is smooth at @xmath94 , @xmath95 .
let @xmath7 and @xmath6 be such that @xmath96 .
an * @xmath6-pointed stable curve * ( resp .
* semistable * ) is an @xmath6-pointed curve such that the number of points where a nonsingular rational component @xmath97 of @xmath21 meets the rest of @xmath21 plus the number of points @xmath94 on @xmath97 is at least @xmath98 ( resp .
@xmath99 ) .
a * family of @xmath6-pointed stable * ( resp . * semistable * ) curves is a flat and proper morphism @xmath83 together with @xmath6 distinct sections @xmath100 such that the geometric fibers @xmath101 together with @xmath102 , @xmath95 , are @xmath6-pointed stable ( resp .
semistable ) curves . note that @xmath6-pointed ( semi)stable curves admit chains of smooth rational curves meeting the rest of the curve in one or two points . by * rational tail * we mean a proper subcurve @xmath103 of @xmath21 with @xmath104 and @xmath105
. instead , proper subcurves @xmath106 of @xmath21 with @xmath107 and @xmath108 will be denoted by * rational bridges*. if @xmath21 is a strictly @xmath6-pointed semistable curve , a nonsingular rational component @xmath97 such that the number of points where @xmath97 meets the rest of @xmath21 plus the number of marked points @xmath94 on @xmath97 is exactly @xmath99 is called a * destabilizing * component .
an * exceptional component * is a destabilizing component without marked points .
[ quasistabledef ] an @xmath6-pointed * quasistable * curve is an @xmath6-pointed semistable curve @xmath21 such that 1 .
all destabilizing components are exceptional ; 2 .
exceptional components can not be contained in rational tails ; 3 .
each rational bridge contains at most one exceptional component .
a * family of @xmath6-pointed quasistable curves * is a proper and flat morphism with @xmath6 distinct sections whose geometric fibers are @xmath6-pointed quasistable curves .
see figure [ notquasistable ] for examples of pointed semistable curves which are not quasistable .
to each proper subcurve @xmath48 of @xmath21 , denote by @xmath109 the number of rational tails meeting @xmath48 .
[ balanced ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath110 and @xmath63 a line bundle on @xmath21 of degree @xmath4 .
we say that @xmath63 ( or its multidegree ) is * balanced * if the following conditions hold : * deg@xmath111 for every exceptional component @xmath97 of @xmath21 ; * the degree of @xmath63 on rational bridges can be either @xmath112 or @xmath113 ; * if @xmath103 is a rational tail of @xmath21 , then deg@xmath114 ; * for every connected proper subcurve @xmath48 of @xmath21 , if @xmath48 is not contained in any rational tail and in any rational bridge of @xmath21 , the following inequality holds @xmath115 denotes the number of rational bridges where the degree of @xmath63 is zero meeting @xmath48 in two points . note that if @xmath11 , @xmath109 and @xmath116 are equal to @xmath112 for all proper subcurves @xmath48 of @xmath21 , and inequality ( [ basic ] ) reduces to the
basic inequalityintroduced by gieseker in @xcite .
in fact , for @xmath11 , definition [ balanced ] coincides with the definition of balanced multidegree for quasistable curves introduced by caporaso in @xcite ( see also @xcite , def .
1.1 ) . using the notation of [ balanced ] , denote by @xmath117 and by @xmath118 then , inequality ( [ basic ] ) can be rewritten in the following way @xmath119 [ combdesc ] let @xmath21 be an @xmath6-pointed quasistable curve and suppose @xmath21 admits a balanced line bundle @xmath63 on @xmath21 of degree @xmath4 , for some @xmath120 .
then , if @xmath48 is a proper subcurve of @xmath21 that is contained in a rational tail , then @xmath121 and if @xmath48 is contained in a rational bridge , then @xmath122 is either equal to @xmath123 or @xmath124 .
in particular , the multidegree of @xmath63 on rational tails is unique and does not depend on @xmath4 .
let us begin by showing that the multidegree of @xmath63 on rational tails is uniquely determined .
so , suppose @xmath103 is a rational tail of @xmath21 . if @xmath103 is irreducible , then the multidegree of @xmath63 on @xmath103 is just the degree of @xmath63 on @xmath103 , which is necessarily @xmath125 .
now , suppose @xmath103 is reducible .
then there is exactly one irreducible component @xmath97 of @xmath103 meeting the rest of the curve ( in exactly one point ) .
we will call @xmath97 the foot of the rational tail .
@xmath97 is a smooth rational curve meeting the rest of @xmath103 in @xmath126 points : denote by @xmath127 the irreducible components of @xmath103 meeting @xmath97 .
then , each @xmath128 , @xmath129 is the foot of a rational tail contained in @xmath103 . in fact , each one of these , if not irreducible , is attached to another rational chain that can not intersect the rest of the curve since in that case @xmath103 would contain cycles ( which would force @xmath130 to be bigger than @xmath112 ) .
so , @xmath103 is the union of @xmath97 with @xmath131 rational tails meeting @xmath97 , and @xmath132 which implies that @xmath133 note that we do nt have to check if inequality ( [ basic ] ) is satisfied since it does not apply for subcurves of @xmath21 contained in rational tails .
now , iterating the same procedure , it is clear that the degree of each irreducible component of @xmath103 will be determined since @xmath103 is the union of @xmath97 with other @xmath126 rational tails with foots @xmath127 . now , consider a rational bridge @xmath106 .
then , @xmath106 meets the rest of the curve in two points , @xmath134 and @xmath135 , and these are linked by a chain of ( rational ) irreducible components of @xmath106 , @xmath136 , each one meeting the previous and the next one , for @xmath137 .
moreover , each @xmath128 can have rational tails attached .
denote by @xmath138 respectively the proper subcurves of @xmath106 consisting of @xmath128 and the rational tails attached to it , for @xmath139 .
so , @xmath140 is the union of @xmath141 rational bridges of length @xmath113 . by definition
, the degree of @xmath63 in @xmath106 can be either @xmath112 or @xmath113 , and the same holds for each @xmath142 , @xmath139 .
if @xmath143 , then , in order to the multidegree of @xmath63 on @xmath142 sum up to @xmath112 , @xmath144 must be equal to the number of rational tails attached to it : @xmath145 .
if , instead , the degree of @xmath63 on @xmath142 is equal to one , then deg@xmath146 must be equal to @xmath147 .
note that inequality ( [ basic ] ) gives that @xmath148 for @xmath149 , so either @xmath150 or @xmath151 are allowed .
the multidegree of @xmath63 on the rest of @xmath142 is fixed since @xmath152 consists of rational tails ( that , of course , can not intersect each other ) .
now , if @xmath106 contains one exceptional component @xmath97 among the @xmath128 s , say @xmath153 , the degree of @xmath106 must be necessarily @xmath113 ( note that on each rational tail we can have at most one exceptional component by definition of pointed quasistable curve ) .
in this case , we must have that @xmath154 , which implies that @xmath153 has no rational tails attached , and the degree of @xmath63 on it must be @xmath113 .
moreover , the degree of @xmath63 on the other rational subcurves @xmath142 , for @xmath155 , must be @xmath112 . if , instead , @xmath106 does not contain any exceptional component , then we can choose the degree of @xmath63 in @xmath106 to be either @xmath113 or @xmath112 .
if we choose it to be @xmath112 , then the degree of @xmath63 on each @xmath142 must be @xmath112 , for @xmath139 . if we choose it to be one , we can freely choose one of the @xmath142 s where the degree of @xmath63 is @xmath113 and in all the others the degree of @xmath63 must be @xmath112 .
[ balcorresp ]
let @xmath21 be an @xmath6-pointed quasistable curve with assigned multidegree on rational bridges .
let @xmath156 be the quasistable curve obtained by contracting all rational tails and rational bridges with assigned degree zero and by forgetting the points . then , for each degree @xmath4 , the set of balanced multidegrees on @xmath156 summing up to @xmath4 and the set of balanced multidegrees on @xmath21 summing up to @xmath4 with the given assigned multidegree on rational bridges are in bijective correspondence .
let @xmath157 be a balanced line bundle on @xmath156 with degree @xmath4 .
this means that , given a proper subcurve @xmath158 of @xmath156 , gieseker s
basic inequalityholds for @xmath158 , that is , @xmath159 and that the degree of @xmath157 on exceptional components is equal to @xmath113 .
let @xmath160 be an irreducible component of @xmath161 such that @xmath160 is not contained in any rational tail and in any rational bridge .
define the multidegree @xmath162 on @xmath21 by declaring that @xmath163 where @xmath164 is the image of @xmath160 on @xmath156 .
then we easily see that this defines a balanced multidegree on @xmath21 ( note that the multidegree of @xmath63 on rational bridges is fixed by hypothesis ) .
in fact , since @xmath165 and @xmath166 , we have that @xmath167 @xmath168 @xmath169 @xmath170 @xmath171 and also that @xmath172 @xmath173 so inequality ( [ basic ] ) holds for @xmath160 if and only if gieseker s basic inequality holds for @xmath164 .
it is easy to see that this is true more generally for any proper subcurve @xmath48 of @xmath21 not contained in any rational tail and in any rational bridge .
[ compstack ] for any integer @xmath4 and @xmath2 , denote by @xmath0 the following category fibered in groupoids over the category of schemes over @xmath46 .
objects over a @xmath46-scheme @xmath30 are families @xmath174 of @xmath6-pointed quasistable curves over @xmath30 and a balanced line bundle @xmath63 on @xmath21 of relative degree @xmath4 .
morphisms between two such objects are given by cartesian diagrams @xmath175^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_{i ' } } } \ ] ] such that @xmath66 , @xmath67 , together with an isomorphism @xmath68 .
note that @xmath0 contains @xmath8 for all @xmath29 . in what follows we will try to prove the following statement .
[ aim ] @xmath0 is a smooth and irreducible algebraic ( artin ) stack of dimension @xmath3 endowed with a universally closed map onto @xmath1 .
recall that , for @xmath11 , @xmath0 coincides with the stack @xmath26 defined in @xcite , section 3 ( see [ n=0 ] above ) , so theorem [ aim ] holds in this case .
now , following knudsen s construction of @xmath9 ( see @xcite ) , we will show that theorem [ aim ] holds for all @xmath29 using the following induction argument .
we will prove that , for @xmath34 , @xmath44 is isomorphic to the universal family over @xmath0 . by universal family over @xmath0
we mean an algebraic stack @xmath176 with a map onto @xmath0 admitting @xmath6-sections @xmath177 and endowed with an ( universal ) invertible sheaf @xmath178 such that , given a family @xmath179 of @xmath6-pointed quasistable curves and a balanced line bundle @xmath63 over @xmath64 of relative degree @xmath4 , the following diagram , commuting both in the upward and downward directions , @xmath180^{\pi_2 } \ar[d]^{f } & { \mathcal{z}_{d , g , n } } \ar[d]\\ { s } \ar[r]_{\mu_f } \ar @{- > } @/^/[u]^{s_i } & { { \overline}{\mathcal p}_{d , g , n } } \ar @{- > } @/_/[u]_{\sigma_{d , g , n}^i } } \ ] ] is cartesian and induces an isomorphism between @xmath181 and @xmath63 .
let @xmath176 be the category whose sections over a scheme @xmath182 are families of @xmath6-pointed quasistable curves @xmath183 endowed with a balanced line bundle @xmath184 of relative degree @xmath4 and with an extra section @xmath185 .
morphisms in @xmath176 are like morphisms in @xmath0 compatible with the extra section .
@xmath176 is an algebraic stack endowed with a forgetful morphism onto @xmath0 admitting @xmath6 sections given by the diagonals @xmath186 .
it is easy to see that , given a family of @xmath6-pointed quasistable curves @xmath179 and a balanced line bundle @xmath63 over @xmath64 of relative degree @xmath4 , diagram ( [ universal ] ) is cartesian , where @xmath187 is defined by associating to the identity morphism @xmath188 the fiber product of @xmath189 with itself @xmath190^{p_2 } \ar[d]^{p_1 } & { c } \ar[d]_{f}\\ { c } \ar[r]_{f } \ar @{- > } @/^/[u]^{f^*s_i } & { s } \ar @{- > } @/_/[u]_{s_i } } \ ] ] endowed with an extra section @xmath191 given by the diagonal and with the relative degree @xmath4 line bundle @xmath192 . given another object @xmath193 of @xmath64 , @xmath194 is defined to be the fiber product of @xmath195 and @xmath134 defined in ( [ identity ] ) , naturally endowed with the @xmath196 pullback sections and with the pullback of @xmath192 .
the universal sheaf over @xmath176 , @xmath178 , is defined by associating to each section @xmath197 of @xmath176 over @xmath182 , the line bundle @xmath198 over @xmath182 .
it is easy to see that this defines an invertible sheaf on @xmath176 .
now we easily check that @xmath178 is the universal sheaf over @xmath176 .
indeed , given an object @xmath193 on @xmath64 , @xmath199 , so it is isomorphic to the sheaf defined by @xmath63 on @xmath64 , considered as a stack .
we have just proved the following .
the algebraic stack @xmath176 defined above endowed with the invertible sheaf @xmath178 is the universal family over @xmath0 for the moduli problem of @xmath6-pointed quasistable curves with a balanced degree @xmath4 line bundle . now , suppose we can show that , for all @xmath29 , there is forgetful morphism @xmath39 from @xmath0 onto @xmath1 such that the image under @xmath39 of an @xmath6-pointed quasistable curve @xmath21 over @xmath30 endowed with a balanced degree @xmath4 line bundle is the stable model of @xmath21 over @xmath30 forgeting the line bundle .
these morphisms would yield commutative diagrams as follows , for all @xmath34 .
@xmath200^{\psi_{d , g , n } } \ar[dl]_{\phi_{d , g , n } } & \\ { { \overline}{\mathcal p}_{d , g , n-1 } } \ar[dr]_{\psi_{d , g , n-1 } } & & { { \overline}{\mathcal m}_{g , n } } \ar[dl]^{\pi_{g , n}}\\ & { { \overline}{\mathcal m}_{g , n-1 } } & } \ ] ] since @xmath201 and @xmath202 are the morphisms from the universal families over @xmath35 and @xmath203 , respectively , it follows that @xmath39 is universally closed ( or proper ) if and only if @xmath204 is . since
, by @xcite , @xmath205 is universally closed , we have that @xmath39 is universally closed for all @xmath29 .
so , our proof of theorem [ aim ] will follow if we can prove the following statement , which is the aim of the present paper .
[ main ] for all @xmath34 , @xmath44 is isomorphic to the algebraic stack @xmath176 .
in this section we prove some technical properties of line bundles over ( reducible ) nodal curves that will be used later in the proof of theorem [ main ] .
[ basicpropgen ] let @xmath21 be a nodal curve of genus @xmath7 and @xmath206 .
if @xmath207 for every connected subcurve @xmath208 , then @xmath209 . moreover , if strict inequality holds above for all @xmath208 , @xmath63 has no base points . to prove lemma [ basicpropgen ]
we will use the following lemma , which is lemma 2.2.2 in @xcite . [ 222 ] let @xmath21 be a nodal curve of genus @xmath7 and @xmath206 . if , for every connected subcurve @xmath48 of @xmath21 , @xmath210 , then @xmath211 .
the first assertion follows immediatly by serre duality and by lemma [ 222 ] .
now , assume that , for every @xmath208 , @xmath212 . we must show that @xmath63 has no base points .
consider a closed @xmath46-rational point @xmath213 in @xmath21 .
suppose that @xmath213 is a nonsingular point of @xmath21 .
we must show that @xmath214 by our assumption on @xmath63 , we can apply again lemma [ 222 ] to @xmath215 to get that @xmath216 . now , suppose @xmath213 is a nodal point of @xmath21 .
we must show that @xmath217 by contradiction , suppose these are equal .
then , if @xmath218 is the partial normalization of @xmath21 at @xmath213 , we get that @xmath219 where @xmath220 and @xmath221 are the preimages of @xmath213 by @xmath222 .
suppose that @xmath213 is not a disconnecting node for @xmath21 .
then , it is easy to see that we can apply lemma [ 222 ] to @xmath223 .
in fact , since @xmath213 is not a disconnecting node for @xmath21 , if @xmath224 contains @xmath220 and @xmath221 , then @xmath225 because @xmath226 , where @xmath208 is a subcurve of @xmath21 such that @xmath227 .
so , we get that @xmath228 , leading us to a contradiction .
suppose now that @xmath213 is a disconnecting node for @xmath21 .
then , @xmath182 is the union of two connected curves @xmath229 and @xmath230 of genus @xmath231 and @xmath232 , respectively , with @xmath233 .
suppose that @xmath234 and @xmath235 .
then , @xmath236 also in this case , we can apply lemma [ 222 ] to @xmath237 and to @xmath238 .
we get that @xmath239 a contradiction .
[ basicdualizing ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath7 with @xmath96 and let @xmath184 be either @xmath240 or @xmath241 ( if @xmath34 ) , where @xmath242 are the @xmath6 marked points of @xmath21 .
then , for all @xmath243 , we have that 1 . @xmath244 ; 2
. @xmath245 is globally generated .
according to lemma [ basicpropgen ] , it is enough to show that , given a subcurve @xmath48 of @xmath21 , @xmath246 , for all @xmath243 .
it is sufficient to prove the result for @xmath247 .
let @xmath48 be a subcurve of @xmath21 .
then , @xmath248 then , @xmath249 now , if @xmath48 is not a rational tail of @xmath21 , @xmath250 . instead
, if @xmath251 is a rational tail of @xmath21 , since @xmath21 is quasistable , it must contain at least two of the @xmath6 marked points and , if @xmath34 , at least one of these is among @xmath252 .
so , @xmath253 and the result follows .
[ basicprop ] let @xmath74 , @xmath34 and @xmath21 an @xmath6-pointed quasistable curve of genus @xmath254 endowed with a balanced line bundle @xmath63 of degree @xmath4 .
denote by @xmath255 the @xmath6 marked points of @xmath21 and let @xmath184 be the line bundle @xmath256 , for any @xmath257 .
then , we have that , for all @xmath258 , 1 . @xmath259 ; 2 .
@xmath260 is globally generated .
again , accordingly to lemma [ basicpropgen ] , the result follows if we prove that , for every subcurve @xmath48 of @xmath21 , @xmath246 .
it is enough to prove the result for @xmath261 .
let @xmath48 be a subcurve of @xmath21 which is not contained in any rational tail or in any rational bridge of @xmath21 . by definition of balanced
( see [ balanced ] above ) , we have that @xmath262 where @xmath263 is independent of @xmath4 .
take @xmath74 .
now , if @xmath48 is rational , @xmath264 , so @xmath265 .
in fact , if @xmath266 , @xmath21 would be rational , which is impossible ; by the other hand , if @xmath267 is @xmath113 or @xmath99 , @xmath48 should be contained in a rational tail or in a rational bridge of @xmath21 , respectively , which can not be the case by our assumption on @xmath48 .
suppose now that @xmath268 .
then , @xmath269 , since otherwise @xmath21 would have genus @xmath113 , which is impossible as well .
so , also in this case , @xmath265 . finally , if @xmath270 , it follows immediately that @xmath265 and the same holds for @xmath271 , which is asymptotically equal to @xmath122 since @xmath74 .
suppose now that @xmath48 is contained in a rational tail or in a rational bridge of @xmath21 .
then , from lemma [ combdesc ] , we have that @xmath272 . finally , if @xmath273 , @xmath274 and @xmath48 has at least @xmath99 marked points of @xmath21 .
so , @xmath275 and @xmath276 .
recall the following definition .
[ normgen ] a coherent sheaf @xmath277 on a scheme @xmath21 is said to be * normally generated * if , for all @xmath258 , the canonical map @xmath278 is surjective .
note that if we take @xmath277 to be an ample line bundle @xmath63 on @xmath21 , then if @xmath63 is normally generated it is , indeed , very ample ( see @xcite , section 1 ) .
in this case , saying that @xmath63 is normally generated is equivalent to say that the embedding of @xmath21 via @xmath63 on @xmath279 , for @xmath280 , is projectively normal . normal generation of line bundles on curves has been widely studied .
for instance , we have the following theorem of mumford : [ mumfordteo ] let @xmath21 be a nonsingular irreducible curve of genus @xmath7 .
then , any line bundle of degree @xmath281 is normally generated .
mumford s proof of theorem [ mumfordteo ] is based on the following lemma .
[ castelnuovo ]
let @xmath282 be a globally generated invertible sheaf on a complete scheme @xmath21 of finite type over @xmath46 and @xmath283 a coherent sheaf on @xmath21 such that @xmath284 then , 1 .
@xmath285 for @xmath286 , @xmath287 .
the natural map @xmath288 is surjective for @xmath289 .
the proof of the following statement uses mainly the arguments of knudsen s proof of theorem 1.8 in @xcite .
[ normgengen ] let @xmath21 be an @xmath6-pointed semistable curve of genus @xmath254 and @xmath290 .
if , for every subcurve @xmath48 of @xmath21 , @xmath212 , then @xmath291 is normally generated , where @xmath292 are the marked points of @xmath21 .
let @xmath293 denote the divisor @xmath294 .
let @xmath48 be a subcurve of @xmath21 .
since the multidegree of @xmath295 is non - negative , @xmath296 , so both statements of lemma [ basicpropgen ] hold also for @xmath297 .
so , we can apply the generalized lemma of castelnuovo with @xmath298 and @xmath299 , for any @xmath300 , and get that the natural map @xmath301 is surjective .
so , to prove that @xmath302 is normally generated , it remains to show that the map @xmath303 is surjective .
start by assuming that @xmath21 has no disconnecting nodes and consider the following commutative diagram @xmath304_{\beta } \ar[r ] & { \gamma(l\otimes\omega_x(d))\otimes \gamma(l\otimes\omega_x(d ) ) } \ar[d]^{\alpha}\\ { \gamma(l\otimes\omega_x^2(d ) ) \otimes \gamma(l(d ) ) } \ar[r]^{\gamma } & { \gamma((l\otimes\omega_x(d))^2 ) } } \ ] ] where @xmath305 indicates @xmath306 .
then , from the proof of theorem 1.8 in knudsen we have that , since @xmath254 and @xmath21 has no disconnecting nodes , @xmath307 is globally generated .
moreover , from lemma [ basicpropgen ] applied to @xmath308 , we get that @xmath309 .
so , we can apply the generalized lemma of castelnuovo with @xmath310 and @xmath311 to conclude that @xmath312 is surjective .
now , since @xmath21 has no disconnecting nodes , it can not have rational tails .
so , we can see @xmath21 as a semistable curve without marked points and apply corollary [ basicdualizing ] to @xmath21 and @xmath47 and get that @xmath313 .
since @xmath308 is globally generated , again by lemma [ basicpropgen ] , we can apply the generalized lemma of castelnuovo with @xmath314 and @xmath315 to conclude that also @xmath316 is surjective .
since the above diagram is commutative , it follows that also @xmath317 is surjective and we conclude . now , to show that @xmath317 is surjective in general ,
let us argue by induction in the number of disconnecting nodes of @xmath21 .
let @xmath213 be a disconnecting node of @xmath21 and @xmath318 and @xmath319 the subcurves of @xmath21 such that @xmath320 .
the surjectivity of @xmath317 follows if we can prove the folowing two statements . 1 . the image of @xmath317 contains sections a section @xmath321 such that @xmath322 ; 2 .
the image of @xmath317 contains @xmath323 .
the first statement follows immediately from the fact that @xmath302 is globally generated ( once more by [ basicpropgen ] ) .
let @xmath184 denote @xmath302 . to prove @xmath324 let us consider @xmath325 .
then , @xmath326 , with @xmath327 @xmath328 by induction hypothesis , @xmath329 is in the image of @xmath330 and @xmath331 in the image of @xmath332 with both @xmath329 and @xmath331 vanishing on @xmath213 .
write @xmath329 as @xmath333 , with @xmath334 and @xmath335 in @xmath336 , for @xmath337 .
let @xmath338 be the partial normalization of @xmath21 in @xmath213 and @xmath220 and @xmath221 be the preimages of @xmath213 on @xmath318 and @xmath319 , respectively , via @xmath222 .
since @xmath339 is globally generated , there is @xmath340 with @xmath341 .
then there are constants @xmath342 and @xmath343 for @xmath344 and @xmath345 such that @xmath346 define the sections @xmath347 and @xmath348 as @xmath334 ( resp .
@xmath335 ) on @xmath319 and as @xmath349 ( resp .
@xmath350 ) on @xmath318 , for @xmath344 . by ( [ incol ] ) , these are global sections of @xmath184 and @xmath351 maps to @xmath329 .
in fact , @xmath352 and , by hypothesis , @xmath353 and @xmath341 .
this implies that @xmath354 , so @xmath355 .
we conclude that @xmath329 is in the image of @xmath317 . in the same way
, we would get that also @xmath331 is in the image of @xmath317 , so @xmath324 holds and we are done .
the next result follows from the proof of theorem 1.8 in @xcite , however we include it here since we shall use it in the following slightly more general form .
[ normgendualizing ] let @xmath21 be an @xmath6-pointed semistable curve of genus @xmath254 and let @xmath356 be the marked points of @xmath21 . then ,
for @xmath357 , @xmath358 is normally generated .
is an immediate consequence of proposition [ normgengen ] and corollary [ basicdualizing ] .
[ normgenprop ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath7 and @xmath63 a balanced line bundle on @xmath21 of degree @xmath74 . then , if @xmath34 , @xmath359 is normally generated .
since @xmath21 is an @xmath6-pointed quasistable curve , it is easy to see that @xmath21 , endowed with the first @xmath360 marked points @xmath361 , is an @xmath92-pointed semistable curve . moreover , by corollary [ basicprop ] , we can apply proposition [ normgengen ] to @xmath362 .
the result follows immediately now .
[ projnormal ] let @xmath74 , @xmath34 and @xmath21 an @xmath6-pointed quasistable curve of genus @xmath254 endowed with a balanced line bundle @xmath63 .
let @xmath184 denote the line bundle @xmath363 , where @xmath364 are the marked points of @xmath21 .
we have : 1 .
@xmath184 is normally generated ; 2 .
@xmath184 is very ample .
statement @xmath365 follows from the proof of the previous proposition , which obviously works for @xmath366 as well . to show @xmath324 it is enough to observe that @xmath184 is ample since its degree on each irreducible component of @xmath21 is positive .
since @xmath184 is also normally generated , it follows that @xmath184 is indeed very ample ( see @xcite , section 1 ) .
the following definition generalizes the notion of contraction introduced by knudsen in @xcite to the more general case of pointed quasistable curves endowed with balanced line bundles .
[ contraction ] let @xmath367 be an @xmath368-pointed curve endowed with a line bundle of relative degree @xmath4 .
a contraction of @xmath21 is an @xmath30-morphism from @xmath21 into an @xmath6-pointed curve @xmath369 endowed with a line bundle of relative degree @xmath4 , @xmath157 , and with an extra section @xmath370 such that 1 .
for @xmath371 , the diagram @xmath372^{f } \ar[d]^{\pi } & { x ' } \ar[dl]_{\pi'}\\ { s } \ar @{- > } @/^/[u]^{s_i }
\ar @{- > } @/_/[ur]_{t_i } } \ ] ] commutes both in the upward and downward directions , 2 .
@xmath373 , 3 .
@xmath374 induces an isomorphism between @xmath375 and @xmath376 , 4 .
the morphism induced by @xmath374 in the geometric fibers @xmath101 is either an isomorphism or there is an irreducible rational component @xmath377 such that @xmath378 which is contracted by @xmath374 into a closed point @xmath379 and @xmath380 is an isomorphism .
[ quasistablecont ] let @xmath381 and @xmath382 a contraction from an @xmath368-pointed curve @xmath383 , endowed with a degree @xmath4 line bundle @xmath63 into an @xmath6-pointed curve @xmath384 , endowed with a degree @xmath4 line bundle @xmath157 and with an extra point @xmath385 .
then , if @xmath386 is quasistable , also @xmath387 is quasistable and , in this case , @xmath63 is balanced if and only if @xmath157 is balanced . clearly , the assertion follows trivially if no irreducible component of @xmath21 gets contracted by @xmath374 .
so , assume that there is an irreducible component @xmath97 of @xmath21 that gets contracted by @xmath374 .
then , necessarily , @xmath388 , so no exceptional component of @xmath21 gets contracted .
moreover , the condition that @xmath389 implies that @xmath390 is trivial on the fibers of @xmath374 , so it must have degree @xmath112 on @xmath97 .
now , we have only two possibilities : either @xmath385 is a smooth point of @xmath156 or it is nodal
. start by considering the case when @xmath385 is smooth . since @xmath391
, we must have that @xmath392 .
so , if @xmath21 is quasistable , @xmath97 must contain exactly another special point @xmath393 , for some @xmath394 and @xmath385 must be a smooth point of @xmath156 .
let @xmath395 be the irreducible component of @xmath156 containing @xmath385 and @xmath283 the correspondent irreducible component of @xmath21 ( recall that @xmath374 establishes an isomorphism between @xmath283 and @xmath395 away from @xmath385 ) .
if @xmath396 , then it is clear that also @xmath156 is quasistable . instead , if @xmath283 is rational , even if @xmath397 , @xmath395 has one more marked point than @xmath283 .
so , @xmath156 has the same destabilizing and exceptional components than @xmath21 and it follows that @xmath156 is a quasistable @xmath6-pointed curve . let us now check that , if we are contracting a rational tail of a quasistable curve , @xmath63 is balanced if and only if @xmath157 is balanced . from the definition of contraction , we get that the multidegree of @xmath398 in the irreducible components of @xmath21 that are not contracted must agree with the multidegree of @xmath399 in their images by @xmath374 . in our case
, this implies that the multidegree of @xmath157 on the irreducible components of @xmath156 coincides with the multidegree of @xmath63 on the corresponding irreducible components of @xmath21 , except on @xmath395 , where we must have that @xmath400 so , given a proper subcurve @xmath158 of @xmath156 , if @xmath158 does not contain @xmath385 , the balanced condition will be clearly satisfied by @xmath63 on @xmath48 if and only if it is satisfied by @xmath157 on @xmath158 since @xmath401 , @xmath402 and @xmath403 .
now , suppose @xmath404 and let @xmath48 be the preimage of @xmath158 by @xmath374 .
then , @xmath405 , @xmath406 , @xmath407 and @xmath408 , which implies that @xmath409 and @xmath410 since also @xmath411 , we conclude that , if @xmath63 is balanced , then @xmath157 is balanced too .
now , to conclude that the fact that @xmath157 is balanced implies that also @xmath63 is balanced we have to further observe that the degree of @xmath63 on @xmath97 is forced to be @xmath125 since @xmath97 contains @xmath99 special points and that the inequality ( [ basic ] ) is verified on @xmath412 ( that does not correspond to any proper subcurve of @xmath156 ) , which follows since @xmath413 . now , suppose @xmath385 is a nodal point of @xmath21 . then , since @xmath391 , we must have that @xmath414 and that the only marked point of @xmath21 in @xmath97 is @xmath415 ( otherwise , the condition that @xmath416 for @xmath394 would imply that one of these @xmath417 s should coincide with @xmath418 , which is nodal , and @xmath387 would not be a pointed curve ) .
we must do a further distinction here .
suppose first that @xmath97 intersects just one irreducible component of @xmath21 : call it @xmath283 and @xmath395 its associated irreducible component on @xmath156 .
now , if @xmath419 , and if @xmath283 is rational , @xmath156 is an irreducible genus @xmath113 curve , which is clearly quasistable . if , instead , @xmath420 or if @xmath421 , we see that all destabilizing and exceptional components of @xmath156 correspond to destabilizing and exceptional components of @xmath21 and are contained in the same type of rational chains
if , instead , @xmath97 intersects two distinct irreducible components of @xmath21 , it is easy to see that , also in this case , all destabilizing and exceptional components of @xmath156 correspond to destabilizing and exceptional components of @xmath21 and are contained in the same type of rational chains .
so , @xmath387 will be quasistable if @xmath386 is .
now , since @xmath415 is the only marked point in @xmath97 , all irreducible components of @xmath156 have the same marked points that the corresponding irreducible components of @xmath21 , so @xmath389 implies that the multidegree of @xmath63 on irreducible components of @xmath156 coincides to the multidegree of @xmath63 on the corresponding irreducible components of @xmath21 and that the degree of @xmath63 on @xmath97 is zero .
let @xmath158 be a proper subcurve of @xmath156 and @xmath48 the corresponding proper subcurve of @xmath21 . if @xmath48 does not intersect @xmath97 or if it intersects @xmath97 in a single point , then it is immediate to see that inequality ( [ basic ] ) holds for @xmath63 and @xmath48 if and only if it holds for @xmath157 and @xmath158 .
if , instead , @xmath48 intersects @xmath97 in two points , then @xmath422 , @xmath423 , @xmath424 and @xmath425 , so , we get that @xmath426 and @xmath427 since also @xmath428 , we conclude that if we are contracting a rational bridge , if @xmath63 is balanced , also @xmath157 will be balanced .
now , to conclude that the fact that @xmath157 is balanced implies that also @xmath63 is balanced we have to further observe that , by definition of contraction , the degree of @xmath63 on @xmath97 is forced to be @xmath112 and that the inequality ( [ basic ] ) is verified on @xmath412 ( that does not correspond to any proper subcurve of @xmath156 ) , which is true since @xmath429 .
the following lemma is corollary 1.5 of @xcite .
[ cor1.5 ] let @xmath21 and @xmath182 be @xmath30-schemes and @xmath430 a proper @xmath30-morphism , whose fibers are at most one - dimensional .
let @xmath277 be a coherent sheaf on @xmath21 , flat over @xmath30 such that @xmath431 for each closed point @xmath432 .
then @xmath433 is @xmath30-flat , @xmath434 and , given any morphism @xmath435 , there is a canonical isomorphism @xmath436 if , moreover , @xmath437 is globally generated we have also that the canonical map @xmath438 is surjective .
[ morebasicprop ] let @xmath439 be an @xmath368-pointed quasistable curve endowed with a balanced line bundle of degree @xmath74 .
let @xmath184 be either the line bundle @xmath375 or @xmath440 .
then , for all @xmath441 , we have that 1 . @xmath442 is @xmath30-flat
; 2 . @xmath443 ; 3 . for all @xmath287 ,
the natural map @xmath444 is surjective ; 4 .
@xmath445 is surjective .
\(1 ) ( 2 ) and ( 4 ) follow immediately from lemma [ cor1.5 ] and corollaries [ basicprop ] with @xmath446 and [ basicdualizing ] , which assert that we can apply lemma [ cor1.5 ] to @xmath447 and @xmath184 , in both cases .
let us now show that ( 3 ) holds . from propositions
[ normgenprop ] and [ normgendualizing ] , the statement holds if @xmath381 . since @xmath184 satisfies the hypothesis of lemma [ cor1.5 ] , the formation of @xmath448 commutes with base change
so , @xmath449 is surjective at every geometric point of @xmath30 and we use nakayama s lemma to conclude that @xmath449 is surjective .
we now show that knudsen s main lemma also holds for quasistable pointed curves and balanced line bundles of high degree .
[ mainlemma ] let @xmath74 and consider a contraction @xmath450 as in definition [ contraction ] .
denote by @xmath184 and @xmath451 , respectively , the line bundles @xmath375 and @xmath452 .
then , for all @xmath258 , we have that 1 . @xmath453 and @xmath454 ; 2 .
@xmath455 3 .
@xmath456 for @xmath289 . that @xmath457 is isomorphic to @xmath260 comes from our definition of contraction morphism .
so , also @xmath458 is isomorphic to @xmath459 .
so , composing this with the canonical map from @xmath460 into @xmath458 , we get a map @xmath461 since the fibers of @xmath374 are at most smooth rational curves and @xmath184 is trivial on them , also @xmath260 is trivial on the fibers of @xmath374 , so we can apply lemma [ cor1.5 ] to it .
since the previous morphism is an isomorphism on the geometric fibers of @xmath374 and @xmath462 is flat over @xmath30 , we conclude that it is an isomorphism over @xmath30 .
that @xmath463 follows directly from lemma [ cor1.5 ] while @xmath464 follows from @xmath365 and the leray spectral sequence , which is degenerate by @xmath324 . from now on , consider @xmath74
. using the contraction morphism defined above , we will try to define a natural transformation from @xmath44 to @xmath176 .
let @xmath367 be an @xmath368-pointed quasistable curve with a balanced line bundle @xmath63 of relative degree @xmath4 . for @xmath289 ,
define @xmath465 since we are considering @xmath74 , then , by corollary [ morebasicprop ] , @xmath466 , so @xmath467 is locally free of rank @xmath468 , for @xmath287 , .
consider @xmath469 again by corollary [ morebasicprop ] , the natural map @xmath470 is surjective , so we get a natural @xmath30-morphism @xmath372^{q } \ar[d]^{\pi } & { \mathbb p(\mathcal s_1 ) } \ar[dl]\\ { s } \ar @{- > } @/^/[u]^{s_i } } \ ] ] define @xmath471 , @xmath472 , and , by abuse of notation , call @xmath221 the ( surjective ) @xmath30-morphism from @xmath21 to @xmath182 .
@xmath282 is an invertible sheaf over @xmath182 and @xmath473 .
moreover , by corollary [ morebasicprop ] ( 3 ) , we have that @xmath474 so , since all @xmath467 are flat over @xmath30 ( again by corollary [ morebasicprop ] ) , also @xmath182 is flat over @xmath30 , so it is a projective curve over @xmath30 of genus @xmath7 ( since the only possible contractions are of rational components ) .
so , if we endow @xmath475 with the sections @xmath476 , for @xmath477 , the extra section @xmath478 and @xmath479 as above , we easily conclude that @xmath480 is a contraction .
now , consider a morphism @xmath175^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_i ' } } \ ] ] of @xmath368-pointed quasistable curves with balanced line bundles @xmath63 and @xmath157 of relative degree @xmath4 in @xmath0 and let us see that @xmath481 , where @xmath482 is the isomorphism between @xmath63 and @xmath483 , induces in a canonical way a morphism in @xmath176 between the contracted curves .
define @xmath484 .
recall that , to give an @xmath485-morphism from @xmath486 to @xmath487 is equivalent to give a line bundle @xmath184 on @xmath486 and a surjection @xmath488 where by @xmath489 we denote the natural morphism @xmath490 .
@xmath491_{\pi^c } \ar @{-- > } @/^18pt/[rrr ] & { x } \ar[l]_{q } \ar[d]^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[r]^{q ' } \ar[d]_{\pi ' } & { \mathbb p(\mathcal s ' ) } \ar[dl]\\ & { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_i ' } } \ ] ] since we are considering @xmath74 , for @xmath492 , @xmath493 is constant and equal to @xmath494 .
so , we can apply the theorem of cohomology and base change to conclude that there is a natural isomorphism @xmath495 since we have also the isomorphism @xmath496 we get a natural isomorphism @xmath497 composing this with the natural surjection @xmath498 we conclude that there is a canonical surjection @xmath499 defining a natural @xmath485-morphism from @xmath500 .
this morphism naturally determines a morphism from @xmath501 to @xmath502 , where @xmath502 is the image of @xmath156 in @xmath487 via @xmath503 , inducing a natural isomorphism between @xmath504 and the pullback @xmath505 , the restriction of @xmath506 to @xmath502 .
the fact that all these morphisms are canonical implies that this construction is compatible with the composition of morphisms , defining a natural transformation .
we have just proved the following proposition .
there is a natural transformation @xmath507 from @xmath44 to @xmath176 given on objects by the contraction morphism defined above .
we can now prove our main theorem .
( of theorem [ main ] ) we must show that the contraction functor is an equivalence of categories , i. e. , it is fully faithful and essentially surjective on objects . the fact that it is full is immediate .
we can also conclude easily that it is faithful from the fact that a morphism of @xmath508 fixing 3 distinct points is necessarily the identity .
in fact , contraction morphisms induce isomorphisms on the geometric fibers away from contracted components and the contracted components have at least 3 special points and it is enough to use flatness to conclude . in order to show that @xmath507 is essentially surjective on objects we will use knudsen s stabilization morphism ( see @xcite , def .
2.3 ) and check that it works also for pointed quasistable curves with balanced line bundles .
so , let @xmath83 be an pointed quasistable curve , with @xmath6 sections @xmath509 , an extra section @xmath510 and a balanced line bundle @xmath63 on @xmath21 , of relative degree @xmath4 .
let @xmath511 be the @xmath512-ideal defining @xmath510 .
define the sheaf @xmath513 on @xmath21 via the exact sequence @xmath514 where @xmath515 is the diagonal morphism , @xmath516 .
define @xmath517 and let @xmath518 be the natural morphism from @xmath519 to @xmath21 .
theorem 2.4 of @xcite asserts that , in the case that @xmath21 is a pointed stable curve , the sections @xmath520 and @xmath510 have unique liftings @xmath521 to @xmath519 making @xmath522 an @xmath368-pointed stable curve and @xmath523 a contraction .
one checks easily that the same construction holds also if @xmath21 is a quasistable pointed curve instead of a stable one .
in fact , the assertion is local on @xmath30 , the problem being the points where @xmath510 meets non - smooth points of the fibre or other sections since in the other points @xmath519 is isomorphic to @xmath21 . in the case where @xmath510 meets a non - smooth point of a geometric fiber , locally @xmath519 is the total transform of the blow - up of @xmath21 at that point with the reduced structure and @xmath524 is a smooth point of the exceptional component . in the case where @xmath510 coincides with another section @xmath525 in a geometric fiber @xmath101 of @xmath21 , then , locally , on @xmath519 is the total transform of the blow - up of @xmath21 at @xmath102 , again with the reduced structure , and @xmath526 and @xmath524 are two distinct smooth points of the exceptional component .
let @xmath527 .
then the multidegree of @xmath528 on a geometric fiber @xmath529 coincides with the multidegree of @xmath63 in the irreducible components of @xmath529 that correspond to irreducible components of @xmath21 and , in the possibly new rational components , the degree is @xmath112 .
so , @xmath528 is balanced of relative degree @xmath4 . to conclude
, we must check that @xmath530 is isomorphic to @xmath21 . by definition , @xmath530 is given by the image of @xmath519 on @xmath531 .
consider the line bundle @xmath375 on @xmath21 . by corollary [ morebasicprop ]
, there is a natural surjection @xmath532 but , since @xmath533 is naturally isomorphic to @xmath534 , we get a natural surjection @xmath535 so , equivalently , a morphism @xmath374 from @xmath21 to @xmath536 .
since @xmath537 induces the natural morphism @xmath538 , whose image is @xmath530 , naturally the image of @xmath374 is @xmath530 .
it is easy to check that @xmath374 is an isomorphism on the geometric fibers , so , by flatness , we conclude that @xmath374 gives an @xmath30-isomorphism between @xmath21 and @xmath530 as pointed quasistable curves and determines an isomorphism between the respective balanced degree @xmath4 line bundles .
now , for each @xmath34 , we will try to construct a morphism @xmath539 fitting in diagram ( [ induction ] ) above .
let @xmath540 , @xmath394 be an @xmath6-pointed quasistable curve over @xmath30 .
denote by @xmath541 the line bundle @xmath542 .
then , by corollary [ morebasicprop ] , @xmath543 , so it is locally free and there is an @xmath30-morphism @xmath544 making the following diagram commute .
@xmath545^{\gamma } \ar[dr]^{\pi } & & { \mathbb p(\pi_*(\omega ) ) } \ar[dl ] \\ & { s } \ar @{- > } @/^/[ul]^{s_i } & } \ ] ] the restriction of @xmath316 to any fiber @xmath101 of @xmath447 maps @xmath101 to its stable model in @xmath546 , which is naturally endowed with the sections @xmath547 , for @xmath548 .
this follows from the fact that @xmath541 is very ample on the stable components of each fiber , whereas it has degree @xmath112 on the exceptional components . moreover , @xmath549 is flat over @xmath30 .
in fact , from corollary [ morebasicprop ] , for any @xmath287 , the natural map @xmath550 is surjective .
it follows that @xmath551 , which is flat over @xmath30 because each @xmath552 is @xmath30-flat , again by corollary [ morebasicprop ] .
it is easy to check that this yields a surjective morphism @xmath39 from @xmath0 onto @xmath1 fitting in diagram ( [ induction ] ) and making it commutative .
let @xmath439 be an @xmath368-pointed quasistable curve of genus @xmath7 endowed with a balanced line bundle @xmath63 of relative degree @xmath4 over @xmath21 .
it is immediate to check that , restricting ourselves to the geometric fibers of @xmath447 , the diagram is commutative since in both directions we get the @xmath6-pointed curve which is the stable model of the initial one , after forgetting the last point .
now , since all families are flat over @xmath30 , we conclude that the diagram is commutative .
the surjectivity of @xmath39 follows from the fact that @xmath205 is surjective ( see @xcite , proposition 4.12 ) and from the commutativity of the diagram because @xmath202 and @xmath201 are the universal morphisms onto @xmath35 and @xmath9 , respectively .
so , the fibers of @xmath39 over a pointed curve @xmath553 are the quasistable pointed curves @xmath21 with stable model @xmath156 endowed with balanced degree @xmath4 line bundles .
let @xmath21 be an @xmath6-pointed quasistable curve over @xmath46 . by applying the contraction morphism
we get an @xmath92-pointed quasistable curve with an extra section .
if we forget about this extra section and we iterate the contraction procedure @xmath6 times , at the end we get a quasistable curve with no marked points , call it @xmath554 . denote by @xmath374 this morphism from @xmath21 to @xmath554 .
let @xmath555 be the dualizing sheaf of @xmath554 .
for each proper subcurve @xmath556 of @xmath554 , the degree of @xmath555 in @xmath556 is @xmath557 . in particular
, it has degree @xmath112 on exceptional components of @xmath554 .
consider now the pullback of @xmath555 via @xmath374 , @xmath558 .
this is a line bundle on @xmath21 having degree @xmath112 on rational bridges and on rational tails ; moreover , given a proper subcurve @xmath48 of @xmath21 whose image under @xmath374 is a proper subcurve @xmath556 of @xmath554 , @xmath558 has degree @xmath559 on @xmath48 .
so , a line bundle @xmath63 of degree @xmath4 on @xmath21 with given balanced multidegree on rational tails and rational bridges of @xmath21 is balanced on @xmath21 if and only if @xmath560 is balanced on @xmath21 of degree @xmath561 and with the same multidegree on rational tails and rational bridges .
in fact , for each proper subcurve @xmath48 of @xmath21 which is not contained in rational tails or rational bridges , we have that @xmath562 @xmath563 @xmath564 and similarly that @xmath565 @xmath566 so @xmath567 satisfies inequality ( [ basic ] ) if and only if @xmath568 does . in conclusion , we have the following result .
let @xmath4 and @xmath40 be integers such that there exists an @xmath90 such that @xmath569 .
then , @xmath0 and @xmath43 are isomorphic .
we must show that there is an equivalence of categories between @xmath0 and @xmath43 .
so , let @xmath570 , @xmath394 be an object of @xmath0 . consider its image under @xmath571 and denote it by @xmath572 . according to [ const ]
, there is an @xmath30-morphism @xmath573 .
then , by what we have seen above , @xmath574 is a balanced line bundle of relative degree @xmath40 over @xmath21 , so @xmath575 .
it is easy to check that this defines an equivalence between @xmath0 and @xmath43 . for all @xmath34 ,
there are forgetful morphisms @xmath576 endowed with @xmath6 sections @xmath577 yielding cartier divisors @xmath578 , @xmath394 such that @xmath579 gives an isomorphism between @xmath0 and @xmath578 .
note that each object @xmath570 , @xmath394 , in @xmath0 has automorphisms given by scalar multiplication by an element of @xmath580 along the fibers of @xmath581 . since these automorphisms fix @xmath582 , there is no hope @xmath0 can be representable over @xmath1 ( see @xcite , 4.4.3 ) .
the rigidification procedure , defined in @xcite , fits exactly on our set up and produces an algebraic stack with those automorphisms removed .
denote by @xmath583 the rigidification of @xmath0 along the action of @xmath36 .
exactly because the action of @xmath36 on @xmath0 leaves @xmath1 invariant , the morphism @xmath39 descends to a morphism from @xmath583 onto @xmath1 , which we will denote again by @xmath39 , making the following diagram commutative .
@xmath584^{\psi_{d , g , n } } \ar[dl]_{\phi_{d , g , n } } & \\ { { \overline}{\mathcal p}_{d , g , n-1 } } \ar[dr]_{\psi_{d , g , n-1 } } & & { { \overline}{\mathcal m}_{g , n } } \ar[dl]^{\pi_{g , n}}\\ & { { \overline}{\mathcal m}_{g , n-1 } } & } \ ] ] so , the same argument we used to show that @xmath39 is universally closed for all @xmath29 if and only if @xmath205 is universally closed holds also in this case .
moreover , since , for @xmath11 , we have that @xmath585\to { \overline}{\mathcal m}_g$ ] is proper and strongly representable if and only if @xmath23 , we have that the same statement holds in general for every @xmath29
. let @xmath586 be the rigidification of @xmath0 under the action of @xmath36 . then ,
if @xmath23 , @xmath583 is a deligne - mumford stack of dimension @xmath3 with a proper and strongly representable morphism onto @xmath1 .
this paper is part of my ph.d . thesis .
i am very grateful to my advisor professor lucia caporaso for the patience with which she followed this work very closely and for always transmitting me lots of encouragement and mathematical enthusiasm .
i am also grateful to simone busonero and filippo viviani for giving me important suggestions .
d. mumford : varieties defined by quadratic equations . with an appendix of g. kempf , in _
questions on algebraic varieties _ , ( c.i.m.e .
, iii ciclo , varenna , 1969 ) pp .
29 - 100 , edizioni cremonese , roma , 1970 .
e. witten , algebraic geometry associated with matrix models of two - dimensional gravity , _ topological methods in modern mathematics ( stony brook , ny , 1991 ) _ , publish or perish , houston , tx ( 1993 ) , 235269 , | in this paper we give a construction of algebraic ( artin ) stacks @xmath0 endowed with a modular map onto the moduli stack of pointed stable curves @xmath1 , for @xmath2 .
the stacks @xmath0 are smooth , irreducible and have dimension @xmath3 .
they yield a geometrically meaningful compactification of the degree @xmath4 universal picard stack over @xmath5 , parametrizing @xmath6-pointed smooth curves together with a degree @xmath4 line bundle .
[ section ] [ teo]proposition [ teo]lemma [ teo]remark [ teo]definition [ teo]example [ teo]examples [ teo]corollary | <s>[INST]consider the degree @xmath4 universal picard stack over @xmath6-pointed smooth curves of genus @xmath7 , @xmath8 , parametrizing families of @xmath6-pointed smooth curves of genus @xmath7 endowed with line bundles of relative degree @xmath4 over these curves .
@xmath8 is , of course , not complete . in the present paper we search for a compactification of @xmath8 over @xmath1 , the moduli stack of stable curves of genus @xmath7 . by this we mean an algebraic stack with a proper ( or at least universally closed ) map onto @xmath1 , containing @xmath8 as a dense open substack
the problem of compactifying the ( generalized ) jacobian of curves or of families of curves has been widely studied in the last decades , starting from the work of igusa @xcite and of mayer and mumford @xcite .
the first solution to this problem , in the case on irreducible curves , was due to dsouza in @xcite and since then , several other solutions where found , the more general one being probably simpson s construction of moduli spaces of coherent sheaves on projective schemes in @xcite ( see @xcite for an overview and comparison results on these constructions ) . on the other hand , the construction of the moduli space of stable curves with marked points was done by knudsen in @xcite , following ideas of mumford , with the scope of proving the projectivity of the moduli space of stable curves . since then , @xmath1 itself became the subject of great interest , because of its rich geometry , and because of several applications . in particular
, @xmath1 has a central role in gromov - witten theory and enumerative geometry .
in fact , in part motivated by witten s conjecture ( @xcite ) , the study of the cohomology ring of @xmath9 attracted the attention of several mathematicians in the last decades and led to very important results .
we recall , for instance , kontsevich s first proof of the witten conjecture in ( @xcite ) ; the interaction between geometry and physics leading to the development of quantum cohomoly and gromov - witten theory ( see e.g. @xcite ) ; the algebro - geometric inductive calculations on the cohomology ring of @xmath1 due to arbarello and cornalba in @xcite ; faber s conjectures on the structure of the tautological ring of @xmath10 and its pointed versions ( @xcite , @xcite ) , the elsv formulas relating intersection formulas in @xmath1 with hurwitz numbers ( @xcite , @xcite ) and the recent proof by faber , shadrin and zvonkine in @xcite of the generalized witten conjecture ( @xcite ) .
so , it is natural to search for a compactification of @xmath8 over @xmath1 and to study its applications .
nevertheless , at least to our knowledge , there was no construction of compactified picard varieties for curves with marked points until now .
the aim of the present paper is to construct an algebraic ( artin ) stack @xmath0 with a geometrically meaningful modular description , giving a solution for the above problem for @xmath2 .
let @xmath11 and consider pic@xmath12 , the
universal picard variety of degree @xmath4over @xmath13 parametrizing isomorphism classes of line bundles of degree @xmath4 over automorphism - free nonsingular curves .
the problem of compactifying @xmath14 over @xmath15 was addressed by caporaso in @xcite and later by pandharipande in @xcite ( the second author s construction holds also for bundles of higher rank ) .
both compactifications were done by means of git - quotients yielding projective varieties endowed with a proper map onto @xmath15 , extending the natural map @xmath16 .
even if the boundary objects used by the two authors have different modular interpretations , it turns out that the resulting varieties coincide .
we here focus on caporaso s original compactification , which works for @xmath2 ; denote it by @xmath17 and by @xmath18 its natural map onto @xmath15 .
given @xmath19\in { \overline}m_g$ ] , @xmath20 is a projective connected scheme with a finite number of components ( that can not exceed a certain numerical invariant of the curve ) and , if @xmath21 has trivial automorphism group , @xmath20 is reduced and its smooth locus is isomorphic to the disjoint union of a finite number of copies of the jacobian of @xmath21 , @xmath22 . later , on @xcite , the same author gives a stack - theoretical description of the above quotient for degrees @xmath4 such that @xmath23 , getting a modular compactification of @xmath24 over @xmath25 .
we considered the same problem in @xcite with no assumption on @xmath4 , getting an algebraic ( artin ) stack @xmath26 with a universally closed morphism @xmath27 onto @xmath25 parametrizing families of _ quasistable _ curves endowed with _ balanced _ line bundles of relative degree @xmath4 .
our stack @xmath0 coincides with @xmath26 for @xmath11 .
let @xmath28 , @xmath29 and @xmath2 .
we define @xmath0 to be the stack whose sections over a scheme @xmath30 are given by families of genus @xmath7 @xmath6-pointed quasistable curves over @xmath30 endowed with a relative degree @xmath4 balanced line bundle ( see definitions [ quasistabledef ] and [ balanced ] below ) .
morphisms between two such sections are given by cartesian diagrams of the families compatible with the sections plus an isomorphism between the line bundles ( see definition [ compstack ] ) .
the principal result of this paper consists in proving that @xmath0 is a smooth and irreducible algebraic ( artin ) stack of dimension @xmath3 , endowed with a universally closed morphism onto @xmath1 .
our interest in constructing such a space is also due to goulden , jackson and vakil s
generalized elsv formulaconjecturing a relation between the intersection theory of a @xmath31-dimensional space and certain double hurwitz numbers ( see @xcite and @xcite ) . according to these authors
, this space should be a suitable compactification of @xmath8 over @xmath1 supporting particular families of classes satisfying certain properties .
unfortunately , we do not know yet if our space supports such classes , except for what they call @xmath32-classes , which turn out to be the pullback of the @xmath32-classes in @xmath1 .
it is certainly interesting to consider this as a future research problem .
our construction of @xmath0 goes in the following way .
for @xmath11 , we define @xmath33 to be equal to @xmath26 .
then , for @xmath34 , along the lines of knudsen s construction of @xmath25 in @xcite , we show that there is an isomorphism between @xmath0 and the universal family over @xmath35 .
this isomorphism is built explicitly and it generalizes knudsen s notion of _ contraction _ and _ stabilization _ of @xmath6-pointed stable curves , in this more general context of quasistable curves endowed with balanced line bundles .
the stacks @xmath0 can never be deligne - mumford since there is an action of @xmath36 given by scalar product on the line bundles , leaving the curves and the sections fixed .
even the rigidification in the sense of @xcite of @xmath0 by this action of @xmath36 , denoted by @xmath37 is not deligne - mumford in general .
in fact , already for @xmath11 , it was proved by caporaso in @xcite that @xmath38 is deligne - mumford if and only if @xmath23 .
this holds in general for any @xmath29 . in order to make the contraction process work
, we also need to prove some technical properties for balanced line bundles over quasistable pointed curves .
in particular , we get general results concerning global and normal generation for line bundles on ( reducible ) nodal curves depending only on their multidegree ( see section [ technical ] ) . in section [ forgetful ]
we show that @xmath0 is endowed with a ( forgetful ) morphism @xmath39 onto @xmath9 .
we also study the fibres of @xmath39 .
finally , in section [ properties ] , we study further properties of @xmath0 . for example , we show that if @xmath4 and @xmath40 are such that @xmath41 divides @xmath42 , then @xmath0 is isomorphic to @xmath43 .
we also study the map form @xmath44 to @xmath0 and its sections and we show that these yield cartier divisors on @xmath44 with interesting intersection properties .
we would also like to observe that another possible approach to the construction of @xmath0 would be to use baldwin and swinarski s git construction of the moduli space of stable maps and , in particular , of @xmath45 , in @xcite , and then procede as caporaso in @xcite .
we will always consider schemes and algebraic stacks locally of finite type over an algebraically closed base field @xmath46 .
a curve @xmath21 will always be a connected projective curve over @xmath46 having at most nodes as singularities . given a curve @xmath21 , we will denote by @xmath47 its canonical or dualizing sheaf .
for each proper subcurve @xmath48 of @xmath21 ( which we always assume to be complete and connected ) , denote by @xmath49 and by @xmath50 its arithmetic genus . recall that , since @xmath48 is connected , the adjunction formula gives @xmath51 for @xmath52 its _ multidegree _ is @xmath53 and its ( total ) degree is @xmath54 , where @xmath55 are the irreducible components of @xmath21 .
given @xmath56 , we set @xmath57 and @xmath58 .
we have that @xmath59 , where @xmath60 .
let @xmath8 be the universal picard stack over the moduli space of smooth curves with @xmath6 marked points .
sections of @xmath8 over a scheme @xmath30 consist of flat and proper families @xmath61 of smooth curves of genus @xmath7 , with @xmath6 distinct sections @xmath62 and a line bundle @xmath63 of relative degree @xmath4 on @xmath64 .
morphisms between two such objects are given by cartesian diagrams @xmath65^{\pi } \ar[r]^{\beta_2 } & { c ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_{i ' } } } \ ] ] such that @xmath66 , @xmath67 , together with an isomorphism @xmath68 .
in the present paper we search for a compactification of @xmath8 over @xmath9 . by this
we mean to construct an algebraic stack @xmath0 with a map @xmath39 onto @xmath1 with the following properties . 1 . @xmath0 and @xmath39 fit in the following diagram ; @xmath69 \ar @{^{(}->}[r ] & { { \overline}{\mathcal p}_{d , g , n } } \ar[d]^{\psi_{d , g , n } } \\
{ \mathcal m_{g , n } } \ar @{^{(}->}[r ] & { { \overline}{\mathcal m}_{g , n } } } \ ] ] 2 .
@xmath39 is proper ( or , ate least , universally closed ) ; 3 .
@xmath8 has a geometrically meaningful modular description .
note that in order to complete @xmath8 over @xmath1 it is not enough to consider the stack of line bundles over families of @xmath6-pointed stable curves , since this is not complete as well .
so , it is necessary to enlarge the category either admitting more general sheaves than line bundles or a bigger class of curves .
our construction of @xmath0 will go as follows .
we will start by noticing that , for @xmath11 , this problem is already solved .
then , for @xmath34 , we will construct @xmath0 by induction on the number of marked points @xmath6 , following the lines of knudsen s construction of @xmath9 .
the problem of constructing compactifications of the picard varieties of singular curves has been widely studied and , in fact , there are several known compactifications .
we will focus on the one built by caporaso in @xcite , which we will now briefly describe .
consider the hilbert scheme @xmath70 of genus @xmath7 curves embedded in @xmath71 as nondegenerate curves of degree @xmath4 , where @xmath72 .
there is a natural action of @xmath73 in @xmath70 corresponding to the choice of the coordinates used to embed the curves .
for @xmath74 , define @xmath75 as the git - quotient of @xmath76 , the locus of git - semistable points for this action . by results of @xcite and @xcite , we know that points in @xmath76 correspond exactly to _
quasistable _ curves embedded by _ balanced _ line bundles ( of degree @xmath4 ) , where quasistable curves are semistable curves such that two exceptional components never meet and balanced is a combinatorial condition on the multidegree of the line bundle on the curve ( see definition [ balanced ] and ( [ giesekerbasic ] ) below ) . by construction , @xmath17 has a proper morphism @xmath77 such that @xmath78 is isomorphic to the
universal picard variety of degree @xmath4 , @xmath14 , which parametrizes isomorphism classes of line bundles of degree @xmath4 over automorphism - free nonsingular curves .
later , in @xcite , caporaso shows that , if @xmath74 and @xmath23 , the quotient stack associated to the git - quotient above , @xmath79 $ ] , is a smooth and irreducible deligne - mumford stack endowed with a proper and strongly representable map onto @xmath80 .
moreover , @xmath79 $ ] has the following modular description .
consider the stack @xmath26 ( over @xmath81 ) whose sections over a @xmath82scheme @xmath30 consist on families @xmath83 of genus @xmath7 quasistable curves over @xmath30 endowed with a balanced line bundle of relative degree @xmath4 over @xmath21 and whose morphisms consist on cartesian diagrams of the curves plus an isomorphism between the line bundles ( as in @xmath8 above , ignoring the sections ) .
there is a natural action of @xmath36 on @xmath84 given by fiberwise scalar multiplication on the line bundles . then @xmath79 $ ]
is the rigidification ( in the sense of @xcite ) of @xmath84 by the action of @xmath36 .
this result uses mainly the fact that the above git - quotient is geometric if and only if @xmath85 . in @xcite
we showed that , for @xmath74 , even if @xmath86 , @xmath84 is isomorphic to @xmath87 $ ] , where @xmath88 acts by projection on @xmath73 .
this implies that @xmath84 is a smooth and irreducible artin stack endowed with a universally closed map onto @xmath25 . since for @xmath4 and @xmath40 such that @xmath89 for some @xmath90
, @xmath26 is isomorphic to @xmath91 , we get that the same statement holds in general for any @xmath28 .
in the present section we will generalize the notions of quasistable curve and of balanced line bundle for curves with marked points .
our definitions will be done in such a way that , for @xmath11 , these coincide with the old notions introduced by gieseker and caporaso ( see definition 1.1 in @xcite ) , and that , for @xmath34 , @xmath6-pointed quasistable curve are the ones we get by applying the stabilization morphism defined by knudsen in @xcite ( see [ proof ] below ) to @xmath92-pointed quasistable curves endowed with an extra section without stability conditions . moreover , balanced line bundles on @xmath6-pointed quasistable curves correspond to balanced line bundles on the quasistable curves obtained by forgetting the points and by contracting the rational components that get _ quasidestabilized _ without the points ( see lemma [ balcorresp ] ) .
we start by recalling the definitions of ( semi)stable pointed curve and by introducing some notation .
[ pointedcurves ] an * @xmath6-pointed curve * is a connected , projective and reduced nodal curve @xmath21 together with @xmath6 distinct marked points @xmath93 such that @xmath21 is smooth at @xmath94 , @xmath95 .
let @xmath7 and @xmath6 be such that @xmath96 .
an * @xmath6-pointed stable curve * ( resp .
* semistable * ) is an @xmath6-pointed curve such that the number of points where a nonsingular rational component @xmath97 of @xmath21 meets the rest of @xmath21 plus the number of points @xmath94 on @xmath97 is at least @xmath98 ( resp .
@xmath99 ) .
a * family of @xmath6-pointed stable * ( resp . * semistable * ) curves is a flat and proper morphism @xmath83 together with @xmath6 distinct sections @xmath100 such that the geometric fibers @xmath101 together with @xmath102 , @xmath95 , are @xmath6-pointed stable ( resp .
semistable ) curves . note that @xmath6-pointed ( semi)stable curves admit chains of smooth rational curves meeting the rest of the curve in one or two points . by * rational tail * we mean a proper subcurve @xmath103 of @xmath21 with @xmath104 and @xmath105
. instead , proper subcurves @xmath106 of @xmath21 with @xmath107 and @xmath108 will be denoted by * rational bridges*. if @xmath21 is a strictly @xmath6-pointed semistable curve , a nonsingular rational component @xmath97 such that the number of points where @xmath97 meets the rest of @xmath21 plus the number of marked points @xmath94 on @xmath97 is exactly @xmath99 is called a * destabilizing * component .
an * exceptional component * is a destabilizing component without marked points .
[ quasistabledef ] an @xmath6-pointed * quasistable * curve is an @xmath6-pointed semistable curve @xmath21 such that 1 .
all destabilizing components are exceptional ; 2 .
exceptional components can not be contained in rational tails ; 3 .
each rational bridge contains at most one exceptional component .
a * family of @xmath6-pointed quasistable curves * is a proper and flat morphism with @xmath6 distinct sections whose geometric fibers are @xmath6-pointed quasistable curves .
see figure [ notquasistable ] for examples of pointed semistable curves which are not quasistable .
to each proper subcurve @xmath48 of @xmath21 , denote by @xmath109 the number of rational tails meeting @xmath48 .
[ balanced ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath110 and @xmath63 a line bundle on @xmath21 of degree @xmath4 .
we say that @xmath63 ( or its multidegree ) is * balanced * if the following conditions hold : * deg@xmath111 for every exceptional component @xmath97 of @xmath21 ; * the degree of @xmath63 on rational bridges can be either @xmath112 or @xmath113 ; * if @xmath103 is a rational tail of @xmath21 , then deg@xmath114 ; * for every connected proper subcurve @xmath48 of @xmath21 , if @xmath48 is not contained in any rational tail and in any rational bridge of @xmath21 , the following inequality holds @xmath115 denotes the number of rational bridges where the degree of @xmath63 is zero meeting @xmath48 in two points . note that if @xmath11 , @xmath109 and @xmath116 are equal to @xmath112 for all proper subcurves @xmath48 of @xmath21 , and inequality ( [ basic ] ) reduces to the
basic inequalityintroduced by gieseker in @xcite .
in fact , for @xmath11 , definition [ balanced ] coincides with the definition of balanced multidegree for quasistable curves introduced by caporaso in @xcite ( see also @xcite , def .
1.1 ) . using the notation of [ balanced ] , denote by @xmath117 and by @xmath118 then , inequality ( [ basic ] ) can be rewritten in the following way @xmath119 [ combdesc ] let @xmath21 be an @xmath6-pointed quasistable curve and suppose @xmath21 admits a balanced line bundle @xmath63 on @xmath21 of degree @xmath4 , for some @xmath120 .
then , if @xmath48 is a proper subcurve of @xmath21 that is contained in a rational tail , then @xmath121 and if @xmath48 is contained in a rational bridge , then @xmath122 is either equal to @xmath123 or @xmath124 .
in particular , the multidegree of @xmath63 on rational tails is unique and does not depend on @xmath4 .
let us begin by showing that the multidegree of @xmath63 on rational tails is uniquely determined .
so , suppose @xmath103 is a rational tail of @xmath21 . if @xmath103 is irreducible , then the multidegree of @xmath63 on @xmath103 is just the degree of @xmath63 on @xmath103 , which is necessarily @xmath125 .
now , suppose @xmath103 is reducible .
then there is exactly one irreducible component @xmath97 of @xmath103 meeting the rest of the curve ( in exactly one point ) .
we will call @xmath97 the foot of the rational tail .
@xmath97 is a smooth rational curve meeting the rest of @xmath103 in @xmath126 points : denote by @xmath127 the irreducible components of @xmath103 meeting @xmath97 .
then , each @xmath128 , @xmath129 is the foot of a rational tail contained in @xmath103 . in fact , each one of these , if not irreducible , is attached to another rational chain that can not intersect the rest of the curve since in that case @xmath103 would contain cycles ( which would force @xmath130 to be bigger than @xmath112 ) .
so , @xmath103 is the union of @xmath97 with @xmath131 rational tails meeting @xmath97 , and @xmath132 which implies that @xmath133 note that we do nt have to check if inequality ( [ basic ] ) is satisfied since it does not apply for subcurves of @xmath21 contained in rational tails .
now , iterating the same procedure , it is clear that the degree of each irreducible component of @xmath103 will be determined since @xmath103 is the union of @xmath97 with other @xmath126 rational tails with foots @xmath127 . now , consider a rational bridge @xmath106 .
then , @xmath106 meets the rest of the curve in two points , @xmath134 and @xmath135 , and these are linked by a chain of ( rational ) irreducible components of @xmath106 , @xmath136 , each one meeting the previous and the next one , for @xmath137 .
moreover , each @xmath128 can have rational tails attached .
denote by @xmath138 respectively the proper subcurves of @xmath106 consisting of @xmath128 and the rational tails attached to it , for @xmath139 .
so , @xmath140 is the union of @xmath141 rational bridges of length @xmath113 . by definition
, the degree of @xmath63 in @xmath106 can be either @xmath112 or @xmath113 , and the same holds for each @xmath142 , @xmath139 .
if @xmath143 , then , in order to the multidegree of @xmath63 on @xmath142 sum up to @xmath112 , @xmath144 must be equal to the number of rational tails attached to it : @xmath145 .
if , instead , the degree of @xmath63 on @xmath142 is equal to one , then deg@xmath146 must be equal to @xmath147 .
note that inequality ( [ basic ] ) gives that @xmath148 for @xmath149 , so either @xmath150 or @xmath151 are allowed .
the multidegree of @xmath63 on the rest of @xmath142 is fixed since @xmath152 consists of rational tails ( that , of course , can not intersect each other ) .
now , if @xmath106 contains one exceptional component @xmath97 among the @xmath128 s , say @xmath153 , the degree of @xmath106 must be necessarily @xmath113 ( note that on each rational tail we can have at most one exceptional component by definition of pointed quasistable curve ) .
in this case , we must have that @xmath154 , which implies that @xmath153 has no rational tails attached , and the degree of @xmath63 on it must be @xmath113 .
moreover , the degree of @xmath63 on the other rational subcurves @xmath142 , for @xmath155 , must be @xmath112 . if , instead , @xmath106 does not contain any exceptional component , then we can choose the degree of @xmath63 in @xmath106 to be either @xmath113 or @xmath112 .
if we choose it to be @xmath112 , then the degree of @xmath63 on each @xmath142 must be @xmath112 , for @xmath139 . if we choose it to be one , we can freely choose one of the @xmath142 s where the degree of @xmath63 is @xmath113 and in all the others the degree of @xmath63 must be @xmath112 .
[ balcorresp ]
let @xmath21 be an @xmath6-pointed quasistable curve with assigned multidegree on rational bridges .
let @xmath156 be the quasistable curve obtained by contracting all rational tails and rational bridges with assigned degree zero and by forgetting the points . then , for each degree @xmath4 , the set of balanced multidegrees on @xmath156 summing up to @xmath4 and the set of balanced multidegrees on @xmath21 summing up to @xmath4 with the given assigned multidegree on rational bridges are in bijective correspondence .
let @xmath157 be a balanced line bundle on @xmath156 with degree @xmath4 .
this means that , given a proper subcurve @xmath158 of @xmath156 , gieseker s
basic inequalityholds for @xmath158 , that is , @xmath159 and that the degree of @xmath157 on exceptional components is equal to @xmath113 .
let @xmath160 be an irreducible component of @xmath161 such that @xmath160 is not contained in any rational tail and in any rational bridge .
define the multidegree @xmath162 on @xmath21 by declaring that @xmath163 where @xmath164 is the image of @xmath160 on @xmath156 .
then we easily see that this defines a balanced multidegree on @xmath21 ( note that the multidegree of @xmath63 on rational bridges is fixed by hypothesis ) .
in fact , since @xmath165 and @xmath166 , we have that @xmath167 @xmath168 @xmath169 @xmath170 @xmath171 and also that @xmath172 @xmath173 so inequality ( [ basic ] ) holds for @xmath160 if and only if gieseker s basic inequality holds for @xmath164 .
it is easy to see that this is true more generally for any proper subcurve @xmath48 of @xmath21 not contained in any rational tail and in any rational bridge .
[ compstack ] for any integer @xmath4 and @xmath2 , denote by @xmath0 the following category fibered in groupoids over the category of schemes over @xmath46 .
objects over a @xmath46-scheme @xmath30 are families @xmath174 of @xmath6-pointed quasistable curves over @xmath30 and a balanced line bundle @xmath63 on @xmath21 of relative degree @xmath4 .
morphisms between two such objects are given by cartesian diagrams @xmath175^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_{i ' } } } \ ] ] such that @xmath66 , @xmath67 , together with an isomorphism @xmath68 .
note that @xmath0 contains @xmath8 for all @xmath29 . in what follows we will try to prove the following statement .
[ aim ] @xmath0 is a smooth and irreducible algebraic ( artin ) stack of dimension @xmath3 endowed with a universally closed map onto @xmath1 .
recall that , for @xmath11 , @xmath0 coincides with the stack @xmath26 defined in @xcite , section 3 ( see [ n=0 ] above ) , so theorem [ aim ] holds in this case .
now , following knudsen s construction of @xmath9 ( see @xcite ) , we will show that theorem [ aim ] holds for all @xmath29 using the following induction argument .
we will prove that , for @xmath34 , @xmath44 is isomorphic to the universal family over @xmath0 . by universal family over @xmath0
we mean an algebraic stack @xmath176 with a map onto @xmath0 admitting @xmath6-sections @xmath177 and endowed with an ( universal ) invertible sheaf @xmath178 such that , given a family @xmath179 of @xmath6-pointed quasistable curves and a balanced line bundle @xmath63 over @xmath64 of relative degree @xmath4 , the following diagram , commuting both in the upward and downward directions , @xmath180^{\pi_2 } \ar[d]^{f } & { \mathcal{z}_{d , g , n } } \ar[d]\\ { s } \ar[r]_{\mu_f } \ar @{- > } @/^/[u]^{s_i } & { { \overline}{\mathcal p}_{d , g , n } } \ar @{- > } @/_/[u]_{\sigma_{d , g , n}^i } } \ ] ] is cartesian and induces an isomorphism between @xmath181 and @xmath63 .
let @xmath176 be the category whose sections over a scheme @xmath182 are families of @xmath6-pointed quasistable curves @xmath183 endowed with a balanced line bundle @xmath184 of relative degree @xmath4 and with an extra section @xmath185 .
morphisms in @xmath176 are like morphisms in @xmath0 compatible with the extra section .
@xmath176 is an algebraic stack endowed with a forgetful morphism onto @xmath0 admitting @xmath6 sections given by the diagonals @xmath186 .
it is easy to see that , given a family of @xmath6-pointed quasistable curves @xmath179 and a balanced line bundle @xmath63 over @xmath64 of relative degree @xmath4 , diagram ( [ universal ] ) is cartesian , where @xmath187 is defined by associating to the identity morphism @xmath188 the fiber product of @xmath189 with itself @xmath190^{p_2 } \ar[d]^{p_1 } & { c } \ar[d]_{f}\\ { c } \ar[r]_{f } \ar @{- > } @/^/[u]^{f^*s_i } & { s } \ar @{- > } @/_/[u]_{s_i } } \ ] ] endowed with an extra section @xmath191 given by the diagonal and with the relative degree @xmath4 line bundle @xmath192 . given another object @xmath193 of @xmath64 , @xmath194 is defined to be the fiber product of @xmath195 and @xmath134 defined in ( [ identity ] ) , naturally endowed with the @xmath196 pullback sections and with the pullback of @xmath192 .
the universal sheaf over @xmath176 , @xmath178 , is defined by associating to each section @xmath197 of @xmath176 over @xmath182 , the line bundle @xmath198 over @xmath182 .
it is easy to see that this defines an invertible sheaf on @xmath176 .
now we easily check that @xmath178 is the universal sheaf over @xmath176 .
indeed , given an object @xmath193 on @xmath64 , @xmath199 , so it is isomorphic to the sheaf defined by @xmath63 on @xmath64 , considered as a stack .
we have just proved the following .
the algebraic stack @xmath176 defined above endowed with the invertible sheaf @xmath178 is the universal family over @xmath0 for the moduli problem of @xmath6-pointed quasistable curves with a balanced degree @xmath4 line bundle . now , suppose we can show that , for all @xmath29 , there is forgetful morphism @xmath39 from @xmath0 onto @xmath1 such that the image under @xmath39 of an @xmath6-pointed quasistable curve @xmath21 over @xmath30 endowed with a balanced degree @xmath4 line bundle is the stable model of @xmath21 over @xmath30 forgeting the line bundle .
these morphisms would yield commutative diagrams as follows , for all @xmath34 .
@xmath200^{\psi_{d , g , n } } \ar[dl]_{\phi_{d , g , n } } & \\ { { \overline}{\mathcal p}_{d , g , n-1 } } \ar[dr]_{\psi_{d , g , n-1 } } & & { { \overline}{\mathcal m}_{g , n } } \ar[dl]^{\pi_{g , n}}\\ & { { \overline}{\mathcal m}_{g , n-1 } } & } \ ] ] since @xmath201 and @xmath202 are the morphisms from the universal families over @xmath35 and @xmath203 , respectively , it follows that @xmath39 is universally closed ( or proper ) if and only if @xmath204 is . since
, by @xcite , @xmath205 is universally closed , we have that @xmath39 is universally closed for all @xmath29 .
so , our proof of theorem [ aim ] will follow if we can prove the following statement , which is the aim of the present paper .
[ main ] for all @xmath34 , @xmath44 is isomorphic to the algebraic stack @xmath176 .
in this section we prove some technical properties of line bundles over ( reducible ) nodal curves that will be used later in the proof of theorem [ main ] .
[ basicpropgen ] let @xmath21 be a nodal curve of genus @xmath7 and @xmath206 .
if @xmath207 for every connected subcurve @xmath208 , then @xmath209 . moreover , if strict inequality holds above for all @xmath208 , @xmath63 has no base points . to prove lemma [ basicpropgen ]
we will use the following lemma , which is lemma 2.2.2 in @xcite . [ 222 ] let @xmath21 be a nodal curve of genus @xmath7 and @xmath206 . if , for every connected subcurve @xmath48 of @xmath21 , @xmath210 , then @xmath211 .
the first assertion follows immediatly by serre duality and by lemma [ 222 ] .
now , assume that , for every @xmath208 , @xmath212 . we must show that @xmath63 has no base points .
consider a closed @xmath46-rational point @xmath213 in @xmath21 .
suppose that @xmath213 is a nonsingular point of @xmath21 .
we must show that @xmath214 by our assumption on @xmath63 , we can apply again lemma [ 222 ] to @xmath215 to get that @xmath216 . now , suppose @xmath213 is a nodal point of @xmath21 .
we must show that @xmath217 by contradiction , suppose these are equal .
then , if @xmath218 is the partial normalization of @xmath21 at @xmath213 , we get that @xmath219 where @xmath220 and @xmath221 are the preimages of @xmath213 by @xmath222 .
suppose that @xmath213 is not a disconnecting node for @xmath21 .
then , it is easy to see that we can apply lemma [ 222 ] to @xmath223 .
in fact , since @xmath213 is not a disconnecting node for @xmath21 , if @xmath224 contains @xmath220 and @xmath221 , then @xmath225 because @xmath226 , where @xmath208 is a subcurve of @xmath21 such that @xmath227 .
so , we get that @xmath228 , leading us to a contradiction .
suppose now that @xmath213 is a disconnecting node for @xmath21 .
then , @xmath182 is the union of two connected curves @xmath229 and @xmath230 of genus @xmath231 and @xmath232 , respectively , with @xmath233 .
suppose that @xmath234 and @xmath235 .
then , @xmath236 also in this case , we can apply lemma [ 222 ] to @xmath237 and to @xmath238 .
we get that @xmath239 a contradiction .
[ basicdualizing ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath7 with @xmath96 and let @xmath184 be either @xmath240 or @xmath241 ( if @xmath34 ) , where @xmath242 are the @xmath6 marked points of @xmath21 .
then , for all @xmath243 , we have that 1 . @xmath244 ; 2
. @xmath245 is globally generated .
according to lemma [ basicpropgen ] , it is enough to show that , given a subcurve @xmath48 of @xmath21 , @xmath246 , for all @xmath243 .
it is sufficient to prove the result for @xmath247 .
let @xmath48 be a subcurve of @xmath21 .
then , @xmath248 then , @xmath249 now , if @xmath48 is not a rational tail of @xmath21 , @xmath250 . instead
, if @xmath251 is a rational tail of @xmath21 , since @xmath21 is quasistable , it must contain at least two of the @xmath6 marked points and , if @xmath34 , at least one of these is among @xmath252 .
so , @xmath253 and the result follows .
[ basicprop ] let @xmath74 , @xmath34 and @xmath21 an @xmath6-pointed quasistable curve of genus @xmath254 endowed with a balanced line bundle @xmath63 of degree @xmath4 .
denote by @xmath255 the @xmath6 marked points of @xmath21 and let @xmath184 be the line bundle @xmath256 , for any @xmath257 .
then , we have that , for all @xmath258 , 1 . @xmath259 ; 2 .
@xmath260 is globally generated .
again , accordingly to lemma [ basicpropgen ] , the result follows if we prove that , for every subcurve @xmath48 of @xmath21 , @xmath246 .
it is enough to prove the result for @xmath261 .
let @xmath48 be a subcurve of @xmath21 which is not contained in any rational tail or in any rational bridge of @xmath21 . by definition of balanced
( see [ balanced ] above ) , we have that @xmath262 where @xmath263 is independent of @xmath4 .
take @xmath74 .
now , if @xmath48 is rational , @xmath264 , so @xmath265 .
in fact , if @xmath266 , @xmath21 would be rational , which is impossible ; by the other hand , if @xmath267 is @xmath113 or @xmath99 , @xmath48 should be contained in a rational tail or in a rational bridge of @xmath21 , respectively , which can not be the case by our assumption on @xmath48 .
suppose now that @xmath268 .
then , @xmath269 , since otherwise @xmath21 would have genus @xmath113 , which is impossible as well .
so , also in this case , @xmath265 . finally , if @xmath270 , it follows immediately that @xmath265 and the same holds for @xmath271 , which is asymptotically equal to @xmath122 since @xmath74 .
suppose now that @xmath48 is contained in a rational tail or in a rational bridge of @xmath21 .
then , from lemma [ combdesc ] , we have that @xmath272 . finally , if @xmath273 , @xmath274 and @xmath48 has at least @xmath99 marked points of @xmath21 .
so , @xmath275 and @xmath276 .
recall the following definition .
[ normgen ] a coherent sheaf @xmath277 on a scheme @xmath21 is said to be * normally generated * if , for all @xmath258 , the canonical map @xmath278 is surjective .
note that if we take @xmath277 to be an ample line bundle @xmath63 on @xmath21 , then if @xmath63 is normally generated it is , indeed , very ample ( see @xcite , section 1 ) .
in this case , saying that @xmath63 is normally generated is equivalent to say that the embedding of @xmath21 via @xmath63 on @xmath279 , for @xmath280 , is projectively normal . normal generation of line bundles on curves has been widely studied .
for instance , we have the following theorem of mumford : [ mumfordteo ] let @xmath21 be a nonsingular irreducible curve of genus @xmath7 .
then , any line bundle of degree @xmath281 is normally generated .
mumford s proof of theorem [ mumfordteo ] is based on the following lemma .
[ castelnuovo ]
let @xmath282 be a globally generated invertible sheaf on a complete scheme @xmath21 of finite type over @xmath46 and @xmath283 a coherent sheaf on @xmath21 such that @xmath284 then , 1 .
@xmath285 for @xmath286 , @xmath287 .
the natural map @xmath288 is surjective for @xmath289 .
the proof of the following statement uses mainly the arguments of knudsen s proof of theorem 1.8 in @xcite .
[ normgengen ] let @xmath21 be an @xmath6-pointed semistable curve of genus @xmath254 and @xmath290 .
if , for every subcurve @xmath48 of @xmath21 , @xmath212 , then @xmath291 is normally generated , where @xmath292 are the marked points of @xmath21 .
let @xmath293 denote the divisor @xmath294 .
let @xmath48 be a subcurve of @xmath21 .
since the multidegree of @xmath295 is non - negative , @xmath296 , so both statements of lemma [ basicpropgen ] hold also for @xmath297 .
so , we can apply the generalized lemma of castelnuovo with @xmath298 and @xmath299 , for any @xmath300 , and get that the natural map @xmath301 is surjective .
so , to prove that @xmath302 is normally generated , it remains to show that the map @xmath303 is surjective .
start by assuming that @xmath21 has no disconnecting nodes and consider the following commutative diagram @xmath304_{\beta } \ar[r ] & { \gamma(l\otimes\omega_x(d))\otimes \gamma(l\otimes\omega_x(d ) ) } \ar[d]^{\alpha}\\ { \gamma(l\otimes\omega_x^2(d ) ) \otimes \gamma(l(d ) ) } \ar[r]^{\gamma } & { \gamma((l\otimes\omega_x(d))^2 ) } } \ ] ] where @xmath305 indicates @xmath306 .
then , from the proof of theorem 1.8 in knudsen we have that , since @xmath254 and @xmath21 has no disconnecting nodes , @xmath307 is globally generated .
moreover , from lemma [ basicpropgen ] applied to @xmath308 , we get that @xmath309 .
so , we can apply the generalized lemma of castelnuovo with @xmath310 and @xmath311 to conclude that @xmath312 is surjective .
now , since @xmath21 has no disconnecting nodes , it can not have rational tails .
so , we can see @xmath21 as a semistable curve without marked points and apply corollary [ basicdualizing ] to @xmath21 and @xmath47 and get that @xmath313 .
since @xmath308 is globally generated , again by lemma [ basicpropgen ] , we can apply the generalized lemma of castelnuovo with @xmath314 and @xmath315 to conclude that also @xmath316 is surjective .
since the above diagram is commutative , it follows that also @xmath317 is surjective and we conclude . now , to show that @xmath317 is surjective in general ,
let us argue by induction in the number of disconnecting nodes of @xmath21 .
let @xmath213 be a disconnecting node of @xmath21 and @xmath318 and @xmath319 the subcurves of @xmath21 such that @xmath320 .
the surjectivity of @xmath317 follows if we can prove the folowing two statements . 1 . the image of @xmath317 contains sections a section @xmath321 such that @xmath322 ; 2 .
the image of @xmath317 contains @xmath323 .
the first statement follows immediately from the fact that @xmath302 is globally generated ( once more by [ basicpropgen ] ) .
let @xmath184 denote @xmath302 . to prove @xmath324 let us consider @xmath325 .
then , @xmath326 , with @xmath327 @xmath328 by induction hypothesis , @xmath329 is in the image of @xmath330 and @xmath331 in the image of @xmath332 with both @xmath329 and @xmath331 vanishing on @xmath213 .
write @xmath329 as @xmath333 , with @xmath334 and @xmath335 in @xmath336 , for @xmath337 .
let @xmath338 be the partial normalization of @xmath21 in @xmath213 and @xmath220 and @xmath221 be the preimages of @xmath213 on @xmath318 and @xmath319 , respectively , via @xmath222 .
since @xmath339 is globally generated , there is @xmath340 with @xmath341 .
then there are constants @xmath342 and @xmath343 for @xmath344 and @xmath345 such that @xmath346 define the sections @xmath347 and @xmath348 as @xmath334 ( resp .
@xmath335 ) on @xmath319 and as @xmath349 ( resp .
@xmath350 ) on @xmath318 , for @xmath344 . by ( [ incol ] ) , these are global sections of @xmath184 and @xmath351 maps to @xmath329 .
in fact , @xmath352 and , by hypothesis , @xmath353 and @xmath341 .
this implies that @xmath354 , so @xmath355 .
we conclude that @xmath329 is in the image of @xmath317 . in the same way
, we would get that also @xmath331 is in the image of @xmath317 , so @xmath324 holds and we are done .
the next result follows from the proof of theorem 1.8 in @xcite , however we include it here since we shall use it in the following slightly more general form .
[ normgendualizing ] let @xmath21 be an @xmath6-pointed semistable curve of genus @xmath254 and let @xmath356 be the marked points of @xmath21 . then ,
for @xmath357 , @xmath358 is normally generated .
is an immediate consequence of proposition [ normgengen ] and corollary [ basicdualizing ] .
[ normgenprop ] let @xmath21 be an @xmath6-pointed quasistable curve of genus @xmath7 and @xmath63 a balanced line bundle on @xmath21 of degree @xmath74 . then , if @xmath34 , @xmath359 is normally generated .
since @xmath21 is an @xmath6-pointed quasistable curve , it is easy to see that @xmath21 , endowed with the first @xmath360 marked points @xmath361 , is an @xmath92-pointed semistable curve . moreover , by corollary [ basicprop ] , we can apply proposition [ normgengen ] to @xmath362 .
the result follows immediately now .
[ projnormal ] let @xmath74 , @xmath34 and @xmath21 an @xmath6-pointed quasistable curve of genus @xmath254 endowed with a balanced line bundle @xmath63 .
let @xmath184 denote the line bundle @xmath363 , where @xmath364 are the marked points of @xmath21 .
we have : 1 .
@xmath184 is normally generated ; 2 .
@xmath184 is very ample .
statement @xmath365 follows from the proof of the previous proposition , which obviously works for @xmath366 as well . to show @xmath324 it is enough to observe that @xmath184 is ample since its degree on each irreducible component of @xmath21 is positive .
since @xmath184 is also normally generated , it follows that @xmath184 is indeed very ample ( see @xcite , section 1 ) .
the following definition generalizes the notion of contraction introduced by knudsen in @xcite to the more general case of pointed quasistable curves endowed with balanced line bundles .
[ contraction ] let @xmath367 be an @xmath368-pointed curve endowed with a line bundle of relative degree @xmath4 .
a contraction of @xmath21 is an @xmath30-morphism from @xmath21 into an @xmath6-pointed curve @xmath369 endowed with a line bundle of relative degree @xmath4 , @xmath157 , and with an extra section @xmath370 such that 1 .
for @xmath371 , the diagram @xmath372^{f } \ar[d]^{\pi } & { x ' } \ar[dl]_{\pi'}\\ { s } \ar @{- > } @/^/[u]^{s_i }
\ar @{- > } @/_/[ur]_{t_i } } \ ] ] commutes both in the upward and downward directions , 2 .
@xmath373 , 3 .
@xmath374 induces an isomorphism between @xmath375 and @xmath376 , 4 .
the morphism induced by @xmath374 in the geometric fibers @xmath101 is either an isomorphism or there is an irreducible rational component @xmath377 such that @xmath378 which is contracted by @xmath374 into a closed point @xmath379 and @xmath380 is an isomorphism .
[ quasistablecont ] let @xmath381 and @xmath382 a contraction from an @xmath368-pointed curve @xmath383 , endowed with a degree @xmath4 line bundle @xmath63 into an @xmath6-pointed curve @xmath384 , endowed with a degree @xmath4 line bundle @xmath157 and with an extra point @xmath385 .
then , if @xmath386 is quasistable , also @xmath387 is quasistable and , in this case , @xmath63 is balanced if and only if @xmath157 is balanced . clearly , the assertion follows trivially if no irreducible component of @xmath21 gets contracted by @xmath374 .
so , assume that there is an irreducible component @xmath97 of @xmath21 that gets contracted by @xmath374 .
then , necessarily , @xmath388 , so no exceptional component of @xmath21 gets contracted .
moreover , the condition that @xmath389 implies that @xmath390 is trivial on the fibers of @xmath374 , so it must have degree @xmath112 on @xmath97 .
now , we have only two possibilities : either @xmath385 is a smooth point of @xmath156 or it is nodal
. start by considering the case when @xmath385 is smooth . since @xmath391
, we must have that @xmath392 .
so , if @xmath21 is quasistable , @xmath97 must contain exactly another special point @xmath393 , for some @xmath394 and @xmath385 must be a smooth point of @xmath156 .
let @xmath395 be the irreducible component of @xmath156 containing @xmath385 and @xmath283 the correspondent irreducible component of @xmath21 ( recall that @xmath374 establishes an isomorphism between @xmath283 and @xmath395 away from @xmath385 ) .
if @xmath396 , then it is clear that also @xmath156 is quasistable . instead , if @xmath283 is rational , even if @xmath397 , @xmath395 has one more marked point than @xmath283 .
so , @xmath156 has the same destabilizing and exceptional components than @xmath21 and it follows that @xmath156 is a quasistable @xmath6-pointed curve . let us now check that , if we are contracting a rational tail of a quasistable curve , @xmath63 is balanced if and only if @xmath157 is balanced . from the definition of contraction , we get that the multidegree of @xmath398 in the irreducible components of @xmath21 that are not contracted must agree with the multidegree of @xmath399 in their images by @xmath374 . in our case
, this implies that the multidegree of @xmath157 on the irreducible components of @xmath156 coincides with the multidegree of @xmath63 on the corresponding irreducible components of @xmath21 , except on @xmath395 , where we must have that @xmath400 so , given a proper subcurve @xmath158 of @xmath156 , if @xmath158 does not contain @xmath385 , the balanced condition will be clearly satisfied by @xmath63 on @xmath48 if and only if it is satisfied by @xmath157 on @xmath158 since @xmath401 , @xmath402 and @xmath403 .
now , suppose @xmath404 and let @xmath48 be the preimage of @xmath158 by @xmath374 .
then , @xmath405 , @xmath406 , @xmath407 and @xmath408 , which implies that @xmath409 and @xmath410 since also @xmath411 , we conclude that , if @xmath63 is balanced , then @xmath157 is balanced too .
now , to conclude that the fact that @xmath157 is balanced implies that also @xmath63 is balanced we have to further observe that the degree of @xmath63 on @xmath97 is forced to be @xmath125 since @xmath97 contains @xmath99 special points and that the inequality ( [ basic ] ) is verified on @xmath412 ( that does not correspond to any proper subcurve of @xmath156 ) , which follows since @xmath413 . now , suppose @xmath385 is a nodal point of @xmath21 . then , since @xmath391 , we must have that @xmath414 and that the only marked point of @xmath21 in @xmath97 is @xmath415 ( otherwise , the condition that @xmath416 for @xmath394 would imply that one of these @xmath417 s should coincide with @xmath418 , which is nodal , and @xmath387 would not be a pointed curve ) .
we must do a further distinction here .
suppose first that @xmath97 intersects just one irreducible component of @xmath21 : call it @xmath283 and @xmath395 its associated irreducible component on @xmath156 .
now , if @xmath419 , and if @xmath283 is rational , @xmath156 is an irreducible genus @xmath113 curve , which is clearly quasistable . if , instead , @xmath420 or if @xmath421 , we see that all destabilizing and exceptional components of @xmath156 correspond to destabilizing and exceptional components of @xmath21 and are contained in the same type of rational chains
if , instead , @xmath97 intersects two distinct irreducible components of @xmath21 , it is easy to see that , also in this case , all destabilizing and exceptional components of @xmath156 correspond to destabilizing and exceptional components of @xmath21 and are contained in the same type of rational chains .
so , @xmath387 will be quasistable if @xmath386 is .
now , since @xmath415 is the only marked point in @xmath97 , all irreducible components of @xmath156 have the same marked points that the corresponding irreducible components of @xmath21 , so @xmath389 implies that the multidegree of @xmath63 on irreducible components of @xmath156 coincides to the multidegree of @xmath63 on the corresponding irreducible components of @xmath21 and that the degree of @xmath63 on @xmath97 is zero .
let @xmath158 be a proper subcurve of @xmath156 and @xmath48 the corresponding proper subcurve of @xmath21 . if @xmath48 does not intersect @xmath97 or if it intersects @xmath97 in a single point , then it is immediate to see that inequality ( [ basic ] ) holds for @xmath63 and @xmath48 if and only if it holds for @xmath157 and @xmath158 .
if , instead , @xmath48 intersects @xmath97 in two points , then @xmath422 , @xmath423 , @xmath424 and @xmath425 , so , we get that @xmath426 and @xmath427 since also @xmath428 , we conclude that if we are contracting a rational bridge , if @xmath63 is balanced , also @xmath157 will be balanced .
now , to conclude that the fact that @xmath157 is balanced implies that also @xmath63 is balanced we have to further observe that , by definition of contraction , the degree of @xmath63 on @xmath97 is forced to be @xmath112 and that the inequality ( [ basic ] ) is verified on @xmath412 ( that does not correspond to any proper subcurve of @xmath156 ) , which is true since @xmath429 .
the following lemma is corollary 1.5 of @xcite .
[ cor1.5 ] let @xmath21 and @xmath182 be @xmath30-schemes and @xmath430 a proper @xmath30-morphism , whose fibers are at most one - dimensional .
let @xmath277 be a coherent sheaf on @xmath21 , flat over @xmath30 such that @xmath431 for each closed point @xmath432 .
then @xmath433 is @xmath30-flat , @xmath434 and , given any morphism @xmath435 , there is a canonical isomorphism @xmath436 if , moreover , @xmath437 is globally generated we have also that the canonical map @xmath438 is surjective .
[ morebasicprop ] let @xmath439 be an @xmath368-pointed quasistable curve endowed with a balanced line bundle of degree @xmath74 .
let @xmath184 be either the line bundle @xmath375 or @xmath440 .
then , for all @xmath441 , we have that 1 . @xmath442 is @xmath30-flat
; 2 . @xmath443 ; 3 . for all @xmath287 ,
the natural map @xmath444 is surjective ; 4 .
@xmath445 is surjective .
\(1 ) ( 2 ) and ( 4 ) follow immediately from lemma [ cor1.5 ] and corollaries [ basicprop ] with @xmath446 and [ basicdualizing ] , which assert that we can apply lemma [ cor1.5 ] to @xmath447 and @xmath184 , in both cases .
let us now show that ( 3 ) holds . from propositions
[ normgenprop ] and [ normgendualizing ] , the statement holds if @xmath381 . since @xmath184 satisfies the hypothesis of lemma [ cor1.5 ] , the formation of @xmath448 commutes with base change
so , @xmath449 is surjective at every geometric point of @xmath30 and we use nakayama s lemma to conclude that @xmath449 is surjective .
we now show that knudsen s main lemma also holds for quasistable pointed curves and balanced line bundles of high degree .
[ mainlemma ] let @xmath74 and consider a contraction @xmath450 as in definition [ contraction ] .
denote by @xmath184 and @xmath451 , respectively , the line bundles @xmath375 and @xmath452 .
then , for all @xmath258 , we have that 1 . @xmath453 and @xmath454 ; 2 .
@xmath455 3 .
@xmath456 for @xmath289 . that @xmath457 is isomorphic to @xmath260 comes from our definition of contraction morphism .
so , also @xmath458 is isomorphic to @xmath459 .
so , composing this with the canonical map from @xmath460 into @xmath458 , we get a map @xmath461 since the fibers of @xmath374 are at most smooth rational curves and @xmath184 is trivial on them , also @xmath260 is trivial on the fibers of @xmath374 , so we can apply lemma [ cor1.5 ] to it .
since the previous morphism is an isomorphism on the geometric fibers of @xmath374 and @xmath462 is flat over @xmath30 , we conclude that it is an isomorphism over @xmath30 .
that @xmath463 follows directly from lemma [ cor1.5 ] while @xmath464 follows from @xmath365 and the leray spectral sequence , which is degenerate by @xmath324 . from now on , consider @xmath74
. using the contraction morphism defined above , we will try to define a natural transformation from @xmath44 to @xmath176 .
let @xmath367 be an @xmath368-pointed quasistable curve with a balanced line bundle @xmath63 of relative degree @xmath4 . for @xmath289 ,
define @xmath465 since we are considering @xmath74 , then , by corollary [ morebasicprop ] , @xmath466 , so @xmath467 is locally free of rank @xmath468 , for @xmath287 , .
consider @xmath469 again by corollary [ morebasicprop ] , the natural map @xmath470 is surjective , so we get a natural @xmath30-morphism @xmath372^{q } \ar[d]^{\pi } & { \mathbb p(\mathcal s_1 ) } \ar[dl]\\ { s } \ar @{- > } @/^/[u]^{s_i } } \ ] ] define @xmath471 , @xmath472 , and , by abuse of notation , call @xmath221 the ( surjective ) @xmath30-morphism from @xmath21 to @xmath182 .
@xmath282 is an invertible sheaf over @xmath182 and @xmath473 .
moreover , by corollary [ morebasicprop ] ( 3 ) , we have that @xmath474 so , since all @xmath467 are flat over @xmath30 ( again by corollary [ morebasicprop ] ) , also @xmath182 is flat over @xmath30 , so it is a projective curve over @xmath30 of genus @xmath7 ( since the only possible contractions are of rational components ) .
so , if we endow @xmath475 with the sections @xmath476 , for @xmath477 , the extra section @xmath478 and @xmath479 as above , we easily conclude that @xmath480 is a contraction .
now , consider a morphism @xmath175^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[d]_{\pi ' } \\ { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_i ' } } \ ] ] of @xmath368-pointed quasistable curves with balanced line bundles @xmath63 and @xmath157 of relative degree @xmath4 in @xmath0 and let us see that @xmath481 , where @xmath482 is the isomorphism between @xmath63 and @xmath483 , induces in a canonical way a morphism in @xmath176 between the contracted curves .
define @xmath484 .
recall that , to give an @xmath485-morphism from @xmath486 to @xmath487 is equivalent to give a line bundle @xmath184 on @xmath486 and a surjection @xmath488 where by @xmath489 we denote the natural morphism @xmath490 .
@xmath491_{\pi^c } \ar @{-- > } @/^18pt/[rrr ] & { x } \ar[l]_{q } \ar[d]^{\pi } \ar[r]^{\beta_2 } & { x ' } \ar[r]^{q ' } \ar[d]_{\pi ' } & { \mathbb p(\mathcal s ' ) } \ar[dl]\\ & { s } \ar[r]_{\beta_1 } \ar @{- > } @/^/[u]^{s_i } & { s ' } \ar @{- > } @/_/[u]_{s_i ' } } \ ] ] since we are considering @xmath74 , for @xmath492 , @xmath493 is constant and equal to @xmath494 .
so , we can apply the theorem of cohomology and base change to conclude that there is a natural isomorphism @xmath495 since we have also the isomorphism @xmath496 we get a natural isomorphism @xmath497 composing this with the natural surjection @xmath498 we conclude that there is a canonical surjection @xmath499 defining a natural @xmath485-morphism from @xmath500 .
this morphism naturally determines a morphism from @xmath501 to @xmath502 , where @xmath502 is the image of @xmath156 in @xmath487 via @xmath503 , inducing a natural isomorphism between @xmath504 and the pullback @xmath505 , the restriction of @xmath506 to @xmath502 .
the fact that all these morphisms are canonical implies that this construction is compatible with the composition of morphisms , defining a natural transformation .
we have just proved the following proposition .
there is a natural transformation @xmath507 from @xmath44 to @xmath176 given on objects by the contraction morphism defined above .
we can now prove our main theorem .
( of theorem [ main ] ) we must show that the contraction functor is an equivalence of categories , i. e. , it is fully faithful and essentially surjective on objects . the fact that it is full is immediate .
we can also conclude easily that it is faithful from the fact that a morphism of @xmath508 fixing 3 distinct points is necessarily the identity .
in fact , contraction morphisms induce isomorphisms on the geometric fibers away from contracted components and the contracted components have at least 3 special points and it is enough to use flatness to conclude . in order to show that @xmath507 is essentially surjective on objects we will use knudsen s stabilization morphism ( see @xcite , def .
2.3 ) and check that it works also for pointed quasistable curves with balanced line bundles .
so , let @xmath83 be an pointed quasistable curve , with @xmath6 sections @xmath509 , an extra section @xmath510 and a balanced line bundle @xmath63 on @xmath21 , of relative degree @xmath4 .
let @xmath511 be the @xmath512-ideal defining @xmath510 .
define the sheaf @xmath513 on @xmath21 via the exact sequence @xmath514 where @xmath515 is the diagonal morphism , @xmath516 .
define @xmath517 and let @xmath518 be the natural morphism from @xmath519 to @xmath21 .
theorem 2.4 of @xcite asserts that , in the case that @xmath21 is a pointed stable curve , the sections @xmath520 and @xmath510 have unique liftings @xmath521 to @xmath519 making @xmath522 an @xmath368-pointed stable curve and @xmath523 a contraction .
one checks easily that the same construction holds also if @xmath21 is a quasistable pointed curve instead of a stable one .
in fact , the assertion is local on @xmath30 , the problem being the points where @xmath510 meets non - smooth points of the fibre or other sections since in the other points @xmath519 is isomorphic to @xmath21 . in the case where @xmath510 meets a non - smooth point of a geometric fiber , locally @xmath519 is the total transform of the blow - up of @xmath21 at that point with the reduced structure and @xmath524 is a smooth point of the exceptional component . in the case where @xmath510 coincides with another section @xmath525 in a geometric fiber @xmath101 of @xmath21 , then , locally , on @xmath519 is the total transform of the blow - up of @xmath21 at @xmath102 , again with the reduced structure , and @xmath526 and @xmath524 are two distinct smooth points of the exceptional component .
let @xmath527 .
then the multidegree of @xmath528 on a geometric fiber @xmath529 coincides with the multidegree of @xmath63 in the irreducible components of @xmath529 that correspond to irreducible components of @xmath21 and , in the possibly new rational components , the degree is @xmath112 .
so , @xmath528 is balanced of relative degree @xmath4 . to conclude
, we must check that @xmath530 is isomorphic to @xmath21 . by definition , @xmath530 is given by the image of @xmath519 on @xmath531 .
consider the line bundle @xmath375 on @xmath21 . by corollary [ morebasicprop ]
, there is a natural surjection @xmath532 but , since @xmath533 is naturally isomorphic to @xmath534 , we get a natural surjection @xmath535 so , equivalently , a morphism @xmath374 from @xmath21 to @xmath536 .
since @xmath537 induces the natural morphism @xmath538 , whose image is @xmath530 , naturally the image of @xmath374 is @xmath530 .
it is easy to check that @xmath374 is an isomorphism on the geometric fibers , so , by flatness , we conclude that @xmath374 gives an @xmath30-isomorphism between @xmath21 and @xmath530 as pointed quasistable curves and determines an isomorphism between the respective balanced degree @xmath4 line bundles .
now , for each @xmath34 , we will try to construct a morphism @xmath539 fitting in diagram ( [ induction ] ) above .
let @xmath540 , @xmath394 be an @xmath6-pointed quasistable curve over @xmath30 .
denote by @xmath541 the line bundle @xmath542 .
then , by corollary [ morebasicprop ] , @xmath543 , so it is locally free and there is an @xmath30-morphism @xmath544 making the following diagram commute .
@xmath545^{\gamma } \ar[dr]^{\pi } & & { \mathbb p(\pi_*(\omega ) ) } \ar[dl ] \\ & { s } \ar @{- > } @/^/[ul]^{s_i } & } \ ] ] the restriction of @xmath316 to any fiber @xmath101 of @xmath447 maps @xmath101 to its stable model in @xmath546 , which is naturally endowed with the sections @xmath547 , for @xmath548 .
this follows from the fact that @xmath541 is very ample on the stable components of each fiber , whereas it has degree @xmath112 on the exceptional components . moreover , @xmath549 is flat over @xmath30 .
in fact , from corollary [ morebasicprop ] , for any @xmath287 , the natural map @xmath550 is surjective .
it follows that @xmath551 , which is flat over @xmath30 because each @xmath552 is @xmath30-flat , again by corollary [ morebasicprop ] .
it is easy to check that this yields a surjective morphism @xmath39 from @xmath0 onto @xmath1 fitting in diagram ( [ induction ] ) and making it commutative .
let @xmath439 be an @xmath368-pointed quasistable curve of genus @xmath7 endowed with a balanced line bundle @xmath63 of relative degree @xmath4 over @xmath21 .
it is immediate to check that , restricting ourselves to the geometric fibers of @xmath447 , the diagram is commutative since in both directions we get the @xmath6-pointed curve which is the stable model of the initial one , after forgetting the last point .
now , since all families are flat over @xmath30 , we conclude that the diagram is commutative .
the surjectivity of @xmath39 follows from the fact that @xmath205 is surjective ( see @xcite , proposition 4.12 ) and from the commutativity of the diagram because @xmath202 and @xmath201 are the universal morphisms onto @xmath35 and @xmath9 , respectively .
so , the fibers of @xmath39 over a pointed curve @xmath553 are the quasistable pointed curves @xmath21 with stable model @xmath156 endowed with balanced degree @xmath4 line bundles .
let @xmath21 be an @xmath6-pointed quasistable curve over @xmath46 . by applying the contraction morphism
we get an @xmath92-pointed quasistable curve with an extra section .
if we forget about this extra section and we iterate the contraction procedure @xmath6 times , at the end we get a quasistable curve with no marked points , call it @xmath554 . denote by @xmath374 this morphism from @xmath21 to @xmath554 .
let @xmath555 be the dualizing sheaf of @xmath554 .
for each proper subcurve @xmath556 of @xmath554 , the degree of @xmath555 in @xmath556 is @xmath557 . in particular
, it has degree @xmath112 on exceptional components of @xmath554 .
consider now the pullback of @xmath555 via @xmath374 , @xmath558 .
this is a line bundle on @xmath21 having degree @xmath112 on rational bridges and on rational tails ; moreover , given a proper subcurve @xmath48 of @xmath21 whose image under @xmath374 is a proper subcurve @xmath556 of @xmath554 , @xmath558 has degree @xmath559 on @xmath48 .
so , a line bundle @xmath63 of degree @xmath4 on @xmath21 with given balanced multidegree on rational tails and rational bridges of @xmath21 is balanced on @xmath21 if and only if @xmath560 is balanced on @xmath21 of degree @xmath561 and with the same multidegree on rational tails and rational bridges .
in fact , for each proper subcurve @xmath48 of @xmath21 which is not contained in rational tails or rational bridges , we have that @xmath562 @xmath563 @xmath564 and similarly that @xmath565 @xmath566 so @xmath567 satisfies inequality ( [ basic ] ) if and only if @xmath568 does . in conclusion , we have the following result .
let @xmath4 and @xmath40 be integers such that there exists an @xmath90 such that @xmath569 .
then , @xmath0 and @xmath43 are isomorphic .
we must show that there is an equivalence of categories between @xmath0 and @xmath43 .
so , let @xmath570 , @xmath394 be an object of @xmath0 . consider its image under @xmath571 and denote it by @xmath572 . according to [ const ]
, there is an @xmath30-morphism @xmath573 .
then , by what we have seen above , @xmath574 is a balanced line bundle of relative degree @xmath40 over @xmath21 , so @xmath575 .
it is easy to check that this defines an equivalence between @xmath0 and @xmath43 . for all @xmath34 ,
there are forgetful morphisms @xmath576 endowed with @xmath6 sections @xmath577 yielding cartier divisors @xmath578 , @xmath394 such that @xmath579 gives an isomorphism between @xmath0 and @xmath578 .
note that each object @xmath570 , @xmath394 , in @xmath0 has automorphisms given by scalar multiplication by an element of @xmath580 along the fibers of @xmath581 . since these automorphisms fix @xmath582 , there is no hope @xmath0 can be representable over @xmath1 ( see @xcite , 4.4.3 ) .
the rigidification procedure , defined in @xcite , fits exactly on our set up and produces an algebraic stack with those automorphisms removed .
denote by @xmath583 the rigidification of @xmath0 along the action of @xmath36 .
exactly because the action of @xmath36 on @xmath0 leaves @xmath1 invariant , the morphism @xmath39 descends to a morphism from @xmath583 onto @xmath1 , which we will denote again by @xmath39 , making the following diagram commutative .
@xmath584^{\psi_{d , g , n } } \ar[dl]_{\phi_{d , g , n } } & \\ { { \overline}{\mathcal p}_{d , g , n-1 } } \ar[dr]_{\psi_{d , g , n-1 } } & & { { \overline}{\mathcal m}_{g , n } } \ar[dl]^{\pi_{g , n}}\\ & { { \overline}{\mathcal m}_{g , n-1 } } & } \ ] ] so , the same argument we used to show that @xmath39 is universally closed for all @xmath29 if and only if @xmath205 is universally closed holds also in this case .
moreover , since , for @xmath11 , we have that @xmath585\to { \overline}{\mathcal m}_g$ ] is proper and strongly representable if and only if @xmath23 , we have that the same statement holds in general for every @xmath29
. let @xmath586 be the rigidification of @xmath0 under the action of @xmath36 . then ,
if @xmath23 , @xmath583 is a deligne - mumford stack of dimension @xmath3 with a proper and strongly representable morphism onto @xmath1 .
this paper is part of my ph.d . thesis .
i am very grateful to my advisor professor lucia caporaso for the patience with which she followed this work very closely and for always transmitting me lots of encouragement and mathematical enthusiasm .
i am also grateful to simone busonero and filippo viviani for giving me important suggestions .
d. mumford : varieties defined by quadratic equations . with an appendix of g. kempf , in _
questions on algebraic varieties _ , ( c.i.m.e .
, iii ciclo , varenna , 1969 ) pp .
29 - 100 , edizioni cremonese , roma , 1970 .
e. witten , algebraic geometry associated with matrix models of two - dimensional gravity , _ topological methods in modern mathematics ( stony brook , ny , 1991 ) _ , publish or perish , houston , tx ( 1993 ) , 235269 ,[/INST] in this paper we give a construction of algebraic ( artin ) stacks @xmath0 endowed with a modular map onto the moduli stack of pointed stable curves @xmath1 , for @xmath2 .
the stacks @xmath0 are smooth , irreducible and have dimension @xmath3 .
they yield a geometrically meaningful compactification of the degree @xmath4 universal picard stack over @xmath5 , parametrizing @xmath6-pointed smooth curves together with a degree @xmath4 line bundle .
[ section ] [ teo]proposition [ teo]lemma [ teo]remark [ teo]definition [ teo]example [ teo]examples [ teo]corollary </s> |
Playboy
It's here! I'm honored to share that @Playboy has named me a 2016 #Renegade and has featured me in their piece!! *LINK IN BIO* πΈ: @gokateshoot A photo posted by Noor Tagouri (@ntagouri) on Sep 22, 2016 at 6:55am PDT
Last year, Playboy made a public decision to shake nude photographs from the brand. The announcement was initially met by skepticism, but since then, the magazine has successfully enhanced the place of actual journalism within its pages. In the latest issue, Playboy reporters wrote about race in a feature on Paul Beatty, a black novelist. They discussed activism in an interview with rapper Vince Staples. And, for the first time ever, Playboy featured a Muslim American in the magazine. Journalist Anna del Gaizo interviewed aspiring news anchor Noor Tagouri about the American-hijabi (headscarf or veil-wearing) experience, her aspirations, and the current political climate. It was a great opportunity for a Muslim woman to get some visibility.
But none of what she talked about seemed to matter to the droves of critics Tagouri, a reporter for Newsy, subsequently encountered online. Articles published in large outlets question whether or not she let Muslims down. On Twitter, users called her ugly names like #hoejabi. One Muslim publication even questioned her commitment to God. As a Muslim man, I try to avoid speaking for Muslim women, as that happens enough as it is. But right now, in a campaign season during which the Republican party has made white supremacy and Islamophobia central to its platform, this controversy around a wonderful interview of an awesome Muslim woman demands a response.
Far too often, Muslim women are being told how to dress and behave by groups who are neither women nor Muslim. Men in Saudi Arabia have constructed laws forcing women into a strict dress code that is simultaneously banned by men in France. Men are using the government to enforce their own principles on an issue that ought to be up to a womanβs free will.
For Muslim women who choose the hijab, the outward presentation of their faith makes them vulnerable to both sides of an increasingly polarizing and politicized conversation about the rights of women. That is why when someone like Noor Tagouri speaks out and treads new ground as an individual, she deserves the full support of the entire Muslim community. ||||| This story appears in the October 2016 issue of Playboy. Subscribe
The men and women in this series will change how you think about business, music, porn, comedy, gaming and more. Theyβve risked it allβeven their livesβto do what they love, showing us what can be accomplished if we break the rules. Meet the Renegades of 2016.
For anyone with preconceived ideas about women who choose to wear a headscarf every day, Noor Tagouri is disorienting. Sheβs simply not what you expect: a 22-year-old journalist (she likes to call herself a storyteller) on the verge of becoming this countryβs first hijab-wearing news anchor. As of June, sheβs an on-air reporter for Newsy, where she provokes the sort of confusion we could use right now, in part by making a surprisingly bold case for modesty. As a badass activist with a passion for demanding change and asking the right questions, accompanied by beauty-ad-campaign looks, Tagouri forces us to ask ourselves why we have such a hard time wrapping our minds around a young woman who consciously covers her head and wonβt take no for an answer.
A West Virginia native and first-generation Libyan American, Tagouri graduated from college at the age of 20. In 2012, her #LetNoorShine campaign went viral. Her 2015 TEDx talk advocated unapologetic individuality, and her YouTube channel draws tens of thousands of viewers. More recently, she collaborated with streetwear brand Lisβn Up Clothing on a fashion line that includes a Jean-Michel Basquiatβinspired sweatshirt. Half the purchase proceeds go to Project Futures, an anti-human-trafficking organization. Americans have a long way to go when it comes to how we regard Muslims, but with Tagouri burning down stereotypes and blazing new paths, weβre a healthy stride closer.
Your goal is to become the first hijabi anchor on commercial U.S. television. Whatβs the biggest challenge you face in your work?
The biggest challenge I face as a storyteller is the process of getting people to trust you enough to tell their stories. Our society has seemingly become so desensitized to violence, abuse, death, rape and trauma. I find that people who go through these traumatic experiences have a hard time trusting reporters. Just a few days ago, I had an anonymous artist tell me he doesnβt do interviews because he doesnβt want reporters to βtake [his] words and run with itβ.
β Being a hijabi Muslim woman helps me gain trust. I say, βI know what itβs like to be misrepresented in the media. I wonβt do that to you.β β
People want to be valued and heard. Their experiences are so personal and they want their voices to come through in a story. Itβs a process, but building that level of trust takes time, effort and patience. Iβm actually struggling with a few powerful stories right now because he people involved are still suffering. Unfortunately theyβre having a hard time being okay with someone sharing their story. Which is totally understandable, but itβs a process.
How have you confronted that?
Being able to share in the vulnerability of the people I talk to helps me gain their trust. I recently did a documentary titled The Trouble Theyβve Seen: The Forest Haven Story, about one of the worst cases of institutional and medical abuse in the history of the U.S. When I decided to do the piece, I knew I needed to talk to people close to the caseβsomeone who lived in the institution, a parent, their family members, an employee and the lawyers involved. It took a few visits with each person to get them to agree to do an interview.
To be honest, I think being a hijabi Muslim woman, helped me gain that trust. I know what itβs like to have the narrative of our community be skewed and exploited in the media. I was like, βHey, I know what itβs like to be misrepresented in the media. I wonβt do that to you. I want to tell your story because itβs important and deserves justice.β I know first-hand that once people are re-empowered, they realize their own story is powerful and they begin to share. Itβs incredibly rewarding and can even help enlighten or save others.
How have you dealt with backlash, especially in our current political climate?
If by backlash you mean hate and criticism, I donβt read or pay attention to any of it. Itβs just negative energy and unhealthy. I make sure to keep a great circle of people around me who keep me grounded. Whether itβs at work or at home, the people who have my best interest at heart voice their concerns and their critiques, and I work on them. Besides that, I just do the best I can to not worry about people who get upset because they donβt like something that I wear or say.
The first story I did with Newsy was on Middle Eastern and North African Americans being considered "whiteβ on the U.S. census and how that might change on the 2020 census. I referred to it as βWhite Without the Privilege.β There was a ton of backlash on Facebook from people who didnβt like the story. It was comical seeing people telling me to βgo back homeβ when in fact, I was born in West Virginia. My team insisted that I never read the comments, so I stopped. The thing is, that story was based on facts. I constantly remind myself to just do the work I believe in and ignore the angry people behind computer screens.
At what point will you feel like youβve succeeded in effecting change?
I will have succeeded in effecting change when all girls realize they can do anything they want without having to sacrifice who they are as a person. I may dress a little differentβIβm a reporter who happens to wear a head scarf and I live in my hoodieβbut being a story teller, motivational speaker, entrepreneur and unapologetically myself has opened so many doors for thousands of people. I recently had a mom come up to me and tell me that her daughter is in the 6th grade and had just started wearing the hijab. She shared how a lot of the other girls tease her and put her down because of the hijab. She went on to tell me that her daughter watches all of my videos and every time she gets picked on, she pulls up my Instagram or tells them to βgoogle Noor Tagouri and then talk to me.β Those are the moments that hit me. And I always remember Maya Angelouβs quote, βI come as one, but I stand as 10,000.β
What is your call to action to readers?
Live your life as your truest self and encourage others to do the same! Support each other. We have to live for the 10,000 who have come before us, who have made it easier for us to get to where we are today, but also for the 10,000 coming after us, so we can continue to break barriers and glass ceilings and reclaim our power. Do good, stay fearless and remember that everything you want is just outside your comfort zone.
Meet the rest of the Renegades here. ||||| Playboy magazine has just featured an article about a hijab-wearing Muslim-American, Noor Taguri, βmaking a forceful case for modesty.β
Yes. You read that correctly.
In its October βRenegadesβ issue, Playboy is showcasing a religious-conservative practice as emblematic of an independent woman.
White religious-conservatism is not often celebrated or glamorized by American liberals and progressives, it is derided. But switch up white Amish or Catholic notions of modesty with brown Muslim ones, take a fashion shoot complete with a graffiti-ridden backdrop, and presto: brown religious-conservative attitudes about hiding the female form in the name of modesty become⦠progressive.
To be fair, many Islamists and Muslim fundamentalists advocate a much stricter form of hijab and βmodesty,β which one presumes would not countenance photo shoots for Playboy. And I applaud anyone who trolls the Muslim religious-police mindset.
So, well done there Noor Taguri! I know you will be criticized by our own fundamentalists, and I stand with you wholeheartedly against those female-obsessed Quran-thumpers. Certainly what you represent is a step forward from the austere Saudi form of hijab that includes the full-face veil, and bans on women driving.
But, it is also a step backward from the progressive feminism many Muslim women enjoyed in the 1980s. That was before theocratic Islamism and Muslim fundamentalism began competing over who is Muslim enough. Now, they punish those who dare to bare too much flesh.
No debate around this issue is complete without solemnly recalling this reverse trajectory for the rights of Muslim women.
In the West, the hijab should be a choice that faces the same liberal scrutiny that all other religious-conservative choices face, which it currently doesnβt.
Globally, though, it is not a choice.
Millions of girls are forced to be βmodestβ by wearing the hijab. Of course women should be left to choose what to wear, but it has only ever been male Quran exegetes who have told women that covering up equates to modesty.
As such, the hijab is enforced by law over female populations in theocratic Muslim states.
Get The Beast In Your Inbox! Daily Digest Start and finish your day with the top stories from The Daily Beast. Cheat Sheet A speedy, smart summary of all the news you need to know (and nothing you don't). By clicking βSubscribe,β you agree to have read the Terms of Use and Privacy Policy Subscribe Thank You! You are now subscribed to the Daily Digest and Cheat Sheet. We will not share your email with anyone for any reason.
This is why the Catholic nunβs habit is no comparison. No state in the world enforces the Catholic habit over all women then punishes them for not complying. And rarely would a nun be glamorized by American liberals, or by Playboy(!), as a symbol of female emancipation.
This need not be a zero sum game. Progressive liberals can simultaneously defend the legal right to wear a hijab, while disputing whether it is right to wear one.
As a reforming secular liberal Muslim, I do not endorse the gender-discriminatory body-shaming and moralizing of the hijab. I will fight fiercely to protect anyoneβs right to wear this medieval flag of female βchastity,β but that doesnβt mean I think the wearer is right to do so. Let us not ban the hijab, but let us not glamorize it either. I prefer leaving that to religious conservatives who are fixated on nudity, βmodesty,β and female βhonor.β This is a conservative, not liberal, view of the human body. Such illiberal, regressive-left promotion of religious conservativismβonly for Muslims mind youβis nothing short of exoticized Orientalism rehashed.
The assumption made by some liberals is that the βauthenticβ Muslim woman is the hijab-wearing one, while non-hijabis are seen as Westernized, inauthentic Muslims. Likewise, the religious-conservative Muslim assumption equates concealing the female form to βmodesty,β as if a woman who shows her hair or reveals her figure is somehow immodest.
This is a not-so-subtle form of bigotry against the female form, and it has real consequences, including rising social-conservative attitudes across Muslim communities around gender and sexual freedom. In too many instances across Muslim-majority societies, including those embedded in Europe, this βmodesty theologyβ has led to slut-shaming of women who do not cover. Worse yet, it can lead to so-called honor killings.
Many non-Muslims simply assume there is only oneβconservativeβway of being Muslim. But we Muslims are no longer this distant and native βotherβ that liberals and conservatives can visit once a year to share a bit of falafel.
We are born and raised among you, and Islam is therefore now firmly native to our societies. So judge us by the same progressive standards you reserve for everyone else. We Muslim reformers have to be able to demand the same progressive rights within our communities that are enjoyed by everyone else. Your intervention and interaction with Muslimsβ intra-religious debate around these issues is not neutral. A civil war is raging within our communities about the future of Islam for Muslims.
Liberal Muslim theologians such as Britainβs Shaykh Salah al-Ansari, Dr. Usama Hasan, and Pakistanβs Javaid Ghamidi, argue that the hijab is not a religious duty (fard) at all. And that is how it used to be.
Up until the 1980s, the female body was not shamed out of public view in Muslim-majority societies. But from the β80s onward, theocratic Islamism began replacing Arab socialism as the ideology of resistance against βthe West.β This struggle against the βotherβ necessitated defining what is βoursβ and what is βtheirsββand women, of course, were deemed βours.β
Suddenly, womenβs bodies became the red line in a cultural war against the West started by theocratic Islamism. A Not Muslim Enough charade was used to identify βtrueβ Muslims against βWesternβ stooges. Religious dress codes became a crucial marker in these cultural purity stakes. Any uncovered woman was now deemed loose, decadent, and attention seeking. In short, aligned to the βWestern enemy.β
Back to the Playboy shoot: The admirably entrepreneurial Noor Taguri advises younger girls who look up to her to βstay fearless and remember that everything you want is just outside your comfort zone.β
My advice to Noor is: I hope you do the same, sister. Do look up the late great Egyptian feminist Huda Sharawi who truly stepped out of her βcomfort zoneβ when, in 1923, she shocked Muslims everywhere by removing her hijab publicly for the first time.
Within months Muslim women the world over were encouraged to shed this gender-discriminatory medieval throwback to βmodesty.β Those were the days when genuine Western progressives supported genuine Muslim feminists. ||||| (CNN) Muslim-American journalist Noor Tagouri will appear in Playboy magazine's October issue wearing a hijab, a decision that has elicited praise in some quarters and provoked condemnation in others.
She'll appear alongside a sex activist, a comedian and novelist as part of the magazine's "Renegade" series, which highlights people who have "risked it all -- even their lives -- to do what they love."
Earlier this year, Playboy enacted several changes, the biggest of which was to do away with fully nude photos
Tagouri, a 22-year-old journalist who reports for Newsy, appears in the issue clad in black jeans, Converse sneakers, a leather jacket and of course, her head covered.
Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabbana's Middle Eastern collection β The fashion industry has embraced hijabs and abayas. For the first time, in 2015, Dolce & Gabbana released a collection of hijabs and abayas targeting Muslim shoppers in the Middle East. Here's a look at their take on modest dressing. Hide Caption 1 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The collection was first revealed on Style.com/Arabia on January 3. Hide Caption 2 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The hijab and abaya are common garments worn throughout the Middle East. Hide Caption 3 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Dolce & Gabbana is typically known for its feminine, overtly sexual designs. Hide Caption 4 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β These looser robes signify a distinct departure from their usual look. Hide Caption 5 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β While they may not fit the usual Dolce & Gabbana silhouettes, they carry other hallmarks. Hide Caption 6 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The robes are made of silky georgette and charmeuse. Hide Caption 7 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Lemon, floral and polka dot motifs are used in their Spring-Summer 2016 collection. Hide Caption 8 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Intricate lace also features prominently. Hide Caption 9 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Dolce & Gabbana is one of many Western brands starting to target the lucrative Muslim fashion industry. Hide Caption 10 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The collection will be available in all of Dolce & Gabbana's Middle East boutiques, and select European stores. Hide Caption 11 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β This is not the first time Dolce & Gabbana has done collections inspired by specific regions and countries. Hide Caption 12 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabbana's Middle Eastern collection β Last year, they created collections inspired by China, Japan, and Moscow. Hide Caption 13 of 13 | β Playboy has stepped into the debate over Islamic dress and women's rights by featuring a hijab-clad woman in its pages for the first time. Muslim-American journalist Noor Tagouri appears in the October issue wearing a sexy snarl, black leather jacket and jeans, and a beige head scarf. (Playboy this year did away with fully nude photos, notes CNN.) The magazine says the 22-year-old Newsy reporter, included in the "Renegades" issue, makes "a forceful case for modesty." Like the greater debate over the hijab, opinions were mixed over its debut in a men's magazine. Tagouri won praise from some quarters for breaking barriers. Noting that "veiled women bear the brunt of the animosity the entire Muslim community faces in America," Aymann Ismail writes in Slate that Tagouri "speaks out and treads new ground as an individual β¦ [and] deserves the full support of the entire Muslim community." "Congrats@NTagouri," one female supporter tweeted. Others were not impressed. "Hijabi posing for playboyβ¦ what has the world come to," another Twitter user wrote. Despite good intentions, Playboy has "fallen into the slut-shaming game of Islamists around the world," writes Maajid Nawaz at the Daily Beast. Tagouri has a choice to wear the hijab, but women in many Muslim countries do not. "I will fight fiercely to protect anyoneβs right to wear this medieval flag of female 'chastity,' but that doesnβt mean I think the wearer is right to do so. Let us not ban the hijab, but let us not glamorize it either." Tagouri, an aspiring on-air reporter, said she's ignoring the backlash. "It's just negative energy and unhealthy," she told the magazine. (This teen created a hijab emoji.) | <s>[INST]Playboy
It's here! I'm honored to share that @Playboy has named me a 2016 #Renegade and has featured me in their piece!! *LINK IN BIO* πΈ: @gokateshoot A photo posted by Noor Tagouri (@ntagouri) on Sep 22, 2016 at 6:55am PDT
Last year, Playboy made a public decision to shake nude photographs from the brand. The announcement was initially met by skepticism, but since then, the magazine has successfully enhanced the place of actual journalism within its pages. In the latest issue, Playboy reporters wrote about race in a feature on Paul Beatty, a black novelist. They discussed activism in an interview with rapper Vince Staples. And, for the first time ever, Playboy featured a Muslim American in the magazine. Journalist Anna del Gaizo interviewed aspiring news anchor Noor Tagouri about the American-hijabi (headscarf or veil-wearing) experience, her aspirations, and the current political climate. It was a great opportunity for a Muslim woman to get some visibility.
But none of what she talked about seemed to matter to the droves of critics Tagouri, a reporter for Newsy, subsequently encountered online. Articles published in large outlets question whether or not she let Muslims down. On Twitter, users called her ugly names like #hoejabi. One Muslim publication even questioned her commitment to God. As a Muslim man, I try to avoid speaking for Muslim women, as that happens enough as it is. But right now, in a campaign season during which the Republican party has made white supremacy and Islamophobia central to its platform, this controversy around a wonderful interview of an awesome Muslim woman demands a response.
Far too often, Muslim women are being told how to dress and behave by groups who are neither women nor Muslim. Men in Saudi Arabia have constructed laws forcing women into a strict dress code that is simultaneously banned by men in France. Men are using the government to enforce their own principles on an issue that ought to be up to a womanβs free will.
For Muslim women who choose the hijab, the outward presentation of their faith makes them vulnerable to both sides of an increasingly polarizing and politicized conversation about the rights of women. That is why when someone like Noor Tagouri speaks out and treads new ground as an individual, she deserves the full support of the entire Muslim community. ||||| This story appears in the October 2016 issue of Playboy. Subscribe
The men and women in this series will change how you think about business, music, porn, comedy, gaming and more. Theyβve risked it allβeven their livesβto do what they love, showing us what can be accomplished if we break the rules. Meet the Renegades of 2016.
For anyone with preconceived ideas about women who choose to wear a headscarf every day, Noor Tagouri is disorienting. Sheβs simply not what you expect: a 22-year-old journalist (she likes to call herself a storyteller) on the verge of becoming this countryβs first hijab-wearing news anchor. As of June, sheβs an on-air reporter for Newsy, where she provokes the sort of confusion we could use right now, in part by making a surprisingly bold case for modesty. As a badass activist with a passion for demanding change and asking the right questions, accompanied by beauty-ad-campaign looks, Tagouri forces us to ask ourselves why we have such a hard time wrapping our minds around a young woman who consciously covers her head and wonβt take no for an answer.
A West Virginia native and first-generation Libyan American, Tagouri graduated from college at the age of 20. In 2012, her #LetNoorShine campaign went viral. Her 2015 TEDx talk advocated unapologetic individuality, and her YouTube channel draws tens of thousands of viewers. More recently, she collaborated with streetwear brand Lisβn Up Clothing on a fashion line that includes a Jean-Michel Basquiatβinspired sweatshirt. Half the purchase proceeds go to Project Futures, an anti-human-trafficking organization. Americans have a long way to go when it comes to how we regard Muslims, but with Tagouri burning down stereotypes and blazing new paths, weβre a healthy stride closer.
Your goal is to become the first hijabi anchor on commercial U.S. television. Whatβs the biggest challenge you face in your work?
The biggest challenge I face as a storyteller is the process of getting people to trust you enough to tell their stories. Our society has seemingly become so desensitized to violence, abuse, death, rape and trauma. I find that people who go through these traumatic experiences have a hard time trusting reporters. Just a few days ago, I had an anonymous artist tell me he doesnβt do interviews because he doesnβt want reporters to βtake [his] words and run with itβ.
β Being a hijabi Muslim woman helps me gain trust. I say, βI know what itβs like to be misrepresented in the media. I wonβt do that to you.β β
People want to be valued and heard. Their experiences are so personal and they want their voices to come through in a story. Itβs a process, but building that level of trust takes time, effort and patience. Iβm actually struggling with a few powerful stories right now because he people involved are still suffering. Unfortunately theyβre having a hard time being okay with someone sharing their story. Which is totally understandable, but itβs a process.
How have you confronted that?
Being able to share in the vulnerability of the people I talk to helps me gain their trust. I recently did a documentary titled The Trouble Theyβve Seen: The Forest Haven Story, about one of the worst cases of institutional and medical abuse in the history of the U.S. When I decided to do the piece, I knew I needed to talk to people close to the caseβsomeone who lived in the institution, a parent, their family members, an employee and the lawyers involved. It took a few visits with each person to get them to agree to do an interview.
To be honest, I think being a hijabi Muslim woman, helped me gain that trust. I know what itβs like to have the narrative of our community be skewed and exploited in the media. I was like, βHey, I know what itβs like to be misrepresented in the media. I wonβt do that to you. I want to tell your story because itβs important and deserves justice.β I know first-hand that once people are re-empowered, they realize their own story is powerful and they begin to share. Itβs incredibly rewarding and can even help enlighten or save others.
How have you dealt with backlash, especially in our current political climate?
If by backlash you mean hate and criticism, I donβt read or pay attention to any of it. Itβs just negative energy and unhealthy. I make sure to keep a great circle of people around me who keep me grounded. Whether itβs at work or at home, the people who have my best interest at heart voice their concerns and their critiques, and I work on them. Besides that, I just do the best I can to not worry about people who get upset because they donβt like something that I wear or say.
The first story I did with Newsy was on Middle Eastern and North African Americans being considered "whiteβ on the U.S. census and how that might change on the 2020 census. I referred to it as βWhite Without the Privilege.β There was a ton of backlash on Facebook from people who didnβt like the story. It was comical seeing people telling me to βgo back homeβ when in fact, I was born in West Virginia. My team insisted that I never read the comments, so I stopped. The thing is, that story was based on facts. I constantly remind myself to just do the work I believe in and ignore the angry people behind computer screens.
At what point will you feel like youβve succeeded in effecting change?
I will have succeeded in effecting change when all girls realize they can do anything they want without having to sacrifice who they are as a person. I may dress a little differentβIβm a reporter who happens to wear a head scarf and I live in my hoodieβbut being a story teller, motivational speaker, entrepreneur and unapologetically myself has opened so many doors for thousands of people. I recently had a mom come up to me and tell me that her daughter is in the 6th grade and had just started wearing the hijab. She shared how a lot of the other girls tease her and put her down because of the hijab. She went on to tell me that her daughter watches all of my videos and every time she gets picked on, she pulls up my Instagram or tells them to βgoogle Noor Tagouri and then talk to me.β Those are the moments that hit me. And I always remember Maya Angelouβs quote, βI come as one, but I stand as 10,000.β
What is your call to action to readers?
Live your life as your truest self and encourage others to do the same! Support each other. We have to live for the 10,000 who have come before us, who have made it easier for us to get to where we are today, but also for the 10,000 coming after us, so we can continue to break barriers and glass ceilings and reclaim our power. Do good, stay fearless and remember that everything you want is just outside your comfort zone.
Meet the rest of the Renegades here. ||||| Playboy magazine has just featured an article about a hijab-wearing Muslim-American, Noor Taguri, βmaking a forceful case for modesty.β
Yes. You read that correctly.
In its October βRenegadesβ issue, Playboy is showcasing a religious-conservative practice as emblematic of an independent woman.
White religious-conservatism is not often celebrated or glamorized by American liberals and progressives, it is derided. But switch up white Amish or Catholic notions of modesty with brown Muslim ones, take a fashion shoot complete with a graffiti-ridden backdrop, and presto: brown religious-conservative attitudes about hiding the female form in the name of modesty become⦠progressive.
To be fair, many Islamists and Muslim fundamentalists advocate a much stricter form of hijab and βmodesty,β which one presumes would not countenance photo shoots for Playboy. And I applaud anyone who trolls the Muslim religious-police mindset.
So, well done there Noor Taguri! I know you will be criticized by our own fundamentalists, and I stand with you wholeheartedly against those female-obsessed Quran-thumpers. Certainly what you represent is a step forward from the austere Saudi form of hijab that includes the full-face veil, and bans on women driving.
But, it is also a step backward from the progressive feminism many Muslim women enjoyed in the 1980s. That was before theocratic Islamism and Muslim fundamentalism began competing over who is Muslim enough. Now, they punish those who dare to bare too much flesh.
No debate around this issue is complete without solemnly recalling this reverse trajectory for the rights of Muslim women.
In the West, the hijab should be a choice that faces the same liberal scrutiny that all other religious-conservative choices face, which it currently doesnβt.
Globally, though, it is not a choice.
Millions of girls are forced to be βmodestβ by wearing the hijab. Of course women should be left to choose what to wear, but it has only ever been male Quran exegetes who have told women that covering up equates to modesty.
As such, the hijab is enforced by law over female populations in theocratic Muslim states.
Get The Beast In Your Inbox! Daily Digest Start and finish your day with the top stories from The Daily Beast. Cheat Sheet A speedy, smart summary of all the news you need to know (and nothing you don't). By clicking βSubscribe,β you agree to have read the Terms of Use and Privacy Policy Subscribe Thank You! You are now subscribed to the Daily Digest and Cheat Sheet. We will not share your email with anyone for any reason.
This is why the Catholic nunβs habit is no comparison. No state in the world enforces the Catholic habit over all women then punishes them for not complying. And rarely would a nun be glamorized by American liberals, or by Playboy(!), as a symbol of female emancipation.
This need not be a zero sum game. Progressive liberals can simultaneously defend the legal right to wear a hijab, while disputing whether it is right to wear one.
As a reforming secular liberal Muslim, I do not endorse the gender-discriminatory body-shaming and moralizing of the hijab. I will fight fiercely to protect anyoneβs right to wear this medieval flag of female βchastity,β but that doesnβt mean I think the wearer is right to do so. Let us not ban the hijab, but let us not glamorize it either. I prefer leaving that to religious conservatives who are fixated on nudity, βmodesty,β and female βhonor.β This is a conservative, not liberal, view of the human body. Such illiberal, regressive-left promotion of religious conservativismβonly for Muslims mind youβis nothing short of exoticized Orientalism rehashed.
The assumption made by some liberals is that the βauthenticβ Muslim woman is the hijab-wearing one, while non-hijabis are seen as Westernized, inauthentic Muslims. Likewise, the religious-conservative Muslim assumption equates concealing the female form to βmodesty,β as if a woman who shows her hair or reveals her figure is somehow immodest.
This is a not-so-subtle form of bigotry against the female form, and it has real consequences, including rising social-conservative attitudes across Muslim communities around gender and sexual freedom. In too many instances across Muslim-majority societies, including those embedded in Europe, this βmodesty theologyβ has led to slut-shaming of women who do not cover. Worse yet, it can lead to so-called honor killings.
Many non-Muslims simply assume there is only oneβconservativeβway of being Muslim. But we Muslims are no longer this distant and native βotherβ that liberals and conservatives can visit once a year to share a bit of falafel.
We are born and raised among you, and Islam is therefore now firmly native to our societies. So judge us by the same progressive standards you reserve for everyone else. We Muslim reformers have to be able to demand the same progressive rights within our communities that are enjoyed by everyone else. Your intervention and interaction with Muslimsβ intra-religious debate around these issues is not neutral. A civil war is raging within our communities about the future of Islam for Muslims.
Liberal Muslim theologians such as Britainβs Shaykh Salah al-Ansari, Dr. Usama Hasan, and Pakistanβs Javaid Ghamidi, argue that the hijab is not a religious duty (fard) at all. And that is how it used to be.
Up until the 1980s, the female body was not shamed out of public view in Muslim-majority societies. But from the β80s onward, theocratic Islamism began replacing Arab socialism as the ideology of resistance against βthe West.β This struggle against the βotherβ necessitated defining what is βoursβ and what is βtheirsββand women, of course, were deemed βours.β
Suddenly, womenβs bodies became the red line in a cultural war against the West started by theocratic Islamism. A Not Muslim Enough charade was used to identify βtrueβ Muslims against βWesternβ stooges. Religious dress codes became a crucial marker in these cultural purity stakes. Any uncovered woman was now deemed loose, decadent, and attention seeking. In short, aligned to the βWestern enemy.β
Back to the Playboy shoot: The admirably entrepreneurial Noor Taguri advises younger girls who look up to her to βstay fearless and remember that everything you want is just outside your comfort zone.β
My advice to Noor is: I hope you do the same, sister. Do look up the late great Egyptian feminist Huda Sharawi who truly stepped out of her βcomfort zoneβ when, in 1923, she shocked Muslims everywhere by removing her hijab publicly for the first time.
Within months Muslim women the world over were encouraged to shed this gender-discriminatory medieval throwback to βmodesty.β Those were the days when genuine Western progressives supported genuine Muslim feminists. ||||| (CNN) Muslim-American journalist Noor Tagouri will appear in Playboy magazine's October issue wearing a hijab, a decision that has elicited praise in some quarters and provoked condemnation in others.
She'll appear alongside a sex activist, a comedian and novelist as part of the magazine's "Renegade" series, which highlights people who have "risked it all -- even their lives -- to do what they love."
Earlier this year, Playboy enacted several changes, the biggest of which was to do away with fully nude photos
Tagouri, a 22-year-old journalist who reports for Newsy, appears in the issue clad in black jeans, Converse sneakers, a leather jacket and of course, her head covered.
Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabbana's Middle Eastern collection β The fashion industry has embraced hijabs and abayas. For the first time, in 2015, Dolce & Gabbana released a collection of hijabs and abayas targeting Muslim shoppers in the Middle East. Here's a look at their take on modest dressing. Hide Caption 1 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The collection was first revealed on Style.com/Arabia on January 3. Hide Caption 2 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The hijab and abaya are common garments worn throughout the Middle East. Hide Caption 3 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Dolce & Gabbana is typically known for its feminine, overtly sexual designs. Hide Caption 4 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β These looser robes signify a distinct departure from their usual look. Hide Caption 5 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β While they may not fit the usual Dolce & Gabbana silhouettes, they carry other hallmarks. Hide Caption 6 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The robes are made of silky georgette and charmeuse. Hide Caption 7 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Lemon, floral and polka dot motifs are used in their Spring-Summer 2016 collection. Hide Caption 8 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Intricate lace also features prominently. Hide Caption 9 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β Dolce & Gabbana is one of many Western brands starting to target the lucrative Muslim fashion industry. Hide Caption 10 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β The collection will be available in all of Dolce & Gabbana's Middle East boutiques, and select European stores. Hide Caption 11 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabanna's Middle Eastern collection β This is not the first time Dolce & Gabbana has done collections inspired by specific regions and countries. Hide Caption 12 of 13 Photos: The hijab goes haute couture The hijab goes haute: Dolce & Gabbana's Middle Eastern collection β Last year, they created collections inspired by China, Japan, and Moscow. Hide Caption 13 of 13[/INST]β Playboy has stepped into the debate over Islamic dress and women's rights by featuring a hijab-clad woman in its pages for the first time. Muslim-American journalist Noor Tagouri appears in the October issue wearing a sexy snarl, black leather jacket and jeans, and a beige head scarf. (Playboy this year did away with fully nude photos, notes CNN.) The magazine says the 22-year-old Newsy reporter, included in the "Renegades" issue, makes "a forceful case for modesty." Like the greater debate over the hijab, opinions were mixed over its debut in a men's magazine. Tagouri won praise from some quarters for breaking barriers. Noting that "veiled women bear the brunt of the animosity the entire Muslim community faces in America," Aymann Ismail writes in Slate that Tagouri "speaks out and treads new ground as an individual β¦ [and] deserves the full support of the entire Muslim community." "Congrats@NTagouri," one female supporter tweeted. Others were not impressed. "Hijabi posing for playboyβ¦ what has the world come to," another Twitter user wrote. Despite good intentions, Playboy has "fallen into the slut-shaming game of Islamists around the world," writes Maajid Nawaz at the Daily Beast. Tagouri has a choice to wear the hijab, but women in many Muslim countries do not. "I will fight fiercely to protect anyoneβs right to wear this medieval flag of female 'chastity,' but that doesnβt mean I think the wearer is right to do so. Let us not ban the hijab, but let us not glamorize it either." Tagouri, an aspiring on-air reporter, said she's ignoring the backlash. "It's just negative energy and unhealthy," she told the magazine. (This teen created a hijab emoji.)</s> |
according to adult learning theory , learning is a self - directed activity requiring motivation , desire , and effort on the part of the learner ( 1 ) .
in fact , it comprises intellectual activities , including recognition and remembering , which relate to what learners should know and understand ( 2 ) .
more specifically , it is the process of recollection and retention through which past memories are remembered in the form of words , meanings , actions , or mental pictures . as learners tend to absorb meaningful , conceptual , and new subjects more deeply , such subjects are expected to be forgotten more slowly ( 3 ) .
andrusyszyn defined knowledge retention as recalling materials 25.5 days after learning ( 4 ) .
despite its importance , retention of knowledge and skills
has rarely been studied ( 4 - 8 ) . because problems related to the retention of nursing knowledge and skills have been documented , selecting the best training method will definitely depend on identifying any factors that may contribute to the problem ( 9 ) .
research has shown that teaching accompanied by colors , illustrations , and animation ( dynamic content ) can enhance the understanding of the material , learners ability to organize the concepts , and retention of knowledge ( 10 - 12 ) .
continuous training after graduation aims at maintaining the acquired skills , qualitative and quantitative promotion of such skills , and teaching new scientific contents and skills .
continuous education programs include seminars , congresses , workshops , conferences , short professional courses , well - organized plans , as well as training , research , and self - education activities ( 13 ) .
internet - based continuous education offers electronic , learner - centered , self - learning courses intending to promote knowledge ( 14 - 17 ) through the engagement of multiple senses ( 18 ) .
educational booklets are also widely used as the first generation of self - directed learning media .
however , during their preparation , readability for the target group , presence of simple pictures and diagrams , boldfacing important words and phrases , including up - to - date information , and using reliable sources have to be considered . on the other hand , previous studies have reported the insufficiency of educational booklets and thus suggested e - learning as a more favorable choice ( 19,20 ) .
scenario - based e - learning can improve participants ' engagement and deeper understanding of content by motivating them to think and analyze before making decisions ( 11,21 ) .
in addition , electronic continuous medical education ( ecme ) facilitates learning using a constructivist orientation .
constructivism is a learning paradigm , which explains how people learn . according to this theory
therefore , instead of transferring knowledge from an educator to a learner , constructivism focuses on learners and assists them to create knowledge and give it an individual meaning ( 23,24 ) . electronic continuous medical education ( ecme )
encourages learning through active involvement with valuable information and provides a responsive learning environment ( with questions and answers ) and learner - centered teaching ( 6,9,23,25 ) .
integration of e - learning and continuous medical education implies that in adult medical education , trainers are not merely the distributors of content but act as learning facilitators .
e - learning improves retention , provokes better use of the content , and consequently increases the accessibility of knowledge , attitude , and skills ( 14,26 ) .
in addition , the production of nursing knowledge is on a constant rise ( 27,28 ) .
the ultimate goal in professional nursing is to provide high - quality biological , psychological , and social care to patients .
therefore , surface learning and incomplete information will affect the performance of the nurses in dealing with patients , and may lead to patients complaints , and managers concerns . to prevent such problems , nursing educators should use modern teaching methods to prevent surface learning and promote t students critical thinking , problem solving , and information retention skills ( 27 ) . evidently , better learning of educational materials on the part of nurses will increase the quality of patient care ( 29 ) .
while time constraints placed on nurses
is a challenge that prevents them from updating their knowledge , the flexibility of distance education may be a good solution for organizations ; i.e. , the knowledge of nurses can simply be completed , modified , and updated through distance education system .
distance - learning delivery methods can range from paper- based to internet- based materials and their impact is not clearly stated .
therefore , this study aimed to compare the efficacy of educational booklets and the electronic continuous medical education system on enhancing the retention and deep learning of the recent advances in diabetes .
as no similar study was found in this field , conducting this research seemed necessary .
this quasi - experimental study aimed to compare nurses ability to retain diabetes updates , which was learned through the electronic method and booklet . considering
the power of 80% with a confidence level of 95% , the needed sample size was about 120 .
convenience sampling was used to select 123 nurses from endocrinology and internal medicine wards of three hospitals affiliated to tehran university of medical sciences ( tehran , iran ) .
these three hospitals had the largest number of patients and nurses in the ward .
the inclusion criteria were at least one year experience of working in endocrinology and internal medicine wards , a minimum of bachelor s degree in nursing , having finished obliged service in remote areas , having access to computers and the internet at home or workplace , and being skilled at working with the internet ( according to the participants themselves ) . at any stage of the study , nurses who were not willing to participate , or were transferred to other wards were excluded .
the eligible nurses were allocated to e - learning ( n=38 ) , booklet ( n=43 ) , and control groups ( n=42 ) . to prevent information exchange between the participants ,
each group was selected from a different hospital ; that is , the names of the hospitals were written on paper and randomly selected .
to measure nurses ' knowledge before the intervention
, all groups were asked to fill out a researcher - made questionnaire about diabetes updates ( pre - test ) .
the booklet and e - learning groups received the educational content in the form of a booklet and ecme ( http://cme.tums.ac.ir ) , respectively . to develop educational materials , extensive library research , and domestic and international website search were conducted .
the educational content was prepared using up - to - date articles , reliable sites and new educational books .
the training content includes muscular and skeletal complications of diabetes such as diabetic hand syndrome , frozen shoulder syndrome , diabetic diet , desired levels of glucose control , insulin and its complications , new treatments for diabetes , common diabetes skin diseases and diabetic foot ulcers .
then the materials were prepared in two formats of booklet and ecme . educational objectives and titles were identical for both groups .
using illustrations and tables , the colored booklet of diabetes updates was prepared and given to the manual group .
for the electronic group , interactive problem- based scenarios were developed , and the content was placed on cme website after the administrative procedures ( confirmed by two reviewers and after obtaining a license from the national continuing education office of ministry of health and medical education ) in collaboration with electronic continuing education center at virtual school of tehran university of medical sciences .
the e - learning group also attended a 30-minute session to learn how to log in to the website and how to use the program .
in the e - cme group , after coordinating with hospital authorities and obtaining the required permissions , with the assistance of the hospital s information technology team , a 24/7 service was provided and the e - learning group could access the website without interruption regardless of time or day .
moreover , to facilitate access to the educational material at the endocrinology and internal wards of the hospital , the website was set as the homepage in " mozilla firefox " and " microsoft internet explorer " .
one week and one month later , the questionnaires were distributed among all the three groups again without notice .
the questionnaire consisted of two parts : the first part included demographic characteristics of the participants , while the second part assessed knowledge about diabetes updates .
the last part was a researcher - made questionnaire to assess knowledge about diabetes updates .
it contained 30 multiple ( three - four ) choice items with one positive score each .
scores 75 , 74 - 51 and 50 represented favorable , moderate , and low levels of knowledge , respectively .
the questionnaire evaluated knowledge about desirable glucose control ( nine items ) , insulin and its complications ( four items ) , complications of diabetes ( four items ) , diabetic diet ( four items ) , musculoskeletal complications of diabetes ( four items ) , novel treatments of diabetes ( two items ) , common dermatological manifestations in diabetics ( two items ) , and diabetic foot ulcer ( one item ) .
the questionnaire was designed according to the conditions and features of the training program , and through library research and review of the literature including the university of michigan diabetes knowledge questionnaire ( 30 ) .
the validity of the whole questionnaire was assessed by expert review ; i.e. , it was handed out to 10 faculty members of school of nursing and midwifery ( tums , tehran , iran ) , and their comments were applied .
to evaluate the test - retest reliability of the questionnaire , 10 nurses with similar characteristics to those of our participants were asked to complete the questionnaire twice , with a two - week interval .
the reliability coefficient of the questionnaire with test - retest was then calculated ( r=0.91 ) .
the results were finally analyzed using variance and chi - square , fisher s exact , friedman , and tukey 's test ; and p<0.05 was considered as statistically significant .
we studied 123 nurses in three groups ( booklet , e - learning , and control ) .
the mean age of the booklet , control , and e - learning groups was 30.65.3 , 32.55.5 , and 29.45.2 yrs .
the three groups were compared using fisher 's exact test and chi- square analysis , and no statistically significant demographic differences were found .
fisher s exact test was used to analyze data related to gender , academic degree and computer skills ; and anova for work experience .
the mean ( sd ) of the pretest and posttest scores for the three groups are shown in table 2 . while the mean scores of the three groups were not significantly different before the intervention ( p=0.211 ) , significant differences were observed between the mean scores of the three groups one and four weeks after the intervention ( f=26.17 , p=0.001 and f=4.07 , p=0.020 , respectively ) .
friedman analysis revealed that both electronic learning and booklet methods could effectively improve nurses ' knowledge ( =23.03 , p=0.001 and =51.71 , p=0.001 , respectively ) , but no significant difference was found in the pre and posttest scores in the control group ( p=0.31 ) .
* anova was used to test for the differences between the mean scores of the three groups ( ecme , booklet and control ) .
* * friedman was used to determine significant differences in the dependent mean scores of each group ( before , after one week and after four week ) .
tukey 's test revealed that the mean scores of knowledge were significantly higher in the e - learning group than in the booklet group ( p=0.024 ) and the control group ( p=0.001 ) one week after the intervention .
the e - learning group had significantly greater mean score of knowledge compared to the control group ( p=0.014 ) four weeks after the intervention , but the difference was not significant between the mean scores of e - learning and booklet groups ( p=0.328 ) .
in this research , we compared the effects of booklets and e - learning on nurses retention of knowledge about diabetes updates .
we found that e - learning could significantly improve nurses knowledge compared to the control group ; in addition , results suggested more desirable retention rate following e - learning .
in support of the above findings , short et al .
found that continuous medical education programs could effectively change the knowledge , attitude , beliefs , and self - reporting behaviors of the physicians .
tsai et al . found e - learning ( with multimedia ) to significantly increase the level of knowledge after one and two weeks ( p<0.001 ) ( 31 ) .
bloomfield et al . compared the effects of computer - assisted learning and traditional face - to - face methods on learning and retention of hand washing skills .
they concluded that although knowledge scores increased significantly in both groups , knowledge obtained through computer - assisted learning was better retained ( 7 ) .
indicated that the use of manuals failed to increase the mean scores of knowledge three weeks after the intervention . in facts , the mean scores decreased from 8.55 before the intervention to 8.47 three weeks after the intervention ( 19 ) .
e - learning is established based on constructivism in which knowledge is not simply transferred from an educator to a learner , but it is instead learned through the creation of associations between the existing knowledge and new information and giving it an individual meaning .
e - learning increases retention , improves the use of the content , and thus leads to better access to knowledge ( 14,32,33 ) .
soleimanpour et al . did not observe a significant difference between e - learning ( using information and communications technology ) and traditional learning ( through lectures ) immediately and one month after intervention .
however , the third post - test ( three months after the intervention ) showed a significant difference between the two groups .
hence , they stated that teaching science based on information and communications technology results in sustainable knowledge in students of the third grade of junior high school ( 17 ) .
in contrast , the aleman et al . showed that when compared to traditional teaching , e - learning led to significantly higher level of knowledge immediately after the intervention .
nevertheless , the retention of knowledge was similar in both groups 10 weeks after the intervention ( 8) .
sustainable learning occurs when the learner is able to organize and relate new concepts and information with his / her mental cognitive structures ( 27,34 ) .
e - learning encourages the learners to participate in learning actively and thus engages them with the content .
interactive learning changes the focus from passive , teacher - centered methods to active , learner - centered methods and results in more efficient learning ( 14 ) .
in conclusion ,
the review of the literature on retention indicated they are few especially on knowledge retention ; for example , aleman in 2011 examined knowledge retention in medical surgical nursing students ( 8) .
two other studies examined the retention of practical skills including beeckman who studied students retention in bedsore care in 2008 , and bloomfield who studied the retention of hand washing in 2010 ( 33,7 ) .
inadequacy of studies on retention makes the conclusion difficult and indicates the need for further studies in this field .
considering the results of studies on ecme and the results of this research , it can be stated that ecme can effectively promote nurses knowledge and retention .
therefore , ecme systems can be used as an alternative or supplement to traditional teaching ( e.g. , booklets and lectures ) in continuous education for nurses .
this method enhances learning and retention by active engagement of the learners in the learning process through an interactive scenario .
superficial learning and incomplete information will affect the performance of nurses in dealing with patients , resulting in patient complaints , and leading to real concerns for nursing managers .
apparently , the quality of nursing care can be increased by promoting the knowledge of nurses . | background : training methods that enhance nurses learning and retention will increase the quality of patient
care .
this study aimed to compare the effectiveness of electronic learning and educational booklet on the nurses
retention of diabetes updates .
methods : in this controlled trial study , convenience sampling was used to select 123 nurses from the endocrinology
and internal medicine wards of three hospitals affiliated to tehran university of medical sciences ( tehran ,
iran ) .
the participants were allocated to three groups of manual , electronic learning , and control .
the booklet
and electronic learning groups were trained using educational booklet and electronic continuous medical education
( cme ) website , respectively .
the control group did not receive any intervention .
in all the three groups ,
the nurses ' knowledge was measured before the intervention , and one and four weeks after the intervention .
data
were collected by a questionnaire .
results : significant differences were observed between the mean scores of the three groups one and four
weeks after the intervention ( f=26.17 , p=0.001 and f=4.07 , p=0.020 , respectively ) , and post hoc test showed
that this difference was due to the higher score in e - learning group . both e - learning and booklet methods could
effectively improve nurses ' knowledge ( =23.03 , p=0.001 and =51.71 , p=0.001 , respectively ) .
conclusion : according to the results of this study , electronic learning was more effective than booklet in enhancing
the learning and retention of knowledge .
electronic learning is suggested as a more suitable method as
it provides appropriate interactions and attractive virtual environments to motivate the learners and promote
retention . | <s>[INST]according to adult learning theory , learning is a self - directed activity requiring motivation , desire , and effort on the part of the learner ( 1 ) .
in fact , it comprises intellectual activities , including recognition and remembering , which relate to what learners should know and understand ( 2 ) .
more specifically , it is the process of recollection and retention through which past memories are remembered in the form of words , meanings , actions , or mental pictures . as learners tend to absorb meaningful , conceptual , and new subjects more deeply , such subjects are expected to be forgotten more slowly ( 3 ) .
andrusyszyn defined knowledge retention as recalling materials 25.5 days after learning ( 4 ) .
despite its importance , retention of knowledge and skills
has rarely been studied ( 4 - 8 ) . because problems related to the retention of nursing knowledge and skills have been documented , selecting the best training method will definitely depend on identifying any factors that may contribute to the problem ( 9 ) .
research has shown that teaching accompanied by colors , illustrations , and animation ( dynamic content ) can enhance the understanding of the material , learners ability to organize the concepts , and retention of knowledge ( 10 - 12 ) .
continuous training after graduation aims at maintaining the acquired skills , qualitative and quantitative promotion of such skills , and teaching new scientific contents and skills .
continuous education programs include seminars , congresses , workshops , conferences , short professional courses , well - organized plans , as well as training , research , and self - education activities ( 13 ) .
internet - based continuous education offers electronic , learner - centered , self - learning courses intending to promote knowledge ( 14 - 17 ) through the engagement of multiple senses ( 18 ) .
educational booklets are also widely used as the first generation of self - directed learning media .
however , during their preparation , readability for the target group , presence of simple pictures and diagrams , boldfacing important words and phrases , including up - to - date information , and using reliable sources have to be considered . on the other hand , previous studies have reported the insufficiency of educational booklets and thus suggested e - learning as a more favorable choice ( 19,20 ) .
scenario - based e - learning can improve participants ' engagement and deeper understanding of content by motivating them to think and analyze before making decisions ( 11,21 ) .
in addition , electronic continuous medical education ( ecme ) facilitates learning using a constructivist orientation .
constructivism is a learning paradigm , which explains how people learn . according to this theory
therefore , instead of transferring knowledge from an educator to a learner , constructivism focuses on learners and assists them to create knowledge and give it an individual meaning ( 23,24 ) . electronic continuous medical education ( ecme )
encourages learning through active involvement with valuable information and provides a responsive learning environment ( with questions and answers ) and learner - centered teaching ( 6,9,23,25 ) .
integration of e - learning and continuous medical education implies that in adult medical education , trainers are not merely the distributors of content but act as learning facilitators .
e - learning improves retention , provokes better use of the content , and consequently increases the accessibility of knowledge , attitude , and skills ( 14,26 ) .
in addition , the production of nursing knowledge is on a constant rise ( 27,28 ) .
the ultimate goal in professional nursing is to provide high - quality biological , psychological , and social care to patients .
therefore , surface learning and incomplete information will affect the performance of the nurses in dealing with patients , and may lead to patients complaints , and managers concerns . to prevent such problems , nursing educators should use modern teaching methods to prevent surface learning and promote t students critical thinking , problem solving , and information retention skills ( 27 ) . evidently , better learning of educational materials on the part of nurses will increase the quality of patient care ( 29 ) .
while time constraints placed on nurses
is a challenge that prevents them from updating their knowledge , the flexibility of distance education may be a good solution for organizations ; i.e. , the knowledge of nurses can simply be completed , modified , and updated through distance education system .
distance - learning delivery methods can range from paper- based to internet- based materials and their impact is not clearly stated .
therefore , this study aimed to compare the efficacy of educational booklets and the electronic continuous medical education system on enhancing the retention and deep learning of the recent advances in diabetes .
as no similar study was found in this field , conducting this research seemed necessary .
this quasi - experimental study aimed to compare nurses ability to retain diabetes updates , which was learned through the electronic method and booklet . considering
the power of 80% with a confidence level of 95% , the needed sample size was about 120 .
convenience sampling was used to select 123 nurses from endocrinology and internal medicine wards of three hospitals affiliated to tehran university of medical sciences ( tehran , iran ) .
these three hospitals had the largest number of patients and nurses in the ward .
the inclusion criteria were at least one year experience of working in endocrinology and internal medicine wards , a minimum of bachelor s degree in nursing , having finished obliged service in remote areas , having access to computers and the internet at home or workplace , and being skilled at working with the internet ( according to the participants themselves ) . at any stage of the study , nurses who were not willing to participate , or were transferred to other wards were excluded .
the eligible nurses were allocated to e - learning ( n=38 ) , booklet ( n=43 ) , and control groups ( n=42 ) . to prevent information exchange between the participants ,
each group was selected from a different hospital ; that is , the names of the hospitals were written on paper and randomly selected .
to measure nurses ' knowledge before the intervention
, all groups were asked to fill out a researcher - made questionnaire about diabetes updates ( pre - test ) .
the booklet and e - learning groups received the educational content in the form of a booklet and ecme ( http://cme.tums.ac.ir ) , respectively . to develop educational materials , extensive library research , and domestic and international website search were conducted .
the educational content was prepared using up - to - date articles , reliable sites and new educational books .
the training content includes muscular and skeletal complications of diabetes such as diabetic hand syndrome , frozen shoulder syndrome , diabetic diet , desired levels of glucose control , insulin and its complications , new treatments for diabetes , common diabetes skin diseases and diabetic foot ulcers .
then the materials were prepared in two formats of booklet and ecme . educational objectives and titles were identical for both groups .
using illustrations and tables , the colored booklet of diabetes updates was prepared and given to the manual group .
for the electronic group , interactive problem- based scenarios were developed , and the content was placed on cme website after the administrative procedures ( confirmed by two reviewers and after obtaining a license from the national continuing education office of ministry of health and medical education ) in collaboration with electronic continuing education center at virtual school of tehran university of medical sciences .
the e - learning group also attended a 30-minute session to learn how to log in to the website and how to use the program .
in the e - cme group , after coordinating with hospital authorities and obtaining the required permissions , with the assistance of the hospital s information technology team , a 24/7 service was provided and the e - learning group could access the website without interruption regardless of time or day .
moreover , to facilitate access to the educational material at the endocrinology and internal wards of the hospital , the website was set as the homepage in " mozilla firefox " and " microsoft internet explorer " .
one week and one month later , the questionnaires were distributed among all the three groups again without notice .
the questionnaire consisted of two parts : the first part included demographic characteristics of the participants , while the second part assessed knowledge about diabetes updates .
the last part was a researcher - made questionnaire to assess knowledge about diabetes updates .
it contained 30 multiple ( three - four ) choice items with one positive score each .
scores 75 , 74 - 51 and 50 represented favorable , moderate , and low levels of knowledge , respectively .
the questionnaire evaluated knowledge about desirable glucose control ( nine items ) , insulin and its complications ( four items ) , complications of diabetes ( four items ) , diabetic diet ( four items ) , musculoskeletal complications of diabetes ( four items ) , novel treatments of diabetes ( two items ) , common dermatological manifestations in diabetics ( two items ) , and diabetic foot ulcer ( one item ) .
the questionnaire was designed according to the conditions and features of the training program , and through library research and review of the literature including the university of michigan diabetes knowledge questionnaire ( 30 ) .
the validity of the whole questionnaire was assessed by expert review ; i.e. , it was handed out to 10 faculty members of school of nursing and midwifery ( tums , tehran , iran ) , and their comments were applied .
to evaluate the test - retest reliability of the questionnaire , 10 nurses with similar characteristics to those of our participants were asked to complete the questionnaire twice , with a two - week interval .
the reliability coefficient of the questionnaire with test - retest was then calculated ( r=0.91 ) .
the results were finally analyzed using variance and chi - square , fisher s exact , friedman , and tukey 's test ; and p<0.05 was considered as statistically significant .
we studied 123 nurses in three groups ( booklet , e - learning , and control ) .
the mean age of the booklet , control , and e - learning groups was 30.65.3 , 32.55.5 , and 29.45.2 yrs .
the three groups were compared using fisher 's exact test and chi- square analysis , and no statistically significant demographic differences were found .
fisher s exact test was used to analyze data related to gender , academic degree and computer skills ; and anova for work experience .
the mean ( sd ) of the pretest and posttest scores for the three groups are shown in table 2 . while the mean scores of the three groups were not significantly different before the intervention ( p=0.211 ) , significant differences were observed between the mean scores of the three groups one and four weeks after the intervention ( f=26.17 , p=0.001 and f=4.07 , p=0.020 , respectively ) .
friedman analysis revealed that both electronic learning and booklet methods could effectively improve nurses ' knowledge ( =23.03 , p=0.001 and =51.71 , p=0.001 , respectively ) , but no significant difference was found in the pre and posttest scores in the control group ( p=0.31 ) .
* anova was used to test for the differences between the mean scores of the three groups ( ecme , booklet and control ) .
* * friedman was used to determine significant differences in the dependent mean scores of each group ( before , after one week and after four week ) .
tukey 's test revealed that the mean scores of knowledge were significantly higher in the e - learning group than in the booklet group ( p=0.024 ) and the control group ( p=0.001 ) one week after the intervention .
the e - learning group had significantly greater mean score of knowledge compared to the control group ( p=0.014 ) four weeks after the intervention , but the difference was not significant between the mean scores of e - learning and booklet groups ( p=0.328 ) .
in this research , we compared the effects of booklets and e - learning on nurses retention of knowledge about diabetes updates .
we found that e - learning could significantly improve nurses knowledge compared to the control group ; in addition , results suggested more desirable retention rate following e - learning .
in support of the above findings , short et al .
found that continuous medical education programs could effectively change the knowledge , attitude , beliefs , and self - reporting behaviors of the physicians .
tsai et al . found e - learning ( with multimedia ) to significantly increase the level of knowledge after one and two weeks ( p<0.001 ) ( 31 ) .
bloomfield et al . compared the effects of computer - assisted learning and traditional face - to - face methods on learning and retention of hand washing skills .
they concluded that although knowledge scores increased significantly in both groups , knowledge obtained through computer - assisted learning was better retained ( 7 ) .
indicated that the use of manuals failed to increase the mean scores of knowledge three weeks after the intervention . in facts , the mean scores decreased from 8.55 before the intervention to 8.47 three weeks after the intervention ( 19 ) .
e - learning is established based on constructivism in which knowledge is not simply transferred from an educator to a learner , but it is instead learned through the creation of associations between the existing knowledge and new information and giving it an individual meaning .
e - learning increases retention , improves the use of the content , and thus leads to better access to knowledge ( 14,32,33 ) .
soleimanpour et al . did not observe a significant difference between e - learning ( using information and communications technology ) and traditional learning ( through lectures ) immediately and one month after intervention .
however , the third post - test ( three months after the intervention ) showed a significant difference between the two groups .
hence , they stated that teaching science based on information and communications technology results in sustainable knowledge in students of the third grade of junior high school ( 17 ) .
in contrast , the aleman et al . showed that when compared to traditional teaching , e - learning led to significantly higher level of knowledge immediately after the intervention .
nevertheless , the retention of knowledge was similar in both groups 10 weeks after the intervention ( 8) .
sustainable learning occurs when the learner is able to organize and relate new concepts and information with his / her mental cognitive structures ( 27,34 ) .
e - learning encourages the learners to participate in learning actively and thus engages them with the content .
interactive learning changes the focus from passive , teacher - centered methods to active , learner - centered methods and results in more efficient learning ( 14 ) .
in conclusion ,
the review of the literature on retention indicated they are few especially on knowledge retention ; for example , aleman in 2011 examined knowledge retention in medical surgical nursing students ( 8) .
two other studies examined the retention of practical skills including beeckman who studied students retention in bedsore care in 2008 , and bloomfield who studied the retention of hand washing in 2010 ( 33,7 ) .
inadequacy of studies on retention makes the conclusion difficult and indicates the need for further studies in this field .
considering the results of studies on ecme and the results of this research , it can be stated that ecme can effectively promote nurses knowledge and retention .
therefore , ecme systems can be used as an alternative or supplement to traditional teaching ( e.g. , booklets and lectures ) in continuous education for nurses .
this method enhances learning and retention by active engagement of the learners in the learning process through an interactive scenario .
superficial learning and incomplete information will affect the performance of nurses in dealing with patients , resulting in patient complaints , and leading to real concerns for nursing managers .
apparently , the quality of nursing care can be increased by promoting the knowledge of nurses .[/INST]background : training methods that enhance nurses learning and retention will increase the quality of patient
care .
this study aimed to compare the effectiveness of electronic learning and educational booklet on the nurses
retention of diabetes updates .
methods : in this controlled trial study , convenience sampling was used to select 123 nurses from the endocrinology
and internal medicine wards of three hospitals affiliated to tehran university of medical sciences ( tehran ,
iran ) .
the participants were allocated to three groups of manual , electronic learning , and control .
the booklet
and electronic learning groups were trained using educational booklet and electronic continuous medical education
( cme ) website , respectively .
the control group did not receive any intervention .
in all the three groups ,
the nurses ' knowledge was measured before the intervention , and one and four weeks after the intervention .
data
were collected by a questionnaire .
results : significant differences were observed between the mean scores of the three groups one and four
weeks after the intervention ( f=26.17 , p=0.001 and f=4.07 , p=0.020 , respectively ) , and post hoc test showed
that this difference was due to the higher score in e - learning group . both e - learning and booklet methods could
effectively improve nurses ' knowledge ( =23.03 , p=0.001 and =51.71 , p=0.001 , respectively ) .
conclusion : according to the results of this study , electronic learning was more effective than booklet in enhancing
the learning and retention of knowledge .
electronic learning is suggested as a more suitable method as
it provides appropriate interactions and attractive virtual environments to motivate the learners and promote
retention .</s> |
Belgian prosecutors launched a public appeal Thursday seeking any information on the "man in hat" suspect in the Brussels Airport suicide bombings that killed 16 people.
Belgian Federal Prosecutor Eric Van der Sypt said authorities were especially interested in any people who might have filmed or photographed the man.
He was seen at the airport with two suicide bombers before they died in the March 22 attacks. A subsequent explosion at Brussels' Maelbeek subway station killed another 16 people the same morning.
Photos released by prosecutors showed the "man in hat" leaving the airport on foot, walking to the nearby town of Zaventem and then into Brussels, where all traces of him were reportedly lost.
The suspect also wore a white jacket but discarded it at some point, prosecutors said.
The appeal for public assistance more than two weeks after the suicide bombings indicated that investigators have hit a standstill. Three bombers, two at the airport and one in the subway, also died in the attacks, which were claimed by Islamic State.
According to a video reconstitution of the suspect's itinerary presented to reporters, the man left the Brussels Airport terminal at 7:58 a.m. before two other men he was with in the building exploded suitcases laden with explosives. He passed by a Sheraton hotel, walked through the town of Zaventem, discarded his jacket, and was seen on video footage at Meiser square in northeastern Brussels at 9:42 a.m.
3 Brussels attackers dead, more sought Interpol photos Clockwise from left: Najim Laachraoui and Ibrahim El Bakraoui are dead, killed in suicide blasts at the Brussels airport, authorities said. Khalid El Bakraoui, Ibrahim's brother, died in the suicide attack on the Brussels subway a short while later. A third man, the "man in hat" was seen on security video at the airport with the two dead attackers and is being sought by authorities. Clockwise from left: Najim Laachraoui and Ibrahim El Bakraoui are dead, killed in suicide blasts at the Brussels airport, authorities said. Khalid El Bakraoui, Ibrahim's brother, died in the suicide attack on the Brussels subway a short while later. A third man, the "man in hat" was seen on security video at the airport with the two dead attackers and is being sought by authorities. (Interpol photos) (Interpol photos)
Eight minutes later, his trail vanishes.
Belgian authorities are hoping that they or someone finds the discarded light-colored jacket, saying it could yield precious clues. Federal Prosecutor Thierry Werts also said there had been many people around the hotel when the suspect walked by who may now be overseas, and asked for their assistance as well.
Prosecutors asked "people who might have filmed or taken a photograph of the suspect or think they can provide extra information" to call a special telephone number or to email authorities.
Earlier Thursday, the lawyer for Paris attacks suspect Salah Abdeslam said it will take some weeks before his client can be extradited from Belgium to France.
Sven Mary spoke after a legal hearing on the Belgian-born French citizen's continuing detention in Belgium. He said the existing "Belgian arrest warrant must be lifted for (Abdeslam's) transfer" to France, in accordance with the extradition request.
Shrapnel Laurent Dubrule / EPA A piece of steel and a screw recovered from the body of a person injured in the March 22 terrorist attacks, at a hospital in Leuven, Belgium, on March 24, 2016. A piece of steel and a screw recovered from the body of a person injured in the March 22 terrorist attacks, at a hospital in Leuven, Belgium, on March 24, 2016. (Laurent Dubrule / EPA) (Laurent Dubrule / EPA)
Mary said before Belgian authorities allow Abdeslam to leave they want to question the 26-year-old about another case β a deadly police raid in the Forest neighborhood of Brussels days before his arrest.
Abdeslam fled to Belgium after the deadly Nov. 13 attacks on Paris and was arrested March 18 after four months on the run. Since his arrest he has been in a prison in the Belgian city of Bruges.
He faces preliminary terrorism charges in France for the Paris attacks, which killed 130 people and left hundreds wounded.
Associated Press ||||| Skip Ad Ad Loading... x Embed x Share Belgian Federal police released this video showing what they believe is the escape route of one of the terrorists involved in the attack on the Brussels airport. Video by Jasper Colt, USA TODAY
A photo presented by Belgian federal prosecutors shows a suspect wanted in connection with the Brussels attacks of March 22. (Photo: Olivier Hoslet, epa)
Belgian prosecutors released new video footage Thursday of a suspected Brussels Airport attacker, showing the apparent route he took after fleeing the carnage.
The video shows the suspect walking down streets in the town of Zaventem, where the airport is located, and later in Brussels. It also provides an animated aerial view of his path.
Eric Van Der Sypt, spokesman for the federal prosecutor's office, asked anyone who may have seen or inadvertently photographed the man to come forward. Van Der Sypt said the man apparently discarded his jacket, and urged anyone who may have found the clothing to turn it in.
"The jacket he left behind is bright with a hood which is dark inside. Should this jacket be found, this might give invaluable information to the investigators," Van Der Sypt said. He said the suspect's shirt was bright blue with yokes on the elbows. He was also wearing dark trousers and brown shoes with a large white sole.
The attacks at the airport and a subway station March 22 left 32 victims and three suicide bombers dead. The Islamic State claimed responsibility for the strikes.
Two bombers died in the blasts at the airport. On previously released surveillance video, the suspected third attacker, wearing a hat and light-colored jacket, is shown walking beside the two other terrorists. A still frame seen around the world shows the man pushing a cart with luggage that authorities say contained a 35-pound bomb. That bomb, the largest the terrorists made for that day, did not detonate.
An intensive manhunt has been underway for the man, notoriously known as either "the man in the hat" or "the man in white." Police took a man into custody more than week ago but released him a short time later saying he apparently was not the man they sought from the video.
The other two men in the airport surveillance video have been identified as Ibrahim El Bakraoui, 29, and Najim Laachraoui, a bomb-maker linked by DNA to the Paris terror attacks in November that killed 130 people.
The European Parliament said Wednesday that Laachraoui worked for a parliament cleaning contractor for about a month in 2009 and again in 2010 while he as a student.
Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels bombers originally planned more attacks in Paris | 0:56 Prosecutors say the Brussels attackers were originally targeting Paris in a second wave of attacks.Video provided by Newsy Newslook 1 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 'Man in hat' among several Brussels bombing suspects arrested | 0:45 Authorities have arrested several suspects in the Brussels bombings, including one of the wanted men seen in airport surveillance footage.Video provided by Newsy Newslook 2 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Muslims Honor Brussels Attacks Victims | 0:55 Representatives of Belgium's Muslim communities gathered outside Maelbeek Metro station on Saturday to pay their respects to those killed in an attack at the station last month. (April 9) AP 3 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Police Continue Raid Operations in Brussels | 1:27 A police operation was under way on Saturday in the Brussels district of Etterbeek after Belgian officials confirmed a sixth arrest over suspected links to the March 22 Brussels bombings. Five others were arrested on Friday. (April 9) AP 4 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Belgian police arrest 6th suspect in attacks | 0:25 Belgium's justice minister Koen Geens said Belgian authorities arrested a sixth person late on Friday in connection with the suicide attacks in Brussels. Wochit 5 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: New Images of Brussels Airport Suspect | 1:07 Belgium's Federal Prosecutor's Office has released new video and surveillance photographs of a suspect wanted in connection with the deadly Brussels airport attack. (April 7) AP 6 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels attacker's escape route traced by Belgian police | 2:09 Belgian Federal police released this video showing what they believe is the escape route of one of the terrorists involved in the attack on the Brussels airport. Video by Jasper Colt, USA TODAY 7 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels death toll revised to 32 | 0:37 Belgian authorities have lowered the death toll from last week's Brussels suicide attacks to 32 victims after "thorough verification," a day after they had raised the number of dead to 35. Video provided by AFP Newslook 8 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION U.S. couple dead in Brussels were avid travelers | 0:44 Justin and Stephanie Shults moved to Belgium a few years after getting married. They loved exploring new cities together. VPC 9 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Parents of Belgium survivor thankful for support | 1:10 The parents of a U.S. teen injured in the Brussels attacks said Friday they are thankful for the support they have received from around the world. (March 25) AP 10 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels attack: What we know so far | 1:06 Americans were among those killed in the Brussels terror attacks, confirmed by U.S. Secretary of State John Kerry, who traveled to Belgium to hold counter-terrorism talks with European officials. VPC 11 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels Attack Survivor: βI Feel Luckyβ | 2:39 Mason Wells, a 19-year-old from Utah, is expected to make a full recovery after surviving the bombing attack at the Brussels airport on Tuesday. (March 25) AP 12 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 5 things to know about the Brussels terror attacks | 1:00 Tragedy struck Brussels when bombers targeted Brussels Airport and a city metro station. ISIL is claiming responsibility for the violence. VPC 13 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 3 things we still don't know about the Brussels attack | 0:44 While investigators try to piece together the Brussels attack, many questions about the terrorists involved and missing victims still remain unanswered. VPC 14 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Kerry confirms that Americans died in Brussels attack | 0:46 U.S. Secretary of State John Kerry confirmed that Americans were among the dead after the terrorist attacks in Belgium. USA TODAY 15 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Hundreds Honor Brussels Attack Victims | 1:13 Hundreds of people gathered at Place de La Bourse in central Brussels on Thursday to observe a minute of silence for the victims of attacks that hit the city two days ago. (March 24) AP 16 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Ohio volunteers return home from Brussels attack | 0:49 Two volunteers from Ohio have returned home after being in the Brussels airport when two bombs exploded, killing at least 30 people and injuring scores. (March 24) AP 17 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: EU Lawmakers Pay Respects In Belgium | 0:55 Lawmakers and the King and Queen of Belgium held a minute of silence on Wednesday for the victims of the Brussels attacks that claimed 34 lives and injured dozens on Tuesday. Officials also laid a wreath at the Maelbeek metro station. (March 23) AP 18 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION ISIL claims responsibility for deadly explosions in Brussels | 1:40 The multiple explosions have killed at least 34 people at an airport and a subway station in Brussels.Video provided by Newsy Newslook 19 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Manhunt Underway For Brussels Bombing Suspect | 1:41 Belgian authorities searched Wednesday for a man pictured with two apparent suicide bombers, a day after 34 people were killed, including three suicide bombers, and more than 200 wounded in attacks at the Brussels airport and subway. (March 23) AP 20 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 3 Mormon missionaries from Utah hurt in Brussels attacks | 1:03 Three Mormon missionaries from Utah were injured during the explosions at Brussels' international airport. Video provided by Newsy Newslook 21 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION U.S. cities step up security after Belgium attacks | 1:54 US Cities ramped up security at airports, transit systems and landmarks across the country Tuesday following the deadly terror attacks in Brussels. Still, officials assured Americans they knew of no specific or credible threats. (March 22) AP 22 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Obama: We 'stand in solidarity' with people of Belgium | 0:48 President Barack Obama commented on the Brussels terror attacks before addressing the people of Cuba in Havana. He said the world needs to unite to fight violence and terrorism. USA TODAY 23 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Fear, panic as people escape from Brussels attacks | 1:21 Dramatic raw videos show people fleeing from Brussels airport and a metro station after several deadly explosions rocked the city. USA TODAY 24 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Brussels airport damaged after attacks | 0:51 Attackers detonated bombs at the airport and on a metro train beneath the European Union's capital on Tuesday, killing at least 31 people and wounding dozens. AP 25 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION France to deploy 1,600 extra police after Brussels attacks | 1:05 French Interior Minister Bernard Cazeneuve Tuesday said Paris was deploying 1,600 additional police to border crossings and air, sea and rail infrastructure after the Brussels attacks which killed at least 21 people. Newslook 26 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Inside Brussels airport and subway attacks | 2:34 Video of passengers trapped inside the Brussels airport and inside the underground transport system in immediate aftermath of two explosions at the airport and one in the metro system. AP 27 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Inside Belgium airport after attack | 2:09 The immediate aftermath of the explosion at the departure terminal at Brussels' Zavantem airport was caught on camera on Tuesday. AP 28 of 28 Last VideoNext Video Brussels bombers originally planned more attacks in Paris
'Man in hat' among several Brussels bombing suspects arrested
Raw: Muslims Honor Brussels Attacks Victims
Raw: Police Continue Raid Operations in Brussels
Belgian police arrest 6th suspect in attacks
Raw: New Images of Brussels Airport Suspect
Brussels attacker's escape route traced by Belgian police
Brussels death toll revised to 32
U.S. couple dead in Brussels were avid travelers
Parents of Belgium survivor thankful for support
Brussels attack: What we know so far
Brussels Attack Survivor: βI Feel Luckyβ
5 things to know about the Brussels terror attacks
3 things we still don't know about the Brussels attack
Kerry confirms that Americans died in Brussels attack
Raw: Hundreds Honor Brussels Attack Victims
Ohio volunteers return home from Brussels attack
Raw: EU Lawmakers Pay Respects In Belgium
ISIL claims responsibility for deadly explosions in Brussels
Manhunt Underway For Brussels Bombing Suspect
3 Mormon missionaries from Utah hurt in Brussels attacks
U.S. cities step up security after Belgium attacks
Obama: We 'stand in solidarity' with people of Belgium
Fear, panic as people escape from Brussels attacks
Raw: Brussels airport damaged after attacks
France to deploy 1,600 extra police after Brussels attacks
Raw: Inside Brussels airport and subway attacks
Raw: Inside Belgium airport after attack
Also identified in the Brussels attacks is Khalid El Bakraoui, 27, Ibrahim's brother, who blew himself up in a subway car at a metro station.
Earlier Thursday, lawyers for Salah Abdeslam said it could be weeks before the Paris bombing suspect is extradited from Belgium to France. Abdeslam is accused of helping plan the Paris attacks and then fleeing the city in the hours of chaos following the violence. He was captured in Belgium four days before the Brussels attack.
On Tuesday, the U.S. State Department designated Abdeslam a global terrorist. The department said witnesses identified Abdeslam as the driver of a car full of gunmen who killed patrons at Paris restaurants, and that authorities found his DNA on a discarded suicide belt and along with traces of explosives in a Brussels apartment.
"Abdeslam stated after his arrest that he planned on conducting a suicide bombing outside of the Paris soccer stadium, but had βbacked out,'" the State Department said in a statement.
Read or Share this story: http://usat.ly/1MUK25U ||||| Breaking News Emails Get breaking news alerts and special reports. The news and stories that matter, delivered weekday mornings.
Police released new images Thursday showing the so-called man in white behind the Brussels Airport bombing and appealed for help from the public in tracing his escape from the scene of the attack.
Prosecutors in Belgium confirmed that the unidentified man was still on the run and said he ditched his light-colored jacket in the minutes after the bombing.
Sureveillance footage shows new images of the Brussels terror attack suspect. Belgian Police Department
Surveillance video showed the figure, also dubbed "the man in hat," walking past the nearby Sheraton hotel and an Avis car rental parking lot. He was later seen in the town of Zaventem wearing just a bright shirt with rolled-up sleeves and elbow patches.
He appears to be walking calmly but at one point breaks into a slow jog.
Federal prosecutor's spokesman Eric Van der Sypt said that authorities were especially appealing to people who might have filmed or photographed the man, and said the discarded jacket could also yield clues to the March 22 atrocity.
Earlier video of the suspect at the airport showed him wearing a dark hat and glasses while pushing a luggage cart loaded with a black bag.
Two other men next to him in that video β Najim Laachraoui and Ibrahim El Bakraoui β blew themselves up in the attack. Bakraouiβs brother, Khalid, carried out an attack in the Brussels subway on the same day. Thirty-two victims were killed in the bombings.
Police sources had at one point named the man in the hat and light jacket as Laachraoui, a suspected bomb maker in the November 13 attack in Paris. However, officials later corrected that and said Laachraoui had died in the Brussels attack.
Earlier Thursday, the lawyer for Paris attacks suspect Salah Abdeslam said it will take some weeks before his client can be extradited from Belgium to France.
Sven Mary spoke after a legal hearing on the Belgian-born French citizen's continuing detention in Belgium.
Separately, a court in Brussels extended the detention of other suspects linked to the Brussels attacks β Mohamed B., 37, Yassine A., 30, and Aboubaker O., 28. They were arrested March 27. ||||| The footage released on Thursday by the Belgian federal police, with French and Flemish voice-overs, provided a first look at how the man in the hat left the airport right after the bombings, and where he went.
βAfter the bombs exploded at 7:58, the man wearing a bright jacket and a hat went out of the building, walked past the Sheraton hotel, turned right toward the Avis car parking lot and left the airport area,β the video commentary said.
To Share Information
The video, using images from Google Maps, outlines the suspectβs trajectory with a red dot. The surveillance footage shows him walking away from the airport in the midst of travelers and bystanders. Although at one point he can be seen jogging lightly, he appears to be walking at a normal pace most of the time.
The suspect then walked through Zaventem, the town several miles northeast of Brussels where the airport is, and got rid of his jacket, according to the video commentary.
βThe jacket he left behind is bright, with a hood which is dark inside,β the video said, providing close-up pictures of the clothing. βShould this jacket be found, this might give invaluable information to the investigators.β
The suspect was seen at 8:50 a.m. at the intersection of two roads in Zaventem, at which point he was wearing βa bright shirt with rolled-up sleeves,β which the police said appeared to be βbright blue with yokes on the elbows.β He was also wearing βdark trousers and brown shoes with a large white sole,β the video said.
Advertisement Continue reading the main story
The suspect was then recorded by closed-circuit TV in Schaerbeek, a neighborhood of Brussels that is southwest of Zaventem β first at 9:42 a.m. and again at 9:49 a.m. He was last caught on camera at 9:50 a.m., at the intersection of the Avenue de la BrabanΓ§onne and the Rue du Noyer in Schaerbeek, according to the police video.
Schaerbeek, a mixed community with a sizeable immigrant population, has been tied to both the Brussels attacks and the Nov. 13 attacks in Paris.
The DNA of Najim Laachraoui, one of the Brussels Airport suicide bombers, was found in a rented apartment there on Rue Henri BergΓ©. Investigators believe the apartment was used as a place to make suicide vests for the Paris assailants.
After the Brussels attacks, Belgian police discovered bomb-making equipment in another apartment in Schaerbeek, on Rue Max Roos, where investigators also found a discarded computer containing the βwillβ of the second airport suicide bomber, Ibrahim el-Bakraoui. His brother, Khalid, was the subway station bomber.
βIf you saw a left-behind bright-colored jacket between the airport and the ChaussΓ©e de Louvain,β the narrator says, referring to a street that enters Schaerbeek, βor if you saw the offender while he was on the run, or if you know which way he went afterward, please contact the investigators.β
Todayβs Headlines: European Morning Get news and analysis from Europe and around the world delivered to your inbox every day in the European morning.
The Belgian federal prosecutorβs office also made a series of announcements later on Thursday over cases that are not directly connected to the Brussels attacks, but that have underscored the complex array of networks and suspected terrorist plots currently being investigated in France and Belgium.
The prosecutorβs office said that a court in Brussels had extended by one month the detentions of three men arrested on March 27 in connection with an unspecified terrorism investigation, of two Algerian men linked to a foiled plot in France, and of three Belgian men who were detained in connection with the Paris attacks.
The prosecutorβs office also announced one additional month of detention for Salah Abdeslam, believed to be the sole surviving direct participant in the Paris attacks, who was arrested in Brussels on March 18 after a four-month manhunt.
Advertisement Continue reading the main story
Earlier on Thursday, Mr. Abdeslamβs Belgian lawyer, Sven Mary, told reporters in Brussels that it would take several weeks before his client was extradited to France and that the Belgian authorities wanted to question him about a deadly raid in the Forest section of Brussels that police officers conducted several days before Mr. Abdeslamβs arrest.
The detention of a suspected accomplice of Mr. Abdeslam, who was arrested alongside him and has been identified as Amine Choukri, but also Soufien Ayari, was also extended, the prosecutorβs office said.
Separately, the police in Copenhagen arrested four men suspected of joining the Islamic State while in Syria, with the intention of committing terrorist crimes, the authorities said on Thursday.
The men were detained in several different areas of the Danish capital around 10 a.m., said Mads Jensen, a spokesman for the Copenhagen police, as part of a joint operation with the Danish security services.
He added that searches had been performed, and that ammunition and weapons had been seized. The suspects will be arraigned on Friday at a closed hearing.
According to an April report released by the International Center for Counterterrorism in The Hague, more fighters have returned to Denmark from Syria on a per-capita basis than to any other country in Europe.
In neighboring Sweden, a 20-year-old man who was taken into custody in Stockholm on Feb. 11 on suspicion of planning a terrorist act was charged on Thursday. The prosecutor said the man, whose identity has not been released, was planning a suicide attack. It would have been the first in Sweden since Taimour Abdulwahab al-Abdaly killed himself and wounded two others in 2010. | β Almost two weeks after admitting they arrested the wrong man, Belgian authorities say the real "man in the hat" has surfaced in surveillance video from after the Brussels attacks. The footage shows the alleged terroristβwearing a hat, glasses, and a light-colored jacketβleaving the Brussels Airport near Zaventem at 7:58am on March 22 and passing a Sheraton hotel, reports the Chicago Tribune. He's then spotted at an intersection in Zaventem around 8:50am wearing a bright blue shirt, having discarded his jacket, per the New York Times. He's captured on video again at Meiser Square in northeastern Brussels at 9:42am but disappears in the Schaerbeek neighborhood eight minutes later. "The jacket he left behind is bright with a hood which is dark inside. Should this jacket be found, this might give invaluable information to the investigators," an official says. Authorities are also asking people who may have seen or photographed the manβincluding tourists who've returned homeβto come forward, per USA Today. The "man in the hat" first sparked interest when he was spotted on the morning of the attacks alongside Najim Laachraoui and Ibrahim El Bakraoui, who later blew themselves up; Bakraoui's brother, Khalid, attacked the Brussels subway, per NBC News. Authorities now say he was pushing luggage containing a 35-pound bomb that failed to explode. | <s>[INST]Belgian prosecutors launched a public appeal Thursday seeking any information on the "man in hat" suspect in the Brussels Airport suicide bombings that killed 16 people.
Belgian Federal Prosecutor Eric Van der Sypt said authorities were especially interested in any people who might have filmed or photographed the man.
He was seen at the airport with two suicide bombers before they died in the March 22 attacks. A subsequent explosion at Brussels' Maelbeek subway station killed another 16 people the same morning.
Photos released by prosecutors showed the "man in hat" leaving the airport on foot, walking to the nearby town of Zaventem and then into Brussels, where all traces of him were reportedly lost.
The suspect also wore a white jacket but discarded it at some point, prosecutors said.
The appeal for public assistance more than two weeks after the suicide bombings indicated that investigators have hit a standstill. Three bombers, two at the airport and one in the subway, also died in the attacks, which were claimed by Islamic State.
According to a video reconstitution of the suspect's itinerary presented to reporters, the man left the Brussels Airport terminal at 7:58 a.m. before two other men he was with in the building exploded suitcases laden with explosives. He passed by a Sheraton hotel, walked through the town of Zaventem, discarded his jacket, and was seen on video footage at Meiser square in northeastern Brussels at 9:42 a.m.
3 Brussels attackers dead, more sought Interpol photos Clockwise from left: Najim Laachraoui and Ibrahim El Bakraoui are dead, killed in suicide blasts at the Brussels airport, authorities said. Khalid El Bakraoui, Ibrahim's brother, died in the suicide attack on the Brussels subway a short while later. A third man, the "man in hat" was seen on security video at the airport with the two dead attackers and is being sought by authorities. Clockwise from left: Najim Laachraoui and Ibrahim El Bakraoui are dead, killed in suicide blasts at the Brussels airport, authorities said. Khalid El Bakraoui, Ibrahim's brother, died in the suicide attack on the Brussels subway a short while later. A third man, the "man in hat" was seen on security video at the airport with the two dead attackers and is being sought by authorities. (Interpol photos) (Interpol photos)
Eight minutes later, his trail vanishes.
Belgian authorities are hoping that they or someone finds the discarded light-colored jacket, saying it could yield precious clues. Federal Prosecutor Thierry Werts also said there had been many people around the hotel when the suspect walked by who may now be overseas, and asked for their assistance as well.
Prosecutors asked "people who might have filmed or taken a photograph of the suspect or think they can provide extra information" to call a special telephone number or to email authorities.
Earlier Thursday, the lawyer for Paris attacks suspect Salah Abdeslam said it will take some weeks before his client can be extradited from Belgium to France.
Sven Mary spoke after a legal hearing on the Belgian-born French citizen's continuing detention in Belgium. He said the existing "Belgian arrest warrant must be lifted for (Abdeslam's) transfer" to France, in accordance with the extradition request.
Shrapnel Laurent Dubrule / EPA A piece of steel and a screw recovered from the body of a person injured in the March 22 terrorist attacks, at a hospital in Leuven, Belgium, on March 24, 2016. A piece of steel and a screw recovered from the body of a person injured in the March 22 terrorist attacks, at a hospital in Leuven, Belgium, on March 24, 2016. (Laurent Dubrule / EPA) (Laurent Dubrule / EPA)
Mary said before Belgian authorities allow Abdeslam to leave they want to question the 26-year-old about another case β a deadly police raid in the Forest neighborhood of Brussels days before his arrest.
Abdeslam fled to Belgium after the deadly Nov. 13 attacks on Paris and was arrested March 18 after four months on the run. Since his arrest he has been in a prison in the Belgian city of Bruges.
He faces preliminary terrorism charges in France for the Paris attacks, which killed 130 people and left hundreds wounded.
Associated Press ||||| Skip Ad Ad Loading... x Embed x Share Belgian Federal police released this video showing what they believe is the escape route of one of the terrorists involved in the attack on the Brussels airport. Video by Jasper Colt, USA TODAY
A photo presented by Belgian federal prosecutors shows a suspect wanted in connection with the Brussels attacks of March 22. (Photo: Olivier Hoslet, epa)
Belgian prosecutors released new video footage Thursday of a suspected Brussels Airport attacker, showing the apparent route he took after fleeing the carnage.
The video shows the suspect walking down streets in the town of Zaventem, where the airport is located, and later in Brussels. It also provides an animated aerial view of his path.
Eric Van Der Sypt, spokesman for the federal prosecutor's office, asked anyone who may have seen or inadvertently photographed the man to come forward. Van Der Sypt said the man apparently discarded his jacket, and urged anyone who may have found the clothing to turn it in.
"The jacket he left behind is bright with a hood which is dark inside. Should this jacket be found, this might give invaluable information to the investigators," Van Der Sypt said. He said the suspect's shirt was bright blue with yokes on the elbows. He was also wearing dark trousers and brown shoes with a large white sole.
The attacks at the airport and a subway station March 22 left 32 victims and three suicide bombers dead. The Islamic State claimed responsibility for the strikes.
Two bombers died in the blasts at the airport. On previously released surveillance video, the suspected third attacker, wearing a hat and light-colored jacket, is shown walking beside the two other terrorists. A still frame seen around the world shows the man pushing a cart with luggage that authorities say contained a 35-pound bomb. That bomb, the largest the terrorists made for that day, did not detonate.
An intensive manhunt has been underway for the man, notoriously known as either "the man in the hat" or "the man in white." Police took a man into custody more than week ago but released him a short time later saying he apparently was not the man they sought from the video.
The other two men in the airport surveillance video have been identified as Ibrahim El Bakraoui, 29, and Najim Laachraoui, a bomb-maker linked by DNA to the Paris terror attacks in November that killed 130 people.
The European Parliament said Wednesday that Laachraoui worked for a parliament cleaning contractor for about a month in 2009 and again in 2010 while he as a student.
Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels bombers originally planned more attacks in Paris | 0:56 Prosecutors say the Brussels attackers were originally targeting Paris in a second wave of attacks.Video provided by Newsy Newslook 1 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 'Man in hat' among several Brussels bombing suspects arrested | 0:45 Authorities have arrested several suspects in the Brussels bombings, including one of the wanted men seen in airport surveillance footage.Video provided by Newsy Newslook 2 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Muslims Honor Brussels Attacks Victims | 0:55 Representatives of Belgium's Muslim communities gathered outside Maelbeek Metro station on Saturday to pay their respects to those killed in an attack at the station last month. (April 9) AP 3 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Police Continue Raid Operations in Brussels | 1:27 A police operation was under way on Saturday in the Brussels district of Etterbeek after Belgian officials confirmed a sixth arrest over suspected links to the March 22 Brussels bombings. Five others were arrested on Friday. (April 9) AP 4 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Belgian police arrest 6th suspect in attacks | 0:25 Belgium's justice minister Koen Geens said Belgian authorities arrested a sixth person late on Friday in connection with the suicide attacks in Brussels. Wochit 5 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: New Images of Brussels Airport Suspect | 1:07 Belgium's Federal Prosecutor's Office has released new video and surveillance photographs of a suspect wanted in connection with the deadly Brussels airport attack. (April 7) AP 6 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels attacker's escape route traced by Belgian police | 2:09 Belgian Federal police released this video showing what they believe is the escape route of one of the terrorists involved in the attack on the Brussels airport. Video by Jasper Colt, USA TODAY 7 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels death toll revised to 32 | 0:37 Belgian authorities have lowered the death toll from last week's Brussels suicide attacks to 32 victims after "thorough verification," a day after they had raised the number of dead to 35. Video provided by AFP Newslook 8 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION U.S. couple dead in Brussels were avid travelers | 0:44 Justin and Stephanie Shults moved to Belgium a few years after getting married. They loved exploring new cities together. VPC 9 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Parents of Belgium survivor thankful for support | 1:10 The parents of a U.S. teen injured in the Brussels attacks said Friday they are thankful for the support they have received from around the world. (March 25) AP 10 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels attack: What we know so far | 1:06 Americans were among those killed in the Brussels terror attacks, confirmed by U.S. Secretary of State John Kerry, who traveled to Belgium to hold counter-terrorism talks with European officials. VPC 11 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Brussels Attack Survivor: βI Feel Luckyβ | 2:39 Mason Wells, a 19-year-old from Utah, is expected to make a full recovery after surviving the bombing attack at the Brussels airport on Tuesday. (March 25) AP 12 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 5 things to know about the Brussels terror attacks | 1:00 Tragedy struck Brussels when bombers targeted Brussels Airport and a city metro station. ISIL is claiming responsibility for the violence. VPC 13 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 3 things we still don't know about the Brussels attack | 0:44 While investigators try to piece together the Brussels attack, many questions about the terrorists involved and missing victims still remain unanswered. VPC 14 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Kerry confirms that Americans died in Brussels attack | 0:46 U.S. Secretary of State John Kerry confirmed that Americans were among the dead after the terrorist attacks in Belgium. USA TODAY 15 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Hundreds Honor Brussels Attack Victims | 1:13 Hundreds of people gathered at Place de La Bourse in central Brussels on Thursday to observe a minute of silence for the victims of attacks that hit the city two days ago. (March 24) AP 16 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Ohio volunteers return home from Brussels attack | 0:49 Two volunteers from Ohio have returned home after being in the Brussels airport when two bombs exploded, killing at least 30 people and injuring scores. (March 24) AP 17 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: EU Lawmakers Pay Respects In Belgium | 0:55 Lawmakers and the King and Queen of Belgium held a minute of silence on Wednesday for the victims of the Brussels attacks that claimed 34 lives and injured dozens on Tuesday. Officials also laid a wreath at the Maelbeek metro station. (March 23) AP 18 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION ISIL claims responsibility for deadly explosions in Brussels | 1:40 The multiple explosions have killed at least 34 people at an airport and a subway station in Brussels.Video provided by Newsy Newslook 19 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Manhunt Underway For Brussels Bombing Suspect | 1:41 Belgian authorities searched Wednesday for a man pictured with two apparent suicide bombers, a day after 34 people were killed, including three suicide bombers, and more than 200 wounded in attacks at the Brussels airport and subway. (March 23) AP 20 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION 3 Mormon missionaries from Utah hurt in Brussels attacks | 1:03 Three Mormon missionaries from Utah were injured during the explosions at Brussels' international airport. Video provided by Newsy Newslook 21 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION U.S. cities step up security after Belgium attacks | 1:54 US Cities ramped up security at airports, transit systems and landmarks across the country Tuesday following the deadly terror attacks in Brussels. Still, officials assured Americans they knew of no specific or credible threats. (March 22) AP 22 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Obama: We 'stand in solidarity' with people of Belgium | 0:48 President Barack Obama commented on the Brussels terror attacks before addressing the people of Cuba in Havana. He said the world needs to unite to fight violence and terrorism. USA TODAY 23 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Fear, panic as people escape from Brussels attacks | 1:21 Dramatic raw videos show people fleeing from Brussels airport and a metro station after several deadly explosions rocked the city. USA TODAY 24 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Brussels airport damaged after attacks | 0:51 Attackers detonated bombs at the airport and on a metro train beneath the European Union's capital on Tuesday, killing at least 31 people and wounding dozens. AP 25 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION France to deploy 1,600 extra police after Brussels attacks | 1:05 French Interior Minister Bernard Cazeneuve Tuesday said Paris was deploying 1,600 additional police to border crossings and air, sea and rail infrastructure after the Brussels attacks which killed at least 21 people. Newslook 26 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Inside Brussels airport and subway attacks | 2:34 Video of passengers trapped inside the Brussels airport and inside the underground transport system in immediate aftermath of two explosions at the airport and one in the metro system. AP 27 of 28 Skip Ad Ad Loading... x Embed x Share TERROR ATTACKS ROCK BRUSSELS AIRPORT, METRO STATION Raw: Inside Belgium airport after attack | 2:09 The immediate aftermath of the explosion at the departure terminal at Brussels' Zavantem airport was caught on camera on Tuesday. AP 28 of 28 Last VideoNext Video Brussels bombers originally planned more attacks in Paris
'Man in hat' among several Brussels bombing suspects arrested
Raw: Muslims Honor Brussels Attacks Victims
Raw: Police Continue Raid Operations in Brussels
Belgian police arrest 6th suspect in attacks
Raw: New Images of Brussels Airport Suspect
Brussels attacker's escape route traced by Belgian police
Brussels death toll revised to 32
U.S. couple dead in Brussels were avid travelers
Parents of Belgium survivor thankful for support
Brussels attack: What we know so far
Brussels Attack Survivor: βI Feel Luckyβ
5 things to know about the Brussels terror attacks
3 things we still don't know about the Brussels attack
Kerry confirms that Americans died in Brussels attack
Raw: Hundreds Honor Brussels Attack Victims
Ohio volunteers return home from Brussels attack
Raw: EU Lawmakers Pay Respects In Belgium
ISIL claims responsibility for deadly explosions in Brussels
Manhunt Underway For Brussels Bombing Suspect
3 Mormon missionaries from Utah hurt in Brussels attacks
U.S. cities step up security after Belgium attacks
Obama: We 'stand in solidarity' with people of Belgium
Fear, panic as people escape from Brussels attacks
Raw: Brussels airport damaged after attacks
France to deploy 1,600 extra police after Brussels attacks
Raw: Inside Brussels airport and subway attacks
Raw: Inside Belgium airport after attack
Also identified in the Brussels attacks is Khalid El Bakraoui, 27, Ibrahim's brother, who blew himself up in a subway car at a metro station.
Earlier Thursday, lawyers for Salah Abdeslam said it could be weeks before the Paris bombing suspect is extradited from Belgium to France. Abdeslam is accused of helping plan the Paris attacks and then fleeing the city in the hours of chaos following the violence. He was captured in Belgium four days before the Brussels attack.
On Tuesday, the U.S. State Department designated Abdeslam a global terrorist. The department said witnesses identified Abdeslam as the driver of a car full of gunmen who killed patrons at Paris restaurants, and that authorities found his DNA on a discarded suicide belt and along with traces of explosives in a Brussels apartment.
"Abdeslam stated after his arrest that he planned on conducting a suicide bombing outside of the Paris soccer stadium, but had βbacked out,'" the State Department said in a statement.
Read or Share this story: http://usat.ly/1MUK25U ||||| Breaking News Emails Get breaking news alerts and special reports. The news and stories that matter, delivered weekday mornings.
Police released new images Thursday showing the so-called man in white behind the Brussels Airport bombing and appealed for help from the public in tracing his escape from the scene of the attack.
Prosecutors in Belgium confirmed that the unidentified man was still on the run and said he ditched his light-colored jacket in the minutes after the bombing.
Sureveillance footage shows new images of the Brussels terror attack suspect. Belgian Police Department
Surveillance video showed the figure, also dubbed "the man in hat," walking past the nearby Sheraton hotel and an Avis car rental parking lot. He was later seen in the town of Zaventem wearing just a bright shirt with rolled-up sleeves and elbow patches.
He appears to be walking calmly but at one point breaks into a slow jog.
Federal prosecutor's spokesman Eric Van der Sypt said that authorities were especially appealing to people who might have filmed or photographed the man, and said the discarded jacket could also yield clues to the March 22 atrocity.
Earlier video of the suspect at the airport showed him wearing a dark hat and glasses while pushing a luggage cart loaded with a black bag.
Two other men next to him in that video β Najim Laachraoui and Ibrahim El Bakraoui β blew themselves up in the attack. Bakraouiβs brother, Khalid, carried out an attack in the Brussels subway on the same day. Thirty-two victims were killed in the bombings.
Police sources had at one point named the man in the hat and light jacket as Laachraoui, a suspected bomb maker in the November 13 attack in Paris. However, officials later corrected that and said Laachraoui had died in the Brussels attack.
Earlier Thursday, the lawyer for Paris attacks suspect Salah Abdeslam said it will take some weeks before his client can be extradited from Belgium to France.
Sven Mary spoke after a legal hearing on the Belgian-born French citizen's continuing detention in Belgium.
Separately, a court in Brussels extended the detention of other suspects linked to the Brussels attacks β Mohamed B., 37, Yassine A., 30, and Aboubaker O., 28. They were arrested March 27. ||||| The footage released on Thursday by the Belgian federal police, with French and Flemish voice-overs, provided a first look at how the man in the hat left the airport right after the bombings, and where he went.
βAfter the bombs exploded at 7:58, the man wearing a bright jacket and a hat went out of the building, walked past the Sheraton hotel, turned right toward the Avis car parking lot and left the airport area,β the video commentary said.
To Share Information
The video, using images from Google Maps, outlines the suspectβs trajectory with a red dot. The surveillance footage shows him walking away from the airport in the midst of travelers and bystanders. Although at one point he can be seen jogging lightly, he appears to be walking at a normal pace most of the time.
The suspect then walked through Zaventem, the town several miles northeast of Brussels where the airport is, and got rid of his jacket, according to the video commentary.
βThe jacket he left behind is bright, with a hood which is dark inside,β the video said, providing close-up pictures of the clothing. βShould this jacket be found, this might give invaluable information to the investigators.β
The suspect was seen at 8:50 a.m. at the intersection of two roads in Zaventem, at which point he was wearing βa bright shirt with rolled-up sleeves,β which the police said appeared to be βbright blue with yokes on the elbows.β He was also wearing βdark trousers and brown shoes with a large white sole,β the video said.
Advertisement Continue reading the main story
The suspect was then recorded by closed-circuit TV in Schaerbeek, a neighborhood of Brussels that is southwest of Zaventem β first at 9:42 a.m. and again at 9:49 a.m. He was last caught on camera at 9:50 a.m., at the intersection of the Avenue de la BrabanΓ§onne and the Rue du Noyer in Schaerbeek, according to the police video.
Schaerbeek, a mixed community with a sizeable immigrant population, has been tied to both the Brussels attacks and the Nov. 13 attacks in Paris.
The DNA of Najim Laachraoui, one of the Brussels Airport suicide bombers, was found in a rented apartment there on Rue Henri BergΓ©. Investigators believe the apartment was used as a place to make suicide vests for the Paris assailants.
After the Brussels attacks, Belgian police discovered bomb-making equipment in another apartment in Schaerbeek, on Rue Max Roos, where investigators also found a discarded computer containing the βwillβ of the second airport suicide bomber, Ibrahim el-Bakraoui. His brother, Khalid, was the subway station bomber.
βIf you saw a left-behind bright-colored jacket between the airport and the ChaussΓ©e de Louvain,β the narrator says, referring to a street that enters Schaerbeek, βor if you saw the offender while he was on the run, or if you know which way he went afterward, please contact the investigators.β
Todayβs Headlines: European Morning Get news and analysis from Europe and around the world delivered to your inbox every day in the European morning.
The Belgian federal prosecutorβs office also made a series of announcements later on Thursday over cases that are not directly connected to the Brussels attacks, but that have underscored the complex array of networks and suspected terrorist plots currently being investigated in France and Belgium.
The prosecutorβs office said that a court in Brussels had extended by one month the detentions of three men arrested on March 27 in connection with an unspecified terrorism investigation, of two Algerian men linked to a foiled plot in France, and of three Belgian men who were detained in connection with the Paris attacks.
The prosecutorβs office also announced one additional month of detention for Salah Abdeslam, believed to be the sole surviving direct participant in the Paris attacks, who was arrested in Brussels on March 18 after a four-month manhunt.
Advertisement Continue reading the main story
Earlier on Thursday, Mr. Abdeslamβs Belgian lawyer, Sven Mary, told reporters in Brussels that it would take several weeks before his client was extradited to France and that the Belgian authorities wanted to question him about a deadly raid in the Forest section of Brussels that police officers conducted several days before Mr. Abdeslamβs arrest.
The detention of a suspected accomplice of Mr. Abdeslam, who was arrested alongside him and has been identified as Amine Choukri, but also Soufien Ayari, was also extended, the prosecutorβs office said.
Separately, the police in Copenhagen arrested four men suspected of joining the Islamic State while in Syria, with the intention of committing terrorist crimes, the authorities said on Thursday.
The men were detained in several different areas of the Danish capital around 10 a.m., said Mads Jensen, a spokesman for the Copenhagen police, as part of a joint operation with the Danish security services.
He added that searches had been performed, and that ammunition and weapons had been seized. The suspects will be arraigned on Friday at a closed hearing.
According to an April report released by the International Center for Counterterrorism in The Hague, more fighters have returned to Denmark from Syria on a per-capita basis than to any other country in Europe.
In neighboring Sweden, a 20-year-old man who was taken into custody in Stockholm on Feb. 11 on suspicion of planning a terrorist act was charged on Thursday. The prosecutor said the man, whose identity has not been released, was planning a suicide attack. It would have been the first in Sweden since Taimour Abdulwahab al-Abdaly killed himself and wounded two others in 2010.[/INST]β Almost two weeks after admitting they arrested the wrong man, Belgian authorities say the real "man in the hat" has surfaced in surveillance video from after the Brussels attacks. The footage shows the alleged terroristβwearing a hat, glasses, and a light-colored jacketβleaving the Brussels Airport near Zaventem at 7:58am on March 22 and passing a Sheraton hotel, reports the Chicago Tribune. He's then spotted at an intersection in Zaventem around 8:50am wearing a bright blue shirt, having discarded his jacket, per the New York Times. He's captured on video again at Meiser Square in northeastern Brussels at 9:42am but disappears in the Schaerbeek neighborhood eight minutes later. "The jacket he left behind is bright with a hood which is dark inside. Should this jacket be found, this might give invaluable information to the investigators," an official says. Authorities are also asking people who may have seen or photographed the manβincluding tourists who've returned homeβto come forward, per USA Today. The "man in the hat" first sparked interest when he was spotted on the morning of the attacks alongside Najim Laachraoui and Ibrahim El Bakraoui, who later blew themselves up; Bakraoui's brother, Khalid, attacked the Brussels subway, per NBC News. Authorities now say he was pushing luggage containing a 35-pound bomb that failed to explode.</s> |
we reviewed 6533 meld / peld exception applications derived and extracted from the unos database via a data request submission to the scientific registry of transplant recipients .
these meld appeals for exception points were submitted to rrbs through unet between 2005 and 2008 , representing 3337 patients .
this analysis included all sequential initial applications as well as subsequent appeals of denied applications and threemonth extensions for each patient included in the original rrb application .
any application that was in effect at unos during this time period but was submitted and approved prior to january 1 , 2005 , was excluded from this data extraction and analysis .
other exclusions included applications for hcc that did not meet the criteria in policy 3.6.4.4 , including patients with tumors outside the t2 criteria and patients with downstaged
this analysis also excluded patients automatically not approved due to some administrative reason ( e.g. , missed extension deadline ) .
to establish the patients ' clinical profiles for this data analysis , three reviews of the data set were carried out . to maintain consistency in the scoring system , one analyst completed the initial review process and scored each patient blindly , after which two additional analysts did separate reviews to confirm the scoring .
the first review established a complete list of all diagnoses that were presented to the rrbs via electronic submission as the reason for the rrb appeal for meld exception points .
the second case review scored each case and each subsequent appeal , if applicable , and identified up to 10 exception diagnoses which were placed as the exception code(s ) for each patient .
exception code because many patients had multiple diagnoses that were included in the appeal for review points and which could be a specific lifethreatening disease , such as gi bleeding or infection .
an example of the latter would be diagnoses such as gi bleeding and sepsis that could result in being discussed and possibly listed for transplantation with a primary exception score or being listed for retransplantation .
these perceived lifethreatening medical complications were presented to the rrbs when the patient 's advocate determined that the singular or composite diagnosis could influence wait list mortality or wait list removal as too ill .
after completion of this initial process , two additional analysts separately performed secondary validations of the scoring ; one analyst reviewed the entire data set ; the second analyst reviewed a randomly selected subset representing 10% of the patient cohort ; both reviews confirmed the accuracy and consistency of the exception coding .
specifically , 16 endofthemonth snapshots from 2005 to 2008 were extracted from the optn database .
the percentage of patients with an exception was calculated as an average across all 16 time points . to include similar candidates in the numerator and denominator , candidates listed as status 1a/1b or temporarily inactive
the percentage of exception applications that were denied by the rrb was computed for each of the 11 regions .
only initial applications were included in this analysis ( appeals and extensions excluded ) . due to limitation in the sample sizes when stratified by both region and diagnosis , the analysis was limited to the three most common diagnoses for exception ( ascites / hepatic hydrothorax , cholangitis / bacteremia , and bleeding ) .
a generalized linear mixedeffects model with logit link function was fit for the outcome of rrb decision using region as a covariate ; a second model was fit to adjust for the number of diagnoses designated as bases for exception as well as region .
both models include a random intercept grouped by patient i d to account for correlation between multiple applications from the same patient .
all regions , including the region with no denials , were included in the mixedeffects modeling .
likelihood ratio tests were used to assess the overall significance of the variable region . before further analyzing transplantation rates ,
the dataset was reduced to one record per unique patient i d by deleting duplicate applications and concatenating or removing multiple applications for the same patient .
the rates of removal due to transplant were computed , and homogeneity across regions in the rates was tested using a pearson 's chisquared test .
independence between rrb decision and removal for transplantation was assessed using a chisquared test for both the overall sample and within each region , and odds ratios comparing approved and denied patients were computed .
a likelihood ratio test was used to assess the regional variation in the effect of application status on the odds of receiving transplantation .
mortality rates for exception approved and denied patients were calculated using the kaplan meier estimate ; the difference in survival between the groups was assessed using the logrank test .
the hazard ratio for denied vs. approved patients was estimated using the cox proportional hazards model .
patients with removal code 8 in the optn database ( indicating removal due to death ) were recorded as having had the event ; survival times for all other removal codes were treated as censored .
the analyses were performed using the statistical software r : a language and environment for statistical computing , version 3.1.1 .
we reviewed 6533 meld / peld exception applications derived and extracted from the unos database via a data request submission to the scientific registry of transplant recipients .
these meld appeals for exception points were submitted to rrbs through unet between 2005 and 2008 , representing 3337 patients .
this analysis included all sequential initial applications as well as subsequent appeals of denied applications and threemonth extensions for each patient included in the original rrb application .
any application that was in effect at unos during this time period but was submitted and approved prior to january 1 , 2005 , was excluded from this data extraction and analysis .
other exclusions included applications for hcc that did not meet the criteria in policy 3.6.4.4 , including patients with tumors outside the t2 criteria and patients with downstaged
this analysis also excluded patients automatically not approved due to some administrative reason ( e.g. , missed extension deadline ) .
to establish the patients ' clinical profiles for this data analysis , three reviews of the data set were carried out . to maintain consistency in the scoring system , one analyst completed the initial review process and scored each patient blindly , after which two additional analysts did separate reviews to confirm the scoring .
the first review established a complete list of all diagnoses that were presented to the rrbs via electronic submission as the reason for the rrb appeal for meld exception points .
the second case review scored each case and each subsequent appeal , if applicable , and identified up to 10 exception diagnoses which were placed as the exception code(s ) for each patient .
exception code because many patients had multiple diagnoses that were included in the appeal for review points and which could be a specific lifethreatening disease , such as gi bleeding or infection .
an example of the latter would be diagnoses such as gi bleeding and sepsis that could result in being discussed and possibly listed for transplantation with a primary exception score or being listed for retransplantation .
these perceived lifethreatening medical complications were presented to the rrbs when the patient 's advocate determined that the singular or composite diagnosis could influence wait list mortality or wait list removal as too ill .
after completion of this initial process , two additional analysts separately performed secondary validations of the scoring ; one analyst reviewed the entire data set ; the second analyst reviewed a randomly selected subset representing 10% of the patient cohort ; both reviews confirmed the accuracy and consistency of the exception coding .
the percentage of patients on the liver waiting list with exceptions was calculated using snapshots of the waiting list at a point in time .
specifically , 16 endofthemonth snapshots from 2005 to 2008 were extracted from the optn database .
the percentage of patients with an exception was calculated as an average across all 16 time points . to include similar candidates in the numerator and denominator , candidates listed as status 1a/1b or temporarily inactive
the percentage of exception applications that were denied by the rrb was computed for each of the 11 regions .
only initial applications were included in this analysis ( appeals and extensions excluded ) . due to limitation in the sample sizes when stratified by both region and diagnosis , the analysis was limited to the three most common diagnoses for exception ( ascites / hepatic hydrothorax , cholangitis / bacteremia , and bleeding ) .
a generalized linear mixedeffects model with logit link function was fit for the outcome of rrb decision using region as a covariate ; a second model was fit to adjust for the number of diagnoses designated as bases for exception as well as region .
both models include a random intercept grouped by patient i d to account for correlation between multiple applications from the same patient .
all regions , including the region with no denials , were included in the mixedeffects modeling .
likelihood ratio tests were used to assess the overall significance of the variable region . before further analyzing transplantation rates ,
the dataset was reduced to one record per unique patient i d by deleting duplicate applications and concatenating or removing multiple applications for the same patient .
the rates of removal due to transplant were computed , and homogeneity across regions in the rates was tested using a pearson 's chisquared test .
independence between rrb decision and removal for transplantation was assessed using a chisquared test for both the overall sample and within each region , and odds ratios comparing approved and denied patients were computed .
a likelihood ratio test was used to assess the regional variation in the effect of application status on the odds of receiving transplantation .
mortality rates for exception approved and denied patients were calculated using the kaplan meier estimate ; the difference in survival between the groups was assessed using the logrank test .
the hazard ratio for denied vs. approved patients was estimated using the cox proportional hazards model .
patients with removal code 8 in the optn database ( indicating removal due to death ) were recorded as having had the event ; survival times for all other removal codes were treated as censored .
the analyses were performed using the statistical software r : a language and environment for statistical computing , version 3.1.1 .
the median age of patients was 50 ; 60% were male ; 73% were white ; 12% hispanic ; and 8.1% black .
the top 10 diagnoses and combined diagnoses which were the bases for exceptions for initial applications are shown in tables 1 , 2 , 3 , 4 .
diagnoses such as cholangitis , infection , and bacteremia were grouped , as were diagnoses such as quality of life , pain , and pruritus . the number of patients who were appealed for each region ranged from 62 to 443 . when adjusted by total number of active , nonstatus one patients ,
the range was 2.76.6% , including hcc cases , and 1.12.8% , excluding hcc cases .
bases for exception for all applications combineda : top 10 diagnoses these top 10 diagnoses represent 85% of all patients . including initial applications , appeals , and extensions .
bases for exceptions for initial applications only : top 10 diagnoses these top 10 diagnoses represent 84% of all patients .
bases for exception for all applications combineda : top 10 pairs of diagnoses including initial applications , appeals , and extensions .
bases for exception for all applications combineda : top 10 triples of diagnoses including initial applications , appeals , and extensions .
the chance of approval by region ranged from 54.7% to 100% ( p <
0.0001 ) ; inversely , denial rates ranged from 0% to 45.3% ( fig . 1 ) .
for refractory ascites / hepatic hydrothorax , the denial rate by region ranged from 24.1% to 80% ( excluding one region with 0% denials ) , p < 0.0001 ( fig . 1 ) . for cholangitis / bacteremia ,
< 0.0001 ) and for bleeding , 8.3% to 75% ( p = 0.0026 ; fig . 1 ) . the percentage of initial exception applications that were denied by regional review boards in each of the 11 regions .
the percentage of initial exception applications that were denied is shown on the vertical axis .
top left : all bases for exception ; top right : ascites / hepatic hydrothorax only ; bottom left : cholangitis / bacteremia only ; bottom right : bleeding only .
based on the likelihood ratio test , there was significant variation by region in the odds of denial , even when controlling for number of diagnoses ( p < 0.0001 ) .
when adjusting for region , number of diagnoses was not found to be significant ( p = 0.074 ) .
number of diagnoses did not appear to have a large impact on the effect for region , as suggested by the relatively small perturbation of estimated effects between the two models displayed in table 5 .
fig . 2 displays a heat map visualizing the proportion of applications denied , crosstabulated by region and number of diagnoses . the data for these analyses include region 6 , which had no denials .
generalized linear mixedeffects model fits for impact of region on the odds of denial the estimated coefficients represent the effects of region and number of diagnoses on the log odds of denial ; larger values correspond to greater odds that a patient is denied .
region 8 is used as the reference level and its effect appears as the intercept term .
region 6 has very large negative coefficients and standard errors because there were zero denials in this region .
heat map displaying proportion of applications denied , crosstabulated by region and number of diagnoses .
cells for which there were zero applications for a given region and number of diagnoses are colored gray . after reducing the dataset to one record per patient ,
2178 subjects had their request for exception points approved and 882 had their request denied .
of these 3060 subjects , 2320 received a transplant , 666 were removed from the list for a reason other than transplant , and 74 had censored removal time .
there was significant evidence that transplantation rate varies by region ( p < 0.001 ; table 6 ) .
the chance of removal for transplant was found to be significantly different ( p < 0.001 ) between patients approved for exception points ( 82.4% ) and those who were not approved ( 65.7% ; table 7 ) .
the effect of exception application status on the odds of removal for transplant was not found to vary significantly across regions ( p = 0.526 ) .
corresponding results for removal due to reasons other than transplant are given in tables 6 and 7 ; the chance of removal for reasons other than transplant was found to be significantly different ( p < 0.001 ) between patients approved for exception points ( 17.6% ) and those who were not approved ( 34.3% ) , with the odds for approved patients in the overall sample estimated to be 0.41 times that of patients not approved . among patients removed from the list for reasons other than transplant , death ( 40.5% ) and deteriorating health condition ( 26.7% ) were the most frequent causes of removal , together accounting for just over twothirds of all such removals .
improving health conditions were responsible for just 12.6% of all patients removed from the wait list without a transplant ( fig . 3 ) .
transplantation rates by region transplantation rates by region , according to regional review board decision reasons for removal from the wait list other than receiving transplant .
there was a significant difference in survival following rrb decision between approved and denied patients ( p = 0.025 ) , with denied patients having a higher risk of mortality while on the waiting list than approved patients ( hazard ratio 1.322 , 95% confidence interval , 1.036 , 1.688 ) .
estimated mortality rates for 90day , 180day , oneyr , threeyr , and fiveyr survival are given in table 8 .
curves for the five most frequent diagnoses specified as the main basis for exception among denied patients are plotted in fig .
kaplan meier estimates of mortality ( 95% confidence intervals )
kaplan meier curves for approved and denied patients .
kaplan meier curves within denied patients , stratified by top five most frequent diagnoses .
with the ultimate goal of achieving fair and equitable allocation of organs , a number of modifications of liver allocation policies have been described , including those related to socioeconomic issues , transplant benefit , preventing discrimination , feasibility , and geography .
the latter was given particular prominence as an area of concern with the april 1998 publication by united states department of health & human services ( hhs ) of the organ procurement and transplantation network ; final rule which specifically mandated that neither place of residence nor place of listing shall be a major determinant of access to a transplant 6 .
at the time this rule was announced , hhs summarized its intent as being to assure that allocation of scarce organs will be based on common medical criteria , not accidents of geography 7 .
more than a decade and a half later , we have found a large and highly statistically significant variation in denial rates in various unos regions for appeals by patients with medical illnesses that are not addressed by the meld components .
although such discrepancies are widely observed and recognized in the transplant community , our study is one of only a handful of studies to both determine the regional variation in rrb approval rates and show the serious consequences of this variation for the transplantation rates themselves , for which we also found strong evidence of substantial variation by region .
it comes as no surprise that approved exception applicants were shown to have a statistically significant increase in the odds of transplantation , with their odds of receiving a transplant approximately two and onehalf times that of patients not approved .
we found that this effect does not appear to vary by region , suggesting that the variation in transplant rates is driven , at least in part , by the variation in appeal denial rates .
we also clearly showed that among those patients who are eventually removed from the wait list for reasons other than transplant , a deterioration in health condition or death account for slightly more than twothirds of removals .
this highlights the accuracy of appeals to rrbs where the providers are predicting a high risk of death or medical deterioration where the patient may not survive until the liver transplantation using standard meld criteria for organ allocation .
contrary to the opinion that has sometimes been expressed , only a small percentage of removals ( 12.6% ) are the result of improving health .
a potential limitation of this study is that it does not fully explore the role that may be played by diagnosis type and severity as explanatory factors of the regional variation in rrb decisions . when considering the list of top five diagnoses within each region , refractory ascites and cholangitis appear in the lists for all 11 regions ,
while hepatocellular carcinoma and bleeding occur in ten and nine of the lists , respectively .
thus , in terms of diagnoses , the regions are fairly similar but not uniform .
estimation of the specific effect of regional differences in diagnosis types is an area for further study .
regional differences in severity may also have some effect on the observed phenomenon . while data on the severity for each case were not available , we did attempt to adjust for some measure of patient status by including the number of diagnoses listed as a covariate in the glm analysis . while not ideal , this measure may capture some of the information on severity and
looking at the overall results of our analyses , it seems very clear that , for some patients , accidents of geography are still a factor in determining transplantation outcome and , ultimately , survival . in june 2010 ,
the optn / unos board charged the liver and intestinal organ transplantation committee with making recommendations to reduce geographic disparities in waitlist mortality 8 . with consideration of public feedback , the concept document : next steps toward improving liver distribution was developed 8 .
the three key concepts proposed for further consideration were share 15 national , expedited graft placement , and tiered regional sharing and sharing threshold .
share 15 national and share 35 regional were implemented in june 2013 . in share 15
national , adult deceased donor livers are offered nationally to status 1 patients and patients with meld 15 or higher before local / regional / national patients with meld scores < 15 . in share 35 regional , adult deceased donor livers are offered to regional patients with meld scores above 35 before local patients below a meld score of 35 .
all of these concepts assume that meld scores are assigned in the same manner throughout the nation .
our data clearly demonstrate wide variations across regions for patients with nonstandard meld exception conditions . as share 15 national and share 35 regional
however , there have been ongoing and evolving discussions by the liver and intestinal organ transplantation committee related to making recommendations to further reduce geographic disparities in wait list mortality by moving to expanded sharing policies .
having agreed in 2012 that the geographic disparities in organ allocation were unacceptably high , the optn / unos board of directors charged the liver and intestinal organ transplantation committee to investigate how the current geographic patterns of organ distribution may affect transplant candidates ' chances to receive organ offers . in the concept paper presented by the committee in june 2014 ,
it is clearly acknowledged that despite changes over the years , geographic variation in the level of medical urgency many candidates must reach to receive liver transplants has not been significantly reduced , with candidates in some parts of the country having to wait until they are much more severely ill compared to patients in other areas 9 .
one possibility suggested to decrease overall variation in meld / peld scores at which candidates receive a transplant is organ distribution based on a limited number of allocation districts instead of the existing local and regional boundaries .
statistical modeling shows that these optimized maps might reduce variation in the meld / peld scores at transplant and reduce both waiting list and total deaths .
the committee also proposed consideration of changing to a national review board , noting that , just as we have shown in our study , the current rrb system does not promote consistent reviews of the meld / peld scores nationwide . in an ideal world , research identifying factors associated with wait list removals for patients with each of the nonred conditions would have been carried out and used to construct a predictive model that accurately estimates risk of waiting list removals .
that identified risk could then serve as the measure by which prioritization is determined . unfortunately , little research has yet been performed and
because many such conditions occur infrequently , valid cohort studies that could result in reproducible , clinically relevant results may not be possible in the near term , if ever .
thus , for the foreseeable future , expert opinion will continue to play a key role in prioritization policy .
the large variation across unos regions in denial rates for patient appeals which we report here gives strong support for the creation of an alternate system .
we suggest simultaneously moving toward super regional / national sharing concepts and , as has been proposed by the liver and intestinal organ transplantation committee and other authors 2 , 5 , a national review board to replace the current rrb system for nonstandard conditions which require meld exceptions .
ideally , a national review board process that uses current clinical knowledge combined with standardized data collection methods and analysis protocols could assign priority on a consistent basis .
a new program that includes a national policy with consistency in the medical criteria and scores assigned for nonred conditions could help to prevent meld creep or meld inflation , greatly reduce regionally driven meld inequities , and disincentivize today 's situation in which some patients with resources ( especially financial ) pursue centers with high rates of approval for exceptions and shorter wait times . at the same time , data on transplant benefit and wait list removals for disease progression should be collected for each nonred condition to improve the knowledge base with which guidelines can be developed .
ultimately , a rational approach to a national system created through changes in unos policy may be our best hope for equalizing the assignment of meld exception points and providing equity for transplant candidates in all regions with the singular or composite medical illnesses that currently fall in the category of nonred conditions .
robert g. gish : concept / design , data collection , drafting article , critical revision of article , and approval of article ; robert j. wong : data analysis / interpretation , critical revision of article , and approval of article ; gordon honerkampsmith : statistics , data analysis / interpretation , critical revision of article , and approval of article ; ronghui xu : statistics , data analysis / interpretation , approval of article ; robert w. osorio : data analysis / interpretation , drafting article , critical revision of article , and approval of article . | abstractalthough it has been generally recognized that there are inconsistencies among regional review boards in the assignment of points for model for endstage liver disease ( meld)/pediatric endstage liver disease ( peld ) exception patients with resulting considerable variation in appeal denial rates , data to actually prove this have been limited .
we reviewed 6533 meld / peld exception applications submitted between 2005 and 2008 , calculated the variation in approval / denial rates , and followed these cases through mid2013 to assess the effects on patient outcomes .
we found highly significant regional variations in denial rates for appeals by exception patients and in transplantation rates .
the odds of transplant for patients whose appeals are approved is 2.45 times that of patients not approved ; that this effect does not vary by region suggests that the variation in transplant rates is driven , at least in part , by the variation in appeal denial rates .
health deterioration or death accounts for more than twothirds of wait list removals among patients removed for reasons other than transplant .
our findings add to the weight of evidence that a national review board that uses current clinical expertise , peer review literature , and data to consistently assign priority could reduce regional inequities and move toward equitable allocation of organs and compliance with the united states department of health & human services final rule . | <s>[INST]we reviewed 6533 meld / peld exception applications derived and extracted from the unos database via a data request submission to the scientific registry of transplant recipients .
these meld appeals for exception points were submitted to rrbs through unet between 2005 and 2008 , representing 3337 patients .
this analysis included all sequential initial applications as well as subsequent appeals of denied applications and threemonth extensions for each patient included in the original rrb application .
any application that was in effect at unos during this time period but was submitted and approved prior to january 1 , 2005 , was excluded from this data extraction and analysis .
other exclusions included applications for hcc that did not meet the criteria in policy 3.6.4.4 , including patients with tumors outside the t2 criteria and patients with downstaged
this analysis also excluded patients automatically not approved due to some administrative reason ( e.g. , missed extension deadline ) .
to establish the patients ' clinical profiles for this data analysis , three reviews of the data set were carried out . to maintain consistency in the scoring system , one analyst completed the initial review process and scored each patient blindly , after which two additional analysts did separate reviews to confirm the scoring .
the first review established a complete list of all diagnoses that were presented to the rrbs via electronic submission as the reason for the rrb appeal for meld exception points .
the second case review scored each case and each subsequent appeal , if applicable , and identified up to 10 exception diagnoses which were placed as the exception code(s ) for each patient .
exception code because many patients had multiple diagnoses that were included in the appeal for review points and which could be a specific lifethreatening disease , such as gi bleeding or infection .
an example of the latter would be diagnoses such as gi bleeding and sepsis that could result in being discussed and possibly listed for transplantation with a primary exception score or being listed for retransplantation .
these perceived lifethreatening medical complications were presented to the rrbs when the patient 's advocate determined that the singular or composite diagnosis could influence wait list mortality or wait list removal as too ill .
after completion of this initial process , two additional analysts separately performed secondary validations of the scoring ; one analyst reviewed the entire data set ; the second analyst reviewed a randomly selected subset representing 10% of the patient cohort ; both reviews confirmed the accuracy and consistency of the exception coding .
specifically , 16 endofthemonth snapshots from 2005 to 2008 were extracted from the optn database .
the percentage of patients with an exception was calculated as an average across all 16 time points . to include similar candidates in the numerator and denominator , candidates listed as status 1a/1b or temporarily inactive
the percentage of exception applications that were denied by the rrb was computed for each of the 11 regions .
only initial applications were included in this analysis ( appeals and extensions excluded ) . due to limitation in the sample sizes when stratified by both region and diagnosis , the analysis was limited to the three most common diagnoses for exception ( ascites / hepatic hydrothorax , cholangitis / bacteremia , and bleeding ) .
a generalized linear mixedeffects model with logit link function was fit for the outcome of rrb decision using region as a covariate ; a second model was fit to adjust for the number of diagnoses designated as bases for exception as well as region .
both models include a random intercept grouped by patient i d to account for correlation between multiple applications from the same patient .
all regions , including the region with no denials , were included in the mixedeffects modeling .
likelihood ratio tests were used to assess the overall significance of the variable region . before further analyzing transplantation rates ,
the dataset was reduced to one record per unique patient i d by deleting duplicate applications and concatenating or removing multiple applications for the same patient .
the rates of removal due to transplant were computed , and homogeneity across regions in the rates was tested using a pearson 's chisquared test .
independence between rrb decision and removal for transplantation was assessed using a chisquared test for both the overall sample and within each region , and odds ratios comparing approved and denied patients were computed .
a likelihood ratio test was used to assess the regional variation in the effect of application status on the odds of receiving transplantation .
mortality rates for exception approved and denied patients were calculated using the kaplan meier estimate ; the difference in survival between the groups was assessed using the logrank test .
the hazard ratio for denied vs. approved patients was estimated using the cox proportional hazards model .
patients with removal code 8 in the optn database ( indicating removal due to death ) were recorded as having had the event ; survival times for all other removal codes were treated as censored .
the analyses were performed using the statistical software r : a language and environment for statistical computing , version 3.1.1 .
we reviewed 6533 meld / peld exception applications derived and extracted from the unos database via a data request submission to the scientific registry of transplant recipients .
these meld appeals for exception points were submitted to rrbs through unet between 2005 and 2008 , representing 3337 patients .
this analysis included all sequential initial applications as well as subsequent appeals of denied applications and threemonth extensions for each patient included in the original rrb application .
any application that was in effect at unos during this time period but was submitted and approved prior to january 1 , 2005 , was excluded from this data extraction and analysis .
other exclusions included applications for hcc that did not meet the criteria in policy 3.6.4.4 , including patients with tumors outside the t2 criteria and patients with downstaged
this analysis also excluded patients automatically not approved due to some administrative reason ( e.g. , missed extension deadline ) .
to establish the patients ' clinical profiles for this data analysis , three reviews of the data set were carried out . to maintain consistency in the scoring system , one analyst completed the initial review process and scored each patient blindly , after which two additional analysts did separate reviews to confirm the scoring .
the first review established a complete list of all diagnoses that were presented to the rrbs via electronic submission as the reason for the rrb appeal for meld exception points .
the second case review scored each case and each subsequent appeal , if applicable , and identified up to 10 exception diagnoses which were placed as the exception code(s ) for each patient .
exception code because many patients had multiple diagnoses that were included in the appeal for review points and which could be a specific lifethreatening disease , such as gi bleeding or infection .
an example of the latter would be diagnoses such as gi bleeding and sepsis that could result in being discussed and possibly listed for transplantation with a primary exception score or being listed for retransplantation .
these perceived lifethreatening medical complications were presented to the rrbs when the patient 's advocate determined that the singular or composite diagnosis could influence wait list mortality or wait list removal as too ill .
after completion of this initial process , two additional analysts separately performed secondary validations of the scoring ; one analyst reviewed the entire data set ; the second analyst reviewed a randomly selected subset representing 10% of the patient cohort ; both reviews confirmed the accuracy and consistency of the exception coding .
the percentage of patients on the liver waiting list with exceptions was calculated using snapshots of the waiting list at a point in time .
specifically , 16 endofthemonth snapshots from 2005 to 2008 were extracted from the optn database .
the percentage of patients with an exception was calculated as an average across all 16 time points . to include similar candidates in the numerator and denominator , candidates listed as status 1a/1b or temporarily inactive
the percentage of exception applications that were denied by the rrb was computed for each of the 11 regions .
only initial applications were included in this analysis ( appeals and extensions excluded ) . due to limitation in the sample sizes when stratified by both region and diagnosis , the analysis was limited to the three most common diagnoses for exception ( ascites / hepatic hydrothorax , cholangitis / bacteremia , and bleeding ) .
a generalized linear mixedeffects model with logit link function was fit for the outcome of rrb decision using region as a covariate ; a second model was fit to adjust for the number of diagnoses designated as bases for exception as well as region .
both models include a random intercept grouped by patient i d to account for correlation between multiple applications from the same patient .
all regions , including the region with no denials , were included in the mixedeffects modeling .
likelihood ratio tests were used to assess the overall significance of the variable region . before further analyzing transplantation rates ,
the dataset was reduced to one record per unique patient i d by deleting duplicate applications and concatenating or removing multiple applications for the same patient .
the rates of removal due to transplant were computed , and homogeneity across regions in the rates was tested using a pearson 's chisquared test .
independence between rrb decision and removal for transplantation was assessed using a chisquared test for both the overall sample and within each region , and odds ratios comparing approved and denied patients were computed .
a likelihood ratio test was used to assess the regional variation in the effect of application status on the odds of receiving transplantation .
mortality rates for exception approved and denied patients were calculated using the kaplan meier estimate ; the difference in survival between the groups was assessed using the logrank test .
the hazard ratio for denied vs. approved patients was estimated using the cox proportional hazards model .
patients with removal code 8 in the optn database ( indicating removal due to death ) were recorded as having had the event ; survival times for all other removal codes were treated as censored .
the analyses were performed using the statistical software r : a language and environment for statistical computing , version 3.1.1 .
the median age of patients was 50 ; 60% were male ; 73% were white ; 12% hispanic ; and 8.1% black .
the top 10 diagnoses and combined diagnoses which were the bases for exceptions for initial applications are shown in tables 1 , 2 , 3 , 4 .
diagnoses such as cholangitis , infection , and bacteremia were grouped , as were diagnoses such as quality of life , pain , and pruritus . the number of patients who were appealed for each region ranged from 62 to 443 . when adjusted by total number of active , nonstatus one patients ,
the range was 2.76.6% , including hcc cases , and 1.12.8% , excluding hcc cases .
bases for exception for all applications combineda : top 10 diagnoses these top 10 diagnoses represent 85% of all patients . including initial applications , appeals , and extensions .
bases for exceptions for initial applications only : top 10 diagnoses these top 10 diagnoses represent 84% of all patients .
bases for exception for all applications combineda : top 10 pairs of diagnoses including initial applications , appeals , and extensions .
bases for exception for all applications combineda : top 10 triples of diagnoses including initial applications , appeals , and extensions .
the chance of approval by region ranged from 54.7% to 100% ( p <
0.0001 ) ; inversely , denial rates ranged from 0% to 45.3% ( fig . 1 ) .
for refractory ascites / hepatic hydrothorax , the denial rate by region ranged from 24.1% to 80% ( excluding one region with 0% denials ) , p < 0.0001 ( fig . 1 ) . for cholangitis / bacteremia ,
< 0.0001 ) and for bleeding , 8.3% to 75% ( p = 0.0026 ; fig . 1 ) . the percentage of initial exception applications that were denied by regional review boards in each of the 11 regions .
the percentage of initial exception applications that were denied is shown on the vertical axis .
top left : all bases for exception ; top right : ascites / hepatic hydrothorax only ; bottom left : cholangitis / bacteremia only ; bottom right : bleeding only .
based on the likelihood ratio test , there was significant variation by region in the odds of denial , even when controlling for number of diagnoses ( p < 0.0001 ) .
when adjusting for region , number of diagnoses was not found to be significant ( p = 0.074 ) .
number of diagnoses did not appear to have a large impact on the effect for region , as suggested by the relatively small perturbation of estimated effects between the two models displayed in table 5 .
fig . 2 displays a heat map visualizing the proportion of applications denied , crosstabulated by region and number of diagnoses . the data for these analyses include region 6 , which had no denials .
generalized linear mixedeffects model fits for impact of region on the odds of denial the estimated coefficients represent the effects of region and number of diagnoses on the log odds of denial ; larger values correspond to greater odds that a patient is denied .
region 8 is used as the reference level and its effect appears as the intercept term .
region 6 has very large negative coefficients and standard errors because there were zero denials in this region .
heat map displaying proportion of applications denied , crosstabulated by region and number of diagnoses .
cells for which there were zero applications for a given region and number of diagnoses are colored gray . after reducing the dataset to one record per patient ,
2178 subjects had their request for exception points approved and 882 had their request denied .
of these 3060 subjects , 2320 received a transplant , 666 were removed from the list for a reason other than transplant , and 74 had censored removal time .
there was significant evidence that transplantation rate varies by region ( p < 0.001 ; table 6 ) .
the chance of removal for transplant was found to be significantly different ( p < 0.001 ) between patients approved for exception points ( 82.4% ) and those who were not approved ( 65.7% ; table 7 ) .
the effect of exception application status on the odds of removal for transplant was not found to vary significantly across regions ( p = 0.526 ) .
corresponding results for removal due to reasons other than transplant are given in tables 6 and 7 ; the chance of removal for reasons other than transplant was found to be significantly different ( p < 0.001 ) between patients approved for exception points ( 17.6% ) and those who were not approved ( 34.3% ) , with the odds for approved patients in the overall sample estimated to be 0.41 times that of patients not approved . among patients removed from the list for reasons other than transplant , death ( 40.5% ) and deteriorating health condition ( 26.7% ) were the most frequent causes of removal , together accounting for just over twothirds of all such removals .
improving health conditions were responsible for just 12.6% of all patients removed from the wait list without a transplant ( fig . 3 ) .
transplantation rates by region transplantation rates by region , according to regional review board decision reasons for removal from the wait list other than receiving transplant .
there was a significant difference in survival following rrb decision between approved and denied patients ( p = 0.025 ) , with denied patients having a higher risk of mortality while on the waiting list than approved patients ( hazard ratio 1.322 , 95% confidence interval , 1.036 , 1.688 ) .
estimated mortality rates for 90day , 180day , oneyr , threeyr , and fiveyr survival are given in table 8 .
curves for the five most frequent diagnoses specified as the main basis for exception among denied patients are plotted in fig .
kaplan meier estimates of mortality ( 95% confidence intervals )
kaplan meier curves for approved and denied patients .
kaplan meier curves within denied patients , stratified by top five most frequent diagnoses .
with the ultimate goal of achieving fair and equitable allocation of organs , a number of modifications of liver allocation policies have been described , including those related to socioeconomic issues , transplant benefit , preventing discrimination , feasibility , and geography .
the latter was given particular prominence as an area of concern with the april 1998 publication by united states department of health & human services ( hhs ) of the organ procurement and transplantation network ; final rule which specifically mandated that neither place of residence nor place of listing shall be a major determinant of access to a transplant 6 .
at the time this rule was announced , hhs summarized its intent as being to assure that allocation of scarce organs will be based on common medical criteria , not accidents of geography 7 .
more than a decade and a half later , we have found a large and highly statistically significant variation in denial rates in various unos regions for appeals by patients with medical illnesses that are not addressed by the meld components .
although such discrepancies are widely observed and recognized in the transplant community , our study is one of only a handful of studies to both determine the regional variation in rrb approval rates and show the serious consequences of this variation for the transplantation rates themselves , for which we also found strong evidence of substantial variation by region .
it comes as no surprise that approved exception applicants were shown to have a statistically significant increase in the odds of transplantation , with their odds of receiving a transplant approximately two and onehalf times that of patients not approved .
we found that this effect does not appear to vary by region , suggesting that the variation in transplant rates is driven , at least in part , by the variation in appeal denial rates .
we also clearly showed that among those patients who are eventually removed from the wait list for reasons other than transplant , a deterioration in health condition or death account for slightly more than twothirds of removals .
this highlights the accuracy of appeals to rrbs where the providers are predicting a high risk of death or medical deterioration where the patient may not survive until the liver transplantation using standard meld criteria for organ allocation .
contrary to the opinion that has sometimes been expressed , only a small percentage of removals ( 12.6% ) are the result of improving health .
a potential limitation of this study is that it does not fully explore the role that may be played by diagnosis type and severity as explanatory factors of the regional variation in rrb decisions . when considering the list of top five diagnoses within each region , refractory ascites and cholangitis appear in the lists for all 11 regions ,
while hepatocellular carcinoma and bleeding occur in ten and nine of the lists , respectively .
thus , in terms of diagnoses , the regions are fairly similar but not uniform .
estimation of the specific effect of regional differences in diagnosis types is an area for further study .
regional differences in severity may also have some effect on the observed phenomenon . while data on the severity for each case were not available , we did attempt to adjust for some measure of patient status by including the number of diagnoses listed as a covariate in the glm analysis . while not ideal , this measure may capture some of the information on severity and
looking at the overall results of our analyses , it seems very clear that , for some patients , accidents of geography are still a factor in determining transplantation outcome and , ultimately , survival . in june 2010 ,
the optn / unos board charged the liver and intestinal organ transplantation committee with making recommendations to reduce geographic disparities in waitlist mortality 8 . with consideration of public feedback , the concept document : next steps toward improving liver distribution was developed 8 .
the three key concepts proposed for further consideration were share 15 national , expedited graft placement , and tiered regional sharing and sharing threshold .
share 15 national and share 35 regional were implemented in june 2013 . in share 15
national , adult deceased donor livers are offered nationally to status 1 patients and patients with meld 15 or higher before local / regional / national patients with meld scores < 15 . in share 35 regional , adult deceased donor livers are offered to regional patients with meld scores above 35 before local patients below a meld score of 35 .
all of these concepts assume that meld scores are assigned in the same manner throughout the nation .
our data clearly demonstrate wide variations across regions for patients with nonstandard meld exception conditions . as share 15 national and share 35 regional
however , there have been ongoing and evolving discussions by the liver and intestinal organ transplantation committee related to making recommendations to further reduce geographic disparities in wait list mortality by moving to expanded sharing policies .
having agreed in 2012 that the geographic disparities in organ allocation were unacceptably high , the optn / unos board of directors charged the liver and intestinal organ transplantation committee to investigate how the current geographic patterns of organ distribution may affect transplant candidates ' chances to receive organ offers . in the concept paper presented by the committee in june 2014 ,
it is clearly acknowledged that despite changes over the years , geographic variation in the level of medical urgency many candidates must reach to receive liver transplants has not been significantly reduced , with candidates in some parts of the country having to wait until they are much more severely ill compared to patients in other areas 9 .
one possibility suggested to decrease overall variation in meld / peld scores at which candidates receive a transplant is organ distribution based on a limited number of allocation districts instead of the existing local and regional boundaries .
statistical modeling shows that these optimized maps might reduce variation in the meld / peld scores at transplant and reduce both waiting list and total deaths .
the committee also proposed consideration of changing to a national review board , noting that , just as we have shown in our study , the current rrb system does not promote consistent reviews of the meld / peld scores nationwide . in an ideal world , research identifying factors associated with wait list removals for patients with each of the nonred conditions would have been carried out and used to construct a predictive model that accurately estimates risk of waiting list removals .
that identified risk could then serve as the measure by which prioritization is determined . unfortunately , little research has yet been performed and
because many such conditions occur infrequently , valid cohort studies that could result in reproducible , clinically relevant results may not be possible in the near term , if ever .
thus , for the foreseeable future , expert opinion will continue to play a key role in prioritization policy .
the large variation across unos regions in denial rates for patient appeals which we report here gives strong support for the creation of an alternate system .
we suggest simultaneously moving toward super regional / national sharing concepts and , as has been proposed by the liver and intestinal organ transplantation committee and other authors 2 , 5 , a national review board to replace the current rrb system for nonstandard conditions which require meld exceptions .
ideally , a national review board process that uses current clinical knowledge combined with standardized data collection methods and analysis protocols could assign priority on a consistent basis .
a new program that includes a national policy with consistency in the medical criteria and scores assigned for nonred conditions could help to prevent meld creep or meld inflation , greatly reduce regionally driven meld inequities , and disincentivize today 's situation in which some patients with resources ( especially financial ) pursue centers with high rates of approval for exceptions and shorter wait times . at the same time , data on transplant benefit and wait list removals for disease progression should be collected for each nonred condition to improve the knowledge base with which guidelines can be developed .
ultimately , a rational approach to a national system created through changes in unos policy may be our best hope for equalizing the assignment of meld exception points and providing equity for transplant candidates in all regions with the singular or composite medical illnesses that currently fall in the category of nonred conditions .
robert g. gish : concept / design , data collection , drafting article , critical revision of article , and approval of article ; robert j. wong : data analysis / interpretation , critical revision of article , and approval of article ; gordon honerkampsmith : statistics , data analysis / interpretation , critical revision of article , and approval of article ; ronghui xu : statistics , data analysis / interpretation , approval of article ; robert w. osorio : data analysis / interpretation , drafting article , critical revision of article , and approval of article .[/INST]abstractalthough it has been generally recognized that there are inconsistencies among regional review boards in the assignment of points for model for endstage liver disease ( meld)/pediatric endstage liver disease ( peld ) exception patients with resulting considerable variation in appeal denial rates , data to actually prove this have been limited .
we reviewed 6533 meld / peld exception applications submitted between 2005 and 2008 , calculated the variation in approval / denial rates , and followed these cases through mid2013 to assess the effects on patient outcomes .
we found highly significant regional variations in denial rates for appeals by exception patients and in transplantation rates .
the odds of transplant for patients whose appeals are approved is 2.45 times that of patients not approved ; that this effect does not vary by region suggests that the variation in transplant rates is driven , at least in part , by the variation in appeal denial rates .
health deterioration or death accounts for more than twothirds of wait list removals among patients removed for reasons other than transplant .
our findings add to the weight of evidence that a national review board that uses current clinical expertise , peer review literature , and data to consistently assign priority could reduce regional inequities and move toward equitable allocation of organs and compliance with the united states department of health & human services final rule .</s> |
SECTION 1. SHORT TITLE; TABLE OF CONTENTS.
(a) Short Title.--This Act may be cited as the ``America
Implementing New National Opportunities To Vigorously Accelerate
Technology, Energy, and Science Act'' or the ``America INNOVATES Act''.
(b) Table of Contents.--The table of contents of this Act is as
follows:
Sec. 1. Short title; table of contents.
Sec. 2. Definitions.
Sec. 3. Savings clause.
TITLE I--INNOVATION MANAGEMENT AT DEPARTMENT OF ENERGY
Sec. 101. Under Secretary for Science and Energy.
Sec. 102. Technology transfer and transitions assessment.
TITLE II--CROSS-SECTOR PARTNERSHIPS AND GRANT COMPETITIVENESS
Sec. 201. Agreements for Commercializing Technology pilot program.
Sec. 202. Public-private partnerships for commercialization.
Sec. 203. Inclusion of early-stage technology demonstration in
authorized technology transfer activities.
Sec. 204. Information and resources for startups and small businesses.
Sec. 205. Funding competitiveness for institutions of higher education
and other nonprofit institutions.
TITLE III--ASSESSMENT OF IMPACT
Sec. 301. Report by Government Accountability Office.
SEC. 2. DEFINITIONS.
In this Act:
(1) Department.--The term ``Department'' means the
Department of Energy.
(2) National laboratory.--
(A) In general.--The term ``National Laboratory''
means a nonmilitary national laboratory owned by the
Department.
(B) Inclusions.--The term ``National Laboratory''
includes--
(i) Ames Laboratory;
(ii) Argonne National Laboratory;
(iii) Brookhaven National Laboratory;
(iv) Fermi National Accelerator Laboratory;
(v) Idaho National Laboratory;
(vi) Lawrence Berkeley National Laboratory;
(vii) National Energy Technology
Laboratory;
(viii) National Renewable Energy
Laboratory;
(ix) Oak Ridge National Laboratory;
(x) Pacific Northwest National Laboratory;
(xi) Princeton Plasma Physics Laboratory;
(xii) Savannah River National Laboratory;
(xiii) Stanford Linear Accelerator Center;
(xiv) Thomas Jefferson National Accelerator
Facility; and
(xv) any laboratory operated by the
National Nuclear Security Administration, with
respect to the civilian energy activities
conducted at the laboratory.
(3) Secretary.--The term ``Secretary'' means the Secretary
of Energy.
SEC. 3. SAVINGS CLAUSE.
Nothing in this Act or an amendment made by this Act abrogates or
otherwise affects the primary responsibilities of any National
Laboratory to the Department.
TITLE I--INNOVATION MANAGEMENT AT DEPARTMENT OF ENERGY
SEC. 101. UNDER SECRETARY FOR SCIENCE AND ENERGY.
(a) In General.--Section 202(b) of the Department of Energy
Organization Act (42 U.S.C. 7132(b)) is amended--
(1) by striking ``Under Secretary for Science'' each place
it appears and inserting ``Under Secretary for Science and
Energy''; and
(2) in paragraph (4)--
(A) in subparagraph (F), by striking ``and'' at the
end;
(B) in subparagraph (G), by striking the period at
the end and inserting a semicolon; and
(C) by inserting after subparagraph (G) the
following:
``(H) establish appropriate linkages between
offices under the jurisdiction of the Under Secretary;
and
``(I) perform such functions and duties as the
Secretary shall prescribe, consistent with this
section.''.
(b) Conforming Amendments.--
(1) Section 3164(b)(1) of the Department of Energy Science
Education Enhancement Act (42 U.S.C. 7381a(b)(1)) is amended by
striking ``Under Secretary for Science'' and inserting ``Under
Secretary for Science and Energy''.
(2) Section 641(h)(2) of the United States Energy Storage
Competitiveness Act of 2007 (42 U.S.C. 17231(h)(2)) is amended
by striking ``Under Secretary for Science'' and inserting
``Under Secretary for Science and Energy''.
SEC. 102. TECHNOLOGY TRANSFER AND TRANSITIONS ASSESSMENT.
Not later than 1 year after the date of enactment of this Act, and
annually thereafter, the Secretary shall submit to the Committee on
Energy and Natural Resources of the Senate and the Committee on
Science, Space, and Technology of the House of Representatives a report
that includes--
(1) an assessment of the ability of the Department to carry
out the goals of section 1001 of the Energy Policy Act of 2005
(42 U.S.C. 16391), including an assessment of the role and
effectiveness of the Director of the Office of Technology
Transitions; and
(2) recommendations for policy changes for the Department
and legislative changes to section 1001 of the Energy Policy
Act of 2005 (42 U.S.C. 16391) to improve the ability of the
Department to successfully transfer new energy technologies to
the private sector.
TITLE II--CROSS-SECTOR PARTNERSHIPS AND GRANT COMPETITIVENESS
SEC. 201. AGREEMENTS FOR COMMERCIALIZING TECHNOLOGY PILOT PROGRAM.
(a) In General.--The Secretary shall carry out the Agreements for
Commercializing Technology pilot program of the Department, as
announced by the Secretary on December 8, 2011, in accordance with this
section.
(b) Terms.--Each agreement entered into pursuant to the pilot
program referred to in subsection (a) shall provide to the contractor
of the applicable National Laboratory, to the maximum extent determined
to be appropriate by the Secretary, increased authority to negotiate
contract terms, such as intellectual property rights, indemnification,
payment structures, performance guarantees, and multiparty
collaborations.
(c) Eligibility.--
(1) In general.--Notwithstanding any other provision of law
(including regulations), any National Laboratory may enter into
an agreement pursuant to the pilot program referred to in
subsection (a).
(2) Agreements with non-federal entities.--To carry out
paragraph (1) and subject to paragraph (3), the Secretary shall
permit the directors of the National Laboratories to execute
agreements with non-Federal entities, including non-Federal
entities already receiving Federal funding that will be used to
support activities under agreements executed pursuant to
paragraph (1).
(3) Restriction.--The requirements of chapter 18 of title
35, United States Code (commonly known as the ``Bayh-Dole
Act'') shall apply if--
(A) the agreement is a funding agreement (as that
term is defined in section 201 of that title); and
(B) at least 1 of the parties to the funding
agreement is eligible to receive rights under that
chapter.
(d) Submission to Secretary.--Each affected director of a National
Laboratory shall submit to the Secretary, with respect to each
agreement entered into under this section--
(1) a summary of information relating to the relevant
project;
(2) the total estimated costs of the project;
(3) estimated commencement and completion dates of the
project; and
(4) other documentation determined to be appropriate by the
Secretary.
(e) Certification.--The Secretary shall require the contractor of
the affected National Laboratory to certify that each activity carried
out under a project for which an agreement is entered into under this
section--
(1) is not in direct competition with the private sector;
and
(2) does not present, or minimizes, any apparent conflict
of interest, and avoids or neutralizes any actual conflict of
interest, as a result of the agreement under this section.
(f) Extension.--The pilot program referred to in subsection (a)
shall be extended for a term of 3 years after the date of enactment of
this Act.
(g) Reports.--
(1) Initial report.--Not later than 60 days after the date
described in subsection (f), the Secretary, in coordination
with directors of the National Laboratories, shall submit to
the Committee on Energy and Natural Resources of the Senate and
the Committee on Science, Space, and Technology of the House of
Representatives a report that--
(A) assesses the overall effectiveness of the pilot
program referred to in subsection (a);
(B) identifies opportunities to improve the
effectiveness of the pilot program;
(C) assesses the potential for program activities
to interfere with the responsibilities of the National
Laboratories to the Department; and
(D) provides a recommendation regarding the future
of the pilot program.
(2) Annual reports.--Annually, the Secretary, in
coordination with the directors of the National Laboratories,
shall submit to the Committee on Energy and Natural Resources
of the Senate and the Committee on Science, Space, and
Technology of the House of Representatives a report that
accounts for all incidences of, and provides a justification
for, non-Federal entities using funds derived from a Federal
contract or award to carry out agreements entered into under
this section.
SEC. 202. PUBLIC-PRIVATE PARTNERSHIPS FOR COMMERCIALIZATION.
(a) In General.--Subject to subsections (b) through (d), the
Secretary shall delegate to directors of the National Laboratories
signature authority with respect to any agreement described in
subsection (b) the total cost of which (including the National
Laboratory contributions and project recipient cost share) is less than
$1,000,000.
(b) Agreements.--Subsection (a) applies to--
(1) a cooperative research and development agreement;
(2) a non-Federal work-for-others agreement; and
(3) any other agreement determined to be appropriate by the
Secretary, in collaboration with the directors of the National
Laboratories.
(c) Limitation.--Subsection (a) does not apply to an agreement with
a majority-foreign-owned company.
(d) Administration.--
(1) Accountability.--The director of the affected National
Laboratory and the affected contractor shall carry out an
agreement under this section in accordance with applicable
policies of the Department, including by ensuring that the
agreement does not compromise any national security, economic,
or environmental interest of the United States.
(2) Certification.--The director of the affected National
Laboratory and the affected contractor shall certify that each
activity carried out under a project for which an agreement is
entered into under this section does not present, or minimizes,
any apparent conflict of interest, and avoids or neutralizes
any actual conflict of interest, as a result of the agreement
under this section.
(3) Availability of records.--On entering an agreement
under this section, the director of a National Laboratory shall
submit to the Secretary for monitoring and review all records
of the National Laboratory relating to the agreement.
(4) Rates.--The director of a National Laboratory may
charge higher rates for services performed under a partnership
agreement entered into pursuant to this section, regardless of
the full cost of recovery, if the funds are exclusively used to
support further research and development activities at the
applicable National Laboratory.
(e) Conforming Amendment.--Section 12 of the Stevenson-Wydler
Technology Innovation Act of 1980 (15 U.S.C. 3710a) is amended--
(1) in subsection (a)--
(A) by redesignating paragraphs (1) and (2) as
subparagraphs (A) and (B), respectively, and indenting
the subparagraphs appropriately;
(B) by striking ``Each Federal agency'' and
inserting the following:
``(1) In general.--Except as provided in paragraph (2),
each Federal agency''; and
(C) by adding at the end the following:
``(2) Exception.--Notwithstanding paragraph (1), in
accordance with section 202(a) of the America INNOVATES Act,
approval by the Secretary of Energy shall not be required for
any technology transfer agreement proposed to be entered into
by a National Laboratory of the Department of Energy, the total
cost of which (including the National Laboratory contributions
and project recipient cost share) is less than $1,000,000.'';
and
(2) in subsection (b), by striking ``subsection (a)(1)''
each place it appears and inserting ``subsection (a)(1)(A)''.
SEC. 203. INCLUSION OF EARLY-STAGE TECHNOLOGY DEMONSTRATION IN
AUTHORIZED TECHNOLOGY TRANSFER ACTIVITIES.
Section 1001 of the Energy Policy Act of 2005 (42 U.S.C. 16391) is
amended--
(1) by redesignating subsection (g) as subsection (h); and
(2) by inserting after subsection (f) the following:
``(g) Early-Stage Technology Demonstration.--The Secretary shall
permit the directors of the National Laboratories to use funds
authorized to support technology transfer within the Department to
carry out early-stage and precommercial technology demonstration
activities to remove technology barriers that limit private sector
interest and demonstrate potential commercial applications of any
research and technologies arising from National Laboratory
activities.''.
SEC. 204. INFORMATION AND RESOURCES FOR STARTUPS AND SMALL BUSINESSES.
Section 9 of the Small Business Act (15 U.S.C. 638) is amended by
adding at the end the following:
``(tt) Information.--In carrying out the SBIR and STTR programs of
the Department of Energy, the Secretary of Energy shall provide to
small business concerns seeking funding under the programs information
concerning resources that are available to small business concerns at
National Laboratories and federally funded research and development
centers.''.
SEC. 205. FUNDING COMPETITIVENESS FOR INSTITUTIONS OF HIGHER EDUCATION
AND OTHER NONPROFIT INSTITUTIONS.
Section 988(b) of the Energy Policy Act of 2005 (42 U.S.C.
16352(b)) is amended--
(1) in paragraph (1), by striking ``Except as provided in
paragraphs (2) and (3)'' and inserting ``Except as provided in
paragraphs (2), (3), and (4)''; and
(2) by adding at the end the following:
``(4) Exemption for institutions of higher education and
other nonprofit institutions.--
``(A) In general.--Paragraph (1) shall not apply to
a research or development activity performed by an
institution of higher education or nonprofit
institution (as defined in section 4 of the Stevenson-
Wydler Technology Innovation Act of 1980 (15 U.S.C.
3703)).
``(B) Termination date.--The exemption under
subparagraph (A) shall apply during the 6-year period
beginning on the date of enactment of this
paragraph.''.
TITLE III--ASSESSMENT OF IMPACT
SEC. 301. REPORT BY GOVERNMENT ACCOUNTABILITY OFFICE.
Not later than 3 years after the date of enactment of this Act, the
Comptroller General of the United States shall submit to Congress a
report--
(1) describing the results of the projects developed under
sections 201, 202, and 203, including information regarding--
(A) partnerships initiated as a result of those
projects and the potential linkages presented by those
partnerships with respect to national priorities and
other taxpayer-funded research; and
(B) whether the activities carried out under those
projects result in--
(i) fiscal savings;
(ii) expansion of National Laboratory
capabilities;
(iii) increased efficiency of technology
transfers; or
(iv) an increase in general efficiency of
the National Laboratory system;
(2) assessing the scale, scope, efficacy, and impact of the
efforts of the Department to promote technology transfer and
private sector engagement at the National Laboratories; and
(3) making recommendations on ways in which the Department
could improve the activities described under paragraph (1). | America Implementing New National Opportunities To Vigorously Accelerate Technology, Energy, and Science Act or the America INNOVATES ActAmends the Department of Energy Organization Act to rename the Under Secretary for Science as the Under Secretary for Science and Energy. Directs the Department of Energy (DOE) to report annually on DOE's ability to improve the technology transfer and commercialization of energy technologies. Directs DOE to carry out the Agreements for Commercializing Technology pilot program, in part by giving the contractors of the DOE nonmilitary national laboratories (national laboratories) increased authority to negotiate contract terms and making every such facility eligible for the program. Extends the pilot program for a term of three years after the enactment of this Act. Requires DOE to delegate to the directors of the national laboratories signature authority with respect to certain agreements (except those with a majority foreign-owned company) whose total cost is less than $1 million. Permits the directors of national laboratories to use funds authorized to support technology transfer within DOE to carry out early-stage and precommercial technology demonstration activities to: (1) remove technology barriers that limit private sector interest, and (2) demonstrate potential commercial applications of any research and technologies arising from national laboratory activities. Amends the Small Business Act to require DOE, in carrying out its Small Business Innovation Research (SBIR) and the Small Business Technology Transfer (STTR) programs, to provide to small businesses seeking funding under these programs information concerning resources available to them at national laboratories and federally funded research and development centers. Amends the Energy Policy Act of 2005 to exempt, for six years after enactment of this Act, institutions of higher education and nonprofit institutions from the cost-sharing requirements for research and development. Requires the Government Accountability Office to report to Congress on the results of projects developed under this Act and on DOE efforts to promote technology transfer and private sector engagement at the national laboratories. | <s>[INST]SECTION 1. SHORT TITLE; TABLE OF CONTENTS.
(a) Short Title.--This Act may be cited as the ``America
Implementing New National Opportunities To Vigorously Accelerate
Technology, Energy, and Science Act'' or the ``America INNOVATES Act''.
(b) Table of Contents.--The table of contents of this Act is as
follows:
Sec. 1. Short title; table of contents.
Sec. 2. Definitions.
Sec. 3. Savings clause.
TITLE I--INNOVATION MANAGEMENT AT DEPARTMENT OF ENERGY
Sec. 101. Under Secretary for Science and Energy.
Sec. 102. Technology transfer and transitions assessment.
TITLE II--CROSS-SECTOR PARTNERSHIPS AND GRANT COMPETITIVENESS
Sec. 201. Agreements for Commercializing Technology pilot program.
Sec. 202. Public-private partnerships for commercialization.
Sec. 203. Inclusion of early-stage technology demonstration in
authorized technology transfer activities.
Sec. 204. Information and resources for startups and small businesses.
Sec. 205. Funding competitiveness for institutions of higher education
and other nonprofit institutions.
TITLE III--ASSESSMENT OF IMPACT
Sec. 301. Report by Government Accountability Office.
SEC. 2. DEFINITIONS.
In this Act:
(1) Department.--The term ``Department'' means the
Department of Energy.
(2) National laboratory.--
(A) In general.--The term ``National Laboratory''
means a nonmilitary national laboratory owned by the
Department.
(B) Inclusions.--The term ``National Laboratory''
includes--
(i) Ames Laboratory;
(ii) Argonne National Laboratory;
(iii) Brookhaven National Laboratory;
(iv) Fermi National Accelerator Laboratory;
(v) Idaho National Laboratory;
(vi) Lawrence Berkeley National Laboratory;
(vii) National Energy Technology
Laboratory;
(viii) National Renewable Energy
Laboratory;
(ix) Oak Ridge National Laboratory;
(x) Pacific Northwest National Laboratory;
(xi) Princeton Plasma Physics Laboratory;
(xii) Savannah River National Laboratory;
(xiii) Stanford Linear Accelerator Center;
(xiv) Thomas Jefferson National Accelerator
Facility; and
(xv) any laboratory operated by the
National Nuclear Security Administration, with
respect to the civilian energy activities
conducted at the laboratory.
(3) Secretary.--The term ``Secretary'' means the Secretary
of Energy.
SEC. 3. SAVINGS CLAUSE.
Nothing in this Act or an amendment made by this Act abrogates or
otherwise affects the primary responsibilities of any National
Laboratory to the Department.
TITLE I--INNOVATION MANAGEMENT AT DEPARTMENT OF ENERGY
SEC. 101. UNDER SECRETARY FOR SCIENCE AND ENERGY.
(a) In General.--Section 202(b) of the Department of Energy
Organization Act (42 U.S.C. 7132(b)) is amended--
(1) by striking ``Under Secretary for Science'' each place
it appears and inserting ``Under Secretary for Science and
Energy''; and
(2) in paragraph (4)--
(A) in subparagraph (F), by striking ``and'' at the
end;
(B) in subparagraph (G), by striking the period at
the end and inserting a semicolon; and
(C) by inserting after subparagraph (G) the
following:
``(H) establish appropriate linkages between
offices under the jurisdiction of the Under Secretary;
and
``(I) perform such functions and duties as the
Secretary shall prescribe, consistent with this
section.''.
(b) Conforming Amendments.--
(1) Section 3164(b)(1) of the Department of Energy Science
Education Enhancement Act (42 U.S.C. 7381a(b)(1)) is amended by
striking ``Under Secretary for Science'' and inserting ``Under
Secretary for Science and Energy''.
(2) Section 641(h)(2) of the United States Energy Storage
Competitiveness Act of 2007 (42 U.S.C. 17231(h)(2)) is amended
by striking ``Under Secretary for Science'' and inserting
``Under Secretary for Science and Energy''.
SEC. 102. TECHNOLOGY TRANSFER AND TRANSITIONS ASSESSMENT.
Not later than 1 year after the date of enactment of this Act, and
annually thereafter, the Secretary shall submit to the Committee on
Energy and Natural Resources of the Senate and the Committee on
Science, Space, and Technology of the House of Representatives a report
that includes--
(1) an assessment of the ability of the Department to carry
out the goals of section 1001 of the Energy Policy Act of 2005
(42 U.S.C. 16391), including an assessment of the role and
effectiveness of the Director of the Office of Technology
Transitions; and
(2) recommendations for policy changes for the Department
and legislative changes to section 1001 of the Energy Policy
Act of 2005 (42 U.S.C. 16391) to improve the ability of the
Department to successfully transfer new energy technologies to
the private sector.
TITLE II--CROSS-SECTOR PARTNERSHIPS AND GRANT COMPETITIVENESS
SEC. 201. AGREEMENTS FOR COMMERCIALIZING TECHNOLOGY PILOT PROGRAM.
(a) In General.--The Secretary shall carry out the Agreements for
Commercializing Technology pilot program of the Department, as
announced by the Secretary on December 8, 2011, in accordance with this
section.
(b) Terms.--Each agreement entered into pursuant to the pilot
program referred to in subsection (a) shall provide to the contractor
of the applicable National Laboratory, to the maximum extent determined
to be appropriate by the Secretary, increased authority to negotiate
contract terms, such as intellectual property rights, indemnification,
payment structures, performance guarantees, and multiparty
collaborations.
(c) Eligibility.--
(1) In general.--Notwithstanding any other provision of law
(including regulations), any National Laboratory may enter into
an agreement pursuant to the pilot program referred to in
subsection (a).
(2) Agreements with non-federal entities.--To carry out
paragraph (1) and subject to paragraph (3), the Secretary shall
permit the directors of the National Laboratories to execute
agreements with non-Federal entities, including non-Federal
entities already receiving Federal funding that will be used to
support activities under agreements executed pursuant to
paragraph (1).
(3) Restriction.--The requirements of chapter 18 of title
35, United States Code (commonly known as the ``Bayh-Dole
Act'') shall apply if--
(A) the agreement is a funding agreement (as that
term is defined in section 201 of that title); and
(B) at least 1 of the parties to the funding
agreement is eligible to receive rights under that
chapter.
(d) Submission to Secretary.--Each affected director of a National
Laboratory shall submit to the Secretary, with respect to each
agreement entered into under this section--
(1) a summary of information relating to the relevant
project;
(2) the total estimated costs of the project;
(3) estimated commencement and completion dates of the
project; and
(4) other documentation determined to be appropriate by the
Secretary.
(e) Certification.--The Secretary shall require the contractor of
the affected National Laboratory to certify that each activity carried
out under a project for which an agreement is entered into under this
section--
(1) is not in direct competition with the private sector;
and
(2) does not present, or minimizes, any apparent conflict
of interest, and avoids or neutralizes any actual conflict of
interest, as a result of the agreement under this section.
(f) Extension.--The pilot program referred to in subsection (a)
shall be extended for a term of 3 years after the date of enactment of
this Act.
(g) Reports.--
(1) Initial report.--Not later than 60 days after the date
described in subsection (f), the Secretary, in coordination
with directors of the National Laboratories, shall submit to
the Committee on Energy and Natural Resources of the Senate and
the Committee on Science, Space, and Technology of the House of
Representatives a report that--
(A) assesses the overall effectiveness of the pilot
program referred to in subsection (a);
(B) identifies opportunities to improve the
effectiveness of the pilot program;
(C) assesses the potential for program activities
to interfere with the responsibilities of the National
Laboratories to the Department; and
(D) provides a recommendation regarding the future
of the pilot program.
(2) Annual reports.--Annually, the Secretary, in
coordination with the directors of the National Laboratories,
shall submit to the Committee on Energy and Natural Resources
of the Senate and the Committee on Science, Space, and
Technology of the House of Representatives a report that
accounts for all incidences of, and provides a justification
for, non-Federal entities using funds derived from a Federal
contract or award to carry out agreements entered into under
this section.
SEC. 202. PUBLIC-PRIVATE PARTNERSHIPS FOR COMMERCIALIZATION.
(a) In General.--Subject to subsections (b) through (d), the
Secretary shall delegate to directors of the National Laboratories
signature authority with respect to any agreement described in
subsection (b) the total cost of which (including the National
Laboratory contributions and project recipient cost share) is less than
$1,000,000.
(b) Agreements.--Subsection (a) applies to--
(1) a cooperative research and development agreement;
(2) a non-Federal work-for-others agreement; and
(3) any other agreement determined to be appropriate by the
Secretary, in collaboration with the directors of the National
Laboratories.
(c) Limitation.--Subsection (a) does not apply to an agreement with
a majority-foreign-owned company.
(d) Administration.--
(1) Accountability.--The director of the affected National
Laboratory and the affected contractor shall carry out an
agreement under this section in accordance with applicable
policies of the Department, including by ensuring that the
agreement does not compromise any national security, economic,
or environmental interest of the United States.
(2) Certification.--The director of the affected National
Laboratory and the affected contractor shall certify that each
activity carried out under a project for which an agreement is
entered into under this section does not present, or minimizes,
any apparent conflict of interest, and avoids or neutralizes
any actual conflict of interest, as a result of the agreement
under this section.
(3) Availability of records.--On entering an agreement
under this section, the director of a National Laboratory shall
submit to the Secretary for monitoring and review all records
of the National Laboratory relating to the agreement.
(4) Rates.--The director of a National Laboratory may
charge higher rates for services performed under a partnership
agreement entered into pursuant to this section, regardless of
the full cost of recovery, if the funds are exclusively used to
support further research and development activities at the
applicable National Laboratory.
(e) Conforming Amendment.--Section 12 of the Stevenson-Wydler
Technology Innovation Act of 1980 (15 U.S.C. 3710a) is amended--
(1) in subsection (a)--
(A) by redesignating paragraphs (1) and (2) as
subparagraphs (A) and (B), respectively, and indenting
the subparagraphs appropriately;
(B) by striking ``Each Federal agency'' and
inserting the following:
``(1) In general.--Except as provided in paragraph (2),
each Federal agency''; and
(C) by adding at the end the following:
``(2) Exception.--Notwithstanding paragraph (1), in
accordance with section 202(a) of the America INNOVATES Act,
approval by the Secretary of Energy shall not be required for
any technology transfer agreement proposed to be entered into
by a National Laboratory of the Department of Energy, the total
cost of which (including the National Laboratory contributions
and project recipient cost share) is less than $1,000,000.'';
and
(2) in subsection (b), by striking ``subsection (a)(1)''
each place it appears and inserting ``subsection (a)(1)(A)''.
SEC. 203. INCLUSION OF EARLY-STAGE TECHNOLOGY DEMONSTRATION IN
AUTHORIZED TECHNOLOGY TRANSFER ACTIVITIES.
Section 1001 of the Energy Policy Act of 2005 (42 U.S.C. 16391) is
amended--
(1) by redesignating subsection (g) as subsection (h); and
(2) by inserting after subsection (f) the following:
``(g) Early-Stage Technology Demonstration.--The Secretary shall
permit the directors of the National Laboratories to use funds
authorized to support technology transfer within the Department to
carry out early-stage and precommercial technology demonstration
activities to remove technology barriers that limit private sector
interest and demonstrate potential commercial applications of any
research and technologies arising from National Laboratory
activities.''.
SEC. 204. INFORMATION AND RESOURCES FOR STARTUPS AND SMALL BUSINESSES.
Section 9 of the Small Business Act (15 U.S.C. 638) is amended by
adding at the end the following:
``(tt) Information.--In carrying out the SBIR and STTR programs of
the Department of Energy, the Secretary of Energy shall provide to
small business concerns seeking funding under the programs information
concerning resources that are available to small business concerns at
National Laboratories and federally funded research and development
centers.''.
SEC. 205. FUNDING COMPETITIVENESS FOR INSTITUTIONS OF HIGHER EDUCATION
AND OTHER NONPROFIT INSTITUTIONS.
Section 988(b) of the Energy Policy Act of 2005 (42 U.S.C.
16352(b)) is amended--
(1) in paragraph (1), by striking ``Except as provided in
paragraphs (2) and (3)'' and inserting ``Except as provided in
paragraphs (2), (3), and (4)''; and
(2) by adding at the end the following:
``(4) Exemption for institutions of higher education and
other nonprofit institutions.--
``(A) In general.--Paragraph (1) shall not apply to
a research or development activity performed by an
institution of higher education or nonprofit
institution (as defined in section 4 of the Stevenson-
Wydler Technology Innovation Act of 1980 (15 U.S.C.
3703)).
``(B) Termination date.--The exemption under
subparagraph (A) shall apply during the 6-year period
beginning on the date of enactment of this
paragraph.''.
TITLE III--ASSESSMENT OF IMPACT
SEC. 301. REPORT BY GOVERNMENT ACCOUNTABILITY OFFICE.
Not later than 3 years after the date of enactment of this Act, the
Comptroller General of the United States shall submit to Congress a
report--
(1) describing the results of the projects developed under
sections 201, 202, and 203, including information regarding--
(A) partnerships initiated as a result of those
projects and the potential linkages presented by those
partnerships with respect to national priorities and
other taxpayer-funded research; and
(B) whether the activities carried out under those
projects result in--
(i) fiscal savings;
(ii) expansion of National Laboratory
capabilities;
(iii) increased efficiency of technology
transfers; or
(iv) an increase in general efficiency of
the National Laboratory system;
(2) assessing the scale, scope, efficacy, and impact of the
efforts of the Department to promote technology transfer and
private sector engagement at the National Laboratories; and
(3) making recommendations on ways in which the Department
could improve the activities described under paragraph (1).[/INST]America Implementing New National Opportunities To Vigorously Accelerate Technology, Energy, and Science Act or the America INNOVATES ActAmends the Department of Energy Organization Act to rename the Under Secretary for Science as the Under Secretary for Science and Energy. Directs the Department of Energy (DOE) to report annually on DOE's ability to improve the technology transfer and commercialization of energy technologies. Directs DOE to carry out the Agreements for Commercializing Technology pilot program, in part by giving the contractors of the DOE nonmilitary national laboratories (national laboratories) increased authority to negotiate contract terms and making every such facility eligible for the program. Extends the pilot program for a term of three years after the enactment of this Act. Requires DOE to delegate to the directors of the national laboratories signature authority with respect to certain agreements (except those with a majority foreign-owned company) whose total cost is less than $1 million. Permits the directors of national laboratories to use funds authorized to support technology transfer within DOE to carry out early-stage and precommercial technology demonstration activities to: (1) remove technology barriers that limit private sector interest, and (2) demonstrate potential commercial applications of any research and technologies arising from national laboratory activities. Amends the Small Business Act to require DOE, in carrying out its Small Business Innovation Research (SBIR) and the Small Business Technology Transfer (STTR) programs, to provide to small businesses seeking funding under these programs information concerning resources available to them at national laboratories and federally funded research and development centers. Amends the Energy Policy Act of 2005 to exempt, for six years after enactment of this Act, institutions of higher education and nonprofit institutions from the cost-sharing requirements for research and development. Requires the Government Accountability Office to report to Congress on the results of projects developed under this Act and on DOE efforts to promote technology transfer and private sector engagement at the national laboratories. </s> |
although dentistry has developed new materials and techniques used in the rehabilitation of completely edentulous patients , mucosa - supported dentures still act as possible agents of tissue damages .
the continuous use of dentures and the lack of regular monitoring provide the development of injuries11,19 , stomatitis being the most frequently observed .
denture - induced stomatitis is an inflammatory reaction of the denture - bearing mucosa that affects approximately 65% of complete upper denture wearers28 and is characterized by different degrees of erythema1,6,8,12 .
it has a multifactorial etiology , and c. albicans is reported as the primary etiologic agent1,21 .
poor hygiene of dentures is also associated with the disease4 , demonstrating the importance of denture cleansing by mechanical and/or chemical methods .
the most commonly used mechanical methods are brushing with dentifrice or neutral soap and use of ultrasonic devices .
the chemical methods involve denture immersion in chemical products , such as sodium perborate and sodium hypochlorite , hydrochloride , phosphoric and benzoic acids , chlorhexidine digluconate , and enzymes , like proteases and mutanases2,3 . despite the large number of currently available commercial denture - cleansing products , less than 60% of the wearers make use of anyone4 , possibly because of the low purchasing power of great part of the brazilian population .
the vinegar is a sour and astringent liquid consisting mainly of acetic acid , resulting from the fermentation of an alcoholic beverage , mainly white and red wines .
this is product is cheap , easily found in the market , and seems to have antimicrobial potential18,26,27,30 .
estrela , et al.9 ( 2004 ) evaluated the use of vinegar as an irrigating solution and intracanal medicament in microbial elimination from dog 's teeth with apical periodontitis .
basson , et al.2 ( 1992 ) showed the effectiveness of undiluted vinegar solutions in killing adherent microorganisms when used as disinfection agent for denture cleansing . in vitro experiments
have already shown that low fungicidal doses of acetic acid induce programmed cell death in c. albican
22 .
the aim of this study was to verify the effectiveness of a 10% vinegar solution in the control of candida spp .
in oral cavity of complete upper denture wearers , evaluating the presence of stomatitis and candida yeast counts in saliva .
after approval by the local research ethics committee , 55 patients of both genders aged 32 to 81 years old , wearers of complete upper denture for more than 6 months , were invited to participate in this study .
the exclusion criteria were : absence of yeasts in oral cavity , presence of diabetes mellitus , arterial hypertension or xerostomy , and use of antifungal , antibiotic and antidepressant drugs in the 6 months preceding the study .
all the participants were informed about the study objectives and methodology and signed an informed consent form .
after detailed clinical interview , two previously calibrated examiners investigated the occurrence of stomatitis and other injuries on oral mucosa .
denture - induced stomatitis , if present , was assessed according to newton 's classification , which is based on the clinical appearance of the inflamed mucosa under complete dentures : type i : petechiae dispersed throughout all or any part of palatal mucosa in contact with the denture ; type ii : diffuse erythema confined to the denture bearing area ; and type iii : papillary hyperplasia with diffuse erythema confined to the denture bearing area20 .
the examiners also evaluated the hygiene of the dentures , considering it unsatisfactory when debris , biofilm accumulation or both were observed in any region of dentures .
after that , a sample ( 2 to 3 ml ) of non - stimulated saliva was collected from each patient , with the denture in place , using a disposable sterile collector .
the samples were kept in ice and thermal bag during the transportation to the microbiology laboratory , respecting the period of 3 h between sample collection and processing .
subjects were instructed to remove their denture at night ( during approximately 8 h ) , to brush the denture at least 3 times a day during 1 min , after meals , using an appropriate toothbrush ( bitufe , itupeva , sp , brazil ) and neutral coconut soap ( dias d'vila , dias d'vila , ba , brazil ) and , after that , to keep the denture immersed in 100 ml of a 10% vinegar solution ( ph<3 ) .
the solution was prepared using a red wine vinegar base ( minhoto , raymundo da fonte group , torres galvo , paulista , pe , brazil ) with 4%volatile acidity , which was diluted in sterile distilled water .
ltd . , piracicaba , sp , brazil ) , confirming an acidity of less than 3 .
the experimental period had the duration of 45 days and after this time the patients were reexamined and new saliva sample was collected from each participant .
all saliva samples ( 0.1 ml ) were plated in duplicate in sabouraud dextrose agar ( difco laboratories , detroit , mi , usa ) added with chloramphenicol ( 0.1 mg / ml ) , and incubated at 37c for 48 h. after that , the number of colonies forming units per milliliter of saliva ( cfu / ml ) was counted .
the presence of yeasts in suggestive colonies was confirmed after preparation of gram - stained smears and observation under optical microscopy .
pure cultures in sabouraud dextrose agar were obtained from three different colonies of each morphology , which were identified by phenotypical tests24 , as follows : germ tube formation in sterile human sera ; chlamidoconidia production in corn meal agar ( difco ) added with 1% tween 80 ( interlab distribuidora de produtos cientficos s.a .
, so paulo , sp , brazil ) ; sugar fermentation ( glucose , galactose , sucrose , maltose and lactose ) in phenol red broth ( difco ) and sugar assimilation in chemically defined culture medium .
the data of the first collection were submitted to the kruskal - wallis test to evaluate if the time of denture use was related with the cfu / ml counts .
student 's t - test was applied to verify the effect of the treatment in cfu / ml counts .
biostat statistical software ( bioestat , goinia , go , brazil ) was used for both tests . in order to correlate the presence of stomatitis with the cfu / ml counts , before and after the treatment ,
the data were submitted to spearman 's correlation using the sas statistical software ( statistical analysis system ; sas institute incorporation , campus drive cary , nc , usa ) .
the 55 patients enrolled in this study had a mean age of 5711.3 years , and were using the complete upper denture for 6 months to 25 years ( mean of 7.6 years ) .
yeasts of candida genus were present in 48 ( 87.3% ) patients , from whom 62 isolates were obtained .
patients who showed no yeasts in the oral cavity were instructed to follow the treatment , but were excluded from the study .
comparison between the mean of cfu / ml of candida yeasts , before and after the treatment , is shown in table 1 .
the obtained t value was positive ( t=8.91880 ) , indicating a significant reduction in cfu / ml counts of candida after the use of vinegar solution . statistically significant difference ( p 0.05 ) .
a reduction in the incidence of stomatitis was observed after the treatment of the dentures with the vinegar solution ( table 2 ) .
the correlation between the number of microorganisms and presence of stomatitis before and after the use of vinegar solution can be observed in table 3 .
the results of spearman 's correlation demonstrated a positive correlation between the presence of candida and denture stomatitis after the use of vinegar solution ( p<0.05 ) , that is , the reduction of cfu / ml counts was correlated with a reduction in the number of patients with denture stomatitis ( 34 before and 14 after the use of the vinegar solution ) .
the age of the patients did not show any correlation with the number of candida in saliva .
angular queilitis was present in 19 patients ( 34.6% ) before the treatment and this result did not change after the use of vinegar .
other injuries were not observed in studied patients . statistically significant if p < 0.05 . in the second saliva collection ,
the number of candida strains decreased by 29% ( from 62 to 44 ) . before the treatment ,
10 patients showed two species of candida in saliva and 2 other patients showed an association of 3 species ( figure 1 ) .
after the treatment , only one patient showed association of 2 species ( c. albicans and c. krusei ) .
c. guilliermondii , c. lusitaniae and c. parapsilosis strains were absent after the use of vinegar solution .
the isolated species , before and after vinegar use , are displayed in table 4 .
the kruskal - wallis test did not show significant difference between the mean cfu / ml of the first collection and the time of denture use .
the obtained results were : time of denture use between 0.5 and 3 years : mean cfu / ml = 1063.3 ; between 4 and 8 years : mean cfu / ml = 1039.3 ; between 9 and 15 years : mean cfu / ml = 1056.6 ; and between 16 and 25 years : mean cfu / ml = 1073.7 ( p=0.9107 ) .
an important decrease in the number of patients with unsatisfactory hygiene after the use of vinegar was observed . before the treatment , all 48 patients presented poorly cleaned dentures , and this number dropped to 8 after the use of vinegar .
in the present study , daily disinfection of complete dentures with vinegar for 45 days was undertaken and the number of candida genus yeasts was analyzed .
the evaluation of candida in saliva was chosen to investigate whether denture cleaning and disinfection could change yeast counts in oral cavity , since the saliva reflects , in general , the whole oral microbiota .
another reason for this choice was the possibility to express the results per ml , and thus to quantify the microorganisms using a more accurate method . although the use of the vinegar solution has reduced the candida counts in the saliva of the patients , the high prevalence of c. albicans was still observed , being isolated 37 strains in the first saliva collection and 34 in the second one
likewise , geenwalt , et al.10 ( 1998 ) , evaluated the antimicrobial action of a fermented drink ( kombucha ) with a concentration of 7 g l-1 of acetic acid and did not find an inhibitory action against c. albicans .
it is likely that the acid ph favored the adherence of c. albicans to the denture acrylic and then to the mucosa15,17 .
bernab , et al.3 ( 2004 ) also verified no reduction in c. albicans counts using 0.5% of sodium hypochlorite and coconut soap as antimicrobial agents .
however , as hypochlorite has an unpleasant smell and taste , the denture must to be properly washed to remove the product , and its continued use can produce stains on the denture surface , which did not occur with the use of 10% vinegar in the present study .
c. albicans is an opportunistic pathogen frequently isolated from oral cavity of denture wearers28 , being considered the main etiological agent of the denture - induced stomatitis1,21 , which is characterized by a pathological modification of the oral mucosa that covers the denture bearing tissues .
it is more frequently found in patients wearing poorly cleaned and poorly fitted dentures for long periods4,25 .
the results of the present study showed the presence of denture - induced stomatitis in 70.8% of the studied population , confirming the high frequency of this disease in complete denture wearers .
denture use can reduce the salivary flow , which interferes with the physiological cleaning function of the tongue and creates a favorable environment for microbial survival4 .
in addition to this , candida cells seem to have affinity with denture acrylic23 , favoring the adhesion of epithelial cells to the oral mucosa and the onset of denture stomatitis29 .
denture use can thus be related to the presence of candida , which can be associated with the severity of denture - induced stomatitis , as observed in this study .
after use of vinegar solution , an expressive reduction in number of stomatitis cases was observed , mainly in patients with type ii stomatitis , according to newton classification . when denture use is analyzed alone , c. albicans was the most common specie , representing 77% of the isolated microorganisms14 . c. albicans was the most prevalent specie in this research , followed by c. glabrata , c. tropicalis , c. krusei , c. guilliermondii , and c. lusitaniae .
similar results have been reported by davenport7 ( 1972 ) and mcmullan - vogel , et al.16 ( 1999 ) , who had identified c. albicans in the saliva of 70% and 75% of complete denture wearers with stomatitis , respectively . however , in complete denture wearers who have more predisposing factors , many others species can be isolated13 .
the results of the present study demonstrated a higher prevalence of other candida species before the use of vinegar ( c. guilliermondii , c. lusitaniae and c. parapsilosis ) .
another interesting fact was the reduction in the number of associations with two and three species after the treatment .
a significant reduction in the number of patients with unsatisfactory denture hygiene after the treatment was observed in this study , demonstrating the efficiency of denture brushing followed by overnight immersion in the vinegar solution . brushing associated with some kind of detergent , soap or dentifrice
however , the effectiveness of brushing alone seems to be limited15 , probably because of the existence of irregularities in the acrylic resins , which makes difficult the mechanical removal of microorganisms7,15 .
therefore , in order to obtain high - quality denture cleaning , brushing and immersion in chemical agents must be associated . in spite of the development of new techniques and materials for complete denture cleaning , patient 's lack of information , low purchasing power , reduced visual accuracy and the limited manual dexterity , which are common characteristics of elderly people ,
although the vinegar solution was not able to eliminate c. albicans completely , it was effective in controlling other candida species , since the counts of candida spp . were reduced after the treatment .
the results of this study demonstrate that the search for new alternatives for the control of c. albicans in complete denture wearers should persist , since the 10% vinegar solution was not able to remove efficiently this yeast , which is the main etiological agent of denture - induced stomatitis .
the immersion of complete dentures in 10% vinegar solution , during the night , reduced the counts ( cfu / ml ) of candida spp . in saliva and the presence of denture - induced stomatitis in the studied population . | the use of denture is known to increase the carriage of candida in healthy patients , and the proliferation of candida albicans strains can be associated with denture - induced stomatitis .
the aim of this study was to evaluate the use of vinegar as an antimicrobial agent for control of candida spp .
in complete upper denture wearers .
fifty - five patients were submitted to a detailed clinical interview and oral clinical examination , and were instructed to keep their dentures immersed in a 10% vinegar solution ( ph less than 3 ) overnight for 45 days .
before and after the experimental period , saliva samples were collected for detection of candida , counting of cfu / ml and identification of species by phenotypical tests ( germ tube formation , chlamidoconidia production , and carbohydrate fermentation and assimilation ) .
the results were analyzed using spearman 's correlation and student 's t - test ( p0.05 ) .
candida yeasts were present in 87.3% of saliva samples before the treatment .
a significant reduction was verified in cfu / ml counts of candida after treatment . a positive correlation between candida and denture stomatitis
was verified , since the decrease of cfu / ml counts was correlated with a reduction in cases of denture stomatitis .
although it was not able to eliminate c. albicans , the immersion of the complete denture in 10% vinegar solution , during the night , reduced the amounts ( cfu / ml ) of candida spp . in the saliva and the presence of denture stomatitis in the studied patients
. | <s>[INST]although dentistry has developed new materials and techniques used in the rehabilitation of completely edentulous patients , mucosa - supported dentures still act as possible agents of tissue damages .
the continuous use of dentures and the lack of regular monitoring provide the development of injuries11,19 , stomatitis being the most frequently observed .
denture - induced stomatitis is an inflammatory reaction of the denture - bearing mucosa that affects approximately 65% of complete upper denture wearers28 and is characterized by different degrees of erythema1,6,8,12 .
it has a multifactorial etiology , and c. albicans is reported as the primary etiologic agent1,21 .
poor hygiene of dentures is also associated with the disease4 , demonstrating the importance of denture cleansing by mechanical and/or chemical methods .
the most commonly used mechanical methods are brushing with dentifrice or neutral soap and use of ultrasonic devices .
the chemical methods involve denture immersion in chemical products , such as sodium perborate and sodium hypochlorite , hydrochloride , phosphoric and benzoic acids , chlorhexidine digluconate , and enzymes , like proteases and mutanases2,3 . despite the large number of currently available commercial denture - cleansing products , less than 60% of the wearers make use of anyone4 , possibly because of the low purchasing power of great part of the brazilian population .
the vinegar is a sour and astringent liquid consisting mainly of acetic acid , resulting from the fermentation of an alcoholic beverage , mainly white and red wines .
this is product is cheap , easily found in the market , and seems to have antimicrobial potential18,26,27,30 .
estrela , et al.9 ( 2004 ) evaluated the use of vinegar as an irrigating solution and intracanal medicament in microbial elimination from dog 's teeth with apical periodontitis .
basson , et al.2 ( 1992 ) showed the effectiveness of undiluted vinegar solutions in killing adherent microorganisms when used as disinfection agent for denture cleansing . in vitro experiments
have already shown that low fungicidal doses of acetic acid induce programmed cell death in c. albican
22 .
the aim of this study was to verify the effectiveness of a 10% vinegar solution in the control of candida spp .
in oral cavity of complete upper denture wearers , evaluating the presence of stomatitis and candida yeast counts in saliva .
after approval by the local research ethics committee , 55 patients of both genders aged 32 to 81 years old , wearers of complete upper denture for more than 6 months , were invited to participate in this study .
the exclusion criteria were : absence of yeasts in oral cavity , presence of diabetes mellitus , arterial hypertension or xerostomy , and use of antifungal , antibiotic and antidepressant drugs in the 6 months preceding the study .
all the participants were informed about the study objectives and methodology and signed an informed consent form .
after detailed clinical interview , two previously calibrated examiners investigated the occurrence of stomatitis and other injuries on oral mucosa .
denture - induced stomatitis , if present , was assessed according to newton 's classification , which is based on the clinical appearance of the inflamed mucosa under complete dentures : type i : petechiae dispersed throughout all or any part of palatal mucosa in contact with the denture ; type ii : diffuse erythema confined to the denture bearing area ; and type iii : papillary hyperplasia with diffuse erythema confined to the denture bearing area20 .
the examiners also evaluated the hygiene of the dentures , considering it unsatisfactory when debris , biofilm accumulation or both were observed in any region of dentures .
after that , a sample ( 2 to 3 ml ) of non - stimulated saliva was collected from each patient , with the denture in place , using a disposable sterile collector .
the samples were kept in ice and thermal bag during the transportation to the microbiology laboratory , respecting the period of 3 h between sample collection and processing .
subjects were instructed to remove their denture at night ( during approximately 8 h ) , to brush the denture at least 3 times a day during 1 min , after meals , using an appropriate toothbrush ( bitufe , itupeva , sp , brazil ) and neutral coconut soap ( dias d'vila , dias d'vila , ba , brazil ) and , after that , to keep the denture immersed in 100 ml of a 10% vinegar solution ( ph<3 ) .
the solution was prepared using a red wine vinegar base ( minhoto , raymundo da fonte group , torres galvo , paulista , pe , brazil ) with 4%volatile acidity , which was diluted in sterile distilled water .
ltd . , piracicaba , sp , brazil ) , confirming an acidity of less than 3 .
the experimental period had the duration of 45 days and after this time the patients were reexamined and new saliva sample was collected from each participant .
all saliva samples ( 0.1 ml ) were plated in duplicate in sabouraud dextrose agar ( difco laboratories , detroit , mi , usa ) added with chloramphenicol ( 0.1 mg / ml ) , and incubated at 37c for 48 h. after that , the number of colonies forming units per milliliter of saliva ( cfu / ml ) was counted .
the presence of yeasts in suggestive colonies was confirmed after preparation of gram - stained smears and observation under optical microscopy .
pure cultures in sabouraud dextrose agar were obtained from three different colonies of each morphology , which were identified by phenotypical tests24 , as follows : germ tube formation in sterile human sera ; chlamidoconidia production in corn meal agar ( difco ) added with 1% tween 80 ( interlab distribuidora de produtos cientficos s.a .
, so paulo , sp , brazil ) ; sugar fermentation ( glucose , galactose , sucrose , maltose and lactose ) in phenol red broth ( difco ) and sugar assimilation in chemically defined culture medium .
the data of the first collection were submitted to the kruskal - wallis test to evaluate if the time of denture use was related with the cfu / ml counts .
student 's t - test was applied to verify the effect of the treatment in cfu / ml counts .
biostat statistical software ( bioestat , goinia , go , brazil ) was used for both tests . in order to correlate the presence of stomatitis with the cfu / ml counts , before and after the treatment ,
the data were submitted to spearman 's correlation using the sas statistical software ( statistical analysis system ; sas institute incorporation , campus drive cary , nc , usa ) .
the 55 patients enrolled in this study had a mean age of 5711.3 years , and were using the complete upper denture for 6 months to 25 years ( mean of 7.6 years ) .
yeasts of candida genus were present in 48 ( 87.3% ) patients , from whom 62 isolates were obtained .
patients who showed no yeasts in the oral cavity were instructed to follow the treatment , but were excluded from the study .
comparison between the mean of cfu / ml of candida yeasts , before and after the treatment , is shown in table 1 .
the obtained t value was positive ( t=8.91880 ) , indicating a significant reduction in cfu / ml counts of candida after the use of vinegar solution . statistically significant difference ( p 0.05 ) .
a reduction in the incidence of stomatitis was observed after the treatment of the dentures with the vinegar solution ( table 2 ) .
the correlation between the number of microorganisms and presence of stomatitis before and after the use of vinegar solution can be observed in table 3 .
the results of spearman 's correlation demonstrated a positive correlation between the presence of candida and denture stomatitis after the use of vinegar solution ( p<0.05 ) , that is , the reduction of cfu / ml counts was correlated with a reduction in the number of patients with denture stomatitis ( 34 before and 14 after the use of the vinegar solution ) .
the age of the patients did not show any correlation with the number of candida in saliva .
angular queilitis was present in 19 patients ( 34.6% ) before the treatment and this result did not change after the use of vinegar .
other injuries were not observed in studied patients . statistically significant if p < 0.05 . in the second saliva collection ,
the number of candida strains decreased by 29% ( from 62 to 44 ) . before the treatment ,
10 patients showed two species of candida in saliva and 2 other patients showed an association of 3 species ( figure 1 ) .
after the treatment , only one patient showed association of 2 species ( c. albicans and c. krusei ) .
c. guilliermondii , c. lusitaniae and c. parapsilosis strains were absent after the use of vinegar solution .
the isolated species , before and after vinegar use , are displayed in table 4 .
the kruskal - wallis test did not show significant difference between the mean cfu / ml of the first collection and the time of denture use .
the obtained results were : time of denture use between 0.5 and 3 years : mean cfu / ml = 1063.3 ; between 4 and 8 years : mean cfu / ml = 1039.3 ; between 9 and 15 years : mean cfu / ml = 1056.6 ; and between 16 and 25 years : mean cfu / ml = 1073.7 ( p=0.9107 ) .
an important decrease in the number of patients with unsatisfactory hygiene after the use of vinegar was observed . before the treatment , all 48 patients presented poorly cleaned dentures , and this number dropped to 8 after the use of vinegar .
in the present study , daily disinfection of complete dentures with vinegar for 45 days was undertaken and the number of candida genus yeasts was analyzed .
the evaluation of candida in saliva was chosen to investigate whether denture cleaning and disinfection could change yeast counts in oral cavity , since the saliva reflects , in general , the whole oral microbiota .
another reason for this choice was the possibility to express the results per ml , and thus to quantify the microorganisms using a more accurate method . although the use of the vinegar solution has reduced the candida counts in the saliva of the patients , the high prevalence of c. albicans was still observed , being isolated 37 strains in the first saliva collection and 34 in the second one
likewise , geenwalt , et al.10 ( 1998 ) , evaluated the antimicrobial action of a fermented drink ( kombucha ) with a concentration of 7 g l-1 of acetic acid and did not find an inhibitory action against c. albicans .
it is likely that the acid ph favored the adherence of c. albicans to the denture acrylic and then to the mucosa15,17 .
bernab , et al.3 ( 2004 ) also verified no reduction in c. albicans counts using 0.5% of sodium hypochlorite and coconut soap as antimicrobial agents .
however , as hypochlorite has an unpleasant smell and taste , the denture must to be properly washed to remove the product , and its continued use can produce stains on the denture surface , which did not occur with the use of 10% vinegar in the present study .
c. albicans is an opportunistic pathogen frequently isolated from oral cavity of denture wearers28 , being considered the main etiological agent of the denture - induced stomatitis1,21 , which is characterized by a pathological modification of the oral mucosa that covers the denture bearing tissues .
it is more frequently found in patients wearing poorly cleaned and poorly fitted dentures for long periods4,25 .
the results of the present study showed the presence of denture - induced stomatitis in 70.8% of the studied population , confirming the high frequency of this disease in complete denture wearers .
denture use can reduce the salivary flow , which interferes with the physiological cleaning function of the tongue and creates a favorable environment for microbial survival4 .
in addition to this , candida cells seem to have affinity with denture acrylic23 , favoring the adhesion of epithelial cells to the oral mucosa and the onset of denture stomatitis29 .
denture use can thus be related to the presence of candida , which can be associated with the severity of denture - induced stomatitis , as observed in this study .
after use of vinegar solution , an expressive reduction in number of stomatitis cases was observed , mainly in patients with type ii stomatitis , according to newton classification . when denture use is analyzed alone , c. albicans was the most common specie , representing 77% of the isolated microorganisms14 . c. albicans was the most prevalent specie in this research , followed by c. glabrata , c. tropicalis , c. krusei , c. guilliermondii , and c. lusitaniae .
similar results have been reported by davenport7 ( 1972 ) and mcmullan - vogel , et al.16 ( 1999 ) , who had identified c. albicans in the saliva of 70% and 75% of complete denture wearers with stomatitis , respectively . however , in complete denture wearers who have more predisposing factors , many others species can be isolated13 .
the results of the present study demonstrated a higher prevalence of other candida species before the use of vinegar ( c. guilliermondii , c. lusitaniae and c. parapsilosis ) .
another interesting fact was the reduction in the number of associations with two and three species after the treatment .
a significant reduction in the number of patients with unsatisfactory denture hygiene after the treatment was observed in this study , demonstrating the efficiency of denture brushing followed by overnight immersion in the vinegar solution . brushing associated with some kind of detergent , soap or dentifrice
however , the effectiveness of brushing alone seems to be limited15 , probably because of the existence of irregularities in the acrylic resins , which makes difficult the mechanical removal of microorganisms7,15 .
therefore , in order to obtain high - quality denture cleaning , brushing and immersion in chemical agents must be associated . in spite of the development of new techniques and materials for complete denture cleaning , patient 's lack of information , low purchasing power , reduced visual accuracy and the limited manual dexterity , which are common characteristics of elderly people ,
although the vinegar solution was not able to eliminate c. albicans completely , it was effective in controlling other candida species , since the counts of candida spp . were reduced after the treatment .
the results of this study demonstrate that the search for new alternatives for the control of c. albicans in complete denture wearers should persist , since the 10% vinegar solution was not able to remove efficiently this yeast , which is the main etiological agent of denture - induced stomatitis .
the immersion of complete dentures in 10% vinegar solution , during the night , reduced the counts ( cfu / ml ) of candida spp . in saliva and the presence of denture - induced stomatitis in the studied population .[/INST]the use of denture is known to increase the carriage of candida in healthy patients , and the proliferation of candida albicans strains can be associated with denture - induced stomatitis .
the aim of this study was to evaluate the use of vinegar as an antimicrobial agent for control of candida spp .
in complete upper denture wearers .
fifty - five patients were submitted to a detailed clinical interview and oral clinical examination , and were instructed to keep their dentures immersed in a 10% vinegar solution ( ph less than 3 ) overnight for 45 days .
before and after the experimental period , saliva samples were collected for detection of candida , counting of cfu / ml and identification of species by phenotypical tests ( germ tube formation , chlamidoconidia production , and carbohydrate fermentation and assimilation ) .
the results were analyzed using spearman 's correlation and student 's t - test ( p0.05 ) .
candida yeasts were present in 87.3% of saliva samples before the treatment .
a significant reduction was verified in cfu / ml counts of candida after treatment . a positive correlation between candida and denture stomatitis
was verified , since the decrease of cfu / ml counts was correlated with a reduction in cases of denture stomatitis .
although it was not able to eliminate c. albicans , the immersion of the complete denture in 10% vinegar solution , during the night , reduced the amounts ( cfu / ml ) of candida spp . in the saliva and the presence of denture stomatitis in the studied patients
.</s> |
a variety of sampling techniques are now available to provide options for clinicians and patients who require biopsy of a lung nodule or nodules .
these range from computed tomography ( ct ) guided percutaneous biopsy , to video assisted thoracoscopic surgery ( vats ) and , more recently , the development of a system that combines three - dimensional chest computed tomography ( ct ) reconstruction of a virtual bronchoscopic image , with electromagnetic guidance . electromagnetic navigation bronchoscopy ( enb ) uses a steerable probe and a narrow extended working channel , which are coupled together .
this combined probe and working channel fits through the working channel of a standard therapeutic fiberoptic bronchoscope , and this system is the subject of this review .
provide excellent evidence - based guidelines for the management of lung nodules elsewhere and this is not covered here , other than to say that application of enb must be considered in the context of a multidisciplinary approach in the care of patients with lung nodules .
many patients with lung nodules either require no biopsy because they are considered at very low risk for lung cancer and a more conservative approach ( serial observation ) may be more reasonable , while others are at such high risk that biopsy ( other than at the time of surgical exploration ) is not useful . however , there are patients for whom surgery is not an option , in whom a tissue diagnosis is required to guide treatment decisions .
these include patients who have significant co - morbid illnesses that preclude surgery , and those with suspected metastatic disease .
once a decision has been made to attempt to biopsy a lung nodule , the options should be discussed with the patient in the context of local expertise , and the relative risks and benefits of each option . in general , choosing among options for biopsy comes down to a trade - off between certainty ( sensitivity of the technique ) and risk ( degree of invasiveness ) .
the most invasive biopsy is a surgical exploration ; video assisted thoracoscopic surgery ( vats ) or thoracotomy provides the most definitive tissue sample for the pathologist .
however , for most patients , and for the purpose of this review , biopsy refers to tissue taken at the time of a ct guided percutaneous procedure , or a bronchoscopic procedure . until recently ,
the ct guided percutaneous biopsy was the preferred choice for biopsy of peripheral nodules in non - surgical patients , due to the lack of sensitivity of transbronchial biopsy .
the development of enb provides another option for biopsy of peripheral nodules , one with a lower risk of pneumothorax , and also gives clinicians a tool for locating nodules with fiducial markers ( for stereotactic radiation therapy ) and pleural tattoos to guide surgeons resecting small nodules that are not palpable .
in the evaluation of patients with suspected lung cancer , fiberoptic bronchoscopy is useful for accessing centrally located lesions and mediastinal lymph nodes .
transbronchial needle aspiration of enlarged mediastinal lymph nodes is safe and has a reasonable diagnostic accuracy in cases of malignant mediastinal lymph node metastasis .
real time linear probe endobronchial ultrasound increases sensitivity and permits the biopsy of much smaller lymph nodes in both the mediastinum and hilar lymph node stations .
the accuracy of bronchoscopy for lung parenchymal lesions declines rapidly as the distance from the main stem bronchi increases , so that traditional transbronchial sampling techniques have less than 20% sensitivity for peripheral lung nodules .
experienced users of this newer technique report a 6980% sensitivity for the diagnosis of small peripheral lung nodules ( as small as 7 mm , ranging up to 8 cm , and average size less than 2 cm ) .
it should be noted that this is less than what is reported for ct guided biopsy , hence the trade - off between accuracy , and a lower risk of pneumothorax .
the enb system is divided into three phases , pre - planning , registration , and navigation .
dicom formatted data from the patent 's ct scan are loaded from a disc onto a planning computer ( superdimension , minneapolis , mn ) , allowing the software to reconstruct axial , sagittal , and coronal images of the chest from the ct data .
the software also displays a three - dimensional virtual bronchoscopic view , through which the user navigates using an intuitive interface with a standard computer mouse ( fig .
the quality of the three - dimensional virtual bronchoscopic images ( and consequently of the planning process ) is highly dependent upon the ct scan parameters .
the maximum slice thickness of the scan should be 3.0 mm , with 50% overlap between the slices .
as long as the overlap is 50% , then the thinner the slices , the better for planning purposes .
one exception to this is that the software can not process a data file containing more than approximately 650 images .
the thinnest slice thickness i have used for planning is 1.25 mm slices at 0.625 mm intervals . at this size a diagnostic ct of an average size adult yields 400500 images , a volume of data handled easily by the current software .
these thinner slices result in excellent detail of bronchi down to a few millimeters in diameter in the virtual model of the airway .
any respiratory motion artifact on the ct will degrade the accuracy of the registration , and therefore ct scans are best obtained during a full breath hold as is the standard with diagnostic ct scanning .
if the patient has already had a diagnostic ct scan that fits the parameters described above , no additional ct is required . for most patients ,
the ct scan obtained for initial evaluation of the nodule is all that is required .
figure 1software planning user interface displaying ( clockwise from bottom right panel ) three - dimensional bronchoscopic
tip view , along with coronal , axial , and sagittal planar reconstruction of the dicom formatted ct data .
software planning user interface displaying ( clockwise from bottom right panel ) three - dimensional bronchoscopic
tip view , along with coronal , axial , and sagittal planar reconstruction of the dicom formatted ct data .
as the user navigates through the virtual airway , the view is displayed as it would appear through the bronchoscope .
the operator selects and marks well - recognized anatomic landmarks in the planning phase using the mouse by touching each spot ; usually the main carina , and the carinae delineating the right upper lobe , middle lobe , a basilar segment from the right lower lobe , the left upper lobe , and one of the left lower lobe basilar segments ( fig .
any easily recognizable landmark is appropriate , as long as it can be seen through the bronchoscope . during the planning phase the target(s ) to be biopsied are also marked .
the ability to biopsy multiple nodules in one procedure without an appreciable increase in the risk of pneumothorax must be considered one of the advantages of enb .
the size and location of each target nodule are marked , and the planning software then saves a compressed version of the data to a removable usb drive .
this drive can then be inserted into the usb slot of the computer located in the procedure room . in the procedure room , the location board ,
this location board is connected to the location processor , and from that to a computer that also has the enb software ( superdimension , inreach. fig .
the location board and processor generate a sensing volume , and when the patient is positioned properly on the table , the patient 's chest is encompassed by this volume .
three sensors are also placed on the patient 's chest within the sensing volume , and these allow for tracking of the lung motion during spontaneous respiration ( fig .
the procedure can be done with conscious sedation or with deeper sedation given with an endotracheal tube in place .
the operator performs the procedure with a steerable probe ( the locatable guide ( lg ) , fig .
2e ) inserted into an extended working channel ( ewc ; a hollow plastic catheter , see fig .
2e ) , both of which fit in the working channel of a therapeutic bronchoscope .
the three - dimensional position of the tip of the lg within the chest ( x , y , and z coordinates and roll , pitch , and yaw ) is also detected by the location processor .
( a , b ) fluoroscopy table with the location board underneath the patient 's chest .
( c ) procedure cart containing the location processor , cables , and a pc with the planning software .
( d ) patient sensors ( black arrows ) that allow tracking of the lungs during respiratory motion .
( e ) the locatable guide ( large arrow ) and extended working channel ( small arrow ) combine ( f ) to allow steering of the working channel to the target lesion(s ) .
( a , b ) fluoroscopy table with the location board underneath the patient 's chest .
( c ) procedure cart containing the location processor , cables , and a pc with the planning software .
( d ) patient sensors ( black arrows ) that allow tracking of the lungs during respiratory motion . ( e ) the locatable guide ( large arrow ) and extended working channel ( small arrow ) combine ( f ) to allow steering of the working channel to the target lesion(s ) .
once the patient is adequately sedated , the bronchoscopist inspects the airway with the fiberoptic scope , and then places the combined lg and ewc into the airway via the scope 's working channel .
the operator advances the scope and locatable guide to each of the anatomic registration points entered during the planning phase , and registers them within the patient by touching the same spots with the probe , and entering the point with a foot pedal ( fig .
once the landmarks have been registered in the patient , the computer will report an average fiducial target registration error ( aftre ) , which gives an estimation of the divergence between the ct anatomy and the patient 's anatomy .
the ideal aftre is less than 5 mm , but error rates less than 4 mm are achievable . in my experience , an aftre that is less than the size of the nodule is desirable .
it is not necessary to use all the registration points entered during the planning phase if one proves particularly difficult to register accurately .
the software may suggest particular points to re - register , or the user may select problematic points to delete from the registration .
it is critical to have at least four accurately marked registration points that are well separated in space , with at least one on each side of the thorax , and one registration point should always be the main carina .
after registration , the computer prompts the user to continue to the navigation phase , or allows a return to registration to improve accuracy .
figure 3registration of anatomic landmarks with side - by - side view of the virtual and real - time bronchoscopic images .
registration of anatomic landmarks with side - by - side view of the virtual and real - time bronchoscopic images .
the navigation is achieved initially by approaching the proper airway segment containing the target with the bronchoscope .
once the scope is wedged into the target segment , the lg ewc is advanced through the working channel and steered to the target using the four views displayed on the computer .
axial , sagittal , and coronal views of the chest move along with the tip of the lg , and the tip - view is displayed alongside the planar views of the ct scan ( fig .
the tip - view displays the distance to the nodule , and an arrow indicating the direction of turn required to reach the nodule . on the proximal end of the lg in the operators hand
is a click - wheel with an identical arrow , and the operator can steer the distal end of the guide to the lesion by matching the clock position of the arrows on the guide with that suggested on the tip - view , and squeezing the trigger to deflect the tip in the direction of the target ( see fig .
the tip is advanced toward the nodule until it is in sufficiently close proximity to allow biopsy tools to reach the lesion .
once in position , the operator locks the ewc in place at the entrance to the scope 's working channel , and removes the lg , leaving the extended working channel in place near the nodule .
various techniques can be used for real time confirmation of the location of the ewc near or within the nodule as suggested by the virtual images generated by the location processor .
fluoroscopic images can be used , as well as a radial probe ultrasound catheter that fits through the working channel ( fig .
a new and useful tool for visualizing the peripheral lung tissue in real time is a micro - endoscopic confocal laser catheter ( celllvizio ) which passes easily through the ewc , and displays real time video on a microscopic level ( fig .
investigators are just beginning to establish a pattern of recognition for normal and diseased lung tissue using this system .
as with any transbronchial biopsy , the actual sampling should be done with fluoroscopic visualization to observe the position of the biopsy tools .
figure 4display during the navigation phase of the procedure shows real - time location of the tip of the locatable guide with simultaneous axial , sagittal , coronal , and
figure 5when performing biopsies , some form of real time confirmation of the location of the working channel is necessary .
this can be done with ( a ) bi - planar fluoroscopy , ( b ) a radial ultrasound probe advanced through the working channel , or ( c , d ) confocal laser micro - endoscope ( ( c ) showing normal lung ; ( d ) showing abnormal lung architecture ) .
display during the navigation phase of the procedure shows real - time location of the tip of the locatable guide with simultaneous axial , sagittal , coronal , and
when performing biopsies , some form of real time confirmation of the location of the working channel is necessary .
this can be done with ( a ) bi - planar fluoroscopy , ( b ) a radial ultrasound probe advanced through the working channel , or ( c , d ) confocal laser micro - endoscope ( ( c ) showing normal lung ; ( d ) showing abnormal lung architecture ) . once the ewc position is confirmed to the satisfaction if the bronchoscopist , biopsy tools can be advanced to the nodule through the ewc to take samples .
prior to the procedure , it is standard practice to mark the tools at their proximal end , so the operator knows how far to advance the tool prior to its emergence from the distal end of the ewc .
the choice of biopsy tool is up to the operator , but any standard needle , cytology brush , or transbronchial forceps can be used to obtain either cytologic , or histopathologic material from the nodule . between each pass of a biopsy tool ,
it is good practice to re - insert the locatable guide , to confirm that the ewc was not displaced from its location within or near the nodule by the act of taking the tissue sample .
fluoroscopy during the procedure is also useful to monitor the location of the ewc and biopsy tools .
likewise , the use of a radial probe ultrasound image to re - confirm the location of the ewc is very helpful .
enb is now gaining wider use as a tool for diagnosis of peripheral lung nodules , and there have been other uses published for this system .
in addition , there are nodules that a surgeon plans to biopsy or resect with a vats approach , but is concerned that they will not be able to palpate the nodule through a thoracoscopic incision . in these cases , enb permits the bronchoscopist to navigate the overlying pleura and deliver a tattoo through a needle passed via the ewc ( usually indigo - carmine ) .
the surgeon then visualizes the tattoo through the thoracoscope eliminating the need to palpate the nodule .
this approach can reduce the duration of the procedure and reduce the likelihood of conversion to thoracotomy .
some users have developed the technique for delivering brachytherapy by a transbronchial route for patients who can not tolerate external beam radiotherapy ( t. mclemore , tyler , tx , personal communication ) .
this emerging technology was originally developed for the diagnosis of malignancy in the lung , but it also provides the bronchoscopist with a tool to use in the diagnosis and treatment of a variety of lung diseases . for radiologists ,
it is important to be aware of enb so that they can work with users of this system to assure ct scan parameters are appropriate if the use of enb is considered likely in the management of their patients . | abstractthis review describes the technique and applications of an emerging bronchoscopic approach utilizing three - dimensional reconstructions of chest computed tomography scans to facilitate electromagnetic guidance to peripheral lung nodules .
this approach , electromagnetic navigation bronchoscopy , is useful for biopsy , placement of fiducial markers , or dye marking of overlying pleura prior to thoracoscopic wedge resection .
this technique offers some potential advantages over other forms of biopsy . the design , application , relative advantages and pitfalls of this system are the subject of this review . | <s>[INST]a variety of sampling techniques are now available to provide options for clinicians and patients who require biopsy of a lung nodule or nodules .
these range from computed tomography ( ct ) guided percutaneous biopsy , to video assisted thoracoscopic surgery ( vats ) and , more recently , the development of a system that combines three - dimensional chest computed tomography ( ct ) reconstruction of a virtual bronchoscopic image , with electromagnetic guidance . electromagnetic navigation bronchoscopy ( enb ) uses a steerable probe and a narrow extended working channel , which are coupled together .
this combined probe and working channel fits through the working channel of a standard therapeutic fiberoptic bronchoscope , and this system is the subject of this review .
provide excellent evidence - based guidelines for the management of lung nodules elsewhere and this is not covered here , other than to say that application of enb must be considered in the context of a multidisciplinary approach in the care of patients with lung nodules .
many patients with lung nodules either require no biopsy because they are considered at very low risk for lung cancer and a more conservative approach ( serial observation ) may be more reasonable , while others are at such high risk that biopsy ( other than at the time of surgical exploration ) is not useful . however , there are patients for whom surgery is not an option , in whom a tissue diagnosis is required to guide treatment decisions .
these include patients who have significant co - morbid illnesses that preclude surgery , and those with suspected metastatic disease .
once a decision has been made to attempt to biopsy a lung nodule , the options should be discussed with the patient in the context of local expertise , and the relative risks and benefits of each option . in general , choosing among options for biopsy comes down to a trade - off between certainty ( sensitivity of the technique ) and risk ( degree of invasiveness ) .
the most invasive biopsy is a surgical exploration ; video assisted thoracoscopic surgery ( vats ) or thoracotomy provides the most definitive tissue sample for the pathologist .
however , for most patients , and for the purpose of this review , biopsy refers to tissue taken at the time of a ct guided percutaneous procedure , or a bronchoscopic procedure . until recently ,
the ct guided percutaneous biopsy was the preferred choice for biopsy of peripheral nodules in non - surgical patients , due to the lack of sensitivity of transbronchial biopsy .
the development of enb provides another option for biopsy of peripheral nodules , one with a lower risk of pneumothorax , and also gives clinicians a tool for locating nodules with fiducial markers ( for stereotactic radiation therapy ) and pleural tattoos to guide surgeons resecting small nodules that are not palpable .
in the evaluation of patients with suspected lung cancer , fiberoptic bronchoscopy is useful for accessing centrally located lesions and mediastinal lymph nodes .
transbronchial needle aspiration of enlarged mediastinal lymph nodes is safe and has a reasonable diagnostic accuracy in cases of malignant mediastinal lymph node metastasis .
real time linear probe endobronchial ultrasound increases sensitivity and permits the biopsy of much smaller lymph nodes in both the mediastinum and hilar lymph node stations .
the accuracy of bronchoscopy for lung parenchymal lesions declines rapidly as the distance from the main stem bronchi increases , so that traditional transbronchial sampling techniques have less than 20% sensitivity for peripheral lung nodules .
experienced users of this newer technique report a 6980% sensitivity for the diagnosis of small peripheral lung nodules ( as small as 7 mm , ranging up to 8 cm , and average size less than 2 cm ) .
it should be noted that this is less than what is reported for ct guided biopsy , hence the trade - off between accuracy , and a lower risk of pneumothorax .
the enb system is divided into three phases , pre - planning , registration , and navigation .
dicom formatted data from the patent 's ct scan are loaded from a disc onto a planning computer ( superdimension , minneapolis , mn ) , allowing the software to reconstruct axial , sagittal , and coronal images of the chest from the ct data .
the software also displays a three - dimensional virtual bronchoscopic view , through which the user navigates using an intuitive interface with a standard computer mouse ( fig .
the quality of the three - dimensional virtual bronchoscopic images ( and consequently of the planning process ) is highly dependent upon the ct scan parameters .
the maximum slice thickness of the scan should be 3.0 mm , with 50% overlap between the slices .
as long as the overlap is 50% , then the thinner the slices , the better for planning purposes .
one exception to this is that the software can not process a data file containing more than approximately 650 images .
the thinnest slice thickness i have used for planning is 1.25 mm slices at 0.625 mm intervals . at this size a diagnostic ct of an average size adult yields 400500 images , a volume of data handled easily by the current software .
these thinner slices result in excellent detail of bronchi down to a few millimeters in diameter in the virtual model of the airway .
any respiratory motion artifact on the ct will degrade the accuracy of the registration , and therefore ct scans are best obtained during a full breath hold as is the standard with diagnostic ct scanning .
if the patient has already had a diagnostic ct scan that fits the parameters described above , no additional ct is required . for most patients ,
the ct scan obtained for initial evaluation of the nodule is all that is required .
figure 1software planning user interface displaying ( clockwise from bottom right panel ) three - dimensional bronchoscopic
tip view , along with coronal , axial , and sagittal planar reconstruction of the dicom formatted ct data .
software planning user interface displaying ( clockwise from bottom right panel ) three - dimensional bronchoscopic
tip view , along with coronal , axial , and sagittal planar reconstruction of the dicom formatted ct data .
as the user navigates through the virtual airway , the view is displayed as it would appear through the bronchoscope .
the operator selects and marks well - recognized anatomic landmarks in the planning phase using the mouse by touching each spot ; usually the main carina , and the carinae delineating the right upper lobe , middle lobe , a basilar segment from the right lower lobe , the left upper lobe , and one of the left lower lobe basilar segments ( fig .
any easily recognizable landmark is appropriate , as long as it can be seen through the bronchoscope . during the planning phase the target(s ) to be biopsied are also marked .
the ability to biopsy multiple nodules in one procedure without an appreciable increase in the risk of pneumothorax must be considered one of the advantages of enb .
the size and location of each target nodule are marked , and the planning software then saves a compressed version of the data to a removable usb drive .
this drive can then be inserted into the usb slot of the computer located in the procedure room . in the procedure room , the location board ,
this location board is connected to the location processor , and from that to a computer that also has the enb software ( superdimension , inreach. fig .
the location board and processor generate a sensing volume , and when the patient is positioned properly on the table , the patient 's chest is encompassed by this volume .
three sensors are also placed on the patient 's chest within the sensing volume , and these allow for tracking of the lung motion during spontaneous respiration ( fig .
the procedure can be done with conscious sedation or with deeper sedation given with an endotracheal tube in place .
the operator performs the procedure with a steerable probe ( the locatable guide ( lg ) , fig .
2e ) inserted into an extended working channel ( ewc ; a hollow plastic catheter , see fig .
2e ) , both of which fit in the working channel of a therapeutic bronchoscope .
the three - dimensional position of the tip of the lg within the chest ( x , y , and z coordinates and roll , pitch , and yaw ) is also detected by the location processor .
( a , b ) fluoroscopy table with the location board underneath the patient 's chest .
( c ) procedure cart containing the location processor , cables , and a pc with the planning software .
( d ) patient sensors ( black arrows ) that allow tracking of the lungs during respiratory motion .
( e ) the locatable guide ( large arrow ) and extended working channel ( small arrow ) combine ( f ) to allow steering of the working channel to the target lesion(s ) .
( a , b ) fluoroscopy table with the location board underneath the patient 's chest .
( c ) procedure cart containing the location processor , cables , and a pc with the planning software .
( d ) patient sensors ( black arrows ) that allow tracking of the lungs during respiratory motion . ( e ) the locatable guide ( large arrow ) and extended working channel ( small arrow ) combine ( f ) to allow steering of the working channel to the target lesion(s ) .
once the patient is adequately sedated , the bronchoscopist inspects the airway with the fiberoptic scope , and then places the combined lg and ewc into the airway via the scope 's working channel .
the operator advances the scope and locatable guide to each of the anatomic registration points entered during the planning phase , and registers them within the patient by touching the same spots with the probe , and entering the point with a foot pedal ( fig .
once the landmarks have been registered in the patient , the computer will report an average fiducial target registration error ( aftre ) , which gives an estimation of the divergence between the ct anatomy and the patient 's anatomy .
the ideal aftre is less than 5 mm , but error rates less than 4 mm are achievable . in my experience , an aftre that is less than the size of the nodule is desirable .
it is not necessary to use all the registration points entered during the planning phase if one proves particularly difficult to register accurately .
the software may suggest particular points to re - register , or the user may select problematic points to delete from the registration .
it is critical to have at least four accurately marked registration points that are well separated in space , with at least one on each side of the thorax , and one registration point should always be the main carina .
after registration , the computer prompts the user to continue to the navigation phase , or allows a return to registration to improve accuracy .
figure 3registration of anatomic landmarks with side - by - side view of the virtual and real - time bronchoscopic images .
registration of anatomic landmarks with side - by - side view of the virtual and real - time bronchoscopic images .
the navigation is achieved initially by approaching the proper airway segment containing the target with the bronchoscope .
once the scope is wedged into the target segment , the lg ewc is advanced through the working channel and steered to the target using the four views displayed on the computer .
axial , sagittal , and coronal views of the chest move along with the tip of the lg , and the tip - view is displayed alongside the planar views of the ct scan ( fig .
the tip - view displays the distance to the nodule , and an arrow indicating the direction of turn required to reach the nodule . on the proximal end of the lg in the operators hand
is a click - wheel with an identical arrow , and the operator can steer the distal end of the guide to the lesion by matching the clock position of the arrows on the guide with that suggested on the tip - view , and squeezing the trigger to deflect the tip in the direction of the target ( see fig .
the tip is advanced toward the nodule until it is in sufficiently close proximity to allow biopsy tools to reach the lesion .
once in position , the operator locks the ewc in place at the entrance to the scope 's working channel , and removes the lg , leaving the extended working channel in place near the nodule .
various techniques can be used for real time confirmation of the location of the ewc near or within the nodule as suggested by the virtual images generated by the location processor .
fluoroscopic images can be used , as well as a radial probe ultrasound catheter that fits through the working channel ( fig .
a new and useful tool for visualizing the peripheral lung tissue in real time is a micro - endoscopic confocal laser catheter ( celllvizio ) which passes easily through the ewc , and displays real time video on a microscopic level ( fig .
investigators are just beginning to establish a pattern of recognition for normal and diseased lung tissue using this system .
as with any transbronchial biopsy , the actual sampling should be done with fluoroscopic visualization to observe the position of the biopsy tools .
figure 4display during the navigation phase of the procedure shows real - time location of the tip of the locatable guide with simultaneous axial , sagittal , coronal , and
figure 5when performing biopsies , some form of real time confirmation of the location of the working channel is necessary .
this can be done with ( a ) bi - planar fluoroscopy , ( b ) a radial ultrasound probe advanced through the working channel , or ( c , d ) confocal laser micro - endoscope ( ( c ) showing normal lung ; ( d ) showing abnormal lung architecture ) .
display during the navigation phase of the procedure shows real - time location of the tip of the locatable guide with simultaneous axial , sagittal , coronal , and
when performing biopsies , some form of real time confirmation of the location of the working channel is necessary .
this can be done with ( a ) bi - planar fluoroscopy , ( b ) a radial ultrasound probe advanced through the working channel , or ( c , d ) confocal laser micro - endoscope ( ( c ) showing normal lung ; ( d ) showing abnormal lung architecture ) . once the ewc position is confirmed to the satisfaction if the bronchoscopist , biopsy tools can be advanced to the nodule through the ewc to take samples .
prior to the procedure , it is standard practice to mark the tools at their proximal end , so the operator knows how far to advance the tool prior to its emergence from the distal end of the ewc .
the choice of biopsy tool is up to the operator , but any standard needle , cytology brush , or transbronchial forceps can be used to obtain either cytologic , or histopathologic material from the nodule . between each pass of a biopsy tool ,
it is good practice to re - insert the locatable guide , to confirm that the ewc was not displaced from its location within or near the nodule by the act of taking the tissue sample .
fluoroscopy during the procedure is also useful to monitor the location of the ewc and biopsy tools .
likewise , the use of a radial probe ultrasound image to re - confirm the location of the ewc is very helpful .
enb is now gaining wider use as a tool for diagnosis of peripheral lung nodules , and there have been other uses published for this system .
in addition , there are nodules that a surgeon plans to biopsy or resect with a vats approach , but is concerned that they will not be able to palpate the nodule through a thoracoscopic incision . in these cases , enb permits the bronchoscopist to navigate the overlying pleura and deliver a tattoo through a needle passed via the ewc ( usually indigo - carmine ) .
the surgeon then visualizes the tattoo through the thoracoscope eliminating the need to palpate the nodule .
this approach can reduce the duration of the procedure and reduce the likelihood of conversion to thoracotomy .
some users have developed the technique for delivering brachytherapy by a transbronchial route for patients who can not tolerate external beam radiotherapy ( t. mclemore , tyler , tx , personal communication ) .
this emerging technology was originally developed for the diagnosis of malignancy in the lung , but it also provides the bronchoscopist with a tool to use in the diagnosis and treatment of a variety of lung diseases . for radiologists ,
it is important to be aware of enb so that they can work with users of this system to assure ct scan parameters are appropriate if the use of enb is considered likely in the management of their patients .[/INST]abstractthis review describes the technique and applications of an emerging bronchoscopic approach utilizing three - dimensional reconstructions of chest computed tomography scans to facilitate electromagnetic guidance to peripheral lung nodules .
this approach , electromagnetic navigation bronchoscopy , is useful for biopsy , placement of fiducial markers , or dye marking of overlying pleura prior to thoracoscopic wedge resection .
this technique offers some potential advantages over other forms of biopsy . the design , application , relative advantages and pitfalls of this system are the subject of this review .</s> |
Prosecutors have released video footage of Trayvon Martin buying sweets and a drink in a Florida convenience store minutes before he was shot and killed in a confrontation with a neighbourhood watch leader.
The scenes recorded at the 7-Eleven close to the Retreat at Twin Lakes development in Sanford show Martin, 17, wearing a black hooded top and beige trousers, walking up to the counter and paying.
Soon after leaving the shop Martin got into a fight with George Zimmerman, who had already called police to report a "suspicious" black male in the neighbourhood. Martin was shot dead by a single shot to the chest at point-blank range, the gunshot heard on recordings of several 911 calls made by neighbours.
The video is among the latest in a batch of evidence released on Friday by prosecutors who have charged Zimmerman, 28, with second-degree murder.
It represents the first public glimpse of the unarmed teenager on 26 February, the night he was killed in an incident that led to race protests and the resignation of the local police chief. The Sanford police department originally released Zimmerman without charge after he claimed he acted in self-defence, and he was arrested in April only after the appointment of a special prosecutor to re-examine the evidence.
The haul of evidence released by state attorney Angela Corey's office over the last two days includes a toxicology report that showed Martin had traces of marijuana in his system, medical records confirming bloody injuries to Zimmerman's head, and testimony by Martin's father that it was not his son's voice heard on 911 recordings crying for help.
Additionally, there were numerous witness statements, many contradicting each other over such details as how many shots were fired and which of the two was on top of the other during their fight. And one police report reveals that detectives wanted to charge Zimmerman with manslaughter even after Bill Lee, then the chief of the Sanford police department, had told reporters there was insufficient evidence to justify such a charge.
The confrontation was "entirely avoidable", detective Chris Serino wrote, if Zimmerman had returned to his car or engaged Martin in conversation.
Among the various audio recordings of interviews with witnesses is one of a teenage girl in Miami, where Martin lived, who told prosecutors she was on the phone to her friend and heard Zimmerman approach him.
The girl, whose identity has not been revealed, said she heard Martin say: "Why you following me for?"
She said: "I hear this man, like this old man, say, 'What are you doing around here?'" then said she heard a bumping sound followed by what she thought was a scuffle.
"I could hear it a little bit, 'Get off, get off,' then the phone just hung up," she said.
Zimmerman faces at least 25 years in jail if he is convicted. No date has yet been set for the trial and he remains free on $150,000 bail.
His lawyer, Mark O'Mara, warned on Friday it would be a mistake to draw any conclusion from the partial evidence so far released. "Looking at it piecemeal is what has caused some of the problems in the past with the case," he said in an interview with CBS News.
"It's sort of important that we all wait until all the evidence is out. Let's deal with it all once we have it, and deal with it in the courtroom." ||||| The recording is one of several dozen released by State Attorney Angela B. Corey, who has charged the gunman, George Zimmerman, 28, with second-degree murder. It is part of the discovery material made public this week that also includes hundreds of pages of documents and photographs. Mr. Zimmerman has pleaded not guilty.
Mr. Zimmerman was a neighborhood watch volunteer at the gated community called Retreat at Twin Lakes, in Sanford, Fla., where the shooting took place. He suffered a broken nose, black eyes, cuts to the back of his head and back pains, all of which he said were the result of a struggle with Mr. Martin, who was unarmed.
Mr. Zimmerman has told the police that he saw a suspicious teenager roaming around the Retreat and followed him on foot before losing sight of him. As Mr. Zimmerman was walking back to his vehicle, he told investigators, Mr. Martin emerged and punched him in the nose before jumping on top of him and attacking him. Mr. Zimmerman said that he then shot Mr. Martin to save his own life.
Mr. Zimmermanβs lawyer, Mark OβMara, said he was unable to discuss specific evidence. But he said the claims from Mr. Martinβs friend βmake up one piece of evidence in the case and that it has to be taken within the context of all the other evidence.β
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 You will receive emails containing news content , updates and promotions from The New York Times. You may opt-out at any time. You agree to 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 the taped interview with a state prosecutor, the girl said that Mr. Martin, after evading Mr. Zimmerman for a while, noticed that he was being pursued again and mentioned this to her.
A sense of urgency grew. Mr. Martin alerted the girl to the fact that Mr. Zimmerman βwas getting close to him.β She strongly urged him to run, but she could tell he did not because he was out of breath and tired, and kept saying he was close to the town house where he was a guest.
The girl, who talked with Mr. Martin several times that evening, told the investigator that she then heard Mr. Martin ask, βWhy are you following me for?β She heard the other man ask, βWhat are you doing around here?β Earlier, Mr. Martin had temporarily sought cover from the rain by one of the buildings.
After calling out βTrayvonβ several times over the phone, and getting no response, she heard somebody bump Mr. Martin.
Advertisement Continue reading the main story
Subsequently she heard him utter what sounded like, βGet off, get off.β Then the call ended.
Several weeks after Mr. Martinβs death, his father, Tracy, discovered that his son had been talking to the girl just before he was shot. He learned this by reviewing Mr. Martinβs phone bills. She was subsequently interviewed by the Martin familyβs lawyer, Benjamin L. Crump, but not by the Sanford police.
One police document contained in the discovery concluded, βThe encounter between George Zimmerman and Trayvon Martin was ultimately avoidable by Zimmerman, if Zimmerman had remained in his vehicle and awaited the arrival of law enforcement, or conversely if he had identified himself to Martin as a concerned citizen and initiated dialogue in an effort to dispel each partyβs concerns.β
It added, βThere is no indication that Trayvon Martin was involved in any criminal activity at the time of the encounter.β | β Next up in the Florida prosecutors' evidence dump in the Trayvon Martin case: video, of Trayvon at the 7-Eleven, minutes before he was killed, reports the Guardian. The video shows Trayvon dressed in his hoodie and light-brown trousers, buying candy and a drink. He got into the altercation with George Zimmerman soon after leaving the store. Prosecutors also released a recording of an interview with the girl Trayvon was talking to on the phone that night, and she said he complained that a "crazy and creepy" man was watching him from a car and then following him on foot, reports the New York Times. She heard Trayvon ask the man why he was following him. Then, "I hear this man, like this old man, say, 'What are you doing around here?'" before an apparent scuffle started. "I could hear it a little bit, 'Get off, get off,' then the phone just hung up," she said. | <s>[INST]Prosecutors have released video footage of Trayvon Martin buying sweets and a drink in a Florida convenience store minutes before he was shot and killed in a confrontation with a neighbourhood watch leader.
The scenes recorded at the 7-Eleven close to the Retreat at Twin Lakes development in Sanford show Martin, 17, wearing a black hooded top and beige trousers, walking up to the counter and paying.
Soon after leaving the shop Martin got into a fight with George Zimmerman, who had already called police to report a "suspicious" black male in the neighbourhood. Martin was shot dead by a single shot to the chest at point-blank range, the gunshot heard on recordings of several 911 calls made by neighbours.
The video is among the latest in a batch of evidence released on Friday by prosecutors who have charged Zimmerman, 28, with second-degree murder.
It represents the first public glimpse of the unarmed teenager on 26 February, the night he was killed in an incident that led to race protests and the resignation of the local police chief. The Sanford police department originally released Zimmerman without charge after he claimed he acted in self-defence, and he was arrested in April only after the appointment of a special prosecutor to re-examine the evidence.
The haul of evidence released by state attorney Angela Corey's office over the last two days includes a toxicology report that showed Martin had traces of marijuana in his system, medical records confirming bloody injuries to Zimmerman's head, and testimony by Martin's father that it was not his son's voice heard on 911 recordings crying for help.
Additionally, there were numerous witness statements, many contradicting each other over such details as how many shots were fired and which of the two was on top of the other during their fight. And one police report reveals that detectives wanted to charge Zimmerman with manslaughter even after Bill Lee, then the chief of the Sanford police department, had told reporters there was insufficient evidence to justify such a charge.
The confrontation was "entirely avoidable", detective Chris Serino wrote, if Zimmerman had returned to his car or engaged Martin in conversation.
Among the various audio recordings of interviews with witnesses is one of a teenage girl in Miami, where Martin lived, who told prosecutors she was on the phone to her friend and heard Zimmerman approach him.
The girl, whose identity has not been revealed, said she heard Martin say: "Why you following me for?"
She said: "I hear this man, like this old man, say, 'What are you doing around here?'" then said she heard a bumping sound followed by what she thought was a scuffle.
"I could hear it a little bit, 'Get off, get off,' then the phone just hung up," she said.
Zimmerman faces at least 25 years in jail if he is convicted. No date has yet been set for the trial and he remains free on $150,000 bail.
His lawyer, Mark O'Mara, warned on Friday it would be a mistake to draw any conclusion from the partial evidence so far released. "Looking at it piecemeal is what has caused some of the problems in the past with the case," he said in an interview with CBS News.
"It's sort of important that we all wait until all the evidence is out. Let's deal with it all once we have it, and deal with it in the courtroom." ||||| The recording is one of several dozen released by State Attorney Angela B. Corey, who has charged the gunman, George Zimmerman, 28, with second-degree murder. It is part of the discovery material made public this week that also includes hundreds of pages of documents and photographs. Mr. Zimmerman has pleaded not guilty.
Mr. Zimmerman was a neighborhood watch volunteer at the gated community called Retreat at Twin Lakes, in Sanford, Fla., where the shooting took place. He suffered a broken nose, black eyes, cuts to the back of his head and back pains, all of which he said were the result of a struggle with Mr. Martin, who was unarmed.
Mr. Zimmerman has told the police that he saw a suspicious teenager roaming around the Retreat and followed him on foot before losing sight of him. As Mr. Zimmerman was walking back to his vehicle, he told investigators, Mr. Martin emerged and punched him in the nose before jumping on top of him and attacking him. Mr. Zimmerman said that he then shot Mr. Martin to save his own life.
Mr. Zimmermanβs lawyer, Mark OβMara, said he was unable to discuss specific evidence. But he said the claims from Mr. Martinβs friend βmake up one piece of evidence in the case and that it has to be taken within the context of all the other evidence.β
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 You will receive emails containing news content , updates and promotions from The New York Times. You may opt-out at any time. You agree to 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 the taped interview with a state prosecutor, the girl said that Mr. Martin, after evading Mr. Zimmerman for a while, noticed that he was being pursued again and mentioned this to her.
A sense of urgency grew. Mr. Martin alerted the girl to the fact that Mr. Zimmerman βwas getting close to him.β She strongly urged him to run, but she could tell he did not because he was out of breath and tired, and kept saying he was close to the town house where he was a guest.
The girl, who talked with Mr. Martin several times that evening, told the investigator that she then heard Mr. Martin ask, βWhy are you following me for?β She heard the other man ask, βWhat are you doing around here?β Earlier, Mr. Martin had temporarily sought cover from the rain by one of the buildings.
After calling out βTrayvonβ several times over the phone, and getting no response, she heard somebody bump Mr. Martin.
Advertisement Continue reading the main story
Subsequently she heard him utter what sounded like, βGet off, get off.β Then the call ended.
Several weeks after Mr. Martinβs death, his father, Tracy, discovered that his son had been talking to the girl just before he was shot. He learned this by reviewing Mr. Martinβs phone bills. She was subsequently interviewed by the Martin familyβs lawyer, Benjamin L. Crump, but not by the Sanford police.
One police document contained in the discovery concluded, βThe encounter between George Zimmerman and Trayvon Martin was ultimately avoidable by Zimmerman, if Zimmerman had remained in his vehicle and awaited the arrival of law enforcement, or conversely if he had identified himself to Martin as a concerned citizen and initiated dialogue in an effort to dispel each partyβs concerns.β
It added, βThere is no indication that Trayvon Martin was involved in any criminal activity at the time of the encounter.β[/INST]β Next up in the Florida prosecutors' evidence dump in the Trayvon Martin case: video, of Trayvon at the 7-Eleven, minutes before he was killed, reports the Guardian. The video shows Trayvon dressed in his hoodie and light-brown trousers, buying candy and a drink. He got into the altercation with George Zimmerman soon after leaving the store. Prosecutors also released a recording of an interview with the girl Trayvon was talking to on the phone that night, and she said he complained that a "crazy and creepy" man was watching him from a car and then following him on foot, reports the New York Times. She heard Trayvon ask the man why he was following him. Then, "I hear this man, like this old man, say, 'What are you doing around here?'" before an apparent scuffle started. "I could hear it a little bit, 'Get off, get off,' then the phone just hung up," she said.</s> |
recent advances in x - ray spectroscopy , currently exemplified by the _ asca _ satellite ( tanaka , holt & inoue 1994 ) , have allowed new insights into the astrophysics of the central engines of active galactic nuclei ( agn ) . due to their proximity , and comparatively high brightness
, the most complete studies have focussed upon seyfert galaxies .
whereas the underlying emission in seyfert nuclei over the intrinsic _ asca _ band ( 0.510kev ) is found to be well approximated by a power - law form , most seyfert nuclei display additional spectral complexity .
substantial photoelectric absorption by cold and/or ionized circumnuclear material is seen in half of all seyfert 1 nuclei ( fabian et al .
1994 ; reynolds 1997 ) and all seyfert 2 nuclei .
this circumnuclear material may be related to the putative molecular torus , a warped accretion disk , and/or a disk - wind .
in addition , almost all seyfert 1 nuclei are seen to possess a broad , skewed iron k@xmath0 emission line ( mushotzky et al .
1995 ; tanaka et al . 1995 ; nandra et al . 1997 ; reynolds 1997 ) .
this line is thought to be due to fluorescence from the inner regions of the black hole accretion disk that occurs when the disk is strongly irradiated by the x - ray emitting plasma ( tanaka et al .
1995 ; fabian et al .
these lines are typically seen to have a full width at half maximum ( fwhm ) of @xmath1 and equivalent widths ( ew ) of @xmath2 . a compton backscattered continuum ( the so - called reflection continuum )
accompanies these lines at approximately the strength expected on the basis of the x - ray reprocessing model ( george & fabian 1991 ; matt , perola & piro 1991 ) .
detailed x - ray spectroscopic studies of radio - loud agn are rather less complete than that of seyfert galaxies .
this is primarily due to the comparative rarity of radio - loud objects ( and , thus , the fact that we have to observe them at greater distance ) .
however , this is a subject of some importance : if the radio - loud / radio - quiet dichotomy reflects fundamental differences in central engine structure , we would expect those differences to be most directly revealed in the x - ray band .
the _ asca _
spectrum of the powerful broad line radio galaxy ( blrg ) 3c 109 reveals a fairly strong and broad iron line with fwhm@xmath3 and ew@xmath4 ( allen et al .
this suggests a fundamental similarity between the central engine of this radio galaxy and typical seyfert nuclei , i.e. that the central parts of the accretion flow are in the form of a geometrically - thin , radiatively - efficient accretion disk .
however , 3c 109 might be the exception rather than the rule .
zdziarski et al .
( 1995 ) and woniak et al .
( 1997 ) have shown that blrgs tend to have slightly weaker iron lines , and appreciably weaker reflection continua , as compared to seyfert nuclei . in this paper , we report the results of an _ asca _ observation of 3c 111 ( @xmath5 ) .
this is an x - ray bright blrg which is classified as an fr - ii source with a double - lobe / single - jet morphology ( linfield & perley 1984 ) .
the inner jet has been seen to display superluminal motion , with apparent outflow velocities of @xmath6 ( vermeulen & cohen 1994 ) .
assuming that the pattern speed is intrinsically sub - luminal , the standard theory of superluminal motion ( e.g. , see blandford 1990 ) implies an upper limit on the angle between the line of sight and the jet axis of @xmath7 .
section 2 reviews the previous x - ray observations of this source . in section 3 we describe the basic _ asca _ data analysis and present the results of our spectral fitting .
section 4 discusses the astrophysical implications of our findings .
section 5 draws together our conclusions .
we assume that @xmath8 and @xmath9 throughout this work .
[ cols="<,^,^,^,^ , < " , ] all spectral analysis reported in this paper is based upon joint fitting of the sis and gis data .
the normalizations of the model for each of the four instruments were left as free parameters to allow for the @xmath10 per cent uncertainties in the overall flux calibration of the different instruments .
however , we have noted a slight discrepancy between the sis and gis data .
when taken alone , the sis data present marginal evidence for a spectral break at @xmath11 with photon indices @xmath12 below the break and @xmath13 above the break ( @xmath14 for two additional degrees of freedom as compared with the unbroken power - law ) .
however , this break is _ not _ required when the gis data are also considered . furthermore , the gis data taken alone show no evidence for an iron emission line whereas the sis data do show marginal evidence .
given the marginal nature of these differences , and the remaining calibration uncertainties present in the current analysis tools , we have chosen to take the conservative approach and deal only with the joint sis / gis spectrum .
initially , we fitted the joint spectrum with a power - law form modified only by galactic absorption at the level indicated by the 21-cm measurements . as can be seen from table 3 , this fit is a dreadful description of the data , yielding a goodness of fit parameter @xmath15/dof=5293/1725 .
inspection of the residuals clearly indicates the need for absorption in excess of that indicated by the 21-cm measurements ( see fig .
thus , we consider additional column densities of neutral absorbing material placed either in our galaxy ( i.e. @xmath16 ) or at 3c 111 ( i.e. @xmath5 ) . both of these cases provided a statistically satisfactory description of the overall spectrum , with required addition column densities of @xmath17 and @xmath18 for the @xmath16 and @xmath5 absorbers respectively .
figure 1b shows the spectral fit for the case of the @xmath16 absorber ( although a very similar fit results for the @xmath5 absorber ) .
inspection of fig .
1 shows that the sis0 data argue for extra soft emission beyond that predicted by the model .
however , this conclusion is not supported by data from sis1
. furthermore , examination of gis2/gis3 data below 1kev ( not shown on fig .
1 ) also fails to provide any evidence for a ` soft excess ' .
the level of this soft feature is much greater than the sis0 background level at those energies , and so we rule out the possibility that poor background subtraction is responsible for this contradiction .
we must conclude that this soft feature seen in sis0 is not physical and results from an extreme statistical fluctuation or some currently unrecognized instrumental anomaly . for completeness
, we have also examined the possibility of absorption by partially photoionized line - of - sight gas .
such absorption is commonly seen in the soft x - ray spectrum of seyfert 1 galaxies where it is often referred to as ` warm ' absorption .
we have constructed a photoionization model of an incident power - law spectrum passing through a slab of gas with total column density @xmath19 and ionization parameter @xmath20 .
this ionization parameter is defined by @xmath21 where @xmath22 is the ionizing luminosity ( i.e. the luminosity in photons above @xmath23 ) , @xmath24 is the electron number density of the gas , and @xmath25 is the distance of the gas from the ionizing source .
for detailed of this photoionization model , see reynolds ( 1997 ) for a wide range of parameter space , the ionization state of the gas , and hence its x - ray opacity , depends only on @xmath20 .
this is presented as model - d in table 3 . from table 3
it can be seen that the data do not require an ionized absorber as is apparent from the fact that we can only impose an upper limit on the ionization parameter @xmath26 .
note that even this upper limit is significantly below the typical values found in seyfert galaxies , @xmath27 .
the k@xmath0 iron emission line is of some importance since it probes structures deep within the central engine . here
, we examine the 3c 111 data for evidence of such a line . throughout this section
, we take the simple absorbed power - law model ( model b in table 3 ) as our base model . to this base model , we added a narrow gaussian feature at @xmath28 ( in the rest frame of 3c 111 ) and performed a @xmath15 minimization ( leaving the energy @xmath29 and normalization of the line as free parameters , but constraining the line to be narrow ) .
the results are given in table 3 ( model e ) .
the improvement in the goodness of fit , @xmath30 is _ not _ significant at the 90 per cent level according to the f - test for two extra degrees of freedom .
however , we obtain a stronger result if we add a broad gaussian line to model b ( reported as model f in table 3 ) : the improvement in the goodness of fit parameter , @xmath31 , is significant at the 90 per cent level , but not at the 95 per cent level . thus , we claim a marginal detection of a broad iron line . however , due to the marginality of the detection , the best fitting parameters of the broad gaussian are very poorly constrained , as can be seen by inspection of table 3 . to make further progress , we assume that this line arises by the fluorescence of ` cold ' . ]
iron in an accretion disk around a schwarzschild black hole .
the expected line profiles for this case have been calculated by fabian et al .
( 1989 ) and are incorporated into the spectral fitting package xspec as the ` diskline ' model .
we considered two cases . in the first case ( model g ) , the inner radius of the line emitting region was fixed to correspond to the radius of marginal stability @xmath32 , where @xmath33 is the gravitational radius of the black hole .
the outer radius of the line emitting region was fixed at @xmath34 .
we can justify fixing this parameter since the line profile is insensitive to @xmath35 provided that @xmath36 and the line emissivity declines with radius in the disk faster than @xmath37 .
we make the canonical simplification that the line emissivity depends on the radius in a power - law sense , @xmath38 , where @xmath39 is left as a free parameter in the fit .
the inclination of the disk , @xmath40 , and normalization of the line were also left as free parameters in the fit .
our second case ( model h ) is similar except that we fix the emissivity index to be @xmath41 and allow the inner radius of the line emitting region to be a free parameter . this line emissivity law ( @xmath41 )
is the asymptotic behaviour for large @xmath25 in the case where the primary x - ray source is either a point x - ray source on the symmetry axis of the disk , or is a thin corona with a local power that tracks the viscous dissipation in the underlying disk ( page & thorne 1974 ) .
the results of spectral fitting with models g and h are shown in table 3 .
several of these results are noteworthy .
first , both models imply a disk inclination of @xmath42 , completely consistent with the limits on the angle between the line of sight and the jet axis imposed by observations of the superluminal motion ( see introduction ) .
secondly , interesting constraints can be placed on the equivalent width of the iron line , @xmath43 ( 90 per cent bounds ) .
this contrasts with the broad gaussian parameterization , with which only a lower limit on @xmath44 could be obtained .
the reason for this is easily seen .
the broad gaussian fit is subject to a statistical instability in which both the width and equivalent width of the gaussian grow arbitrary large . in other words , the gaussian component can mimic the high - energy region of the continuum making meaningful constraints on the ew of the line impossible .
however , the disk - line model imposes a physical limit on the maximum width of the iron line , thereby allowing the equivalent width to be usefully constrained .
thirdly , model h shows that the line emitting region must extend at least down to within @xmath45 of the black hole .
these _ asca _ data confirm the need for a substantial amount of absorption beyond that expected on the basis of 21-cm galactic hi measurements . however , these data can not distinguish between an absorber which is intrinsic to the 3c 111 system ( i.e. , at @xmath5 ) or one that is more local to us .
the small difference in the goodness of fit between model b ( i.e. the local absorber ) and model c ( i.e. , the absorber at @xmath5 ) may be influenced by the small soft excess seen in the sis0 data .
since we presume this soft excess to be spurious ( section 3.2.1 ) , we must treat model b and model c as providing similarly good fits to these data
. given this freedom in the spectral data , there are at least three possibilities for the nature of this absorber .
first , the excess absorbing material may be the neutral component of the ism of the 3c 111 host galaxy . given the large column of material required ( almost @xmath46 ) , this would suggest that the host galaxy was a disk galaxy viewed at high inclination .
this is inconsistent with the apparent cd nature of the host galaxy ( owen & laing 1989 ) .
thus , we argue against this possibility . secondly , the excess absorbing material maybe circumnuclear material associated directly with the agn ( e.g. , the putative molecular torus of agn unification schemes or the outer parts of a warped accretion disk . ) observations of the iron line and , independently , superluminal motion imply a central engine inclination of @xmath42 ( i.e. , we are viewing the central engine somewhat face - on ) . within the `` circumnuclear absorber '' picture ,
we would be led to the conclusion that a relatively large quantity of neutral material must exist at high latitudes within the system .
this would suggest a molecular torus with a small opening angle or a highly warped accretion disk . in most cases , x - ray absorption towards an agn in excess of that suggested by galactic hi measurements is taken to be firm evidence for intrinsic absorption associated with either the agn or its host galaxy .
whilst the absorbing material seen towards 3c 111 may indeed be circumnuclear in nature , we might question this inference given the fact that 3c 111 lies behind a well known giant molecular cloud ( containing taurus b and the taurus - perseus complexes ) estimated to lie at a distance of 350pc ( ungerechts & thaddeus 1987 ) .
there are two ways in which the presence of this cloud complex can cause deviations between the actual galactic absorption along the line of sight and that inferred from 21-cm measurements : small scale inhomogeneities and the presence of molecular hydrogen .
we note that turner et al .
( 1995 ) made a similar suggestion for the case of nrao 140 .
marscher , moore & bania ( 1993 ) and moore & marscher ( 1995 ) have used 3c 111 as a background radio continuum source to probe details of the 4.83ghz h@xmath47co absorption line arising from material in this molecular cloud . on the basis of temporal variability in the strength and profile of the absorption line , they argue that the cloud complex contains inhomogeneities on the sub - parsec , or even au , scales .
these authors estimate that between 30100 clumps lie along the line - of - sight to 3c 111 and that poisson fluctuations in this number give rise to the observed molecular line changes .
the 21-cm studies of elvis , lockman & wilkes ( 1989 ) use a @xmath48arcmin@xmath49 beam ( lockman , jahoda & mccammon 1986 ) measurements of the neutral hydrogen column densities are necessarily averaged over this beam and hence insensitive to the small scale inhomogeneities indicated by the molecular absorption line studies .
thus , these inhomogeneities could give rise to differences between the 21-cm column density and observed absorbing column .
however , given that 3c 111 appears _ not _ to be blocked by one ( or a small number ) especially dense clump , it is difficult to envisage the factor of 3 discrepancy between the 21-cm measurements and x - ray absorption as arising purely from these inhomogeneities .
clearly , we expect there to be molecular hydrogen along our line of sight to 3c 111 associated with the molecular cloud .
this gas , and the metals / dust associated with it , will act as a source of x - ray opacity which is indistinguishable from atomic gas at the spectral resolution of _
since it does not contribute to the 21-cm emission , this molecular gas is another possible cause for the discrepancy between the 21-cm measurements and the x - ray absorbing column .
if 6070 per cent of the gas along the line of sight to 3c 111 is in molecular form , the discrepancy between the 21-cm measurements and the x - ray absorbing column is resolved .
furthermore , the clear temporal change in absorption between the two _ exosat _ me spectra discussed in section 2 might be due to a particularly large inhomogeneity / knot in this molecular gas that drifts across the line of sight to the core of 3c 111 .
we also claim the marginal detection of a broad iron line .
although the constraints are poor , the data are consistent with a cold iron line originating from the central regions of an accretion disk around a schwarzschild black hole .
the disk inclination is constrained to be @xmath42 .
the equivalent width , @xmath43 , is rather weak as compared to seyfert nuclei ( nandra et al .
1997 ; reynolds 1997 ) .
this is consistent with the results of woniak et al .
( 1997 ) who examine _ osse_/_ginga _ data and find an iron line ew of @xmath50 and a weak reflection continuum .
this authors find that the inferred solid angle subtended by the ` reflector ' at the x - ray source is @xmath51 .
as mentioned in the introduction , this is found to be a general trend differentiating radio - quiet seyfert nuclei from blrgs .
these iron line studies suggest both fundamental similarities and differences between the central engines of radio - quiet seyfert nuclei and blrgs .
the fact that blrgs display resolved iron lines at all is evidence for the existence of a geometrically - thin , radiatively efficient accretion disk extending down to @xmath52 , as is the case for seyfert nuclei ( note that in the seyfert case , iron line studies seem to suggest that the disk remains geometrically - thin and radiatively - efficient essentially all of the way down to the black hole ) .
the comparative weakness of the lines / reflection - continua in blrg could arise for several reasons .
first , there might be a component of the x - ray emission that is associated with the radio jet and is beamed along the jet axis thereby diluting the seyfert - like reflection features that are intrinsically present .
secondly , the inner accretion disk ( i.e. the inner @xmath53 or so ) might not be in a physical state capable of producing the x - ray reflection features . for example , the disk might undergo a transition into an optically - thin advection dominated disk ( add ) which would be totally ionized and hence incapable of producing x - ray reflection signatures . if most of the primary x - ray flux still originated from the central most regions , the solid angle covered by material capable of producing reflection features could be rather small . such models ( with a thin - disk / add transition ) have previously been discussed in the context of galactic black hole candidates ( e.g. , see esin , mcclintock & narayan 1997 and references therein ) .
our _ asca _ data for 3c 111 clearly reveal the presence of absorption in excess to that suggested by 21-cm measurements of the galactic hi column . whilst this may be evidence for absorption intrinsic to the 3c 111 system
, we suggest that inhomogeneities and molecular material in the foreground ( galactic ) giant molecular cloud may also be responsible for this excess absorption .
molecular absorption line studies of this cloud lend strength to this possibility .
we also claim the marginal detection of a broad iron k@xmath0 line .
the detection of a broad line at all suggests the existence of a geometrically - thin , radiatively - efficient accretion disk within @xmath54 of the black hole .
however , the weakness of this line ( and the associated backscattered continuum ) as compared to typical seyfert galaxies suggests that either x - ray beaming is important , or that the innermost regions of the disk are in a state incapable of producing the x - ray reflection signatures .
one possibility is that the disk undergoes a transition to an add state in its innermost regions .
we acknowledge support from pparc ( csr , csc , ki ) , the royal society ( acf ) , the national science foundation under grant ast9529175 ( csr ) , and nasa under grant nasa - nag5 - 6337 ( csr ) .
allen s. w. , fabian a. c. , idesawa e. , inoue h. , kii t. , otani c. , 1997 , mnras , 286 , 765 blandford r. d. , 1990 , in active galactic nuclei , ed t.j .- l.courvoisier & m.mayor ( saas - fee advanced course 20 ) ( berlin : springer ) , p.161 elvis m. , lockman f. j. , wilkes b. j. , 1989 , aj , 97 , 777 esin a. a. , mcclintock j. e. , narayan r. , 1997 , apj , submitted fabian a. c. , rees m. j. , stellar l. , white n. e. , 1989 , mnras , 238 , 729 fabian a. c. et al .
1994 , pasj , 46 , l59 fabian a. c. et al .
1995 , mnras , 277 , l11 george i. m. , fabian a. c. , 1991 , mnras , 249 , 352 linfield r. , perley r. , 1984 , apj , 279 , 60 lockman f. j. , jahoda k. , mccammon d. , 1986 , apj , 302 , 432 marscher a. p. , moore e. m. , bania t. m. , 1993 , apj , 419 , l101 matt g. , perola g. c. , piro l. , 1991 , a&a , 247 , 25 moore e. m. , marscher a. p. , 1995 ,
apj , 452 , 671 mushotzky r. f. , fabian a. c. , iwasawa k. , kunieda h. , matsuoka m. , nandra k. , tanaka y. , 1995 , mnras , 272 , l9 nandra k. , pounds k. a. , 1994 , mnras , 268 , 405 nandra k. , george i. m. , mushotzky r. f. , turner t. j. , yaqoob t. , 1997 , apj , 477 , 602 owen f. n. , laing r. a. , 1989 , mnras , 238 , 357 page d. n. , thorne k. s. , 1974 , apj , 499 , 191 reynolds c. s. , 1997 , mnras , 286 , 513 tanaka y. , inoue h. , holt s. s. , 1994 , pasj , 46 , l37 tanaka y. et al . , 1995 , nat , 375 , 659 thoraval s. , boisse p. , stark r. , 1996 , a&a , 312 , 973 turner t. j. , pounds k. a. , 1989 , mnras , 240 , 833 turner t. j. , weaver k. a. , mushotzky r. f. , holt s. s. , madejski g. m. , 1991 , apj , 381 , 85 turner t. j. , george i. m. , madejski g. m. , kitamoto s. , suzuki t. , 1995 , apj , 445 , 660 ungerechts h. , thaddeus p. , 1987 ,
apjs , 63 , 645 vermeulen r. c. , cohen m. h. , 1994 , apj , 430 , 467 weaver k. a. , arnaud k. a. , mushotzky r. f. , 1995 , apj , 447 , 121 woniak p. r. , zdziarski a. a. , smith d. , madejski g. m. , johnson w. n. , 1997 , mnras , submitted zdziarski a. a. , johnson w. n. , done c. , smith d. , mcnaron - brown k. , 1995 , apj , 438 , l63 | we present an _ asca _
observation of the broad line radio galaxy 3c 111 .
the x - ray spectrum is well described by a model consisting of a photoelectrically - absorbed power - law form .
the inferred absorbing column density is significantly greater than expected on the basis of 21-cm measurements of galactic hi . whilst this may be due intrinsic absorption from a circumnuclear torus or highly warped accretion disk , inhomogeneities and molecular gas within the foreground giant molecular cloud
may also be responsible for some of this excess absorption .
we also claim a marginal detection of a broad iron k@xmath0 line which is well explained as being a fluorescent line originating from the central regions of a radiatively - efficient accretion disk .
this line appears weak in comparison to those found in ( radio - quiet ) seyfert nuclei .
we briefly discuss the implications of this fact . #
1to 0pt#1 # 1 # 1 to size # 1 to size # 1 = cmr10 scaled2 = cmbx10 scaled2 = cmti10 scaled2 ps . = -1.5 cm accretion , accretion discs galaxies : active galaxies : individual : 3c 111 x - rays : galaxies | <s>[INST]recent advances in x - ray spectroscopy , currently exemplified by the _ asca _ satellite ( tanaka , holt & inoue 1994 ) , have allowed new insights into the astrophysics of the central engines of active galactic nuclei ( agn ) . due to their proximity , and comparatively high brightness
, the most complete studies have focussed upon seyfert galaxies .
whereas the underlying emission in seyfert nuclei over the intrinsic _ asca _ band ( 0.510kev ) is found to be well approximated by a power - law form , most seyfert nuclei display additional spectral complexity .
substantial photoelectric absorption by cold and/or ionized circumnuclear material is seen in half of all seyfert 1 nuclei ( fabian et al .
1994 ; reynolds 1997 ) and all seyfert 2 nuclei .
this circumnuclear material may be related to the putative molecular torus , a warped accretion disk , and/or a disk - wind .
in addition , almost all seyfert 1 nuclei are seen to possess a broad , skewed iron k@xmath0 emission line ( mushotzky et al .
1995 ; tanaka et al . 1995 ; nandra et al . 1997 ; reynolds 1997 ) .
this line is thought to be due to fluorescence from the inner regions of the black hole accretion disk that occurs when the disk is strongly irradiated by the x - ray emitting plasma ( tanaka et al .
1995 ; fabian et al .
these lines are typically seen to have a full width at half maximum ( fwhm ) of @xmath1 and equivalent widths ( ew ) of @xmath2 . a compton backscattered continuum ( the so - called reflection continuum )
accompanies these lines at approximately the strength expected on the basis of the x - ray reprocessing model ( george & fabian 1991 ; matt , perola & piro 1991 ) .
detailed x - ray spectroscopic studies of radio - loud agn are rather less complete than that of seyfert galaxies .
this is primarily due to the comparative rarity of radio - loud objects ( and , thus , the fact that we have to observe them at greater distance ) .
however , this is a subject of some importance : if the radio - loud / radio - quiet dichotomy reflects fundamental differences in central engine structure , we would expect those differences to be most directly revealed in the x - ray band .
the _ asca _
spectrum of the powerful broad line radio galaxy ( blrg ) 3c 109 reveals a fairly strong and broad iron line with fwhm@xmath3 and ew@xmath4 ( allen et al .
this suggests a fundamental similarity between the central engine of this radio galaxy and typical seyfert nuclei , i.e. that the central parts of the accretion flow are in the form of a geometrically - thin , radiatively - efficient accretion disk .
however , 3c 109 might be the exception rather than the rule .
zdziarski et al .
( 1995 ) and woniak et al .
( 1997 ) have shown that blrgs tend to have slightly weaker iron lines , and appreciably weaker reflection continua , as compared to seyfert nuclei . in this paper , we report the results of an _ asca _ observation of 3c 111 ( @xmath5 ) .
this is an x - ray bright blrg which is classified as an fr - ii source with a double - lobe / single - jet morphology ( linfield & perley 1984 ) .
the inner jet has been seen to display superluminal motion , with apparent outflow velocities of @xmath6 ( vermeulen & cohen 1994 ) .
assuming that the pattern speed is intrinsically sub - luminal , the standard theory of superluminal motion ( e.g. , see blandford 1990 ) implies an upper limit on the angle between the line of sight and the jet axis of @xmath7 .
section 2 reviews the previous x - ray observations of this source . in section 3 we describe the basic _ asca _ data analysis and present the results of our spectral fitting .
section 4 discusses the astrophysical implications of our findings .
section 5 draws together our conclusions .
we assume that @xmath8 and @xmath9 throughout this work .
[ cols="<,^,^,^,^ , < " , ] all spectral analysis reported in this paper is based upon joint fitting of the sis and gis data .
the normalizations of the model for each of the four instruments were left as free parameters to allow for the @xmath10 per cent uncertainties in the overall flux calibration of the different instruments .
however , we have noted a slight discrepancy between the sis and gis data .
when taken alone , the sis data present marginal evidence for a spectral break at @xmath11 with photon indices @xmath12 below the break and @xmath13 above the break ( @xmath14 for two additional degrees of freedom as compared with the unbroken power - law ) .
however , this break is _ not _ required when the gis data are also considered . furthermore , the gis data taken alone show no evidence for an iron emission line whereas the sis data do show marginal evidence .
given the marginal nature of these differences , and the remaining calibration uncertainties present in the current analysis tools , we have chosen to take the conservative approach and deal only with the joint sis / gis spectrum .
initially , we fitted the joint spectrum with a power - law form modified only by galactic absorption at the level indicated by the 21-cm measurements . as can be seen from table 3 , this fit is a dreadful description of the data , yielding a goodness of fit parameter @xmath15/dof=5293/1725 .
inspection of the residuals clearly indicates the need for absorption in excess of that indicated by the 21-cm measurements ( see fig .
thus , we consider additional column densities of neutral absorbing material placed either in our galaxy ( i.e. @xmath16 ) or at 3c 111 ( i.e. @xmath5 ) . both of these cases provided a statistically satisfactory description of the overall spectrum , with required addition column densities of @xmath17 and @xmath18 for the @xmath16 and @xmath5 absorbers respectively .
figure 1b shows the spectral fit for the case of the @xmath16 absorber ( although a very similar fit results for the @xmath5 absorber ) .
inspection of fig .
1 shows that the sis0 data argue for extra soft emission beyond that predicted by the model .
however , this conclusion is not supported by data from sis1
. furthermore , examination of gis2/gis3 data below 1kev ( not shown on fig .
1 ) also fails to provide any evidence for a ` soft excess ' .
the level of this soft feature is much greater than the sis0 background level at those energies , and so we rule out the possibility that poor background subtraction is responsible for this contradiction .
we must conclude that this soft feature seen in sis0 is not physical and results from an extreme statistical fluctuation or some currently unrecognized instrumental anomaly . for completeness
, we have also examined the possibility of absorption by partially photoionized line - of - sight gas .
such absorption is commonly seen in the soft x - ray spectrum of seyfert 1 galaxies where it is often referred to as ` warm ' absorption .
we have constructed a photoionization model of an incident power - law spectrum passing through a slab of gas with total column density @xmath19 and ionization parameter @xmath20 .
this ionization parameter is defined by @xmath21 where @xmath22 is the ionizing luminosity ( i.e. the luminosity in photons above @xmath23 ) , @xmath24 is the electron number density of the gas , and @xmath25 is the distance of the gas from the ionizing source .
for detailed of this photoionization model , see reynolds ( 1997 ) for a wide range of parameter space , the ionization state of the gas , and hence its x - ray opacity , depends only on @xmath20 .
this is presented as model - d in table 3 . from table 3
it can be seen that the data do not require an ionized absorber as is apparent from the fact that we can only impose an upper limit on the ionization parameter @xmath26 .
note that even this upper limit is significantly below the typical values found in seyfert galaxies , @xmath27 .
the k@xmath0 iron emission line is of some importance since it probes structures deep within the central engine . here
, we examine the 3c 111 data for evidence of such a line . throughout this section
, we take the simple absorbed power - law model ( model b in table 3 ) as our base model . to this base model , we added a narrow gaussian feature at @xmath28 ( in the rest frame of 3c 111 ) and performed a @xmath15 minimization ( leaving the energy @xmath29 and normalization of the line as free parameters , but constraining the line to be narrow ) .
the results are given in table 3 ( model e ) .
the improvement in the goodness of fit , @xmath30 is _ not _ significant at the 90 per cent level according to the f - test for two extra degrees of freedom .
however , we obtain a stronger result if we add a broad gaussian line to model b ( reported as model f in table 3 ) : the improvement in the goodness of fit parameter , @xmath31 , is significant at the 90 per cent level , but not at the 95 per cent level . thus , we claim a marginal detection of a broad iron line . however , due to the marginality of the detection , the best fitting parameters of the broad gaussian are very poorly constrained , as can be seen by inspection of table 3 . to make further progress , we assume that this line arises by the fluorescence of ` cold ' . ]
iron in an accretion disk around a schwarzschild black hole .
the expected line profiles for this case have been calculated by fabian et al .
( 1989 ) and are incorporated into the spectral fitting package xspec as the ` diskline ' model .
we considered two cases . in the first case ( model g ) , the inner radius of the line emitting region was fixed to correspond to the radius of marginal stability @xmath32 , where @xmath33 is the gravitational radius of the black hole .
the outer radius of the line emitting region was fixed at @xmath34 .
we can justify fixing this parameter since the line profile is insensitive to @xmath35 provided that @xmath36 and the line emissivity declines with radius in the disk faster than @xmath37 .
we make the canonical simplification that the line emissivity depends on the radius in a power - law sense , @xmath38 , where @xmath39 is left as a free parameter in the fit .
the inclination of the disk , @xmath40 , and normalization of the line were also left as free parameters in the fit .
our second case ( model h ) is similar except that we fix the emissivity index to be @xmath41 and allow the inner radius of the line emitting region to be a free parameter . this line emissivity law ( @xmath41 )
is the asymptotic behaviour for large @xmath25 in the case where the primary x - ray source is either a point x - ray source on the symmetry axis of the disk , or is a thin corona with a local power that tracks the viscous dissipation in the underlying disk ( page & thorne 1974 ) .
the results of spectral fitting with models g and h are shown in table 3 .
several of these results are noteworthy .
first , both models imply a disk inclination of @xmath42 , completely consistent with the limits on the angle between the line of sight and the jet axis imposed by observations of the superluminal motion ( see introduction ) .
secondly , interesting constraints can be placed on the equivalent width of the iron line , @xmath43 ( 90 per cent bounds ) .
this contrasts with the broad gaussian parameterization , with which only a lower limit on @xmath44 could be obtained .
the reason for this is easily seen .
the broad gaussian fit is subject to a statistical instability in which both the width and equivalent width of the gaussian grow arbitrary large . in other words , the gaussian component can mimic the high - energy region of the continuum making meaningful constraints on the ew of the line impossible .
however , the disk - line model imposes a physical limit on the maximum width of the iron line , thereby allowing the equivalent width to be usefully constrained .
thirdly , model h shows that the line emitting region must extend at least down to within @xmath45 of the black hole .
these _ asca _ data confirm the need for a substantial amount of absorption beyond that expected on the basis of 21-cm galactic hi measurements . however , these data can not distinguish between an absorber which is intrinsic to the 3c 111 system ( i.e. , at @xmath5 ) or one that is more local to us .
the small difference in the goodness of fit between model b ( i.e. the local absorber ) and model c ( i.e. , the absorber at @xmath5 ) may be influenced by the small soft excess seen in the sis0 data .
since we presume this soft excess to be spurious ( section 3.2.1 ) , we must treat model b and model c as providing similarly good fits to these data
. given this freedom in the spectral data , there are at least three possibilities for the nature of this absorber .
first , the excess absorbing material may be the neutral component of the ism of the 3c 111 host galaxy . given the large column of material required ( almost @xmath46 ) , this would suggest that the host galaxy was a disk galaxy viewed at high inclination .
this is inconsistent with the apparent cd nature of the host galaxy ( owen & laing 1989 ) .
thus , we argue against this possibility . secondly , the excess absorbing material maybe circumnuclear material associated directly with the agn ( e.g. , the putative molecular torus of agn unification schemes or the outer parts of a warped accretion disk . ) observations of the iron line and , independently , superluminal motion imply a central engine inclination of @xmath42 ( i.e. , we are viewing the central engine somewhat face - on ) . within the `` circumnuclear absorber '' picture ,
we would be led to the conclusion that a relatively large quantity of neutral material must exist at high latitudes within the system .
this would suggest a molecular torus with a small opening angle or a highly warped accretion disk . in most cases , x - ray absorption towards an agn in excess of that suggested by galactic hi measurements is taken to be firm evidence for intrinsic absorption associated with either the agn or its host galaxy .
whilst the absorbing material seen towards 3c 111 may indeed be circumnuclear in nature , we might question this inference given the fact that 3c 111 lies behind a well known giant molecular cloud ( containing taurus b and the taurus - perseus complexes ) estimated to lie at a distance of 350pc ( ungerechts & thaddeus 1987 ) .
there are two ways in which the presence of this cloud complex can cause deviations between the actual galactic absorption along the line of sight and that inferred from 21-cm measurements : small scale inhomogeneities and the presence of molecular hydrogen .
we note that turner et al .
( 1995 ) made a similar suggestion for the case of nrao 140 .
marscher , moore & bania ( 1993 ) and moore & marscher ( 1995 ) have used 3c 111 as a background radio continuum source to probe details of the 4.83ghz h@xmath47co absorption line arising from material in this molecular cloud . on the basis of temporal variability in the strength and profile of the absorption line , they argue that the cloud complex contains inhomogeneities on the sub - parsec , or even au , scales .
these authors estimate that between 30100 clumps lie along the line - of - sight to 3c 111 and that poisson fluctuations in this number give rise to the observed molecular line changes .
the 21-cm studies of elvis , lockman & wilkes ( 1989 ) use a @xmath48arcmin@xmath49 beam ( lockman , jahoda & mccammon 1986 ) measurements of the neutral hydrogen column densities are necessarily averaged over this beam and hence insensitive to the small scale inhomogeneities indicated by the molecular absorption line studies .
thus , these inhomogeneities could give rise to differences between the 21-cm column density and observed absorbing column .
however , given that 3c 111 appears _ not _ to be blocked by one ( or a small number ) especially dense clump , it is difficult to envisage the factor of 3 discrepancy between the 21-cm measurements and x - ray absorption as arising purely from these inhomogeneities .
clearly , we expect there to be molecular hydrogen along our line of sight to 3c 111 associated with the molecular cloud .
this gas , and the metals / dust associated with it , will act as a source of x - ray opacity which is indistinguishable from atomic gas at the spectral resolution of _
since it does not contribute to the 21-cm emission , this molecular gas is another possible cause for the discrepancy between the 21-cm measurements and the x - ray absorbing column .
if 6070 per cent of the gas along the line of sight to 3c 111 is in molecular form , the discrepancy between the 21-cm measurements and the x - ray absorbing column is resolved .
furthermore , the clear temporal change in absorption between the two _ exosat _ me spectra discussed in section 2 might be due to a particularly large inhomogeneity / knot in this molecular gas that drifts across the line of sight to the core of 3c 111 .
we also claim the marginal detection of a broad iron line .
although the constraints are poor , the data are consistent with a cold iron line originating from the central regions of an accretion disk around a schwarzschild black hole .
the disk inclination is constrained to be @xmath42 .
the equivalent width , @xmath43 , is rather weak as compared to seyfert nuclei ( nandra et al .
1997 ; reynolds 1997 ) .
this is consistent with the results of woniak et al .
( 1997 ) who examine _ osse_/_ginga _ data and find an iron line ew of @xmath50 and a weak reflection continuum .
this authors find that the inferred solid angle subtended by the ` reflector ' at the x - ray source is @xmath51 .
as mentioned in the introduction , this is found to be a general trend differentiating radio - quiet seyfert nuclei from blrgs .
these iron line studies suggest both fundamental similarities and differences between the central engines of radio - quiet seyfert nuclei and blrgs .
the fact that blrgs display resolved iron lines at all is evidence for the existence of a geometrically - thin , radiatively efficient accretion disk extending down to @xmath52 , as is the case for seyfert nuclei ( note that in the seyfert case , iron line studies seem to suggest that the disk remains geometrically - thin and radiatively - efficient essentially all of the way down to the black hole ) .
the comparative weakness of the lines / reflection - continua in blrg could arise for several reasons .
first , there might be a component of the x - ray emission that is associated with the radio jet and is beamed along the jet axis thereby diluting the seyfert - like reflection features that are intrinsically present .
secondly , the inner accretion disk ( i.e. the inner @xmath53 or so ) might not be in a physical state capable of producing the x - ray reflection features . for example , the disk might undergo a transition into an optically - thin advection dominated disk ( add ) which would be totally ionized and hence incapable of producing x - ray reflection signatures . if most of the primary x - ray flux still originated from the central most regions , the solid angle covered by material capable of producing reflection features could be rather small . such models ( with a thin - disk / add transition ) have previously been discussed in the context of galactic black hole candidates ( e.g. , see esin , mcclintock & narayan 1997 and references therein ) .
our _ asca _ data for 3c 111 clearly reveal the presence of absorption in excess to that suggested by 21-cm measurements of the galactic hi column . whilst this may be evidence for absorption intrinsic to the 3c 111 system
, we suggest that inhomogeneities and molecular material in the foreground ( galactic ) giant molecular cloud may also be responsible for this excess absorption .
molecular absorption line studies of this cloud lend strength to this possibility .
we also claim the marginal detection of a broad iron k@xmath0 line .
the detection of a broad line at all suggests the existence of a geometrically - thin , radiatively - efficient accretion disk within @xmath54 of the black hole .
however , the weakness of this line ( and the associated backscattered continuum ) as compared to typical seyfert galaxies suggests that either x - ray beaming is important , or that the innermost regions of the disk are in a state incapable of producing the x - ray reflection signatures .
one possibility is that the disk undergoes a transition to an add state in its innermost regions .
we acknowledge support from pparc ( csr , csc , ki ) , the royal society ( acf ) , the national science foundation under grant ast9529175 ( csr ) , and nasa under grant nasa - nag5 - 6337 ( csr ) .
allen s. w. , fabian a. c. , idesawa e. , inoue h. , kii t. , otani c. , 1997 , mnras , 286 , 765 blandford r. d. , 1990 , in active galactic nuclei , ed t.j .- l.courvoisier & m.mayor ( saas - fee advanced course 20 ) ( berlin : springer ) , p.161 elvis m. , lockman f. j. , wilkes b. j. , 1989 , aj , 97 , 777 esin a. a. , mcclintock j. e. , narayan r. , 1997 , apj , submitted fabian a. c. , rees m. j. , stellar l. , white n. e. , 1989 , mnras , 238 , 729 fabian a. c. et al .
1994 , pasj , 46 , l59 fabian a. c. et al .
1995 , mnras , 277 , l11 george i. m. , fabian a. c. , 1991 , mnras , 249 , 352 linfield r. , perley r. , 1984 , apj , 279 , 60 lockman f. j. , jahoda k. , mccammon d. , 1986 , apj , 302 , 432 marscher a. p. , moore e. m. , bania t. m. , 1993 , apj , 419 , l101 matt g. , perola g. c. , piro l. , 1991 , a&a , 247 , 25 moore e. m. , marscher a. p. , 1995 ,
apj , 452 , 671 mushotzky r. f. , fabian a. c. , iwasawa k. , kunieda h. , matsuoka m. , nandra k. , tanaka y. , 1995 , mnras , 272 , l9 nandra k. , pounds k. a. , 1994 , mnras , 268 , 405 nandra k. , george i. m. , mushotzky r. f. , turner t. j. , yaqoob t. , 1997 , apj , 477 , 602 owen f. n. , laing r. a. , 1989 , mnras , 238 , 357 page d. n. , thorne k. s. , 1974 , apj , 499 , 191 reynolds c. s. , 1997 , mnras , 286 , 513 tanaka y. , inoue h. , holt s. s. , 1994 , pasj , 46 , l37 tanaka y. et al . , 1995 , nat , 375 , 659 thoraval s. , boisse p. , stark r. , 1996 , a&a , 312 , 973 turner t. j. , pounds k. a. , 1989 , mnras , 240 , 833 turner t. j. , weaver k. a. , mushotzky r. f. , holt s. s. , madejski g. m. , 1991 , apj , 381 , 85 turner t. j. , george i. m. , madejski g. m. , kitamoto s. , suzuki t. , 1995 , apj , 445 , 660 ungerechts h. , thaddeus p. , 1987 ,
apjs , 63 , 645 vermeulen r. c. , cohen m. h. , 1994 , apj , 430 , 467 weaver k. a. , arnaud k. a. , mushotzky r. f. , 1995 , apj , 447 , 121 woniak p. r. , zdziarski a. a. , smith d. , madejski g. m. , johnson w. n. , 1997 , mnras , submitted zdziarski a. a. , johnson w. n. , done c. , smith d. , mcnaron - brown k. , 1995 , apj , 438 , l63[/INST] we present an _ asca _
observation of the broad line radio galaxy 3c 111 .
the x - ray spectrum is well described by a model consisting of a photoelectrically - absorbed power - law form .
the inferred absorbing column density is significantly greater than expected on the basis of 21-cm measurements of galactic hi . whilst this may be due intrinsic absorption from a circumnuclear torus or highly warped accretion disk , inhomogeneities and molecular gas within the foreground giant molecular cloud
may also be responsible for some of this excess absorption .
we also claim a marginal detection of a broad iron k@xmath0 line which is well explained as being a fluorescent line originating from the central regions of a radiatively - efficient accretion disk .
this line appears weak in comparison to those found in ( radio - quiet ) seyfert nuclei .
we briefly discuss the implications of this fact . #
1to 0pt#1 # 1 # 1 to size # 1 to size # 1 = cmr10 scaled2 = cmbx10 scaled2 = cmti10 scaled2 ps . = -1.5 cm accretion , accretion discs galaxies : active galaxies : individual : 3c 111 x - rays : galaxies </s> |
shift work is defined as work at times other than the daytime hours of 7:00 a.m. to 6:00 p.m. it is estimated that almost 15% of full - time workers in the united states ( i.e. , 15 million americans ) are shift workers who work evening , night , or rotating shifts . social needs and economic factors
shift workers provide critical services , including police and fire protection , health care , transportation , communications , public utilities , military service , and services in industries that require continuous processing .
shift work has been documented to cause adverse health effects , by disturbing three factors : circadian rhythms , sleep , and personal ( i.e. , family and social ) life . in the long term , because of disturbance of circadian rhythms such as the sleep - wake cycle , morbidity and mortality rates in shift workers will be increased.[36 ] some previous studies have demonstrated an increased risk of medical conditions , including cardiovascular disease , arthritis , diabetes mellitus , and certain cancers in association with sleep deprivation.[612 ] a number of studies have suggested that sleep disorders such as sleep loss , narcolepsy , and sleep apnea are associated with elevated inflammatory markers such as interleukin 6 ( il-6 ) , tumor necrosis factor - alpha ( tnf- ) , c - reactive protein ( crp ) , and white blood cells ( wbc).[1219 ] the purpose of this study was to evaluate the relationship between night work and elevation of inflammatory markers .
regards to the side effects of shift work and circadian rhythms and sleep disturbance as one of the important cause of these side effects and on the other hand the elevation of inflammatory markers after sleep deprivation , the purpose of this study was to evaluate the relationship between night work shifts and elevation of inflammatory markers .
the relationship between increased inflammatory markers and medical conditions , which is the same as side effects of shift work , has been observed in some studies .
if further studies support the results of this study , we can use inflammatory markers for early detection of long - term health side effects of shift work in future for prevention of them .
the subjects included 50 healthy workers who gave consent and were paid for participation in this study .
workers were excluded from the study if they had any history of inflammatory disease , cancer , chronic disease , psychotic disorder , drug or alcohol abuse , body mass index ( bmi ) > 30 , or smoking history ( as determined by review of pre - employment and annual employment medical records ) .
workers who were determined to have sleep disorders according to their score on the epworth sleepiness scale ( ess ) and insomnia questionnaires were also excluded .
they were also excluded if they developed any acute disease or reported poor sleep during the study period .
we designed a randomized clinical cross over trial study with a specific shift work schedule .
group 1 ( 25 workers ) : they were scheduled on three days of day shift work , followed by one day off ( wash out period ) , and then three nights of night shift work .
group 2 ( 25 workers ) : they were scheduled on three days of night shift work , followed by one day off ( wash out period ) , and then three days of day shift work .
blood samples were divided into two parts ; one part was transferred to a clot tube and centrifuged as soon as possible .
the serum was frozen at 25c until the enzyme - linked immunosorbent assay was performed . il-6 and
high - sensitive crp was also measured by elisa ( ibl - international , hamburg , germany ) .
the lower detection limit was 0.01 mg / ml . the second part of the sample was mixed with edta ( anti - coagulant ) for complete blood count and differential and analysis by a cell counter h1 device .
spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t - test .
the subjects included 50 healthy workers who gave consent and were paid for participation in this study .
workers were excluded from the study if they had any history of inflammatory disease , cancer , chronic disease , psychotic disorder , drug or alcohol abuse , body mass index ( bmi ) > 30 , or smoking history ( as determined by review of pre - employment and annual employment medical records ) .
workers who were determined to have sleep disorders according to their score on the epworth sleepiness scale ( ess ) and insomnia questionnaires were also excluded .
they were also excluded if they developed any acute disease or reported poor sleep during the study period .
we designed a randomized clinical cross over trial study with a specific shift work schedule .
group 1 ( 25 workers ) : they were scheduled on three days of day shift work , followed by one day off ( wash out period ) , and then three nights of night shift work .
group 2 ( 25 workers ) : they were scheduled on three days of night shift work , followed by one day off ( wash out period ) , and then three days of day shift work .
blood samples were divided into two parts ; one part was transferred to a clot tube and centrifuged as soon as possible .
the serum was frozen at 25c until the enzyme - linked immunosorbent assay was performed . il-6 and
high - sensitive crp was also measured by elisa ( ibl - international , hamburg , germany ) .
the lower detection limit was 0.01 mg / ml . the second part of the sample was mixed with edta ( anti - coagulant ) for complete blood count and differential and analysis by a cell counter h1 device .
spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t - test .
descriptions of age , weight , height , bmi , ess , and insomnia questionnaires scores of workers are shown in table 1 . despite random allocation of workers between the two groups
for omission of confounder effects of these variables , we used multivariant regression . description of age , weight , height , body mass index , epworth sleepiness scale , and insomnia questionnaire scores of workers there were no carry over effects in the two periods of study on outcomes except il-6 .
compared with day work shifts , night work shifts were associated with increased levels of il-6 , tnf- , crp , wbc , neutrophils , lymphocytes , and platelets , but for tnf- was not statistically significant . there was no significant change in monocytes [ tables 2 and 3 ] .
il6 after day work and night work shifts difference between night to day and day to night groups for out comes multivariant regression analysis was done for omitting the confounder effects of age and ess between two groups [ table 4 ] .
adjusted data after multivariant regression analysis to determine the best model for eliminating the confounder effects of age bmi , ess , and insomnia questionnaire score , lr - test was done and none of these variables had significant effect .
association of elevation of inflammatory factors and sleep deprivation has been demonstrated in some studies , and we have demonstrated this association with night work shifts . in this study ,
statistically significant increased levels of il-6 , crp , wbc , neutrophils , lymphocytes , and platelets were shown .
hence , to limit the diurnal variation of secretion of cytokines , we measured the outcomes between 7:a.m .
so a one day wash out period was considered to be sufficient . however , in our study a carry over effect for il-6 was observed with no precise description , so it may be prudent to further investigate the relationship between night shift work and il-6 .
the study by irwin et al . suggested that elevation of il-6 and tnf- is due to gene expression of inflammatory markers in each monocyte rather than overall increase in monocyte counts .
mounting evidence has demonstrated an association between elevation of inflammatory markers and the risk of medical conditions , including cardiovascular disease , arthritis , diabetes mellitus , and certain cancers , which are reported in shift workers too .
thereby these results favor the hypothesis that the side effects of shift work may be related to elevation of inflammatory markers .
further studies are necessary to support our findings and if so , inflammatory markers can be used for early detection of health effects of shift work .
if this hypothesis is proven , new studies need to be done to evaluate the effects of work place interventions such as bright light or rest breaks on inflammatory markers .
if these markers decrease after these interventions , side effects of shift work may be preventable .
if further studies support the results of this study , we can use inflammatory markers for early detection of long - term health side effects of shift work in future for prevention of them . at present , it is premature to extend this speculation into clinical decision making other than to consider a modification of work place .
because of limitations in financial sources and workers cooperation , it was not possible to measure the inflammatory markers in every night and day work , and so the trend of changes could not be detected . | background : various adverse health effects associated with shift work have been documented in the medical literature .
these include increased risk of cardiovascular disorders , cerebrovascular disorders , and mortality .
sleep deprivation has been shown to be associated with an elevation in inflammatory makers such as interleukin 6 ( il-6 ) , tumor necrosis factor - alpha ( tnf- ) , and c - reactive protein ( crp ) .
it is hypothesized that the increased risk of many disorders associated with shift work may be due to inflammatory processes resulting from sleep deprivation .
the purpose of this study was to investigate the relationship between night work and inflammatory markers.materials and methods : fifty workers were selected according to the specified inclusion and exclusion criteria and randomly assigned to one of two groups in a cross over study .
the 25 workers in group 1 were scheduled to work the following consecutive shifts : three day shifts , one day off , and three night shifts .
group 2 were scheduled to work the following consecutive shifts : three night shifts , one day off , and three day shifts .
blood samples were obtained between 7:a.m . and 8:a.m .
after the periods of day work and night work and tested for inflammatory markers.statistical analyses : spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t-test.results:there was a statistically significant increase in il-6 , crp , white blood cells , neutrophils , lymphocytes , and platelets following night work compared with day work .
tnf- was increased but it was not statistically significant , and also the change in monocyte counts was not significant.conclusion:this study demonstrated an increase in inflammatory markers following night work , as reported in several pervious studies on sleep deprivation .
no significant changes in monocyte count can be justified by the results of a study which showed that the elevation in blood levels of inflammatory markers is due to increase in gene expression , not in monocyte counts . | <s>[INST]shift work is defined as work at times other than the daytime hours of 7:00 a.m. to 6:00 p.m. it is estimated that almost 15% of full - time workers in the united states ( i.e. , 15 million americans ) are shift workers who work evening , night , or rotating shifts . social needs and economic factors
shift workers provide critical services , including police and fire protection , health care , transportation , communications , public utilities , military service , and services in industries that require continuous processing .
shift work has been documented to cause adverse health effects , by disturbing three factors : circadian rhythms , sleep , and personal ( i.e. , family and social ) life . in the long term , because of disturbance of circadian rhythms such as the sleep - wake cycle , morbidity and mortality rates in shift workers will be increased.[36 ] some previous studies have demonstrated an increased risk of medical conditions , including cardiovascular disease , arthritis , diabetes mellitus , and certain cancers in association with sleep deprivation.[612 ] a number of studies have suggested that sleep disorders such as sleep loss , narcolepsy , and sleep apnea are associated with elevated inflammatory markers such as interleukin 6 ( il-6 ) , tumor necrosis factor - alpha ( tnf- ) , c - reactive protein ( crp ) , and white blood cells ( wbc).[1219 ] the purpose of this study was to evaluate the relationship between night work and elevation of inflammatory markers .
regards to the side effects of shift work and circadian rhythms and sleep disturbance as one of the important cause of these side effects and on the other hand the elevation of inflammatory markers after sleep deprivation , the purpose of this study was to evaluate the relationship between night work shifts and elevation of inflammatory markers .
the relationship between increased inflammatory markers and medical conditions , which is the same as side effects of shift work , has been observed in some studies .
if further studies support the results of this study , we can use inflammatory markers for early detection of long - term health side effects of shift work in future for prevention of them .
the subjects included 50 healthy workers who gave consent and were paid for participation in this study .
workers were excluded from the study if they had any history of inflammatory disease , cancer , chronic disease , psychotic disorder , drug or alcohol abuse , body mass index ( bmi ) > 30 , or smoking history ( as determined by review of pre - employment and annual employment medical records ) .
workers who were determined to have sleep disorders according to their score on the epworth sleepiness scale ( ess ) and insomnia questionnaires were also excluded .
they were also excluded if they developed any acute disease or reported poor sleep during the study period .
we designed a randomized clinical cross over trial study with a specific shift work schedule .
group 1 ( 25 workers ) : they were scheduled on three days of day shift work , followed by one day off ( wash out period ) , and then three nights of night shift work .
group 2 ( 25 workers ) : they were scheduled on three days of night shift work , followed by one day off ( wash out period ) , and then three days of day shift work .
blood samples were divided into two parts ; one part was transferred to a clot tube and centrifuged as soon as possible .
the serum was frozen at 25c until the enzyme - linked immunosorbent assay was performed . il-6 and
high - sensitive crp was also measured by elisa ( ibl - international , hamburg , germany ) .
the lower detection limit was 0.01 mg / ml . the second part of the sample was mixed with edta ( anti - coagulant ) for complete blood count and differential and analysis by a cell counter h1 device .
spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t - test .
the subjects included 50 healthy workers who gave consent and were paid for participation in this study .
workers were excluded from the study if they had any history of inflammatory disease , cancer , chronic disease , psychotic disorder , drug or alcohol abuse , body mass index ( bmi ) > 30 , or smoking history ( as determined by review of pre - employment and annual employment medical records ) .
workers who were determined to have sleep disorders according to their score on the epworth sleepiness scale ( ess ) and insomnia questionnaires were also excluded .
they were also excluded if they developed any acute disease or reported poor sleep during the study period .
we designed a randomized clinical cross over trial study with a specific shift work schedule .
group 1 ( 25 workers ) : they were scheduled on three days of day shift work , followed by one day off ( wash out period ) , and then three nights of night shift work .
group 2 ( 25 workers ) : they were scheduled on three days of night shift work , followed by one day off ( wash out period ) , and then three days of day shift work .
blood samples were divided into two parts ; one part was transferred to a clot tube and centrifuged as soon as possible .
the serum was frozen at 25c until the enzyme - linked immunosorbent assay was performed . il-6 and
high - sensitive crp was also measured by elisa ( ibl - international , hamburg , germany ) .
the lower detection limit was 0.01 mg / ml . the second part of the sample was mixed with edta ( anti - coagulant ) for complete blood count and differential and analysis by a cell counter h1 device .
spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t - test .
descriptions of age , weight , height , bmi , ess , and insomnia questionnaires scores of workers are shown in table 1 . despite random allocation of workers between the two groups
for omission of confounder effects of these variables , we used multivariant regression . description of age , weight , height , body mass index , epworth sleepiness scale , and insomnia questionnaire scores of workers there were no carry over effects in the two periods of study on outcomes except il-6 .
compared with day work shifts , night work shifts were associated with increased levels of il-6 , tnf- , crp , wbc , neutrophils , lymphocytes , and platelets , but for tnf- was not statistically significant . there was no significant change in monocytes [ tables 2 and 3 ] .
il6 after day work and night work shifts difference between night to day and day to night groups for out comes multivariant regression analysis was done for omitting the confounder effects of age and ess between two groups [ table 4 ] .
adjusted data after multivariant regression analysis to determine the best model for eliminating the confounder effects of age bmi , ess , and insomnia questionnaire score , lr - test was done and none of these variables had significant effect .
association of elevation of inflammatory factors and sleep deprivation has been demonstrated in some studies , and we have demonstrated this association with night work shifts . in this study ,
statistically significant increased levels of il-6 , crp , wbc , neutrophils , lymphocytes , and platelets were shown .
hence , to limit the diurnal variation of secretion of cytokines , we measured the outcomes between 7:a.m .
so a one day wash out period was considered to be sufficient . however , in our study a carry over effect for il-6 was observed with no precise description , so it may be prudent to further investigate the relationship between night shift work and il-6 .
the study by irwin et al . suggested that elevation of il-6 and tnf- is due to gene expression of inflammatory markers in each monocyte rather than overall increase in monocyte counts .
mounting evidence has demonstrated an association between elevation of inflammatory markers and the risk of medical conditions , including cardiovascular disease , arthritis , diabetes mellitus , and certain cancers , which are reported in shift workers too .
thereby these results favor the hypothesis that the side effects of shift work may be related to elevation of inflammatory markers .
further studies are necessary to support our findings and if so , inflammatory markers can be used for early detection of health effects of shift work .
if this hypothesis is proven , new studies need to be done to evaluate the effects of work place interventions such as bright light or rest breaks on inflammatory markers .
if these markers decrease after these interventions , side effects of shift work may be preventable .
if further studies support the results of this study , we can use inflammatory markers for early detection of long - term health side effects of shift work in future for prevention of them . at present , it is premature to extend this speculation into clinical decision making other than to consider a modification of work place .
because of limitations in financial sources and workers cooperation , it was not possible to measure the inflammatory markers in every night and day work , and so the trend of changes could not be detected .[/INST]background : various adverse health effects associated with shift work have been documented in the medical literature .
these include increased risk of cardiovascular disorders , cerebrovascular disorders , and mortality .
sleep deprivation has been shown to be associated with an elevation in inflammatory makers such as interleukin 6 ( il-6 ) , tumor necrosis factor - alpha ( tnf- ) , and c - reactive protein ( crp ) .
it is hypothesized that the increased risk of many disorders associated with shift work may be due to inflammatory processes resulting from sleep deprivation .
the purpose of this study was to investigate the relationship between night work and inflammatory markers.materials and methods : fifty workers were selected according to the specified inclusion and exclusion criteria and randomly assigned to one of two groups in a cross over study .
the 25 workers in group 1 were scheduled to work the following consecutive shifts : three day shifts , one day off , and three night shifts .
group 2 were scheduled to work the following consecutive shifts : three night shifts , one day off , and three day shifts .
blood samples were obtained between 7:a.m . and 8:a.m .
after the periods of day work and night work and tested for inflammatory markers.statistical analyses : spss 11.5 and s - data were used to analyze data using the student 's t - test and paired t-test.results:there was a statistically significant increase in il-6 , crp , white blood cells , neutrophils , lymphocytes , and platelets following night work compared with day work .
tnf- was increased but it was not statistically significant , and also the change in monocyte counts was not significant.conclusion:this study demonstrated an increase in inflammatory markers following night work , as reported in several pervious studies on sleep deprivation .
no significant changes in monocyte count can be justified by the results of a study which showed that the elevation in blood levels of inflammatory markers is due to increase in gene expression , not in monocyte counts .</s> |
tight - fitting powered air - purifying respirators ( paprs ) can be used in situations where contaminated air must be filtered , with the additional work of drawing air through the filter supplied by a battery - powered blower rather than the wearer 's respiratory muscles .
tight - fitting paprs form a tight seal with the face , which should minimize exposure to contaminated air .
maintenance of a positive pressure within the facepiece portends that any face seal leakage that does occur should flow outward rather than inward .
performance of work while wearing paprs in the heat is influenced also by the cooling flow of air across the face . despite these advantages ,
is the protection afforded by tight - fitting papr wear as good as it would seem ?
is there opportunity for contamination to enter the facepiece and be inhaled by the wearer ? is inward leakage , if it exists , likely to lead to inhaled contaminant ? in this study , we have been motivated to explore these issues .
this study was conducted to determine if ( 1 ) there is possible leakage of ambient air into the papr facepieces and ( 2 ) whether contaminant leakage actually reaches the mouth where it can be inhaled .
the second objective has been considered to be the more important of the two because it relates directly to the safety and health of the wearer .
the first objective can be achieved by measuring blower flows and comparing them to inhaled flows .
the second objective could be accomplished by visual detection inside the papr facepiece , especially at the mouth .
the major hurdle to overcome is the fact that tight - fitting paprs almost always include visually opaque facepieces , unlike loose - fitting paprs .
two commercially available tight - fitting paprs ( se 400 ; sea , meadowlands , pa ; 3 m breathe easy ; st .
paul , mn ) were tested on a breathing machine head form ( krug life sciences , houston , tx ) .
the se 400 papr is a breathing - demand device with a blower that adjusts to the breathing flow rates of the wearer .
the 3 m breathe - easy papr has a blower that is supposed to supply a constant 114 l / min flow rate to the facepiece ( this figure was obtained from the manufacturer 's literature ) .
the se 400 blower was operated with a fully charged battery ; the 3 m breathe - easy blower had accessible electrical connections and was attached to a dc power supply at 4.8 volts in order to assure a constant rate of flow .
for each of these tests , the krug breathing machine was operated at 40 breaths / min and with a tidal volume of about 2.25 l. both paprs were installed , in turn , on the head form and the head straps adjusted for tight , uniform fits ( figure 1 ) .
however , the surface of the head form is hard and smooth , certainly not like the flesh of the face . because of this , any leakage that would occur around the periphery of the head form would not necessarily be indicative of leakage that would occur around the periphery of a human wearer
therefore , two additional sets of measurements were made with ample modeling clay applied around the facepiece periphery to obstruct any inadvertent leaks formed at the face seal .
one of these compared blower and breathing machine flow rates , and the other focused on the exhalation valves as the most likely sources of external leakage .
5038773 pitot - tube flowmeters were used , one measuring blower flow to the facepiece and another measuring flow into the breathing machine .
the difference between the two measured flow rates would indicate leakage somewhere in the system .
this difference , when integrated over the inhalation time , gave the total volume of air leaked from the outside into the facepiece during a single inhalation .
the flow meter measuring blower flow on the se 400 was attached to the inlets of the filters with a custom - made adapter ; the flow meter for the 3 m breathe - easy blower was inserted in the hose between the filter and the facepiece .
careful calibration of the flow meters was necessary because the difference in their readings was so important .
each flow meter was attached to a validyne ( northridge , ca ) dp-15 differential pressure transducer and a validyne cd-12 demodulator transducer indicator .
these were calibrated first with an inclined manometer ; a t - connector was used to apply the same pressure simultaneously to both pressure transducers . once the pressure transducers were calibrated and connected to the flow meters , both flow meters were calibrated with the same flow from the breathing machine .
they were arranged in series with three 3.8 cm ( 1.5 in ) diameter , 38.1 cm ( 15 in ) long pipes to stabilize the flow velocity profile upstream from the flow meters , between the flow meters , and downstream from the flow meters .
3 ( phipps and bird ; richmond , va ) pneumotach inside the breathing machine served as the flow reference .
regression analysis was performed with the aid of excel software ( microsoft ; redman , wa ) .
the entire breathing machine and papr were located inside a phone booth - sized box of dimensions 137 cm ( 54 in ) by 76 cm ( 30 in ) by 180 cm ( 71 in ) .
the upper part of the box was made from lexan transparent plastic material in order to see what was going on inside .
glycerol fog was formed with a fogstorm 1200 hd ( los angeles , ca ) generator that can generate 200 m fog per minute .
this fog was introduced into the test chamber through a hose inserted through the side of the chamber .
although no measurements were made to characterize this fog , theatrical fog usually has a concentration less than 10 mg / m with droplets 2030 m in size
. of primary interest was the point at which fog reached the mouth . because both paprs had opaque facepieces , a bronchoscope ( pentax model b011471 ; asabi optical , tokyo , japan ) was placed inside the tube leading to the mouth of the head form , with its tip at the mouth and facing the cavity between the papr facepiece and the head form .
the place where the bronchoscope penetrated the head form breathing tube was sealed around the bronchoscope with silicone sealant .
the bronchoscope consisted of a bundle of optical fibers that conducted light toward the tip and an image back from the tip .
the image was converted into video form by a small television camera , and the resulting image was displayed on a television monitor .
evidence of the presence of fog could be detected from the monitor . to assure that the image produced by the bronchoscope was sufficiently sensitive to be able to detect the fog
when it was present , fog was deliberately introduced at the mouth of the head form . when fog was known to be present ,
it was visually detectable ; when no fog was present , there was no indication of fog .
although there was no direct measure of the concentration of fog as a surrogate contaminant , it could be assumed that the absence of visually detectible fog corresponded with negligible hazard . because it was difficult to adapt the bronchoscope television image to a form that permitted frame - by - frame analysis , a sony ( tokyo , japan ) dcr - hc90 video camera with 3 megapixel resolution
an s - video jack on the bronchoscope monitor was plugged into the sony camera , and the signal was recorded digitally at 40 frames / sec .
also included in the bronchoscope image were two light - emitting diodes ( leds ) located at the mouth of the head form .
a green led driven by a 10 hz square - wave electrical signal was used to help synchronize recorded images .
a red led was connected to a comparator circuit that detected inhalation . in this way
after it became apparent from the flow rate differential that there was a source of leakage into the facepiece , clay was used to seal around the facepiece periphery and the test was repeated .
when leakage was still detected , attention turned to the exhalation valves . with modeling clay still in place
, the test was again repeated , but the video camera was moved from the bronchoscope monitor and aimed at the exhalation valve , so that it could detect valve actions .
duplicate green and red leds outside the facepiece maintained the ability to keep track of time and phase of the breathing cycle .
the exhalation valve cover from the 3 m breathe easy was removed for better viewing .
the valve cover from the se 400 did not have to be removed and was kept in place .
a pitot - tube flow meter should theoretically relate pressure to the square of the flow .
when negative calibration pressures were inverted , a complete parabola resulted ( figure 3 ) .
a quadratic regression equation forced through the origin gave a very high correlation coefficient . in order to check that both flow meters had identical characteristics ,
the ideal regression line relating the two flow meters would be y = x , a line with slope of 1.0 and zero intercept of 0.0 . from figure 4 , it can be seen that readings from both flow meters were nearly perfectly correlated . in figure 5
are shown the results from the 3 m breathe easy without clay sealing the facepiece to the head form .
on the left , the breathing machine was off ( no flow ) , and the blower supplied a constant flow of nearly 100 l / min . at 19 seconds , the breathing machine was turned on , and both flows increased .
this difference was integrated to obtain leakage volume during the time that blower flow was less than breathing machine flow , and the results are shown in the lower diagram of figure 5 .
this shows that nearly 0.26 l of outside air leaked into the facepiece during each inhalation .
this air was presumably swept from the facial volume during exhalation . also to be noted here
it varied during the breathing cycle , becoming about 230 l / min during inhalation peaks and falling to nearly zero during exhalation .
the power required to move the extra air through the filters must necessarily be coming from the breathing machine .
at least part of the hose between the blower and the facepiece is also being filled with respired air .
this papr has no check valve in the blower circuit to prevent backwards flow . in figure 6
are shown the same two flow measurements ( a ) and the same volumes ( b ) as in the previous figure , except that the time scale has been compressed .
both the blower and the breathing machine were off until 10 sec , when the blower was turned on . at 20 sec ,
when clay was carefully used around the mask periphery , the leakage volume decreased to about 0.21
l to 0.24 l from 0.26 to 0.29 l for each inhalation ( figure 7 ) .
results for the se 400 with clay around the face seal are shown in figure 8 .
the blower was turned on at 10 seconds and maintained a steady flow rate of about 25 l / min until the breathing machine was turned on at about 25 seconds .
for the first few breaths after the breathing machine was turned on , leakage volume was about 0.19 l. it subsequently decreased and varied throughout the range of 0.04 to 0.18 l. the leakage volume value seemed to depend on whether the blower was actively increasing or decreasing speed , but the exact dependence was not determined . when the blower was turned off at about 75 seconds , leakage volume increased to 0.22 l. again , the bronchoscope detected no fog at the mouth .
leakage volumes from both paprs with clay sealing their peripheries seemed to indicate that inward flow was coming through the exhalation valves .
indeed , an inspection of the videos taken of both exhalation valves showed that neither valve closed instantaneously when inhalation began .
the exhalation valve on the se 400 is larger than the corresponding valve on the 3 m breathe easy .
the se 400 valve tended to flutter , opening about three times after inhalation began .
leakage volume for the se 400 could not be determined because it was too difficult to see exactly when the valve was opened or completely closed .
the 3 m valve did not flutter but stayed open long enough to let pass about 0.01 l of air before it apparently closed ( the range was measured at 0.00 to 0.03 l ) .
this open valve leakage volume was determined as the volume of air that was measured by the two flow meters during the time that the valve was visually observed to be open .
it was only a small portion of the total leakage volume measured during each inhalation .
the remainder of the leakage may have come while the valve was closed or from other undetermined pathways .
these results demonstrated that these tight - fitting paprs do not exclude all contaminated air from the facepiece .
is that there was no contaminant that appeared to reach the mouth of the head form .
leakage amounts in respirators are important , but the health and safety of the wearer are of primary importance .
thus , no matter what amount of leakage is present , and what pathway that it takes if it occurs , if the contaminant has no affect on the wearer , then the wearer is protected .
it was not possible for us to determine the actual pathways of the fog from the points of leakage to the mouth because of the opaque facepieces .
perhaps this could be done with miniature cameras inside the facepieces , but these were not available to us .
the reason that the pathway is important is that a long enough pathway would dictate that leaked contaminants take long enough to reach the mouth that the inhalation phase of breathing would cease and contamination would be swept out of the breathing zone .
respirators designed to lengthen this pathway would presumably be more able to accommodate leakages and still protect the wearer .
knowing where leakages are likely to occur is important for this type of design .
if the only means to detect leakage in this study was the difference between blower flow rate and inhaled flow rate , then the conclusion might have been that the wearer of either of these devices could be at risk for breathing contaminant leaking from the outside . by visualizing fog that either did or did not reach the mouth , that ambiguity was eliminated .
although a very small amount of leakage did occur , it would have had no affect on the wearer .
confirmation of these conclusions is based upon the detection of fog in proximity to the mouth .
tests to determine the sensitivity of visual detection of fog have shown that the methods used here are sufficient to detect the presence of fog when it should be found , and that fog was not detected when it was not present .
the visual demarcation at the edge of the fog was sufficiently sharp to see the fog .
inhalation times are very short , ranging from about 2.5 seconds at rest to 0.25 seconds during extreme exertion .
exotic gases may be used as contaminant surrogates , and these could be detected , but , again , required sampling times are too long .
the two methods used here , differential flow rates and visual detection , can provide real - time data . there were no methods available to us to determine the minimum concentration of fog that could be detected , and , therefore , it can not be said definitively what concentration level of fog reached the mouth .
thus , conclusions about the leakage hazard based upon the fog as a surrogate contaminant can not be made for sure .
even if the fog concentration could have been determined , another atmospheric contaminant of the form of a vapor , gas , or aerosol with different properties could be transported differently within the facepiece .
hence , the fog gives an indication that contaminant leakage would not reach the mouth and be inhaled , but further studies would be necessary to determine if representative contaminants have the same behavior as the fog
. such studies would be valuable , given that contamination inside the facepiece could be tolerated as long as hazardous doses of contaminant were not inhaled .
because the flow pathways for the fog could not be followed from the point of entry through the space in front of the face , it was not possible to say definitively where the leakage came from .
the se 400 exhalation valve fluttered whenever the breathing machine flow was higher than its blower flow .
when the valve actually closed could not be determined exactly , so the leakage volume due to valve action could not be estimated .
it was easier to determine when the 3 m breathe - easy exhalation valve closed or did not close . in both cases , leakage probably came through the exhalation valves even when apparently closed , because there just was no other obvious entry point for contaminant leakage .
these results agree with those published years ago by burgess and anderson , who demonstrated that exhalation valve leakage was of minor consequence .
amounts of leakage in the present study were determined with protective covers in place , with the valve cover removed for the breathe easy only to view the valve action during exhalation .
the breathing demand se 400 definitely had lower leakage volume than the 3 m breathe easy .
leakage in the se 400 was often accompanied by short bursts of its negative - pressure alarm .
the dead volume of a respirator is the volume inside the facepiece that could accumulate exhaled carbon dioxide .
dead volumes of these masks were not measured but should fall in the range of about 0.97 l , which is the measured interior volume of the similar 3 m frm40 facepiece . measured
dead volume of the frm40 nose cup is about 0.09 l. these were measured as the volumes of water filling the space between the facepiece and the head form .
what this tells us is that the leakage volumes for both respirators tested in this experiment were much less than the dead volumes of the facepieces .
contaminant leakages can occur in respirators , but if contaminants are not inhaled , then they have no health consequence .
it would therefore be expected that contaminated air would not reach the mouth and be breathed by the wearer .
however , one might make the case that it is the volume inside the nose cup that matters .
this is because the exhalation valve is located directly in front of the nose cup .
leakage coming through an imperfectly closed exhalation valve could possibly follow a direct route to the mouth .
however , no fog was observed at the mouth , so leakage apparently did not follow a direct route to the mouth . an indirect flow pathway , one that lengthens the distance from the point where leakage occurs to the mouth , is an effective protective strategy .
we also found interesting that the blower on the 3 m device did not deliver a constant flow rate but instead delivered an amount dependent upon the inhaled flow rate .
the extra energy needed to draw extra air across the filter , blower , and tubing resistance would have to have come from the breathing machine .
if a human had to supply the same amount of energy , breathing through this respirator could become very tiring .
the fact that air could flow backwards , even by a small amount , in the tube that supplied filtered air to the facepiece means that the effective dead volume of the device would be increased because some of the exhaled carbon dioxide could be rebreathed .
the amount , as measured herein , was small , and so not likely of consequence for the average wearer .
should there be less blower flow , perhaps from lower battery voltage , then the amount of rebreathed air could become more significant .
it is not likely that exhaled breath moisture could reach the filter , but , if it could , filter life could be adversely affected .
figures 57 have been included in this paper despite the fact that leakages occurring at the face seal of the head form are not likely to resemble leakages that could occur at the face seal of a human .
these figures have been meant to illustrate experimental techniques used and to show that face seal leakages do indeed occur on the head form .
more valid to the meaning of this study are the figures of data obtained with clay sealing the peripheries of both devices .
the clay was applied generously enough that no leakage could have occurred where it was used .
the steady blower flow of somewhat less than 100 l / min does not reach the niosh certification requirement of 115 l / min . the blower battery in this test was replaced by a power supply that maintained the fully charged battery voltage throughout the whole procedure , so the lower than expected blower flow could not have been the result of low voltage to the blower motor .
blower flow rate may have been low because of the resistance of the flow circuit through the exhalation valve when inhalation was not happening .
it can be seen from the figures that blower flow rate increases significantly once inhalation starts and would possibly be high enough to pass certification testing . if it could be maintained , a constant flow from the blower has the advantage of simplicity , with only a slight filter capacity penalty for filtering more air than is needed during less - demanding circumstances .
the tidal volumes used in this testing were extremely high , as indicated previously , so smaller tidal volumes would not be as difficult for the blower to match .
even so , the respirator was able to supply the required rate of air flow .
in addition , if significant amounts of contaminants were to leak into the facepiece , then additional blower flow would help to purge them from inside the respirator .
there are two ways in which the breathing machine used in this experiment differed from a human .
the first is that the breathing machine acted as an ideal flow source : its flow rate was largely independent of the resistance of the device attached to it , quite like a positive - displacement pump .
the breathing machine developed whatever pressure it needed to draw the required flow rate , and this pressure was limited only by the mechanical strength of the machine .
a human respiratory system is different ; first , the maximum pressure it can develop is very low in comparison to the mechanical strength of steel parts ; second , this pressure varies as lung volume changes ; third , the respiratory system has resistance and compliance elements that make it far from an ideal flow source .
consequently , one would expect a human to adjust his flow rate to the limits of the device . the second difference between the breathing machine and a human involves the tidal volume used .
a tidal volume of 2.25 l is large for a human of medium size and is normally only reached during extreme activity .
we used this large tidal volume to make clear what results we could obtain from these two respirators . under more normal circumstances ,
how much less is difficult to say , especially for the breathing - demand respirator .
osha has published a list of assigned protection factors ( apfs ) for various classes of respirators .
granted that there were small amounts of leakage of air into the facepieces , but amounts were less than the volumes inside the masks , and so not likely to be inhaled , depending on the flow path within the respirator .
the lack of fog seen at the mouth indicated that the wearer would have been protected adequately for contaminants acting similar to the fog .
besides , the leakage that occurred , probably as a result of exhalation valve dynamics , was of very short duration and may not result in a significant concentration of contaminant inside the facepiece .
many of these concentrations are measured with particle counters , but other devices can be used for vapors and gases .
the position of the sampling tube inside the respirator is usually near the mouth . unless the contaminant reaches the mouth , little , if any
, contaminant is registered , and unless the contaminant is present at the mouth for a long enough time , the average contaminant reading would be small .
thus , despite the fact that leakage volumes in this study were measured as 2%10% of the tidal volume tested , if no contaminant ( fog ) reached the mouth , the protection factors for these respirators would be found to be extremely high .
we have investigated leakages in two powered air - purifying respirators from two reputable manufacturers .
there is reason to expect that similar types of respirators from other manufacturers would be as safe to wear as these seem to be . in the technological cycle of product improvement
, tests such as these can lead to focus on items that limit performance . from such tests come devices that are safer , and | a combination of local flow measurement techniques and fog flow visualization was used to determine the inward leakage for two tight - fitting powered air - purifying respirators ( paprs ) , the 3 m breathe - easy papr and the se 400 breathing demand papr .
the paprs were mounted on a breathing machine head form , and flows were measured from the blower and into the breathing machine . both respirators leaked a little at the beginning of inhalation , probably through their exhalation valves .
in both cases , the leakage was not enough for fog to appear at the mouth of the head form . | <s>[INST]tight - fitting powered air - purifying respirators ( paprs ) can be used in situations where contaminated air must be filtered , with the additional work of drawing air through the filter supplied by a battery - powered blower rather than the wearer 's respiratory muscles .
tight - fitting paprs form a tight seal with the face , which should minimize exposure to contaminated air .
maintenance of a positive pressure within the facepiece portends that any face seal leakage that does occur should flow outward rather than inward .
performance of work while wearing paprs in the heat is influenced also by the cooling flow of air across the face . despite these advantages ,
is the protection afforded by tight - fitting papr wear as good as it would seem ?
is there opportunity for contamination to enter the facepiece and be inhaled by the wearer ? is inward leakage , if it exists , likely to lead to inhaled contaminant ? in this study , we have been motivated to explore these issues .
this study was conducted to determine if ( 1 ) there is possible leakage of ambient air into the papr facepieces and ( 2 ) whether contaminant leakage actually reaches the mouth where it can be inhaled .
the second objective has been considered to be the more important of the two because it relates directly to the safety and health of the wearer .
the first objective can be achieved by measuring blower flows and comparing them to inhaled flows .
the second objective could be accomplished by visual detection inside the papr facepiece , especially at the mouth .
the major hurdle to overcome is the fact that tight - fitting paprs almost always include visually opaque facepieces , unlike loose - fitting paprs .
two commercially available tight - fitting paprs ( se 400 ; sea , meadowlands , pa ; 3 m breathe easy ; st .
paul , mn ) were tested on a breathing machine head form ( krug life sciences , houston , tx ) .
the se 400 papr is a breathing - demand device with a blower that adjusts to the breathing flow rates of the wearer .
the 3 m breathe - easy papr has a blower that is supposed to supply a constant 114 l / min flow rate to the facepiece ( this figure was obtained from the manufacturer 's literature ) .
the se 400 blower was operated with a fully charged battery ; the 3 m breathe - easy blower had accessible electrical connections and was attached to a dc power supply at 4.8 volts in order to assure a constant rate of flow .
for each of these tests , the krug breathing machine was operated at 40 breaths / min and with a tidal volume of about 2.25 l. both paprs were installed , in turn , on the head form and the head straps adjusted for tight , uniform fits ( figure 1 ) .
however , the surface of the head form is hard and smooth , certainly not like the flesh of the face . because of this , any leakage that would occur around the periphery of the head form would not necessarily be indicative of leakage that would occur around the periphery of a human wearer
therefore , two additional sets of measurements were made with ample modeling clay applied around the facepiece periphery to obstruct any inadvertent leaks formed at the face seal .
one of these compared blower and breathing machine flow rates , and the other focused on the exhalation valves as the most likely sources of external leakage .
5038773 pitot - tube flowmeters were used , one measuring blower flow to the facepiece and another measuring flow into the breathing machine .
the difference between the two measured flow rates would indicate leakage somewhere in the system .
this difference , when integrated over the inhalation time , gave the total volume of air leaked from the outside into the facepiece during a single inhalation .
the flow meter measuring blower flow on the se 400 was attached to the inlets of the filters with a custom - made adapter ; the flow meter for the 3 m breathe - easy blower was inserted in the hose between the filter and the facepiece .
careful calibration of the flow meters was necessary because the difference in their readings was so important .
each flow meter was attached to a validyne ( northridge , ca ) dp-15 differential pressure transducer and a validyne cd-12 demodulator transducer indicator .
these were calibrated first with an inclined manometer ; a t - connector was used to apply the same pressure simultaneously to both pressure transducers . once the pressure transducers were calibrated and connected to the flow meters , both flow meters were calibrated with the same flow from the breathing machine .
they were arranged in series with three 3.8 cm ( 1.5 in ) diameter , 38.1 cm ( 15 in ) long pipes to stabilize the flow velocity profile upstream from the flow meters , between the flow meters , and downstream from the flow meters .
3 ( phipps and bird ; richmond , va ) pneumotach inside the breathing machine served as the flow reference .
regression analysis was performed with the aid of excel software ( microsoft ; redman , wa ) .
the entire breathing machine and papr were located inside a phone booth - sized box of dimensions 137 cm ( 54 in ) by 76 cm ( 30 in ) by 180 cm ( 71 in ) .
the upper part of the box was made from lexan transparent plastic material in order to see what was going on inside .
glycerol fog was formed with a fogstorm 1200 hd ( los angeles , ca ) generator that can generate 200 m fog per minute .
this fog was introduced into the test chamber through a hose inserted through the side of the chamber .
although no measurements were made to characterize this fog , theatrical fog usually has a concentration less than 10 mg / m with droplets 2030 m in size
. of primary interest was the point at which fog reached the mouth . because both paprs had opaque facepieces , a bronchoscope ( pentax model b011471 ; asabi optical , tokyo , japan ) was placed inside the tube leading to the mouth of the head form , with its tip at the mouth and facing the cavity between the papr facepiece and the head form .
the place where the bronchoscope penetrated the head form breathing tube was sealed around the bronchoscope with silicone sealant .
the bronchoscope consisted of a bundle of optical fibers that conducted light toward the tip and an image back from the tip .
the image was converted into video form by a small television camera , and the resulting image was displayed on a television monitor .
evidence of the presence of fog could be detected from the monitor . to assure that the image produced by the bronchoscope was sufficiently sensitive to be able to detect the fog
when it was present , fog was deliberately introduced at the mouth of the head form . when fog was known to be present ,
it was visually detectable ; when no fog was present , there was no indication of fog .
although there was no direct measure of the concentration of fog as a surrogate contaminant , it could be assumed that the absence of visually detectible fog corresponded with negligible hazard . because it was difficult to adapt the bronchoscope television image to a form that permitted frame - by - frame analysis , a sony ( tokyo , japan ) dcr - hc90 video camera with 3 megapixel resolution
an s - video jack on the bronchoscope monitor was plugged into the sony camera , and the signal was recorded digitally at 40 frames / sec .
also included in the bronchoscope image were two light - emitting diodes ( leds ) located at the mouth of the head form .
a green led driven by a 10 hz square - wave electrical signal was used to help synchronize recorded images .
a red led was connected to a comparator circuit that detected inhalation . in this way
after it became apparent from the flow rate differential that there was a source of leakage into the facepiece , clay was used to seal around the facepiece periphery and the test was repeated .
when leakage was still detected , attention turned to the exhalation valves . with modeling clay still in place
, the test was again repeated , but the video camera was moved from the bronchoscope monitor and aimed at the exhalation valve , so that it could detect valve actions .
duplicate green and red leds outside the facepiece maintained the ability to keep track of time and phase of the breathing cycle .
the exhalation valve cover from the 3 m breathe easy was removed for better viewing .
the valve cover from the se 400 did not have to be removed and was kept in place .
a pitot - tube flow meter should theoretically relate pressure to the square of the flow .
when negative calibration pressures were inverted , a complete parabola resulted ( figure 3 ) .
a quadratic regression equation forced through the origin gave a very high correlation coefficient . in order to check that both flow meters had identical characteristics ,
the ideal regression line relating the two flow meters would be y = x , a line with slope of 1.0 and zero intercept of 0.0 . from figure 4 , it can be seen that readings from both flow meters were nearly perfectly correlated . in figure 5
are shown the results from the 3 m breathe easy without clay sealing the facepiece to the head form .
on the left , the breathing machine was off ( no flow ) , and the blower supplied a constant flow of nearly 100 l / min . at 19 seconds , the breathing machine was turned on , and both flows increased .
this difference was integrated to obtain leakage volume during the time that blower flow was less than breathing machine flow , and the results are shown in the lower diagram of figure 5 .
this shows that nearly 0.26 l of outside air leaked into the facepiece during each inhalation .
this air was presumably swept from the facial volume during exhalation . also to be noted here
it varied during the breathing cycle , becoming about 230 l / min during inhalation peaks and falling to nearly zero during exhalation .
the power required to move the extra air through the filters must necessarily be coming from the breathing machine .
at least part of the hose between the blower and the facepiece is also being filled with respired air .
this papr has no check valve in the blower circuit to prevent backwards flow . in figure 6
are shown the same two flow measurements ( a ) and the same volumes ( b ) as in the previous figure , except that the time scale has been compressed .
both the blower and the breathing machine were off until 10 sec , when the blower was turned on . at 20 sec ,
when clay was carefully used around the mask periphery , the leakage volume decreased to about 0.21
l to 0.24 l from 0.26 to 0.29 l for each inhalation ( figure 7 ) .
results for the se 400 with clay around the face seal are shown in figure 8 .
the blower was turned on at 10 seconds and maintained a steady flow rate of about 25 l / min until the breathing machine was turned on at about 25 seconds .
for the first few breaths after the breathing machine was turned on , leakage volume was about 0.19 l. it subsequently decreased and varied throughout the range of 0.04 to 0.18 l. the leakage volume value seemed to depend on whether the blower was actively increasing or decreasing speed , but the exact dependence was not determined . when the blower was turned off at about 75 seconds , leakage volume increased to 0.22 l. again , the bronchoscope detected no fog at the mouth .
leakage volumes from both paprs with clay sealing their peripheries seemed to indicate that inward flow was coming through the exhalation valves .
indeed , an inspection of the videos taken of both exhalation valves showed that neither valve closed instantaneously when inhalation began .
the exhalation valve on the se 400 is larger than the corresponding valve on the 3 m breathe easy .
the se 400 valve tended to flutter , opening about three times after inhalation began .
leakage volume for the se 400 could not be determined because it was too difficult to see exactly when the valve was opened or completely closed .
the 3 m valve did not flutter but stayed open long enough to let pass about 0.01 l of air before it apparently closed ( the range was measured at 0.00 to 0.03 l ) .
this open valve leakage volume was determined as the volume of air that was measured by the two flow meters during the time that the valve was visually observed to be open .
it was only a small portion of the total leakage volume measured during each inhalation .
the remainder of the leakage may have come while the valve was closed or from other undetermined pathways .
these results demonstrated that these tight - fitting paprs do not exclude all contaminated air from the facepiece .
is that there was no contaminant that appeared to reach the mouth of the head form .
leakage amounts in respirators are important , but the health and safety of the wearer are of primary importance .
thus , no matter what amount of leakage is present , and what pathway that it takes if it occurs , if the contaminant has no affect on the wearer , then the wearer is protected .
it was not possible for us to determine the actual pathways of the fog from the points of leakage to the mouth because of the opaque facepieces .
perhaps this could be done with miniature cameras inside the facepieces , but these were not available to us .
the reason that the pathway is important is that a long enough pathway would dictate that leaked contaminants take long enough to reach the mouth that the inhalation phase of breathing would cease and contamination would be swept out of the breathing zone .
respirators designed to lengthen this pathway would presumably be more able to accommodate leakages and still protect the wearer .
knowing where leakages are likely to occur is important for this type of design .
if the only means to detect leakage in this study was the difference between blower flow rate and inhaled flow rate , then the conclusion might have been that the wearer of either of these devices could be at risk for breathing contaminant leaking from the outside . by visualizing fog that either did or did not reach the mouth , that ambiguity was eliminated .
although a very small amount of leakage did occur , it would have had no affect on the wearer .
confirmation of these conclusions is based upon the detection of fog in proximity to the mouth .
tests to determine the sensitivity of visual detection of fog have shown that the methods used here are sufficient to detect the presence of fog when it should be found , and that fog was not detected when it was not present .
the visual demarcation at the edge of the fog was sufficiently sharp to see the fog .
inhalation times are very short , ranging from about 2.5 seconds at rest to 0.25 seconds during extreme exertion .
exotic gases may be used as contaminant surrogates , and these could be detected , but , again , required sampling times are too long .
the two methods used here , differential flow rates and visual detection , can provide real - time data . there were no methods available to us to determine the minimum concentration of fog that could be detected , and , therefore , it can not be said definitively what concentration level of fog reached the mouth .
thus , conclusions about the leakage hazard based upon the fog as a surrogate contaminant can not be made for sure .
even if the fog concentration could have been determined , another atmospheric contaminant of the form of a vapor , gas , or aerosol with different properties could be transported differently within the facepiece .
hence , the fog gives an indication that contaminant leakage would not reach the mouth and be inhaled , but further studies would be necessary to determine if representative contaminants have the same behavior as the fog
. such studies would be valuable , given that contamination inside the facepiece could be tolerated as long as hazardous doses of contaminant were not inhaled .
because the flow pathways for the fog could not be followed from the point of entry through the space in front of the face , it was not possible to say definitively where the leakage came from .
the se 400 exhalation valve fluttered whenever the breathing machine flow was higher than its blower flow .
when the valve actually closed could not be determined exactly , so the leakage volume due to valve action could not be estimated .
it was easier to determine when the 3 m breathe - easy exhalation valve closed or did not close . in both cases , leakage probably came through the exhalation valves even when apparently closed , because there just was no other obvious entry point for contaminant leakage .
these results agree with those published years ago by burgess and anderson , who demonstrated that exhalation valve leakage was of minor consequence .
amounts of leakage in the present study were determined with protective covers in place , with the valve cover removed for the breathe easy only to view the valve action during exhalation .
the breathing demand se 400 definitely had lower leakage volume than the 3 m breathe easy .
leakage in the se 400 was often accompanied by short bursts of its negative - pressure alarm .
the dead volume of a respirator is the volume inside the facepiece that could accumulate exhaled carbon dioxide .
dead volumes of these masks were not measured but should fall in the range of about 0.97 l , which is the measured interior volume of the similar 3 m frm40 facepiece . measured
dead volume of the frm40 nose cup is about 0.09 l. these were measured as the volumes of water filling the space between the facepiece and the head form .
what this tells us is that the leakage volumes for both respirators tested in this experiment were much less than the dead volumes of the facepieces .
contaminant leakages can occur in respirators , but if contaminants are not inhaled , then they have no health consequence .
it would therefore be expected that contaminated air would not reach the mouth and be breathed by the wearer .
however , one might make the case that it is the volume inside the nose cup that matters .
this is because the exhalation valve is located directly in front of the nose cup .
leakage coming through an imperfectly closed exhalation valve could possibly follow a direct route to the mouth .
however , no fog was observed at the mouth , so leakage apparently did not follow a direct route to the mouth . an indirect flow pathway , one that lengthens the distance from the point where leakage occurs to the mouth , is an effective protective strategy .
we also found interesting that the blower on the 3 m device did not deliver a constant flow rate but instead delivered an amount dependent upon the inhaled flow rate .
the extra energy needed to draw extra air across the filter , blower , and tubing resistance would have to have come from the breathing machine .
if a human had to supply the same amount of energy , breathing through this respirator could become very tiring .
the fact that air could flow backwards , even by a small amount , in the tube that supplied filtered air to the facepiece means that the effective dead volume of the device would be increased because some of the exhaled carbon dioxide could be rebreathed .
the amount , as measured herein , was small , and so not likely of consequence for the average wearer .
should there be less blower flow , perhaps from lower battery voltage , then the amount of rebreathed air could become more significant .
it is not likely that exhaled breath moisture could reach the filter , but , if it could , filter life could be adversely affected .
figures 57 have been included in this paper despite the fact that leakages occurring at the face seal of the head form are not likely to resemble leakages that could occur at the face seal of a human .
these figures have been meant to illustrate experimental techniques used and to show that face seal leakages do indeed occur on the head form .
more valid to the meaning of this study are the figures of data obtained with clay sealing the peripheries of both devices .
the clay was applied generously enough that no leakage could have occurred where it was used .
the steady blower flow of somewhat less than 100 l / min does not reach the niosh certification requirement of 115 l / min . the blower battery in this test was replaced by a power supply that maintained the fully charged battery voltage throughout the whole procedure , so the lower than expected blower flow could not have been the result of low voltage to the blower motor .
blower flow rate may have been low because of the resistance of the flow circuit through the exhalation valve when inhalation was not happening .
it can be seen from the figures that blower flow rate increases significantly once inhalation starts and would possibly be high enough to pass certification testing . if it could be maintained , a constant flow from the blower has the advantage of simplicity , with only a slight filter capacity penalty for filtering more air than is needed during less - demanding circumstances .
the tidal volumes used in this testing were extremely high , as indicated previously , so smaller tidal volumes would not be as difficult for the blower to match .
even so , the respirator was able to supply the required rate of air flow .
in addition , if significant amounts of contaminants were to leak into the facepiece , then additional blower flow would help to purge them from inside the respirator .
there are two ways in which the breathing machine used in this experiment differed from a human .
the first is that the breathing machine acted as an ideal flow source : its flow rate was largely independent of the resistance of the device attached to it , quite like a positive - displacement pump .
the breathing machine developed whatever pressure it needed to draw the required flow rate , and this pressure was limited only by the mechanical strength of the machine .
a human respiratory system is different ; first , the maximum pressure it can develop is very low in comparison to the mechanical strength of steel parts ; second , this pressure varies as lung volume changes ; third , the respiratory system has resistance and compliance elements that make it far from an ideal flow source .
consequently , one would expect a human to adjust his flow rate to the limits of the device . the second difference between the breathing machine and a human involves the tidal volume used .
a tidal volume of 2.25 l is large for a human of medium size and is normally only reached during extreme activity .
we used this large tidal volume to make clear what results we could obtain from these two respirators . under more normal circumstances ,
how much less is difficult to say , especially for the breathing - demand respirator .
osha has published a list of assigned protection factors ( apfs ) for various classes of respirators .
granted that there were small amounts of leakage of air into the facepieces , but amounts were less than the volumes inside the masks , and so not likely to be inhaled , depending on the flow path within the respirator .
the lack of fog seen at the mouth indicated that the wearer would have been protected adequately for contaminants acting similar to the fog .
besides , the leakage that occurred , probably as a result of exhalation valve dynamics , was of very short duration and may not result in a significant concentration of contaminant inside the facepiece .
many of these concentrations are measured with particle counters , but other devices can be used for vapors and gases .
the position of the sampling tube inside the respirator is usually near the mouth . unless the contaminant reaches the mouth , little , if any
, contaminant is registered , and unless the contaminant is present at the mouth for a long enough time , the average contaminant reading would be small .
thus , despite the fact that leakage volumes in this study were measured as 2%10% of the tidal volume tested , if no contaminant ( fog ) reached the mouth , the protection factors for these respirators would be found to be extremely high .
we have investigated leakages in two powered air - purifying respirators from two reputable manufacturers .
there is reason to expect that similar types of respirators from other manufacturers would be as safe to wear as these seem to be . in the technological cycle of product improvement
, tests such as these can lead to focus on items that limit performance . from such tests come devices that are safer , and[/INST]a combination of local flow measurement techniques and fog flow visualization was used to determine the inward leakage for two tight - fitting powered air - purifying respirators ( paprs ) , the 3 m breathe - easy papr and the se 400 breathing demand papr .
the paprs were mounted on a breathing machine head form , and flows were measured from the blower and into the breathing machine . both respirators leaked a little at the beginning of inhalation , probably through their exhalation valves .
in both cases , the leakage was not enough for fog to appear at the mouth of the head form .</s> |
the ratchet mechanism to produce directional current or motion has become a paradigm of the interplay of nonlinear phenomena with brownian motion and external noise in mesoscopic systems@xcite .
we shall use the term `` ratchet '' for any conservative mechanical system that has an ingrained spatial asymmetry ; a one - dimensional example is a particle in a saw - tooth like potential . due to the potentiality of these systems to describe mesoscopic systems and their processes , such as biological ones@xcite
, one should consider the ratchet to be immersed in a thermal bath , giving rise to brownian motion .
this adds dissipative and stochastic thermal forces that are related to each other through the fluctuation - dissipation theorem@xcite . as it was clearly pointed out by feynman in his _
lectures_@xcite , the second law of thermodynamics implies that a ratchet under the above conditions can not generate directional motion .
it is by now very well established that in order to obtain current or directional motion , it is indispensable to have the presence of an _ external _ unbiased time dependent force .
this force can be deterministic , a so - called `` rocking '' ratchet , see ref.@xcite , or stochastic in nature , see ref.@xcite . in any case , any of those forces should be of zero average in time in order not to produce any biased current ; in the present article we shall be concerned with external stochastic forces only .
it is the opinion of the authors that the origin of the appearance of the current is not fully understood yet , although it is clear what the conditions are for its existence . in particular
, a lot of attention has been devoted to the case in which the ratchet variable is periodic , such as an angle @xmath0 $ ] , and many analytic and numerical results have been obtained@xcite , yielding a clear picture of how current occurs in a stationary state .
we believe the studies are not as exhaustive for the cases where the ratchet variable is not periodic , namely when the particle can move in all space , namely , when the position of the particle can take all real values , @xmath1 . in this case , even in the absence of external forces , the system does not reach an stationary state@xcite .
one of the purposes of this article is to add to the understanding of the appearance of the current in the latter situation , by studying a novel _ non - periodic _ one - dimensional overdamped ratchet ; this is done in section 2 .
having established the conditions for the production of current in one dimension , we then proceed to the second purpose of the article and extend the model to more than one dimension in order to study two biology - related problems .
one is the case of the motion of a kinesin protein on a microtubule , in section 3 , and the other is the process of protein folding in section 4 .
the first has been studied already by several authors@xcite but here we consider a protein in two dimensions and the microtubule as a quasi - one dimensional structure .
our model of protein folding is at present speculative , and the idea is centered on the hypothesis that the energy landscape of the protein has a ratchet - like structure ; by further assuming that there is an _ external _ agent that consumes energy , which could be the presence of chaperone proteins@xcite , one has all the ingredients to obtain directed motion .
we shall show that , understanding by protein folding the search and finding of a target point or small section in the energy landscape , the ratchet mechanism is extremely fast with an almost perfect efficiency .
an interesting consequence of this process is that the landscape need not have a funnel structure@xcite .
in this section we revisit the one - dimensional overdamped ratchet system , considering both periodic and non - periodic potentials . the main purpose here is to argue that the appearance of a current is a _
generic _ property of bounded asymmetric conservative systems , in interaction with a thermal bath , due to the presence of external ( stochastic or deterministic ) non - biased time dependent forces .
that is , by showing that the absence of current without the external force must follow from the second law , we argue that there is nothing to prevent a current once the conditions required by the second law have been relaxed .
the details of the numerical techniques we use can be found in refs.@xcite .
we initiate by writing down the the langevin equation in the overdamped case for a particle subjected to a conservative potential @xmath2 , without an external time dependent force , @xmath3 we consider a ratchet potential with a `` quenched '' random disorder both in the potential barriers and in the spatial periods , namely , @xmath4 \nonumber \\ & & \>\>\>\>{\rm
if } \>\>\>y_{i } \le x < y_{i+1 } , \label{ratchet}\end{aligned}\ ] ] with @xmath5 taking all integer values and where the positions @xmath6 are chosen at random ; @xmath7 is arbitrarily set equal to 0 .
clearly , the spatial periods are given by @xmath8 .
a typical form of the ratchet potential @xmath2 is shown in fig .
[ pot - ran ] .
note that this potential is not periodic .
the usual _ periodic _ ratchet potential is @xmath9 and @xmath10 for all @xmath5@xcite .
returning to the langevin equation ( [ langevin ] ) , @xmath11 is the friction coefficient and @xmath12 is the thermal force exerted by the thermal bath .
the stochastic properties of this force are @xmath13 it is further assumed that this process is gaussian , so that eqs.([ft ] ) suffice to completely specify the process @xmath12 . in the second equation @xmath14
is the temperature of the bath and the expression for the correlation of the force is the fluctuation - dissipation relation for this problem ; it imposes detailed balance@xcite . since the process @xmath15 representing the position of the particle is markovian , then , knowledge of the conditional probability distribution @xmath16 is enough to determine the process .
it can be shown that this function obeys the following fokker - planck equation@xcite , @xmath17 supplemented by the initial condition @xmath18 . in this discussion
we are considering that the particle can move in all space , namely , @xmath19 .
thus , the normalization of the distribution , @xmath20 imposes the boundary conditions @xmath21 the fokker - planck equation , eq.([fp ] ) , is a continuity equation for the probability distribution .
therefore , one can read off the probability density current , @xmath22 we may define the total " current as , @xmath23 where the last two lines follow from the definition of the density current and the fokker - planck equation , eqs.([j ] ) and ( [ fp ] ) .
if there exists a stationary distribution , @xmath24 , then detailed balance means that the stationary density current vanishes , @xmath25 , and therefore that the stationary distribution is @xmath26 with @xmath27 .
further , if @xmath28 is not the stationary distribution , then , detailed balance implies that as @xmath29 , such a distribution approaches the stationary one .
this is equivalent to the @xmath30-theorem . in the context of ratchet - like potentials
, one is faced with potentials that are bounded , that is , @xmath31 , for all @xmath32 .
thus , strictly speaking , a stationary distribution can not be reached@xcite .
however , it is clear that stationarity is achieved in the following sense , @xmath33 therefore , it must be true that , in the above sense , the probability density current @xmath34 and the total current @xmath35 must vanish as @xmath36 .
however , this does not suffice to prevent an arbitrary current or displacement of the particle , as is routinely asserted in essentially all articles dealing with this problem .
the main point that we want to emphasize here is that , since detailed balance is in accordance with the second law of thermodynamics , the total current @xmath35 must be bounded for all times . using eq.([j ] ) , this can be more precisely written as the following requirement , @xmath37 where @xmath38 is the initial position of the particle and @xmath39 is the distance between the adjacent local maxima of the potential where the particle was initially at @xmath40 .
we have exhaustively numerically verified that this holds for ratchet potentials such as those ones in fig .
[ pot - ran ] , and the results are exemplified in fig .
[ prom ] . for ratchet potentials
this means that _ on the average _ the particle can not leave the local well where it was initially ; if it did , nothing would prevent the particle to jump " to another well , and so on , thus moving an arbitrary distance .
in other words , eq.([bound ] ) expresses that fact that it is not possible to obtain a current that , on the average , could generate motion that would transport the particle farther than its initial well .
otherwise , this would yield the possibility to perform work on some external load or agent@xcite violating kelvin s statement of the second law : a transformation whose only final result is to transform into work heat extracted from a source which is at the same temperature throughout is impossible"@xcite . in the opinion of the authors , this is what feynman , in his _
lectures_@xcite , wants to convey in his discussion of a ratchet engine .
it is important to stress that we consider high enough temperatures so that the particle , even though it does not move on the average , it does perform normal diffusion .
this is shown in fig .
[ seg ] . in the presence of a time - dependent external force @xmath41 ,
the langevin equation reads , @xmath42 where the thermal force @xmath12 obeys the same properties as before , see eqs.([ft ] ) . as an example
, the external force @xmath41 may be generated by an orstein - uhlenbeck process @xmath43 with @xmath44 a given gaussian , white , stochastic process : @xmath45 the parameters @xmath46 and @xmath47 determine the process .
the first one is the correlation time for @xmath41 and @xmath47 is a measure of its strength . in order to avoid any bias by this force
, one must consider the initial condition @xmath48 .
equations ( [ lang2 ] ) , ( [ ft ] ) , ( [ ou ] ) and ( [ zt ] ) are equivalent to the following bivariate fokker - planck equation@xcite , @xmath49 where @xmath50 is the conditional probability distribution to find values @xmath32 and @xmath51 for the corresponding stochastic variables , given that at @xmath52 , @xmath40 and @xmath53 .
initially , it is @xmath54 .
by simple inspection we find that , even if a stationary distribution @xmath55 exists , equation ( [ fp2 ] ) does not obey detailed balance .
the offending " term is @xmath56 this , of course , only means that @xmath41 is external " .
namely , @xmath51 acts on @xmath32 but not the opposite , thus , there is no mechanism to establish equilibrium among the particle , the thermal bath and the external agent .
therefore , the system can withdraw energy from the external source and generate motion .
in other words , there is nothing to prevent the total current from taking any value different from zero : @xmath57 or @xmath58 in other words , in this case the second law does not impose any restriction on the appearance of a current .
the second law will now impose restrictions on the _ efficiency _ of the process but that is not discussed here . of course , if the potential @xmath2 does have a left - right " symmetry , the current vanishes as one should expect . in fig .
[ current ] we exemplify the appearance of a current , both for the disordered potential and for the periodic one .
on top of the current , the particle also performs normal diffusion , i.e. for long times @xmath59 .
during the last few years there has been an increasing interest in studying the statistical behavior of the transport phenomena inside the cell carried out by protein motors and it has been proposed by several authors that ratchet models may be relevant in the description of these processes@xcite .
protein motors are responsible for carrying diverse kind of vesicles from one site to another in the cell in a much more efficient way than the obtained by simple diffusion@xcite . to accomplish this task they consume chemical energy , usually stored in the form of adenosine - triphosphate ( atp ) , to convert it into mechanical motion @xcite . due to their dimensions ,
the erratic collisions with the solvent molecules represent a non negligible contribution to the protein motors dynamics and appear in the form of friction and thermal stochastic forces .
this is why they are also called brownian motors or molecular motors@xcite . molecular motors , as kinesin and dynein , present directed motion only when they are attached to microtubules ,
otherwise they perform standard brownian motion .
it has been also observed that they do not hydrolyze atp at an appreciable rate unless they are attached@xcite .
experimental observations of kinesin and dynein motion on microtubules@xcite have shown that kinesins move mainly along one single protofilament , while dyneins visit often several protofilaments .
one important characteristic of the microtubules is that they have an intrinsically periodic and asymmetric structure@xcite .
most of the models motivated by these experimental results were initially restricted to the one dimensional case but it has become clear that more dimensions are needed@xcite . some of these works@xcite approach the problem imposing _ ad hoc _ asymmetric probabilities thus obtaining transport .
the others use langevin equations and , in particular , those in refs.@xcite have introduced more detailed models to understand the particular behavior of kinesin in microtubules . as an step forward in the description of these processes , we are considering here a model for a kinesin on a microtubule as a ratchet in a two dimensional space , immersed in a thermal dissipative bath , and subjected to an external force of zero mean varying stochastically in time . at present
we study general statistical properties of the model ; a more detailed study and its comparison with real kinesin proteins will be presented elsewhere .
nevertheless , the results shown here resemble qualitatively what is observed in actual experiments with motor proteins and microtubules@xcite . in order to model the interaction forces between the motor protein and the microtubule a two - dimensional potential
is proposed , whose shape resembles a long attractive filament ( or channel ) with a typical ratchet structure inside on the longitudinal direction , as shown in fig .
[ potcan ] .
the potential @xmath60 , called for simplicity the filament or microtubule potential , is given by the following function @xmath61 , \label{potfil}\ ] ] where @xmath62 is the mean depth of the attractive filament and its width is determined by @xmath63 ; @xmath64 represents the period of the ratchet and @xmath65 the amplitude .
the system is immersed in a thermal bath at temperature @xmath14 and there is present an external random force with zero mean that represents in the model the consumption of atp by the protein motor .
depending on the temperature of the bath and on the statistical properties of the external force , the particle may be inside or outside the microtubule , i.e. @xmath66 or @xmath67 .
inside , it will feel the effect of the ratchet potential and may generate directed motion ; outside , it will perform free brownian motion .
the dynamics of the model are represented by the following coupled langevin equations for a brownian particle moving in an @xmath68 coordinate system : @xmath69 and @xmath70 where @xmath11 is the friction coefficient and @xmath71 , with @xmath72 , is the force exerted by the thermal bath .
the stochastic properties of this force are @xmath73 it is further assumed that these processes are gaussian .
the external force is @xmath74 with @xmath72 . due to the lack of information with respect to the actual statistical properties of atp consumption by the kinesin , and which is one the main difficulties to make precise predictions , we have decided to employ a stochastic force generated by an ornstein - uhlenbeck process @xmath75 with @xmath76 a given gaussian , white , stochastic process @xmath77 the parameters @xmath46 and @xmath47
determine the process and represent the correlation time and the magnitude of the external force , respectively .
as it can be observed , the relations for @xmath78 and @xmath79 are exactly the same for both directions and they are ruled by the same parameters . in consequence
, they act isotropically .
however , each of them arise from an independent gaussian noise , and thus , there is no correlation among them .
we now present the main statistical properties of this model .
in all the results presented here the initial conditions are @xmath80
. variations of the different parameters , a thorough description of the behavior of the first and second moments of the position distribution of the particle , as well as a comparison with actual motor proteins , can not be presented here due to the briefness of this report and will be discussed elsewhere .
as one should expect , the presence of the external time dependent force produces a net current along the @xmath32 direction due to the asymmetric properties of the ratchet inside the filament . in the present case
, the total current is a two - dimensional vector , @xmath81 in fig.[x - cur ] we show the average @xmath32-position of the particle as a function of time , the current @xmath82 being the derivative of such a curve .
the current along @xmath83 is zero , @xmath84 , as expected .
the current occurs , however , in an interesting manner .
first , we realize that the particle feels the effect of the ratchet only when it is inside the filament .
outside , it performs diffusive standard brownian motion .
the net result is that the current tends , asymptotically and very slowly , towards zero .
however , for any finite amount of time , the current is different from zero .
thus , a net transport is always realized .
another form of saying this is that , even though the particle may stay a long time outside the filament , it effectively has directional motion since it eventually returns to it .
this is better seen in fig.[nubes ] , where we present four `` snapshots '' of the position probability distribution @xmath85 for different times , and obtained from 2000 realizations of the process .
the distribution acquires an arrow - like structure because of the ratchet within the filament and the centroid moves always to larger values of @xmath32 , i.e. the distribution appears to be dragged by the filament .
the shape of the position distribution @xmath85 suggests also a peculiar behavior of its second moment , @xmath86 in fig .
[ msd ] we show these three deviations .
the total second moment @xmath87 follows a power law @xmath88 with @xmath89 after @xmath90 time units .
that is , the system effectively presents superdiffusion , in contrast to the one - dimensional case where it is always normal diffusion .
the super diffusive behavior is also present in the @xmath32-direction , while in the @xmath83 direction the diffusion is normal .
the explanation for this behavior appears to be simple : when the particle is bound to the filament it feels the effect of the ratchet and tends to move preferentially in the positive @xmath32 direction . when it is outside of the channel performs a normal random walk , with normal diffusion , but it does not move preferentially to any direction . thus , for those times when it is outside the filament , even though appears statistically to be dragged by the filament as mentioned above , the particle lags behind the centroid , hence effectively producing a wider distribution and a larger second moment .
it is interesting to point out that the superdiffusive behavior is a consequence of `` standard '' noises coupled to a highly nonlinear process and does not arise from an exotic stochastic process@xcite .
following the classical work of anfinsen@xcite on protein folding , levinthal@xcite argued that if the multidimensional ( free ) energy landscape had a `` golf course '' like shape , with the hole being the protein native state , it would take essentially forever for a protein to fold correctly , provided the search were performed at random , namely , by brownian motion . since proteins _ in vivo _ fold extremely fast and efficiently@xcite the concept of a _ funneled _ energy landscape was developed@xcite , with the further possibility of folding pathways in which the protein folds following a path towards or within the funnel leading to the native state .
but very importantly , the process being driven essentially by free energy differences , that is , by `` falling '' into the state of lowest free energy .
this idea has been central in the study of protein folding and we do not pretend to review all the advances made by the many groups working on this field@xcite nor to point out any possible pitfalls of the theories .
rather , we would like to point out an alternative way out to the so - called levinthal paradox , without necessarily requiring a _ funnel _ leading to the native state .
we shall appeal to a ratchet mechanism for the process of protein folding .
this model requires , in addition to having a ratchet - like energy landscape as we discuss below , that the folding is a non - equilibrium process being driven by an `` external '' source .
the model consists of a `` particle '' moving in a multidimensional space , the coordinates representing the different configurations of a protein , or effective degrees of freedom@xcite .
the particle is affected by a conservative ratchet potential which maybe flat on the average ( i.e. no need of a funnel ) and with a `` small and deep enough hole '' representing the native state .
on top of the average potential there is an asymmetry that makes the potential _ toward _ the native state , different than in the opposite direction .
[ land - prot ] is a two - dimensional example for visualization , but we have realized many multidimensional potentials with the same type of `` toward - away '' asymmetry , see below . although we can not justify the existence of such a potential , one may argue that the regularity specially in the secondary structures , at least at first order , suggest a kind of `` universal '' regular potential .
our proposal , undoubtedly not quite justified , is that such a regularity may have a ratchet - like form ; after all , any coiling structure has an asymmetry since it distinguishes between `` right '' and `` left '' .
the presence of the thermal bath needs no justification and simply represents the effect of a viscous environment at a fixed temperature . with only the last two ingredients , the ratchet potential and the bath ,
the `` particle '' will obey levinthal paradox and would not find its way in a reasonable time , specially in a multidimensional space .
however , if the there is an _ external _ source of energy , with random properties and zero bias , acting on the particle , the latter will definitely find its way toward the native state and , on the average , could do so in a short time .
the efficiency of the process , of course , will depend on the values of the different parameters .
what is the origin of the external source ?
we may generically argue that processes in living organisms are through states of non - equilibrium with all sorts of gradients of different physical properties , and that the maintenance of those gradients may be traced back to the consumption of atp . in a more specific way , although it is not clear that occurs in all proteins , it is known that many proteins fold assisted by chaperone proteins , which in turn , consume atp@xcite .
thus , the proposed mechanism requires the presence of an external source , which in our opinion , is physically appealing since life needs such a source for occurring as required by the second law .
nonetheless , we can not say exactly what the mechanism is at the level of the protein .
the mathematical model is , therefore , a multidimensional version of eqs.([elx ] ) and ( [ ely ] ) for the kinesin - on - a - microtubule model , but now the ratchet potential has an overall ( topologically equivalent ) spherical symmetry , with a `` towards - away '' asymmetry . for the numerical results we present below we consider periodic potentials such as the following , @xmath91 \nonumber \\ & & -v_1 e^{- c r^2 } .
\label{ratch - prot}\end{aligned}\ ] ] where @xmath92 is the dimension of the space , namely , the number of effective degrees of freedom of the protein ; @xmath93 ; and @xmath94 , @xmath95 , @xmath96 , @xmath65 and @xmath62 real positive numbers . the last term in eq.([ratch - prot ] ) represents the `` hole '' of the native state .
we want to insist that the ratchet potential need not be periodic , that is , the saw - tooth structure can have `` quenched ''
random distances between maxima and minima , such as in the one - dimensional case , see fig .
2 . furthermore
, the landscape does not have to be flat , namely , it can have valleys and peaks , wider and higher or lower than the average peaks of the ratchet , and the particle can still climb over the peaks provided they are not above the stall load of the ratchet@xcite .
full analysis of these cases are beyond the briefness of this report and it will be presented elsewhere .
fig.[fold ] shows a typical example of the many different cases we have analyzed .
it corresponds to a `` protein '' with 6 degrees of freedom .
we show the average evolution of the protein coordinates @xmath97 , with @xmath98 over 100 runs for the same initial condition . in the presence of the external force , and for those parameters
, we found more than 95@xmath99 `` folding '' , namely , the particle reached the `` native '' state in the arbitrary maximum time of 15000 units .
the average time of folding can be read off the graph and corresponds to 4000 unit times approximately , very short even in cpu time scales .
when the external field was turned off , needles to say , we found 0@xmath99 `` folding '' , and we believe it will essentially never find its way no matter how long we run the program .
in this article we have revisited overdamped ratchet systems in one dimension and extended it to several dimensions in order to study biology related systems . for the case of one dimension we analyzed a novel _ disordered _ ratchet for the purpose of making explicit the fact that the space in which the systems move do not correspond to a periodic variable , as it is routinely done in the literature . for these systems , strictly speaking , do not exist a stationary state .
the main result that we want to stress here is the fact that , in the absence of external time dependent forces , stochastic or deterministic , there can not be a current for all times and not only as an asymptotic condition .
this is a requirement of the second law .
once there is an external time dependent force , and the system shows an intrinsic asymmetry , such as a `` left - right '' one , there is nothing to prevent a current .
the second law now acts by setting limits for the amount of work released , namely on the efficiency of the process .
we did not address the latter limits although several workers have discussed this point@xcite .
the ratchet mechanism has become a potential candidate for many biological process , since , on the one hand resembles a thermal engine at a mesoscopic level , but on the other it does not appear to need a specific design such as the man - made engines .
that is , by its inherent capacity to deliver work in the form of directional motion , one may be prompted to use it as a model in somewhat obvious biological situations in which a transport process , of some kind , is present .
this has been the case of the motion of kinesin proteins on microtubules , where the protein appears to truly `` walk '' using atp as the necessary input energy ; there are other cases where ratchets have been used as models of intracellular motion , or as molecular motors , such as in the mitosis of the cell@xcite .
granted , all the models are still at a very premature level of comparison with actual situations , mainly because the complicated biochemical processes involved in real life can hardly be thought to be described by systems with one or two degrees of freedom .
nevertheless , we believe it is worthwhile to keep exploring these models not only by its potential relevance in biological systems but for their own sake . here , we have presented a two dimensional model of a kinesin in the presence of a quasi one - dimensional microtubule .
the typical walks of the particle , wandering around until they hit the microtubule and then directionally moving , show a striking similarity with actual kinesin motion , as seen in videos of these systems@xcite . although one can always try to fit these simple results to known conditions , such as speed of kinesin walks or the energy released by the consumption of atp , we believe further research is needed in two aspects of the model : first
, we must confidently know how to relate the ratchet potential with the actual periodic structure of the microtubule and the form in which the protein attaches to it , and second , how to describe the consumption of atp by means of an appropriate statistical process .
the third section of this article on considering protein folding as being driven by a ratchet mechanism is highly speculative , but we believe it is worthwhile to pursue it because , again , protein folding appears as a process with directional motion .
traditionally , this process has been thought to be driven by free energy differences leading towards a minimum , similarly to a chemical reaction@xcite , and thus the idea of a funnel in the free energy landscape of the protein .
the presence of catalyzers and/or chaperone proteins may accelerate this process and their presence is welcome in the theory . here
, by following the idea that life processes consume energy to yield their products , similarly to a man - made thermal engine , we have speculated that protein folding is driven by an `` engine '' in which the protein itself is part of it .
this now makes a necessity the presence of choperones and/or catalyzers that in turn consume energy . at this moment ,
the hardest part to justify in our model is the ratchet structure of the energy landscape , and the best that we can say is that it is motivating to see that the secondary structure of proteins is universally made of @xmath100-helices and @xmath101-sheets , structures with certain periodicity and asymmetry . on the other hand
, we do not have evidence neither pro nor con that a ratchet structure is present since this would have to be seen in the highly multidimensional energy landscape .
as mentioned before , the `` folding '' with this mechanism does not need a funnel , but of course , the interplay of both properties would make the process even more efficient .
the simulations that we have performed , so far up to a landscape in 6 dimensions , are extremely encouraging since they can easily be tuned to a very fast and almost 100 @xmath99 `` folding '' . extending to an arbitrary number of dimensions only requires longer computer time and , at present , does not add anything fundamentally different .
what is really needed is the actual form of an energy landscape , a hard problem with many researchers very much interested in it .
however , without yet knowing the actual form of an energy landscape in its many dimensions , we can make models in which the ratchet is not periodic and in which the landscape have valleys and peaks to test the efficiency of the search for the `` native '' state .
we shall present those results in future contributions . the multidimensional free energy landscape may already have the information that the system is immersed in water .
that is , the interaction potential should have all effective interactions due to the hydrophilic or hydrophobic properties of the different aminoacids . | the overdamped thermal ratchet driven by an external ( orstein - uhlenbeck ) noise is revisited .
the ratchet we consider is unbounded in space and not necessarily periodic .
we briefly discuss the conditions under which current is obtained by analyzing the corresponding fokker - planck equation and its lack of stationary states .
next , two examples in more than one dimension and related to biological systems are presented .
first , a two - dimensional model of a `` kinesin protein '' on a `` microtubule '' is analyzed and , second , we suggest that a ratchet mechanism may be behind the folding of proteins ; the latter is elaborated with a multidimensional ratchet model . and thermal ratchets , kinesin transport , protein folding . | <s>[INST]the ratchet mechanism to produce directional current or motion has become a paradigm of the interplay of nonlinear phenomena with brownian motion and external noise in mesoscopic systems@xcite .
we shall use the term `` ratchet '' for any conservative mechanical system that has an ingrained spatial asymmetry ; a one - dimensional example is a particle in a saw - tooth like potential . due to the potentiality of these systems to describe mesoscopic systems and their processes , such as biological ones@xcite
, one should consider the ratchet to be immersed in a thermal bath , giving rise to brownian motion .
this adds dissipative and stochastic thermal forces that are related to each other through the fluctuation - dissipation theorem@xcite . as it was clearly pointed out by feynman in his _
lectures_@xcite , the second law of thermodynamics implies that a ratchet under the above conditions can not generate directional motion .
it is by now very well established that in order to obtain current or directional motion , it is indispensable to have the presence of an _ external _ unbiased time dependent force .
this force can be deterministic , a so - called `` rocking '' ratchet , see ref.@xcite , or stochastic in nature , see ref.@xcite . in any case , any of those forces should be of zero average in time in order not to produce any biased current ; in the present article we shall be concerned with external stochastic forces only .
it is the opinion of the authors that the origin of the appearance of the current is not fully understood yet , although it is clear what the conditions are for its existence . in particular
, a lot of attention has been devoted to the case in which the ratchet variable is periodic , such as an angle @xmath0 $ ] , and many analytic and numerical results have been obtained@xcite , yielding a clear picture of how current occurs in a stationary state .
we believe the studies are not as exhaustive for the cases where the ratchet variable is not periodic , namely when the particle can move in all space , namely , when the position of the particle can take all real values , @xmath1 . in this case , even in the absence of external forces , the system does not reach an stationary state@xcite .
one of the purposes of this article is to add to the understanding of the appearance of the current in the latter situation , by studying a novel _ non - periodic _ one - dimensional overdamped ratchet ; this is done in section 2 .
having established the conditions for the production of current in one dimension , we then proceed to the second purpose of the article and extend the model to more than one dimension in order to study two biology - related problems .
one is the case of the motion of a kinesin protein on a microtubule , in section 3 , and the other is the process of protein folding in section 4 .
the first has been studied already by several authors@xcite but here we consider a protein in two dimensions and the microtubule as a quasi - one dimensional structure .
our model of protein folding is at present speculative , and the idea is centered on the hypothesis that the energy landscape of the protein has a ratchet - like structure ; by further assuming that there is an _ external _ agent that consumes energy , which could be the presence of chaperone proteins@xcite , one has all the ingredients to obtain directed motion .
we shall show that , understanding by protein folding the search and finding of a target point or small section in the energy landscape , the ratchet mechanism is extremely fast with an almost perfect efficiency .
an interesting consequence of this process is that the landscape need not have a funnel structure@xcite .
in this section we revisit the one - dimensional overdamped ratchet system , considering both periodic and non - periodic potentials . the main purpose here is to argue that the appearance of a current is a _
generic _ property of bounded asymmetric conservative systems , in interaction with a thermal bath , due to the presence of external ( stochastic or deterministic ) non - biased time dependent forces .
that is , by showing that the absence of current without the external force must follow from the second law , we argue that there is nothing to prevent a current once the conditions required by the second law have been relaxed .
the details of the numerical techniques we use can be found in refs.@xcite .
we initiate by writing down the the langevin equation in the overdamped case for a particle subjected to a conservative potential @xmath2 , without an external time dependent force , @xmath3 we consider a ratchet potential with a `` quenched '' random disorder both in the potential barriers and in the spatial periods , namely , @xmath4 \nonumber \\ & & \>\>\>\>{\rm
if } \>\>\>y_{i } \le x < y_{i+1 } , \label{ratchet}\end{aligned}\ ] ] with @xmath5 taking all integer values and where the positions @xmath6 are chosen at random ; @xmath7 is arbitrarily set equal to 0 .
clearly , the spatial periods are given by @xmath8 .
a typical form of the ratchet potential @xmath2 is shown in fig .
[ pot - ran ] .
note that this potential is not periodic .
the usual _ periodic _ ratchet potential is @xmath9 and @xmath10 for all @xmath5@xcite .
returning to the langevin equation ( [ langevin ] ) , @xmath11 is the friction coefficient and @xmath12 is the thermal force exerted by the thermal bath .
the stochastic properties of this force are @xmath13 it is further assumed that this process is gaussian , so that eqs.([ft ] ) suffice to completely specify the process @xmath12 . in the second equation @xmath14
is the temperature of the bath and the expression for the correlation of the force is the fluctuation - dissipation relation for this problem ; it imposes detailed balance@xcite . since the process @xmath15 representing the position of the particle is markovian , then , knowledge of the conditional probability distribution @xmath16 is enough to determine the process .
it can be shown that this function obeys the following fokker - planck equation@xcite , @xmath17 supplemented by the initial condition @xmath18 . in this discussion
we are considering that the particle can move in all space , namely , @xmath19 .
thus , the normalization of the distribution , @xmath20 imposes the boundary conditions @xmath21 the fokker - planck equation , eq.([fp ] ) , is a continuity equation for the probability distribution .
therefore , one can read off the probability density current , @xmath22 we may define the total " current as , @xmath23 where the last two lines follow from the definition of the density current and the fokker - planck equation , eqs.([j ] ) and ( [ fp ] ) .
if there exists a stationary distribution , @xmath24 , then detailed balance means that the stationary density current vanishes , @xmath25 , and therefore that the stationary distribution is @xmath26 with @xmath27 .
further , if @xmath28 is not the stationary distribution , then , detailed balance implies that as @xmath29 , such a distribution approaches the stationary one .
this is equivalent to the @xmath30-theorem . in the context of ratchet - like potentials
, one is faced with potentials that are bounded , that is , @xmath31 , for all @xmath32 .
thus , strictly speaking , a stationary distribution can not be reached@xcite .
however , it is clear that stationarity is achieved in the following sense , @xmath33 therefore , it must be true that , in the above sense , the probability density current @xmath34 and the total current @xmath35 must vanish as @xmath36 .
however , this does not suffice to prevent an arbitrary current or displacement of the particle , as is routinely asserted in essentially all articles dealing with this problem .
the main point that we want to emphasize here is that , since detailed balance is in accordance with the second law of thermodynamics , the total current @xmath35 must be bounded for all times . using eq.([j ] ) , this can be more precisely written as the following requirement , @xmath37 where @xmath38 is the initial position of the particle and @xmath39 is the distance between the adjacent local maxima of the potential where the particle was initially at @xmath40 .
we have exhaustively numerically verified that this holds for ratchet potentials such as those ones in fig .
[ pot - ran ] , and the results are exemplified in fig .
[ prom ] . for ratchet potentials
this means that _ on the average _ the particle can not leave the local well where it was initially ; if it did , nothing would prevent the particle to jump " to another well , and so on , thus moving an arbitrary distance .
in other words , eq.([bound ] ) expresses that fact that it is not possible to obtain a current that , on the average , could generate motion that would transport the particle farther than its initial well .
otherwise , this would yield the possibility to perform work on some external load or agent@xcite violating kelvin s statement of the second law : a transformation whose only final result is to transform into work heat extracted from a source which is at the same temperature throughout is impossible"@xcite . in the opinion of the authors , this is what feynman , in his _
lectures_@xcite , wants to convey in his discussion of a ratchet engine .
it is important to stress that we consider high enough temperatures so that the particle , even though it does not move on the average , it does perform normal diffusion .
this is shown in fig .
[ seg ] . in the presence of a time - dependent external force @xmath41 ,
the langevin equation reads , @xmath42 where the thermal force @xmath12 obeys the same properties as before , see eqs.([ft ] ) . as an example
, the external force @xmath41 may be generated by an orstein - uhlenbeck process @xmath43 with @xmath44 a given gaussian , white , stochastic process : @xmath45 the parameters @xmath46 and @xmath47 determine the process .
the first one is the correlation time for @xmath41 and @xmath47 is a measure of its strength . in order to avoid any bias by this force
, one must consider the initial condition @xmath48 .
equations ( [ lang2 ] ) , ( [ ft ] ) , ( [ ou ] ) and ( [ zt ] ) are equivalent to the following bivariate fokker - planck equation@xcite , @xmath49 where @xmath50 is the conditional probability distribution to find values @xmath32 and @xmath51 for the corresponding stochastic variables , given that at @xmath52 , @xmath40 and @xmath53 .
initially , it is @xmath54 .
by simple inspection we find that , even if a stationary distribution @xmath55 exists , equation ( [ fp2 ] ) does not obey detailed balance .
the offending " term is @xmath56 this , of course , only means that @xmath41 is external " .
namely , @xmath51 acts on @xmath32 but not the opposite , thus , there is no mechanism to establish equilibrium among the particle , the thermal bath and the external agent .
therefore , the system can withdraw energy from the external source and generate motion .
in other words , there is nothing to prevent the total current from taking any value different from zero : @xmath57 or @xmath58 in other words , in this case the second law does not impose any restriction on the appearance of a current .
the second law will now impose restrictions on the _ efficiency _ of the process but that is not discussed here . of course , if the potential @xmath2 does have a left - right " symmetry , the current vanishes as one should expect . in fig .
[ current ] we exemplify the appearance of a current , both for the disordered potential and for the periodic one .
on top of the current , the particle also performs normal diffusion , i.e. for long times @xmath59 .
during the last few years there has been an increasing interest in studying the statistical behavior of the transport phenomena inside the cell carried out by protein motors and it has been proposed by several authors that ratchet models may be relevant in the description of these processes@xcite .
protein motors are responsible for carrying diverse kind of vesicles from one site to another in the cell in a much more efficient way than the obtained by simple diffusion@xcite . to accomplish this task they consume chemical energy , usually stored in the form of adenosine - triphosphate ( atp ) , to convert it into mechanical motion @xcite . due to their dimensions ,
the erratic collisions with the solvent molecules represent a non negligible contribution to the protein motors dynamics and appear in the form of friction and thermal stochastic forces .
this is why they are also called brownian motors or molecular motors@xcite . molecular motors , as kinesin and dynein , present directed motion only when they are attached to microtubules ,
otherwise they perform standard brownian motion .
it has been also observed that they do not hydrolyze atp at an appreciable rate unless they are attached@xcite .
experimental observations of kinesin and dynein motion on microtubules@xcite have shown that kinesins move mainly along one single protofilament , while dyneins visit often several protofilaments .
one important characteristic of the microtubules is that they have an intrinsically periodic and asymmetric structure@xcite .
most of the models motivated by these experimental results were initially restricted to the one dimensional case but it has become clear that more dimensions are needed@xcite . some of these works@xcite approach the problem imposing _ ad hoc _ asymmetric probabilities thus obtaining transport .
the others use langevin equations and , in particular , those in refs.@xcite have introduced more detailed models to understand the particular behavior of kinesin in microtubules . as an step forward in the description of these processes , we are considering here a model for a kinesin on a microtubule as a ratchet in a two dimensional space , immersed in a thermal dissipative bath , and subjected to an external force of zero mean varying stochastically in time . at present
we study general statistical properties of the model ; a more detailed study and its comparison with real kinesin proteins will be presented elsewhere .
nevertheless , the results shown here resemble qualitatively what is observed in actual experiments with motor proteins and microtubules@xcite . in order to model the interaction forces between the motor protein and the microtubule a two - dimensional potential
is proposed , whose shape resembles a long attractive filament ( or channel ) with a typical ratchet structure inside on the longitudinal direction , as shown in fig .
[ potcan ] .
the potential @xmath60 , called for simplicity the filament or microtubule potential , is given by the following function @xmath61 , \label{potfil}\ ] ] where @xmath62 is the mean depth of the attractive filament and its width is determined by @xmath63 ; @xmath64 represents the period of the ratchet and @xmath65 the amplitude .
the system is immersed in a thermal bath at temperature @xmath14 and there is present an external random force with zero mean that represents in the model the consumption of atp by the protein motor .
depending on the temperature of the bath and on the statistical properties of the external force , the particle may be inside or outside the microtubule , i.e. @xmath66 or @xmath67 .
inside , it will feel the effect of the ratchet potential and may generate directed motion ; outside , it will perform free brownian motion .
the dynamics of the model are represented by the following coupled langevin equations for a brownian particle moving in an @xmath68 coordinate system : @xmath69 and @xmath70 where @xmath11 is the friction coefficient and @xmath71 , with @xmath72 , is the force exerted by the thermal bath .
the stochastic properties of this force are @xmath73 it is further assumed that these processes are gaussian .
the external force is @xmath74 with @xmath72 . due to the lack of information with respect to the actual statistical properties of atp consumption by the kinesin , and which is one the main difficulties to make precise predictions , we have decided to employ a stochastic force generated by an ornstein - uhlenbeck process @xmath75 with @xmath76 a given gaussian , white , stochastic process @xmath77 the parameters @xmath46 and @xmath47
determine the process and represent the correlation time and the magnitude of the external force , respectively .
as it can be observed , the relations for @xmath78 and @xmath79 are exactly the same for both directions and they are ruled by the same parameters . in consequence
, they act isotropically .
however , each of them arise from an independent gaussian noise , and thus , there is no correlation among them .
we now present the main statistical properties of this model .
in all the results presented here the initial conditions are @xmath80
. variations of the different parameters , a thorough description of the behavior of the first and second moments of the position distribution of the particle , as well as a comparison with actual motor proteins , can not be presented here due to the briefness of this report and will be discussed elsewhere .
as one should expect , the presence of the external time dependent force produces a net current along the @xmath32 direction due to the asymmetric properties of the ratchet inside the filament . in the present case
, the total current is a two - dimensional vector , @xmath81 in fig.[x - cur ] we show the average @xmath32-position of the particle as a function of time , the current @xmath82 being the derivative of such a curve .
the current along @xmath83 is zero , @xmath84 , as expected .
the current occurs , however , in an interesting manner .
first , we realize that the particle feels the effect of the ratchet only when it is inside the filament .
outside , it performs diffusive standard brownian motion .
the net result is that the current tends , asymptotically and very slowly , towards zero .
however , for any finite amount of time , the current is different from zero .
thus , a net transport is always realized .
another form of saying this is that , even though the particle may stay a long time outside the filament , it effectively has directional motion since it eventually returns to it .
this is better seen in fig.[nubes ] , where we present four `` snapshots '' of the position probability distribution @xmath85 for different times , and obtained from 2000 realizations of the process .
the distribution acquires an arrow - like structure because of the ratchet within the filament and the centroid moves always to larger values of @xmath32 , i.e. the distribution appears to be dragged by the filament .
the shape of the position distribution @xmath85 suggests also a peculiar behavior of its second moment , @xmath86 in fig .
[ msd ] we show these three deviations .
the total second moment @xmath87 follows a power law @xmath88 with @xmath89 after @xmath90 time units .
that is , the system effectively presents superdiffusion , in contrast to the one - dimensional case where it is always normal diffusion .
the super diffusive behavior is also present in the @xmath32-direction , while in the @xmath83 direction the diffusion is normal .
the explanation for this behavior appears to be simple : when the particle is bound to the filament it feels the effect of the ratchet and tends to move preferentially in the positive @xmath32 direction . when it is outside of the channel performs a normal random walk , with normal diffusion , but it does not move preferentially to any direction . thus , for those times when it is outside the filament , even though appears statistically to be dragged by the filament as mentioned above , the particle lags behind the centroid , hence effectively producing a wider distribution and a larger second moment .
it is interesting to point out that the superdiffusive behavior is a consequence of `` standard '' noises coupled to a highly nonlinear process and does not arise from an exotic stochastic process@xcite .
following the classical work of anfinsen@xcite on protein folding , levinthal@xcite argued that if the multidimensional ( free ) energy landscape had a `` golf course '' like shape , with the hole being the protein native state , it would take essentially forever for a protein to fold correctly , provided the search were performed at random , namely , by brownian motion . since proteins _ in vivo _ fold extremely fast and efficiently@xcite the concept of a _ funneled _ energy landscape was developed@xcite , with the further possibility of folding pathways in which the protein folds following a path towards or within the funnel leading to the native state .
but very importantly , the process being driven essentially by free energy differences , that is , by `` falling '' into the state of lowest free energy .
this idea has been central in the study of protein folding and we do not pretend to review all the advances made by the many groups working on this field@xcite nor to point out any possible pitfalls of the theories .
rather , we would like to point out an alternative way out to the so - called levinthal paradox , without necessarily requiring a _ funnel _ leading to the native state .
we shall appeal to a ratchet mechanism for the process of protein folding .
this model requires , in addition to having a ratchet - like energy landscape as we discuss below , that the folding is a non - equilibrium process being driven by an `` external '' source .
the model consists of a `` particle '' moving in a multidimensional space , the coordinates representing the different configurations of a protein , or effective degrees of freedom@xcite .
the particle is affected by a conservative ratchet potential which maybe flat on the average ( i.e. no need of a funnel ) and with a `` small and deep enough hole '' representing the native state .
on top of the average potential there is an asymmetry that makes the potential _ toward _ the native state , different than in the opposite direction .
[ land - prot ] is a two - dimensional example for visualization , but we have realized many multidimensional potentials with the same type of `` toward - away '' asymmetry , see below . although we can not justify the existence of such a potential , one may argue that the regularity specially in the secondary structures , at least at first order , suggest a kind of `` universal '' regular potential .
our proposal , undoubtedly not quite justified , is that such a regularity may have a ratchet - like form ; after all , any coiling structure has an asymmetry since it distinguishes between `` right '' and `` left '' .
the presence of the thermal bath needs no justification and simply represents the effect of a viscous environment at a fixed temperature . with only the last two ingredients , the ratchet potential and the bath ,
the `` particle '' will obey levinthal paradox and would not find its way in a reasonable time , specially in a multidimensional space .
however , if the there is an _ external _ source of energy , with random properties and zero bias , acting on the particle , the latter will definitely find its way toward the native state and , on the average , could do so in a short time .
the efficiency of the process , of course , will depend on the values of the different parameters .
what is the origin of the external source ?
we may generically argue that processes in living organisms are through states of non - equilibrium with all sorts of gradients of different physical properties , and that the maintenance of those gradients may be traced back to the consumption of atp . in a more specific way , although it is not clear that occurs in all proteins , it is known that many proteins fold assisted by chaperone proteins , which in turn , consume atp@xcite .
thus , the proposed mechanism requires the presence of an external source , which in our opinion , is physically appealing since life needs such a source for occurring as required by the second law .
nonetheless , we can not say exactly what the mechanism is at the level of the protein .
the mathematical model is , therefore , a multidimensional version of eqs.([elx ] ) and ( [ ely ] ) for the kinesin - on - a - microtubule model , but now the ratchet potential has an overall ( topologically equivalent ) spherical symmetry , with a `` towards - away '' asymmetry . for the numerical results we present below we consider periodic potentials such as the following , @xmath91 \nonumber \\ & & -v_1 e^{- c r^2 } .
\label{ratch - prot}\end{aligned}\ ] ] where @xmath92 is the dimension of the space , namely , the number of effective degrees of freedom of the protein ; @xmath93 ; and @xmath94 , @xmath95 , @xmath96 , @xmath65 and @xmath62 real positive numbers . the last term in eq.([ratch - prot ] ) represents the `` hole '' of the native state .
we want to insist that the ratchet potential need not be periodic , that is , the saw - tooth structure can have `` quenched ''
random distances between maxima and minima , such as in the one - dimensional case , see fig .
2 . furthermore
, the landscape does not have to be flat , namely , it can have valleys and peaks , wider and higher or lower than the average peaks of the ratchet , and the particle can still climb over the peaks provided they are not above the stall load of the ratchet@xcite .
full analysis of these cases are beyond the briefness of this report and it will be presented elsewhere .
fig.[fold ] shows a typical example of the many different cases we have analyzed .
it corresponds to a `` protein '' with 6 degrees of freedom .
we show the average evolution of the protein coordinates @xmath97 , with @xmath98 over 100 runs for the same initial condition . in the presence of the external force , and for those parameters
, we found more than 95@xmath99 `` folding '' , namely , the particle reached the `` native '' state in the arbitrary maximum time of 15000 units .
the average time of folding can be read off the graph and corresponds to 4000 unit times approximately , very short even in cpu time scales .
when the external field was turned off , needles to say , we found 0@xmath99 `` folding '' , and we believe it will essentially never find its way no matter how long we run the program .
in this article we have revisited overdamped ratchet systems in one dimension and extended it to several dimensions in order to study biology related systems . for the case of one dimension we analyzed a novel _ disordered _ ratchet for the purpose of making explicit the fact that the space in which the systems move do not correspond to a periodic variable , as it is routinely done in the literature . for these systems , strictly speaking , do not exist a stationary state .
the main result that we want to stress here is the fact that , in the absence of external time dependent forces , stochastic or deterministic , there can not be a current for all times and not only as an asymptotic condition .
this is a requirement of the second law .
once there is an external time dependent force , and the system shows an intrinsic asymmetry , such as a `` left - right '' one , there is nothing to prevent a current .
the second law now acts by setting limits for the amount of work released , namely on the efficiency of the process .
we did not address the latter limits although several workers have discussed this point@xcite .
the ratchet mechanism has become a potential candidate for many biological process , since , on the one hand resembles a thermal engine at a mesoscopic level , but on the other it does not appear to need a specific design such as the man - made engines .
that is , by its inherent capacity to deliver work in the form of directional motion , one may be prompted to use it as a model in somewhat obvious biological situations in which a transport process , of some kind , is present .
this has been the case of the motion of kinesin proteins on microtubules , where the protein appears to truly `` walk '' using atp as the necessary input energy ; there are other cases where ratchets have been used as models of intracellular motion , or as molecular motors , such as in the mitosis of the cell@xcite .
granted , all the models are still at a very premature level of comparison with actual situations , mainly because the complicated biochemical processes involved in real life can hardly be thought to be described by systems with one or two degrees of freedom .
nevertheless , we believe it is worthwhile to keep exploring these models not only by its potential relevance in biological systems but for their own sake . here , we have presented a two dimensional model of a kinesin in the presence of a quasi one - dimensional microtubule .
the typical walks of the particle , wandering around until they hit the microtubule and then directionally moving , show a striking similarity with actual kinesin motion , as seen in videos of these systems@xcite . although one can always try to fit these simple results to known conditions , such as speed of kinesin walks or the energy released by the consumption of atp , we believe further research is needed in two aspects of the model : first
, we must confidently know how to relate the ratchet potential with the actual periodic structure of the microtubule and the form in which the protein attaches to it , and second , how to describe the consumption of atp by means of an appropriate statistical process .
the third section of this article on considering protein folding as being driven by a ratchet mechanism is highly speculative , but we believe it is worthwhile to pursue it because , again , protein folding appears as a process with directional motion .
traditionally , this process has been thought to be driven by free energy differences leading towards a minimum , similarly to a chemical reaction@xcite , and thus the idea of a funnel in the free energy landscape of the protein .
the presence of catalyzers and/or chaperone proteins may accelerate this process and their presence is welcome in the theory . here
, by following the idea that life processes consume energy to yield their products , similarly to a man - made thermal engine , we have speculated that protein folding is driven by an `` engine '' in which the protein itself is part of it .
this now makes a necessity the presence of choperones and/or catalyzers that in turn consume energy . at this moment ,
the hardest part to justify in our model is the ratchet structure of the energy landscape , and the best that we can say is that it is motivating to see that the secondary structure of proteins is universally made of @xmath100-helices and @xmath101-sheets , structures with certain periodicity and asymmetry . on the other hand
, we do not have evidence neither pro nor con that a ratchet structure is present since this would have to be seen in the highly multidimensional energy landscape .
as mentioned before , the `` folding '' with this mechanism does not need a funnel , but of course , the interplay of both properties would make the process even more efficient .
the simulations that we have performed , so far up to a landscape in 6 dimensions , are extremely encouraging since they can easily be tuned to a very fast and almost 100 @xmath99 `` folding '' . extending to an arbitrary number of dimensions only requires longer computer time and , at present , does not add anything fundamentally different .
what is really needed is the actual form of an energy landscape , a hard problem with many researchers very much interested in it .
however , without yet knowing the actual form of an energy landscape in its many dimensions , we can make models in which the ratchet is not periodic and in which the landscape have valleys and peaks to test the efficiency of the search for the `` native '' state .
we shall present those results in future contributions . the multidimensional free energy landscape may already have the information that the system is immersed in water .
that is , the interaction potential should have all effective interactions due to the hydrophilic or hydrophobic properties of the different aminoacids .[/INST] the overdamped thermal ratchet driven by an external ( orstein - uhlenbeck ) noise is revisited .
the ratchet we consider is unbounded in space and not necessarily periodic .
we briefly discuss the conditions under which current is obtained by analyzing the corresponding fokker - planck equation and its lack of stationary states .
next , two examples in more than one dimension and related to biological systems are presented .
first , a two - dimensional model of a `` kinesin protein '' on a `` microtubule '' is analyzed and , second , we suggest that a ratchet mechanism may be behind the folding of proteins ; the latter is elaborated with a multidimensional ratchet model . and thermal ratchets , kinesin transport , protein folding . </s> |
optimization is an important subject with many important application , and algorithms for optimization are diverse with a wide range of successful applications @xcite . among these optimization algorithms ,
modern metaheuristics are becoming increasingly popular , leading to a new branch of optimization , called metaheuristic optimization .
most metaheuristic algorithms are nature - inspired @xcite , from simulated annealing @xcite to ant colony optimization @xcite , and from particle swarm optimization @xcite to cuckoo search @xcite .
since the appearance of swarm intelligence algorithms such as pso in the 1990s , more than a dozen new metaheuristic algorithms have been developed and these algorithms have been applied to almost all areas of optimization , design , scheduling and planning , data mining , machine intelligence , and many others .
thousands of research papers and dozens of books have been published @xcite . despite the rapid development of metaheuristics ,
their mathematical analysis remains partly unsolved , and many open problems need urgent attention .
this difficulty is largely due to the fact the interaction of various components in metaheuristic algorithms are highly nonlinear , complex , and stochastic .
studies have attempted to carry out convergence analysis @xcite , and some important results concerning pso were obtained @xcite . however , for other metaheuristics such as firefly algorithms and ant colony optimization , it remains an active , challenging topic . on the other hand , even we have not proved or can not prove their convergence , we still can compare the performance of various algorithms .
this has indeed formed a majority of current research in algorithm development in the research community of optimization and machine intelligence @xcite . in combinatorial optimization
, many important developments exist on complexity analysis , run time and convergence analysis @xcite . for continuous optimization , no - free - lunch - theorems do not hold @xcite . as a relatively young field
, many open problems still remain in the field of randomized search heuristics @xcite . in practice , most assume that metaheuristic algorithms tend to be less complex for implementation , and in many cases , problem sizes are not directly linked with the algorithm complexity .
however , metaheuristics can often solve very tough np - hard optimization , while our understanding of the efficiency and convergence of metaheuristics lacks far behind .
apart from the complex interactions among multiple search agents ( making the mathematical analysis intractable ) , another important issue is the various randomization techniques used for modern metaheuristics , from simple randomization such as uniform distribution to random walks , and to more elaborate lvy flights @xcite .
there is no unified approach to analyze these mathematically . in this paper , we intend to review the convergence of two metaheuristic algorithms including simulated annealing and pso , followed by the new convergence analysis of the firefly algorithm . then , we try to formulate a framework for algorithm analysis in terms of markov chain monte carlo .
we also try to analyze the mathematical and statistical foundations for randomization techniques from simple random walks to lvy flights . finally , we will discuss some of important open questions as further research topics .
the formulation and numerical studies of various metaheuristics have been the main focus of most research studies .
many successful applications have demonstrated the efficiency of metaheuristics in various context , either through comparison with other algorithms and/or applications to well - known problems .
in contrast , the mathematical analysis lacks behind , and convergence analysis has been carried out for only a minority few algorithms such as simulated annealing and particle swarm optimization @xcite .
the main approach is often for very simplified systems using dynamical theory and other ad hoc approaches . here in this section ,
we first review the simulated annealing and its convergence , and we move onto the population - based algorithms such as pso .
we then take the recently developed firefly algorithm as a further example to carry out its convergence analysis .
simulated annealing ( sa ) is one of the widely used metaheuristics , and is also one of the most studies in terms of convergence analysis @xcite .
the essence of simulated annealing is a trajectory - based random walk of a single agent , starting from an initial guess @xmath0 .
the next move only depends on the current state or location and the acceptance probability @xmath1 .
this is essentially a markov chain whose transition probability from the current state to the next state is given by p= , where @xmath2 is boltzmann s constant , and @xmath3 is the temperature . here
the energy change @xmath4 can be linked with the change of objective values .
a few studies on the convergence of simulated annealing have paved the way for analysis for all simulated annealing - based algorithms @xcite .
bertsimas and tsitsiklis provided an excellent review of the convergence of sa under various assumptions @xcite . by using the assumptions that sa forms an inhomogeneous markov chain with finite states , they proved a probabilistic convergence function @xmath5 , rather than almost sure convergence , that p , where @xmath6 is the optimal set , and @xmath7 and @xmath8 are positive constants @xcite .
this is for the cooling schedule @xmath9 , where @xmath10 is the iteration counter or pseudo time .
these studies largely used markov chains as the main tool .
we will come back later to a more general framework of markov chain monte carlo ( mcmc ) in this paper @xcite .
particle swarm optimization ( pso ) was developed by kennedy and eberhart in 1995 @xcite , based on the swarm behaviour such as fish and bird schooling in nature . since then
, pso has generated much wider interests , and forms an exciting , ever - expanding research subject , called swarm intelligence .
pso has been applied to almost every area in optimization , computational intelligence , and design / scheduling applications .
the movement of a swarming particle consists of two major components : a stochastic component and a deterministic component .
each particle is attracted toward the position of the current global best @xmath11 and its own best location @xmath12 in history , while at the same time it has a tendency to move randomly .
let @xmath13 and @xmath14 be the position vector and velocity for particle @xmath15 , respectively .
the new velocity and location updating formulas are determined by _ i^t+1= _
i^t + _ 1 [ ^*-_i^t ] + _ 2 [ _ i^*-_i^t ] .
[ pso - speed-100 ] _ i^t+1=_i^t + _ i^t+1 , [ pso - speed-140 ] where @xmath16 and @xmath17 are two random vectors , and each entry taking the values between 0 and 1
. the parameters @xmath18 and @xmath19 are the learning parameters or acceleration constants , which can typically be taken as , say , @xmath20
. there are at least two dozen pso variants which extend the standard pso algorithm , and the most noticeable improvement is probably to use inertia function @xmath21 so that @xmath22 is replaced by @xmath23 where @xmath24 $ ] @xcite .
this is equivalent to introducing a virtual mass to stabilize the motion of the particles , and thus the algorithm is expected to converge more quickly .
the first convergence analysis of pso was carried out by clerc and kennedy in 2002 @xcite using the theory of dynamical systems .
mathematically , if we ignore the random factors , we can view the system formed by ( [ pso - speed-100 ] ) and ( [ pso - speed-140 ] ) as a dynamical system .
if we focus on a single particle @xmath15 and imagine that there is only one particle in this system , then the global best @xmath11 is the same as its current best @xmath12 . in this case
, we have _ i^t+1 = _ i^t + ( ^*-_i^t ) , = + , and _
i^t + _ i^t+1 . considering the 1d dynamical system for particle swarm optimization , we can replace @xmath11 by a parameter constant @xmath1 so that we can see if or not the particle of interest will converge towards @xmath1 . by setting @xmath25 and using the notations for dynamical systems , we have a simple dynamical system v_t+1=v_t + u_t , u_t+1 = -v_t + ( 1- ) u_t , or y_t+1 = a y_t , a= ( cccc 1 & & + -1 & & 1- ) , y_t= ( ccccv_t + u_t ) . the general solution of this dynamical system can be written as @xmath26 $ ] .
the system behaviour can be characterized by the eigenvalues @xmath27 of @xmath7 , and we have @xmath28 .
it can be seen clearly that @xmath29 leads to a bifurcation . following a straightforward analysis of this dynamical system , we can have three cases .
for @xmath30 , cyclic and/or quasi - cyclic trajectories exist . in this case , when randomness is gradually reduced , some convergence can be observed . for @xmath31
, non - cyclic behaviour can be expected and the distance from @xmath32 to the center @xmath33 is monotonically increasing with @xmath10 . in a special case @xmath29 , some convergence behaviour can be observed . for detailed analysis
, please refer to clerc and kennedy @xcite .
since @xmath1 is linked with the global best , as the iterations continue , it can be expected that all particles will aggregate towards the the global best .
firefly algorithm ( fa ) was developed by yang @xcite , which was based on the flashing patterns and behaviour of fireflies .
in essence , each firefly will be attracted to brighter ones , while at the same time , it explores and searches for prey randomly . in addition , the brightness of a firefly is determined by the landscape of the objective function . the movement of a firefly @xmath15 is attracted to another more attractive ( brighter ) firefly @xmath34 is determined by _
i^t+1 = _ i^t + _ 0 e^-r^2_ij ( _ j^t-_i^t ) + _ i^t , [ fa - equ-50 ] where the second term is due to the attraction .
the third term is randomization with @xmath18 being the randomization parameter , and @xmath35 is a vector of random numbers drawn from a gaussian distribution or other distributions . obviously ,
for a given firefly , there are often many more attractive fireflies , then we can either go through all of them via a loop or use the most attractive one . for multiple modal problems , using a loop while moving toward each brighter one is usually more effective , though this will lead to a slight increase of algorithm complexity .
here is @xmath36 $ ] is the attractiveness at @xmath37 , and @xmath38 is the @xmath39-norm or cartesian distance . for other problems such as scheduling ,
any measure that can effectively characterize the quantities of interest in the optimization problem can be used as the ` distance ' @xmath40 . for most implementations , we can take @xmath41 , @xmath42 and @xmath43 .
it is worth pointing out that ( [ fa - equ-50 ] ) is essentially a random walk biased towards the brighter fireflies .
if @xmath44 , it becomes a simple random walk .
furthermore , the randomization term can easily be extended to other distributions such as lvy flights @xcite . ) in the firefly algorithm and the transition between from periodic / multiple states to chaos .
[ fap - fig-100 ] , title="fig:",width=216,height=192 ] ) in the firefly algorithm and the transition between from periodic / multiple states to chaos .
[ fap - fig-100 ] , title="fig:",width=240,height=192 ] we now can carry out the convergence analysis for the firefly algorithm in a framework similar to clerc and kennedy s dynamical analysis . for simplicity , we start from the equation for firefly motion without the randomness term _ i^t+1=_i^t + _ 0 e^-r_ij^2 ( _ j^t - _ i^t ) . if we focus on a single agent , we can replace @xmath45 by the global best @xmath46 found so far , and we have _ i^t+1 = _
i^t + _ 0 e^-r_i^2 ( g-_i^t ) , where the distance @xmath47 can be given by the @xmath39-norm @xmath48 .
in an even simpler 1-d case , we can set @xmath49 , and we have y_t+1 = y_t - _ 0 e^-y_t^2 y_t .
[ fa - dynamics-25 ] we can see that @xmath50 is a scaling parameter which only affects the scales / size of the firefly movement .
in fact , we can let @xmath51 and we have u_t+1=u_t [ 1-_0 e^-u_t^2 ] .
[ fa - dynamics-150 ] these equations can be analyzed easily using the same methodology for studying the well - known logistic map u_t+1=u_t ( 1-u_t ) .
[ fa - chaos-55 ] the chaotic map is shown in fig .
[ fap - fig-100 ] , and the focus on the transition from periodic multiple states to chaotic behaviour is shown in the same figure . as we can see from fig .
[ fap - fig-100 ] that convergence can be achieved for @xmath52 .
there is a transition from periodic to chaos at @xmath53 .
this may be surprising , as the aim of designing a metaheuristic algorithm is to try to find the optimal solution efficiently and accurately .
however , chaotic behaviour is not necessarily a nuisance ; in fact , we can use it to the advantage of the firefly algorithm .
simple chaotic characteristics from ( [ fa - chaos-55 ] ) can often be used as an efficient mixing technique for generating diverse solutions .
statistically , the logistic mapping ( [ fa - chaos-55 ] ) with @xmath54 for the initial states in ( 0,1 ) corresponds a beta distribution b(u , p , q)= u^p-1 ( 1-u)^q-1 , when @xmath55 . here
@xmath56 is the gamma function ( z ) = _
0^ t^z-1 e^-t dt . in the case
when @xmath57 is an integer , we have @xmath58 . in addition , @xmath59 . from the algorithm implementation point of view
, we can use higher attractiveness @xmath60 during the early stage of iterations so that the fireflies can explore , even chaotically , the search space more effectively . as the search continues and convergence approaches , we can reduce the attractiveness @xmath60 gradually , which may increase the overall efficiency of the algorithm .
obviously , more studies are highly needed to confirm this . from the above convergence analysis ,
we know that there is no mathematical framework in general to provide insights into the working mechanisms , the stability and convergence of a give algorithm . despite the increasing popularity of metaheuristics ,
mathematical analysis remains fragmental , and many open problems need urgent attention .
monte carlo methods have been applied in many applications @xcite , including almost all areas of sciences and engineering .
for example , monte carlo methods are widely used in uncertainty and sensitivity analysis @xcite . from the statistical point of view
, most metaheuristic algorithms can be viewed in the framework of markov chains @xcite .
for example , simulated annealing @xcite is a markov chain , as the next state or new solution in sa only depends on the current state / solution and the transition probability . for a given markov chain with certain ergodicity ,
a stability probability distribution and convergence can be achieved .
now if look at the pso closely using the framework of markov chain monte carlo @xcite , each particle in pso essentially forms a markov chain , though this markov chain is biased towards to the current best , as the transition probability often leads to the acceptance of the move towards the current global best .
other population - based algorithms can also be viewed in this framework .
in essence , all metaheuristic algorithms with piecewise , interacting paths can be analyzed in the general framework of markov chain monte carlo .
the main challenge is to realize this and to use the appropriate markov chain theory to study metaheuristic algorithms .
more fruitful studies will surely emerge in the future .
metaheuristics can be considered as an efficient way to produce acceptable solutions by trial and error to a complex problem in a reasonably practical time .
the complexity of the problem of interest makes it impossible to search every possible solution or combination , the aim is to find good feasible solutions in an acceptable timescale .
there is no guarantee that the best solutions can be found , and we even do not know whether an algorithm will work and why if it does work .
the idea is to have an efficient but practical algorithm that will work most the time and is able to produce good quality solutions . among the found quality solutions
, it is expected some of them are nearly optimal , though there is no guarantee for such optimality .
the main components of any metaheuristic algorithms are : intensification and diversification , or exploitation and exploration @xcite .
diversification means to generate diverse solutions so as to explore the search space on the global scale , while intensification means to focus on the search in a local region by exploiting the information that a current good solution is found in this region .
this is in combination with with the selection of the best solutions . as discussed earlier ,
an important component in swarm intelligence and modern metaheuristics is randomization , which enables an algorithm to have the ability to jump out of any local optimum so as to search globally .
randomization can also be used for local search around the current best if steps are limited to a local region .
fine - tuning the randomness and balance of local search and global search is crucially important in controlling the performance of any metaheuristic algorithm .
randomization techniques can be a very simple method using uniform distributions , or more complex methods as those used in monte carlo simulations @xcite .
they can also be more elaborate , from brownian random walks to lvy flights .
a random walk is a random process which consists of taking a series of consecutive random steps .
mathematically speaking , let @xmath61 denotes the sum of each consecutive random step @xmath62 , then @xmath61 forms a random walk u_n=_i=1^n s_i = s_1 + ... + s_n = u_n-1 + s_n , [ walk - markov-50 ] where @xmath62 is a random step drawn from a random distribution .
this suggests that the next state @xmath61 will only depend the current existing state @xmath63 and the motion or transition @xmath61 from the existing state to the next state . in theory , as the number of steps @xmath64 increases
, the central limit theorem implies that the random walk ( [ walk - markov-50 ] ) should approaches a gaussian distribution .
in addition , there is no reason why each step length should be fixed .
in fact , the step size can also vary according to a known distribution .
if the step length obeys the gaussian distribution , the random walk becomes the standard brownian motion @xcite . from metaheuristic point of view
, all paths of search agents form a random walk , including a particle s trajectory in simulated annealing , a zig - zag path of a particle in pso , or the piecewise path of a firefly in fa .
the only difference is that transition probabilities are different , and change with time and locations . under simplest assumptions ,
we know that a gaussian distribution is stable . for a particle starts with an initial location @xmath0 , its final location @xmath65 after @xmath64 time steps is _
n = _ 0 + _
i=1^n _ i s_i , where @xmath66 is a parameters controlling the step sizes or scalings .
if @xmath62 is drawn from a normal distribution @xmath67 , then the conditions of stable distributions lead to a combined gaussian distribution _
n ~n ( _ * , _ * ^2 ) , _ * = _ i=1^n _ i _ i , _ * ^2=_i=1^n _ i [ _ i^2 + ( _ * -_i)^2 ] .
we can see that that the mean location changes with @xmath64 and the variances increases as @xmath64 increases , this makes it possible to reach any areas in the search space if @xmath64 is large enough
. a diffusion process can be viewed as a series of brownian motion , and the motion obeys the gaussian distribution . for this reason , standard diffusion
is often referred to as the gaussian diffusion .
as the mean of particle locations is obviously zero if @xmath68 , their variance will increase linearly with @xmath10 .
in general , in the @xmath69-dimensional space , the variance of brownian random walks can be written as ^2(t ) = |v_0|^2 t^2 + ( 2 d d ) t , where @xmath70 is the drift velocity of the system . here
@xmath71 is the effective diffusion coefficient which is related to the step length @xmath72 over a short time interval @xmath73 during each jump .
if the motion at each step is not gaussian , then the diffusion is called non - gaussian diffusion .
if the step length obeys other distribution , we have to deal with more generalized random walks .
a very special case is when the step length obeys the lvy distribution , such a random walk is called lvy flight or lvy walk . in nature ,
animals search for food in a random or quasi - random manner .
in general , the foraging path of an animal is effectively a random walk because the next move is based on the current location / state and the transition probability to the next location .
which direction it chooses depends implicitly on a probability which can be modelled mathematically @xcite .
for example , various studies have shown that the flight behaviour of many animals and insects has demonstrated the typical characteristics of lvy flights @xcite .
subsequently , such behaviour has been applied to optimization and optimal search , and preliminary results show its promising capability @xcite . in general ,
lvy distribution is stable , and can be defined in terms of a characteristic function or the following fourier transform f(k)= , 0 < 2 , where @xmath18 is a scale parameter .
the inverse of this integral is not easy , as it does not have nay analytical form , except for a few special cases @xcite . for the case of @xmath74
, we have @xmath75 $ ] , whose inverse fourier transform corresponds to a gaussian distribution .
another special case is @xmath76 , which corresponds to a cauchy distribution for the general case , the inverse integral l(s ) = _ 0^ ( k s ) dk , can be estimated only when @xmath72 is large .
we have l(s ) , s .
lvy flights are more efficient than brownian random walks in exploring unknown , large - scale search space .
there are many reasons to explain this efficiency , and one of them is due to the fact that the variance of lvy flights takes the following form ^2(t ) ~t^3- , 1 2 , which increases much faster than the linear relationship ( i.e. , @xmath77 ) of brownian random walks .
studies show that lvy flights can maximize the efficiency of resource searches in uncertain environments .
in fact , lvy flights have been observed among foraging patterns of albatrosses and fruit flies @xcite .
in addition , lvy flights have many applications . many physical phenomena such as the diffusion of fluorenscent molecules , cooling behavior and noise could show lvy - flight characteristics under the right conditions @xcite .
it is no exaggeration to say that metahueristic algorithms have been a great success in solving various tough optimization problems . despite this huge success
, there are many important questions which remain unanswered . we know how these heuristic algorithms work , and we also partly understand why these algorithms work . however , it is difficult to analyze mathematically why these algorithms are so successful , though significant progress has been made in the last few years @xcite .
however , many open problems still remain . for all population - based metaheuristics ,
multiple search agents form multiple interacting markov chains . at the moment ,
theoretical development in these areas are still at early stage .
therefore , the mathematical analysis concerning of the rate of convergence is very difficult , if not impossible .
apart from the mathematical analysis on a limited few metaheuristics , convergence of all other algorithms has not been proved mathematically , at least up to now .
any mathematical analysis will thus provide important insight into these algorithms .
it will also be valuable for providing new directions for further important modifications on these algorithms or even pointing out innovative ways of developing new algorithms . for almost all metaheuristics including future new algorithms ,
an important issue to be addresses is to provide a balanced trade - off between local intensification and global diversification @xcite . at present ,
different algorithm uses different techniques and mechanism with various parameters to control this , they are far from optimal .
important questions are : is there any optimal way to achieve this balance ?
if yes , how ? if not , what is the best we can achieve ?
furthermore , it is still only partly understood why different components of heuristics and metaheuristics interact in a coherent and balanced way so that they produce efficient algorithms which converge under the given conditions .
for example , why does a balanced combination of randomization and a deterministic component lead to a much more efficient algorithm ( than a purely deterministic and/or a purely random algorithm ) ?
how to measure or test if a balance is reached ? how to prove that the use of memory can significantly increase the search efficiency of an algorithm ?
under what conditions ?
in addition , from the well - known no - free - lunch theorems @xcite , we know that they have been proved for single objective optimization for finite search domains , but they do not hold for continuous infinite domains @xcite .
in addition , they remain unproved for multiobjective optimization . if they are proved to be true ( or not ) for multiobjective optimization , what are the implications for algorithm development ?
another important question is about the performance comparison . at the moment
, there is no agreed measure for comparing performance of different algorithms , though the absolute objective value and the number of function evaluations are two widely used measures .
however , a formal theoretical analysis is yet to be developed .
nature provides almost unlimited ways for problem - solving .
if we can observe carefully , we are surely inspired to develop more powerful and efficient new generation algorithms .
intelligence is a product of biological evolution in nature .
ultimately some intelligent algorithms ( or systems ) may appear in the future , so that they can evolve and optimally adapt to solve np - hard optimization problems efficiently and intelligently .
finally , a current trend is to use simplified metaheuristic algorithms to deal with complex optimization problems .
possibly , there is a need to develop more complex metaheuristic algorithms which can truly mimic the exact working mechanism of some natural or biological systems , leading to more powerful next - generation , self - regulating , self - evolving , and truly intelligent metaheuristics .
l. steinhofel , a. albrecht and c. k. wong , convergence analysis of simulated annealing - based algorithms solving flow shop scheduling problems , lecture notes in computer science , * 1767 * , 277 - 290 ( 2000 ) . | metaheuristic algorithms are becoming an important part of modern optimization .
a wide range of metaheuristic algorithms have emerged over the last two decades , and many metaheuristics such as particle swarm optimization are becoming increasingly popular . despite their popularity , mathematical analysis of these algorithms
lacks behind .
convergence analysis still remains unsolved for the majority of metaheuristic algorithms , while efficiency analysis is equally challenging . in this paper , we intend to provide an overview of convergence and efficiency studies of metaheuristics , and try to provide a framework for analyzing metaheuristics in terms of convergence and efficiency .
this can form a basis for analyzing other algorithms .
we also outline some open questions as further research topics .
+ * citation details * : yang , x. s. , ( 2011 ) .
metaheuristic optimization : algorithm analysis and open problems , in : proceedings of 10th international symposium on experimental algorithms ( sea 2011 ) ( eds .
p. m. pardalos and s. rebennack ) , kolimpari , chania , greece , may 5 - 7 ( 2011 ) , lecture notes in computer sciences , vol .
6630 , pp .
21 - 32 . | <s>[INST]optimization is an important subject with many important application , and algorithms for optimization are diverse with a wide range of successful applications @xcite . among these optimization algorithms ,
modern metaheuristics are becoming increasingly popular , leading to a new branch of optimization , called metaheuristic optimization .
most metaheuristic algorithms are nature - inspired @xcite , from simulated annealing @xcite to ant colony optimization @xcite , and from particle swarm optimization @xcite to cuckoo search @xcite .
since the appearance of swarm intelligence algorithms such as pso in the 1990s , more than a dozen new metaheuristic algorithms have been developed and these algorithms have been applied to almost all areas of optimization , design , scheduling and planning , data mining , machine intelligence , and many others .
thousands of research papers and dozens of books have been published @xcite . despite the rapid development of metaheuristics ,
their mathematical analysis remains partly unsolved , and many open problems need urgent attention .
this difficulty is largely due to the fact the interaction of various components in metaheuristic algorithms are highly nonlinear , complex , and stochastic .
studies have attempted to carry out convergence analysis @xcite , and some important results concerning pso were obtained @xcite . however , for other metaheuristics such as firefly algorithms and ant colony optimization , it remains an active , challenging topic . on the other hand , even we have not proved or can not prove their convergence , we still can compare the performance of various algorithms .
this has indeed formed a majority of current research in algorithm development in the research community of optimization and machine intelligence @xcite . in combinatorial optimization
, many important developments exist on complexity analysis , run time and convergence analysis @xcite . for continuous optimization , no - free - lunch - theorems do not hold @xcite . as a relatively young field
, many open problems still remain in the field of randomized search heuristics @xcite . in practice , most assume that metaheuristic algorithms tend to be less complex for implementation , and in many cases , problem sizes are not directly linked with the algorithm complexity .
however , metaheuristics can often solve very tough np - hard optimization , while our understanding of the efficiency and convergence of metaheuristics lacks far behind .
apart from the complex interactions among multiple search agents ( making the mathematical analysis intractable ) , another important issue is the various randomization techniques used for modern metaheuristics , from simple randomization such as uniform distribution to random walks , and to more elaborate lvy flights @xcite .
there is no unified approach to analyze these mathematically . in this paper , we intend to review the convergence of two metaheuristic algorithms including simulated annealing and pso , followed by the new convergence analysis of the firefly algorithm . then , we try to formulate a framework for algorithm analysis in terms of markov chain monte carlo .
we also try to analyze the mathematical and statistical foundations for randomization techniques from simple random walks to lvy flights . finally , we will discuss some of important open questions as further research topics .
the formulation and numerical studies of various metaheuristics have been the main focus of most research studies .
many successful applications have demonstrated the efficiency of metaheuristics in various context , either through comparison with other algorithms and/or applications to well - known problems .
in contrast , the mathematical analysis lacks behind , and convergence analysis has been carried out for only a minority few algorithms such as simulated annealing and particle swarm optimization @xcite .
the main approach is often for very simplified systems using dynamical theory and other ad hoc approaches . here in this section ,
we first review the simulated annealing and its convergence , and we move onto the population - based algorithms such as pso .
we then take the recently developed firefly algorithm as a further example to carry out its convergence analysis .
simulated annealing ( sa ) is one of the widely used metaheuristics , and is also one of the most studies in terms of convergence analysis @xcite .
the essence of simulated annealing is a trajectory - based random walk of a single agent , starting from an initial guess @xmath0 .
the next move only depends on the current state or location and the acceptance probability @xmath1 .
this is essentially a markov chain whose transition probability from the current state to the next state is given by p= , where @xmath2 is boltzmann s constant , and @xmath3 is the temperature . here
the energy change @xmath4 can be linked with the change of objective values .
a few studies on the convergence of simulated annealing have paved the way for analysis for all simulated annealing - based algorithms @xcite .
bertsimas and tsitsiklis provided an excellent review of the convergence of sa under various assumptions @xcite . by using the assumptions that sa forms an inhomogeneous markov chain with finite states , they proved a probabilistic convergence function @xmath5 , rather than almost sure convergence , that p , where @xmath6 is the optimal set , and @xmath7 and @xmath8 are positive constants @xcite .
this is for the cooling schedule @xmath9 , where @xmath10 is the iteration counter or pseudo time .
these studies largely used markov chains as the main tool .
we will come back later to a more general framework of markov chain monte carlo ( mcmc ) in this paper @xcite .
particle swarm optimization ( pso ) was developed by kennedy and eberhart in 1995 @xcite , based on the swarm behaviour such as fish and bird schooling in nature . since then
, pso has generated much wider interests , and forms an exciting , ever - expanding research subject , called swarm intelligence .
pso has been applied to almost every area in optimization , computational intelligence , and design / scheduling applications .
the movement of a swarming particle consists of two major components : a stochastic component and a deterministic component .
each particle is attracted toward the position of the current global best @xmath11 and its own best location @xmath12 in history , while at the same time it has a tendency to move randomly .
let @xmath13 and @xmath14 be the position vector and velocity for particle @xmath15 , respectively .
the new velocity and location updating formulas are determined by _ i^t+1= _
i^t + _ 1 [ ^*-_i^t ] + _ 2 [ _ i^*-_i^t ] .
[ pso - speed-100 ] _ i^t+1=_i^t + _ i^t+1 , [ pso - speed-140 ] where @xmath16 and @xmath17 are two random vectors , and each entry taking the values between 0 and 1
. the parameters @xmath18 and @xmath19 are the learning parameters or acceleration constants , which can typically be taken as , say , @xmath20
. there are at least two dozen pso variants which extend the standard pso algorithm , and the most noticeable improvement is probably to use inertia function @xmath21 so that @xmath22 is replaced by @xmath23 where @xmath24 $ ] @xcite .
this is equivalent to introducing a virtual mass to stabilize the motion of the particles , and thus the algorithm is expected to converge more quickly .
the first convergence analysis of pso was carried out by clerc and kennedy in 2002 @xcite using the theory of dynamical systems .
mathematically , if we ignore the random factors , we can view the system formed by ( [ pso - speed-100 ] ) and ( [ pso - speed-140 ] ) as a dynamical system .
if we focus on a single particle @xmath15 and imagine that there is only one particle in this system , then the global best @xmath11 is the same as its current best @xmath12 . in this case
, we have _ i^t+1 = _ i^t + ( ^*-_i^t ) , = + , and _
i^t + _ i^t+1 . considering the 1d dynamical system for particle swarm optimization , we can replace @xmath11 by a parameter constant @xmath1 so that we can see if or not the particle of interest will converge towards @xmath1 . by setting @xmath25 and using the notations for dynamical systems , we have a simple dynamical system v_t+1=v_t + u_t , u_t+1 = -v_t + ( 1- ) u_t , or y_t+1 = a y_t , a= ( cccc 1 & & + -1 & & 1- ) , y_t= ( ccccv_t + u_t ) . the general solution of this dynamical system can be written as @xmath26 $ ] .
the system behaviour can be characterized by the eigenvalues @xmath27 of @xmath7 , and we have @xmath28 .
it can be seen clearly that @xmath29 leads to a bifurcation . following a straightforward analysis of this dynamical system , we can have three cases .
for @xmath30 , cyclic and/or quasi - cyclic trajectories exist . in this case , when randomness is gradually reduced , some convergence can be observed . for @xmath31
, non - cyclic behaviour can be expected and the distance from @xmath32 to the center @xmath33 is monotonically increasing with @xmath10 . in a special case @xmath29 , some convergence behaviour can be observed . for detailed analysis
, please refer to clerc and kennedy @xcite .
since @xmath1 is linked with the global best , as the iterations continue , it can be expected that all particles will aggregate towards the the global best .
firefly algorithm ( fa ) was developed by yang @xcite , which was based on the flashing patterns and behaviour of fireflies .
in essence , each firefly will be attracted to brighter ones , while at the same time , it explores and searches for prey randomly . in addition , the brightness of a firefly is determined by the landscape of the objective function . the movement of a firefly @xmath15 is attracted to another more attractive ( brighter ) firefly @xmath34 is determined by _
i^t+1 = _ i^t + _ 0 e^-r^2_ij ( _ j^t-_i^t ) + _ i^t , [ fa - equ-50 ] where the second term is due to the attraction .
the third term is randomization with @xmath18 being the randomization parameter , and @xmath35 is a vector of random numbers drawn from a gaussian distribution or other distributions . obviously ,
for a given firefly , there are often many more attractive fireflies , then we can either go through all of them via a loop or use the most attractive one . for multiple modal problems , using a loop while moving toward each brighter one is usually more effective , though this will lead to a slight increase of algorithm complexity .
here is @xmath36 $ ] is the attractiveness at @xmath37 , and @xmath38 is the @xmath39-norm or cartesian distance . for other problems such as scheduling ,
any measure that can effectively characterize the quantities of interest in the optimization problem can be used as the ` distance ' @xmath40 . for most implementations , we can take @xmath41 , @xmath42 and @xmath43 .
it is worth pointing out that ( [ fa - equ-50 ] ) is essentially a random walk biased towards the brighter fireflies .
if @xmath44 , it becomes a simple random walk .
furthermore , the randomization term can easily be extended to other distributions such as lvy flights @xcite . ) in the firefly algorithm and the transition between from periodic / multiple states to chaos .
[ fap - fig-100 ] , title="fig:",width=216,height=192 ] ) in the firefly algorithm and the transition between from periodic / multiple states to chaos .
[ fap - fig-100 ] , title="fig:",width=240,height=192 ] we now can carry out the convergence analysis for the firefly algorithm in a framework similar to clerc and kennedy s dynamical analysis . for simplicity , we start from the equation for firefly motion without the randomness term _ i^t+1=_i^t + _ 0 e^-r_ij^2 ( _ j^t - _ i^t ) . if we focus on a single agent , we can replace @xmath45 by the global best @xmath46 found so far , and we have _ i^t+1 = _
i^t + _ 0 e^-r_i^2 ( g-_i^t ) , where the distance @xmath47 can be given by the @xmath39-norm @xmath48 .
in an even simpler 1-d case , we can set @xmath49 , and we have y_t+1 = y_t - _ 0 e^-y_t^2 y_t .
[ fa - dynamics-25 ] we can see that @xmath50 is a scaling parameter which only affects the scales / size of the firefly movement .
in fact , we can let @xmath51 and we have u_t+1=u_t [ 1-_0 e^-u_t^2 ] .
[ fa - dynamics-150 ] these equations can be analyzed easily using the same methodology for studying the well - known logistic map u_t+1=u_t ( 1-u_t ) .
[ fa - chaos-55 ] the chaotic map is shown in fig .
[ fap - fig-100 ] , and the focus on the transition from periodic multiple states to chaotic behaviour is shown in the same figure . as we can see from fig .
[ fap - fig-100 ] that convergence can be achieved for @xmath52 .
there is a transition from periodic to chaos at @xmath53 .
this may be surprising , as the aim of designing a metaheuristic algorithm is to try to find the optimal solution efficiently and accurately .
however , chaotic behaviour is not necessarily a nuisance ; in fact , we can use it to the advantage of the firefly algorithm .
simple chaotic characteristics from ( [ fa - chaos-55 ] ) can often be used as an efficient mixing technique for generating diverse solutions .
statistically , the logistic mapping ( [ fa - chaos-55 ] ) with @xmath54 for the initial states in ( 0,1 ) corresponds a beta distribution b(u , p , q)= u^p-1 ( 1-u)^q-1 , when @xmath55 . here
@xmath56 is the gamma function ( z ) = _
0^ t^z-1 e^-t dt . in the case
when @xmath57 is an integer , we have @xmath58 . in addition , @xmath59 . from the algorithm implementation point of view
, we can use higher attractiveness @xmath60 during the early stage of iterations so that the fireflies can explore , even chaotically , the search space more effectively . as the search continues and convergence approaches , we can reduce the attractiveness @xmath60 gradually , which may increase the overall efficiency of the algorithm .
obviously , more studies are highly needed to confirm this . from the above convergence analysis ,
we know that there is no mathematical framework in general to provide insights into the working mechanisms , the stability and convergence of a give algorithm . despite the increasing popularity of metaheuristics ,
mathematical analysis remains fragmental , and many open problems need urgent attention .
monte carlo methods have been applied in many applications @xcite , including almost all areas of sciences and engineering .
for example , monte carlo methods are widely used in uncertainty and sensitivity analysis @xcite . from the statistical point of view
, most metaheuristic algorithms can be viewed in the framework of markov chains @xcite .
for example , simulated annealing @xcite is a markov chain , as the next state or new solution in sa only depends on the current state / solution and the transition probability . for a given markov chain with certain ergodicity ,
a stability probability distribution and convergence can be achieved .
now if look at the pso closely using the framework of markov chain monte carlo @xcite , each particle in pso essentially forms a markov chain , though this markov chain is biased towards to the current best , as the transition probability often leads to the acceptance of the move towards the current global best .
other population - based algorithms can also be viewed in this framework .
in essence , all metaheuristic algorithms with piecewise , interacting paths can be analyzed in the general framework of markov chain monte carlo .
the main challenge is to realize this and to use the appropriate markov chain theory to study metaheuristic algorithms .
more fruitful studies will surely emerge in the future .
metaheuristics can be considered as an efficient way to produce acceptable solutions by trial and error to a complex problem in a reasonably practical time .
the complexity of the problem of interest makes it impossible to search every possible solution or combination , the aim is to find good feasible solutions in an acceptable timescale .
there is no guarantee that the best solutions can be found , and we even do not know whether an algorithm will work and why if it does work .
the idea is to have an efficient but practical algorithm that will work most the time and is able to produce good quality solutions . among the found quality solutions
, it is expected some of them are nearly optimal , though there is no guarantee for such optimality .
the main components of any metaheuristic algorithms are : intensification and diversification , or exploitation and exploration @xcite .
diversification means to generate diverse solutions so as to explore the search space on the global scale , while intensification means to focus on the search in a local region by exploiting the information that a current good solution is found in this region .
this is in combination with with the selection of the best solutions . as discussed earlier ,
an important component in swarm intelligence and modern metaheuristics is randomization , which enables an algorithm to have the ability to jump out of any local optimum so as to search globally .
randomization can also be used for local search around the current best if steps are limited to a local region .
fine - tuning the randomness and balance of local search and global search is crucially important in controlling the performance of any metaheuristic algorithm .
randomization techniques can be a very simple method using uniform distributions , or more complex methods as those used in monte carlo simulations @xcite .
they can also be more elaborate , from brownian random walks to lvy flights .
a random walk is a random process which consists of taking a series of consecutive random steps .
mathematically speaking , let @xmath61 denotes the sum of each consecutive random step @xmath62 , then @xmath61 forms a random walk u_n=_i=1^n s_i = s_1 + ... + s_n = u_n-1 + s_n , [ walk - markov-50 ] where @xmath62 is a random step drawn from a random distribution .
this suggests that the next state @xmath61 will only depend the current existing state @xmath63 and the motion or transition @xmath61 from the existing state to the next state . in theory , as the number of steps @xmath64 increases
, the central limit theorem implies that the random walk ( [ walk - markov-50 ] ) should approaches a gaussian distribution .
in addition , there is no reason why each step length should be fixed .
in fact , the step size can also vary according to a known distribution .
if the step length obeys the gaussian distribution , the random walk becomes the standard brownian motion @xcite . from metaheuristic point of view
, all paths of search agents form a random walk , including a particle s trajectory in simulated annealing , a zig - zag path of a particle in pso , or the piecewise path of a firefly in fa .
the only difference is that transition probabilities are different , and change with time and locations . under simplest assumptions ,
we know that a gaussian distribution is stable . for a particle starts with an initial location @xmath0 , its final location @xmath65 after @xmath64 time steps is _
n = _ 0 + _
i=1^n _ i s_i , where @xmath66 is a parameters controlling the step sizes or scalings .
if @xmath62 is drawn from a normal distribution @xmath67 , then the conditions of stable distributions lead to a combined gaussian distribution _
n ~n ( _ * , _ * ^2 ) , _ * = _ i=1^n _ i _ i , _ * ^2=_i=1^n _ i [ _ i^2 + ( _ * -_i)^2 ] .
we can see that that the mean location changes with @xmath64 and the variances increases as @xmath64 increases , this makes it possible to reach any areas in the search space if @xmath64 is large enough
. a diffusion process can be viewed as a series of brownian motion , and the motion obeys the gaussian distribution . for this reason , standard diffusion
is often referred to as the gaussian diffusion .
as the mean of particle locations is obviously zero if @xmath68 , their variance will increase linearly with @xmath10 .
in general , in the @xmath69-dimensional space , the variance of brownian random walks can be written as ^2(t ) = |v_0|^2 t^2 + ( 2 d d ) t , where @xmath70 is the drift velocity of the system . here
@xmath71 is the effective diffusion coefficient which is related to the step length @xmath72 over a short time interval @xmath73 during each jump .
if the motion at each step is not gaussian , then the diffusion is called non - gaussian diffusion .
if the step length obeys other distribution , we have to deal with more generalized random walks .
a very special case is when the step length obeys the lvy distribution , such a random walk is called lvy flight or lvy walk . in nature ,
animals search for food in a random or quasi - random manner .
in general , the foraging path of an animal is effectively a random walk because the next move is based on the current location / state and the transition probability to the next location .
which direction it chooses depends implicitly on a probability which can be modelled mathematically @xcite .
for example , various studies have shown that the flight behaviour of many animals and insects has demonstrated the typical characteristics of lvy flights @xcite .
subsequently , such behaviour has been applied to optimization and optimal search , and preliminary results show its promising capability @xcite . in general ,
lvy distribution is stable , and can be defined in terms of a characteristic function or the following fourier transform f(k)= , 0 < 2 , where @xmath18 is a scale parameter .
the inverse of this integral is not easy , as it does not have nay analytical form , except for a few special cases @xcite . for the case of @xmath74
, we have @xmath75 $ ] , whose inverse fourier transform corresponds to a gaussian distribution .
another special case is @xmath76 , which corresponds to a cauchy distribution for the general case , the inverse integral l(s ) = _ 0^ ( k s ) dk , can be estimated only when @xmath72 is large .
we have l(s ) , s .
lvy flights are more efficient than brownian random walks in exploring unknown , large - scale search space .
there are many reasons to explain this efficiency , and one of them is due to the fact that the variance of lvy flights takes the following form ^2(t ) ~t^3- , 1 2 , which increases much faster than the linear relationship ( i.e. , @xmath77 ) of brownian random walks .
studies show that lvy flights can maximize the efficiency of resource searches in uncertain environments .
in fact , lvy flights have been observed among foraging patterns of albatrosses and fruit flies @xcite .
in addition , lvy flights have many applications . many physical phenomena such as the diffusion of fluorenscent molecules , cooling behavior and noise could show lvy - flight characteristics under the right conditions @xcite .
it is no exaggeration to say that metahueristic algorithms have been a great success in solving various tough optimization problems . despite this huge success
, there are many important questions which remain unanswered . we know how these heuristic algorithms work , and we also partly understand why these algorithms work . however , it is difficult to analyze mathematically why these algorithms are so successful , though significant progress has been made in the last few years @xcite .
however , many open problems still remain . for all population - based metaheuristics ,
multiple search agents form multiple interacting markov chains . at the moment ,
theoretical development in these areas are still at early stage .
therefore , the mathematical analysis concerning of the rate of convergence is very difficult , if not impossible .
apart from the mathematical analysis on a limited few metaheuristics , convergence of all other algorithms has not been proved mathematically , at least up to now .
any mathematical analysis will thus provide important insight into these algorithms .
it will also be valuable for providing new directions for further important modifications on these algorithms or even pointing out innovative ways of developing new algorithms . for almost all metaheuristics including future new algorithms ,
an important issue to be addresses is to provide a balanced trade - off between local intensification and global diversification @xcite . at present ,
different algorithm uses different techniques and mechanism with various parameters to control this , they are far from optimal .
important questions are : is there any optimal way to achieve this balance ?
if yes , how ? if not , what is the best we can achieve ?
furthermore , it is still only partly understood why different components of heuristics and metaheuristics interact in a coherent and balanced way so that they produce efficient algorithms which converge under the given conditions .
for example , why does a balanced combination of randomization and a deterministic component lead to a much more efficient algorithm ( than a purely deterministic and/or a purely random algorithm ) ?
how to measure or test if a balance is reached ? how to prove that the use of memory can significantly increase the search efficiency of an algorithm ?
under what conditions ?
in addition , from the well - known no - free - lunch theorems @xcite , we know that they have been proved for single objective optimization for finite search domains , but they do not hold for continuous infinite domains @xcite .
in addition , they remain unproved for multiobjective optimization . if they are proved to be true ( or not ) for multiobjective optimization , what are the implications for algorithm development ?
another important question is about the performance comparison . at the moment
, there is no agreed measure for comparing performance of different algorithms , though the absolute objective value and the number of function evaluations are two widely used measures .
however , a formal theoretical analysis is yet to be developed .
nature provides almost unlimited ways for problem - solving .
if we can observe carefully , we are surely inspired to develop more powerful and efficient new generation algorithms .
intelligence is a product of biological evolution in nature .
ultimately some intelligent algorithms ( or systems ) may appear in the future , so that they can evolve and optimally adapt to solve np - hard optimization problems efficiently and intelligently .
finally , a current trend is to use simplified metaheuristic algorithms to deal with complex optimization problems .
possibly , there is a need to develop more complex metaheuristic algorithms which can truly mimic the exact working mechanism of some natural or biological systems , leading to more powerful next - generation , self - regulating , self - evolving , and truly intelligent metaheuristics .
l. steinhofel , a. albrecht and c. k. wong , convergence analysis of simulated annealing - based algorithms solving flow shop scheduling problems , lecture notes in computer science , * 1767 * , 277 - 290 ( 2000 ) .[/INST] metaheuristic algorithms are becoming an important part of modern optimization .
a wide range of metaheuristic algorithms have emerged over the last two decades , and many metaheuristics such as particle swarm optimization are becoming increasingly popular . despite their popularity , mathematical analysis of these algorithms
lacks behind .
convergence analysis still remains unsolved for the majority of metaheuristic algorithms , while efficiency analysis is equally challenging . in this paper , we intend to provide an overview of convergence and efficiency studies of metaheuristics , and try to provide a framework for analyzing metaheuristics in terms of convergence and efficiency .
this can form a basis for analyzing other algorithms .
we also outline some open questions as further research topics .
+ * citation details * : yang , x. s. , ( 2011 ) .
metaheuristic optimization : algorithm analysis and open problems , in : proceedings of 10th international symposium on experimental algorithms ( sea 2011 ) ( eds .
p. m. pardalos and s. rebennack ) , kolimpari , chania , greece , may 5 - 7 ( 2011 ) , lecture notes in computer sciences , vol .
6630 , pp .
21 - 32 . </s> |
helicobacter pylori ( h. pylori ) infections usually occur during childhood , continue throughout the life , and cause severe diseases such as gastritis , gastric ulcer , gastric carcinoma , and duodenum ulcer in adulthood .
h. pylori is a well - known gastric pathogen infecting more than half of the world 's people .
the outcomes of h. pylori infection seem to be dependent on some factors like gene regulation factors , genetic predisposition of the patient , receptor gene polymorphisms , particular cytokine , constituents , and environmental influences [ 2 , 3 ] .
fortunately , most of the infected children do not develop any complications ; however , the immunological events which usually develop in the children gastric mucosa are probably decisive in the immune response determining the final outcome the infection .
the colonization of the stomach by this pathogen bacterium causes an inflammatory response and recruits neutrophils , lymphocytes , dendritic cells , and macrophages , to the gastric mucosa [ 4 , 5 ] .
there are complex mechanisms by which h. pylori may start and maintain the local immune response ; however , cytokines produced by both adaptive immune and innate systems may lead to the development of gastric mucosa - associated lymphoid tissue lymphoma , gastric adenocarcinoma , and other ulcerative diseases ; studies in h. pylori infection have revealed that childhood h. pylori infection is usually associated with significantly lower levels of gastric inflammation and ulceration in comparison to adults .
therefore , this review study was aimed to provide the critical findings of the available literature about comparative immune system in children and adults with h. pylori infection .
helicobacter pylori may express the virulence factors associated with inflammation as well as inflammatory symptoms in infected patients .
the main pathogenicity factors of helicobacter pylori include -glutamyl transpeptidase ( ggt ) , cytotoxin - associated gene a ( caga ) product , and virulence components vacuolating toxin ( vaca ) , in addition to pathogen - associated molecular patterns ( pamps ) such as flagella and lipopolysaccharide ( lps ) [ 69 ] . the cytotoxin - associated gene ( cag ) pathogenicity island ( pai ) is one of these factors which has been extensively studied in regard to inflammation [ 1012 ] .
colonization with the strains that possess caga is more frequently associated with peptic ulceration gastric adenocarcinoma or other gastric mucosal complications than the caga strains [ 13 , 14 ] .
it has been shown that caga may play a role in production of il-8 as well as activation of nuclear factor kappa - b ( nf-b ) .
furthermore , expression of caga induces production of il-8 and translocation of nf-b nuclear in gastric epithelial cells [ 13 , 16 ] .
the vaca from h. pylori is capable of inducing intracellular vacuolation in gastric epithelial cells .
hence , it has been hypothesized that it may contribute in damage of gastric and duodenal mucosa which ultimately leads to ulcer formation , in vivo .
moreover , the bacterial virulence factors vaca and caga have important roles in pathogenesis of h. pylori infection .
others like blood group antigen - binding adhesion ( baba ) , outer inflammatory protein ( oipa ) , sialic acid - binding adhesion ( saba ) , icea ( induced by contact with epithelium ) , and duodenal ulcer promoting gene ( dupa ) may promote colonization of the mucosa , too . in regard to virulence factors caga and vaca , these bacteria are very heterogeneous .
a lot of evidences have revealed that these genetic variations may have an important role in the outcome of infection [ 19 , 20 ] .
t helper ( th ) cells have been shown to differentiate into functional classes of two major cd4 including th1 cells ( able to produce some cytokines such as il-2 and ifn- ) and th2 cells ( producing cytokines like il-4 , il-5 , and il-10 ) [ 21 , 22 ] .
th1 cells mediated cell immunity , which has an important role against intracellular parasites . however , th2 generates humoral immunity as well as prevention of intestinal helminthes .
other than th1/th2 paradigm , a unique subset of il-17 producing th17 cells has been discovered [ 2426 ] .
it has been revealed that il-17 possesses 6 family members ( il-17a f ) , il-17a ( simply called il-17 ) being the prototypic il-17 family member [ 28 , 29 ] .
furthermore , il-17a exerts proinflammatory effects by stimulation of the production of chemokines such as il-1 , il-6 , cytokines , monocyte chemoattractant protein-1 , and upregulation of cell adhesion molecules like vascular cell adhesion molecule-1 and intercellular adhesion molecule-1 .
the il-17a plays a crucial role in induction of autoimmune diseases such as inflammatory bowel disease ( ibd ) , experimental autoimmune encephalomyelitis ( eae ) , and rheumatoid arthritis ( ra ) , as well as chronic inflammatory diseases [ 3033 ] .
regulatory t ( treg ) cells , by proliferation of antigen specific t cells and suppressing the activation , have important role in chronic inflammation .
it should be noted that depletion or dysfunction of treg cells is usually associated with inflammatory bowel disease , allergy , and autoimmune disease .
treg cells comprise different subsets : tr1 cells secreting interleukin il-10 , th3 cells characterized by transforming growth factor ( tgf-1 ) secretion , and naturally occurring foxp3-expressing cd4cd25 treg cells [ 35 , 36 ] .
the foxp3cd4cd25 treg cells are further divided into two subsets : thymus derived naturally occurring foxp3cd4cd25 treg cells and peripherally induced foxp3cd4cd25 treg cells .
the human gastric mucosal biopsies revealed that people who were persistently infected with h. pylori , in comparison to uninfected ones , show an increased and higher level of infiltrated various types of leukocytes . in these specimens , lymphocytes ( t and b cells ) , monocytes , mast cells , neutrophils , macrophages ,
cd4 t cells , b cells and dendritic cells may be organized in lymphoid follicles indicating ongoing chronic immune responses and antigen presentation . in peripheral blood and gastric mucosa of infected humans ,
the h. pylori - specific cd4 t cells are detectable which is not detectable in uninfected individuals .
the cytokines such as tnf- , ifn- , il-1 , il-6 , il-7 , il-8 , il-10 , il-17 , il-18 , and il-23 have usually increased levels in the stomach of h. pylori - infected patients in comparison to the uninfected subjects [ 2 , 41 , 42 ] .
il-4 is not usually detectable in the gastric mucosa of h. pylori - infected patients .
hence , to show , in children , the mucosal regulation of h. pylori infection , which can provide a window to the early host response to bacteria , the mucosal cytokine response to the infection , the associated cellular infiltrate , and the characterized bacteria might be helpful
. studies on h. pylori - infected children and adults have shown that children possess reduced gastric inflammation in comparison to the infected adults , in spite of similarity in h. pylori colonization level . furthermore , inflammation in children
has been shown to be less in comparison to that of adults , indicating a downregulation in immune response to infection in children [ 44 , 45 ] .
moreover , the sequence analysis revealed that the bacteria isolated from the infected children and adults might have similar caga and vaca gene profiles .
the difference in bacterial strains and common virulence factors were not the cause of low level of inflammation in infected children in comparison to adults .
pylori - infected children in comparison to infected adults possess lower levels of protein and gastric il-17-specific mrna as well as fewer gastric th17 cells , indicating more reduction in the mucosal th17 response in infected children .
moreover , the gastric mucosa of the infected children has lower level of ifn- mrna , confirming the findings indicated of reduced th1 response in children with h. pylori infection [ 46 , 47 ] .
recent study indicated that the gastric concentrations of cytokines representative of the innate and th1 response were higher in the h. pylori - positive than in the h. pylori - negative children and adults .
the gastric concentrations of il-1 and tnf- were significantly higher , while those of il-2 , il-12p70 , and ifn- were lower in the infected children than in the infected adults . in the infected children , the gastric concentration of il-1 , il-2 , il-12p70 , and ifn- increased , whereas in adults
the gastric concentrations of ifn- and il-12p70 decreased with aging . increased gastric concentration of th1-associated cytokines correlated with increased degree of gastritis , that is , the background lesion for the development of the h. pylori - associated severe diseases .
treg cells are described as the key regulator of the immune system in the maintenance of immunologic tolerance .
recently , the close relationship between h. pylori infection and immunosuppressive treg cells has been reported in animal and human models .
treg cells suppress h. pylori - induced th1-mediated immune response to contribute to the bacteria 's persistent colonization in the gastric mucosa and therefore may play a major role in inducing chronic gastritis .
the tgf-1 and il-10 gastric levels and the gastric number of treg foxp3 cells in h. pylori - positive groups are higher in children than in adults ( table 1 ) [ 44 , 46 , 4951 ] .
tgf- is required for the differentiation of both treg cells and th17 by inducing key transcription factors , foxp3 and rort / rorc , respectively [ 5254 ] .
but , in absence of il-6 , an exclusive treg differentiation might occur as foxp3 is capable of associating with and inhibiting the rort .
in contrast , in presence of il-6 , this inhibition might be abrogated allowing th17 differentiation . in a paradoxical pattern ,
the gastric concentration of il-6 is usually less in infected adults than in infected children . in this regard
, it might be hypothesized that these results are due to the higher gastric levels of il-23 in adults , compared with children , which might prevent the amplification / stabilization of the shifted th17 cells .
the other possibility might be the higher level of tgf- in the gastric milieu of infected children .
it should be noted that , at low levels , tgf- synergizes with il-6 to promote il-23 receptor expression in favor of th17 cell commitment .
however , the high level of tgf- represses il-23 receptor expression favoring foxp3 treg cell differentiation [ 49 , 56 ] . a recently published study revealed that il-6 overproductions by il-6 transgenic mice do not affect the function and development of natural treg . in this regard ,
the predominant treg differentiation in children infected with h. pylori might account for more susceptibility of children to the h. pylori infection as well as to the bacterium persistence .
study in mouse stomach showed that h. pylori - induced dendritic cells skew the th17/treg balance toward a treg - biased response that suppresses th17 immunity through a caga and vaca independent , tgf- and il-10-dependent mechanism [ 58 , 59 ] .
in support of these findings , recent study showed that h. pylori was capable of stimulating human gastric dendritic cells to produce il-10 , potentially supplementing treg suppression of inflammation in the gastric mucosa [ 60 , 61 ] ( figure 1 ) . from these findings
we might conclude that h. pylori - induced gastritis in adult is the consequence of both th1 and th17 immune - mediated inflammatory pathway involvement and that both pathways might be downregulated in the gastric mucosa of infected children .
in conclusion , h. pylori infection in children is associated with high treg response , as well as low th1 and th17 response [ 44 , 46 ] .
but , h. pylori - specific th17/th1 detection in chronically infected patients may reveal that the initial response is progressively lost [ 43 , 62 ] , indicating that , with progression of time , the mucosal immune system probably identifies h. pylori , as a pathogen .
hence , th1 , th17 , and treg results may imply gastric mucosal response to h. pylori .
more data from immune - mediated mechanism(s ) of mucosal inflammation is required to provide strategies against this challenging pathogen , particularly for children who are living in countries with high rate of gastric cancer and/or h. pylori infection . | helicobacter pylori ( h. pylori ) infection is generally acquired during early childhood ; therefore , the immune response which usually takes place at this age may influence or even determine susceptibility to the infection contributing to the clinical outcomes in adulthood .
several cytokines including il-6 , il-10 , and tgf-1 as well as foxp3 + cell numbers have been shown to be higher ; however , some other cytokines consisting of il-1 , il-17a , and il-23 are lower in infected children than in infected adults .
immune response to h. pylori infection in children is predominant treg instead of th17 cell response .
these results indicate that immune system responses probably play a role in persistent h. pylori infection .
childhood h. pylori infection is also associated with significantly lower levels of inflammation and ulceration compared with adults .
this review , therefore , aimed to provide critical findings of the available literature about comparative immune system in children and adults with h. pylori infection . | <s>[INST]helicobacter pylori ( h. pylori ) infections usually occur during childhood , continue throughout the life , and cause severe diseases such as gastritis , gastric ulcer , gastric carcinoma , and duodenum ulcer in adulthood .
h. pylori is a well - known gastric pathogen infecting more than half of the world 's people .
the outcomes of h. pylori infection seem to be dependent on some factors like gene regulation factors , genetic predisposition of the patient , receptor gene polymorphisms , particular cytokine , constituents , and environmental influences [ 2 , 3 ] .
fortunately , most of the infected children do not develop any complications ; however , the immunological events which usually develop in the children gastric mucosa are probably decisive in the immune response determining the final outcome the infection .
the colonization of the stomach by this pathogen bacterium causes an inflammatory response and recruits neutrophils , lymphocytes , dendritic cells , and macrophages , to the gastric mucosa [ 4 , 5 ] .
there are complex mechanisms by which h. pylori may start and maintain the local immune response ; however , cytokines produced by both adaptive immune and innate systems may lead to the development of gastric mucosa - associated lymphoid tissue lymphoma , gastric adenocarcinoma , and other ulcerative diseases ; studies in h. pylori infection have revealed that childhood h. pylori infection is usually associated with significantly lower levels of gastric inflammation and ulceration in comparison to adults .
therefore , this review study was aimed to provide the critical findings of the available literature about comparative immune system in children and adults with h. pylori infection .
helicobacter pylori may express the virulence factors associated with inflammation as well as inflammatory symptoms in infected patients .
the main pathogenicity factors of helicobacter pylori include -glutamyl transpeptidase ( ggt ) , cytotoxin - associated gene a ( caga ) product , and virulence components vacuolating toxin ( vaca ) , in addition to pathogen - associated molecular patterns ( pamps ) such as flagella and lipopolysaccharide ( lps ) [ 69 ] . the cytotoxin - associated gene ( cag ) pathogenicity island ( pai ) is one of these factors which has been extensively studied in regard to inflammation [ 1012 ] .
colonization with the strains that possess caga is more frequently associated with peptic ulceration gastric adenocarcinoma or other gastric mucosal complications than the caga strains [ 13 , 14 ] .
it has been shown that caga may play a role in production of il-8 as well as activation of nuclear factor kappa - b ( nf-b ) .
furthermore , expression of caga induces production of il-8 and translocation of nf-b nuclear in gastric epithelial cells [ 13 , 16 ] .
the vaca from h. pylori is capable of inducing intracellular vacuolation in gastric epithelial cells .
hence , it has been hypothesized that it may contribute in damage of gastric and duodenal mucosa which ultimately leads to ulcer formation , in vivo .
moreover , the bacterial virulence factors vaca and caga have important roles in pathogenesis of h. pylori infection .
others like blood group antigen - binding adhesion ( baba ) , outer inflammatory protein ( oipa ) , sialic acid - binding adhesion ( saba ) , icea ( induced by contact with epithelium ) , and duodenal ulcer promoting gene ( dupa ) may promote colonization of the mucosa , too . in regard to virulence factors caga and vaca , these bacteria are very heterogeneous .
a lot of evidences have revealed that these genetic variations may have an important role in the outcome of infection [ 19 , 20 ] .
t helper ( th ) cells have been shown to differentiate into functional classes of two major cd4 including th1 cells ( able to produce some cytokines such as il-2 and ifn- ) and th2 cells ( producing cytokines like il-4 , il-5 , and il-10 ) [ 21 , 22 ] .
th1 cells mediated cell immunity , which has an important role against intracellular parasites . however , th2 generates humoral immunity as well as prevention of intestinal helminthes .
other than th1/th2 paradigm , a unique subset of il-17 producing th17 cells has been discovered [ 2426 ] .
it has been revealed that il-17 possesses 6 family members ( il-17a f ) , il-17a ( simply called il-17 ) being the prototypic il-17 family member [ 28 , 29 ] .
furthermore , il-17a exerts proinflammatory effects by stimulation of the production of chemokines such as il-1 , il-6 , cytokines , monocyte chemoattractant protein-1 , and upregulation of cell adhesion molecules like vascular cell adhesion molecule-1 and intercellular adhesion molecule-1 .
the il-17a plays a crucial role in induction of autoimmune diseases such as inflammatory bowel disease ( ibd ) , experimental autoimmune encephalomyelitis ( eae ) , and rheumatoid arthritis ( ra ) , as well as chronic inflammatory diseases [ 3033 ] .
regulatory t ( treg ) cells , by proliferation of antigen specific t cells and suppressing the activation , have important role in chronic inflammation .
it should be noted that depletion or dysfunction of treg cells is usually associated with inflammatory bowel disease , allergy , and autoimmune disease .
treg cells comprise different subsets : tr1 cells secreting interleukin il-10 , th3 cells characterized by transforming growth factor ( tgf-1 ) secretion , and naturally occurring foxp3-expressing cd4cd25 treg cells [ 35 , 36 ] .
the foxp3cd4cd25 treg cells are further divided into two subsets : thymus derived naturally occurring foxp3cd4cd25 treg cells and peripherally induced foxp3cd4cd25 treg cells .
the human gastric mucosal biopsies revealed that people who were persistently infected with h. pylori , in comparison to uninfected ones , show an increased and higher level of infiltrated various types of leukocytes . in these specimens , lymphocytes ( t and b cells ) , monocytes , mast cells , neutrophils , macrophages ,
cd4 t cells , b cells and dendritic cells may be organized in lymphoid follicles indicating ongoing chronic immune responses and antigen presentation . in peripheral blood and gastric mucosa of infected humans ,
the h. pylori - specific cd4 t cells are detectable which is not detectable in uninfected individuals .
the cytokines such as tnf- , ifn- , il-1 , il-6 , il-7 , il-8 , il-10 , il-17 , il-18 , and il-23 have usually increased levels in the stomach of h. pylori - infected patients in comparison to the uninfected subjects [ 2 , 41 , 42 ] .
il-4 is not usually detectable in the gastric mucosa of h. pylori - infected patients .
hence , to show , in children , the mucosal regulation of h. pylori infection , which can provide a window to the early host response to bacteria , the mucosal cytokine response to the infection , the associated cellular infiltrate , and the characterized bacteria might be helpful
. studies on h. pylori - infected children and adults have shown that children possess reduced gastric inflammation in comparison to the infected adults , in spite of similarity in h. pylori colonization level . furthermore , inflammation in children
has been shown to be less in comparison to that of adults , indicating a downregulation in immune response to infection in children [ 44 , 45 ] .
moreover , the sequence analysis revealed that the bacteria isolated from the infected children and adults might have similar caga and vaca gene profiles .
the difference in bacterial strains and common virulence factors were not the cause of low level of inflammation in infected children in comparison to adults .
pylori - infected children in comparison to infected adults possess lower levels of protein and gastric il-17-specific mrna as well as fewer gastric th17 cells , indicating more reduction in the mucosal th17 response in infected children .
moreover , the gastric mucosa of the infected children has lower level of ifn- mrna , confirming the findings indicated of reduced th1 response in children with h. pylori infection [ 46 , 47 ] .
recent study indicated that the gastric concentrations of cytokines representative of the innate and th1 response were higher in the h. pylori - positive than in the h. pylori - negative children and adults .
the gastric concentrations of il-1 and tnf- were significantly higher , while those of il-2 , il-12p70 , and ifn- were lower in the infected children than in the infected adults . in the infected children , the gastric concentration of il-1 , il-2 , il-12p70 , and ifn- increased , whereas in adults
the gastric concentrations of ifn- and il-12p70 decreased with aging . increased gastric concentration of th1-associated cytokines correlated with increased degree of gastritis , that is , the background lesion for the development of the h. pylori - associated severe diseases .
treg cells are described as the key regulator of the immune system in the maintenance of immunologic tolerance .
recently , the close relationship between h. pylori infection and immunosuppressive treg cells has been reported in animal and human models .
treg cells suppress h. pylori - induced th1-mediated immune response to contribute to the bacteria 's persistent colonization in the gastric mucosa and therefore may play a major role in inducing chronic gastritis .
the tgf-1 and il-10 gastric levels and the gastric number of treg foxp3 cells in h. pylori - positive groups are higher in children than in adults ( table 1 ) [ 44 , 46 , 4951 ] .
tgf- is required for the differentiation of both treg cells and th17 by inducing key transcription factors , foxp3 and rort / rorc , respectively [ 5254 ] .
but , in absence of il-6 , an exclusive treg differentiation might occur as foxp3 is capable of associating with and inhibiting the rort .
in contrast , in presence of il-6 , this inhibition might be abrogated allowing th17 differentiation . in a paradoxical pattern ,
the gastric concentration of il-6 is usually less in infected adults than in infected children . in this regard
, it might be hypothesized that these results are due to the higher gastric levels of il-23 in adults , compared with children , which might prevent the amplification / stabilization of the shifted th17 cells .
the other possibility might be the higher level of tgf- in the gastric milieu of infected children .
it should be noted that , at low levels , tgf- synergizes with il-6 to promote il-23 receptor expression in favor of th17 cell commitment .
however , the high level of tgf- represses il-23 receptor expression favoring foxp3 treg cell differentiation [ 49 , 56 ] . a recently published study revealed that il-6 overproductions by il-6 transgenic mice do not affect the function and development of natural treg . in this regard ,
the predominant treg differentiation in children infected with h. pylori might account for more susceptibility of children to the h. pylori infection as well as to the bacterium persistence .
study in mouse stomach showed that h. pylori - induced dendritic cells skew the th17/treg balance toward a treg - biased response that suppresses th17 immunity through a caga and vaca independent , tgf- and il-10-dependent mechanism [ 58 , 59 ] .
in support of these findings , recent study showed that h. pylori was capable of stimulating human gastric dendritic cells to produce il-10 , potentially supplementing treg suppression of inflammation in the gastric mucosa [ 60 , 61 ] ( figure 1 ) . from these findings
we might conclude that h. pylori - induced gastritis in adult is the consequence of both th1 and th17 immune - mediated inflammatory pathway involvement and that both pathways might be downregulated in the gastric mucosa of infected children .
in conclusion , h. pylori infection in children is associated with high treg response , as well as low th1 and th17 response [ 44 , 46 ] .
but , h. pylori - specific th17/th1 detection in chronically infected patients may reveal that the initial response is progressively lost [ 43 , 62 ] , indicating that , with progression of time , the mucosal immune system probably identifies h. pylori , as a pathogen .
hence , th1 , th17 , and treg results may imply gastric mucosal response to h. pylori .
more data from immune - mediated mechanism(s ) of mucosal inflammation is required to provide strategies against this challenging pathogen , particularly for children who are living in countries with high rate of gastric cancer and/or h. pylori infection .[/INST]helicobacter pylori ( h. pylori ) infection is generally acquired during early childhood ; therefore , the immune response which usually takes place at this age may influence or even determine susceptibility to the infection contributing to the clinical outcomes in adulthood .
several cytokines including il-6 , il-10 , and tgf-1 as well as foxp3 + cell numbers have been shown to be higher ; however , some other cytokines consisting of il-1 , il-17a , and il-23 are lower in infected children than in infected adults .
immune response to h. pylori infection in children is predominant treg instead of th17 cell response .
these results indicate that immune system responses probably play a role in persistent h. pylori infection .
childhood h. pylori infection is also associated with significantly lower levels of inflammation and ulceration compared with adults .
this review , therefore , aimed to provide critical findings of the available literature about comparative immune system in children and adults with h. pylori infection .</s> |
Sorry, the page you requested was not found.
Please check the URL for proper spelling and capitalization. If you're having trouble locating a destination on Yahoo!, try visiting the Yahoo! home page or look through a list of Yahoo!'s online services. Also, you may find what you're looking for if you try searching below.
Search the Web advanced search | most popular
Please try Yahoo! Help Central if you need more assistance. ||||| Ginny Thomas thinks Anita Hill should apologize? Wow, that's an amazing twist on history. How soon we forget. Rare are the times in recent history when sexual harassers have admitted their wrongdoing without having incontrovertible evidence placed in front of them. Sen. Bob Packwood of Oregon vehemently denied that he had harassed his female staffers. He went so far as to edit his own personal diaries to delete references to sexual encounters with female staffers and abusive behavior. The Senate Ethics Committee forced him to hand over his diaries, and the evidence was so incontrovertible, the Senate forced him to resign or be expelled. One of my family members was one of Packwood's victims. She had no reason to make this stuff up. It was real, it was insulting, it was denigrating, and it was wrong.
Does Ginny Thomas think she should apologize too?
While the Clarence Thomas confirmation hearings were under way in 1991, Washington Post columnist Juan Williams emerged as one of Thomas's chief defenders. Williams minimized the gravity of Thomas's alleged sexual harassment of Anita Hill. Boys will be boys, after all. But it's no surprise Williams thought it was no big deal. At the time, he was involved in repeated episodes of sexual harassment in The Post newsroom. It was only after several women in the newsroom spoke up that The Post took action -- forcing Williams to sit in an isolated part of the newsroom where he could be watched at all times.
Does Ginny Thomas think those Washington Post staffers should apologize to Juan Williams?
I don't fault Ginny Thomas for standing by her man, but as a woman, she should at least be aware that her husband and all men of that era, despite their adamant denials, were entirely capable of doing what Anita Hill alleged because those were the accepted norms of the time. Anita Hill and other bold women stood up and declared that this unacceptable behavior had to stop. Millions of men across America got the message very quickly that they had to change their attitudes and actions. That was a good thing. It had to happen.
And there's nothing for Anita Hill to apologize for. | β Juan Williams is catching plenty of flak for what he said on Wednesday. But it's what he said nearly two decades ago that has Bonnie ErbΓ© chiming inβand arguing not about whether or not he should have been fired, but protesting the fact that NPR hired him in the first place. ErbΓ©, who worked with Williams when the two were regular commentators on a weekly news program in DC, explains that the Washington Post disciplined Williams in 1991 for what Williams himself called "wrong" and "inappropriate" verbal conduct toward women. ErbΓ© says the Post remained tight-lipped about the details, as well as why he ultimately left the paper. (She points out that a Dallas Morning News article says Williams was forced "to sit in an isolated part of the newsroom where he could be watched at all times.") "Given the serious allegations against him ... I was saddened when NPR resurrected his reputation as a serious, credentialed journalist. It sent to me and many others the message that sexual harassment is not taken seriously by the so-called boys on the bus." Click here for more from ErbΓ©'s Politics Daily column. | <s>[INST]Sorry, the page you requested was not found.
Please check the URL for proper spelling and capitalization. If you're having trouble locating a destination on Yahoo!, try visiting the Yahoo! home page or look through a list of Yahoo!'s online services. Also, you may find what you're looking for if you try searching below.
Search the Web advanced search | most popular
Please try Yahoo! Help Central if you need more assistance. ||||| Ginny Thomas thinks Anita Hill should apologize? Wow, that's an amazing twist on history. How soon we forget. Rare are the times in recent history when sexual harassers have admitted their wrongdoing without having incontrovertible evidence placed in front of them. Sen. Bob Packwood of Oregon vehemently denied that he had harassed his female staffers. He went so far as to edit his own personal diaries to delete references to sexual encounters with female staffers and abusive behavior. The Senate Ethics Committee forced him to hand over his diaries, and the evidence was so incontrovertible, the Senate forced him to resign or be expelled. One of my family members was one of Packwood's victims. She had no reason to make this stuff up. It was real, it was insulting, it was denigrating, and it was wrong.
Does Ginny Thomas think she should apologize too?
While the Clarence Thomas confirmation hearings were under way in 1991, Washington Post columnist Juan Williams emerged as one of Thomas's chief defenders. Williams minimized the gravity of Thomas's alleged sexual harassment of Anita Hill. Boys will be boys, after all. But it's no surprise Williams thought it was no big deal. At the time, he was involved in repeated episodes of sexual harassment in The Post newsroom. It was only after several women in the newsroom spoke up that The Post took action -- forcing Williams to sit in an isolated part of the newsroom where he could be watched at all times.
Does Ginny Thomas think those Washington Post staffers should apologize to Juan Williams?
I don't fault Ginny Thomas for standing by her man, but as a woman, she should at least be aware that her husband and all men of that era, despite their adamant denials, were entirely capable of doing what Anita Hill alleged because those were the accepted norms of the time. Anita Hill and other bold women stood up and declared that this unacceptable behavior had to stop. Millions of men across America got the message very quickly that they had to change their attitudes and actions. That was a good thing. It had to happen.
And there's nothing for Anita Hill to apologize for.[/INST]β Juan Williams is catching plenty of flak for what he said on Wednesday. But it's what he said nearly two decades ago that has Bonnie ErbΓ© chiming inβand arguing not about whether or not he should have been fired, but protesting the fact that NPR hired him in the first place. ErbΓ©, who worked with Williams when the two were regular commentators on a weekly news program in DC, explains that the Washington Post disciplined Williams in 1991 for what Williams himself called "wrong" and "inappropriate" verbal conduct toward women. ErbΓ© says the Post remained tight-lipped about the details, as well as why he ultimately left the paper. (She points out that a Dallas Morning News article says Williams was forced "to sit in an isolated part of the newsroom where he could be watched at all times.") "Given the serious allegations against him ... I was saddened when NPR resurrected his reputation as a serious, credentialed journalist. It sent to me and many others the message that sexual harassment is not taken seriously by the so-called boys on the bus." Click here for more from ErbΓ©'s Politics Daily column.</s> |
the indomalayan region ( mainland tropical asia ) is divided into indian and indochinese sub - regions and earlier studies reported that the species from both the regions have independent radiation , , , as well as hybridization .
the river brahmaputra passing through bangladesh and northeast india forms the boundaries of indian and indochinese subregions , respectively .
therefore , it would be interesting to determine if intraspecific sequence variation occurs in species of indian and indochinese subregions in the case of butterflies .
mitochondrial dna has become popular in phylogenetic , comparative and evolutionary genomics , population genetics and molecular evolution studies among various animal taxa . in particular , the full - length mitogenome sequences have phylogenetic utility within several insect lineages including lepidoptera .
many biological studies like ecology , conservation , evolutionary and developmental studies have been done in the lepidopteran family as they are present all over the world .
the nymphalidae butterfly family are the most diverse with 12 subfamilies , 559 genera and 6152 species and for the present study , junonia iphita , a well - known group of brush - footed butterflies was selected .
we examined the presence of intraspecific variation within j. iphita collected from the indian and indochinese sub - regions i.e. north and south of brahmaputra river by comparing the mitochondrial genomes .
adult butterfly j. iphita ( ji_az ) was collected from rangpo , sikkim , northeast india from the north of brahmaputra river .
the leg was washed with distilled water , dried and macerated with the help of scissors in 1.5 ml eppendorf tube and homogenized with pestle and mortar and 250 l of extraction buffer ( 50 mm trishcl , 25 mm nacl , 25 mm edta , 1% sds ) was added and mixed gently .
two l of proteinase k ( 20 mg / ml ) was added and incubated in an oven at 56 c for 30 min .
250 l of phenol / chloroform ( 1:1 ) was added , mixed gently and centrifuged at 13,000 rpm for 5 min .
450 l of absolute ice cold ethanol was added to the supernatant and mixed gently by inverting the tube several times and kept in 20 c for 30 min .
the sample was centrifuged at 13,000 rpm for 5 min . at 4 c .
ethanol was poured off without dislodging the pellet , and 200 l of 70% ethanol was added , flash spin at 6000 rpm for 1 min . the ethanol was poured off and the pellet was dried in an oven for 5 min .
30 l of distilled water was added to the tube ; the pellet was re - suspended by gently flicking the tube and was stored at 20 c for further use .
the near complete mitochondrial genome sequence of j. iphita ( sikkim , india ) was obtained through illumina miseq platform ( scigenome , cochin , india ) .
the raw data obtained was subjected to quality checking based on base quality score distribution , average base content per read and gc distribution .
based on the quality score , the fastq files were trimmed before performing assembly . reads contaminated with illumina adapter were also removed using cutadapt .
genome annotation was done for j. iphita from north brahmaputra river and compared with the already published j. iphita ( ji_mz ) from south brahmaputra to check for any intraspecific variations .
two j. iphita species from north and south of brahmaputra river were used to build the phylogenetic tree along with sixteen other nymphalidae mitogenomes which were downloaded from ncbi .
nucleic acid sequences of 13 concatenated protein - coding genes ( pcgs ) from all the species were used in phylogenetic analysis .
the nucleic acid sequences of 13 mitochondrial pcgs were aligned with clustal w using mega 5 .
maximum parsimony ( mp ) trees were obtained using paup * by heuristic search option with tree - bisection - reconnection ( tbr ) branch - swapping .
starting tree was obtained via stepwise addition and the number of trees held at each step during stepwise addition equals 1 .
multistate taxa were interpreted as uncertainty , topological constraint was not enforced and the generated 50% consensus trees were saved as tree file .
the near complete mitogenome of j. iphita is a circular molecule of 14,892 bp in length ( ncbi genbank accession number srp053322 ) .
the nucleotide compositions are significantly biased toward at ( 80% ) which is similar to other work on nymphalids j. orithya 80.4% and j.iphita 80.5% .
the mitogenome nucleotide skewness ( at - skew = 0.002 , gc - skew = 0.213 ) indicate a slight at skew and moderate gc skew .
the phylogenetic tree was constructed for the whole mitochondrial genome using mp method ( fig .
in order to study the phylogenetic relationship of the two j. iphita samples in relation to other butterfly mitogenomes , a dataset containing concatenated 13 protein coding genes was generated .
the final alignment contains 13,269 sites in the matrix with 18 in - group and one out - group taxa . of these sites ,
7547 conserved , 5713 variables and 3963 parsimony informative sites were found . in mp analysis , two heliconiinae species clustered together and limentidinae form the basal clade . within nymphalinae
subfamily , the four junonia species clustered together with high bootstrap support , which further subdivided into two clade , one clade consist of the j. almana and j. orithya ; the other clade comprising the two j. iphita individuals .
the phylogenetic tree constructed for the whole mitogenomes using the 13 pcgs region defines the genetic relatedness of the two j. iphita species .
the two j. iphita from the north and south brahmaputra river were compared to study the presence of any intraspecific variations between them and comparison between these two sequences revealed minor variations at 51 sites along the length of the genome .
we observed that the nad1 region of ji_az ended with a single t while that of ji_mz ends with ta . in the case of nad5
, ji_az ends with an incomplete stop codon t and ji _ mz ends with a complete stop codon taa .
analysis of the trna structure revealed similar structures except for the trna of glycine . here , it was observed that ji _ mz has an a a mismatch in its anti - codon stem .
minor variations were observed in the number of nucleotide residues ( a , t , g , c ) , in the number of intergenic spacers and also in the number of base pairs of nad5 , cytb , rrnal and rrnas .
although , minor variations were observed within j. iphita collected from two different regions , their genome shows 99% similar which might be because of hybridization event .
the draft mitogenome information reported here provides opportunity for further research on intraspecific variation within species of indian and indochinese subregions .
| in the present study , the near complete mitochondrial genome ( mitogenome ) of junonia iphita ( lepidoptera : nymphalidae : nymphalinae ) was determined to be 14,892 bp .
the gene order and orientation are identical to those in other butterfly species .
the phylogenetic tree constructed from the whole mitogenomes using the 13 protein coding genes ( pcgs ) defines the genetic relatedness of the two j. iphita species collected from two different regions .
all the junonia species clustered together , and were further subdivided into clade one consisting of j. almana and j. orithya and clade two comprising of the two j. iphita which were collected from indo and indochinese subregions separated by river barrier .
comparison between the two j. iphita sequences revealed minor variations and single nucleotide polymorphisms were identified at 51 sites amounting to 0.4% of the entire mitochondrial genome . | <s>[INST]the indomalayan region ( mainland tropical asia ) is divided into indian and indochinese sub - regions and earlier studies reported that the species from both the regions have independent radiation , , , as well as hybridization .
the river brahmaputra passing through bangladesh and northeast india forms the boundaries of indian and indochinese subregions , respectively .
therefore , it would be interesting to determine if intraspecific sequence variation occurs in species of indian and indochinese subregions in the case of butterflies .
mitochondrial dna has become popular in phylogenetic , comparative and evolutionary genomics , population genetics and molecular evolution studies among various animal taxa . in particular , the full - length mitogenome sequences have phylogenetic utility within several insect lineages including lepidoptera .
many biological studies like ecology , conservation , evolutionary and developmental studies have been done in the lepidopteran family as they are present all over the world .
the nymphalidae butterfly family are the most diverse with 12 subfamilies , 559 genera and 6152 species and for the present study , junonia iphita , a well - known group of brush - footed butterflies was selected .
we examined the presence of intraspecific variation within j. iphita collected from the indian and indochinese sub - regions i.e. north and south of brahmaputra river by comparing the mitochondrial genomes .
adult butterfly j. iphita ( ji_az ) was collected from rangpo , sikkim , northeast india from the north of brahmaputra river .
the leg was washed with distilled water , dried and macerated with the help of scissors in 1.5 ml eppendorf tube and homogenized with pestle and mortar and 250 l of extraction buffer ( 50 mm trishcl , 25 mm nacl , 25 mm edta , 1% sds ) was added and mixed gently .
two l of proteinase k ( 20 mg / ml ) was added and incubated in an oven at 56 c for 30 min .
250 l of phenol / chloroform ( 1:1 ) was added , mixed gently and centrifuged at 13,000 rpm for 5 min .
450 l of absolute ice cold ethanol was added to the supernatant and mixed gently by inverting the tube several times and kept in 20 c for 30 min .
the sample was centrifuged at 13,000 rpm for 5 min . at 4 c .
ethanol was poured off without dislodging the pellet , and 200 l of 70% ethanol was added , flash spin at 6000 rpm for 1 min . the ethanol was poured off and the pellet was dried in an oven for 5 min .
30 l of distilled water was added to the tube ; the pellet was re - suspended by gently flicking the tube and was stored at 20 c for further use .
the near complete mitochondrial genome sequence of j. iphita ( sikkim , india ) was obtained through illumina miseq platform ( scigenome , cochin , india ) .
the raw data obtained was subjected to quality checking based on base quality score distribution , average base content per read and gc distribution .
based on the quality score , the fastq files were trimmed before performing assembly . reads contaminated with illumina adapter were also removed using cutadapt .
genome annotation was done for j. iphita from north brahmaputra river and compared with the already published j. iphita ( ji_mz ) from south brahmaputra to check for any intraspecific variations .
two j. iphita species from north and south of brahmaputra river were used to build the phylogenetic tree along with sixteen other nymphalidae mitogenomes which were downloaded from ncbi .
nucleic acid sequences of 13 concatenated protein - coding genes ( pcgs ) from all the species were used in phylogenetic analysis .
the nucleic acid sequences of 13 mitochondrial pcgs were aligned with clustal w using mega 5 .
maximum parsimony ( mp ) trees were obtained using paup * by heuristic search option with tree - bisection - reconnection ( tbr ) branch - swapping .
starting tree was obtained via stepwise addition and the number of trees held at each step during stepwise addition equals 1 .
multistate taxa were interpreted as uncertainty , topological constraint was not enforced and the generated 50% consensus trees were saved as tree file .
the near complete mitogenome of j. iphita is a circular molecule of 14,892 bp in length ( ncbi genbank accession number srp053322 ) .
the nucleotide compositions are significantly biased toward at ( 80% ) which is similar to other work on nymphalids j. orithya 80.4% and j.iphita 80.5% .
the mitogenome nucleotide skewness ( at - skew = 0.002 , gc - skew = 0.213 ) indicate a slight at skew and moderate gc skew .
the phylogenetic tree was constructed for the whole mitochondrial genome using mp method ( fig .
in order to study the phylogenetic relationship of the two j. iphita samples in relation to other butterfly mitogenomes , a dataset containing concatenated 13 protein coding genes was generated .
the final alignment contains 13,269 sites in the matrix with 18 in - group and one out - group taxa . of these sites ,
7547 conserved , 5713 variables and 3963 parsimony informative sites were found . in mp analysis , two heliconiinae species clustered together and limentidinae form the basal clade . within nymphalinae
subfamily , the four junonia species clustered together with high bootstrap support , which further subdivided into two clade , one clade consist of the j. almana and j. orithya ; the other clade comprising the two j. iphita individuals .
the phylogenetic tree constructed for the whole mitogenomes using the 13 pcgs region defines the genetic relatedness of the two j. iphita species .
the two j. iphita from the north and south brahmaputra river were compared to study the presence of any intraspecific variations between them and comparison between these two sequences revealed minor variations at 51 sites along the length of the genome .
we observed that the nad1 region of ji_az ended with a single t while that of ji_mz ends with ta . in the case of nad5
, ji_az ends with an incomplete stop codon t and ji _ mz ends with a complete stop codon taa .
analysis of the trna structure revealed similar structures except for the trna of glycine . here , it was observed that ji _ mz has an a a mismatch in its anti - codon stem .
minor variations were observed in the number of nucleotide residues ( a , t , g , c ) , in the number of intergenic spacers and also in the number of base pairs of nad5 , cytb , rrnal and rrnas .
although , minor variations were observed within j. iphita collected from two different regions , their genome shows 99% similar which might be because of hybridization event .
the draft mitogenome information reported here provides opportunity for further research on intraspecific variation within species of indian and indochinese subregions .
[/INST]in the present study , the near complete mitochondrial genome ( mitogenome ) of junonia iphita ( lepidoptera : nymphalidae : nymphalinae ) was determined to be 14,892 bp .
the gene order and orientation are identical to those in other butterfly species .
the phylogenetic tree constructed from the whole mitogenomes using the 13 protein coding genes ( pcgs ) defines the genetic relatedness of the two j. iphita species collected from two different regions .
all the junonia species clustered together , and were further subdivided into clade one consisting of j. almana and j. orithya and clade two comprising of the two j. iphita which were collected from indo and indochinese subregions separated by river barrier .
comparison between the two j. iphita sequences revealed minor variations and single nucleotide polymorphisms were identified at 51 sites amounting to 0.4% of the entire mitochondrial genome .</s> |
despite the impressive success of the standard model ( sm ) in describing all experimental data , it contains many unsolved problems , such as , origin of mass and cp violation , hierarchy problem , number of generations , baryon anti - baryon asymmetry , etc . for solution of these problems
it is necessary to go beyond sm . to obtain a `` natural '' solution to hierarchy problem little higgs models @xcite
are introduced . in little higgs models new physics
is introduced at @xmath3 scale ; these models predict existence of new particles and new interactions of these particles with sm particles as well as interactions among themselves .
the phenomenologies of the little higgs models are reviewed widely@xcite , and the constraints on little higgs models are studied @xcite . among little higgs models ,
there are several variations which differ in the assumed higher symmetry group and in the representation of the scalar multiplets , one of which is the littlest higgs model@xcite .
the existence of new particles in littlest higgs model includes new heavy gauge bosons and a new scalar sector consisting of a neutral heavy scalar ( @xmath4 ) , a neutral pseudo - scalar ( @xmath5 ) , a singly charged scalar ( @xmath6 ) and a doubly charged scalar ( @xmath7 ) receives special attention .
the charged scalars @xmath6 and @xmath7 of the littlest higgs model are under special interest since they have distinct signatures in future colliders .
productions of charged scalars and their signatures at ilc , lhc and thera are studied via @xmath8 , @xmath9 and @xmath10 processes@xcite .
also @xmath11 associated productions and final collider signatures of charged scalars are studied via @xmath12 and @xmath13 processes at a linear collider@xcite . in this work , the productions of single and doubly charged scalar pairs via @xmath14 and @xmath15 processes at future @xmath16 colliders , namely , international linear collider ( ilc ) @xcite and compact linear collider ( clic ) @xcite are examined .
the dependence of cross sections to the littlest higgs model parameters at the range allowed by electroweak precision observables are calculated .
it is found that the production rates of the single charged scalar pairs are less than the production rates of doubly charged scalar pairs , but both channels will be achieved at future @xmath16 colliders at @xmath17 .
in addition to production rates , the final signatures of the productions are also analyzed considering the lepton flavor violating decays of the charged and the double charged scalars , whose branching ratios have been studied by t.han et al@xcite .
it is found that pair productions of charged and double charged scalars lead to distinct signatures in @xmath0 colliders including lepton number and lepton flavor violating ones .
the paper is organized as follows : in section @xmath18 , the cross sections of pair productions of charged scalars at @xmath16 colliders are calculated .
section @xmath19 contains our numerical results and discussions .
before examining the pair productions of the charged scalars , we remind the main ingredients of the littlest higgs model and lepton flavor violation in littlest higgs model .
the littlest higgs model assumes a higher symmetry group @xmath20 with a weakly gauged subgroup of @xmath21 . among consecutive symmetry breakings first @xmath20
is broken to @xmath22 at @xmath3 scale , and simultaneously subgauged group @xmath21 is broken to @xmath23 . then at @xmath24 ordinary electroweak symmetry breaking ( ewsb ) occurs . as a result of higher symmetry breaking new scalar sector enters the model , which is the scalar triplet at the end whose members are @xmath4 , @xmath5 , @xmath6 and @xmath7 . also from symmetry breaking of gauged group
@xmath21 new bosons @xmath25 , @xmath26 and @xmath27 gain mass . in summary , littlest higgs model contain four physical scalars ; higgs scalar : @xmath28 , new heavy scalars : @xmath4 , @xmath6 and @xmath7 , and a new heavy pseudo - scalar : @xmath5 .
all scalars excluding @xmath28 are degenerate in mass : @xmath29 where @xmath30 is the mass of the higgs boson , @xmath31 is the higher symmetry breaking scale of the littlest higgs model , @xmath32 and @xmath33 are the vacuum expectation values ( vevs ) of the higgs field and the scalar triplet respectively .
the vacuum expectation values of higgs field and scalar triplet are given as ; @xmath34 bounded by electroweak precision data , where @xmath35 .
in the littlest higgs model , the masses of the new gauge bosons @xmath25 , @xmath26 and @xmath27 are given as@xcite : @xmath36 , \nonumber \\
\nn m_{a_h}^2 & = & \frac{f^2 g^{\prime 2}}{20 s^{\prime 2 } c^{\prime 2 } } - \frac{1}{4 } g^{\prime 2 } v^2 + g^2 v^2 \frac{x_h}{4s^2c^2}\\ \nn & = & m_z^2 s_{\w}^2 \left ( \frac { f^2 } { 5 s^{\prime 2 } c^{\prime 2}v^2 } - 1 + \frac{x_h c_{\w}^2}{4s^2c^2 s_{\w}^2 } \right ) , \nonumber \\ m_{z_h}^2 & = & \frac{f^2g^2}{4s^2c^2 } - \frac{1}{4 } g^2 v^2 - g^{\prime 2 } v^2 \frac{x_h}{4s^{\prime 2}c^{\prime 2}}\\ \nn & = & m_w^2 \left ( \frac{f^2}{s^2c^2 v^2 } - 1 - \frac{x_h s_{\w}^2}{s^{\prime 2}c^{\prime 2}c_{\w}^2}\right ) , \end{aligned}\ ] ] where @xmath37 and @xmath38 , @xmath39 and @xmath40 are the usual sm weak mixing angles , @xmath41 and @xmath42 . in eq .
[ massesvectors ] , @xmath43 and @xmath44 are the mixing angles of @xmath45 and @xmath46 subgroups respectively .
one of the interesting features of littlest higgs model is that as a result of the extended higgs sector , it predicts lepton flavor violation by unit two by implementing a majorana type mass in yukawa lagrangian@xcite , such as : @xmath47 where @xmath48 are the lepton doublets @xmath49 , and @xmath50 is the yukawa coupling with @xmath51 and @xmath52 .
the values of yukawa couplings @xmath53 and @xmath54 are restricted by the current constraints on the neutrino masses@xcite , given as ; @xmath55 . since the vacuum expectation value @xmath33 has only an upper bound ; @xmath56 , @xmath50 can be taken up to order of unity without making @xmath33 unnaturally small . in this work the values of the yukawa mixings
are taken to be @xmath57 , @xmath58 , and the vacuum expectation value @xmath59 . in littlest higgs model , the symmetry braking scale @xmath31 and mixing angles @xmath60 and @xmath61 are free parameters and they are constrained by observables@xcite .
the recent data from tevatron and lepii constrain the mass of the lightest heavy vector boson as @xmath62@xcite . in the original formulation of the littlest higgs model ,
these data imposes strong constraints on symmetry breaking scale(@xmath63 ) .
but in this work by gauging fermions in both @xmath46 subgroups , fermion boson couplings are modified as done in@xcite . with this modification
the symmetry breaking scale can be lowered to @xmath64 , which allows the mass of the @xmath25 to be at the order of few @xmath65s . in this case
the allowed parameter region of the littlest higgs model is as follows . for low values of the symmetry breaking scale @xmath66 , mixing angles @xmath60 and @xmath61 between gauge bosons are in the range @xmath67 and @xmath68 , and for @xmath69 they have acceptable values in the range @xmath70 and @xmath71 . for the higher values of the symmetry breaking scale @xmath72 ,
the mixing angles are less constrained , since the corrections to sm observables from model comes in the form @xmath73 and higher orders . for calculation of production rates and decays of charged scalar pairs ,
the couplings between fermions and neutral vector bosons are needed .
the couplings of fermions with gauge bosons are written as @xmath74 where @xmath75 corresponds to @xmath11 , @xmath26 , @xmath25 and @xmath76 respectively .
these couplings of vectors with @xmath16 are given in table [ gvga ] , where @xmath77 , @xmath78 for anomaly cancelations , @xmath79 and @xmath80 .
it is seen from table [ gvga ] that vector and axial vector couplings of sm @xmath81 vertex also gets contributions from littlest higgs model . as a result total decay widths of sm vector bosons also gets corrections of the order @xmath73 , since the decay widths of vectors to fermion couples are written as ; @xmath82 where @xmath83 for quarks , and @xmath84 for fermions .
total decay widths of new vectors @xmath25 and @xmath26 are given as @xcite : @xmath85 .the vector and axial vector couplings of @xmath86 with vector bosons .
feynman rules for @xmath87 vertexes are given as @xmath88 @xcite .
[ cols="^,^,^,^",options="header " , ] the amplitudes corresponding to these feynman diagrams are written as : @xmath89 i \gmm g_{v_4}u[p_1](i ) \frac{g^{\alpha\mu}}{q^2}i e_{4 } ( p_3 - p_4)_{\alpha},\ ] ] @xmath90 i \gmm ( \gvi + \gai \gff)u[p_1](i ) \frac{g^{\alpha\mu}-\frac{q^{\mu}q^{\alpha}}{m^{2}_{i}}}{q^2-m^{2}_{i}+i\dwi } i e_{i } ( p_3 - p_4)_{\alpha},\ ] ] where @xmath91 and coefficients @xmath92 are given in table [ pp11vcouplings]([pp22vcouplings ] ) for single(doubly ) charged scalar pair and @xmath93 is for the photon propagating diagram .
the pair production cross sections are calculated by squaring the amplitudes and integrating over phase space . the analytical expression for cross section
is found as @xmath94,\end{aligned}\ ] ] where @xmath95 and @xmath92 for the process @xmath96 ( @xmath97 ) .
the scattering amplitudes of the processes @xmath98 and @xmath99 are dependent on the free parameters of littlest higgs model @xmath100 . in this work ,
the dependence of the cross sections on mixing angles @xmath101 at @xmath64 is examined . for larger values of @xmath31 , the processes are not accessible for @xmath102 because of the kinematical limits of high masses of scalars .
the processes are also strongly dependent on mass of the higgs scalar . in this work
the input parameters are taken as : the higgs mass @xmath103 and the mass of the standard model gauge bosons @xmath104 , @xmath105 and @xmath106 consistent with recent data@xcite .
the total cross sections for the single charged pair productions are plotted in figure [ hpc1 ] with respect to center of mass energy . within the range of electroweak precision data ,
the direct production cross section gets a value of @xmath107 for @xmath108 and @xmath64 for energies @xmath109
. this will give up to @xmath110 productions per year for luminosities of @xmath111 .
for higher values of symmetry breaking scale parameter ( @xmath112 ) , the production process is not accessible for ilc and clic because of the kinematical constraints of high scalar mass . at the final state ,
the decays of the single charged scalar pair strongly depends on the values of the yukawa couplings @xmath53 and @xmath54 as seen from equation [ dwp1 ] . for @xmath115 @xmath116
dominantly decays into same family leptons @xmath117 , violating lepton number . for small values @xmath118
the dominant decay mode is to sm pairs @xmath119 and @xmath120 .
the decay into different families of leptons @xmath121 is proportional to @xmath122 and since the flavor mixing yukawa coupling @xmath54 is constrained to be small no such signals are expected . where @xmath129 $ ] is the branching ratio to sm particles . finally ,
if @xmath130 , about @xmath131 events per year can be observed at an @xmath0 collider with luminosity of @xmath111 for @xmath132 .
the final states will be @xmath133 , which will be detected as two leptons and missing energy .
unfortunately this signal does not allow observing distinct features of the littlest higgs model and lepton flavor violation , since the neutrino flavors can not be identified .
thus this channel contain high sm background , and these signals can have significance only if a detailed background analysis is done . for the process
@xmath134 the total cross section of the production event is examined for @xmath64 .
the dependence of the total cross section of the @xmath134 process on @xmath135 at fixed values of the littlest higgs model parameters are presented in fig .
[ hpc2 ] . for the mixing angles
@xmath136 , the production cross section is maximum with a value of @xmath137 for @xmath64 at @xmath109 . for the parameter sets @xmath138 for @xmath64 ,
the total cross section is is slightly lower but still in the order of @xmath139 at @xmath109 .
thus for an @xmath0 collider with an integrated luminosity of @xmath111 , yearly @xmath140 double charged pair production can be observed .
it is seen from the final decay modes of the doubly charged pair given in eq.[dwp2 ] that the final state analysis is strongly dependent on the value of the yukawa coupling @xmath53 , thus on the value of the triplet vev @xmath33 .
the dependence of the final collider signatures of the process @xmath141 on @xmath53 are plotted in figure [ br2 ] . for @xmath142 ,
the final decays of the doubly charged scalars are dominated by sm charged bosons , and the final collider signature will be @xmath143 . in this case with a subtraction from background , doubly charged scalars can be identified by reconstructing the same sign boson pairs . for @xmath144 , the semi leptonic decay modes , @xmath145 will be observed . for @xmath146 ,
the production rates for these modes are calculated as ; @xmath147 , leading to @xmath148 collider signals per year at collider with a luminosity of @xmath111 at @xmath109 . the cleanest signal in this case
will be observed when both @xmath149 decay into jets ( @xmath150 ) . in this scenario
there will be yearly @xmath151 signal of two same sign leptons of same family plus jets , violating lepton number and flavor by two , which can be directly detectable free from any backgrounds .
the most interesting scenario happens when the yukawa coupling is close to unity , @xmath152 . in this case
all final doubly charged scalars will decay into same family leptons , and the final collider signal will be either @xmath153 or @xmath154 .
the mixed states @xmath155 resulting from the final decays of the doubly charged scalars into different families of leptons are suppressed because of the low production rates due to the value of the yukawa mixing coupling @xmath54 . the branching ratio into the final signal @xmath153 when @xmath156 is calculated as @xmath157 , which will give @xmath158 observable signals per year at an integrated luminosity of @xmath111 when @xmath109 .
for this final signal , the lepton flavor is violated explicitly , free from any backgrounds .
the double charged scalars in this case can be reconstructed from invariant mass distributions of same charged leptons
. for the final state @xmath154 , there will be additional observable @xmath159 events per year .
for this case lepton flavor violation can not be observed directly even if it happens via the lepton flavor violating decays of doubly charged scalars .
although this signal has a huge sm background , with a proper background analysis , the existence of doubly charged scalars and so on their lepton flavor violating decays can be identified . in conclusion , it is found that pair productions of single and doubly charged scalars are in the reach for @xmath1 colliders when @xmath2 .
the production rates of the single charged pair are quite low and final signatures are not promising since neutrinos in the final states can not be identified . for the pair production of doubly charged scalar via process @xmath99 , the production rates are promising and also the final state signatures are distinct observable collider signals depending on final decay modes of the doubly charged pair which were discussed in@xcite . when @xmath160 , the final state will be semileptonic ; i.e : jets plus two same sign leptons of same family , giving an explicit signature of lepton number violation by two .
and also for the case when @xmath161 , the final decays of the doubly charged pair will be leptonic , including an explicit lepton flavor violation in the final state @xmath153 .
these both final signatures are due to distinct features of littlest higgs model and will be free from any backgrounds .
99 n. arkani - hamed , a.g .
cohen , e. katz , and a.e .
nelson , jhep**0207**(2002)034 , arxiv : hep - ph/0206021 . n.
arkani - hamed _
et al . _ , jhep**0208**(2002)021 , arxiv : hep - ph/0206020 . m. schmaltz , nucl.phys.proc.suppl.*117*(2003),arxiv:hep-ph/0210415 .
d.e.kaplan and m. schmaltz , jhep**0310**(2003)039 , arxiv : hep - ph/0302049 . m. perelstein , prog.part.nucl.phys.*58*(2007)247-291 , arxiv : hep - ph/0512128
. t. han , h. e. logan , b. mcelrath and l - t .
wang , phys.rev .
* d67*(2003)095004 , arxiv : hep - ph/0301040 . m. schmaltz and d. tucker - smith , ann.rev.nucl.part.sci.*55*(2005)229-270 , arxiv : hep - ph/0502182 . c. csaki , j. hubisz , g.d .
kribs , p. meade , j. terning , phys . rev .
* d67 * ( 2003 ) 115002 , arxiv : hep - ph/0211124v2
. j. hubisz , p. maeda , a. noble and m. perelstein , jhep**01**(2006)135 .
j. l. hewett , f. j. petriello and t. g. rizzo , jhep * 0310 * ( 2003 ) 062 , arxiv : hep - ph/0211218 .
chen and s. dawson , phys.rev.*d70*(2004)015003 , arxiv : hep - ph/0311032 .
w. killian and j. reuter , phys.rev .
* d70 * ( 2004 ) 015004 , arxiv : hep - ph/0311095 .
dias , c.a . de s. pires p.s .
rodrigues da silva , phys.rev.*d77*(2008)055001 , arxiv : hep - ph/0711.1154 .
c. csaki , j. hubisz , g. d. kribs , p. maede and j. terning , phys.rev .
* d68 * ( 2003 ) 035009 , arxiv : hep - ph/0303236 .
chong - xing yue , shuang zhao , wei ma , nucl.phys.*b 784 * ( 2007 ) , arxiv : hep - ph/0706.0232 .
ayse cagil , mehmet t. zeyrek , phys.rev . * * d80**055021(2009 ) , arxiv : hep - ph/0908.3581 .
* d 74 * , 095003 ( 2006 ) [ erratum - ibid .
d * 74 * , 099905 ( 2006 ) ] , [ arxiv : hep - ph/0609119 ] . j. brau ( ed . ) _ et al _ , by ilc collaboration , _
lc reference design report : ilc global design effort and world wide study .
fermilab - apc , aug 2007 , arxiv : acc - ph/0712.1950 .
r.w . assmann _
_ , the clic study team , _ a 3 tev @xmath162 linear collider based on clic technology _ , cern 2000 - 008 , geneva , 2000 ; e. accomando _ et al . _ , by clic physics working group , _ physics at the clic multi - tev linear collider
_ , cern-2004 - 005 , arxiv : hep - ph/0412251 ; h. braun _ et al .
, by clic study team , _
clic 2008 parameters _
, cern - open-2008 - 021 , clic - note-764 . t. han , h.e .
logan , b. mukhopadhyaya and r. srikanth , phys.rev . *
d72 * ( 2005 ) 053007 , arxiv : hep - ph/0505260 .
choudhury , n. gaur and a. goyal , phys.rev . *
d72 * ( 2005 ) 097702 , arxiv : hep - ph/0508146 .
yue and s. zhao , eur.phys.j.*c50*(2007)897-903 , arxiv : hep - ph/0701017 .
et al . _ ,
phys.rev.*d75*(2007)055011 , arxiv : hep - ph/0612327 .
et al _ , phys .
d**70 * * , 113003(2004 ) ; m. tegmark _
et al _ , sdss collabration , phys .
d**69 * * , 103501(2004 ) .
t. aaltonen , et al , cdf collaboration , phys.rev.lett.99:171802,2007 .
yue , w. yang and f. zhang , nucl.phys .
* b716 * ( 2005 ) 199 - 214 , arxiv : hep - ph/0409066 . | in this work pair productions of charged and doubly charged scalars in the framework of littlest higgs model at @xmath0 colliders are studied . in the allowed parameter space of the littlest higgs model ,
the production rates of the scalar pairs are calculated .
it is obtained that pair productions of charged and doubly charged scalars are reachable at @xmath1 colliders with energy @xmath2 . using the lepton flavor violating decays of charged scalars calculated in literature , final state analysis is done for pair production processes . this analysis show that depending on the model parameters , lepton number and lepton flavor violations can be observed free from any backgrounds . | <s>[INST]despite the impressive success of the standard model ( sm ) in describing all experimental data , it contains many unsolved problems , such as , origin of mass and cp violation , hierarchy problem , number of generations , baryon anti - baryon asymmetry , etc . for solution of these problems
it is necessary to go beyond sm . to obtain a `` natural '' solution to hierarchy problem little higgs models @xcite
are introduced . in little higgs models new physics
is introduced at @xmath3 scale ; these models predict existence of new particles and new interactions of these particles with sm particles as well as interactions among themselves .
the phenomenologies of the little higgs models are reviewed widely@xcite , and the constraints on little higgs models are studied @xcite . among little higgs models ,
there are several variations which differ in the assumed higher symmetry group and in the representation of the scalar multiplets , one of which is the littlest higgs model@xcite .
the existence of new particles in littlest higgs model includes new heavy gauge bosons and a new scalar sector consisting of a neutral heavy scalar ( @xmath4 ) , a neutral pseudo - scalar ( @xmath5 ) , a singly charged scalar ( @xmath6 ) and a doubly charged scalar ( @xmath7 ) receives special attention .
the charged scalars @xmath6 and @xmath7 of the littlest higgs model are under special interest since they have distinct signatures in future colliders .
productions of charged scalars and their signatures at ilc , lhc and thera are studied via @xmath8 , @xmath9 and @xmath10 processes@xcite .
also @xmath11 associated productions and final collider signatures of charged scalars are studied via @xmath12 and @xmath13 processes at a linear collider@xcite . in this work , the productions of single and doubly charged scalar pairs via @xmath14 and @xmath15 processes at future @xmath16 colliders , namely , international linear collider ( ilc ) @xcite and compact linear collider ( clic ) @xcite are examined .
the dependence of cross sections to the littlest higgs model parameters at the range allowed by electroweak precision observables are calculated .
it is found that the production rates of the single charged scalar pairs are less than the production rates of doubly charged scalar pairs , but both channels will be achieved at future @xmath16 colliders at @xmath17 .
in addition to production rates , the final signatures of the productions are also analyzed considering the lepton flavor violating decays of the charged and the double charged scalars , whose branching ratios have been studied by t.han et al@xcite .
it is found that pair productions of charged and double charged scalars lead to distinct signatures in @xmath0 colliders including lepton number and lepton flavor violating ones .
the paper is organized as follows : in section @xmath18 , the cross sections of pair productions of charged scalars at @xmath16 colliders are calculated .
section @xmath19 contains our numerical results and discussions .
before examining the pair productions of the charged scalars , we remind the main ingredients of the littlest higgs model and lepton flavor violation in littlest higgs model .
the littlest higgs model assumes a higher symmetry group @xmath20 with a weakly gauged subgroup of @xmath21 . among consecutive symmetry breakings first @xmath20
is broken to @xmath22 at @xmath3 scale , and simultaneously subgauged group @xmath21 is broken to @xmath23 . then at @xmath24 ordinary electroweak symmetry breaking ( ewsb ) occurs . as a result of higher symmetry breaking new scalar sector enters the model , which is the scalar triplet at the end whose members are @xmath4 , @xmath5 , @xmath6 and @xmath7 . also from symmetry breaking of gauged group
@xmath21 new bosons @xmath25 , @xmath26 and @xmath27 gain mass . in summary , littlest higgs model contain four physical scalars ; higgs scalar : @xmath28 , new heavy scalars : @xmath4 , @xmath6 and @xmath7 , and a new heavy pseudo - scalar : @xmath5 .
all scalars excluding @xmath28 are degenerate in mass : @xmath29 where @xmath30 is the mass of the higgs boson , @xmath31 is the higher symmetry breaking scale of the littlest higgs model , @xmath32 and @xmath33 are the vacuum expectation values ( vevs ) of the higgs field and the scalar triplet respectively .
the vacuum expectation values of higgs field and scalar triplet are given as ; @xmath34 bounded by electroweak precision data , where @xmath35 .
in the littlest higgs model , the masses of the new gauge bosons @xmath25 , @xmath26 and @xmath27 are given as@xcite : @xmath36 , \nonumber \\
\nn m_{a_h}^2 & = & \frac{f^2 g^{\prime 2}}{20 s^{\prime 2 } c^{\prime 2 } } - \frac{1}{4 } g^{\prime 2 } v^2 + g^2 v^2 \frac{x_h}{4s^2c^2}\\ \nn & = & m_z^2 s_{\w}^2 \left ( \frac { f^2 } { 5 s^{\prime 2 } c^{\prime 2}v^2 } - 1 + \frac{x_h c_{\w}^2}{4s^2c^2 s_{\w}^2 } \right ) , \nonumber \\ m_{z_h}^2 & = & \frac{f^2g^2}{4s^2c^2 } - \frac{1}{4 } g^2 v^2 - g^{\prime 2 } v^2 \frac{x_h}{4s^{\prime 2}c^{\prime 2}}\\ \nn & = & m_w^2 \left ( \frac{f^2}{s^2c^2 v^2 } - 1 - \frac{x_h s_{\w}^2}{s^{\prime 2}c^{\prime 2}c_{\w}^2}\right ) , \end{aligned}\ ] ] where @xmath37 and @xmath38 , @xmath39 and @xmath40 are the usual sm weak mixing angles , @xmath41 and @xmath42 . in eq .
[ massesvectors ] , @xmath43 and @xmath44 are the mixing angles of @xmath45 and @xmath46 subgroups respectively .
one of the interesting features of littlest higgs model is that as a result of the extended higgs sector , it predicts lepton flavor violation by unit two by implementing a majorana type mass in yukawa lagrangian@xcite , such as : @xmath47 where @xmath48 are the lepton doublets @xmath49 , and @xmath50 is the yukawa coupling with @xmath51 and @xmath52 .
the values of yukawa couplings @xmath53 and @xmath54 are restricted by the current constraints on the neutrino masses@xcite , given as ; @xmath55 . since the vacuum expectation value @xmath33 has only an upper bound ; @xmath56 , @xmath50 can be taken up to order of unity without making @xmath33 unnaturally small . in this work the values of the yukawa mixings
are taken to be @xmath57 , @xmath58 , and the vacuum expectation value @xmath59 . in littlest higgs model , the symmetry braking scale @xmath31 and mixing angles @xmath60 and @xmath61 are free parameters and they are constrained by observables@xcite .
the recent data from tevatron and lepii constrain the mass of the lightest heavy vector boson as @xmath62@xcite . in the original formulation of the littlest higgs model ,
these data imposes strong constraints on symmetry breaking scale(@xmath63 ) .
but in this work by gauging fermions in both @xmath46 subgroups , fermion boson couplings are modified as done in@xcite . with this modification
the symmetry breaking scale can be lowered to @xmath64 , which allows the mass of the @xmath25 to be at the order of few @xmath65s . in this case
the allowed parameter region of the littlest higgs model is as follows . for low values of the symmetry breaking scale @xmath66 , mixing angles @xmath60 and @xmath61 between gauge bosons are in the range @xmath67 and @xmath68 , and for @xmath69 they have acceptable values in the range @xmath70 and @xmath71 . for the higher values of the symmetry breaking scale @xmath72 ,
the mixing angles are less constrained , since the corrections to sm observables from model comes in the form @xmath73 and higher orders . for calculation of production rates and decays of charged scalar pairs ,
the couplings between fermions and neutral vector bosons are needed .
the couplings of fermions with gauge bosons are written as @xmath74 where @xmath75 corresponds to @xmath11 , @xmath26 , @xmath25 and @xmath76 respectively .
these couplings of vectors with @xmath16 are given in table [ gvga ] , where @xmath77 , @xmath78 for anomaly cancelations , @xmath79 and @xmath80 .
it is seen from table [ gvga ] that vector and axial vector couplings of sm @xmath81 vertex also gets contributions from littlest higgs model . as a result total decay widths of sm vector bosons also gets corrections of the order @xmath73 , since the decay widths of vectors to fermion couples are written as ; @xmath82 where @xmath83 for quarks , and @xmath84 for fermions .
total decay widths of new vectors @xmath25 and @xmath26 are given as @xcite : @xmath85 .the vector and axial vector couplings of @xmath86 with vector bosons .
feynman rules for @xmath87 vertexes are given as @xmath88 @xcite .
[ cols="^,^,^,^",options="header " , ] the amplitudes corresponding to these feynman diagrams are written as : @xmath89 i \gmm g_{v_4}u[p_1](i ) \frac{g^{\alpha\mu}}{q^2}i e_{4 } ( p_3 - p_4)_{\alpha},\ ] ] @xmath90 i \gmm ( \gvi + \gai \gff)u[p_1](i ) \frac{g^{\alpha\mu}-\frac{q^{\mu}q^{\alpha}}{m^{2}_{i}}}{q^2-m^{2}_{i}+i\dwi } i e_{i } ( p_3 - p_4)_{\alpha},\ ] ] where @xmath91 and coefficients @xmath92 are given in table [ pp11vcouplings]([pp22vcouplings ] ) for single(doubly ) charged scalar pair and @xmath93 is for the photon propagating diagram .
the pair production cross sections are calculated by squaring the amplitudes and integrating over phase space . the analytical expression for cross section
is found as @xmath94,\end{aligned}\ ] ] where @xmath95 and @xmath92 for the process @xmath96 ( @xmath97 ) .
the scattering amplitudes of the processes @xmath98 and @xmath99 are dependent on the free parameters of littlest higgs model @xmath100 . in this work ,
the dependence of the cross sections on mixing angles @xmath101 at @xmath64 is examined . for larger values of @xmath31 , the processes are not accessible for @xmath102 because of the kinematical limits of high masses of scalars .
the processes are also strongly dependent on mass of the higgs scalar . in this work
the input parameters are taken as : the higgs mass @xmath103 and the mass of the standard model gauge bosons @xmath104 , @xmath105 and @xmath106 consistent with recent data@xcite .
the total cross sections for the single charged pair productions are plotted in figure [ hpc1 ] with respect to center of mass energy . within the range of electroweak precision data ,
the direct production cross section gets a value of @xmath107 for @xmath108 and @xmath64 for energies @xmath109
. this will give up to @xmath110 productions per year for luminosities of @xmath111 .
for higher values of symmetry breaking scale parameter ( @xmath112 ) , the production process is not accessible for ilc and clic because of the kinematical constraints of high scalar mass . at the final state ,
the decays of the single charged scalar pair strongly depends on the values of the yukawa couplings @xmath53 and @xmath54 as seen from equation [ dwp1 ] . for @xmath115 @xmath116
dominantly decays into same family leptons @xmath117 , violating lepton number . for small values @xmath118
the dominant decay mode is to sm pairs @xmath119 and @xmath120 .
the decay into different families of leptons @xmath121 is proportional to @xmath122 and since the flavor mixing yukawa coupling @xmath54 is constrained to be small no such signals are expected . where @xmath129 $ ] is the branching ratio to sm particles . finally ,
if @xmath130 , about @xmath131 events per year can be observed at an @xmath0 collider with luminosity of @xmath111 for @xmath132 .
the final states will be @xmath133 , which will be detected as two leptons and missing energy .
unfortunately this signal does not allow observing distinct features of the littlest higgs model and lepton flavor violation , since the neutrino flavors can not be identified .
thus this channel contain high sm background , and these signals can have significance only if a detailed background analysis is done . for the process
@xmath134 the total cross section of the production event is examined for @xmath64 .
the dependence of the total cross section of the @xmath134 process on @xmath135 at fixed values of the littlest higgs model parameters are presented in fig .
[ hpc2 ] . for the mixing angles
@xmath136 , the production cross section is maximum with a value of @xmath137 for @xmath64 at @xmath109 . for the parameter sets @xmath138 for @xmath64 ,
the total cross section is is slightly lower but still in the order of @xmath139 at @xmath109 .
thus for an @xmath0 collider with an integrated luminosity of @xmath111 , yearly @xmath140 double charged pair production can be observed .
it is seen from the final decay modes of the doubly charged pair given in eq.[dwp2 ] that the final state analysis is strongly dependent on the value of the yukawa coupling @xmath53 , thus on the value of the triplet vev @xmath33 .
the dependence of the final collider signatures of the process @xmath141 on @xmath53 are plotted in figure [ br2 ] . for @xmath142 ,
the final decays of the doubly charged scalars are dominated by sm charged bosons , and the final collider signature will be @xmath143 . in this case with a subtraction from background , doubly charged scalars can be identified by reconstructing the same sign boson pairs . for @xmath144 , the semi leptonic decay modes , @xmath145 will be observed . for @xmath146 ,
the production rates for these modes are calculated as ; @xmath147 , leading to @xmath148 collider signals per year at collider with a luminosity of @xmath111 at @xmath109 . the cleanest signal in this case
will be observed when both @xmath149 decay into jets ( @xmath150 ) . in this scenario
there will be yearly @xmath151 signal of two same sign leptons of same family plus jets , violating lepton number and flavor by two , which can be directly detectable free from any backgrounds .
the most interesting scenario happens when the yukawa coupling is close to unity , @xmath152 . in this case
all final doubly charged scalars will decay into same family leptons , and the final collider signal will be either @xmath153 or @xmath154 .
the mixed states @xmath155 resulting from the final decays of the doubly charged scalars into different families of leptons are suppressed because of the low production rates due to the value of the yukawa mixing coupling @xmath54 . the branching ratio into the final signal @xmath153 when @xmath156 is calculated as @xmath157 , which will give @xmath158 observable signals per year at an integrated luminosity of @xmath111 when @xmath109 .
for this final signal , the lepton flavor is violated explicitly , free from any backgrounds .
the double charged scalars in this case can be reconstructed from invariant mass distributions of same charged leptons
. for the final state @xmath154 , there will be additional observable @xmath159 events per year .
for this case lepton flavor violation can not be observed directly even if it happens via the lepton flavor violating decays of doubly charged scalars .
although this signal has a huge sm background , with a proper background analysis , the existence of doubly charged scalars and so on their lepton flavor violating decays can be identified . in conclusion , it is found that pair productions of single and doubly charged scalars are in the reach for @xmath1 colliders when @xmath2 .
the production rates of the single charged pair are quite low and final signatures are not promising since neutrinos in the final states can not be identified . for the pair production of doubly charged scalar via process @xmath99 , the production rates are promising and also the final state signatures are distinct observable collider signals depending on final decay modes of the doubly charged pair which were discussed in@xcite . when @xmath160 , the final state will be semileptonic ; i.e : jets plus two same sign leptons of same family , giving an explicit signature of lepton number violation by two .
and also for the case when @xmath161 , the final decays of the doubly charged pair will be leptonic , including an explicit lepton flavor violation in the final state @xmath153 .
these both final signatures are due to distinct features of littlest higgs model and will be free from any backgrounds .
99 n. arkani - hamed , a.g .
cohen , e. katz , and a.e .
nelson , jhep**0207**(2002)034 , arxiv : hep - ph/0206021 . n.
arkani - hamed _
et al . _ , jhep**0208**(2002)021 , arxiv : hep - ph/0206020 . m. schmaltz , nucl.phys.proc.suppl.*117*(2003),arxiv:hep-ph/0210415 .
d.e.kaplan and m. schmaltz , jhep**0310**(2003)039 , arxiv : hep - ph/0302049 . m. perelstein , prog.part.nucl.phys.*58*(2007)247-291 , arxiv : hep - ph/0512128
. t. han , h. e. logan , b. mcelrath and l - t .
wang , phys.rev .
* d67*(2003)095004 , arxiv : hep - ph/0301040 . m. schmaltz and d. tucker - smith , ann.rev.nucl.part.sci.*55*(2005)229-270 , arxiv : hep - ph/0502182 . c. csaki , j. hubisz , g.d .
kribs , p. meade , j. terning , phys . rev .
* d67 * ( 2003 ) 115002 , arxiv : hep - ph/0211124v2
. j. hubisz , p. maeda , a. noble and m. perelstein , jhep**01**(2006)135 .
j. l. hewett , f. j. petriello and t. g. rizzo , jhep * 0310 * ( 2003 ) 062 , arxiv : hep - ph/0211218 .
chen and s. dawson , phys.rev.*d70*(2004)015003 , arxiv : hep - ph/0311032 .
w. killian and j. reuter , phys.rev .
* d70 * ( 2004 ) 015004 , arxiv : hep - ph/0311095 .
dias , c.a . de s. pires p.s .
rodrigues da silva , phys.rev.*d77*(2008)055001 , arxiv : hep - ph/0711.1154 .
c. csaki , j. hubisz , g. d. kribs , p. maede and j. terning , phys.rev .
* d68 * ( 2003 ) 035009 , arxiv : hep - ph/0303236 .
chong - xing yue , shuang zhao , wei ma , nucl.phys.*b 784 * ( 2007 ) , arxiv : hep - ph/0706.0232 .
ayse cagil , mehmet t. zeyrek , phys.rev . * * d80**055021(2009 ) , arxiv : hep - ph/0908.3581 .
* d 74 * , 095003 ( 2006 ) [ erratum - ibid .
d * 74 * , 099905 ( 2006 ) ] , [ arxiv : hep - ph/0609119 ] . j. brau ( ed . ) _ et al _ , by ilc collaboration , _
lc reference design report : ilc global design effort and world wide study .
fermilab - apc , aug 2007 , arxiv : acc - ph/0712.1950 .
r.w . assmann _
_ , the clic study team , _ a 3 tev @xmath162 linear collider based on clic technology _ , cern 2000 - 008 , geneva , 2000 ; e. accomando _ et al . _ , by clic physics working group , _ physics at the clic multi - tev linear collider
_ , cern-2004 - 005 , arxiv : hep - ph/0412251 ; h. braun _ et al .
, by clic study team , _
clic 2008 parameters _
, cern - open-2008 - 021 , clic - note-764 . t. han , h.e .
logan , b. mukhopadhyaya and r. srikanth , phys.rev . *
d72 * ( 2005 ) 053007 , arxiv : hep - ph/0505260 .
choudhury , n. gaur and a. goyal , phys.rev . *
d72 * ( 2005 ) 097702 , arxiv : hep - ph/0508146 .
yue and s. zhao , eur.phys.j.*c50*(2007)897-903 , arxiv : hep - ph/0701017 .
et al . _ ,
phys.rev.*d75*(2007)055011 , arxiv : hep - ph/0612327 .
et al _ , phys .
d**70 * * , 113003(2004 ) ; m. tegmark _
et al _ , sdss collabration , phys .
d**69 * * , 103501(2004 ) .
t. aaltonen , et al , cdf collaboration , phys.rev.lett.99:171802,2007 .
yue , w. yang and f. zhang , nucl.phys .
* b716 * ( 2005 ) 199 - 214 , arxiv : hep - ph/0409066 .[/INST] in this work pair productions of charged and doubly charged scalars in the framework of littlest higgs model at @xmath0 colliders are studied . in the allowed parameter space of the littlest higgs model ,
the production rates of the scalar pairs are calculated .
it is obtained that pair productions of charged and doubly charged scalars are reachable at @xmath1 colliders with energy @xmath2 . using the lepton flavor violating decays of charged scalars calculated in literature , final state analysis is done for pair production processes . this analysis show that depending on the model parameters , lepton number and lepton flavor violations can be observed free from any backgrounds . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Stop Tuberculosis (TB) Now Act''.
SEC. 2. FINDINGS.
Congress finds the following:
(1)(A) Tuberculosis is a great health and economic burden
to impoverished nations and a health and security threat to the
United States and other industrialized countries.
(B) Tuberculosis is one of the greatest infectious causes
of death of adults worldwide, killing nearly 2,000,000 people
per year--one person every 15 seconds.
(2) An estimated 8,000,000 individuals develop active
tuberculosis each year.
(3) Today, tuberculosis is the leading killer of women of
reproductive age and of people who are HIV-positive.
(4) Tuberculosis is spreading as a result of inadequate
treatment and is a disease that knows no national borders.
(5) With over 50 percent of tuberculosis cases in the
United States attributable to foreign-born individuals and with
the increase in international travel, commerce, and migration,
elimination of tuberculosis in the United States depends on
efforts to control the disease in developing countries.
(6) The threat that tuberculosis poses for Americans
derives from the global spread of tuberculosis and the
emergence and spread of strains of multi-drug resistant
tuberculosis (MDR-TB).
(7) Up to 50,000,000 individuals may be infected with
multi-drug resistant tuberculosis.
(8) In the United States, tuberculosis treatment, normally
about $2,000 per patient, increases to as much as $1,000,000
per patient to treat multi-drug resistant tuberculosis, and
treatment may not even be successful.
(9) Without access to treatment, multi-drug resistant
tuberculosis is a virtual death sentence.
(10) There is a highly effective and inexpensive treatment
for standard tuberculosis. Recommended by the World Health
Organization (WHO) as the best curative method for
tuberculosis, this strategy, known as DOTS (Directly Observed
Treatment Short-course), includes low-cost effective diagnosis,
treatment, monitoring, and record keeping, as well as a
reliable drug supply. A centerpiece of DOTS is observing
patients to ensure that they take their medication and complete
treatment.
(11) DOTS is one of the most cost-effective health
interventions available today. A full course of DOTS drugs
costs as little as $10 in low-income countries.
(12) Proper DOTS treatment is imperative to prevent the
development of dangerous multi-drug resistant tuberculosis that
arises through improper or incomplete tuberculosis treatment.
(13) Building upon the DOTS strategy, DOTS-Plus is a
comprehensive tuberculosis management strategy that works as a
supplement to the standard DOTS strategy to address areas where
there is high prevalence of multi-drug resistant tuberculosis.
(14) The Global Fund to Fight AIDS, Tuberculosis and
Malaria is an important new global partnership established to
combat these 3 infectious diseases that together kill 6,000,000
people a year. Expansion of effective tuberculosis treatment
programs constitutes a major component of Global Fund
investment, along with integrated efforts to address HIV and
tuberculosis in areas of high prevalence.
(15) The Centers for Disease Control and Prevention (CDC)
is actively involved with global tuberculosis control efforts
since the global tuberculosis epidemic directly impacts
tuberculosis in the United States, and because Congress has
strongly urged the CDC each year to increase its involvement
with international tuberculosis control efforts.
(16) The CDC is assisting countries with a high burden of
tuberculosis--
(A) to implement the World Health Organization-
recommended control strategies, DOTS and DOTS-Plus;
(B) to identify and treat persons with multi-drug
resistant tuberculosis; and
(C) to conduct research to identify new
diagnostics, treatments, and interventions to control
tuberculosis.
SEC. 3. FOREIGN ASSISTANCE FOR TUBERCULOSIS PREVENTION, TREATMENT, AND
CONTROL.
(a) Amendment to Foreign Assistance Act of 1961.--Chapter 1 of part
I of the Foreign Assistance Act of 1961 (22 U.S.C. 2151 et seq.) is
amended by inserting after section 104 the following new section:
``SEC. 104A. ASSISTANCE FOR TUBERCULOSIS PREVENTION, TREATMENT, AND
CONTROL.
``(a) Statement of Policy.--Congress recognizes the growing
international problem of tuberculosis and the impact its continued
existence has on those nations that had previously largely controlled
the disease. Congress further recognizes that the means exist to
control and treat tuberculosis, and that it is therefore a major
objective of the foreign assistance program to control the disease.
``(b) Assistance.--
``(1) In general.--In meeting the objective described in
subsection (a), the President shall provide assistance for the
prevention, treatment, and control of tuberculosis.
``(2) Additional requirements.--In carrying out paragraph
(1), the President shall--
``(A) coordinate with the World Health Organization
(WHO), the Global Fund to Fight AIDS, Tuberculosis and
Malaria, the Department of Health and Human Services
(including Centers for Disease Control and Prevention
and the National Institutes of Health), and other
organizations with respect to the development and
implementation of a comprehensive tuberculosis control
program;
``(B) set as a goal the detection of at least 70
percent of the cases of infectious tuberculosis, the
cure of at least 85 percent of the cases detected by
focusing efforts on the use of the Directly Observed
Treatment Short-course (DOTS) strategy or other
internationally accepted primary tuberculosis control
strategies, in those countries in which the United
States Agency for International Development has
established development programs, by December 31, 2010,
and the reduction of tuberculosis-related deaths by 50
percent, by December 31, 2010; and
``(C) give priority to activities that increase
Directly Observed Treatment Short-course (DOTS)
coverage and treatment of multi-drug resistant
tuberculosis where needed using DOTS-Plus, including
funding for the Global Tuberculosis Drug Facility, the
Stop Tuberculosis Partnership, and the Global Alliance
for TB Drug Development.
``(c) Allocation of Funds.--In carrying out subsection (b), the
President shall ensure that--
``(1) not less than 75 percent of the amount made available
to carry out this section for a fiscal year shall be expended
for antituberculosis drugs, supplies, direct patient services,
and training in diagnosis and treatment for Directly Observed
Treatment Short-course (DOTS) coverage and treatment of multi-
drug resistant tuberculosis using DOTS-Plus; and
``(2) not less than 10 percent of the amount made available
to carry out this section for a fiscal year shall be expended
to provide a United States contribution to the Global
Tuberculosis Drug Facility.
``(d) Annual Report.--Not later than January 31 of each year, the
President shall transmit to the appropriate congressional committees a
report that contains a summary of all programs, projects, and
activities carried out under this section for the preceding fiscal
year, including a description of the increase in the number of
individuals treated and cured through each program, project, and
activity.
``(e) Authorization of Appropriations.--
``(1) In general.--There are authorized to be appropriated
to the President to carry out this section $200,000,000 for
each of the fiscal years 2004 and 2005.
``(2) Availability.--Amounts appropriated pursuant to the
authorization of appropriations under paragraph (1) are
authorized to remain available until expended.
``(f) Definitions.--In this section:
``(1) Appropriate congressional committees.--The term
`appropriate congressional committees' means the Committee on
International Relations of the House of Representatives and the
Committee on Foreign Relations of the Senate.
``(2) DOTS.--The term `DOTS' or `Directly Observed
Treatment Short-course' means the World Health Organization-
recommended strategy for treating tuberculosis.
``(3) DOTS-plus.--The term `DOTS-Plus' means a
comprehensive tuberculosis management strategy that is built
upon and works as a supplement to the standard DOTS strategy,
and which takes into account specific issues (such as use of
second line anti-tuberculosis drugs) that need to be addressed
in areas where there is high prevalence of multi-drug resistant
tuberculosis.
``(4) Global alliance for tuberculosis drug development.--
The term `Global Alliance for Tuberculosis Drug Development'
means the public-private partnership that brings together
leaders in health, science, philanthropy, and private industry
to ensure that new medications are available and affordable in
high tuberculosis burden countries and other affected
countries.
``(5) Global tuberculosis drug facility.--The term `Global
Tuberculosis Drug Facility (GDF)' means the new initiative of
the Stop Tuberculosis Partnership to increase access to high-
quality tuberculosis drugs to facilitate DOTS expansion.
``(6) Stop tuberculosis partnership.--The term `Stop
Tuberculosis Partnership' means the partnership of the World
Health Organization, donors including the United States, high
tuberculosis burden countries, multilateral agencies, and
nongovernmental and technical agencies committed to short- and
long-term measures required to control and eventually eliminate
tuberculosis as a public health problem in the world.''.
(b) Conforming Amendment.--Section 104(c) of the Foreign Assistance
Act of 1961 (22 U.S.C. 2151b(c)) is amended by striking paragraph (7).
(c) Effective Date.--The amendments made by this section shall take
effect on October 1, 2003, or the date of the enactment of this Act,
whichever occurs later.
SEC. 4. AUTHORIZATION OF APPROPRIATIONS FOR GLOBAL TUBERCULOSIS
ACTIVITIES OF THE CENTERS FOR DISEASE CONTROL AND
PREVENTION.
For the purpose of carrying out global tuberculosis activities
through the Centers for Disease Control and Prevention, there are
authorized to be appropriated $30,000,000 for fiscal year 2004, and
such sums as may be necessary for fiscal year 2005. Such authorization
is in addition to other authorizations of appropriations that are
available for such purpose. Amounts appropriated under this section
shall remain available until expended. | Stop Tuberculosis (TB) Now Act - Amends the Foreign Assistance Act of 1961 to direct the President to provide assistance for the prevention, treatment and control of tuberculosis. Requires the President to: (1) coordinate with specified health agencies worldwide to develop and implement a comprehensive tuberculosis control program; (2) set as a goal the detection of at least 70 percent of the cases of infectious tuberculosis, the cure of at least 85 percent of the cases detected, and the reduction of tuberculosis-related deaths by 50 percent by December 31, 2010; (3) give priority to activities that increase Directly Observed Treatment Short-course (DOTS) coverage (World Health Organization-recommended strategy for treating tuberculosis) and treatment of multi-drug resistant tuberculosis using DOTS-Plus; (4) expend at least 75 percent of the allocated funds on antituberculosis drugs, supplies, direct patient service, and training in diagnosis and treatment of DOTS and DOTS-Plus; (5) expend at least 10 percent of the allocated funds on a U.S. contribution to the Global Tuberculosis Drug Facility.
Authorizes appropriations for global tuberculosis activities of the Centers for Disease Control and Prevention. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Stop Tuberculosis (TB) Now Act''.
SEC. 2. FINDINGS.
Congress finds the following:
(1)(A) Tuberculosis is a great health and economic burden
to impoverished nations and a health and security threat to the
United States and other industrialized countries.
(B) Tuberculosis is one of the greatest infectious causes
of death of adults worldwide, killing nearly 2,000,000 people
per year--one person every 15 seconds.
(2) An estimated 8,000,000 individuals develop active
tuberculosis each year.
(3) Today, tuberculosis is the leading killer of women of
reproductive age and of people who are HIV-positive.
(4) Tuberculosis is spreading as a result of inadequate
treatment and is a disease that knows no national borders.
(5) With over 50 percent of tuberculosis cases in the
United States attributable to foreign-born individuals and with
the increase in international travel, commerce, and migration,
elimination of tuberculosis in the United States depends on
efforts to control the disease in developing countries.
(6) The threat that tuberculosis poses for Americans
derives from the global spread of tuberculosis and the
emergence and spread of strains of multi-drug resistant
tuberculosis (MDR-TB).
(7) Up to 50,000,000 individuals may be infected with
multi-drug resistant tuberculosis.
(8) In the United States, tuberculosis treatment, normally
about $2,000 per patient, increases to as much as $1,000,000
per patient to treat multi-drug resistant tuberculosis, and
treatment may not even be successful.
(9) Without access to treatment, multi-drug resistant
tuberculosis is a virtual death sentence.
(10) There is a highly effective and inexpensive treatment
for standard tuberculosis. Recommended by the World Health
Organization (WHO) as the best curative method for
tuberculosis, this strategy, known as DOTS (Directly Observed
Treatment Short-course), includes low-cost effective diagnosis,
treatment, monitoring, and record keeping, as well as a
reliable drug supply. A centerpiece of DOTS is observing
patients to ensure that they take their medication and complete
treatment.
(11) DOTS is one of the most cost-effective health
interventions available today. A full course of DOTS drugs
costs as little as $10 in low-income countries.
(12) Proper DOTS treatment is imperative to prevent the
development of dangerous multi-drug resistant tuberculosis that
arises through improper or incomplete tuberculosis treatment.
(13) Building upon the DOTS strategy, DOTS-Plus is a
comprehensive tuberculosis management strategy that works as a
supplement to the standard DOTS strategy to address areas where
there is high prevalence of multi-drug resistant tuberculosis.
(14) The Global Fund to Fight AIDS, Tuberculosis and
Malaria is an important new global partnership established to
combat these 3 infectious diseases that together kill 6,000,000
people a year. Expansion of effective tuberculosis treatment
programs constitutes a major component of Global Fund
investment, along with integrated efforts to address HIV and
tuberculosis in areas of high prevalence.
(15) The Centers for Disease Control and Prevention (CDC)
is actively involved with global tuberculosis control efforts
since the global tuberculosis epidemic directly impacts
tuberculosis in the United States, and because Congress has
strongly urged the CDC each year to increase its involvement
with international tuberculosis control efforts.
(16) The CDC is assisting countries with a high burden of
tuberculosis--
(A) to implement the World Health Organization-
recommended control strategies, DOTS and DOTS-Plus;
(B) to identify and treat persons with multi-drug
resistant tuberculosis; and
(C) to conduct research to identify new
diagnostics, treatments, and interventions to control
tuberculosis.
SEC. 3. FOREIGN ASSISTANCE FOR TUBERCULOSIS PREVENTION, TREATMENT, AND
CONTROL.
(a) Amendment to Foreign Assistance Act of 1961.--Chapter 1 of part
I of the Foreign Assistance Act of 1961 (22 U.S.C. 2151 et seq.) is
amended by inserting after section 104 the following new section:
``SEC. 104A. ASSISTANCE FOR TUBERCULOSIS PREVENTION, TREATMENT, AND
CONTROL.
``(a) Statement of Policy.--Congress recognizes the growing
international problem of tuberculosis and the impact its continued
existence has on those nations that had previously largely controlled
the disease. Congress further recognizes that the means exist to
control and treat tuberculosis, and that it is therefore a major
objective of the foreign assistance program to control the disease.
``(b) Assistance.--
``(1) In general.--In meeting the objective described in
subsection (a), the President shall provide assistance for the
prevention, treatment, and control of tuberculosis.
``(2) Additional requirements.--In carrying out paragraph
(1), the President shall--
``(A) coordinate with the World Health Organization
(WHO), the Global Fund to Fight AIDS, Tuberculosis and
Malaria, the Department of Health and Human Services
(including Centers for Disease Control and Prevention
and the National Institutes of Health), and other
organizations with respect to the development and
implementation of a comprehensive tuberculosis control
program;
``(B) set as a goal the detection of at least 70
percent of the cases of infectious tuberculosis, the
cure of at least 85 percent of the cases detected by
focusing efforts on the use of the Directly Observed
Treatment Short-course (DOTS) strategy or other
internationally accepted primary tuberculosis control
strategies, in those countries in which the United
States Agency for International Development has
established development programs, by December 31, 2010,
and the reduction of tuberculosis-related deaths by 50
percent, by December 31, 2010; and
``(C) give priority to activities that increase
Directly Observed Treatment Short-course (DOTS)
coverage and treatment of multi-drug resistant
tuberculosis where needed using DOTS-Plus, including
funding for the Global Tuberculosis Drug Facility, the
Stop Tuberculosis Partnership, and the Global Alliance
for TB Drug Development.
``(c) Allocation of Funds.--In carrying out subsection (b), the
President shall ensure that--
``(1) not less than 75 percent of the amount made available
to carry out this section for a fiscal year shall be expended
for antituberculosis drugs, supplies, direct patient services,
and training in diagnosis and treatment for Directly Observed
Treatment Short-course (DOTS) coverage and treatment of multi-
drug resistant tuberculosis using DOTS-Plus; and
``(2) not less than 10 percent of the amount made available
to carry out this section for a fiscal year shall be expended
to provide a United States contribution to the Global
Tuberculosis Drug Facility.
``(d) Annual Report.--Not later than January 31 of each year, the
President shall transmit to the appropriate congressional committees a
report that contains a summary of all programs, projects, and
activities carried out under this section for the preceding fiscal
year, including a description of the increase in the number of
individuals treated and cured through each program, project, and
activity.
``(e) Authorization of Appropriations.--
``(1) In general.--There are authorized to be appropriated
to the President to carry out this section $200,000,000 for
each of the fiscal years 2004 and 2005.
``(2) Availability.--Amounts appropriated pursuant to the
authorization of appropriations under paragraph (1) are
authorized to remain available until expended.
``(f) Definitions.--In this section:
``(1) Appropriate congressional committees.--The term
`appropriate congressional committees' means the Committee on
International Relations of the House of Representatives and the
Committee on Foreign Relations of the Senate.
``(2) DOTS.--The term `DOTS' or `Directly Observed
Treatment Short-course' means the World Health Organization-
recommended strategy for treating tuberculosis.
``(3) DOTS-plus.--The term `DOTS-Plus' means a
comprehensive tuberculosis management strategy that is built
upon and works as a supplement to the standard DOTS strategy,
and which takes into account specific issues (such as use of
second line anti-tuberculosis drugs) that need to be addressed
in areas where there is high prevalence of multi-drug resistant
tuberculosis.
``(4) Global alliance for tuberculosis drug development.--
The term `Global Alliance for Tuberculosis Drug Development'
means the public-private partnership that brings together
leaders in health, science, philanthropy, and private industry
to ensure that new medications are available and affordable in
high tuberculosis burden countries and other affected
countries.
``(5) Global tuberculosis drug facility.--The term `Global
Tuberculosis Drug Facility (GDF)' means the new initiative of
the Stop Tuberculosis Partnership to increase access to high-
quality tuberculosis drugs to facilitate DOTS expansion.
``(6) Stop tuberculosis partnership.--The term `Stop
Tuberculosis Partnership' means the partnership of the World
Health Organization, donors including the United States, high
tuberculosis burden countries, multilateral agencies, and
nongovernmental and technical agencies committed to short- and
long-term measures required to control and eventually eliminate
tuberculosis as a public health problem in the world.''.
(b) Conforming Amendment.--Section 104(c) of the Foreign Assistance
Act of 1961 (22 U.S.C. 2151b(c)) is amended by striking paragraph (7).
(c) Effective Date.--The amendments made by this section shall take
effect on October 1, 2003, or the date of the enactment of this Act,
whichever occurs later.
SEC. 4. AUTHORIZATION OF APPROPRIATIONS FOR GLOBAL TUBERCULOSIS
ACTIVITIES OF THE CENTERS FOR DISEASE CONTROL AND
PREVENTION.
For the purpose of carrying out global tuberculosis activities
through the Centers for Disease Control and Prevention, there are
authorized to be appropriated $30,000,000 for fiscal year 2004, and
such sums as may be necessary for fiscal year 2005. Such authorization
is in addition to other authorizations of appropriations that are
available for such purpose. Amounts appropriated under this section
shall remain available until expended.[/INST]Stop Tuberculosis (TB) Now Act - Amends the Foreign Assistance Act of 1961 to direct the President to provide assistance for the prevention, treatment and control of tuberculosis. Requires the President to: (1) coordinate with specified health agencies worldwide to develop and implement a comprehensive tuberculosis control program; (2) set as a goal the detection of at least 70 percent of the cases of infectious tuberculosis, the cure of at least 85 percent of the cases detected, and the reduction of tuberculosis-related deaths by 50 percent by December 31, 2010; (3) give priority to activities that increase Directly Observed Treatment Short-course (DOTS) coverage (World Health Organization-recommended strategy for treating tuberculosis) and treatment of multi-drug resistant tuberculosis using DOTS-Plus; (4) expend at least 75 percent of the allocated funds on antituberculosis drugs, supplies, direct patient service, and training in diagnosis and treatment of DOTS and DOTS-Plus; (5) expend at least 10 percent of the allocated funds on a U.S. contribution to the Global Tuberculosis Drug Facility.
Authorizes appropriations for global tuberculosis activities of the Centers for Disease Control and Prevention.</s> |
benign prostatic hyperplasia ( bph ) is found in over half of 60-year - old men and in almost all 80-year - old men who develop bladder outlet obstruction ( boo ) and lower urinary tract symptoms ( luts ) .
boo is the initial pathophysiological change caused by an enlarged adenoma and is followed by detrusor overactivity ( do ) or underactivity ( dua ) .
the degree of boo is an important factor that can reflect the severity of disease and that can aid in choosing a treatment method as well as in measuring the outcome of the treatment .
it has been shown that one third of male patients with luts do not have definite boo and that 5 to 35% of the patients with luts and undefined boo do not have favorable symptom recovery after transurethral resection of the prostate ( turp ) [ 2 - 7 ] .
relevant examinations ranging from serum prostate - specific antigen ( psa ) to urodynamics can all reflect different aspects of the severity of bph .
urodynamics is the only method , however , that can quantify the degree of boo and the status of detrusor contractility .
therefore , guidelines from the international scientific committee and the american urological association on the management of bph both recommend the use of urodynamics to evaluate bph patients considered as candidates for invasive therapy .
however , the routine use of preoperative urodynamics is still a controversial point in published articles because of the invasiveness and high costs of the method . in this research , we attempted to determine whether other parameters could be used to measure the severity of boo through less - invasive or noninvasive examinations by analyzing correlations among parameters from clinical history , symptoms , ultrasonography , and urodynamics .
this retrospective analysis was conducted on patients with bph who had received either medication or surgical treatment at this hospital between may 2010 and june 2011 . the therapeutic decision for turp
all patients were evaluated with the international prostate symptom score ( ipss , including the total score ; subtotal score of storage symptoms comprising the summation of nocturia , urgency , and an increased frequency score ; and subtotal score of voiding symptoms comprising the summation of hesitancy , intermittency , and weak stream score ) and quality of life ( qol ) questionnaires in addition to undergoing basic clinical evaluations ( medical history , physical examination , urinalysis , and renal function assessment ) before treatment .
free flowmetry measurement was performed for all patients with the result being adopted when the voiding volume was more than 150 ml .
urodynamics was performed only for patients needing surgery by use of a multichannel system ( uds64-iii , laborie co. , quebec , canada ) .
first , water - filling cystometry was done with the patients in the supine position with the use of a transurethral 12 fr double - lumen catheter and the simultaneous monitoring of rectal pressure .
filling was performed at a rate of 50 ml / min with normal saline and was stopped if the patient had a strong desire to void . pressure flow study ( pfs )
was then performed by asking the patients to void in an upright position with a suprapubically placed 6 fr cystostomy tube to monitor the bladder pressure . maximum urinary flow ( qmax ) and pressure of the detrusor at qmax ( pdetqmax ) were recorded . the bladder outlet obstruction index ( booi , by " pdetqmax-2qmax " ) and the bladder contractility index ( by " pdetqmax+5qmax " ) were then calculated by use of equations from the ics
. total prostate volume ( tpv ) , transitional zone volume ( tzv ) , intravesical prostatic protrusion ( ipp ) , and post - voiding residual ( pvr ) were measured by transrectal ultrasonography ( trus ) with the transitional zone index ( tzi , by " tzv / tpv " ) being calculated for all patients .
the exclusion criteria for enrolled subjects were 1 ) booi less than 20 or qmax more than 20 ml / s , 2 ) disease with boo other than bph , 3 ) history of prostatic or urethral surgery , 4 ) diagnosed carcinoma of the prostate or bladder , 5 ) known bladder stones or neurogenic bladder dysfunction , and 6 ) not having taken standard medication involving both alpha - adrenergic blockers and 5-alpha - reductase inhibitors for over 6 months .
the relevant clinical data of the subjects were recorded and classified by degree of ipp ( < 10 mm , 10 to 20 mm , and > 20 mm ) and tzi value ( < 0.5 , 0.5 to 0.7 , and > 0.7 ) . all quantitative variables were tested for the type of distribution by use of the one - sample kolmogorov - smirnov test .
univariate analyses including one - way analysis of variance and kruskal - wallis test were used for variables with normal or skewed distributions , respectively , to assess the differences between patients receiving drug therapy and those undergoing surgical therapy and between patients with different degrees of ipp and tzi values .
the -test was used for categorical variables to identify whether there were different incidences of acute urinary retention ( aur ) influenced by different ipp or tzi grade .
finally , bivariate correlation and multiple regression analysis were used to assess correlations between parameters from trus and pfs .
all analyses were performed by using the routines of the ibm spss ver . 19.0 ( ibm co. , new york , ny , usa ) , and
the research attained ethical approval from the ethics committee of xin hua hospital , and all subjects gave written informed consent .
a total of 365 patients were enrolled in the research study , with 203 patients receiving medication and the remainder having undergone turp .
the clinical data of all subjects were classified according to therapy and degree of ipp and tzi and are listed in tables 1 and 2 .
univariate analyses showed significant differences in the total , storage , and voiding scores of the ipss ; qol score ; tpv ; tzv ; tzi ; ipp ; and qmax between the therapy groups ( p<0.05 ) .
baseline total prostate - specific antigen , tpv , tzv , ipp , qmax , pdetqmax , and booi classified by different degrees of tzi were also found to be significantly different ( p<0.05 ) .
differences were also found in the voiding symptom score , tpv , tzv , tzi , qmax , and booi classified by degree of ipp ( p<0.05 ) .
ipp ( p=0.000 ) and tzi ( p=0.000 ) both had statistically significant effects on the cause of aur ( table 2 ) by -test .
the bivariate correlation analysis of parameters from symptom score , trus , and urodynamics showed significant correlations between tzi and qmax ( r=-0.887 , p=0.001 ) , pdetqmax ( r=0.725 , p=0.028 ) , and booi ( r=0.508 , p=0.029 ) and between ipp and voiding symptom score ( r=0.353 , p=0.033 ) , qmax ( r=-0.852 , p=0.014 ) , and booi ( r=0.469 , p=0.042 ) .
multiple regression analysis in the subjects who underwent turp showed that both tzi and ipp had significant correlations with qmax and booi , whereas tzi had a significant correlation with pdetqmax ( table 3 ) .
prostatic adenoma enlargement increases urethral resistance and leads to boo , further resulting in compensatory changes in bladder function .
however , the elevated detrusor pressure required to maintain urinary flow in the presence of increased outflow resistance occurs at the expense of normal bladder storage function , which is the source of do . with the continuation of obstruction , decompensation of the detrusor and dua
the degree of boo is correlated with the severity of obstruction - relevant symptoms , and the recovery of boo is used to evaluate the efficacy of treatment of bph .
furthermore , the baseline degree of boo was recently found to influence the outcome of treatment .
research has shown that patients with boo have better outcomes from turp than do those without boo [ 11 - 14 ] .
one research study showed that patients with boo will still have a favorable surgical outcome even if they have do or dua .
therefore , some hospitals use urodynamics as a routine preoperative examination to confirm whether the candidates have explicit boo and good detrusor contractility .
however , urodynamic study is not totally innocuous , with significant evidence of discomfort and urinary infections associated with performing the examination , as well as imposing additional cost to the patient or to the institution . for this reason
, some research has been initiated to find less - invasive or noninvasive examinations for evaluating the degree of boo .
ipp measured as the shortest distance connecting the protruded end of the prostate into the bladder based on the bladder neck in the sagittal plane reflects the maximum longitudinal length of the prostate and may help in assessing the obstructive level of the prostate .
first studied the correlation between ipp and the booi in 30 male outpatients in 2005 and found that ipp grading correlated well with the booi .
analyzed 206 bph patients classified by different ipp grade and found that the ipp value positively correlated with tpv , psa , pvr , qmax , pdetqmax , and booi as well as the incidence of aur , bladder trabeculation , detrusor overactivity , and low bladder compliance .
analyzed 260 men with luts and found that the booi was higher in patients with apparent ipp than in those without .
the tzi calculated as tzv divided by tpv may also correlate with the obstructive level because higher volumes of the transition zone will result in harder pressure on the urethra .
kaplan et al . evaluated 61 men with symptomatic bph and found a significant correlation between tzi and symptoms , qmax , and pdetqmax .
analyzed 116 bph patients and found that tzi and tzv were both positively correlated with booi and ipss .
milonas et al . reported that lower tzi was an independent predictor of ineffective surgical outcome . in the present study
, we found significant correlations in surgical patients between both tzi and ipp with parameters reflecting the level of boo , such as qmax , pdetqmax , and booi .
these results are consistent with the results of former research and suggest that tzi and ipp may be appropriate parameters in diagnosing and classifying boo . for a long period
, turp has been the gold standard surgical procedure based on the concept of removing the whole enlarged adenoma involved in static and dynamic urethral obstruction .
however , the development of medication such as alpha - adrenergic blockers and 5-alpha - reductase inhibitors has decreased the progression of bph and the operation rate in patients in recent years .
however , some patients can not achieve favorable recovery from drug therapy and need a surgeon to relieve the symptoms .
the patients needing surgical therapy in our research were found to have higher values of both ipp and tzi than the patients needing only drug therapy .
this result suggests that ipp and tzi could measure the disease progression in bph patients receiving medication and might have predictive value for medication efficacy .
higher ipp grade was found to correlate with higher voiding symptom score , which demonstrated that ipp could reflect the severity of bph from not only an objective aspect but also a subjective aspect .
aur is one of the most serious complications of bph and an indication for surgical intervention .
this research has found positive correlations between not only ipp but also tzi and the incidence of aur , which further suggests that these 2 factors might be used to predict the progression of bph and the possibility of undergoing surgical therapy .
in general , this research investigated tzi and ipp from trus in bph patients and found positive correlations between these indexes and symptoms , boo level , and the incidence of aur .
tzi and ipp were also found to differ significantly between bph patients receiving medication and those undergoing surgical therapy .
the results demonstrated that the two parameters had favorable value for assessing severity and progression in patients with bph .
however , this research was retrospective only , with inevitable bias from subject selection and follow - up time . therefore , more prospective research should be launched to investigate the predictive value of the two parameters for the progression and treatment efficacy of bph . | purposethe aim of this research was to assess the value of the transitional zone index ( tzi ) and intravesical prostatic protrusion ( ipp ) from transrectal ultrasonography in evaluating the severity and progression of disease by analyzing the relationship between the 2 parameters and symptoms , clinical history , and urodynamics in benign prostatic hyperplasia ( bph ) patients undergoing different treatment.materials and methodsa total of 203 patients receiving medication and 162 patients who underwent transurethral resection of the prostate because of bph were enrolled in this retrospective analysis .
the clinical history and subjective and objective examination results of all patients were recorded and compared after being classified by tzi and ipp level .
linear regression was used to find correlations between ipp , tzi , and urodynamics.resultsthe 2 parameters were found to differ significantly between patients receiving medication and patients undergoing surgical therapy ( p<0.05 ) .
psa , maximum flow rate ( qmax ) , detrusor pressure at qmax ( pdetqmax ) , and the bladder outlet obstruction index ( booi ) differed according to various tzi levels ( p<0.05 ) .
in addition , the voiding symptom score , qmax , and booi of subgroups with various ipp levels were also significantly different ( p<0.05 ) .
both tzi and ipp had significant effects on qmax , booi , and pdetqmax ( p<0.05 ) and the incidence of acute urinary retention ( p=0.000).conclusionsthe results demonstrated that both tzi and ipp had favorable value for assessing severity and progression in patients with bph .
further studies are needed to confirm whether the two parameters have predictive value in the efficacy of bph treatment and could be considered as factors in the selection of therapy . | <s>[INST]benign prostatic hyperplasia ( bph ) is found in over half of 60-year - old men and in almost all 80-year - old men who develop bladder outlet obstruction ( boo ) and lower urinary tract symptoms ( luts ) .
boo is the initial pathophysiological change caused by an enlarged adenoma and is followed by detrusor overactivity ( do ) or underactivity ( dua ) .
the degree of boo is an important factor that can reflect the severity of disease and that can aid in choosing a treatment method as well as in measuring the outcome of the treatment .
it has been shown that one third of male patients with luts do not have definite boo and that 5 to 35% of the patients with luts and undefined boo do not have favorable symptom recovery after transurethral resection of the prostate ( turp ) [ 2 - 7 ] .
relevant examinations ranging from serum prostate - specific antigen ( psa ) to urodynamics can all reflect different aspects of the severity of bph .
urodynamics is the only method , however , that can quantify the degree of boo and the status of detrusor contractility .
therefore , guidelines from the international scientific committee and the american urological association on the management of bph both recommend the use of urodynamics to evaluate bph patients considered as candidates for invasive therapy .
however , the routine use of preoperative urodynamics is still a controversial point in published articles because of the invasiveness and high costs of the method . in this research , we attempted to determine whether other parameters could be used to measure the severity of boo through less - invasive or noninvasive examinations by analyzing correlations among parameters from clinical history , symptoms , ultrasonography , and urodynamics .
this retrospective analysis was conducted on patients with bph who had received either medication or surgical treatment at this hospital between may 2010 and june 2011 . the therapeutic decision for turp
all patients were evaluated with the international prostate symptom score ( ipss , including the total score ; subtotal score of storage symptoms comprising the summation of nocturia , urgency , and an increased frequency score ; and subtotal score of voiding symptoms comprising the summation of hesitancy , intermittency , and weak stream score ) and quality of life ( qol ) questionnaires in addition to undergoing basic clinical evaluations ( medical history , physical examination , urinalysis , and renal function assessment ) before treatment .
free flowmetry measurement was performed for all patients with the result being adopted when the voiding volume was more than 150 ml .
urodynamics was performed only for patients needing surgery by use of a multichannel system ( uds64-iii , laborie co. , quebec , canada ) .
first , water - filling cystometry was done with the patients in the supine position with the use of a transurethral 12 fr double - lumen catheter and the simultaneous monitoring of rectal pressure .
filling was performed at a rate of 50 ml / min with normal saline and was stopped if the patient had a strong desire to void . pressure flow study ( pfs )
was then performed by asking the patients to void in an upright position with a suprapubically placed 6 fr cystostomy tube to monitor the bladder pressure . maximum urinary flow ( qmax ) and pressure of the detrusor at qmax ( pdetqmax ) were recorded . the bladder outlet obstruction index ( booi , by " pdetqmax-2qmax " ) and the bladder contractility index ( by " pdetqmax+5qmax " ) were then calculated by use of equations from the ics
. total prostate volume ( tpv ) , transitional zone volume ( tzv ) , intravesical prostatic protrusion ( ipp ) , and post - voiding residual ( pvr ) were measured by transrectal ultrasonography ( trus ) with the transitional zone index ( tzi , by " tzv / tpv " ) being calculated for all patients .
the exclusion criteria for enrolled subjects were 1 ) booi less than 20 or qmax more than 20 ml / s , 2 ) disease with boo other than bph , 3 ) history of prostatic or urethral surgery , 4 ) diagnosed carcinoma of the prostate or bladder , 5 ) known bladder stones or neurogenic bladder dysfunction , and 6 ) not having taken standard medication involving both alpha - adrenergic blockers and 5-alpha - reductase inhibitors for over 6 months .
the relevant clinical data of the subjects were recorded and classified by degree of ipp ( < 10 mm , 10 to 20 mm , and > 20 mm ) and tzi value ( < 0.5 , 0.5 to 0.7 , and > 0.7 ) . all quantitative variables were tested for the type of distribution by use of the one - sample kolmogorov - smirnov test .
univariate analyses including one - way analysis of variance and kruskal - wallis test were used for variables with normal or skewed distributions , respectively , to assess the differences between patients receiving drug therapy and those undergoing surgical therapy and between patients with different degrees of ipp and tzi values .
the -test was used for categorical variables to identify whether there were different incidences of acute urinary retention ( aur ) influenced by different ipp or tzi grade .
finally , bivariate correlation and multiple regression analysis were used to assess correlations between parameters from trus and pfs .
all analyses were performed by using the routines of the ibm spss ver . 19.0 ( ibm co. , new york , ny , usa ) , and
the research attained ethical approval from the ethics committee of xin hua hospital , and all subjects gave written informed consent .
a total of 365 patients were enrolled in the research study , with 203 patients receiving medication and the remainder having undergone turp .
the clinical data of all subjects were classified according to therapy and degree of ipp and tzi and are listed in tables 1 and 2 .
univariate analyses showed significant differences in the total , storage , and voiding scores of the ipss ; qol score ; tpv ; tzv ; tzi ; ipp ; and qmax between the therapy groups ( p<0.05 ) .
baseline total prostate - specific antigen , tpv , tzv , ipp , qmax , pdetqmax , and booi classified by different degrees of tzi were also found to be significantly different ( p<0.05 ) .
differences were also found in the voiding symptom score , tpv , tzv , tzi , qmax , and booi classified by degree of ipp ( p<0.05 ) .
ipp ( p=0.000 ) and tzi ( p=0.000 ) both had statistically significant effects on the cause of aur ( table 2 ) by -test .
the bivariate correlation analysis of parameters from symptom score , trus , and urodynamics showed significant correlations between tzi and qmax ( r=-0.887 , p=0.001 ) , pdetqmax ( r=0.725 , p=0.028 ) , and booi ( r=0.508 , p=0.029 ) and between ipp and voiding symptom score ( r=0.353 , p=0.033 ) , qmax ( r=-0.852 , p=0.014 ) , and booi ( r=0.469 , p=0.042 ) .
multiple regression analysis in the subjects who underwent turp showed that both tzi and ipp had significant correlations with qmax and booi , whereas tzi had a significant correlation with pdetqmax ( table 3 ) .
prostatic adenoma enlargement increases urethral resistance and leads to boo , further resulting in compensatory changes in bladder function .
however , the elevated detrusor pressure required to maintain urinary flow in the presence of increased outflow resistance occurs at the expense of normal bladder storage function , which is the source of do . with the continuation of obstruction , decompensation of the detrusor and dua
the degree of boo is correlated with the severity of obstruction - relevant symptoms , and the recovery of boo is used to evaluate the efficacy of treatment of bph .
furthermore , the baseline degree of boo was recently found to influence the outcome of treatment .
research has shown that patients with boo have better outcomes from turp than do those without boo [ 11 - 14 ] .
one research study showed that patients with boo will still have a favorable surgical outcome even if they have do or dua .
therefore , some hospitals use urodynamics as a routine preoperative examination to confirm whether the candidates have explicit boo and good detrusor contractility .
however , urodynamic study is not totally innocuous , with significant evidence of discomfort and urinary infections associated with performing the examination , as well as imposing additional cost to the patient or to the institution . for this reason
, some research has been initiated to find less - invasive or noninvasive examinations for evaluating the degree of boo .
ipp measured as the shortest distance connecting the protruded end of the prostate into the bladder based on the bladder neck in the sagittal plane reflects the maximum longitudinal length of the prostate and may help in assessing the obstructive level of the prostate .
first studied the correlation between ipp and the booi in 30 male outpatients in 2005 and found that ipp grading correlated well with the booi .
analyzed 206 bph patients classified by different ipp grade and found that the ipp value positively correlated with tpv , psa , pvr , qmax , pdetqmax , and booi as well as the incidence of aur , bladder trabeculation , detrusor overactivity , and low bladder compliance .
analyzed 260 men with luts and found that the booi was higher in patients with apparent ipp than in those without .
the tzi calculated as tzv divided by tpv may also correlate with the obstructive level because higher volumes of the transition zone will result in harder pressure on the urethra .
kaplan et al . evaluated 61 men with symptomatic bph and found a significant correlation between tzi and symptoms , qmax , and pdetqmax .
analyzed 116 bph patients and found that tzi and tzv were both positively correlated with booi and ipss .
milonas et al . reported that lower tzi was an independent predictor of ineffective surgical outcome . in the present study
, we found significant correlations in surgical patients between both tzi and ipp with parameters reflecting the level of boo , such as qmax , pdetqmax , and booi .
these results are consistent with the results of former research and suggest that tzi and ipp may be appropriate parameters in diagnosing and classifying boo . for a long period
, turp has been the gold standard surgical procedure based on the concept of removing the whole enlarged adenoma involved in static and dynamic urethral obstruction .
however , the development of medication such as alpha - adrenergic blockers and 5-alpha - reductase inhibitors has decreased the progression of bph and the operation rate in patients in recent years .
however , some patients can not achieve favorable recovery from drug therapy and need a surgeon to relieve the symptoms .
the patients needing surgical therapy in our research were found to have higher values of both ipp and tzi than the patients needing only drug therapy .
this result suggests that ipp and tzi could measure the disease progression in bph patients receiving medication and might have predictive value for medication efficacy .
higher ipp grade was found to correlate with higher voiding symptom score , which demonstrated that ipp could reflect the severity of bph from not only an objective aspect but also a subjective aspect .
aur is one of the most serious complications of bph and an indication for surgical intervention .
this research has found positive correlations between not only ipp but also tzi and the incidence of aur , which further suggests that these 2 factors might be used to predict the progression of bph and the possibility of undergoing surgical therapy .
in general , this research investigated tzi and ipp from trus in bph patients and found positive correlations between these indexes and symptoms , boo level , and the incidence of aur .
tzi and ipp were also found to differ significantly between bph patients receiving medication and those undergoing surgical therapy .
the results demonstrated that the two parameters had favorable value for assessing severity and progression in patients with bph .
however , this research was retrospective only , with inevitable bias from subject selection and follow - up time . therefore , more prospective research should be launched to investigate the predictive value of the two parameters for the progression and treatment efficacy of bph .[/INST]purposethe aim of this research was to assess the value of the transitional zone index ( tzi ) and intravesical prostatic protrusion ( ipp ) from transrectal ultrasonography in evaluating the severity and progression of disease by analyzing the relationship between the 2 parameters and symptoms , clinical history , and urodynamics in benign prostatic hyperplasia ( bph ) patients undergoing different treatment.materials and methodsa total of 203 patients receiving medication and 162 patients who underwent transurethral resection of the prostate because of bph were enrolled in this retrospective analysis .
the clinical history and subjective and objective examination results of all patients were recorded and compared after being classified by tzi and ipp level .
linear regression was used to find correlations between ipp , tzi , and urodynamics.resultsthe 2 parameters were found to differ significantly between patients receiving medication and patients undergoing surgical therapy ( p<0.05 ) .
psa , maximum flow rate ( qmax ) , detrusor pressure at qmax ( pdetqmax ) , and the bladder outlet obstruction index ( booi ) differed according to various tzi levels ( p<0.05 ) .
in addition , the voiding symptom score , qmax , and booi of subgroups with various ipp levels were also significantly different ( p<0.05 ) .
both tzi and ipp had significant effects on qmax , booi , and pdetqmax ( p<0.05 ) and the incidence of acute urinary retention ( p=0.000).conclusionsthe results demonstrated that both tzi and ipp had favorable value for assessing severity and progression in patients with bph .
further studies are needed to confirm whether the two parameters have predictive value in the efficacy of bph treatment and could be considered as factors in the selection of therapy .</s> |
recently a @xmath0=4 staggering effect in the dynamical moment of inertia of some superdeformed bands has been observed @xcite .
this can be interpreted as a bifurcation of the yrast band into two sequences with spins varying by 4 units within each sequence .
the corresponding energy splitting is very small , i.e. , about 100 ev . this effect may occur due to remnants of the @xmath2 symmetry of the system and suggests that presence of hexadecapole deformations or hexadecapole - type multipole interactions may be responsible for the staggering phenomenon
recently , the origin of the staggering has been discussed by means of a phenomenological hamiltonian containing higher - order terms in angular momentum @xcite . in this work
we investigate the effect by means of a more microscopic approach involving schematic multipole - multipole interactions .
the model to test the @xmath0=4 staggering phenomenon should be able to take into account the interplay between rotation and shape dynamics of a many - body system . a degenerate single-@xmath1 shell occupied by identical nucleons @xcite , interacting via quadrupole - quadrupole and hexadecapole - hexadecapole multipole forces has this property .
the corresponding hamiltonian may be written as @xmath3 where @xmath4 and @xmath5 are the quadrupole and hexadecapole moment operators defined as @xmath6=@xmath7 where @xmath8@xmath9@xmath10 , @xmath11 is the time reversal operator , and the dot symbol stands for the scalar product @xmath12@xmath13@xmath12=@xmath14 . in the harmonic oscillator approximation @xcite the values of coupling constants @xmath15 and @xmath16 can be estimated as @xmath17 the results of the diagonalization depend solely on the ratio @xmath18 .
therefore , in the following , we assumed @xmath15=1 mev ( i.e. , @xmath15 is used to fix energy scale ) , while the parameter @xmath16 , describing the relative strength of hexadecapole and quadrupole interactions , was varied to investigate the conditions for an appearance of the staggering effect . in this paper
we discuss the case of @xmath19=8 particles in the @xmath1=15/2 shell , although we have performed a series of calculations for several different shells and particle numbers .
a choice of @xmath19=8 particles corresponds to a half - filled shell , and gives a regular collective yrast band .
the calculations were performed for the parameter @xmath16 ranging from @xmath16=0 to @xmath16=10 mev . for larger values of @xmath16 ,
one only obtains an energy scaling corresponding to the dominating hexadecapole interaction .
to analyse a @xmath0=4 staggering effect in collective bands , we extracted the smooth reference curve according to ref .
quantities @xmath20@xmath9@xmath21@xmath22@xmath23@xmath24@xmath25 and @xmath26@xmath9 @xmath27@xmath22@xmath23@xmath22@xmath28@xmath22@xmath29@xmath24@xmath30/4 $ ] were obtained in this way .
then staggering parameter @xmath31@xmath24@xmath26 was evaluated and plotted in each case .
fig . [ f1 ] shows a complete quadrupole spectrum of hamiltonian ( [ a1 ] ) in case of @xmath16=0 .
solid lines connect states of spins @xmath32 and @xmath32@xmath222 with the largest reduced matrix elements of the quadrupole moment operator .
several quite regular rotational bands were obtained .
the staggering parameter was evaluated for each case , but no @xmath0=4 periodicity was found . in figs .
[ f2 - 3]a and [ f2 - 3]b the collective energies @xmath33 and the parameters @xmath31@xmath24@xmath26 of the yrast sequence are presented as open circles . when the hexadecapole interaction is switched on
, the staggering @xmath0=4 appears .
this is seen in fig .
[ f2 - 3]b , where full circles denote the staggering parameters of the yrast band for @xmath16=0.3 , 0.4 , and 0.5 mev , while the corresponding yrast spectra are plotted in fig . [ f2 - 3]a .
the staggering effect is small and therefore difficult to be directly seen in the yrast spectra . the amplitude of the staggering increases with @xmath16 ,
but for the values of @xmath16 larger than 0.5 mev , the yrast states are no longer connected by the enhanced e2 transitions ; i.e. , the band structure is lost .
[ f4 - 5]a shows the yrast states for @xmath16=4 mev .
this corresponds to the situation where the hexadecapole interaction dominates and the yrast sequence is strongly perturbed .
there are no strong e2 transitions linking the yrast states , but the staggering parameter extracted from the energies of the yrast sequence exhibits the @xmath0=4 periodicity ( fig .
[ f4 - 5]b ) .
similar effects can be obtained for other values of @xmath1 and @xmath19 .
we would like to stress that it was impossible to obtain similar staggering by using the quadrupole - quadrupole interaction alone . on the other hand , for @xmath1=15/2 and @xmath19=8
, the staggering appears only in the yrast band .
the examples presented here show that the hexadecapole interaction may generate the @xmath0=4 irregularities .
the proper treatment of the hexadecapole interaction seems to be crucial for the understanding of this intriguing staggering phenomenon .
this research was supported in part by the polish state committee for scientific research under contract nos .
20450 91 01 and 2 p 302 056 06 , and by the computational grant from the interdisciplinary centre for mathematical and computational modeling ( icm ) of warsaw university .
oak ridge national laboratory is managed for the u.s .
department of energy by martin marietta energy systems , inc .
under contract no .
de - ac0584or21400 .
the joint institute for heavy ion research has as member institutions the university of tennessee , vanderbilt university , and the oak ridge national laboratory ; it is supported by the members and by the department of energy through contract no .
de - fg05 - 87er40361 with the university of tennessee .
theoretical nuclear physics research at the university of tennessee is supported by the u.s .
department of energy through contract no . de - fg05 - 93er40770 . | a role of the multipole interaction in the description of the @xmath0=4 staggering phenomenon is investigated in a model consisting of a single-@xmath1 shell filled by identical nucleons .
exact diagonalization of the quadrupole - plus - hexadecapole hamiltonian shows that the hexadecapole - hexadecapole interaction can produce a @xmath0=4 periodicity in the yrast sequence .
+ pacs numbers : 21.10.re , 21.30.+y , 21.60.cs = 23.7 cm = 15.0 cm =3 true mm = -23 true mm | <s>[INST]recently a @xmath0=4 staggering effect in the dynamical moment of inertia of some superdeformed bands has been observed @xcite .
this can be interpreted as a bifurcation of the yrast band into two sequences with spins varying by 4 units within each sequence .
the corresponding energy splitting is very small , i.e. , about 100 ev . this effect may occur due to remnants of the @xmath2 symmetry of the system and suggests that presence of hexadecapole deformations or hexadecapole - type multipole interactions may be responsible for the staggering phenomenon
recently , the origin of the staggering has been discussed by means of a phenomenological hamiltonian containing higher - order terms in angular momentum @xcite . in this work
we investigate the effect by means of a more microscopic approach involving schematic multipole - multipole interactions .
the model to test the @xmath0=4 staggering phenomenon should be able to take into account the interplay between rotation and shape dynamics of a many - body system . a degenerate single-@xmath1 shell occupied by identical nucleons @xcite , interacting via quadrupole - quadrupole and hexadecapole - hexadecapole multipole forces has this property .
the corresponding hamiltonian may be written as @xmath3 where @xmath4 and @xmath5 are the quadrupole and hexadecapole moment operators defined as @xmath6=@xmath7 where @xmath8@xmath9@xmath10 , @xmath11 is the time reversal operator , and the dot symbol stands for the scalar product @xmath12@xmath13@xmath12=@xmath14 . in the harmonic oscillator approximation @xcite the values of coupling constants @xmath15 and @xmath16 can be estimated as @xmath17 the results of the diagonalization depend solely on the ratio @xmath18 .
therefore , in the following , we assumed @xmath15=1 mev ( i.e. , @xmath15 is used to fix energy scale ) , while the parameter @xmath16 , describing the relative strength of hexadecapole and quadrupole interactions , was varied to investigate the conditions for an appearance of the staggering effect . in this paper
we discuss the case of @xmath19=8 particles in the @xmath1=15/2 shell , although we have performed a series of calculations for several different shells and particle numbers .
a choice of @xmath19=8 particles corresponds to a half - filled shell , and gives a regular collective yrast band .
the calculations were performed for the parameter @xmath16 ranging from @xmath16=0 to @xmath16=10 mev . for larger values of @xmath16 ,
one only obtains an energy scaling corresponding to the dominating hexadecapole interaction .
to analyse a @xmath0=4 staggering effect in collective bands , we extracted the smooth reference curve according to ref .
quantities @xmath20@xmath9@xmath21@xmath22@xmath23@xmath24@xmath25 and @xmath26@xmath9 @xmath27@xmath22@xmath23@xmath22@xmath28@xmath22@xmath29@xmath24@xmath30/4 $ ] were obtained in this way .
then staggering parameter @xmath31@xmath24@xmath26 was evaluated and plotted in each case .
fig . [ f1 ] shows a complete quadrupole spectrum of hamiltonian ( [ a1 ] ) in case of @xmath16=0 .
solid lines connect states of spins @xmath32 and @xmath32@xmath222 with the largest reduced matrix elements of the quadrupole moment operator .
several quite regular rotational bands were obtained .
the staggering parameter was evaluated for each case , but no @xmath0=4 periodicity was found . in figs .
[ f2 - 3]a and [ f2 - 3]b the collective energies @xmath33 and the parameters @xmath31@xmath24@xmath26 of the yrast sequence are presented as open circles . when the hexadecapole interaction is switched on
, the staggering @xmath0=4 appears .
this is seen in fig .
[ f2 - 3]b , where full circles denote the staggering parameters of the yrast band for @xmath16=0.3 , 0.4 , and 0.5 mev , while the corresponding yrast spectra are plotted in fig . [ f2 - 3]a .
the staggering effect is small and therefore difficult to be directly seen in the yrast spectra . the amplitude of the staggering increases with @xmath16 ,
but for the values of @xmath16 larger than 0.5 mev , the yrast states are no longer connected by the enhanced e2 transitions ; i.e. , the band structure is lost .
[ f4 - 5]a shows the yrast states for @xmath16=4 mev .
this corresponds to the situation where the hexadecapole interaction dominates and the yrast sequence is strongly perturbed .
there are no strong e2 transitions linking the yrast states , but the staggering parameter extracted from the energies of the yrast sequence exhibits the @xmath0=4 periodicity ( fig .
[ f4 - 5]b ) .
similar effects can be obtained for other values of @xmath1 and @xmath19 .
we would like to stress that it was impossible to obtain similar staggering by using the quadrupole - quadrupole interaction alone . on the other hand , for @xmath1=15/2 and @xmath19=8
, the staggering appears only in the yrast band .
the examples presented here show that the hexadecapole interaction may generate the @xmath0=4 irregularities .
the proper treatment of the hexadecapole interaction seems to be crucial for the understanding of this intriguing staggering phenomenon .
this research was supported in part by the polish state committee for scientific research under contract nos .
20450 91 01 and 2 p 302 056 06 , and by the computational grant from the interdisciplinary centre for mathematical and computational modeling ( icm ) of warsaw university .
oak ridge national laboratory is managed for the u.s .
department of energy by martin marietta energy systems , inc .
under contract no .
de - ac0584or21400 .
the joint institute for heavy ion research has as member institutions the university of tennessee , vanderbilt university , and the oak ridge national laboratory ; it is supported by the members and by the department of energy through contract no .
de - fg05 - 87er40361 with the university of tennessee .
theoretical nuclear physics research at the university of tennessee is supported by the u.s .
department of energy through contract no . de - fg05 - 93er40770 .[/INST] a role of the multipole interaction in the description of the @xmath0=4 staggering phenomenon is investigated in a model consisting of a single-@xmath1 shell filled by identical nucleons .
exact diagonalization of the quadrupole - plus - hexadecapole hamiltonian shows that the hexadecapole - hexadecapole interaction can produce a @xmath0=4 periodicity in the yrast sequence .
+ pacs numbers : 21.10.re , 21.30.+y , 21.60.cs = 23.7 cm = 15.0 cm =3 true mm = -23 true mm </s> |
double-@xmath0 decay is a process in which a nucleus @xmath14 decays to a nucleus @xmath15 by emitting two electrons or positrons and , usually , other light particles @xmath16 double-@xmath0 decay can be classified in various modes according to the various types of particles emitted in the decay .
the processes where two neutrinos are emitted are predicted by the standard model , and @xmath17 decay has been observed in several nuclei . for processes not allowed by the standard model , i.e. the neutrinoless modes : @xmath18 , @xmath19 , @xmath20 , the half - life can be factorized as @xmath21^{-1}=g_{0\nu}|m_{0\nu}|^2 \left| f(m_i , u_{ei})\right|^2,\ ] ] where @xmath22 is a phase space factor , @xmath23 is the nuclear matrix element , and @xmath24 contains physics beyond the standard model through the masses @xmath25 and mixing matrix elements @xmath26 of neutrino species .
for all processes , two crucial ingredients are the phase space factors ( psfs ) and the nuclear matrix elements ( nmes ) .
recently , we have initiated a program for the evaluation of both quantities and presented results for @xmath1 decay @xcite .
this is the most promising mode for the possible detection of neutrinoless double-@xmath0 decay and thus of a measurement of the absolute neutrino mass scale .
however , in very recent years , interest in the double positron decay , @xmath2 , positron emitting electron capture , @xmath3 , and double electron capture @xmath4 , has been renewed .
this is due to the fact that positron emitting processes have interesting signatures that could be detected experimentally @xcite . in a previous article
@xcite we initiated a systematic study of @xmath2 , @xmath3 , and @xmath4 processes and presented a calculation of phase space factors ( psf ) for @xmath27 , @xmath28 , @xmath29 and @xmath30 , @xmath28 .
the process @xmath20 can not occur to the order of approximation used in @xcite , since the emission of additional particles , @xmath31 or others , is needed to conserve energy and momentum . in this article , we focus on calculation of neutrinoless decay nuclear matrix elements ( nme ) , which are common to all three modes , and half - life predictions for @xmath30 and @xmath32 modes .
results of our calculations are reported for nuclei listed in table [ table1 ] .
lll transition & @xmath33(kev)&@xmath34(% ) + ' '' '' @xmath35ni@xmath36fe@xmath37 & @xmath38 & @xmath39 + @xmath40zn@xmath41ni@xmath42 & @xmath43 & @xmath44 + @xmath45kr@xmath46se@xmath47 & @xmath48 & @xmath49 + @xmath50ru@xmath51mo@xmath52 & @xmath53&@xmath54 + @xmath55cd@xmath56pd@xmath57 & @xmath58&@xmath59 + @xmath60xe@xmath61te@xmath62 & @xmath63 & @xmath64 + @xmath65ba@xmath66xe@xmath67 & @xmath68 & @xmath69 + @xmath70ce@xmath71ba@xmath72 & @xmath73&@xmath74 +
the theory of 0@xmath75 decay was first formulated by furry @xcite and further developed by primakoff and rosen @xcite , molina and pascual @xcite , doi _ et al . _
@xcite , haxton and stephenson @xcite , and , more recently , by tomoda @xcite and imkovic _ et al .
all these formulations often differ by factors of 2 , by the number of terms retained in the non - relativistic expansion of the current and by their contribution . in order to have a standard set of calculations to be compared with the qrpa and the ism , we adopt in this article the formulation of imkovic _ et al . _ @xcite .
a detailed discussion of involved operators can also be found in ref .
@xcite .
we consider the decay of a nucleus @xmath76x@xmath77 into a nucleus @xmath78y@xmath79 .
an example is shown in fig .
[ fig1 ] .
the decay @xmath80cd@xmath81pd@xmath57 , an example of double-@xmath5 decay.,width=325 ] if the decay proceeds through an @xmath82-wave , with two leptons in the final state , we can not form an angular momentum greater than one .
we therefore calculate , in this article , only @xmath18 matrix elements to final @xmath83 states , the ground state @xmath84 , for which , in a previous article @xcite we have calculated the phase space factors , and to the first excited state @xmath85 . in order to evaluate the matrix elements we make use of the microscopic interacting boson model ( ibm-2 ) @xcite .
the method of evaluation is discussed in detail in ref .
@xcite for double electron decay ( @xmath1 ) . for double positron decay ( @xmath2 ) and positron
emitting electron capture ( @xmath3 ) the same method applies except for the interchange @xmath86 in eq .
( 5 ) of @xcite and in the mapped boson operators of eq .
( 18 ) of @xcite .
the matrix elements of the mapped operators are evaluated with realistic wave functions , taken either from the literature , when available , or obtained from a fit to the observed energies and other properties ( @xmath87 values , quadrupole moments , @xmath88 values , magnetic moments , etc . ) .
the values of the parameters used in the calculation are given in appendix a. lcccccccc nucleus & & + ' '' '' & @xmath89 & @xmath90 & @xmath91 & @xmath92 & @xmath89 & @xmath90 & @xmath91 & @xmath92 + ' '' '' @xmath6ni & 2.072 & -0.152 & 0.144 & 2.310 & 2.042 & -0.153 & 0.101 & 2.237 + @xmath7zn & 4.762 & -2.449 & -0.156 & 6.127 & 0.633 & -0.360 & -0.019 & 0.837 + @xmath8kr & 3.384 & -2.146 & -0.238 & 4.478 & 0.771 & -0.479 & -0.055 & 1.014 + @xmath9ru & 2.204 & -0.269 & 0.112 & 2.483 & 0.036 & -0.012 & 0.001 & 0.045 + @xmath10cd & 2.757 & -0.255 & 0.191 & 3.106 & 1.395 & -0.110 & 0.074 & 1.537 + @xmath11xe & 3.967 & -2.224 & -0.192 & 5.156 & 0.647 & -0.359 & -0.032 & 0.839 + @xmath12ba & 3.911 & -2.108 & -0.176 & 5.043 & 0.285 & -0.152 & -0.014 & 0.366 + @xmath13ce & 3.815 & -2.007 & -0.161 & 4.901 & 0.318 & -0.167 & -0.014 & 0.408 + here , we present our calculated nme for the decays of table [ table1 ] .
the nmes depend on many assumptions , in particular on the treatment of the short - range correlations ( src ) . in table
[ table2 ] , we show the results of our calculation of the matrix elements to the ground state , @xmath84 , and to the first excited state , @xmath85 , using the miller - spencer ( ms ) parametrization of src , and broken down into gt , f and t contributions and their sum as @xmath93 we note that we have two classes of nuclei , those in which protons and neutrons occupy the same major shell ( @xmath94 ) and those in which they occupy different major shells ( @xmath95 ) .
the magnitude of the fermi matrix element , which is related to the overlap of the proton and neutron wave functions , is therefore different in these two classes of nuclei , being large in the former and small in the latter case .
this implies a considerable amount of isospin violation for nuclei in the first class .
this problem has been discussed in detail in ref .
@xcite and will form a subject of subsequent investigation .
it is common to most calculations of nme and has been addressed recently within the framework of qrpa in refs .
here we take it into account by assigning a large error to the calculation of the fermi matrix elements . in the same ref .
@xcite it is also shown that the nme depend on the short range correlations ( src ) , and that use of argonne / cd - bonn src increases the nme by a factor of 1.1 - 1.2 .
the same situation occurs for @xmath2 decay . in order to take into account the sensitivity of the calculation to parameter changes , model assumptions and operator assumptions @xcite , we list in table [ final ] ibm-2 nmes with an estimate of the error .
the values of the @xmath96 matrix elements vary between @xmath97 , the matrix element for the @xmath7zn@xmath98ni transition being notably the largest .
they are therefore of the same order of magnitude than the nuclear matrix elements for @xmath1 decay , 2.0 - 5.4 . in the same table
[ final ] we also compare our results with the available qrpa calculations from ref .
@xcite with the addition of some more recent calculations from refs .
the qrpa @xcite nmes are calculated taking into account gt and f contributions , and using the value @xmath99 . as in the case of @xmath1 decay , qrpa tend to give larger values than ibm-2 and these two methods seem to be in a rather good correspondence with each other .
lccccc decay & & + ' '' '' & ibm-2 & & ibm-2 & qrpa + ' '' '' @xmath6ni & 2.31(37 ) & 1.55 & & 2.24(36 ) & + @xmath7zn & 6.13(116 ) & & & 0.84(16 ) & + @xmath8kr & 4.48(85 ) & 4.19 & & 1.01(19 ) & + @xmath9ru & 2.48(40 ) & 3.25 & 3.22 - 5.83 & 0.05(1 ) & 1.28 - 2.26 + @xmath10cd & 3.11(50 ) & 4.12 & 5.94 - 9.08 & 1.54(25 ) & 0.66 - 0.91 + @xmath11xe & 5.16(98 ) & 4.78 & & 0.84(16 ) & + @xmath12ba & 5.04(96 ) & 4.98 & & 0.37(7 ) & + @xmath13ce & 4.90(93 ) & 3.09 & & 0.41(8 ) & + the calculation of nuclear matrix elements in ibm-2 can now be combined with the phase space factors calculated in @xcite to produce our final results for half - lives for light neutrino exchange in table [ table3 ] and fig .
the half - lives are calculated using the formula @xmath101^{-1}=g_{0\nu}^{i}\left\vert m_{0\nu}\right\vert ^{2}\left\vert \frac{\left\langle m_{\nu}\right\rangle } { m_{e}}\right\vert ^{2},\ ] ] where @xmath102 .
the values in table [ table3 ] and fig
. [ fig2 ] are for @xmath103ev .
they scale with @xmath104 for other values .
lcc & + nucleus & @xmath2 & @xmath3 + ' '' '' @xmath6ni & & 213 + @xmath7zn & & 52.9 + @xmath8kr & 2.01 & 0.79 + @xmath9ru & 19.3 & 1.70 + @xmath10cd & 10.8 & 0.80 + @xmath11xe & 3.32 & 0.19 + @xmath12ba & 15.4 & 0.23 + @xmath13ce & 174 & 0.27 + ( color online ) expected half - lives for @xmath105 ev , @xmath106 . the figure is in semilogarithmic scale.,width=325 ] comparing the half - life predictions listed in table [ table3 ] to the ones reported in ref .
@xcite for @xmath107 we can see that values reported here are much larger . this is due to the fact that in cases studied here the available kinetic energy is much smaller compared to @xmath1 decay .
furthermore , the coulomb repulsion on positrons from the nucleus gives a smaller decay rate .
as concluded also in refs .
@xcite , the @xmath11xe @xmath32decay is expected to have the shortest half - live . in case of the neutrinoless double electron capture process , @xmath20 ,
the available kinetic energy is larger and coulomb repulsion does not play a role .
however , this decay mode can not occur to the order of approximation we are considering , since it must be accompanied by the emission of one or two particles in order to conserve energy , momentum and angular momentum .
in this article we have presented evaluation of nuclear matrix elements in 0@xmath108/0@xmath109/0@xmath110 within the framework of ibm-2 in the closure approximation .
the closure approximation is expected to be good for these decays since the virtual neutrino momentum is of order 100 mev / c and thus much larger than the scale of nuclear excitations . by using these matrix elements and the phase space factors of ref .
@xcite , we have calculated the expected 0@xmath108/0@xmath109 half - lives in all nuclei of interest with @xmath111 and @xmath112 , given in table [ table3 ] and fig .
[ fig2 ] .
this work was performed in part under the us doe grant de - fg-02 - 91er-40608 and fondecyt grant no .
we wish to thank k. zuber for stimulating discussions .
a detailed description of the ibm-2 hamiltonian is given in @xcite and @xcite .
for most nuclei , the hamiltonian parameters are taken from the literature @xcite .
the values of the hamiltonian parameters , as well as the references from which they were taken , are given in table [ tab : ibm2parameters ] .
the quality of the description can be seen from these references and ranges from very good to excellent .
@xmath127 & 1.454 & & & & & & & & & & & & & + @xmath128 & 0.98 & 0.98 & -0.26 & 0.00 & -0.40 & 0.80 & 0.80 & 0.80 & & & & & & + @xmath129 @xcite & 1.20 & 1.20 & -0.22 & -0.25 & -0.75 & -0.18 & 0.24 & -0.18 & -0.30 & -0.50 & 0.30 & -0.30 & -0.50 & 0.30 + @xmath130 & 1.346 & & & & & & & & & -0.415 & 0.082 & & & + @xmath131 @xcite & 0.96 & 0.96 & -0.18 & -0.495 & -1.127 & -0.10 & & -0.10 & & & & & & + @xmath132 @xcite & 0.99 & 0.99 & -0.21 & 0.71 & -0.90 & & & -0.10 & & & & & & + @xmath133 & 1.08 & 1.08 & -0.21 & 0.80 & 0.40 & 0.25 & 0.25 & 0.25 & 0.30 & 0.10 & -0.50 & & & + @xmath134 @xcite & 0.73 & 1.10 & -0.09 & -1.20 & 0.40 & -0.10 & 0.10 & -0.10 & -0.50 & 0.10 & & & & + @xmath135 @xcite & 1.05 & 1.05 & -0.325 & 1.25 & 0.00 & -0.18 & 0.24 & -0.18 & 0.20 & 0.15 & 0.00 & & & + @xmath136 @xcite & 0.760 & 0.844 & -0.160 & -0.22 & -0.30 & 0.20 & 0.05 & 0.00 & -0.45 & -0.20 & 0.01 & & & + @xmath137 @xcite & 0.70 & 0.70 & -0.14 & 0.00 & -0.80 & -0.18 & 0.24 & -0.18 & 0.05 & -0.16 & & & & + @xmath138 @xcite & 0.82 & 0.82 & -0.15 & 0.00 & -1.20 & -0.18 & 0.24 & -0.18 & 0.10 & & & & & + @xmath139 @xcite & 0.70 & 0.70 & -0.175 & 0.32 & -0.90 & -0.18 & 0.24 & -0.18 & 0.26 & & & & & + @xmath140 @xcite & 0.76 & 0.76 & -0.19 & 0.50 & -0.80 & -0.18 & 0.24 & -0.18 & 0.30 & 0.22 & & & & + @xmath141 @xcite & 0.90 & 0.90 & -0.21 & 0.79 & -1.00 & -0.18 & 0.24 & -0.18 & 0.26 & -0.11 & & & & + @xmath142 @xcite & 1.03 & 1.03 & -0.23 & 1.00 & -0.90 & -0.18 & 0.24 & -0.18 & 0.30 & 0.10 & & & & + 100 j. barea and f. iachello , phys .
c * 79 * , 044301 ( 2009 ) .
j. kotila and f. iachello , phys .
c * 85 * , 034316 ( 2012 ) .
j. barea , j. kotila and f. iachello , phys .
. lett . * 109 * , 042501 ( 2012 ) .
j. barea , j. kotila and f. iachello , phys .
c * 87 * , 014315 ( 2013 ) .
j. barea and j. kotila , aip conf . proc . * 1488 * , 334 ( 2012 ) . j. kotila and j. barea , aip conf
. proc . * 1488 * , 342 ( 2012 ) .
d. fink _ et al .
* 108 * , 062502 ( 2012 ) .
k. zuber , private communication .
j. kotila and f. iachello , phys .
c * 87 * , 024313 ( 2013 ) .
nudat 2.6 , http://www.nndc.bnl.gov/nudat2/ s. eliseev _
c * 83 * , 038501 ( 2011 ) .
m. goncharov _
et al . _ ,
phys . rev .
c * 84 * , 028501 ( 2011 ) .
et al . _ ,
b * 697 * 116 ( 2011 ) .
w.h . furry , phys . rev . * 56 * , 1184 ( 1939 ) .
w. c. haxton and g. j. stephenson jr .
* 12 * , 409 ( 1984 ) .
t. tomoda , rep .
* 54 * , 53 ( 1991 )
. f. imkovic , g. pantis , j.d .
vergados , and a. faessler , phys .
c * 60 * , 055502 ( 1999 ) .
v. rodin and a. faessler , phys .
c * 84 * , 014322 ( 2011 ) .
f. imkovic , v. rodin , a. faessler , and p. vogel , arxiv:1302.1509v2 ( 2013 ) .
m. hirsch , k. muto , t. oda , and h. v. klapdor - kleingrothaus , z. phys .
a * 347 * , 151 ( 1994 ) . c. h. druce , j. d. mccullen , p. d. duval , and b. r. barrett , j. phys .
* 8 * , 1565 ( 1982 ) .
u. kaup and a. gelberg , z. physik a * 293 * , 311 ( 1979 ) .
u. kaup , c. mnkemeyer , and p. v. brentano , z. physik a * 310 * , 129 ( 1983 ) . h. dejbakhsh , d. latypov , g. ajupova , and s. shlomo , phys . rev .
c * 46 * , 2326 ( 1992 ) .
m. sambataro , nucl .
a * 380 * , 365 ( 1982 ) . | neutrinoless double-@xmath0 decay is of fundamental importance for determining the neutrino mass .
although double electron ( @xmath1 ) decay is the most promising mode , in very recent years interest in double positron ( @xmath2 ) decay , positron emitting electron capture ( @xmath3 ) , and double electron capture ( @xmath4 ) has been renewed .
we present here results of a calculation of nuclear matrix elements for neutrinoless double-@xmath5 decay and positron emitting electron capture within the framework of the microscopic interacting boson model ( ibm-2 ) for @xmath6ni , @xmath7zn , @xmath8kr , @xmath9ru , @xmath10cd , @xmath11xe , @xmath12ba , and @xmath13ce decay . by combining these with a calculation of phase space factors we calculate expected half - lives . | <s>[INST]double-@xmath0 decay is a process in which a nucleus @xmath14 decays to a nucleus @xmath15 by emitting two electrons or positrons and , usually , other light particles @xmath16 double-@xmath0 decay can be classified in various modes according to the various types of particles emitted in the decay .
the processes where two neutrinos are emitted are predicted by the standard model , and @xmath17 decay has been observed in several nuclei . for processes not allowed by the standard model , i.e. the neutrinoless modes : @xmath18 , @xmath19 , @xmath20 , the half - life can be factorized as @xmath21^{-1}=g_{0\nu}|m_{0\nu}|^2 \left| f(m_i , u_{ei})\right|^2,\ ] ] where @xmath22 is a phase space factor , @xmath23 is the nuclear matrix element , and @xmath24 contains physics beyond the standard model through the masses @xmath25 and mixing matrix elements @xmath26 of neutrino species .
for all processes , two crucial ingredients are the phase space factors ( psfs ) and the nuclear matrix elements ( nmes ) .
recently , we have initiated a program for the evaluation of both quantities and presented results for @xmath1 decay @xcite .
this is the most promising mode for the possible detection of neutrinoless double-@xmath0 decay and thus of a measurement of the absolute neutrino mass scale .
however , in very recent years , interest in the double positron decay , @xmath2 , positron emitting electron capture , @xmath3 , and double electron capture @xmath4 , has been renewed .
this is due to the fact that positron emitting processes have interesting signatures that could be detected experimentally @xcite . in a previous article
@xcite we initiated a systematic study of @xmath2 , @xmath3 , and @xmath4 processes and presented a calculation of phase space factors ( psf ) for @xmath27 , @xmath28 , @xmath29 and @xmath30 , @xmath28 .
the process @xmath20 can not occur to the order of approximation used in @xcite , since the emission of additional particles , @xmath31 or others , is needed to conserve energy and momentum . in this article , we focus on calculation of neutrinoless decay nuclear matrix elements ( nme ) , which are common to all three modes , and half - life predictions for @xmath30 and @xmath32 modes .
results of our calculations are reported for nuclei listed in table [ table1 ] .
lll transition & @xmath33(kev)&@xmath34(% ) + ' '' '' @xmath35ni@xmath36fe@xmath37 & @xmath38 & @xmath39 + @xmath40zn@xmath41ni@xmath42 & @xmath43 & @xmath44 + @xmath45kr@xmath46se@xmath47 & @xmath48 & @xmath49 + @xmath50ru@xmath51mo@xmath52 & @xmath53&@xmath54 + @xmath55cd@xmath56pd@xmath57 & @xmath58&@xmath59 + @xmath60xe@xmath61te@xmath62 & @xmath63 & @xmath64 + @xmath65ba@xmath66xe@xmath67 & @xmath68 & @xmath69 + @xmath70ce@xmath71ba@xmath72 & @xmath73&@xmath74 +
the theory of 0@xmath75 decay was first formulated by furry @xcite and further developed by primakoff and rosen @xcite , molina and pascual @xcite , doi _ et al . _
@xcite , haxton and stephenson @xcite , and , more recently , by tomoda @xcite and imkovic _ et al .
all these formulations often differ by factors of 2 , by the number of terms retained in the non - relativistic expansion of the current and by their contribution . in order to have a standard set of calculations to be compared with the qrpa and the ism , we adopt in this article the formulation of imkovic _ et al . _ @xcite .
a detailed discussion of involved operators can also be found in ref .
@xcite .
we consider the decay of a nucleus @xmath76x@xmath77 into a nucleus @xmath78y@xmath79 .
an example is shown in fig .
[ fig1 ] .
the decay @xmath80cd@xmath81pd@xmath57 , an example of double-@xmath5 decay.,width=325 ] if the decay proceeds through an @xmath82-wave , with two leptons in the final state , we can not form an angular momentum greater than one .
we therefore calculate , in this article , only @xmath18 matrix elements to final @xmath83 states , the ground state @xmath84 , for which , in a previous article @xcite we have calculated the phase space factors , and to the first excited state @xmath85 . in order to evaluate the matrix elements we make use of the microscopic interacting boson model ( ibm-2 ) @xcite .
the method of evaluation is discussed in detail in ref .
@xcite for double electron decay ( @xmath1 ) . for double positron decay ( @xmath2 ) and positron
emitting electron capture ( @xmath3 ) the same method applies except for the interchange @xmath86 in eq .
( 5 ) of @xcite and in the mapped boson operators of eq .
( 18 ) of @xcite .
the matrix elements of the mapped operators are evaluated with realistic wave functions , taken either from the literature , when available , or obtained from a fit to the observed energies and other properties ( @xmath87 values , quadrupole moments , @xmath88 values , magnetic moments , etc . ) .
the values of the parameters used in the calculation are given in appendix a. lcccccccc nucleus & & + ' '' '' & @xmath89 & @xmath90 & @xmath91 & @xmath92 & @xmath89 & @xmath90 & @xmath91 & @xmath92 + ' '' '' @xmath6ni & 2.072 & -0.152 & 0.144 & 2.310 & 2.042 & -0.153 & 0.101 & 2.237 + @xmath7zn & 4.762 & -2.449 & -0.156 & 6.127 & 0.633 & -0.360 & -0.019 & 0.837 + @xmath8kr & 3.384 & -2.146 & -0.238 & 4.478 & 0.771 & -0.479 & -0.055 & 1.014 + @xmath9ru & 2.204 & -0.269 & 0.112 & 2.483 & 0.036 & -0.012 & 0.001 & 0.045 + @xmath10cd & 2.757 & -0.255 & 0.191 & 3.106 & 1.395 & -0.110 & 0.074 & 1.537 + @xmath11xe & 3.967 & -2.224 & -0.192 & 5.156 & 0.647 & -0.359 & -0.032 & 0.839 + @xmath12ba & 3.911 & -2.108 & -0.176 & 5.043 & 0.285 & -0.152 & -0.014 & 0.366 + @xmath13ce & 3.815 & -2.007 & -0.161 & 4.901 & 0.318 & -0.167 & -0.014 & 0.408 + here , we present our calculated nme for the decays of table [ table1 ] .
the nmes depend on many assumptions , in particular on the treatment of the short - range correlations ( src ) . in table
[ table2 ] , we show the results of our calculation of the matrix elements to the ground state , @xmath84 , and to the first excited state , @xmath85 , using the miller - spencer ( ms ) parametrization of src , and broken down into gt , f and t contributions and their sum as @xmath93 we note that we have two classes of nuclei , those in which protons and neutrons occupy the same major shell ( @xmath94 ) and those in which they occupy different major shells ( @xmath95 ) .
the magnitude of the fermi matrix element , which is related to the overlap of the proton and neutron wave functions , is therefore different in these two classes of nuclei , being large in the former and small in the latter case .
this implies a considerable amount of isospin violation for nuclei in the first class .
this problem has been discussed in detail in ref .
@xcite and will form a subject of subsequent investigation .
it is common to most calculations of nme and has been addressed recently within the framework of qrpa in refs .
here we take it into account by assigning a large error to the calculation of the fermi matrix elements . in the same ref .
@xcite it is also shown that the nme depend on the short range correlations ( src ) , and that use of argonne / cd - bonn src increases the nme by a factor of 1.1 - 1.2 .
the same situation occurs for @xmath2 decay . in order to take into account the sensitivity of the calculation to parameter changes , model assumptions and operator assumptions @xcite , we list in table [ final ] ibm-2 nmes with an estimate of the error .
the values of the @xmath96 matrix elements vary between @xmath97 , the matrix element for the @xmath7zn@xmath98ni transition being notably the largest .
they are therefore of the same order of magnitude than the nuclear matrix elements for @xmath1 decay , 2.0 - 5.4 . in the same table
[ final ] we also compare our results with the available qrpa calculations from ref .
@xcite with the addition of some more recent calculations from refs .
the qrpa @xcite nmes are calculated taking into account gt and f contributions , and using the value @xmath99 . as in the case of @xmath1 decay , qrpa tend to give larger values than ibm-2 and these two methods seem to be in a rather good correspondence with each other .
lccccc decay & & + ' '' '' & ibm-2 & & ibm-2 & qrpa + ' '' '' @xmath6ni & 2.31(37 ) & 1.55 & & 2.24(36 ) & + @xmath7zn & 6.13(116 ) & & & 0.84(16 ) & + @xmath8kr & 4.48(85 ) & 4.19 & & 1.01(19 ) & + @xmath9ru & 2.48(40 ) & 3.25 & 3.22 - 5.83 & 0.05(1 ) & 1.28 - 2.26 + @xmath10cd & 3.11(50 ) & 4.12 & 5.94 - 9.08 & 1.54(25 ) & 0.66 - 0.91 + @xmath11xe & 5.16(98 ) & 4.78 & & 0.84(16 ) & + @xmath12ba & 5.04(96 ) & 4.98 & & 0.37(7 ) & + @xmath13ce & 4.90(93 ) & 3.09 & & 0.41(8 ) & + the calculation of nuclear matrix elements in ibm-2 can now be combined with the phase space factors calculated in @xcite to produce our final results for half - lives for light neutrino exchange in table [ table3 ] and fig .
the half - lives are calculated using the formula @xmath101^{-1}=g_{0\nu}^{i}\left\vert m_{0\nu}\right\vert ^{2}\left\vert \frac{\left\langle m_{\nu}\right\rangle } { m_{e}}\right\vert ^{2},\ ] ] where @xmath102 .
the values in table [ table3 ] and fig
. [ fig2 ] are for @xmath103ev .
they scale with @xmath104 for other values .
lcc & + nucleus & @xmath2 & @xmath3 + ' '' '' @xmath6ni & & 213 + @xmath7zn & & 52.9 + @xmath8kr & 2.01 & 0.79 + @xmath9ru & 19.3 & 1.70 + @xmath10cd & 10.8 & 0.80 + @xmath11xe & 3.32 & 0.19 + @xmath12ba & 15.4 & 0.23 + @xmath13ce & 174 & 0.27 + ( color online ) expected half - lives for @xmath105 ev , @xmath106 . the figure is in semilogarithmic scale.,width=325 ] comparing the half - life predictions listed in table [ table3 ] to the ones reported in ref .
@xcite for @xmath107 we can see that values reported here are much larger . this is due to the fact that in cases studied here the available kinetic energy is much smaller compared to @xmath1 decay .
furthermore , the coulomb repulsion on positrons from the nucleus gives a smaller decay rate .
as concluded also in refs .
@xcite , the @xmath11xe @xmath32decay is expected to have the shortest half - live . in case of the neutrinoless double electron capture process , @xmath20 ,
the available kinetic energy is larger and coulomb repulsion does not play a role .
however , this decay mode can not occur to the order of approximation we are considering , since it must be accompanied by the emission of one or two particles in order to conserve energy , momentum and angular momentum .
in this article we have presented evaluation of nuclear matrix elements in 0@xmath108/0@xmath109/0@xmath110 within the framework of ibm-2 in the closure approximation .
the closure approximation is expected to be good for these decays since the virtual neutrino momentum is of order 100 mev / c and thus much larger than the scale of nuclear excitations . by using these matrix elements and the phase space factors of ref .
@xcite , we have calculated the expected 0@xmath108/0@xmath109 half - lives in all nuclei of interest with @xmath111 and @xmath112 , given in table [ table3 ] and fig .
[ fig2 ] .
this work was performed in part under the us doe grant de - fg-02 - 91er-40608 and fondecyt grant no .
we wish to thank k. zuber for stimulating discussions .
a detailed description of the ibm-2 hamiltonian is given in @xcite and @xcite .
for most nuclei , the hamiltonian parameters are taken from the literature @xcite .
the values of the hamiltonian parameters , as well as the references from which they were taken , are given in table [ tab : ibm2parameters ] .
the quality of the description can be seen from these references and ranges from very good to excellent .
@xmath127 & 1.454 & & & & & & & & & & & & & + @xmath128 & 0.98 & 0.98 & -0.26 & 0.00 & -0.40 & 0.80 & 0.80 & 0.80 & & & & & & + @xmath129 @xcite & 1.20 & 1.20 & -0.22 & -0.25 & -0.75 & -0.18 & 0.24 & -0.18 & -0.30 & -0.50 & 0.30 & -0.30 & -0.50 & 0.30 + @xmath130 & 1.346 & & & & & & & & & -0.415 & 0.082 & & & + @xmath131 @xcite & 0.96 & 0.96 & -0.18 & -0.495 & -1.127 & -0.10 & & -0.10 & & & & & & + @xmath132 @xcite & 0.99 & 0.99 & -0.21 & 0.71 & -0.90 & & & -0.10 & & & & & & + @xmath133 & 1.08 & 1.08 & -0.21 & 0.80 & 0.40 & 0.25 & 0.25 & 0.25 & 0.30 & 0.10 & -0.50 & & & + @xmath134 @xcite & 0.73 & 1.10 & -0.09 & -1.20 & 0.40 & -0.10 & 0.10 & -0.10 & -0.50 & 0.10 & & & & + @xmath135 @xcite & 1.05 & 1.05 & -0.325 & 1.25 & 0.00 & -0.18 & 0.24 & -0.18 & 0.20 & 0.15 & 0.00 & & & + @xmath136 @xcite & 0.760 & 0.844 & -0.160 & -0.22 & -0.30 & 0.20 & 0.05 & 0.00 & -0.45 & -0.20 & 0.01 & & & + @xmath137 @xcite & 0.70 & 0.70 & -0.14 & 0.00 & -0.80 & -0.18 & 0.24 & -0.18 & 0.05 & -0.16 & & & & + @xmath138 @xcite & 0.82 & 0.82 & -0.15 & 0.00 & -1.20 & -0.18 & 0.24 & -0.18 & 0.10 & & & & & + @xmath139 @xcite & 0.70 & 0.70 & -0.175 & 0.32 & -0.90 & -0.18 & 0.24 & -0.18 & 0.26 & & & & & + @xmath140 @xcite & 0.76 & 0.76 & -0.19 & 0.50 & -0.80 & -0.18 & 0.24 & -0.18 & 0.30 & 0.22 & & & & + @xmath141 @xcite & 0.90 & 0.90 & -0.21 & 0.79 & -1.00 & -0.18 & 0.24 & -0.18 & 0.26 & -0.11 & & & & + @xmath142 @xcite & 1.03 & 1.03 & -0.23 & 1.00 & -0.90 & -0.18 & 0.24 & -0.18 & 0.30 & 0.10 & & & & + 100 j. barea and f. iachello , phys .
c * 79 * , 044301 ( 2009 ) .
j. kotila and f. iachello , phys .
c * 85 * , 034316 ( 2012 ) .
j. barea , j. kotila and f. iachello , phys .
. lett . * 109 * , 042501 ( 2012 ) .
j. barea , j. kotila and f. iachello , phys .
c * 87 * , 014315 ( 2013 ) .
j. barea and j. kotila , aip conf . proc . * 1488 * , 334 ( 2012 ) . j. kotila and j. barea , aip conf
. proc . * 1488 * , 342 ( 2012 ) .
d. fink _ et al .
* 108 * , 062502 ( 2012 ) .
k. zuber , private communication .
j. kotila and f. iachello , phys .
c * 87 * , 024313 ( 2013 ) .
nudat 2.6 , http://www.nndc.bnl.gov/nudat2/ s. eliseev _
c * 83 * , 038501 ( 2011 ) .
m. goncharov _
et al . _ ,
phys . rev .
c * 84 * , 028501 ( 2011 ) .
et al . _ ,
b * 697 * 116 ( 2011 ) .
w.h . furry , phys . rev . * 56 * , 1184 ( 1939 ) .
w. c. haxton and g. j. stephenson jr .
* 12 * , 409 ( 1984 ) .
t. tomoda , rep .
* 54 * , 53 ( 1991 )
. f. imkovic , g. pantis , j.d .
vergados , and a. faessler , phys .
c * 60 * , 055502 ( 1999 ) .
v. rodin and a. faessler , phys .
c * 84 * , 014322 ( 2011 ) .
f. imkovic , v. rodin , a. faessler , and p. vogel , arxiv:1302.1509v2 ( 2013 ) .
m. hirsch , k. muto , t. oda , and h. v. klapdor - kleingrothaus , z. phys .
a * 347 * , 151 ( 1994 ) . c. h. druce , j. d. mccullen , p. d. duval , and b. r. barrett , j. phys .
* 8 * , 1565 ( 1982 ) .
u. kaup and a. gelberg , z. physik a * 293 * , 311 ( 1979 ) .
u. kaup , c. mnkemeyer , and p. v. brentano , z. physik a * 310 * , 129 ( 1983 ) . h. dejbakhsh , d. latypov , g. ajupova , and s. shlomo , phys . rev .
c * 46 * , 2326 ( 1992 ) .
m. sambataro , nucl .
a * 380 * , 365 ( 1982 ) .[/INST] neutrinoless double-@xmath0 decay is of fundamental importance for determining the neutrino mass .
although double electron ( @xmath1 ) decay is the most promising mode , in very recent years interest in double positron ( @xmath2 ) decay , positron emitting electron capture ( @xmath3 ) , and double electron capture ( @xmath4 ) has been renewed .
we present here results of a calculation of nuclear matrix elements for neutrinoless double-@xmath5 decay and positron emitting electron capture within the framework of the microscopic interacting boson model ( ibm-2 ) for @xmath6ni , @xmath7zn , @xmath8kr , @xmath9ru , @xmath10cd , @xmath11xe , @xmath12ba , and @xmath13ce decay . by combining these with a calculation of phase space factors we calculate expected half - lives . </s> |
according to the data from the 2002 national hypertension survey of china , the prevalence rate of hypertension in chinese adults over 18 years of age is 18.8% , and estimates are that there are more than 200 million hypertensive people in china .
this means that 1 in 10 adults have hypertension , and that approximately 1/5 of the total global population is hypertensive
. however , the awareness , treatment , and control of hypertension in developing countries are still quite poor when compared with those of developed countries , especially in rural or remote areas .
the death rate related to stroke in rural areas exceeds that of stroke deaths in cities . at present , approximately 130 million hypertensive people in china do not know they have hypertension , and there are also close to 3 million patients diagnosed with hypertension who are not receiving any treatment . of the patients receiving antihypertensive therapy ,
prevention and treatment of hypertension in china is still an arduous task . at the same time , with the development of the social economy , the improvements in standard of living and changes in lifestyle have led to the gradual increase of the blood lipid levels of chinese people and the prevalence of dyslipidemia .
elevated total cholesterol ( tc ) and low - density lipoprotein cholesterol ( ldl - c ) are independent risk factors for coronary heart disease and ischemic stroke .
many studies have confirmed that patients with hypertension and primary hyperlipidemia are at high risk for experiencing cardiovascular events .
a common question with regard to treatment with medication is , when is the best time to take the medication ? blood pressure tends to be highest between 8:00 and 11:00 in the morning or 3:00 to 5:00 in the afternoon and may be too low at night .
the onset of the effect of medication commonly occurs 30 min after taking it , and its efficacy peaks 2 to 3 h thereafter .
if patients with hypertension often forget to take their medicine in the daytime and instead take their medication at night , the result may be low blood pressure . for the majority of patients , taking antihypertensive medications at 7:00 in the morning or at 2:00 in the afternoon
statins work via the inhibition of cholesterol synthesis by hydroxyl - methylglutaric - acyl coenzyme a ( hmg - coa ) reductase , which mainly exists in the liver , with its typical circadian rhythm creating the highest levels at night and lower levels during the day . the best time for taking statins , therefore ,
statins also have demonstrated a capability to reduce the rate of cardiovascular events [ 36 ] .
data from the anglo - scandinavian cardiac outcomes trial ( ascot ) support the view that statins protect hypertensive patients from end - organ damage , not only through cholesterol reduction , but also through other pathways . given this background , there arose another question regarding the use of the fixed - dose combination of amlodipine and atorvastatin .
the best time to take amlodipine is 7:00 am or 2:00 pm , while the best time for dosing atorvastatin may be at night .
therefore , what is the best time of day for taking the single - pill combination of amlodipine and atorvastatin ? there are 3 questions that need to be answered : is taking amlodipine at night safe ? ; are the antihypertensive effects the same between day and night ? ; and does taking atorvastatin in the daytime lead to better lipid - lowering effects ?
the study was conducted with prior institutional ethics approval under the requirements of the chinese prevention of cruelty to human subjects and the code of practice for the care and use of human subjects for scientific purposes .
all human subjects of this study were inspected by members of the human subject ethics committee of west china medical centre ( hspc20120407 - 17468 ) and in compliance with the helsinki declaration .
patients who were seen in the outpatient department of the west china hospital from may 2012 to september 2014 and who were at least 18 years of age were eligible if they had the primary diagnoses of hypertension and hypercholesterolemia ( tc > 5.70
the diagnosis of hypertension was made following ambulatory blood pressure monitoring ( abpm ) , with the following levels considered to be hypertensive : average blood pressure > 130/80 mmhg , daytime blood pressure > 135/85 mmhg or nocturnal blood pressure > 125/75 mmhg . to ensure the safety of the single - pill therapy
patients were excluded if they were previously treated with any lipid - lowering therapy or if they had a diagnosis of secondary hypertension , any cerebrovascular disease within the past 6 months , an acute myocardial infarction , congestive heart failure , congenital or rheumatic heart disease , autoimmune disease , severely abnormal liver or kidney values , severe trauma , infection , major surgery , or secondary hyperlipidemia caused by drug therapy . before entering the study , all patients signed informed consent forms approved by the institutional review boards .
the clinical trial was an outpatient , practice - based , case - control study lasting 8 weeks . to evaluate the efficacy and safety of single - pill combination of amlodipine and atorvastatin ,
i , patients were provided with single - pill amlodipine / atorvastatin ( 5/20 mg , hisun - pfizer pharmaceutical , ltd , tai zhou , china , which is also the only dose could be used in china ) at 10 pm every night . in group ii , patients were instructed to take the amlodipine tablet ( 5 mg , pfizer chinese pharmaceutical , ltd . ,
beijing , china ) every morning at 7 am . at the same time , atorvastatin ( 20 mg , pfizer chinese pharmaceutical , ltd . , beijing , china ) was also been given .
the patients were allowed to take the necessary drugs for cardiovascular indications other than hypertension .
all patients from group i and ii then returned for the final visit after 8 weeks . at first visit ,
the average , daytime , nocturnal , and morning blood pressures were measured and recorded by abpm .
other variables collected at this visit included age , sex , smoking status , serum lipid levels , presence of diabetes mellitus , and coronary heart disease ( chd ) .
other laboratory examination indexes , including high - sensitivity c - reaction protein ( hs - crp ) , left ventricular mass index ( lvmi ) , carotid intima - media thickness ( imt ) , and concurrent medications , were also recorded . at the second visit , bp measurements by abpm , serum lipid levels , hs - crp , lvmi , and imt were repeated .
other variables collected at this visit included the occurrence of adverse drug reactions ( adrs ) and the number of pills missing from their prescription bottle ( see flow program below in figure 1 ) .
serum lipid levels were measured by fasting blood samples , which were collected in the early morning .
total cholesterol ( tc ) and triglycerides ( tg ) , as well as low- and high - density lipoprotein cholesterol ( ldl - c and hdl - c ) were all included and analyzed by routine enzymatic assays .
hs - crp was also determined by the same blood samples with double - antibody avidin - biotin complex - elisa ( abc elisa ) method .
carotid imt was detected by the same highly qualified doctor in our hospital . for bilateral carotid artery detection ,
we used the ie 33 type ultrasonic diagnosis instrument , produced by philips company , with probe frequency 7 . 0 mhz .
we put the probe at the distal carotid artery , 11.5 cm below the fork level , avoiding the plaques in accordance with the synchronization ecg in end - diastolic , measured 5 times on every side , and the average index was recorded as the measured value of carotid imt .
lvmi was inspected by using the hp 5500 color doppler ultrasonic diagnostic instrument , with probe frequency 3.5 mhz .
we measured left ventricular end - diastolic ventricular septal thickness ( ivst ) , left ventricular posterior wall thickness ( pwt ) , left ventricular end - diastolic diameter ( lvidd ) , and left ventricular mass ( lvm ) , according to the formula of devereux : the lvm ( g ) = 1.04 [ ( ivst + lvidd + pwt ) ( lvidd ) ] 13.6 .
lvmi = lvm / body surface area ( s ) , s=0.0061height ( cm ) + 0.0128 weight ( kg ) 0.1529 .
all statistical tests were two - tailed , and all analyses were considered statistically significant if p<0.05 .
baseline demographic and clinical characteristics , as well as efficacy variables , were compared between group i and group ii using the paired t test .
the study was conducted with prior institutional ethics approval under the requirements of the chinese prevention of cruelty to human subjects and the code of practice for the care and use of human subjects for scientific purposes .
all human subjects of this study were inspected by members of the human subject ethics committee of west china medical centre ( hspc20120407 - 17468 ) and in compliance with the helsinki declaration .
patients who were seen in the outpatient department of the west china hospital from may 2012 to september 2014 and who were at least 18 years of age were eligible if they had the primary diagnoses of hypertension and hypercholesterolemia ( tc > 5.70
the diagnosis of hypertension was made following ambulatory blood pressure monitoring ( abpm ) , with the following levels considered to be hypertensive : average blood pressure > 130/80 mmhg , daytime blood pressure > 135/85 mmhg or nocturnal blood pressure > 125/75 mmhg . to ensure the safety of the single - pill therapy
patients were excluded if they were previously treated with any lipid - lowering therapy or if they had a diagnosis of secondary hypertension , any cerebrovascular disease within the past 6 months , an acute myocardial infarction , congestive heart failure , congenital or rheumatic heart disease , autoimmune disease , severely abnormal liver or kidney values , severe trauma , infection , major surgery , or secondary hyperlipidemia caused by drug therapy . before entering the study
the clinical trial was an outpatient , practice - based , case - control study lasting 8 weeks . to evaluate the efficacy and safety of single - pill combination of amlodipine and atorvastatin ,
i , patients were provided with single - pill amlodipine / atorvastatin ( 5/20 mg , hisun - pfizer pharmaceutical , ltd , tai zhou , china , which is also the only dose could be used in china ) at 10 pm every night . in group ii , patients were instructed to take the amlodipine tablet ( 5 mg , pfizer chinese pharmaceutical , ltd . ,
beijing , china ) every morning at 7 am . at the same time , atorvastatin ( 20 mg , pfizer chinese pharmaceutical , ltd . , beijing , china ) was also been given .
the patients were allowed to take the necessary drugs for cardiovascular indications other than hypertension .
all patients from group i and ii then returned for the final visit after 8 weeks .
at first visit , the average , daytime , nocturnal , and morning blood pressures were measured and recorded by abpm .
other variables collected at this visit included age , sex , smoking status , serum lipid levels , presence of diabetes mellitus , and coronary heart disease ( chd ) .
other laboratory examination indexes , including high - sensitivity c - reaction protein ( hs - crp ) , left ventricular mass index ( lvmi ) , carotid intima - media thickness ( imt ) , and concurrent medications , were also recorded . at the second visit , bp measurements by abpm , serum lipid levels , hs - crp , lvmi , and imt were repeated .
other variables collected at this visit included the occurrence of adverse drug reactions ( adrs ) and the number of pills missing from their prescription bottle ( see flow program below in figure 1 ) .
serum lipid levels were measured by fasting blood samples , which were collected in the early morning . total cholesterol ( tc ) and triglycerides ( tg ) , as well as low- and high - density lipoprotein cholesterol ( ldl - c and hdl - c )
hs - crp was also determined by the same blood samples with double - antibody avidin - biotin complex - elisa ( abc elisa ) method .
carotid imt was detected by the same highly qualified doctor in our hospital . for bilateral carotid artery detection
, we used the ie 33 type ultrasonic diagnosis instrument , produced by philips company , with probe frequency 7 . 0 mhz .
we put the probe at the distal carotid artery , 11.5 cm below the fork level , avoiding the plaques in accordance with the synchronization ecg in end - diastolic , measured 5 times on every side , and the average index was recorded as the measured value of carotid imt .
lvmi was inspected by using the hp 5500 color doppler ultrasonic diagnostic instrument , with probe frequency 3.5 mhz .
we measured left ventricular end - diastolic ventricular septal thickness ( ivst ) , left ventricular posterior wall thickness ( pwt ) , left ventricular end - diastolic diameter ( lvidd ) , and left ventricular mass ( lvm ) , according to the formula of devereux : the lvm ( g ) = 1.04 [ ( ivst + lvidd + pwt ) ( lvidd ) ] 13.6 .
lvmi = lvm / body surface area ( s ) , s=0.0061height ( cm ) + 0.0128 weight ( kg ) 0.1529 .
all statistical tests were two - tailed , and all analyses were considered statistically significant if p<0.05 .
baseline demographic and clinical characteristics , as well as efficacy variables , were compared between group i and group ii using the paired t test .
the baseline demographic characteristics for the 200 patients included in this analysis are shown in table 1 .
the average age was 53.1 years , and the overall average , daytime , nocturnal , and morning blood pressures were 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mm hg , and 157.3/98.6 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 2.02 mmol / l ) , tc ( 5.99 mmol / l ) , ldl - c ( 3.96 mmol / l ) , and hdl - c ( 1.19
the frequency of the other risk factors included smoking ( 40% ) , diabetes mellitus ( 42% ) , and chd ( 37% ) . in group ii , 51% of the patients were male and 49% were female .
the average age of the patients was 52.7 years , and the average overall , daytime , nocturnal , and morning blood pressures were 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 1.98 mmol / l ) , tc ( 6.01 mmol / l ) , ldl - c ( 4.11 mmol / l ) , and hdl - c ( 1.22 mmol / l ) . the frequency of the other risk factors included smoking ( 38% ) , diabetes mellitus ( 48% ) , and chd ( 32% ) . in group
i , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mmhg , and 157.3/98.6 mmhg to 129.4/75.9 mmhg , 139.7/85.4 mmhg , 117.9/66.2 mmhg , and 139.5/85.2 mmhg , respectively . in group
ii , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg to 131.2/74.4 mmhg , 138.9/82.1 mmhg , 121.6/68.4 mmhg , and 149.9/92.7 mmhg , respectively .
the bp reduction from baseline at week 8 was statistically significant in both groups ( p<0.001 ) , but there was no statistically significant change in the d - value except for in the morning peak group . in group
i , the morning peak bp reduction in sbp and dbp at week 8 was markedly less than in group ii ( see table 2 , figure 2 ) .
serum concentrations of tc , tg , and ldl - c were significantly lower after 8-week treatment ( p<0.01 ) , but hdl - c was increased ( p<0.05 ) in both groups .
however , there was no significant difference in d - value ( p>0.05 ) after 8-week treatment compared with index before ( see table 3 , figure 3 ) .
also , there were no significant differences between before and after 8-week treatment in either group with regard to the hs - crp , lvmi , and carotid -imt ( p>0.05 ) ( see table 4 , figure 4 ) .
ankle edema , the most frequent adverse event , was experienced by 7% ( 7/100 ) in group i and 8% ( 8/100 ) in group ii .
the incidence of headache was 1% ( 1/100 ) in group i and 2% ( 2/100 ) in group ii .
the number of pills missing was much higher in group ii ( once : 29 ; twice : 16 ; 3 times : 10 ; more than 3 times : 7 ) than in group i ( once : 7 ; twice : 5 ; 3 times : 2 ; more than 3 times : 1 ) .
the baseline demographic characteristics for the 200 patients included in this analysis are shown in table 1 .
the average age was 53.1 years , and the overall average , daytime , nocturnal , and morning blood pressures were 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mm hg , and 157.3/98.6 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 2.02 mmol / l ) , tc ( 5.99 mmol / l ) , ldl - c ( 3.96 mmol / l ) , and hdl - c ( 1.19
the frequency of the other risk factors included smoking ( 40% ) , diabetes mellitus ( 42% ) , and chd ( 37% ) . in group ii , 51% of the patients were male and 49% were female .
the average age of the patients was 52.7 years , and the average overall , daytime , nocturnal , and morning blood pressures were 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 1.98 mmol / l ) , tc ( 6.01 mmol / l ) , ldl - c ( 4.11 mmol / l ) , and hdl - c ( 1.22 mmol / l ) . the frequency of the other risk factors included smoking ( 38% ) , diabetes mellitus ( 48% ) , and chd ( 32% ) .
in group i , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mmhg , and 157.3/98.6 mmhg to 129.4/75.9 mmhg , 139.7/85.4 mmhg , 117.9/66.2 mmhg , and 139.5/85.2 mmhg , respectively . in group
ii , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg to 131.2/74.4 mmhg , 138.9/82.1 mmhg , 121.6/68.4 mmhg , and 149.9/92.7 mmhg , respectively .
the bp reduction from baseline at week 8 was statistically significant in both groups ( p<0.001 ) , but there was no statistically significant change in the d - value except for in the morning peak group .
in group i , the morning peak bp reduction in sbp and dbp at week 8 was markedly less than in group ii ( see table 2 , figure 2 ) .
serum concentrations of tc , tg , and ldl - c were significantly lower after 8-week treatment ( p<0.01 ) , but hdl - c was increased ( p<0.05 ) in both groups .
however , there was no significant difference in d - value ( p>0.05 ) after 8-week treatment compared with index before ( see table 3 , figure 3 ) .
also , there were no significant differences between before and after 8-week treatment in either group with regard to the hs - crp , lvmi , and carotid -imt ( p>0.05 ) ( see table 4 , figure 4 ) .
ankle edema , the most frequent adverse event , was experienced by 7% ( 7/100 ) in group i and 8% ( 8/100 ) in group ii .
the incidence of headache was 1% ( 1/100 ) in group i and 2% ( 2/100 ) in group ii .
the number of pills missing was much higher in group ii ( once : 29 ; twice : 16 ; 3 times : 10 ; more than 3 times : 7 ) than in group i ( once : 7 ; twice : 5 ; 3 times : 2 ; more than 3 times : 1 ) .
to address whether the timing of dosing for amlodipine and atorvastatin is important with regard to therapeutic efficacy , our results showed no obvious differences between the different dosing times for amlodipine - atorvastatin in blood pressure control between the 2 groups .
taking amlodipine at night not only lowered blood pressure , but it also provided better control during the peak blood pressures in the morning .
hypercholesterolemia control in the 2 groups was also not significantly different ; taking atorvastatin in the morning was equally as effective as taking it at night in patients with hypercholesterolemia . although no obvious difference was found in adverse drug reactions between the 2 groups , compliance was much better in the single - pill group than in those patients taking the 2 drugs separately .
hypertension is one of the most important causes of and risk factors for a variety of cardiovascular and cerebrovascular diseases , and also affects important organs such as the structure and function of the heart , brain , and kidneys , eventually leading to organ failure . in recent years
, studies have determined that there is a close relationship between endothelial dysfunction and hypertension .
a prospective follow - up study has confirmed that carotid imt can strongly and independently forecast heart or cerebrovascular disease , with the increase of carotid imt corresponding to an increase in the incidence of myocardial infarction and stroke .
leiboritz has confirmed that atorvastatin can improve the small artery elasticity of patients with hyperlipidemia and reduce the diastolic and systolic blood pressures .
the prevent study observed that the carotid imt in the amlodipine group was reduced by 0.013 mm on average , while it increased by an average of 0.033 mm in the placebo group ; this difference was statistically significant .
amlodipine is a long - acting calcium antagonist with powerful , stable , and long - lasting effects on hypertension ; it promotes arterial endothelial function , may effectively improve arterial elasticity , and reduces carotid imt , thus inhibiting the progression of atherosclerosis .
carotid imt was significantly lower after treatment , but no difference was found between the 2 groups .
hypertension and its related complications are often attended by vascular epithelial damnification and other pathological changes .
as one of the important inflammatory markers , serum hs - crp is considered to participate in the process of left ventricular hypertrophy and hypertension [ 15 . during the treatment of patients with hypertension , we need not only effectively control blood pressure , but also must monitor and improve endothelial inflammation and left ventricular remodeling . the effect of the oxidative stress induced by endothelial dysfunction can destroy the function of nitric oxide .
many studies have proven that combination therapy can effectively stimulate the endothelial cells to release nitric oxide and maintain normal vascular function .
statins can reduce the hardening of the arteries , improve arterial compliance , and reverse the remodeling of the aorta , which could reverse the left ventricular hypertrophy caused by changes in arterial structure and function [ 1618 ] .
in addition , atorvastatin can reduce the levels of serum crp and other inflammatory markers , reduce inflammation , and improve endothelial function .
atorvastatin can inhibit hypertrophy and cell proliferation by reducing angiotensin i and improve left ventricular hypertrophy .
our experiment achieved similar results : compared to before treatment , the hs - crp and lvmi were significantly lower after treatment , but no significant difference was found between the 2 groups .
there is another problem which deserves attention : the blood pressure was decreased significantly but not normalized in some patients by using amlodipine 5 mg per day , which indicated that the daily dose of 5 mg of amlodipine was probably too low for these patients . for solving this problem ,
we designed and conducted part ii of this experiment , in which all patients in part i were divided into 4 groups and different doses of spc were been given to these patients .
this clinic research may provide answers allowing us to know how to correct and reasonably use the spc of amlodipine - atorvastatin .
taking the single - pill amlodipine - atorvastatin combination at night lowered blood pressure and reduced the morning peak blood pressure levels on the second day .
this dosing strategy may also improve patient adherence to therapy . in combination with amlodipine , atorvastatin reduced systolic blood pressure , inhibited cardiac hypertrophy in left ventricle and inflammation , then the whole progress of left ventricular remodeling during hypertension could be affected .
all suggests that this combination could be a better choice for hypertensive patients with primary hypercholesterolemia . | backgroundis the timing of dosing for amlodipine and atorvastatin important with regard to therapeutic efficacy ? to answer this question ,
we designed an outpatient , practice - based , case - control study lasting 8 weeks.material/methodstwo hundred patients were divided into 2 groups : in group i , patients were provided with a single pill containing amlodipine / atorvastatin ( 5/20 mg ) to be taken each night at 10 pm , and in group ii , patients were taking amlodipine ( 5 mg ) and atorvastatin ( 20 mg ) each morning at 7 am.resultsour results indicated no obvious difference in blood pressure control between the 2 groups .
taking amlodipine at night not only lowered blood pressure , but it also provided better control during the peak blood pressure in the morning .
hypercholesterolemia control in the 2 groups was also not significantly different , taking atorvastatin in the morning was as effective as dosing at night in patients with hypercholesterolemia . while the carotid imt , hs - crp , and lvmi were significantly lower after treatment , no differences were found between the 2 groups .
although no obvious difference was found in adverse drug reactions between the 2 groups , compliance was much better in the single - pill group than in patients taking the 2 medications separately.conclusionsin conclusion , single - pill amlodipine - atorvastatin taken at night can lower blood pressure and reduce the morning peak blood pressure levels the next day .
additionally , this dosing method could improve patient adherence to the therapy . | <s>[INST]according to the data from the 2002 national hypertension survey of china , the prevalence rate of hypertension in chinese adults over 18 years of age is 18.8% , and estimates are that there are more than 200 million hypertensive people in china .
this means that 1 in 10 adults have hypertension , and that approximately 1/5 of the total global population is hypertensive
. however , the awareness , treatment , and control of hypertension in developing countries are still quite poor when compared with those of developed countries , especially in rural or remote areas .
the death rate related to stroke in rural areas exceeds that of stroke deaths in cities . at present , approximately 130 million hypertensive people in china do not know they have hypertension , and there are also close to 3 million patients diagnosed with hypertension who are not receiving any treatment . of the patients receiving antihypertensive therapy ,
prevention and treatment of hypertension in china is still an arduous task . at the same time , with the development of the social economy , the improvements in standard of living and changes in lifestyle have led to the gradual increase of the blood lipid levels of chinese people and the prevalence of dyslipidemia .
elevated total cholesterol ( tc ) and low - density lipoprotein cholesterol ( ldl - c ) are independent risk factors for coronary heart disease and ischemic stroke .
many studies have confirmed that patients with hypertension and primary hyperlipidemia are at high risk for experiencing cardiovascular events .
a common question with regard to treatment with medication is , when is the best time to take the medication ? blood pressure tends to be highest between 8:00 and 11:00 in the morning or 3:00 to 5:00 in the afternoon and may be too low at night .
the onset of the effect of medication commonly occurs 30 min after taking it , and its efficacy peaks 2 to 3 h thereafter .
if patients with hypertension often forget to take their medicine in the daytime and instead take their medication at night , the result may be low blood pressure . for the majority of patients , taking antihypertensive medications at 7:00 in the morning or at 2:00 in the afternoon
statins work via the inhibition of cholesterol synthesis by hydroxyl - methylglutaric - acyl coenzyme a ( hmg - coa ) reductase , which mainly exists in the liver , with its typical circadian rhythm creating the highest levels at night and lower levels during the day . the best time for taking statins , therefore ,
statins also have demonstrated a capability to reduce the rate of cardiovascular events [ 36 ] .
data from the anglo - scandinavian cardiac outcomes trial ( ascot ) support the view that statins protect hypertensive patients from end - organ damage , not only through cholesterol reduction , but also through other pathways . given this background , there arose another question regarding the use of the fixed - dose combination of amlodipine and atorvastatin .
the best time to take amlodipine is 7:00 am or 2:00 pm , while the best time for dosing atorvastatin may be at night .
therefore , what is the best time of day for taking the single - pill combination of amlodipine and atorvastatin ? there are 3 questions that need to be answered : is taking amlodipine at night safe ? ; are the antihypertensive effects the same between day and night ? ; and does taking atorvastatin in the daytime lead to better lipid - lowering effects ?
the study was conducted with prior institutional ethics approval under the requirements of the chinese prevention of cruelty to human subjects and the code of practice for the care and use of human subjects for scientific purposes .
all human subjects of this study were inspected by members of the human subject ethics committee of west china medical centre ( hspc20120407 - 17468 ) and in compliance with the helsinki declaration .
patients who were seen in the outpatient department of the west china hospital from may 2012 to september 2014 and who were at least 18 years of age were eligible if they had the primary diagnoses of hypertension and hypercholesterolemia ( tc > 5.70
the diagnosis of hypertension was made following ambulatory blood pressure monitoring ( abpm ) , with the following levels considered to be hypertensive : average blood pressure > 130/80 mmhg , daytime blood pressure > 135/85 mmhg or nocturnal blood pressure > 125/75 mmhg . to ensure the safety of the single - pill therapy
patients were excluded if they were previously treated with any lipid - lowering therapy or if they had a diagnosis of secondary hypertension , any cerebrovascular disease within the past 6 months , an acute myocardial infarction , congestive heart failure , congenital or rheumatic heart disease , autoimmune disease , severely abnormal liver or kidney values , severe trauma , infection , major surgery , or secondary hyperlipidemia caused by drug therapy . before entering the study , all patients signed informed consent forms approved by the institutional review boards .
the clinical trial was an outpatient , practice - based , case - control study lasting 8 weeks . to evaluate the efficacy and safety of single - pill combination of amlodipine and atorvastatin ,
i , patients were provided with single - pill amlodipine / atorvastatin ( 5/20 mg , hisun - pfizer pharmaceutical , ltd , tai zhou , china , which is also the only dose could be used in china ) at 10 pm every night . in group ii , patients were instructed to take the amlodipine tablet ( 5 mg , pfizer chinese pharmaceutical , ltd . ,
beijing , china ) every morning at 7 am . at the same time , atorvastatin ( 20 mg , pfizer chinese pharmaceutical , ltd . , beijing , china ) was also been given .
the patients were allowed to take the necessary drugs for cardiovascular indications other than hypertension .
all patients from group i and ii then returned for the final visit after 8 weeks . at first visit ,
the average , daytime , nocturnal , and morning blood pressures were measured and recorded by abpm .
other variables collected at this visit included age , sex , smoking status , serum lipid levels , presence of diabetes mellitus , and coronary heart disease ( chd ) .
other laboratory examination indexes , including high - sensitivity c - reaction protein ( hs - crp ) , left ventricular mass index ( lvmi ) , carotid intima - media thickness ( imt ) , and concurrent medications , were also recorded . at the second visit , bp measurements by abpm , serum lipid levels , hs - crp , lvmi , and imt were repeated .
other variables collected at this visit included the occurrence of adverse drug reactions ( adrs ) and the number of pills missing from their prescription bottle ( see flow program below in figure 1 ) .
serum lipid levels were measured by fasting blood samples , which were collected in the early morning .
total cholesterol ( tc ) and triglycerides ( tg ) , as well as low- and high - density lipoprotein cholesterol ( ldl - c and hdl - c ) were all included and analyzed by routine enzymatic assays .
hs - crp was also determined by the same blood samples with double - antibody avidin - biotin complex - elisa ( abc elisa ) method .
carotid imt was detected by the same highly qualified doctor in our hospital . for bilateral carotid artery detection ,
we used the ie 33 type ultrasonic diagnosis instrument , produced by philips company , with probe frequency 7 . 0 mhz .
we put the probe at the distal carotid artery , 11.5 cm below the fork level , avoiding the plaques in accordance with the synchronization ecg in end - diastolic , measured 5 times on every side , and the average index was recorded as the measured value of carotid imt .
lvmi was inspected by using the hp 5500 color doppler ultrasonic diagnostic instrument , with probe frequency 3.5 mhz .
we measured left ventricular end - diastolic ventricular septal thickness ( ivst ) , left ventricular posterior wall thickness ( pwt ) , left ventricular end - diastolic diameter ( lvidd ) , and left ventricular mass ( lvm ) , according to the formula of devereux : the lvm ( g ) = 1.04 [ ( ivst + lvidd + pwt ) ( lvidd ) ] 13.6 .
lvmi = lvm / body surface area ( s ) , s=0.0061height ( cm ) + 0.0128 weight ( kg ) 0.1529 .
all statistical tests were two - tailed , and all analyses were considered statistically significant if p<0.05 .
baseline demographic and clinical characteristics , as well as efficacy variables , were compared between group i and group ii using the paired t test .
the study was conducted with prior institutional ethics approval under the requirements of the chinese prevention of cruelty to human subjects and the code of practice for the care and use of human subjects for scientific purposes .
all human subjects of this study were inspected by members of the human subject ethics committee of west china medical centre ( hspc20120407 - 17468 ) and in compliance with the helsinki declaration .
patients who were seen in the outpatient department of the west china hospital from may 2012 to september 2014 and who were at least 18 years of age were eligible if they had the primary diagnoses of hypertension and hypercholesterolemia ( tc > 5.70
the diagnosis of hypertension was made following ambulatory blood pressure monitoring ( abpm ) , with the following levels considered to be hypertensive : average blood pressure > 130/80 mmhg , daytime blood pressure > 135/85 mmhg or nocturnal blood pressure > 125/75 mmhg . to ensure the safety of the single - pill therapy
patients were excluded if they were previously treated with any lipid - lowering therapy or if they had a diagnosis of secondary hypertension , any cerebrovascular disease within the past 6 months , an acute myocardial infarction , congestive heart failure , congenital or rheumatic heart disease , autoimmune disease , severely abnormal liver or kidney values , severe trauma , infection , major surgery , or secondary hyperlipidemia caused by drug therapy . before entering the study
the clinical trial was an outpatient , practice - based , case - control study lasting 8 weeks . to evaluate the efficacy and safety of single - pill combination of amlodipine and atorvastatin ,
i , patients were provided with single - pill amlodipine / atorvastatin ( 5/20 mg , hisun - pfizer pharmaceutical , ltd , tai zhou , china , which is also the only dose could be used in china ) at 10 pm every night . in group ii , patients were instructed to take the amlodipine tablet ( 5 mg , pfizer chinese pharmaceutical , ltd . ,
beijing , china ) every morning at 7 am . at the same time , atorvastatin ( 20 mg , pfizer chinese pharmaceutical , ltd . , beijing , china ) was also been given .
the patients were allowed to take the necessary drugs for cardiovascular indications other than hypertension .
all patients from group i and ii then returned for the final visit after 8 weeks .
at first visit , the average , daytime , nocturnal , and morning blood pressures were measured and recorded by abpm .
other variables collected at this visit included age , sex , smoking status , serum lipid levels , presence of diabetes mellitus , and coronary heart disease ( chd ) .
other laboratory examination indexes , including high - sensitivity c - reaction protein ( hs - crp ) , left ventricular mass index ( lvmi ) , carotid intima - media thickness ( imt ) , and concurrent medications , were also recorded . at the second visit , bp measurements by abpm , serum lipid levels , hs - crp , lvmi , and imt were repeated .
other variables collected at this visit included the occurrence of adverse drug reactions ( adrs ) and the number of pills missing from their prescription bottle ( see flow program below in figure 1 ) .
serum lipid levels were measured by fasting blood samples , which were collected in the early morning . total cholesterol ( tc ) and triglycerides ( tg ) , as well as low- and high - density lipoprotein cholesterol ( ldl - c and hdl - c )
hs - crp was also determined by the same blood samples with double - antibody avidin - biotin complex - elisa ( abc elisa ) method .
carotid imt was detected by the same highly qualified doctor in our hospital . for bilateral carotid artery detection
, we used the ie 33 type ultrasonic diagnosis instrument , produced by philips company , with probe frequency 7 . 0 mhz .
we put the probe at the distal carotid artery , 11.5 cm below the fork level , avoiding the plaques in accordance with the synchronization ecg in end - diastolic , measured 5 times on every side , and the average index was recorded as the measured value of carotid imt .
lvmi was inspected by using the hp 5500 color doppler ultrasonic diagnostic instrument , with probe frequency 3.5 mhz .
we measured left ventricular end - diastolic ventricular septal thickness ( ivst ) , left ventricular posterior wall thickness ( pwt ) , left ventricular end - diastolic diameter ( lvidd ) , and left ventricular mass ( lvm ) , according to the formula of devereux : the lvm ( g ) = 1.04 [ ( ivst + lvidd + pwt ) ( lvidd ) ] 13.6 .
lvmi = lvm / body surface area ( s ) , s=0.0061height ( cm ) + 0.0128 weight ( kg ) 0.1529 .
all statistical tests were two - tailed , and all analyses were considered statistically significant if p<0.05 .
baseline demographic and clinical characteristics , as well as efficacy variables , were compared between group i and group ii using the paired t test .
the baseline demographic characteristics for the 200 patients included in this analysis are shown in table 1 .
the average age was 53.1 years , and the overall average , daytime , nocturnal , and morning blood pressures were 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mm hg , and 157.3/98.6 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 2.02 mmol / l ) , tc ( 5.99 mmol / l ) , ldl - c ( 3.96 mmol / l ) , and hdl - c ( 1.19
the frequency of the other risk factors included smoking ( 40% ) , diabetes mellitus ( 42% ) , and chd ( 37% ) . in group ii , 51% of the patients were male and 49% were female .
the average age of the patients was 52.7 years , and the average overall , daytime , nocturnal , and morning blood pressures were 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 1.98 mmol / l ) , tc ( 6.01 mmol / l ) , ldl - c ( 4.11 mmol / l ) , and hdl - c ( 1.22 mmol / l ) . the frequency of the other risk factors included smoking ( 38% ) , diabetes mellitus ( 48% ) , and chd ( 32% ) . in group
i , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mmhg , and 157.3/98.6 mmhg to 129.4/75.9 mmhg , 139.7/85.4 mmhg , 117.9/66.2 mmhg , and 139.5/85.2 mmhg , respectively . in group
ii , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg to 131.2/74.4 mmhg , 138.9/82.1 mmhg , 121.6/68.4 mmhg , and 149.9/92.7 mmhg , respectively .
the bp reduction from baseline at week 8 was statistically significant in both groups ( p<0.001 ) , but there was no statistically significant change in the d - value except for in the morning peak group . in group
i , the morning peak bp reduction in sbp and dbp at week 8 was markedly less than in group ii ( see table 2 , figure 2 ) .
serum concentrations of tc , tg , and ldl - c were significantly lower after 8-week treatment ( p<0.01 ) , but hdl - c was increased ( p<0.05 ) in both groups .
however , there was no significant difference in d - value ( p>0.05 ) after 8-week treatment compared with index before ( see table 3 , figure 3 ) .
also , there were no significant differences between before and after 8-week treatment in either group with regard to the hs - crp , lvmi , and carotid -imt ( p>0.05 ) ( see table 4 , figure 4 ) .
ankle edema , the most frequent adverse event , was experienced by 7% ( 7/100 ) in group i and 8% ( 8/100 ) in group ii .
the incidence of headache was 1% ( 1/100 ) in group i and 2% ( 2/100 ) in group ii .
the number of pills missing was much higher in group ii ( once : 29 ; twice : 16 ; 3 times : 10 ; more than 3 times : 7 ) than in group i ( once : 7 ; twice : 5 ; 3 times : 2 ; more than 3 times : 1 ) .
the baseline demographic characteristics for the 200 patients included in this analysis are shown in table 1 .
the average age was 53.1 years , and the overall average , daytime , nocturnal , and morning blood pressures were 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mm hg , and 157.3/98.6 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 2.02 mmol / l ) , tc ( 5.99 mmol / l ) , ldl - c ( 3.96 mmol / l ) , and hdl - c ( 1.19
the frequency of the other risk factors included smoking ( 40% ) , diabetes mellitus ( 42% ) , and chd ( 37% ) . in group ii , 51% of the patients were male and 49% were female .
the average age of the patients was 52.7 years , and the average overall , daytime , nocturnal , and morning blood pressures were 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg , respectively .
the mean baseline serum lipid levels were : tg ( 1.98 mmol / l ) , tc ( 6.01 mmol / l ) , ldl - c ( 4.11 mmol / l ) , and hdl - c ( 1.22 mmol / l ) . the frequency of the other risk factors included smoking ( 38% ) , diabetes mellitus ( 48% ) , and chd ( 32% ) .
in group i , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 143.5/86.2 mmhg , 155.2/96.8 mmhg , 130.6/75.3 mmhg , and 157.3/98.6 mmhg to 129.4/75.9 mmhg , 139.7/85.4 mmhg , 117.9/66.2 mmhg , and 139.5/85.2 mmhg , respectively . in group
ii , the overall average , daytime , nocturnal , and morning peak blood pressures from baseline to week 8 declined from 145.7/85.1 mmhg , 156.5/94.7 mmhg , 133.0/76.2 mmhg , and 158.0/97.9 mmhg to 131.2/74.4 mmhg , 138.9/82.1 mmhg , 121.6/68.4 mmhg , and 149.9/92.7 mmhg , respectively .
the bp reduction from baseline at week 8 was statistically significant in both groups ( p<0.001 ) , but there was no statistically significant change in the d - value except for in the morning peak group .
in group i , the morning peak bp reduction in sbp and dbp at week 8 was markedly less than in group ii ( see table 2 , figure 2 ) .
serum concentrations of tc , tg , and ldl - c were significantly lower after 8-week treatment ( p<0.01 ) , but hdl - c was increased ( p<0.05 ) in both groups .
however , there was no significant difference in d - value ( p>0.05 ) after 8-week treatment compared with index before ( see table 3 , figure 3 ) .
also , there were no significant differences between before and after 8-week treatment in either group with regard to the hs - crp , lvmi , and carotid -imt ( p>0.05 ) ( see table 4 , figure 4 ) .
ankle edema , the most frequent adverse event , was experienced by 7% ( 7/100 ) in group i and 8% ( 8/100 ) in group ii .
the incidence of headache was 1% ( 1/100 ) in group i and 2% ( 2/100 ) in group ii .
the number of pills missing was much higher in group ii ( once : 29 ; twice : 16 ; 3 times : 10 ; more than 3 times : 7 ) than in group i ( once : 7 ; twice : 5 ; 3 times : 2 ; more than 3 times : 1 ) .
to address whether the timing of dosing for amlodipine and atorvastatin is important with regard to therapeutic efficacy , our results showed no obvious differences between the different dosing times for amlodipine - atorvastatin in blood pressure control between the 2 groups .
taking amlodipine at night not only lowered blood pressure , but it also provided better control during the peak blood pressures in the morning .
hypercholesterolemia control in the 2 groups was also not significantly different ; taking atorvastatin in the morning was equally as effective as taking it at night in patients with hypercholesterolemia . although no obvious difference was found in adverse drug reactions between the 2 groups , compliance was much better in the single - pill group than in those patients taking the 2 drugs separately .
hypertension is one of the most important causes of and risk factors for a variety of cardiovascular and cerebrovascular diseases , and also affects important organs such as the structure and function of the heart , brain , and kidneys , eventually leading to organ failure . in recent years
, studies have determined that there is a close relationship between endothelial dysfunction and hypertension .
a prospective follow - up study has confirmed that carotid imt can strongly and independently forecast heart or cerebrovascular disease , with the increase of carotid imt corresponding to an increase in the incidence of myocardial infarction and stroke .
leiboritz has confirmed that atorvastatin can improve the small artery elasticity of patients with hyperlipidemia and reduce the diastolic and systolic blood pressures .
the prevent study observed that the carotid imt in the amlodipine group was reduced by 0.013 mm on average , while it increased by an average of 0.033 mm in the placebo group ; this difference was statistically significant .
amlodipine is a long - acting calcium antagonist with powerful , stable , and long - lasting effects on hypertension ; it promotes arterial endothelial function , may effectively improve arterial elasticity , and reduces carotid imt , thus inhibiting the progression of atherosclerosis .
carotid imt was significantly lower after treatment , but no difference was found between the 2 groups .
hypertension and its related complications are often attended by vascular epithelial damnification and other pathological changes .
as one of the important inflammatory markers , serum hs - crp is considered to participate in the process of left ventricular hypertrophy and hypertension [ 15 . during the treatment of patients with hypertension , we need not only effectively control blood pressure , but also must monitor and improve endothelial inflammation and left ventricular remodeling . the effect of the oxidative stress induced by endothelial dysfunction can destroy the function of nitric oxide .
many studies have proven that combination therapy can effectively stimulate the endothelial cells to release nitric oxide and maintain normal vascular function .
statins can reduce the hardening of the arteries , improve arterial compliance , and reverse the remodeling of the aorta , which could reverse the left ventricular hypertrophy caused by changes in arterial structure and function [ 1618 ] .
in addition , atorvastatin can reduce the levels of serum crp and other inflammatory markers , reduce inflammation , and improve endothelial function .
atorvastatin can inhibit hypertrophy and cell proliferation by reducing angiotensin i and improve left ventricular hypertrophy .
our experiment achieved similar results : compared to before treatment , the hs - crp and lvmi were significantly lower after treatment , but no significant difference was found between the 2 groups .
there is another problem which deserves attention : the blood pressure was decreased significantly but not normalized in some patients by using amlodipine 5 mg per day , which indicated that the daily dose of 5 mg of amlodipine was probably too low for these patients . for solving this problem ,
we designed and conducted part ii of this experiment , in which all patients in part i were divided into 4 groups and different doses of spc were been given to these patients .
this clinic research may provide answers allowing us to know how to correct and reasonably use the spc of amlodipine - atorvastatin .
taking the single - pill amlodipine - atorvastatin combination at night lowered blood pressure and reduced the morning peak blood pressure levels on the second day .
this dosing strategy may also improve patient adherence to therapy . in combination with amlodipine , atorvastatin reduced systolic blood pressure , inhibited cardiac hypertrophy in left ventricle and inflammation , then the whole progress of left ventricular remodeling during hypertension could be affected .
all suggests that this combination could be a better choice for hypertensive patients with primary hypercholesterolemia .[/INST]backgroundis the timing of dosing for amlodipine and atorvastatin important with regard to therapeutic efficacy ? to answer this question ,
we designed an outpatient , practice - based , case - control study lasting 8 weeks.material/methodstwo hundred patients were divided into 2 groups : in group i , patients were provided with a single pill containing amlodipine / atorvastatin ( 5/20 mg ) to be taken each night at 10 pm , and in group ii , patients were taking amlodipine ( 5 mg ) and atorvastatin ( 20 mg ) each morning at 7 am.resultsour results indicated no obvious difference in blood pressure control between the 2 groups .
taking amlodipine at night not only lowered blood pressure , but it also provided better control during the peak blood pressure in the morning .
hypercholesterolemia control in the 2 groups was also not significantly different , taking atorvastatin in the morning was as effective as dosing at night in patients with hypercholesterolemia . while the carotid imt , hs - crp , and lvmi were significantly lower after treatment , no differences were found between the 2 groups .
although no obvious difference was found in adverse drug reactions between the 2 groups , compliance was much better in the single - pill group than in patients taking the 2 medications separately.conclusionsin conclusion , single - pill amlodipine - atorvastatin taken at night can lower blood pressure and reduce the morning peak blood pressure levels the next day .
additionally , this dosing method could improve patient adherence to the therapy .</s> |
Image copyright Twitter
Billionaire Donald Trump has said he "may sue" a Twitter user who tricked him into retweeting an image of British serial killers Fred and Rose West.
Mr Trump shared the spoof message that claimed the pair looked at him as a "big inspiration" and asked him to "RT for their memory".
Later he tweeted: "I guess this teaches you not to be nice or trusting."
Fred West was charged with a dozen murders in Gloucester but killed himself before the trial in 1995.
Rose West was convicted of 10 murders - many at the couple's home in Gloucester - and jailed for life. She was told when she was sentenced in 1995 that she should never be released.
Mr Trump was contacted by the Twitter user early on Monday, urging him to retweet the image of the Wests.
The tycoon, who features on the US version of reality TV show The Apprentice, later deleted the message after it was widely shared on the social media site.
Image copyright Twitter
Addressing the incident, Mr Trump later tweeted: "Some jerk fraudulently tweeted that his parents said I was a big inspiration to them + pls RT-out of kindness I retweeted. Maybe I'll sue.
"I thought I was being nice to somebody re their parents. I guess this teaches you not to be nice or trusting. Sad!"
Mr Trump has yet to respond to requests for a comment from the BBC. ||||| But his latest mistake is perhaps his most laughable to date β in the very poorest of tastes.
The business magnate accidentally retweeted a message from a follower asking Trump to share an image purportedly of his recently deceased parents in loving tribute to their memory.
βMy parents who passed away always said you were big inspiration,β the post from @Feckhead read.
βCan you pls RT for their memory?β
Unbeknownst to Trump, however, @Feckhead is βfailed comedianβ Phil Bradbury, and the image he posted was actually one of convicted serial killers Fred and Rosemary West.
The response from followers was thus:
@realDonaldTrump @feckhead They seem like lovely, kind caring parents, don't you think Donald? Dom Joly (@domjoly) September 29, 2014
.@realDonaldTrump Congratulations to @feckhead you win the internet today. Veridis Quo (@METAKNlGHT) September 29, 2014
And our personal favourite...
Please retweet for my brother who has a disfiguring skin condition @realDonaldTrump pic.twitter.com/gBQPLARgqh Beaker Police (@OffencePolice) September 29, 2014
The notorious married murderers were found guilty of torturing and raping scores of young girls, and killing 11 of them, between the years 1973 and 1979. Their victims included Fredβs stepdaughter, who Rosemary murdered while Fred was in prison for theft.
The pair were finally charged in 1994. Fred took his own life before the case when to trial. Rosemary was found guilty of 10 counts of murder in November 1995 and is currently serving a life sentence.
The scene of many of their most heinous acts, their Gloucester residence 25 Cromwell Street, was demolished in 1996 and converted into a landscaped footpath.
Last month, Trump caused mild outrage by deliberately tweeting the following about ebola doctors.
Read More: Trump Walks Out Of BBC Interview After Qs About Mafia | β "I guess this teaches you not to be nice or trusting," Donald Trump complained yesterday after he was fooled into retweeting a picture of notorious British serial killers Fred and Rosemary West. The tycoon says he may sue the "jerk" who told him his "parents who passed away always said you were big inspiration" and asked him to retweet the photo in their memory, reports the BBC. Trump quickly deleted the picture of the Westsβwho murdered at least 11 young women in the 1970sβbut not before the mistake had been widely shared, reports the Independent, which rounds up some of its favorite responses, including a picture of Freddy Krueger with the caption "Please retweet for my brother who has a disfiguring skin condition." (Also getting Trump's goat: Critics who say putting his name in 20-foot-tall illuminated letters on a Chicago skyscraper is a little tacky.) | <s>[INST]Image copyright Twitter
Billionaire Donald Trump has said he "may sue" a Twitter user who tricked him into retweeting an image of British serial killers Fred and Rose West.
Mr Trump shared the spoof message that claimed the pair looked at him as a "big inspiration" and asked him to "RT for their memory".
Later he tweeted: "I guess this teaches you not to be nice or trusting."
Fred West was charged with a dozen murders in Gloucester but killed himself before the trial in 1995.
Rose West was convicted of 10 murders - many at the couple's home in Gloucester - and jailed for life. She was told when she was sentenced in 1995 that she should never be released.
Mr Trump was contacted by the Twitter user early on Monday, urging him to retweet the image of the Wests.
The tycoon, who features on the US version of reality TV show The Apprentice, later deleted the message after it was widely shared on the social media site.
Image copyright Twitter
Addressing the incident, Mr Trump later tweeted: "Some jerk fraudulently tweeted that his parents said I was a big inspiration to them + pls RT-out of kindness I retweeted. Maybe I'll sue.
"I thought I was being nice to somebody re their parents. I guess this teaches you not to be nice or trusting. Sad!"
Mr Trump has yet to respond to requests for a comment from the BBC. ||||| But his latest mistake is perhaps his most laughable to date β in the very poorest of tastes.
The business magnate accidentally retweeted a message from a follower asking Trump to share an image purportedly of his recently deceased parents in loving tribute to their memory.
βMy parents who passed away always said you were big inspiration,β the post from @Feckhead read.
βCan you pls RT for their memory?β
Unbeknownst to Trump, however, @Feckhead is βfailed comedianβ Phil Bradbury, and the image he posted was actually one of convicted serial killers Fred and Rosemary West.
The response from followers was thus:
@realDonaldTrump @feckhead They seem like lovely, kind caring parents, don't you think Donald? Dom Joly (@domjoly) September 29, 2014
.@realDonaldTrump Congratulations to @feckhead you win the internet today. Veridis Quo (@METAKNlGHT) September 29, 2014
And our personal favourite...
Please retweet for my brother who has a disfiguring skin condition @realDonaldTrump pic.twitter.com/gBQPLARgqh Beaker Police (@OffencePolice) September 29, 2014
The notorious married murderers were found guilty of torturing and raping scores of young girls, and killing 11 of them, between the years 1973 and 1979. Their victims included Fredβs stepdaughter, who Rosemary murdered while Fred was in prison for theft.
The pair were finally charged in 1994. Fred took his own life before the case when to trial. Rosemary was found guilty of 10 counts of murder in November 1995 and is currently serving a life sentence.
The scene of many of their most heinous acts, their Gloucester residence 25 Cromwell Street, was demolished in 1996 and converted into a landscaped footpath.
Last month, Trump caused mild outrage by deliberately tweeting the following about ebola doctors.
Read More: Trump Walks Out Of BBC Interview After Qs About Mafia[/INST]β "I guess this teaches you not to be nice or trusting," Donald Trump complained yesterday after he was fooled into retweeting a picture of notorious British serial killers Fred and Rosemary West. The tycoon says he may sue the "jerk" who told him his "parents who passed away always said you were big inspiration" and asked him to retweet the photo in their memory, reports the BBC. Trump quickly deleted the picture of the Westsβwho murdered at least 11 young women in the 1970sβbut not before the mistake had been widely shared, reports the Independent, which rounds up some of its favorite responses, including a picture of Freddy Krueger with the caption "Please retweet for my brother who has a disfiguring skin condition." (Also getting Trump's goat: Critics who say putting his name in 20-foot-tall illuminated letters on a Chicago skyscraper is a little tacky.)</s> |
the financial quakes model ( fqm ) that we introduce in this paper is defined on a small - world ( sw ) network @xcite of @xmath1 agents @xmath5 ( `` traders '' ) .
the total number of traders considered is always @xmath3 .
note that the purpose of this model is to generate volatility clustering and power - law distributed avalanche sizes in a simple way , while we are not interested in formulating a realistic micro - model of financial markets or to reproduce the exact power - law exponents .
the purpose of our study is to explore possible ways to destroy dangerous herding effects by simple and effective means . in our fqm model ,
each agent carries a given quantity of information about the financial market considered .
the sw network is obtained from a square 2-dimensional @xmath6 lattice with open boundary conditions , by randomly rewiring the nearest neighbors links with a probability of @xmath7 ( see fig.1 ) .
the resulting network topology allows the information to spread over the lattice through long - range links , but also preserves the clustering properties of the network and its average degree ( @xmath8 ) .
the information spreading is simulated by associating to each trader a real variable @xmath9 @xmath10 , representing the information possessed at time @xmath11 , which initially ( at @xmath12 ) is set to a random value in the interval @xmath13 .
@xmath14 is a threshold value that is assumed to be the same for all agents . at each discrete time step @xmath15 , due to public external information sources , all these variables
are simultaneously increased by a quantity @xmath16 , which is different for each agent and randomly extracted within the interval @xmath17 $ ] , where @xmath18 is the maximum value of the agents information at time @xmath11 .
( a ) s@xmath19p 500 index data used in this paper , with @xmath20 daily index entries @xmath21 ( from september 11 , 1989 , to june 29 , 2012 ) .
( b ) corresponding ( relative ) returns time series , where returns are defined as the ratio @xmath22.,width=326 ] if , at a given time step @xmath23 , the information @xmath24 of one or more
agents @xmath25 exceeds the threshold value @xmath26 , these agents become `` active '' and take the decision of investing a given quantity of money by betting on the bullish ( increasing ) or bearish ( decreasing ) behavior of the market compared to the day before . as mentioned before
, we consider here as a typical example the s@xmath19p @xmath27 index .
the time period ranges from september 11 , 1989 , to june 29 , 2012 , over a total of @xmath28 daily index values @xmath21 ( see fig .
2 ) . notice that the use of this particular series has no special reasons , it just serves to ensure only a realistic market dynamics as input .
other indexes have also been tested with similar results . in order to make their prediction @xmath29 ( positive or negative ) about the sign of the index difference @xmath30 at time @xmath23 , active agents are assumed to follow the standard relative strength index ( rsi ) trading strategy , based on the ratio between the sum of positive returns and the sum of negative returns experienced during the last @xmath31 days ( here we choose @xmath32 ; see ref .
@xcite for further details of the rsi algorithm ) . as for the time series
considered , this strategy has nothing special and has been chosen just because it is a commonly used technical strategy in the trading community . for financial traders
, it is often beneficial to be followed by others , as this increases the likelihood that their investments will be profitable or because they are friends / colleagues and it would be considered appropriate to share part of their own information .
therefore , we assume that the agents , once activated , will transfer some information to the neighbors according the following herding mechanism : @xmath33 here `` nn '' denotes the set of nearest - neighbors of the active agent @xmath34 .
@xmath35 is the number of direct neighbors , and the parameter @xmath36 controls the level of dissipation of the information during the dynamics ( @xmath37 corresponds to the conservative case ) . in analogy with the ofc model for earthquakes
@xcite , we set here @xmath38 ( non - conservative case ) , i.e. we consider some information loss during the herding process .
this value of @xmath36 has been chosen here to drive the system in a critical state and to obtain large avalanches , since our goal is to study how these avalanches can be reduced by the introduction of random traders .
size of avalanches ( `` financial quakes '' ) occurring in our artificial financial market . both positive cascades ( `` bubbles '' ) and negative avalanches ( `` crashes '' ) are found .
see text for further details.,width=340 ] of course , the herding rule ( [ av_dyn ] ) can activate other agents , thereby producing a chain reaction .
the resulting information avalanche may be called a `` financial quake '' : all the agents that are above the threshold become active and invest simultaneously according to eq .
( [ av_dyn ] ) , such that the agent @xmath34 bets with the same prediction @xmath29 as the agent from which they have received the information .
the financial quake is over , when there are no more active agents in the system ( i.e. when @xmath39 @xmath40 ) .
then , the prediction @xmath29 is finally compared with the sign of @xmath41 : if they are in agreement , all the agents who have contributed to the avalanche win , otherwise they lose . in any case , the process of information cascades build up again due to the random public `` information pressure '' acting on the system . the number of investments ( i.e. the number of active agents ) during a single financial quake define the avalanche size @xmath42 . in the next section we present several simulation results obtained by running this model many times , starting each time from a new random initial distribution of the information @xmath43 shared among the agents .
we assume that the avalanche process within our sample trading community does not influence the whole market , i.e. does not have any effect on the behavior of the financial series considered , even if we imagine that the market does exert some influence on our community through `` the information pressure '' @xmath16 .
on the other hand , this pressure , being random and different for each agent , is also independent from the financial time series considered ( here the @xmath44 ) . in a way
, this scenario could be considered analogous to the physical situation of a small closed thermodynamical system in contact with a very large energy _ reservoir _ ( environment ) , typical for statistical mechanics in the canonical ensemble : even if the system can exchange energy with the environment , it is too small to have any influence on the reservoir itself . cumulative distribution of the sizes ( absolute values ) of herding avalanches occurring in the community of investors , with and without random traders . in the absence of random traders ( open circles ) he distribution obeys a power law with an exponent equal to -1.87 ( a fit is also reported as a straight line ) . considering increasing amount of random traders , i.e. @xmath45 ( diamonds ) , @xmath46 ( squares ) , @xmath47 ( full circles ) and @xmath4 ( triangles )
, the distribution tends to become exponential for sufficiently large percentage of random investors .
an exponential fit with exponent equal to @xmath48 is also found for the latter case . in these simulations
the random traders are uniformly distributed ( at random ) over the network , as in fig.1 .
for further details see the main text.,width=340 ]
in fig . 3 we plot the time sequence @xmath49 of the `` financial quake '' sizes during a single simulation run .
a positive sign means that all the involved agents win and a negative sign that they loose .
each avalanche corresponds to an entry of the s&p @xmath27 index series , since each initial investment ( `` bet '' ) on the market coincides with the occurrence of a financial quake ( this means that the series in fig . 2 and fig .
3 have the same length @xmath50 ) . in analogy with the soc behavior characterizing the ofc model , we observe a sequence of quakes that increases in size over time .
in other words , the financial system is progressively driven into a critical - like state , where herding - related avalanches of any size can occur : most of them will be quite small , but sometimes a very big financial quake appears , involving a herding cascade of bets , which can be either profitable ( positive ) or lossfull ( negative ) . notice that the daily data of the s&p @xmath27 series only affect the sign of the avalanches in fig . 3 , while their sizes strictly depend on the internal dynamics of our small trading community considered .
therefore , as we verified with several simulations not reported here , reshuffling data or removing extreme events in the s&p @xmath27 series would not produce any change in the sizes of the financial quakes .
the soc - like nature of this dynamics is well shown in fig . 4 , where we report the probability distribution @xmath51 of financial quakes size , measured by its absolute value and cumulated over 10 simulations ( open circles ) .
the resulting distribution can be very well fitted by a power - law @xmath52 , a slope consistent with the one obtained for earthquakes in the ofc model on a sw topology ( see @xcite ) .
behavior of the maximum size of avalanches as a function of an increasing number of random traders , for three different ways of spreading them over the network : randomly distributed ( circles ) , grouped in one community ( squares ) and grouped in four communities ( diamonds ) .
the results were averaged over 10 different realizations , each one with a different initial random position of traders and communities within the network.,width=336 ] let us now discuss what happens if a certain number of agents in the network adopt a random trading strategy , i.e. if they invest in a completely random way instead of following the standard rsi strategy .
we have already shown @xcite that an individual random trading strategy , if played along the whole s&p 500 series ( and also along other european financial indices ) , performs as well as various standard trading strategies ( such as rsi , macd or momentum @xcite ) , but it is less risky than other strategies . here , we study whether a widespread adoption of such a random investment strategy would also have a beneficial ( collective ) effect at the macro - level ( where other important phenomena like herding , asymmetric information or rational bubbles may matter ) .
would random investment strategies reduce the level of volatility and induce a greater stability of financial markets ? in the following , we test this hypothesis by introducing a certain percentage @xmath53 of random traders ( colored agents in fig.1 ) , uniformly distributed at random among the @xmath3 investors .
we assume that all agents are aware of the trading strategy ( rsi or random ) adopted by their respective neighbors . in this respect
it is worthwhile to stress again that , in our model , traders behave according to a bounded rationality framework with no feedback mechanism on the market .
note that , in contrast to rsi traders , random traders are not activated by their neighbors , since they invest at random .
we also assume that they do not activate their neighbors , since a random trader has no specific information to transfer .
in other words , random traders only receive information from external sources , but do not exchange individual information with other agents apart from the fact that they bet at random .
two different examples of small - world @xmath0 networks , with @xmath2 agents as in fig . 1 , but where random traders ( colored agents , @xmath4 of the total ) are grouped in one community ( left panel ) or four communities ( right panel ) , respectively.,title="fig:",width=158 ] two different examples of small - world @xmath0 networks , with @xmath2 agents as in fig . 1 , but where random traders ( colored agents , @xmath4 of the total ) are grouped in one community ( left panel ) or four communities ( right panel ) , respectively.,title="fig:",width=158 ] in order to simulate random investors within our model , we simply set @xmath54 for them in eq .
( [ av_dyn ] ) .
this means that random traders ( when they overcome their information threshold ) can invest their capital exactly in the same way as other agents , but they do not take part in any herding - related activation avalanche .
coming back again to fig . 4 , one can see the effect of an increasing percentage @xmath53 of random traders on the size distribution of financial quakes . besides the power - law curve already discussed ,
corresponding to @xmath55 , we report also the results obtained considering different percentages of random traders , when namely @xmath45 ( diamonds ) , @xmath46 ( squares ) , @xmath47 ( full circles ) and @xmath4 ( triangles ) .
the data show that the original power - law distribution evolves towards an exponential one .
an exponential fit with an exponent equal to -0.2 ( dashed - dotted curve ) is also reported for the maximum number of random traders considered by us , i.e. @xmath4 . one can also investigate how the size of the avalanche changes with the increase of the amount of random traders considered , if they are uniformly distributed over the network .
this is shown in fig.5 ( full circles ) , where one can see that the maximum size of the avalanches observed drops by a factor of @xmath56 in the presence of only @xmath46 of random traders , reaching almost its final saturation level of @xmath57 when @xmath58 .
these results indicate that even a relatively small number of random investors distributed at random within the market is able to suppress dangerous herding - related avalanches .
but what would happen if these random traders , instead of being uniformly distributed at random over the population , were grouped together in one or more communities ?
capital / wealth distribution of all agents at the end of the simulation , cumulated over 10 realizations , for a network with various percentages of uniformly distributed random traders . in any case
we had a pareto - like power law with an exponent of @xmath59 , independently of the amount of random traders considered.,width=345 ] in fig.6 we show two examples of small - world networks with @xmath4 random traders ( colored agents ) grouped in one or four communities , respectively ( for clarity , we use the same sample network as in fig.1 , with @xmath2 ) .
if one repeats the previous simulations for our network of @xmath3 agents with an increasing percentage of random traders , but now grouping these traders together in either one community or four communities , respectively , the result is that the original power law distribution of avalanches is less affected by random investments for any percentage @xmath53 .
this , in turn , implies a slower decrease of the maximum avalanche sizes as @xmath53 increases , as shown again in fig.5 ( squares and diamonds , respectively ) .
this means that the uniform random distribution of random investors over the whole network is quite crucial in order to significantly dampen avalanche formation ( notice that a percentage between @xmath60 and @xmath45 of uniformly distributed random traders is enough to reduce the financial quakes size as much as @xmath4 grouped random investors would do ) . in this respect ,
the effect of random traders is to increase the frequency of small financial quakes and , consequently , avoid the occurrence of large ones .
it is also interesting to study the capital gain or loss , i.e. the change in wealth , of the agents involved in the trading process during the whole period considered ( in the following we will use the terms `` capital '' and `` wealth '' synonymously ) . at the beginning of each simulation , we assign to each trader ( rsi or random ) an initial capital @xmath61 according to a normal distribution with an average of @xmath62 credits and a standard deviation equal to @xmath63
. then we let them invest in the market according to the following rules : - if an agent wins thanks to a given bet ( for example after being involved in a given , big or small , positive financial quake ) , in the next investment he will bet a quantity @xmath64 of money equal to one half of his / her total capital @xmath61 , i.e. @xmath65 ; - if an agent loses due to an unsuccessful investment ( for example after a negative financial quake ) , the next time he will invest only ten percent of his / her total capital , i.e. @xmath66 .
we have checked , however , that our result are quite robust to adopting a number of different investment criteria . after a financial quake , the capital of each agent involved in the herding - related avalanche will increase or decrease by the quantity @xmath64 .
of course random traders , who do not take part in avalanches , can invest .
their wealth changes only when they overcome their information threshold due to the external information sources . in fig.7
we show the distribution of the total wealth cumulated by all agents during the whole sequence of financial quakes , i.e. over the whole s&p 500 series ( cumulated over 10 different runs ) , for three different trading networks with increasing percentages of random investors ( namely , @xmath67 , @xmath46 and @xmath4 ) .
interestingly , a pareto power law @xcite with an exponent equal to @xmath59 ( see the fit reported as dashed line ) emerges spontaneously from the dynamics of the asymmetric investments , independently of the number of random traders .
we have checked that this result is quite robust and does not substantially change if we modify the quantity @xmath64 that agents choose to invest in case of a win or a loss .
it is also interesting to study the wealth distribution of the random investors in case of a network with @xmath4 random traders ( results are cumulated over @xmath68 realizations ) .
this is reported in fig.8 , in comparison with the corresponding distribution already shown in the previous figure for the whole trading community .
as one can see from the plot , random traders have a final wealth distribution very different from a power law , which can be fitted very well with an exponential curve , represented by a dashed line , with an exponent equal to @xmath69 ( the fact that the random traders component is not changing the global power law distribution of fig.7 is evidently due to its small size , i.e. @xmath70 agents as compared to @xmath71 ) .
in addition , we compare average final wealth of all the traders , 767 credits , with the average wealth of random investors only , 923 credits .
this should be compared with the initial value of the capital which is 1000 credits .
therefore @xmath72 of rsi traders have more wealth in the end than in the beginning , whereas the analogous percentage for random traders is @xmath73 .
comparison between the final capital / wealth distribution for the whole trading network with @xmath4 of random traders shown in fig.7 ( reported again as square symbols ) and the same distribution for the random traders component only ( full circles ) .
the latter can be fitted with an exponential distribution , also reported as dashed line , with an exponent equal to @xmath69 .
we also report the average capital calculated over all the traders ( 767 credits ) and over the random traders only ( 923 credits).see text for details.,width=345 ] these findings allow us to extend our previous results for single traders @xcite to collective effects in a community of traders .
in fact , they suggest that the adoption of random strategies would diminish the probability of extreme events , in this case large increases or losses of wealth , but also ensure almost the same average wealth over a long time period , at variance with technical strategies .
in particular , looking at the details of the two distribution shown in fig.8 , we also find that @xmath74 of rsi traders have a final capital smaller than the worst random trader , whereas only @xmath57 of rsi traders perform better than the best random trader .
this means that , for technical traders , the risk of losses is much greater than the probability of gains , compared to those of random investors .
random trading seems therefore , after all , a very good combination of low risk and high performance . before closing this section
we note that all the numerical simulations presented are quite robust and that similar results were obtained adopting other historical time series , such as , for example , ftse uk or ftse mib .
even though our results were obtained for a `` toy model '' of financial trading , we think that they have potentially interesting policy implications . according to the conventional assumption , neither bubbles or crashes should occur when all agents are provided with the same complete and credible set of information about monetary and asset values traded in the market .
this is the basis of the well - known efficient market hypothesis @xcite , based on the paradigm of rational expectations @xcite .
bubbles and crashes should also not occur according to the wide - spread dynamic stochastic general equilbrium ( dsge ) models @xcite .
however , the wisdom of crowds effect , which induces the equilibrium price , can be undermined by information feedbacks and social influence @xcite .
such social influence may lead to bubbles and crashes . to account for herding effects ,
researchers have started to propose concepts such as `` rational bubbles '' @xcite , recognizing that it can be profitable to follow a trend . however , on average , trend - following is not more successful than random investments it is rather more risky @xcite . from human psychology , we know that people tend to follow others , i.e. to show herding behavior , if it is not clear what is the right thing to do @xcite .
this fact establishes that many traders will be susceptible to the trading decisions of others .
it seems realistic to assume that each agent is endowed with a different quantity and quality of information , coming from private information sources with different reputation , depending on the agents position in the network ( see e.g. refs .
however , such information feedbacks may be harmful , particularly when the market is flooded with volatile and self - referential information .
our paper supports the hypothesis @xcite that introducing `` noisy trading '' ( i.e. random investors ) in financial markets can destroy bubbles and crashes before they become large , and thereby avoid dangerous avalanches . by preventing extreme price variations
, random investments also help to identify the equilibrium price @xcite .
it seems that already a small number of random investors ( relative to the total number of agents ) would be enough to have a beneficial effect on the financial market , particularly if distributed at random .
such investors could be central banks , but also large investors , including pension funds or hedge funds with an interest in reducing the risks of their investments .
we are aware that further studies with more sophisticated and realistic models of financial markets should be performed to explore the full potentials and limitations of random investment strategies .
however , our results suggest that random investments will always reduce both the size and frequency of bubbles / crashes . further research will be devoted to understanding the most opportune timing for the introduction of such random investments and whether this innovative policy instrument can enable a smooth control of financial markets , thereby reducing their fragility .
dh acknowledges partial support by the fet flagship pilot project futurict ( grant number 284709 ) , the eth project `` systemic risks , systemic solutions '' ( chirp ii project eth 4812 - 1 ) and the erc advanced investigator grant `` momentum '' ( grant no . 324247 )
. s. bikhchandani , d. hirshleifer , and i. welch , _ informational cascades and rational herding : an annotated bibliography and resource reference , working paper _ ( anderson school of management , ucla , available at www.info-cascades.info , 2008 ) | building on similarities between earthquakes and extreme financial events , we use a self - organized criticality - generating model to study herding and avalanche dynamics in financial markets .
we consider a community of interacting investors , distributed on a small - world network , who bet on the bullish ( increasing ) or bearish ( decreasing ) behavior of the market which has been specified according to the s&p500 historical time series .
remarkably , we find that the size of herding - related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders , randomly distributed inside the network , who adopt a random investment strategy .
our findings suggest a promising strategy to limit the size of financial bubbles and crashes .
we also obtain that the resulting wealth distribution of all traders corresponds to the well - known pareto power law , while the one of random traders is exponential . in other words , for technical traders ,
the risk of losses is much greater than the probability of gains compared to those of random traders .
financial markets often experience extremes , called `` bubbles '' and `` crashes '' .
the underlying dynamics is related to avalanches , the size of which is distributed according to power laws @xcite .
power laws imply that crashes may reach any size a circumstance that may threaten the functionality of the entire financial system .
many scientists see `` herding behavior '' as the origin of such dangerous avalanches @xcite . in our paper
, we explore whether there is a mechanism that could stop or reduce them .
to generate a power - law dynamics similar to the volatility clustering in financial markets , we use an agent - based model that produces the phenomenon of self - organized criticality ( soc ) @xcite . specifically , we adapt the olami - feder - chrstensen ( ofc ) model @xcite that has been proposed to describe the dynamics of earthquakes @xcite . in this context , we assume information cascades between agents @xcite as the underlying mechanism of financial avalanches . we assume that agents interact within a small - world ( sw ) network of financial trading @xcite and that there is social influence among them @xcite
. such kinds of models are recently becoming popular in economics @xcite and herding effects are also beginning to be observed in lab experiments @xcite . in this connection , it is interesting to consider that humans tend to orient themselves at decisions and behaviors of others , particularly in situations where it is not clear what is the right thing to do @xcite .
such conditions are typical for financial markets , in particular during volatile periods .
in fact , in situations of high uncertainty , personal information exchange may reach market - wide impacts , as the examples of bank runs @xcite and speculative attacks on national currencies @xcite show .
our study explores how huge herding avalanches in financial trading might be reduced by introducing a certain percentage of traders who adopt a random investment strategy . actually , several analogies between socio - economic and physical or biological systems have recently been discussed @xcite , where noise and randomness can have beneficial effects , improving the performance of the system @xcite .
more specifically , in a recent series of papers , it has been explored whether the adoption of random strategies may be advantageous in financial trading from an individual point of view .
scientific evidence suggests that , in the long term , random trading strategies are less risky for a single trader , but provide , on average , gains comparable to those obtained by technical strategies @xcite .
therefore , one might expect that a certain percentage of investors would consider the possibility of adopting a random trading strategy . assuming this and using real data sets of the s&p500 index , we here extend our previous analysis to a sample community of interacting investors .
we investigate whether the presence of randomly distributed agents performing random investments influences the formation of herding - related avalanches and how the wealth of the traders is distributed .
we show that the presence of random traders is able to reduce financial avalanches , which we call - in analogy with earthquakes - financial quakes. furthermore , we find that the wealth distribution , even if normally distributed in the beginning , spontaneously evolves towards the well - known pareto power law . finally , we address possible policy implications . small - world @xmath0 network of @xmath1 traders , as used in our numerical simulations ( here @xmath2 as an example , but in the simulations we always considered @xmath3 agents ) .
short - range and long - range links are simultaneously present .
white agents are rsi traders ( active agents assumed to follow the standard relative strength index ( rsi ) trading strategy ) ; colored agents ( @xmath4 of the total ) are random traders , here uniformly distributed at random among the population
. see text for further details.,width=288 ] | <s>[INST]the financial quakes model ( fqm ) that we introduce in this paper is defined on a small - world ( sw ) network @xcite of @xmath1 agents @xmath5 ( `` traders '' ) .
the total number of traders considered is always @xmath3 .
note that the purpose of this model is to generate volatility clustering and power - law distributed avalanche sizes in a simple way , while we are not interested in formulating a realistic micro - model of financial markets or to reproduce the exact power - law exponents .
the purpose of our study is to explore possible ways to destroy dangerous herding effects by simple and effective means . in our fqm model ,
each agent carries a given quantity of information about the financial market considered .
the sw network is obtained from a square 2-dimensional @xmath6 lattice with open boundary conditions , by randomly rewiring the nearest neighbors links with a probability of @xmath7 ( see fig.1 ) .
the resulting network topology allows the information to spread over the lattice through long - range links , but also preserves the clustering properties of the network and its average degree ( @xmath8 ) .
the information spreading is simulated by associating to each trader a real variable @xmath9 @xmath10 , representing the information possessed at time @xmath11 , which initially ( at @xmath12 ) is set to a random value in the interval @xmath13 .
@xmath14 is a threshold value that is assumed to be the same for all agents . at each discrete time step @xmath15 , due to public external information sources , all these variables
are simultaneously increased by a quantity @xmath16 , which is different for each agent and randomly extracted within the interval @xmath17 $ ] , where @xmath18 is the maximum value of the agents information at time @xmath11 .
( a ) s@xmath19p 500 index data used in this paper , with @xmath20 daily index entries @xmath21 ( from september 11 , 1989 , to june 29 , 2012 ) .
( b ) corresponding ( relative ) returns time series , where returns are defined as the ratio @xmath22.,width=326 ] if , at a given time step @xmath23 , the information @xmath24 of one or more
agents @xmath25 exceeds the threshold value @xmath26 , these agents become `` active '' and take the decision of investing a given quantity of money by betting on the bullish ( increasing ) or bearish ( decreasing ) behavior of the market compared to the day before . as mentioned before
, we consider here as a typical example the s@xmath19p @xmath27 index .
the time period ranges from september 11 , 1989 , to june 29 , 2012 , over a total of @xmath28 daily index values @xmath21 ( see fig .
2 ) . notice that the use of this particular series has no special reasons , it just serves to ensure only a realistic market dynamics as input .
other indexes have also been tested with similar results . in order to make their prediction @xmath29 ( positive or negative ) about the sign of the index difference @xmath30 at time @xmath23 , active agents are assumed to follow the standard relative strength index ( rsi ) trading strategy , based on the ratio between the sum of positive returns and the sum of negative returns experienced during the last @xmath31 days ( here we choose @xmath32 ; see ref .
@xcite for further details of the rsi algorithm ) . as for the time series
considered , this strategy has nothing special and has been chosen just because it is a commonly used technical strategy in the trading community . for financial traders
, it is often beneficial to be followed by others , as this increases the likelihood that their investments will be profitable or because they are friends / colleagues and it would be considered appropriate to share part of their own information .
therefore , we assume that the agents , once activated , will transfer some information to the neighbors according the following herding mechanism : @xmath33 here `` nn '' denotes the set of nearest - neighbors of the active agent @xmath34 .
@xmath35 is the number of direct neighbors , and the parameter @xmath36 controls the level of dissipation of the information during the dynamics ( @xmath37 corresponds to the conservative case ) . in analogy with the ofc model for earthquakes
@xcite , we set here @xmath38 ( non - conservative case ) , i.e. we consider some information loss during the herding process .
this value of @xmath36 has been chosen here to drive the system in a critical state and to obtain large avalanches , since our goal is to study how these avalanches can be reduced by the introduction of random traders .
size of avalanches ( `` financial quakes '' ) occurring in our artificial financial market . both positive cascades ( `` bubbles '' ) and negative avalanches ( `` crashes '' ) are found .
see text for further details.,width=340 ] of course , the herding rule ( [ av_dyn ] ) can activate other agents , thereby producing a chain reaction .
the resulting information avalanche may be called a `` financial quake '' : all the agents that are above the threshold become active and invest simultaneously according to eq .
( [ av_dyn ] ) , such that the agent @xmath34 bets with the same prediction @xmath29 as the agent from which they have received the information .
the financial quake is over , when there are no more active agents in the system ( i.e. when @xmath39 @xmath40 ) .
then , the prediction @xmath29 is finally compared with the sign of @xmath41 : if they are in agreement , all the agents who have contributed to the avalanche win , otherwise they lose . in any case , the process of information cascades build up again due to the random public `` information pressure '' acting on the system . the number of investments ( i.e. the number of active agents ) during a single financial quake define the avalanche size @xmath42 . in the next section we present several simulation results obtained by running this model many times , starting each time from a new random initial distribution of the information @xmath43 shared among the agents .
we assume that the avalanche process within our sample trading community does not influence the whole market , i.e. does not have any effect on the behavior of the financial series considered , even if we imagine that the market does exert some influence on our community through `` the information pressure '' @xmath16 .
on the other hand , this pressure , being random and different for each agent , is also independent from the financial time series considered ( here the @xmath44 ) . in a way
, this scenario could be considered analogous to the physical situation of a small closed thermodynamical system in contact with a very large energy _ reservoir _ ( environment ) , typical for statistical mechanics in the canonical ensemble : even if the system can exchange energy with the environment , it is too small to have any influence on the reservoir itself . cumulative distribution of the sizes ( absolute values ) of herding avalanches occurring in the community of investors , with and without random traders . in the absence of random traders ( open circles ) he distribution obeys a power law with an exponent equal to -1.87 ( a fit is also reported as a straight line ) . considering increasing amount of random traders , i.e. @xmath45 ( diamonds ) , @xmath46 ( squares ) , @xmath47 ( full circles ) and @xmath4 ( triangles )
, the distribution tends to become exponential for sufficiently large percentage of random investors .
an exponential fit with exponent equal to @xmath48 is also found for the latter case . in these simulations
the random traders are uniformly distributed ( at random ) over the network , as in fig.1 .
for further details see the main text.,width=340 ]
in fig . 3 we plot the time sequence @xmath49 of the `` financial quake '' sizes during a single simulation run .
a positive sign means that all the involved agents win and a negative sign that they loose .
each avalanche corresponds to an entry of the s&p @xmath27 index series , since each initial investment ( `` bet '' ) on the market coincides with the occurrence of a financial quake ( this means that the series in fig . 2 and fig .
3 have the same length @xmath50 ) . in analogy with the soc behavior characterizing the ofc model , we observe a sequence of quakes that increases in size over time .
in other words , the financial system is progressively driven into a critical - like state , where herding - related avalanches of any size can occur : most of them will be quite small , but sometimes a very big financial quake appears , involving a herding cascade of bets , which can be either profitable ( positive ) or lossfull ( negative ) . notice that the daily data of the s&p @xmath27 series only affect the sign of the avalanches in fig . 3 , while their sizes strictly depend on the internal dynamics of our small trading community considered .
therefore , as we verified with several simulations not reported here , reshuffling data or removing extreme events in the s&p @xmath27 series would not produce any change in the sizes of the financial quakes .
the soc - like nature of this dynamics is well shown in fig . 4 , where we report the probability distribution @xmath51 of financial quakes size , measured by its absolute value and cumulated over 10 simulations ( open circles ) .
the resulting distribution can be very well fitted by a power - law @xmath52 , a slope consistent with the one obtained for earthquakes in the ofc model on a sw topology ( see @xcite ) .
behavior of the maximum size of avalanches as a function of an increasing number of random traders , for three different ways of spreading them over the network : randomly distributed ( circles ) , grouped in one community ( squares ) and grouped in four communities ( diamonds ) .
the results were averaged over 10 different realizations , each one with a different initial random position of traders and communities within the network.,width=336 ] let us now discuss what happens if a certain number of agents in the network adopt a random trading strategy , i.e. if they invest in a completely random way instead of following the standard rsi strategy .
we have already shown @xcite that an individual random trading strategy , if played along the whole s&p 500 series ( and also along other european financial indices ) , performs as well as various standard trading strategies ( such as rsi , macd or momentum @xcite ) , but it is less risky than other strategies . here , we study whether a widespread adoption of such a random investment strategy would also have a beneficial ( collective ) effect at the macro - level ( where other important phenomena like herding , asymmetric information or rational bubbles may matter ) .
would random investment strategies reduce the level of volatility and induce a greater stability of financial markets ? in the following , we test this hypothesis by introducing a certain percentage @xmath53 of random traders ( colored agents in fig.1 ) , uniformly distributed at random among the @xmath3 investors .
we assume that all agents are aware of the trading strategy ( rsi or random ) adopted by their respective neighbors . in this respect
it is worthwhile to stress again that , in our model , traders behave according to a bounded rationality framework with no feedback mechanism on the market .
note that , in contrast to rsi traders , random traders are not activated by their neighbors , since they invest at random .
we also assume that they do not activate their neighbors , since a random trader has no specific information to transfer .
in other words , random traders only receive information from external sources , but do not exchange individual information with other agents apart from the fact that they bet at random .
two different examples of small - world @xmath0 networks , with @xmath2 agents as in fig . 1 , but where random traders ( colored agents , @xmath4 of the total ) are grouped in one community ( left panel ) or four communities ( right panel ) , respectively.,title="fig:",width=158 ] two different examples of small - world @xmath0 networks , with @xmath2 agents as in fig . 1 , but where random traders ( colored agents , @xmath4 of the total ) are grouped in one community ( left panel ) or four communities ( right panel ) , respectively.,title="fig:",width=158 ] in order to simulate random investors within our model , we simply set @xmath54 for them in eq .
( [ av_dyn ] ) .
this means that random traders ( when they overcome their information threshold ) can invest their capital exactly in the same way as other agents , but they do not take part in any herding - related activation avalanche .
coming back again to fig . 4 , one can see the effect of an increasing percentage @xmath53 of random traders on the size distribution of financial quakes . besides the power - law curve already discussed ,
corresponding to @xmath55 , we report also the results obtained considering different percentages of random traders , when namely @xmath45 ( diamonds ) , @xmath46 ( squares ) , @xmath47 ( full circles ) and @xmath4 ( triangles ) .
the data show that the original power - law distribution evolves towards an exponential one .
an exponential fit with an exponent equal to -0.2 ( dashed - dotted curve ) is also reported for the maximum number of random traders considered by us , i.e. @xmath4 . one can also investigate how the size of the avalanche changes with the increase of the amount of random traders considered , if they are uniformly distributed over the network .
this is shown in fig.5 ( full circles ) , where one can see that the maximum size of the avalanches observed drops by a factor of @xmath56 in the presence of only @xmath46 of random traders , reaching almost its final saturation level of @xmath57 when @xmath58 .
these results indicate that even a relatively small number of random investors distributed at random within the market is able to suppress dangerous herding - related avalanches .
but what would happen if these random traders , instead of being uniformly distributed at random over the population , were grouped together in one or more communities ?
capital / wealth distribution of all agents at the end of the simulation , cumulated over 10 realizations , for a network with various percentages of uniformly distributed random traders . in any case
we had a pareto - like power law with an exponent of @xmath59 , independently of the amount of random traders considered.,width=345 ] in fig.6 we show two examples of small - world networks with @xmath4 random traders ( colored agents ) grouped in one or four communities , respectively ( for clarity , we use the same sample network as in fig.1 , with @xmath2 ) .
if one repeats the previous simulations for our network of @xmath3 agents with an increasing percentage of random traders , but now grouping these traders together in either one community or four communities , respectively , the result is that the original power law distribution of avalanches is less affected by random investments for any percentage @xmath53 .
this , in turn , implies a slower decrease of the maximum avalanche sizes as @xmath53 increases , as shown again in fig.5 ( squares and diamonds , respectively ) .
this means that the uniform random distribution of random investors over the whole network is quite crucial in order to significantly dampen avalanche formation ( notice that a percentage between @xmath60 and @xmath45 of uniformly distributed random traders is enough to reduce the financial quakes size as much as @xmath4 grouped random investors would do ) . in this respect ,
the effect of random traders is to increase the frequency of small financial quakes and , consequently , avoid the occurrence of large ones .
it is also interesting to study the capital gain or loss , i.e. the change in wealth , of the agents involved in the trading process during the whole period considered ( in the following we will use the terms `` capital '' and `` wealth '' synonymously ) . at the beginning of each simulation , we assign to each trader ( rsi or random ) an initial capital @xmath61 according to a normal distribution with an average of @xmath62 credits and a standard deviation equal to @xmath63
. then we let them invest in the market according to the following rules : - if an agent wins thanks to a given bet ( for example after being involved in a given , big or small , positive financial quake ) , in the next investment he will bet a quantity @xmath64 of money equal to one half of his / her total capital @xmath61 , i.e. @xmath65 ; - if an agent loses due to an unsuccessful investment ( for example after a negative financial quake ) , the next time he will invest only ten percent of his / her total capital , i.e. @xmath66 .
we have checked , however , that our result are quite robust to adopting a number of different investment criteria . after a financial quake , the capital of each agent involved in the herding - related avalanche will increase or decrease by the quantity @xmath64 .
of course random traders , who do not take part in avalanches , can invest .
their wealth changes only when they overcome their information threshold due to the external information sources . in fig.7
we show the distribution of the total wealth cumulated by all agents during the whole sequence of financial quakes , i.e. over the whole s&p 500 series ( cumulated over 10 different runs ) , for three different trading networks with increasing percentages of random investors ( namely , @xmath67 , @xmath46 and @xmath4 ) .
interestingly , a pareto power law @xcite with an exponent equal to @xmath59 ( see the fit reported as dashed line ) emerges spontaneously from the dynamics of the asymmetric investments , independently of the number of random traders .
we have checked that this result is quite robust and does not substantially change if we modify the quantity @xmath64 that agents choose to invest in case of a win or a loss .
it is also interesting to study the wealth distribution of the random investors in case of a network with @xmath4 random traders ( results are cumulated over @xmath68 realizations ) .
this is reported in fig.8 , in comparison with the corresponding distribution already shown in the previous figure for the whole trading community .
as one can see from the plot , random traders have a final wealth distribution very different from a power law , which can be fitted very well with an exponential curve , represented by a dashed line , with an exponent equal to @xmath69 ( the fact that the random traders component is not changing the global power law distribution of fig.7 is evidently due to its small size , i.e. @xmath70 agents as compared to @xmath71 ) .
in addition , we compare average final wealth of all the traders , 767 credits , with the average wealth of random investors only , 923 credits .
this should be compared with the initial value of the capital which is 1000 credits .
therefore @xmath72 of rsi traders have more wealth in the end than in the beginning , whereas the analogous percentage for random traders is @xmath73 .
comparison between the final capital / wealth distribution for the whole trading network with @xmath4 of random traders shown in fig.7 ( reported again as square symbols ) and the same distribution for the random traders component only ( full circles ) .
the latter can be fitted with an exponential distribution , also reported as dashed line , with an exponent equal to @xmath69 .
we also report the average capital calculated over all the traders ( 767 credits ) and over the random traders only ( 923 credits).see text for details.,width=345 ] these findings allow us to extend our previous results for single traders @xcite to collective effects in a community of traders .
in fact , they suggest that the adoption of random strategies would diminish the probability of extreme events , in this case large increases or losses of wealth , but also ensure almost the same average wealth over a long time period , at variance with technical strategies .
in particular , looking at the details of the two distribution shown in fig.8 , we also find that @xmath74 of rsi traders have a final capital smaller than the worst random trader , whereas only @xmath57 of rsi traders perform better than the best random trader .
this means that , for technical traders , the risk of losses is much greater than the probability of gains , compared to those of random investors .
random trading seems therefore , after all , a very good combination of low risk and high performance . before closing this section
we note that all the numerical simulations presented are quite robust and that similar results were obtained adopting other historical time series , such as , for example , ftse uk or ftse mib .
even though our results were obtained for a `` toy model '' of financial trading , we think that they have potentially interesting policy implications . according to the conventional assumption , neither bubbles or crashes should occur when all agents are provided with the same complete and credible set of information about monetary and asset values traded in the market .
this is the basis of the well - known efficient market hypothesis @xcite , based on the paradigm of rational expectations @xcite .
bubbles and crashes should also not occur according to the wide - spread dynamic stochastic general equilbrium ( dsge ) models @xcite .
however , the wisdom of crowds effect , which induces the equilibrium price , can be undermined by information feedbacks and social influence @xcite .
such social influence may lead to bubbles and crashes . to account for herding effects ,
researchers have started to propose concepts such as `` rational bubbles '' @xcite , recognizing that it can be profitable to follow a trend . however , on average , trend - following is not more successful than random investments it is rather more risky @xcite . from human psychology , we know that people tend to follow others , i.e. to show herding behavior , if it is not clear what is the right thing to do @xcite .
this fact establishes that many traders will be susceptible to the trading decisions of others .
it seems realistic to assume that each agent is endowed with a different quantity and quality of information , coming from private information sources with different reputation , depending on the agents position in the network ( see e.g. refs .
however , such information feedbacks may be harmful , particularly when the market is flooded with volatile and self - referential information .
our paper supports the hypothesis @xcite that introducing `` noisy trading '' ( i.e. random investors ) in financial markets can destroy bubbles and crashes before they become large , and thereby avoid dangerous avalanches . by preventing extreme price variations
, random investments also help to identify the equilibrium price @xcite .
it seems that already a small number of random investors ( relative to the total number of agents ) would be enough to have a beneficial effect on the financial market , particularly if distributed at random .
such investors could be central banks , but also large investors , including pension funds or hedge funds with an interest in reducing the risks of their investments .
we are aware that further studies with more sophisticated and realistic models of financial markets should be performed to explore the full potentials and limitations of random investment strategies .
however , our results suggest that random investments will always reduce both the size and frequency of bubbles / crashes . further research will be devoted to understanding the most opportune timing for the introduction of such random investments and whether this innovative policy instrument can enable a smooth control of financial markets , thereby reducing their fragility .
dh acknowledges partial support by the fet flagship pilot project futurict ( grant number 284709 ) , the eth project `` systemic risks , systemic solutions '' ( chirp ii project eth 4812 - 1 ) and the erc advanced investigator grant `` momentum '' ( grant no . 324247 )
. s. bikhchandani , d. hirshleifer , and i. welch , _ informational cascades and rational herding : an annotated bibliography and resource reference , working paper _ ( anderson school of management , ucla , available at www.info-cascades.info , 2008 )[/INST] building on similarities between earthquakes and extreme financial events , we use a self - organized criticality - generating model to study herding and avalanche dynamics in financial markets .
we consider a community of interacting investors , distributed on a small - world network , who bet on the bullish ( increasing ) or bearish ( decreasing ) behavior of the market which has been specified according to the s&p500 historical time series .
remarkably , we find that the size of herding - related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders , randomly distributed inside the network , who adopt a random investment strategy .
our findings suggest a promising strategy to limit the size of financial bubbles and crashes .
we also obtain that the resulting wealth distribution of all traders corresponds to the well - known pareto power law , while the one of random traders is exponential . in other words , for technical traders ,
the risk of losses is much greater than the probability of gains compared to those of random traders .
financial markets often experience extremes , called `` bubbles '' and `` crashes '' .
the underlying dynamics is related to avalanches , the size of which is distributed according to power laws @xcite .
power laws imply that crashes may reach any size a circumstance that may threaten the functionality of the entire financial system .
many scientists see `` herding behavior '' as the origin of such dangerous avalanches @xcite . in our paper
, we explore whether there is a mechanism that could stop or reduce them .
to generate a power - law dynamics similar to the volatility clustering in financial markets , we use an agent - based model that produces the phenomenon of self - organized criticality ( soc ) @xcite . specifically , we adapt the olami - feder - chrstensen ( ofc ) model @xcite that has been proposed to describe the dynamics of earthquakes @xcite . in this context , we assume information cascades between agents @xcite as the underlying mechanism of financial avalanches . we assume that agents interact within a small - world ( sw ) network of financial trading @xcite and that there is social influence among them @xcite
. such kinds of models are recently becoming popular in economics @xcite and herding effects are also beginning to be observed in lab experiments @xcite . in this connection , it is interesting to consider that humans tend to orient themselves at decisions and behaviors of others , particularly in situations where it is not clear what is the right thing to do @xcite .
such conditions are typical for financial markets , in particular during volatile periods .
in fact , in situations of high uncertainty , personal information exchange may reach market - wide impacts , as the examples of bank runs @xcite and speculative attacks on national currencies @xcite show .
our study explores how huge herding avalanches in financial trading might be reduced by introducing a certain percentage of traders who adopt a random investment strategy . actually , several analogies between socio - economic and physical or biological systems have recently been discussed @xcite , where noise and randomness can have beneficial effects , improving the performance of the system @xcite .
more specifically , in a recent series of papers , it has been explored whether the adoption of random strategies may be advantageous in financial trading from an individual point of view .
scientific evidence suggests that , in the long term , random trading strategies are less risky for a single trader , but provide , on average , gains comparable to those obtained by technical strategies @xcite .
therefore , one might expect that a certain percentage of investors would consider the possibility of adopting a random trading strategy . assuming this and using real data sets of the s&p500 index , we here extend our previous analysis to a sample community of interacting investors .
we investigate whether the presence of randomly distributed agents performing random investments influences the formation of herding - related avalanches and how the wealth of the traders is distributed .
we show that the presence of random traders is able to reduce financial avalanches , which we call - in analogy with earthquakes - financial quakes. furthermore , we find that the wealth distribution , even if normally distributed in the beginning , spontaneously evolves towards the well - known pareto power law . finally , we address possible policy implications . small - world @xmath0 network of @xmath1 traders , as used in our numerical simulations ( here @xmath2 as an example , but in the simulations we always considered @xmath3 agents ) .
short - range and long - range links are simultaneously present .
white agents are rsi traders ( active agents assumed to follow the standard relative strength index ( rsi ) trading strategy ) ; colored agents ( @xmath4 of the total ) are random traders , here uniformly distributed at random among the population
. see text for further details.,width=288 ] </s> |
The Times will charge $15 every four weeks, or $195 annually, to read more than 20 articles per month on its website. That fee also covers a subscription on the newspaper's software for smart phones. Readers who want unlimited access on the website and the Times' software for Apple Inc.'s iPad tablet computer will have to pay $20 every four weeks, or $260 annually. A digital pass covering the website and both mobile options will cost $35 every four weeks, or $455 annually.
The New York Times will start charging people for unlimited access to its website and mobile services this month, ending the free usage that online readers of the third-largest U.S. newspaper have enjoyed for most of the past 15 years.
Subscribers to the Times' print edition will still get digital access for free while other readers will be limited to 20 free articles on the website each month. People using mobile applications will get the "top news" section free.
The long-awaited pricing system was announced Thursday as The New York Times Co. tries to counter a steep drop in print advertising. The publisher's annual revenue fell 27 percent from $3.3 billion in 2006 to $2.4 billion last year even as higher prices for its print editions have brought in more revenue from readers. While growing, digital ad revenue hasn't been large enough to offset losses in print advertising.
The newspaper is hoping to bring in more revenue from readers without triggering a backlash that diminishes its Web traffic and slows its rapidly growing sales of Internet ads.
Finding that balance is the primary reason the Times spent more than a year studying the way readers use its website and talking to them about what they might be willing to pay. The newspaper began testing the fees Thursday in Canada and will impose them everywhere else beginning March 28.
Other newspaper publishers will be monitoring the Times' effort as they try to decide whether to charge online readers, too. The Times becomes the second major U.S. daily this month to introduce online fees, joining The Dallas Morning News, which is owned by A.H. Belo Corp.
"This is a big moment for newspapers," said Rob Grimshaw, managing director for FT.com, which introduced fees for unlimited digital access to The Financial Times in 2007. "I think this will show that people are willing to pay for high-quality, original reporting."
After the 20 free articles, craftier Web surfers will still be able to read an unlimited number for free if they can find them through search engines run by Microsoft Corp.'s Bing and Yahoo Inc. or through links posted on content-sharing sites such as Facebook and Twitter. The Times is imposing a daily limit of five articles for traffic coming from Google, which processes about two-thirds of all Internet queries.
The digital fees reflect the Times' confidence in the quality of its newspaper, which has won more than 100 Pulitzer Prizes. Executives are betting that the Times coverage is distinctive enough to persuade readers to pay instead settling for news available on hundreds of websites, including some that crib information from the Times and other newspapers.
The Times' digital fees seemed too high to newspaper analyst Ken Doctor of Outsell Inc. He expected a $10-per-month option to reduce the chances of alienating a generation of younger readers who have grown up thinking online news should be free. "They need to be cultivating readers who are going to be their customers," he said.
A recent survey of 755 U.S. adult Internet users by Pew Internet & American Life Project last fall underscores Doctor's concerns. The typical user paid an average of $10 per month for online content, with people ages 30 to 49 most likely to do so. Overall, just 18 percent of the respondents had paid for a digital newspaper, magazine or article. One-third had bought digital music or software online.
The Times has introduced digital subscription fees twice before, only to rescind them because they weren't bringing in enough revenue.
Without providing details, the Times said it will offer introductory discounts to ease the transition to digital fees.
Shares of the Times Co. rose 3 cents to close Thursday at $8.89. ||||| Click to viewElizabeth Edwards, the long-suffering wife of crinkly-faced twit John Edwards, died today after a long battle with breast cancer. So get ready for D.C. establishment types who hated her when she was alive to pretend they admired and liked her!
Edwards, who was smart and ambitious and realistic about her stupid husband and their doomed relationship, was widely disliked by the D.C. pundit class, as our own Alex Pareene documented last year. Why? I could speculate, but it would involve me spending more than ten seconds thinking about Maureen Dowd's feelings, so I won't. And, in the end, no matter how "difficult" Edwards might have been in real life, she didn't deserve the bizarrely personal, kick-her-while-she's-down attacks she had to put up with from people like Dowd.
So it was a special treat to see, as Pareene writes, Time magazine hack Mark Halperin on Chris Matthews' show today, solemnly telling Matthews that Edwards was "valiant," and "so strong" and "a very tough person." Are you sure that's all you want to say, Mark? Because you had a lot of important insight into her personality in your book Game Change! Like how, according to unnamed "Edwards insiders," she was " abusive, intrusive, paranoid, [and] condescending." Oh, and a "crazy-woman"!
But surely Halperin won't be the last pundit who smeared Edwards to suddenly proclaim awe at her "strength" or intelligence or whatever. Who's next? Dowd, maybe? Moe Tkacik suggests Tina Brown. Personally, I'm hoping it's Sally Quinn. Surely, the "On Faith" section of journalism's own little cesspool, The Washington Post, deserves a Quinn-penned remembrance of Edwards?
[Salon] | β Now that Elizabeth Edwards has died, it's time for the "DC establishment types who hated her when she was alive to pretend they admired and liked her," predicts Max Read on Gawker. Edwards wasn't popular among the DC pundits, and even if she was a "difficult" person, Read writes, "she didn't deserve the bizarrely personal, kick-her-while-she's-down attacks she had to put up with." But now, expect those same attackersβor some of them, at leastβto come out of the woodwork with all sorts of fake sentiment. Exhibit A: Mark Halperin, who cited unnamed insiders calling her "an abusive, intrusive, paranoid, condescending crazy-woman" in his book about the 2008 elections, Game Change, appeared on Hardball last nightβwhere, far from calling her crazy again, he described her as "valiant," "so strong," and "a very tough person." Despite the fact that Halperin was likely booked before the news broke, it was "incredibly insensitive" for him to actually speak about her, writes Alex Pareene on Salon. "His mere presence was an insult to her memory." Click to watch the video of Halperin's thoughts on Edwards. | <s>[INST]The Times will charge $15 every four weeks, or $195 annually, to read more than 20 articles per month on its website. That fee also covers a subscription on the newspaper's software for smart phones. Readers who want unlimited access on the website and the Times' software for Apple Inc.'s iPad tablet computer will have to pay $20 every four weeks, or $260 annually. A digital pass covering the website and both mobile options will cost $35 every four weeks, or $455 annually.
The New York Times will start charging people for unlimited access to its website and mobile services this month, ending the free usage that online readers of the third-largest U.S. newspaper have enjoyed for most of the past 15 years.
Subscribers to the Times' print edition will still get digital access for free while other readers will be limited to 20 free articles on the website each month. People using mobile applications will get the "top news" section free.
The long-awaited pricing system was announced Thursday as The New York Times Co. tries to counter a steep drop in print advertising. The publisher's annual revenue fell 27 percent from $3.3 billion in 2006 to $2.4 billion last year even as higher prices for its print editions have brought in more revenue from readers. While growing, digital ad revenue hasn't been large enough to offset losses in print advertising.
The newspaper is hoping to bring in more revenue from readers without triggering a backlash that diminishes its Web traffic and slows its rapidly growing sales of Internet ads.
Finding that balance is the primary reason the Times spent more than a year studying the way readers use its website and talking to them about what they might be willing to pay. The newspaper began testing the fees Thursday in Canada and will impose them everywhere else beginning March 28.
Other newspaper publishers will be monitoring the Times' effort as they try to decide whether to charge online readers, too. The Times becomes the second major U.S. daily this month to introduce online fees, joining The Dallas Morning News, which is owned by A.H. Belo Corp.
"This is a big moment for newspapers," said Rob Grimshaw, managing director for FT.com, which introduced fees for unlimited digital access to The Financial Times in 2007. "I think this will show that people are willing to pay for high-quality, original reporting."
After the 20 free articles, craftier Web surfers will still be able to read an unlimited number for free if they can find them through search engines run by Microsoft Corp.'s Bing and Yahoo Inc. or through links posted on content-sharing sites such as Facebook and Twitter. The Times is imposing a daily limit of five articles for traffic coming from Google, which processes about two-thirds of all Internet queries.
The digital fees reflect the Times' confidence in the quality of its newspaper, which has won more than 100 Pulitzer Prizes. Executives are betting that the Times coverage is distinctive enough to persuade readers to pay instead settling for news available on hundreds of websites, including some that crib information from the Times and other newspapers.
The Times' digital fees seemed too high to newspaper analyst Ken Doctor of Outsell Inc. He expected a $10-per-month option to reduce the chances of alienating a generation of younger readers who have grown up thinking online news should be free. "They need to be cultivating readers who are going to be their customers," he said.
A recent survey of 755 U.S. adult Internet users by Pew Internet & American Life Project last fall underscores Doctor's concerns. The typical user paid an average of $10 per month for online content, with people ages 30 to 49 most likely to do so. Overall, just 18 percent of the respondents had paid for a digital newspaper, magazine or article. One-third had bought digital music or software online.
The Times has introduced digital subscription fees twice before, only to rescind them because they weren't bringing in enough revenue.
Without providing details, the Times said it will offer introductory discounts to ease the transition to digital fees.
Shares of the Times Co. rose 3 cents to close Thursday at $8.89. ||||| Click to viewElizabeth Edwards, the long-suffering wife of crinkly-faced twit John Edwards, died today after a long battle with breast cancer. So get ready for D.C. establishment types who hated her when she was alive to pretend they admired and liked her!
Edwards, who was smart and ambitious and realistic about her stupid husband and their doomed relationship, was widely disliked by the D.C. pundit class, as our own Alex Pareene documented last year. Why? I could speculate, but it would involve me spending more than ten seconds thinking about Maureen Dowd's feelings, so I won't. And, in the end, no matter how "difficult" Edwards might have been in real life, she didn't deserve the bizarrely personal, kick-her-while-she's-down attacks she had to put up with from people like Dowd.
So it was a special treat to see, as Pareene writes, Time magazine hack Mark Halperin on Chris Matthews' show today, solemnly telling Matthews that Edwards was "valiant," and "so strong" and "a very tough person." Are you sure that's all you want to say, Mark? Because you had a lot of important insight into her personality in your book Game Change! Like how, according to unnamed "Edwards insiders," she was " abusive, intrusive, paranoid, [and] condescending." Oh, and a "crazy-woman"!
But surely Halperin won't be the last pundit who smeared Edwards to suddenly proclaim awe at her "strength" or intelligence or whatever. Who's next? Dowd, maybe? Moe Tkacik suggests Tina Brown. Personally, I'm hoping it's Sally Quinn. Surely, the "On Faith" section of journalism's own little cesspool, The Washington Post, deserves a Quinn-penned remembrance of Edwards?
[Salon][/INST]β Now that Elizabeth Edwards has died, it's time for the "DC establishment types who hated her when she was alive to pretend they admired and liked her," predicts Max Read on Gawker. Edwards wasn't popular among the DC pundits, and even if she was a "difficult" person, Read writes, "she didn't deserve the bizarrely personal, kick-her-while-she's-down attacks she had to put up with." But now, expect those same attackersβor some of them, at leastβto come out of the woodwork with all sorts of fake sentiment. Exhibit A: Mark Halperin, who cited unnamed insiders calling her "an abusive, intrusive, paranoid, condescending crazy-woman" in his book about the 2008 elections, Game Change, appeared on Hardball last nightβwhere, far from calling her crazy again, he described her as "valiant," "so strong," and "a very tough person." Despite the fact that Halperin was likely booked before the news broke, it was "incredibly insensitive" for him to actually speak about her, writes Alex Pareene on Salon. "His mere presence was an insult to her memory." Click to watch the video of Halperin's thoughts on Edwards.</s> |
the unique capabilities of the magnetic navigation system ( mns ) offer the possibility to perform ablations that would not be possible manually .
we report the case of a retrograde transaortic approach to perform a pulmonary vein isolation ( pvi ) . a 41-year - old female patient with highly symptomatic atrial fibrillation ( af )
was referred to our department for pvi . since she had undergone closure of an atrial septal defect with an oversized amplatzer device ( aga medical corp .
, golden valley , mn ) 4 years earlier ( figure 1 ) , a classic transseptal puncture was considered to be a risky procedure and a retrograde approach using the mns ( niobe , stereotaxis inc .
a preoperative computed tomography ( ct ) scan showed a common ostium for the right and left pulmonary veins ( pvs ) . one venous access was achieved in the right femoral vein and a diagnostic decapolar catheter ( bard electrophysiology , lowell , ma , usa ) was introduced through the femoral vein and positioned in the coronary sinus .
the arterial access was gained through the right femoral artery using a 9f sheath ( st .
paul , mn ) . a magnetically enabled , steerable tip ablation catheter ( navistar rmt thermocool
, biosense webster , diamond bar , ca , usa ) was introduced through the femoral artery and was connected to the quickcas for remote - controlled magnetic navigation .
this catheter reached the left atrium via a retrograde route , passing through both the aortic and mitral valve ( figure 1 ) .
an electroanatomic map of the left atrium was made using the carto system ( biosense webster , diamond bar , ca , usa ) .
this map was merged with the ct scan . using a sequential point - by - point antrum encirclement of the common ostia ,
a radial collection of 16 points was taken within each pv by gradually changing the magnetic field .
for each of these points , entry and exit block was shown : loss of pv potentials on the ablation catheter and failure to capture the la by pacing ( at 10 ma and 2 ms ) .
the patient was discharged the next day , after transthoracic echocardiography , which excluded any valvular damage or pericardial effusion .
transseptal puncture is the most commonly used technique to perform electrophysiological procedures in the left atrium .
retrograde approach to the left atrium using magnetic navigation and a remote - controlled catheter provides an interesting alternative for pvi , especially when a classic transseptal puncture can not be performed .
the magnetic navigation system , with its soft catheter shaft , provides a stable catheter position and an extreme manoeuvrability even within the most complex anatomical conditions that cross the limits of conventional manually steered catheters [ 2 , 3 ] .
the use of a lasso catheter to check the pvs can be replaced by the stereotaxis bulls eye technique.fig .
the round deformation at the septum is the amplatzer device and the red dots mark the ablation points .
e
white arrow indicates the ablation catheter , black arrow indicates the coronary sinus catheter .
c ablation catheter crosses the aortic valve retrogradely , passes through the left ventricle , crosses the mitral valve retrogradely and is positioned with its tip on the roof of the left atrium .
e ablation catheter is advanced into the left inferior pulmonary vein . in our centre ,
a transoesophageal echocardiogram probe is used during pvi procedures to enable monitoring for cardiac tamponade retrograde pulmonary vein isolation . a postprocedural carto electro - anatomic - ct merge map of the left atrium .
the round deformation at the septum is the amplatzer device and the red dots mark the ablation points .
e
white arrow indicates the ablation catheter , black arrow indicates the coronary sinus catheter .
b ablation catheter is positioned above the aortic valve . c ablation catheter crosses the aortic valve retrogradely , passes through the left ventricle , crosses the mitral valve retrogradely and is positioned with its tip on the roof of the left atrium .
e ablation catheter is advanced into the left inferior pulmonary vein . in our centre , | transseptal puncture is the most commonly used technique to perform electrophysiological procedures in the left atrium .
this case report describes a pulmonary vein isolation in a patient with a paroxysmal atrial fibrillation , complicated by the presence of an oversized amplatzer device ( aga medical corp . ,
golden valley , mn ) . a retrograde approach using the magnetic navigation system ( niobe , stereotaxis inc .
,
st louis , usa ) was performed , and showed to provide a feasible , safe and successful alternative for catheter ablation of cardiac arrhythmias in patients in whom the classic transseptal approach is impossible . | <s>[INST]the unique capabilities of the magnetic navigation system ( mns ) offer the possibility to perform ablations that would not be possible manually .
we report the case of a retrograde transaortic approach to perform a pulmonary vein isolation ( pvi ) . a 41-year - old female patient with highly symptomatic atrial fibrillation ( af )
was referred to our department for pvi . since she had undergone closure of an atrial septal defect with an oversized amplatzer device ( aga medical corp .
, golden valley , mn ) 4 years earlier ( figure 1 ) , a classic transseptal puncture was considered to be a risky procedure and a retrograde approach using the mns ( niobe , stereotaxis inc .
a preoperative computed tomography ( ct ) scan showed a common ostium for the right and left pulmonary veins ( pvs ) . one venous access was achieved in the right femoral vein and a diagnostic decapolar catheter ( bard electrophysiology , lowell , ma , usa ) was introduced through the femoral vein and positioned in the coronary sinus .
the arterial access was gained through the right femoral artery using a 9f sheath ( st .
paul , mn ) . a magnetically enabled , steerable tip ablation catheter ( navistar rmt thermocool
, biosense webster , diamond bar , ca , usa ) was introduced through the femoral artery and was connected to the quickcas for remote - controlled magnetic navigation .
this catheter reached the left atrium via a retrograde route , passing through both the aortic and mitral valve ( figure 1 ) .
an electroanatomic map of the left atrium was made using the carto system ( biosense webster , diamond bar , ca , usa ) .
this map was merged with the ct scan . using a sequential point - by - point antrum encirclement of the common ostia ,
a radial collection of 16 points was taken within each pv by gradually changing the magnetic field .
for each of these points , entry and exit block was shown : loss of pv potentials on the ablation catheter and failure to capture the la by pacing ( at 10 ma and 2 ms ) .
the patient was discharged the next day , after transthoracic echocardiography , which excluded any valvular damage or pericardial effusion .
transseptal puncture is the most commonly used technique to perform electrophysiological procedures in the left atrium .
retrograde approach to the left atrium using magnetic navigation and a remote - controlled catheter provides an interesting alternative for pvi , especially when a classic transseptal puncture can not be performed .
the magnetic navigation system , with its soft catheter shaft , provides a stable catheter position and an extreme manoeuvrability even within the most complex anatomical conditions that cross the limits of conventional manually steered catheters [ 2 , 3 ] .
the use of a lasso catheter to check the pvs can be replaced by the stereotaxis bulls eye technique.fig .
the round deformation at the septum is the amplatzer device and the red dots mark the ablation points .
e
white arrow indicates the ablation catheter , black arrow indicates the coronary sinus catheter .
c ablation catheter crosses the aortic valve retrogradely , passes through the left ventricle , crosses the mitral valve retrogradely and is positioned with its tip on the roof of the left atrium .
e ablation catheter is advanced into the left inferior pulmonary vein . in our centre ,
a transoesophageal echocardiogram probe is used during pvi procedures to enable monitoring for cardiac tamponade retrograde pulmonary vein isolation . a postprocedural carto electro - anatomic - ct merge map of the left atrium .
the round deformation at the septum is the amplatzer device and the red dots mark the ablation points .
e
white arrow indicates the ablation catheter , black arrow indicates the coronary sinus catheter .
b ablation catheter is positioned above the aortic valve . c ablation catheter crosses the aortic valve retrogradely , passes through the left ventricle , crosses the mitral valve retrogradely and is positioned with its tip on the roof of the left atrium .
e ablation catheter is advanced into the left inferior pulmonary vein . in our centre ,[/INST]transseptal puncture is the most commonly used technique to perform electrophysiological procedures in the left atrium .
this case report describes a pulmonary vein isolation in a patient with a paroxysmal atrial fibrillation , complicated by the presence of an oversized amplatzer device ( aga medical corp . ,
golden valley , mn ) . a retrograde approach using the magnetic navigation system ( niobe , stereotaxis inc .
,
st louis , usa ) was performed , and showed to provide a feasible , safe and successful alternative for catheter ablation of cardiac arrhythmias in patients in whom the classic transseptal approach is impossible .</s> |
The IP address has changed.
The IP address for this domain may have changed recently. Check your DNS settings to verify that the domain is set up correctly. It may take 8-24 hours for DNS changes to propagate. It may be possible to restore access to this site by following these instructions for clearing your dns cache. ||||| A group of activists from Greenpeace on Thursday scaled the Shard, the tapered 310m glass tower next to London Bridge station, as a protest against oil and gas drilling in the Arctic.
In an action that was perhaps inevitable at some point after the completion last year of western Europe's tallest building, visible across much of central London, the six climbers began their ascent in the early hours of the morning. The activists reached the top of the building at around 7.10pm.
The Twitter feed for Greenpeace UK carried a photograph of the activists, all women, in their climbing gear before they began the protest, naming them as Wiola Smul (23) from Poland, Ali Garrigan (27) from the UK, Sabine Huyghe (33) from Belgium, Sandra Lamborn (29) from Sweden, Victoria Henry (32) from Canada and Liesbeth Deddens (31) from the Netherlands. Police said all six had been arrested on suspicion of aggravated trespass.
The organisaton also carried a blog post from one of the climbers, Henry, explaining her motivation: "I'm training [the post was written before the climb] for something that I hope will help stop one of the most heartbreaking acts of wanton environmental destruction β drilling for oil in the Arctic. I'm over the moon that I can play any part in the mass resistance to this horrifying practice," she wrote.
Another tweet read: "Look up London. We're attempting to scale the Shard, Europe's tallest skyscraper."
BREAKING: Look up London. Weβre attempting to scale the Shard, Europe's tallest skyscraper. More soon on #iceclimb pic.twitter.com/WCzFlIPd6t β Greenpeace UK (@GreenpeaceUK) July 11, 2013
A picture with that tweet appeared to show the group using ladders to gain access to the bottom of the 72-storey office and residential block from the roof of London Bridge station. A live webcam was following their progress up the tower.
In a later statement, Greenpeace said the Shard was chosen because it was in sight of the three London bases of the energy giant Shell, which is involved in offshore drilling in the Arctic. When the climbers reached the top of the building they aimed to "hang a huge work of art that captures the beauty of the Arctic", it added.
Ali (blue helmet) hangs on while Sandra (black helmet) does... what is she doing? #iceclimb pic.twitter.com/ckY0ojwfU9 β Greenpeace UK (@GreenpeaceUK) July 11, 2013
The statement continued: "Shell is leading the oil companies' drive into the Arctic, investing billions in its Alaskan and Russian drilling programmes. A worldwide movement of millions has sprung up to stop them, but Shell is refusing to abandon its plans."
Shell released a statement that said it respected the right of Greenpeace to engage in an "exchange of views" about their operations. It said oil and gas production in the Arctic was not new.
"If responsibly developed, Arctic energy resources can help offset supply constraints and maintain energy security for consumers throughout the world," said Shell. "We work extensively with global Arctic stakeholders to research and develop standards and best practice on biodiversity, ecology, marine sound, oil spill prevention and response, safety and health."
A Metropolitan police spokesman said: "We were called at 4.20am today to a group of protesters attempting to climb up the Shard. We are in attendance and monitoring the situation along with British transport police."
Sabine & @victohenry clinging on as they attempt #iceclimb << pls keep your support coming. pic.twitter.com/m9R1asDKD1 β Greenpeace UK (@GreenpeaceUK) July 11, 2013
A spokesman for the building, designed by the Italian architect Renzo Piano, said: "The Shard is being used by protesters as part of a campaign. Our primary focus is on the safety of the protesters and the workers and visitors to the building. We are working with the relevant authorities to try to ensure the safety of those concerned."
Greenpeace said the climbers used a combination of traditional mountain climbing techniques, rope access techniques used by commercial building climbers and some free climbing. The building has an external metal frame providing handholds and crossbeams all the way to the top.
Each stage of the climb would require the lead climber to free-climb a section of the building. Once they reached a secure position, they would fix a rope to the external skeleton of the building and the rest of the group would follow using the rope. All the climbers were wearing harnesses, meaning they would not fall more than six metres if they slipped.
The British Mountaineering Council training officer Jon Garside said there was a "rich history of people climbing buildings both for recreation and for protests". He said the climbers appeared to have standard kit used by workers on tall buildings around the world and that what they were doing, while inherently risky, was fairly common practice. "Any Londoner will see all the time access workers abseiling down large buildings like the Shard to clean the windows," he said. ||||| Media playback is unsupported on your device Media caption A protester unveiled a Greenpeace flag at the skyscraper's summit
Greenpeace protesters have climbed to the summit of London's Shard - the tallest building in western Europe.
Two of them then unfurled a blue flag with "Save the Arctic" written on it.
The charity said it was protesting against plans to drill in the Arctic by the oil company Shell, although the firm said drilling there was "not new".
Six climbers accessed the Shard by climbing on to the roof of London Bridge Station. They were later arrested, the Met Police said.
They are being held on suspicion of aggravated trespass.
It took the women 16 hours to reach the top of the building after they started their ascent in the early hours.
The Shard stands at 310m (1,016ft) and has 87 storeys.
'Remarkable achievement'
As the protesters reached the summit, Greenpeace UK executive director John Sauven said: "It is an honour to stand here at the foot of Europe's highest building and witness this remarkable achievement by these women.
"Watching them fly the flag to protect the Arctic from the top of the Shard is a remarkable sight.
Image caption The climb took the women 16 hours
"And I'm not the only one watching this today - the executives of Shell, whose offices are all around this building, simply won't be able to ignore what we have done.
"As a result of our action, 50,000 extra people have joined up to the campaign.
"If Shell continues to ignore the huge groundswell of support for protecting the Arctic then they will do irreversible damage to their reputation."
In a statement Shell said oil and gas production from the Arctic "was not new".
It said: "The Arctic region currently produces about 10% of the world's oil and 25% of its gas.
"If responsibly developed, Arctic energy resources can help offset supply constraints and maintain energy security for consumers throughout the world.
"Shell has been operating in the Arctic and sub-Arctic since the early 20th Century, giving us the technical experience and know-how to explore for and produce oil and gas responsibly."
Ladder-like structure
The viewing platform in the skyscraper was closed to visitors for the safety of the public and the protest group.
Image caption Greenpeace said the location was chosen because it sits in the middle of Shell's three headquarters
A Shard spokesman said the building's emergency response team had advised that "The View" - the platform on floors 68, 69 and 72 which gives a view of London from 800ft (244m) up - should be closed with immediate effect.
"We apologise to guests for the inconvenience caused and The View will be pleased to honour their tickets either later on today or on a different date," he said.
The spokesman added that offices and restaurants in the complex remained open.
BBC reporter Jonathan Savage, who was at the scene, said the group climbed the edge of the building as it has a ladder-like structure, and also used ropes.
Police and ambulance teams remained at the scene.
Greenpeace said the location was chosen because it sits in the middle of Shell's three headquarters and because the building was "modelled on a shard of ice".
The climbers were live-streaming the ascent using helmet cameras.
In its statement, Shell said: "We respect the right of individuals and organisations to engage in a free and frank exchange of views about our operations.
"Recognising the right of individuals to express their point of view, we only ask that they do so with their safety and the safety of others, including Shell personnel and customers in mind."
The Qatari-owned building, which was opened in February, contains offices, restaurants, a hotel and residential apartments. | β Greenpeace is taking its case against Arctic oil drilling to the skies. Demonstrators are climbing the tallest building in western Europe, London's 87-story Shard, to make their point. Safety personnel and police are watching after the team of six women began ascending the building via the roof of a nearby subway station. They're reportedly "free-climbing" the building; part of its exterior is built like a ladder, the BBC reports. The Shard is between the three headquarters of Shell, Greenpeace says, and it resembles a piece of ice. At the top, says a climber, "we'll try to hang a huge art installation ... that will make Shell think twice before sending their rigs into the Arctic." The climbers, who have been live-streaming the event via head-mounted cameras, are all highly trained, says a rep. Monitoring police say they got a call about the protest at 4:20 this morning, the Guardian reports. | <s>[INST]The IP address has changed.
The IP address for this domain may have changed recently. Check your DNS settings to verify that the domain is set up correctly. It may take 8-24 hours for DNS changes to propagate. It may be possible to restore access to this site by following these instructions for clearing your dns cache. ||||| A group of activists from Greenpeace on Thursday scaled the Shard, the tapered 310m glass tower next to London Bridge station, as a protest against oil and gas drilling in the Arctic.
In an action that was perhaps inevitable at some point after the completion last year of western Europe's tallest building, visible across much of central London, the six climbers began their ascent in the early hours of the morning. The activists reached the top of the building at around 7.10pm.
The Twitter feed for Greenpeace UK carried a photograph of the activists, all women, in their climbing gear before they began the protest, naming them as Wiola Smul (23) from Poland, Ali Garrigan (27) from the UK, Sabine Huyghe (33) from Belgium, Sandra Lamborn (29) from Sweden, Victoria Henry (32) from Canada and Liesbeth Deddens (31) from the Netherlands. Police said all six had been arrested on suspicion of aggravated trespass.
The organisaton also carried a blog post from one of the climbers, Henry, explaining her motivation: "I'm training [the post was written before the climb] for something that I hope will help stop one of the most heartbreaking acts of wanton environmental destruction β drilling for oil in the Arctic. I'm over the moon that I can play any part in the mass resistance to this horrifying practice," she wrote.
Another tweet read: "Look up London. We're attempting to scale the Shard, Europe's tallest skyscraper."
BREAKING: Look up London. Weβre attempting to scale the Shard, Europe's tallest skyscraper. More soon on #iceclimb pic.twitter.com/WCzFlIPd6t β Greenpeace UK (@GreenpeaceUK) July 11, 2013
A picture with that tweet appeared to show the group using ladders to gain access to the bottom of the 72-storey office and residential block from the roof of London Bridge station. A live webcam was following their progress up the tower.
In a later statement, Greenpeace said the Shard was chosen because it was in sight of the three London bases of the energy giant Shell, which is involved in offshore drilling in the Arctic. When the climbers reached the top of the building they aimed to "hang a huge work of art that captures the beauty of the Arctic", it added.
Ali (blue helmet) hangs on while Sandra (black helmet) does... what is she doing? #iceclimb pic.twitter.com/ckY0ojwfU9 β Greenpeace UK (@GreenpeaceUK) July 11, 2013
The statement continued: "Shell is leading the oil companies' drive into the Arctic, investing billions in its Alaskan and Russian drilling programmes. A worldwide movement of millions has sprung up to stop them, but Shell is refusing to abandon its plans."
Shell released a statement that said it respected the right of Greenpeace to engage in an "exchange of views" about their operations. It said oil and gas production in the Arctic was not new.
"If responsibly developed, Arctic energy resources can help offset supply constraints and maintain energy security for consumers throughout the world," said Shell. "We work extensively with global Arctic stakeholders to research and develop standards and best practice on biodiversity, ecology, marine sound, oil spill prevention and response, safety and health."
A Metropolitan police spokesman said: "We were called at 4.20am today to a group of protesters attempting to climb up the Shard. We are in attendance and monitoring the situation along with British transport police."
Sabine & @victohenry clinging on as they attempt #iceclimb << pls keep your support coming. pic.twitter.com/m9R1asDKD1 β Greenpeace UK (@GreenpeaceUK) July 11, 2013
A spokesman for the building, designed by the Italian architect Renzo Piano, said: "The Shard is being used by protesters as part of a campaign. Our primary focus is on the safety of the protesters and the workers and visitors to the building. We are working with the relevant authorities to try to ensure the safety of those concerned."
Greenpeace said the climbers used a combination of traditional mountain climbing techniques, rope access techniques used by commercial building climbers and some free climbing. The building has an external metal frame providing handholds and crossbeams all the way to the top.
Each stage of the climb would require the lead climber to free-climb a section of the building. Once they reached a secure position, they would fix a rope to the external skeleton of the building and the rest of the group would follow using the rope. All the climbers were wearing harnesses, meaning they would not fall more than six metres if they slipped.
The British Mountaineering Council training officer Jon Garside said there was a "rich history of people climbing buildings both for recreation and for protests". He said the climbers appeared to have standard kit used by workers on tall buildings around the world and that what they were doing, while inherently risky, was fairly common practice. "Any Londoner will see all the time access workers abseiling down large buildings like the Shard to clean the windows," he said. ||||| Media playback is unsupported on your device Media caption A protester unveiled a Greenpeace flag at the skyscraper's summit
Greenpeace protesters have climbed to the summit of London's Shard - the tallest building in western Europe.
Two of them then unfurled a blue flag with "Save the Arctic" written on it.
The charity said it was protesting against plans to drill in the Arctic by the oil company Shell, although the firm said drilling there was "not new".
Six climbers accessed the Shard by climbing on to the roof of London Bridge Station. They were later arrested, the Met Police said.
They are being held on suspicion of aggravated trespass.
It took the women 16 hours to reach the top of the building after they started their ascent in the early hours.
The Shard stands at 310m (1,016ft) and has 87 storeys.
'Remarkable achievement'
As the protesters reached the summit, Greenpeace UK executive director John Sauven said: "It is an honour to stand here at the foot of Europe's highest building and witness this remarkable achievement by these women.
"Watching them fly the flag to protect the Arctic from the top of the Shard is a remarkable sight.
Image caption The climb took the women 16 hours
"And I'm not the only one watching this today - the executives of Shell, whose offices are all around this building, simply won't be able to ignore what we have done.
"As a result of our action, 50,000 extra people have joined up to the campaign.
"If Shell continues to ignore the huge groundswell of support for protecting the Arctic then they will do irreversible damage to their reputation."
In a statement Shell said oil and gas production from the Arctic "was not new".
It said: "The Arctic region currently produces about 10% of the world's oil and 25% of its gas.
"If responsibly developed, Arctic energy resources can help offset supply constraints and maintain energy security for consumers throughout the world.
"Shell has been operating in the Arctic and sub-Arctic since the early 20th Century, giving us the technical experience and know-how to explore for and produce oil and gas responsibly."
Ladder-like structure
The viewing platform in the skyscraper was closed to visitors for the safety of the public and the protest group.
Image caption Greenpeace said the location was chosen because it sits in the middle of Shell's three headquarters
A Shard spokesman said the building's emergency response team had advised that "The View" - the platform on floors 68, 69 and 72 which gives a view of London from 800ft (244m) up - should be closed with immediate effect.
"We apologise to guests for the inconvenience caused and The View will be pleased to honour their tickets either later on today or on a different date," he said.
The spokesman added that offices and restaurants in the complex remained open.
BBC reporter Jonathan Savage, who was at the scene, said the group climbed the edge of the building as it has a ladder-like structure, and also used ropes.
Police and ambulance teams remained at the scene.
Greenpeace said the location was chosen because it sits in the middle of Shell's three headquarters and because the building was "modelled on a shard of ice".
The climbers were live-streaming the ascent using helmet cameras.
In its statement, Shell said: "We respect the right of individuals and organisations to engage in a free and frank exchange of views about our operations.
"Recognising the right of individuals to express their point of view, we only ask that they do so with their safety and the safety of others, including Shell personnel and customers in mind."
The Qatari-owned building, which was opened in February, contains offices, restaurants, a hotel and residential apartments.[/INST]β Greenpeace is taking its case against Arctic oil drilling to the skies. Demonstrators are climbing the tallest building in western Europe, London's 87-story Shard, to make their point. Safety personnel and police are watching after the team of six women began ascending the building via the roof of a nearby subway station. They're reportedly "free-climbing" the building; part of its exterior is built like a ladder, the BBC reports. The Shard is between the three headquarters of Shell, Greenpeace says, and it resembles a piece of ice. At the top, says a climber, "we'll try to hang a huge art installation ... that will make Shell think twice before sending their rigs into the Arctic." The climbers, who have been live-streaming the event via head-mounted cameras, are all highly trained, says a rep. Monitoring police say they got a call about the protest at 4:20 this morning, the Guardian reports.</s> |
the description of inhomogeneous charge and spin phases in the hubbard model it a topic of current interest , mainly because it is now generally accepted that the high - t@xmath1 compounds , at least in the underdoped regime , are intrinsic electronically inhomogeneous systems .
a powerful tool for the investigation of such inhomogeneous electronic states is the unrestricted hartree - fock ( hf ) scheme which allows for the diagonalization of reasonable cluster sizes .
recently an extension of this approach based on the gutzwiller wave function @xcite has shown to significantly improve the hf solutions which strongly underestimate the attraction between charge carriers . in this paper
we extend the approach of ref .
@xcite to include transversal spin degrees of freedoms which permits the description of coplanar and three - dimensional inhomogeneous spin textures . among coplanar
spin structures homogeneous spiral solutions have been studied by a large variety of methods ( see e.g. @xcite ) which show that a small amount of holes doped into the half - filled system leads to a @xmath2 spiral phase which changes its direction to @xmath3 above some critical concentration . relaxing the constraint of a homogeneous charge distribution the formation of coplanar
, vortexlike phases has been investigated in ref .
@xcite using an unrestricted hf approach .
these are configurations where the antiferromagnetic ( af ) spin order rotates by multiples of 2@xmath4 around the localized hole . due to this twist in the magnetization their energy increases @xmath5 which implies their instability in large clusters .
a three - dimensional spin texture which is known to be topologically stable is the skyrmion as a solution of the o(3 ) non - linear @xmath6-model @xcite .
it has been studied by several authors also for an af background @xcite mainly concentrating on small clusters .
however , it is still controversal wether skyrmion solutions exist also on discrete lattices . whereas unrestricted hf theory for the 2-d hubbard model predicts the decay of skyrmions into conventional spin - polarons @xcite , exact diagonalization studies of a small cluster within the tj - model ref . @xcite
seem to support their existence even when one takes the contribution of the skyrmion far field into acount . within our slave - boson approach
we will show below that skyrmions textures are stable solutions of the discrete two - dimensional hubbard model , when the system is doped with two holes away from half - filling .
connected with the discovery of static stripe order in la@xmath7nio@xmath8 and la@xmath9nd@xmath10sr@xmath11cuo@xmath12 @xcite a lot of work has been done in order to understand the different domain wall structures in these compounds @xcite . whereas in the ni - doped compounds one finds the stripes along the diagonal with one hole per ni - site the charge and spin order in the nd - doped cuprates is along the copper - oxygen bond direction with one hole per every second copper site only . since half - filled horizontal walls are at odds with hf calculations the inclusion of correlations turns out to be a necessary ingredient for the study of domain walls in these systems @xcite .
in addition long - range coulomb interactions can play an important role in stabilizing half - filled vertical stripes @xcite .
based on a landau free - energy analysis of coupled charge and spin - density - wave order parameters it has been shown in ref .
@xcite that within some region of parameter domain walls may have a spiral component .
whereas this type of ordering is not observed in the ni - oxides , some spiral contribution can not be rigorously excluded to be present in the nd - doped compounds @xcite . according to our analysis presented below , elliptical stripes are not stable for concentrations around @xmath13 but may be formed in the very low doping limit .
the rest of the paper is organized as follows : in sec .
ii we give a detailed description of the formalism , in sec .
iii we present the results for vortex , skyrmion and elliptical domain wall solutions respectively , and in sec .
iv we summarize our conclusions .
we consider the two - dimensional hubbard model on a square lattice , with hopping restricted to nearest neighbors ( indicated by the bracket @xmath14 ) @xmath15 where @xmath16 destroys ( creates ) an electron with spin @xmath6 at site i , and @xmath17 .
u is the on - site hubbard repulsion and t the transfer parameter . for the calculations in sec .
iii we take t=1 . in the following we use a spin - rotation - invariant form @xcite of the slave - boson representation introduced by kotliar and ruckenstein in ref .
@xcite . the subsidiary boson fields @xmath18
, @xmath19 stand for the annihilation ( creation ) of empty and doubly occupied sites , respectively , whereas the matrix @xmath20 represents the case of a singly occupied site .
since we consider the mean - field limit all boson operators will be approximated as numbers . besides the completeness condition @xmath21 the boson fields are constrained by the following relations @xmath22 where @xmath23 are the pauli spin matrices and @xmath24 . then , in the physical subspace defined by eqs .
( [ const1],[const2 ] ) the hamiltonian ( [ hm ] ) takes the form @xmath25 where @xmath26 the matrices @xmath27 and @xmath28 guarantee the correct behavior in the limit @xmath29 within the mean - field approximation and @xmath30 is the time - reversal transformed of @xmath31 .
the matrix elements of @xmath32 can be calculated by transforming to a diagonal representation for the @xmath31 ( see appendix ) .
the resulting effective one - particle hamiltonian describes the dynamics of particles which upon hopping between sites are subjected to a modulation of their spin amplitude and spin direction , respectively .
it can be diagonalized by the transformation @xmath33 where the orthogonality of the transformation requires @xmath34 given a system with @xmath35 particles we finally obtain for the total energy @xmath36 which has to be evaluated within the constraints ( [ const1],[const2 ] , [ const3 ] ) .
this is achieved by adding these constraints quadratically to eq .
( [ e1 ] ) following the procedure already applied in the gutzwiller limit @xcite .
the resulting energy functional then has to be minimized with respect to the fermionic and bosonic fields which is most conveniently done by using a standard conjugate gradient algorithm since the gradients of the energy functional can be calculated analytically . in order not to end up in pathological side minimas
we have generally started the minimization from an hf ansatz for the amplitudes @xmath37 .
since in a previous publication @xcite the unrestricted slave - boson approximation has been already applied to the description of collinear spin structures , we will restrict here to textures with two- and three dimensional spin ordering . in this section
we discuss the spin structure of vortex , skyrmion and elliptical domain wall textures which turn out to be stable energy minima within our slave - boson approach . obviously on finite lattices
one has to use open boundary conditions in order to describe higher dimensional spin structures and the cluster sizes we are considering in the following are ranging from @xmath38 up to @xmath39 .
the incorporation of transversal spin degrees of freedom allows for the definition of spin currents @xmath40 .
the flow direction of these currents is along the bonds of the lattice , however , they are additionally vectorial in spin space and within the present approach we obtain for the i - th component of the spin current flowing between sites @xmath41 : @xmath42 where @xmath43 are the pauli matrices and the hopping factors @xmath44 are defined in eq .
( [ zdef ] ) . the i - th component of @xmath45 can be thought of as measuring the spin - twist in the orthogonal directions @xmath46 so that the total current components @xmath47 , which are plotted in the results , visualize the direction of maximal twist in the spin components @xmath48 at lattice site n. the structure of vortex solutions , where the magnetization rotates in a plane by some multiples of @xmath49 around the localized holes , has already been studied in ref .
@xcite within unrestricted hf theory
. we also obtain vortex states as local minima of the energy functional ( [ e1 ] ) , where the total energy is about @xmath50 lower than in the hf approach , depending on lattice size and on - site repulsion u. however , for one hole away from half - filling vortex solutions are always higher in energy than the conventional nel ordered spin polaron . moreover , their total energy increases logarithmically with the cluster size as a consequence of the twist between neighboring magnetization vectors in agreement with ref . @xcite .
spin structure and spin currents for a vortex - antivortex pair on a @xmath0 lattice .
the hubbard on - site repulsion is @xmath51 .
this logarithmic divergency can be compensated when two holes form a vortex - antivortex pair . according to our calculations
the vortex cores are located at the center of diagonally next nearest neighbor plaquettes , thus separated by the plaquette where the two holes are localized .
1 shows the spin structure and spin current of such a vortex - antivortex pair on a @xmath0 cluster and @xmath51 .
all the spins lie in the xy - plane which means that only the z - component of the spin current has a non zero contribution .
the spin field of this texture can be described by @xmath52 where @xmath53 , ( @xmath54 ) refer to the angles between x - axis and the vectors connecting vortex ( antivortex ) core and site @xmath55 .
the af wave vector is denoted by @xmath56 . concerning the stability of the vortex - antivortex pair we obtain for the @xmath0 cluster and @xmath51 a binding energy of @xmath57 with respect to the nel type bipolaron .
taking into account the far field energy , calculated within the xy - model for the spin structure eq .
( [ vaeq ] ) and an exchange constant of @xmath58 still results in a negative binding energy of @xmath59 .
we note that the absolute value of @xmath60 slightly decreases for smaller cluster sizes since the boundary spins do not properly adjust to the solution eq .
( [ vaeq ] ) .
one can therefore safely conclude that vortex - antivortex pairs are also stable in the thermodynamic cluster limit . on a discrete 2-dimensional af lattice the spin structure of skyrmions , originally obtained as solutions of the o(3 ) non - linear @xmath6-model @xcite ,
has the form @xcite @xmath61 where @xmath62 denotes the core size of the skyrmion and its center is located at @xmath63 . in order to enhance convergence we initialized our minimization procedure with ( non self - consistent ) hf
wave functions corresponding to the spin fields eqs .
( [ skf ] ) . despite intensive search
we could not obtain skyrmion states for one hole doped in the half - filled system .
these solutions always converged towards a spin - polaron embedded into a collinear af nel state as already observed in ref .
@xcite .
charge- ( @xmath64 ) and spin - distribution for a skyrmion texture on a @xmath65 lattice for @xmath51 .
xy- , yz- and xz - projections of the spins together with the respective spin currents for the skyrmion shown in fig .
2 2 the situation changes when removing two particles from the half - filled system .
2 displays the charge- and spin structure in case of 62 particles on a @xmath65 lattice for @xmath51 .
the two holes then are localized on a @xmath66 plaquette at the skyrmion center and in their vicinity spins show a remarkable deviation from the z - direction .
this is more easily seen in fig . 3 where we have plotted the xy- , xz- and yz- spin projections , respectively , together with the corresponding spin currents .
the xy - spin components rotate by @xmath67 around the skyrmion center resulting in a circular spin current for @xmath68 .
however , all current components strongly decay for sites far away from the skyrmion center indicating that the core size parameter @xmath62 is small . upon fitting our solutions to the skyrmion field eq .
( [ skf ] ) we obtain @xmath69 for @xmath51 and cluster sizes @xmath70 , @xmath71 and @xmath0 , respectively .
this already indicates that the skyrmion state should survive the limit of large clusters . to assess the question of stability in more detail
we have also calculated the total energy using skyrmionic boundary conditions @xcite .
these are defined through an exchange field @xmath72 to which the spins at the boundary are coupled and @xmath73 has the form of eq .
( [ skf ] ) . for the exchange
constant we take the strong - coupling value of the hubbard model @xmath74 .
the total energy then is evaluated as a function of @xmath62 and in the result we substract the energy contribution of the exchange field .
this energy has to be compared with the corresponding value of a collinear bipolaron where two holes are localized on neighbored sites within the nel ordered system .
the results are plotted in fig . 4 again for @xmath51 and three different cluster sizes .
as can be seen all curves display a clear minimum at some value of @xmath62 indicating the presence of a stable skyrmion solution with a significant lower energy than the collinear bipolaron .
it should be mentioned that these minima for the corresponding one - hole doped systems are always at @xmath75 , i.e. the configuration of a conventional spin - polaron . from the results shown in fig . 4
one further sees that a lowering of energy with respect to the af bipolaron is already obtained for @xmath75 indicating that despite the imposed nel boundaries the system has a skyrmion like core .
this energy shift increases with the system size since the central spins of large lattices can more properly adjust to the skyrmion state .
from the fact that the @xmath75 results for the @xmath65 and @xmath0 coincide within the numerical error we conclude that also in the thermodynamic limit the skyrmion solution should survive .
also plotted in fig .
4 with filled symbols are the energy differences between bipolarons and skyrmions calculated with open boundary conditions .
as already mentioned one obtains the same core parameter @xmath62 for all three cluster sizes which agrees with the position of the minimum of the solid line ( @xmath0 system ) .
also this feature demonstrates that our largest cluster should already correctly describe the skyrmion structure of infinite clusters .
since the skyrmion on small lattices is very much influenced by the boundary conditions the minimum of the dotted curve ( @xmath70 cluster ) is shifted to a higher value of @xmath76 .
total energy of a two - hole - skyrmion with respect to the energy of a nel - type bipolaron as a function of the skyrmion core size parameter @xmath62 .
the boundary spins have been coupled to the skyrmion solution eq .
( [ skf ] ) via a mean - field exchange field .
solid line and circles : @xmath0 lattice ; dashed line and squares : @xmath71 lattice ; dotted line and diamonds : @xmath70 lattice .
the full symbols mark the energies for open boundary conditions .
@xmath51 . in order to compare the stability of skyrmion states with the vortex - antivortex solutions
, one has to take into account the far field contribution to the total energy .
considering again a @xmath0 system and @xmath51 the skyrmion binding energy with respect to the nel - type bipolaron ( cf .
4 ) is @xmath77 . including the far field energy ( taking again @xmath78 ) one obtains @xmath79 which is approximately half the value of the vortex - antivortex binding energy
the possibility that charge - spin coupling in correlated systems may induce the formation of elliptical domain walls was proposed by an analysis of the landau free - energy functional for coupled charge- and spin density waves @xcite .
these are coplanar spin structures where the spin components in the first harmonic are modulated as @xmath80 the eccentricity of the elliptical domain wall is determined by @xmath81 and @xmath82 correspond to the wave vectors of commensurate af and the domain wall periodicity , respectively .
the case @xmath83 describes an ideal spiral solution whereas @xmath84 reduces the spin structure to a collinear classical domain wall .
we have used ( non - self consistent ) hf states corresponding to eq .
( [ edw ] ) as starting fields for our minimization for different values of @xmath81 .
only vertical domain walls have been considered and periodic boundary conditions where applied in the x- and y - direction , respectively . in case of a completely filled domain wall ( i.e. one hole per site along the wall ) we only found the collinear solutions whereas coplanar structures become stable for half - filled walls .
5 . two possible spin structures for elliptical domain walls together with the corresponding spin currents .
the on - site repulsion is @xmath85 and periodic boundary conditions in x- and y - direction have been used .
shown are the results for a @xmath86 lattice doped with 4 holes .
this is shown in fig . 5 for a @xmath87 lattice with 68 particles where we plot two kinds of possible spin structures which are local minima of the energy functional eq . ( [ e1 ] ) .
also shown are the respective spin currents ( only z - components since the magnetization vector is completely in the xy - plane ) .
spin fields and currents display a quadrupled structure along the wall which is a necessary condition for stability within any mean - field approach @xcite . due to the stripe charge structure
the current flows are more complex than for the elliptical solution eq .
( [ edw ] ) which predicts currents flowing in a single direction orthogonal to the wall .
instead we observe also currents along the wall ( fig .
5a ) and a vortex - antivortex structure in fig . 5b .
although the elliptical stripes are local minima of the energy functional eq .
( [ e1 ] ) they are slightly higher in energy ( @xmath88 ) than collinear domain walls . these have been shown to correspond to the ground state when one takes long - range coulomb interactions into account @xcite .
however , we do not expect significant differences of a long - range contribution to collinear and elliptical stripe solutions .
the structures shown in fig . 5 correspond to systems with hole doping @xmath89 and we could not obtain elliptical solutions for higher doping
. however , one can also study the very low doping limit upon using open boundaries in the x - direction . indeed in this case
elliptical half - filled stripes become favored with repect to collinear domain walls for not too large values of the on - site repulsion u ( @xmath90 ) . fig .
the same as in fig . 5 but now for open boundaries in x - direction . in fig
6 we show the same spin structures as in fig . 5 but for open boundaries in x - direction .
the main difference between these two figures concerns the angle of spin rotation @xmath91 across the domain wall which is only @xmath92 of the expected value of @xmath4 according to eq .
( [ edw ] ) .
this is due to the fact that the system now can acquire a state which has zero total spin current , whereas for periodic boundaries the spiral component always requires a net flow in x - direction .
however , since for a regular array of stripes the charge periodicity and the spin modulation have to be related by @xmath93 @xcite the domain wall induced kink type spin rotation has to be supplemented by an additional spiral field .
assuming an exponential relaxation of the spin rotation from @xmath91 to @xmath4 by this spiral field gives an additional energy per site of @xmath94 where @xmath95 is the spin stiffness , @xmath62 defines the length scale of relaxation and l is the stripe separation .
consequently this additional energy can become small enough in the low doping regime so that elliptical stripe configurations are more stable than collinear solutions for small hole concentrations .
summarizing , we have presented the structure of spin textures which we obtained by applying an unrestricted slave - boson mean - field approximation in its spin - rotation invariant form to the 2d hubbard model .
this approach is suited for calculating the charge and spin distribution of electrons ( holes ) in inhomogeneous and strongly correlated systems since it incorporates correlation effects beyond the standard unrestricted hf theory .
these correlation effects turn out to be especially important for the interaction among holes in the 2-d hubbard model where the hf approximation strongly underestimates their attractive potential @xcite . including the effect of transversal degrees of freedom we have shown that within our slave - boson mean - field approach two holes in the half - filled two - dimensional hubbard model are bound by forming a vortex - antivortex pair , oriented along the diagonal direction .
this texture has significantly lower energy than a conventional collinear bipolaron , also when the far field contribution is taken into account .
additionally we have found that skyrmion states can be stable even on discrete lattices .
we attribute this to the inclusion of correlation effects within our approach , since unrestricted hartree - fock theory can not account for skyrmions as self - consistent solutions ( or local minima of energy ) .
indeed it has been also observed by the authors of ref .
@xcite that within the tj - model a semiclassical description can not account for the occurence of skyrmions but that it is the quantum fluctuations which stabilize this texture .
considering the formation of elliptical domain walls it turned out that these structures only appear for half - filled walls in the low doping regime .
similar to the collinear stripes they are stabilized by a quadrupling of the period along the wall .
this can be realized either by alternating on - wall spin currents ( fig .
5a ) or by forming a vortex - antivortex structure ( fig .
5b ) .
our purpose is to calculate the matrix elements of the hopping matrices @xmath96 by transforming to a diagonal representation of the matrix @xmath31 ( eq . ( [ pi ] ) ) according to @xmath97 where the eigenvalues are given by @xmath98 .
the transformation matrix @xmath99 reads as @xmath100 applied to the hopping matrix this transformation yields @xmath101 and since @xmath102 is diagonal it is straightforward to evaluate @xmath103 and @xmath104 as @xmath105 g. seibold , e. sigmund , and v. hizhnyakov , phys .
b*57 * , 6937 ( 1998 ) .
m. fleck , a. i. liechtenstein , a. m. ole , l. hedin , and v. i. anisimov , phys .
lett . * 80 * , 2393 ( 1998 ) .
r. frsard , and p. wlfle , j. phys .
c*4 * , 3625 ( 1992 ) .
j. a. vergs , e. louis , p. s. lomdahl , f. guinea , and a. r. bishop , phys .
rev . b*43 * , 6099 ( 1991 ) .
j. zaanen and o. gunnarsson , phys .
rev . b*40 * , 7391 ( 1989 ) .
a. a. belavin , and a. m. polyakov , jetp lett .
* 22 * ( 10 ) 245 ( 1975 ) .
b. i. shraiman , e. d. siggia , phys .
lett . * 61 * , 467 ( 1988 ) .
r. j. gooding , phys .
lett . * 66 * , 2266 ( 1991 ) .
s. haas , f - c .
zhang , f. mila , t. m. rice , phys .
lett . * 77 * , 3021 ( 1996 ) .
j. m. tranquada , d. j. buttrey , v. sachan , and j. e. lorenzo , phys .
lett . * 73 * , 1003 ( 1994 ) ; j. m. tranquada , b. j. sternlieb , j. d. axe , y. nakamura , and s. uchida , nature * 375 * , 561 ( 1995 ) ; j. m. tranquada , j. d. axe , n. ichikawa , a. r. moodenbaugh , y. nakamura , and s. uchida , phys . rev
. lett . * 78 * , 338 ( 1997 )
. j. m. tranquada , j. d. axe , n. ichikawa , y. nakamura , s. uchida , and b. nachumi , phys .
rev . b*54 * , 7489 ( 1996 ) .
j. zaanen and p. b. littlewood , phys .
b*50 * , 7222 ( 1994 ) ; z. g. yu , j. zang , j. t. gammel , and a. r. bishop , phys .
b*57 * , 3241 ( 1998 ) .
j. zaanen and m. ole , ann .
physik * 5 * , 224 ( 1996 ) .
g. seibold , c. castellani , c. di castro , and m. grilli , cond - mat/9803184 .
s. r. white and d. j. scalapino , cond - mat/9705128 ; s. r. white and d. j. scalapino , phys .
80 * , 1272 ( 1998 ) .
o. zachar , s. a. kivelson , and v. j. emery , phys .
rev . b*57 * , 1422 ( 1998 ) . t. li , p. wlfle , and p. j. hirschfeld , phys .
rev . b*40 * , 6817 ( 1989 ) ; r. frsard , and p. wlfle , int .
b*6 * , 237 ( 1992 ) .
g. kotliar and a. e. ruckenstein , phys .
lett . * 57 * , 1362 ( 1986 ) . | the spin and charge texture around doped holes in the two - dimensional hubbard model is calculated within an unrestricted spin rotational invariant slave - boson approach . in the first part
we examine in detail the spin structure around two holes doped in the half - filled system where we have studied cluster sizes up to @xmath0 .
it turns out that the most stable configuration corresponds to a vortex - antivortex pair which has lower energy than the nel - type bipolaron even when one takes the far field contribution into account .
we also obtain skyrmions as local minima of the energy functional but with higher total energy than the vortex solutions .
additionally we have investigated the stability of elliptical domain walls for commensurate hole concentrations .
we find that ( i ) these phases correspond to local minima of the energy functional only in case of partially filled walls , ( ii ) elliptical domain walls are only stable in the low doping regime .
pacs numbers : 71.27.+a,71.10.fd,75.10.-b,75.60.ch 2 | <s>[INST]the description of inhomogeneous charge and spin phases in the hubbard model it a topic of current interest , mainly because it is now generally accepted that the high - t@xmath1 compounds , at least in the underdoped regime , are intrinsic electronically inhomogeneous systems .
a powerful tool for the investigation of such inhomogeneous electronic states is the unrestricted hartree - fock ( hf ) scheme which allows for the diagonalization of reasonable cluster sizes .
recently an extension of this approach based on the gutzwiller wave function @xcite has shown to significantly improve the hf solutions which strongly underestimate the attraction between charge carriers . in this paper
we extend the approach of ref .
@xcite to include transversal spin degrees of freedoms which permits the description of coplanar and three - dimensional inhomogeneous spin textures . among coplanar
spin structures homogeneous spiral solutions have been studied by a large variety of methods ( see e.g. @xcite ) which show that a small amount of holes doped into the half - filled system leads to a @xmath2 spiral phase which changes its direction to @xmath3 above some critical concentration . relaxing the constraint of a homogeneous charge distribution the formation of coplanar
, vortexlike phases has been investigated in ref .
@xcite using an unrestricted hf approach .
these are configurations where the antiferromagnetic ( af ) spin order rotates by multiples of 2@xmath4 around the localized hole . due to this twist in the magnetization their energy increases @xmath5 which implies their instability in large clusters .
a three - dimensional spin texture which is known to be topologically stable is the skyrmion as a solution of the o(3 ) non - linear @xmath6-model @xcite .
it has been studied by several authors also for an af background @xcite mainly concentrating on small clusters .
however , it is still controversal wether skyrmion solutions exist also on discrete lattices . whereas unrestricted hf theory for the 2-d hubbard model predicts the decay of skyrmions into conventional spin - polarons @xcite , exact diagonalization studies of a small cluster within the tj - model ref . @xcite
seem to support their existence even when one takes the contribution of the skyrmion far field into acount . within our slave - boson approach
we will show below that skyrmions textures are stable solutions of the discrete two - dimensional hubbard model , when the system is doped with two holes away from half - filling .
connected with the discovery of static stripe order in la@xmath7nio@xmath8 and la@xmath9nd@xmath10sr@xmath11cuo@xmath12 @xcite a lot of work has been done in order to understand the different domain wall structures in these compounds @xcite . whereas in the ni - doped compounds one finds the stripes along the diagonal with one hole per ni - site the charge and spin order in the nd - doped cuprates is along the copper - oxygen bond direction with one hole per every second copper site only . since half - filled horizontal walls are at odds with hf calculations the inclusion of correlations turns out to be a necessary ingredient for the study of domain walls in these systems @xcite .
in addition long - range coulomb interactions can play an important role in stabilizing half - filled vertical stripes @xcite .
based on a landau free - energy analysis of coupled charge and spin - density - wave order parameters it has been shown in ref .
@xcite that within some region of parameter domain walls may have a spiral component .
whereas this type of ordering is not observed in the ni - oxides , some spiral contribution can not be rigorously excluded to be present in the nd - doped compounds @xcite . according to our analysis presented below , elliptical stripes are not stable for concentrations around @xmath13 but may be formed in the very low doping limit .
the rest of the paper is organized as follows : in sec .
ii we give a detailed description of the formalism , in sec .
iii we present the results for vortex , skyrmion and elliptical domain wall solutions respectively , and in sec .
iv we summarize our conclusions .
we consider the two - dimensional hubbard model on a square lattice , with hopping restricted to nearest neighbors ( indicated by the bracket @xmath14 ) @xmath15 where @xmath16 destroys ( creates ) an electron with spin @xmath6 at site i , and @xmath17 .
u is the on - site hubbard repulsion and t the transfer parameter . for the calculations in sec .
iii we take t=1 . in the following we use a spin - rotation - invariant form @xcite of the slave - boson representation introduced by kotliar and ruckenstein in ref .
@xcite . the subsidiary boson fields @xmath18
, @xmath19 stand for the annihilation ( creation ) of empty and doubly occupied sites , respectively , whereas the matrix @xmath20 represents the case of a singly occupied site .
since we consider the mean - field limit all boson operators will be approximated as numbers . besides the completeness condition @xmath21 the boson fields are constrained by the following relations @xmath22 where @xmath23 are the pauli spin matrices and @xmath24 . then , in the physical subspace defined by eqs .
( [ const1],[const2 ] ) the hamiltonian ( [ hm ] ) takes the form @xmath25 where @xmath26 the matrices @xmath27 and @xmath28 guarantee the correct behavior in the limit @xmath29 within the mean - field approximation and @xmath30 is the time - reversal transformed of @xmath31 .
the matrix elements of @xmath32 can be calculated by transforming to a diagonal representation for the @xmath31 ( see appendix ) .
the resulting effective one - particle hamiltonian describes the dynamics of particles which upon hopping between sites are subjected to a modulation of their spin amplitude and spin direction , respectively .
it can be diagonalized by the transformation @xmath33 where the orthogonality of the transformation requires @xmath34 given a system with @xmath35 particles we finally obtain for the total energy @xmath36 which has to be evaluated within the constraints ( [ const1],[const2 ] , [ const3 ] ) .
this is achieved by adding these constraints quadratically to eq .
( [ e1 ] ) following the procedure already applied in the gutzwiller limit @xcite .
the resulting energy functional then has to be minimized with respect to the fermionic and bosonic fields which is most conveniently done by using a standard conjugate gradient algorithm since the gradients of the energy functional can be calculated analytically . in order not to end up in pathological side minimas
we have generally started the minimization from an hf ansatz for the amplitudes @xmath37 .
since in a previous publication @xcite the unrestricted slave - boson approximation has been already applied to the description of collinear spin structures , we will restrict here to textures with two- and three dimensional spin ordering . in this section
we discuss the spin structure of vortex , skyrmion and elliptical domain wall textures which turn out to be stable energy minima within our slave - boson approach . obviously on finite lattices
one has to use open boundary conditions in order to describe higher dimensional spin structures and the cluster sizes we are considering in the following are ranging from @xmath38 up to @xmath39 .
the incorporation of transversal spin degrees of freedom allows for the definition of spin currents @xmath40 .
the flow direction of these currents is along the bonds of the lattice , however , they are additionally vectorial in spin space and within the present approach we obtain for the i - th component of the spin current flowing between sites @xmath41 : @xmath42 where @xmath43 are the pauli matrices and the hopping factors @xmath44 are defined in eq .
( [ zdef ] ) . the i - th component of @xmath45 can be thought of as measuring the spin - twist in the orthogonal directions @xmath46 so that the total current components @xmath47 , which are plotted in the results , visualize the direction of maximal twist in the spin components @xmath48 at lattice site n. the structure of vortex solutions , where the magnetization rotates in a plane by some multiples of @xmath49 around the localized holes , has already been studied in ref .
@xcite within unrestricted hf theory
. we also obtain vortex states as local minima of the energy functional ( [ e1 ] ) , where the total energy is about @xmath50 lower than in the hf approach , depending on lattice size and on - site repulsion u. however , for one hole away from half - filling vortex solutions are always higher in energy than the conventional nel ordered spin polaron . moreover , their total energy increases logarithmically with the cluster size as a consequence of the twist between neighboring magnetization vectors in agreement with ref . @xcite .
spin structure and spin currents for a vortex - antivortex pair on a @xmath0 lattice .
the hubbard on - site repulsion is @xmath51 .
this logarithmic divergency can be compensated when two holes form a vortex - antivortex pair . according to our calculations
the vortex cores are located at the center of diagonally next nearest neighbor plaquettes , thus separated by the plaquette where the two holes are localized .
1 shows the spin structure and spin current of such a vortex - antivortex pair on a @xmath0 cluster and @xmath51 .
all the spins lie in the xy - plane which means that only the z - component of the spin current has a non zero contribution .
the spin field of this texture can be described by @xmath52 where @xmath53 , ( @xmath54 ) refer to the angles between x - axis and the vectors connecting vortex ( antivortex ) core and site @xmath55 .
the af wave vector is denoted by @xmath56 . concerning the stability of the vortex - antivortex pair we obtain for the @xmath0 cluster and @xmath51 a binding energy of @xmath57 with respect to the nel type bipolaron .
taking into account the far field energy , calculated within the xy - model for the spin structure eq .
( [ vaeq ] ) and an exchange constant of @xmath58 still results in a negative binding energy of @xmath59 .
we note that the absolute value of @xmath60 slightly decreases for smaller cluster sizes since the boundary spins do not properly adjust to the solution eq .
( [ vaeq ] ) .
one can therefore safely conclude that vortex - antivortex pairs are also stable in the thermodynamic cluster limit . on a discrete 2-dimensional af lattice the spin structure of skyrmions , originally obtained as solutions of the o(3 ) non - linear @xmath6-model @xcite ,
has the form @xcite @xmath61 where @xmath62 denotes the core size of the skyrmion and its center is located at @xmath63 . in order to enhance convergence we initialized our minimization procedure with ( non self - consistent ) hf
wave functions corresponding to the spin fields eqs .
( [ skf ] ) . despite intensive search
we could not obtain skyrmion states for one hole doped in the half - filled system .
these solutions always converged towards a spin - polaron embedded into a collinear af nel state as already observed in ref .
@xcite .
charge- ( @xmath64 ) and spin - distribution for a skyrmion texture on a @xmath65 lattice for @xmath51 .
xy- , yz- and xz - projections of the spins together with the respective spin currents for the skyrmion shown in fig .
2 2 the situation changes when removing two particles from the half - filled system .
2 displays the charge- and spin structure in case of 62 particles on a @xmath65 lattice for @xmath51 .
the two holes then are localized on a @xmath66 plaquette at the skyrmion center and in their vicinity spins show a remarkable deviation from the z - direction .
this is more easily seen in fig . 3 where we have plotted the xy- , xz- and yz- spin projections , respectively , together with the corresponding spin currents .
the xy - spin components rotate by @xmath67 around the skyrmion center resulting in a circular spin current for @xmath68 .
however , all current components strongly decay for sites far away from the skyrmion center indicating that the core size parameter @xmath62 is small . upon fitting our solutions to the skyrmion field eq .
( [ skf ] ) we obtain @xmath69 for @xmath51 and cluster sizes @xmath70 , @xmath71 and @xmath0 , respectively .
this already indicates that the skyrmion state should survive the limit of large clusters . to assess the question of stability in more detail
we have also calculated the total energy using skyrmionic boundary conditions @xcite .
these are defined through an exchange field @xmath72 to which the spins at the boundary are coupled and @xmath73 has the form of eq .
( [ skf ] ) . for the exchange
constant we take the strong - coupling value of the hubbard model @xmath74 .
the total energy then is evaluated as a function of @xmath62 and in the result we substract the energy contribution of the exchange field .
this energy has to be compared with the corresponding value of a collinear bipolaron where two holes are localized on neighbored sites within the nel ordered system .
the results are plotted in fig . 4 again for @xmath51 and three different cluster sizes .
as can be seen all curves display a clear minimum at some value of @xmath62 indicating the presence of a stable skyrmion solution with a significant lower energy than the collinear bipolaron .
it should be mentioned that these minima for the corresponding one - hole doped systems are always at @xmath75 , i.e. the configuration of a conventional spin - polaron . from the results shown in fig . 4
one further sees that a lowering of energy with respect to the af bipolaron is already obtained for @xmath75 indicating that despite the imposed nel boundaries the system has a skyrmion like core .
this energy shift increases with the system size since the central spins of large lattices can more properly adjust to the skyrmion state .
from the fact that the @xmath75 results for the @xmath65 and @xmath0 coincide within the numerical error we conclude that also in the thermodynamic limit the skyrmion solution should survive .
also plotted in fig .
4 with filled symbols are the energy differences between bipolarons and skyrmions calculated with open boundary conditions .
as already mentioned one obtains the same core parameter @xmath62 for all three cluster sizes which agrees with the position of the minimum of the solid line ( @xmath0 system ) .
also this feature demonstrates that our largest cluster should already correctly describe the skyrmion structure of infinite clusters .
since the skyrmion on small lattices is very much influenced by the boundary conditions the minimum of the dotted curve ( @xmath70 cluster ) is shifted to a higher value of @xmath76 .
total energy of a two - hole - skyrmion with respect to the energy of a nel - type bipolaron as a function of the skyrmion core size parameter @xmath62 .
the boundary spins have been coupled to the skyrmion solution eq .
( [ skf ] ) via a mean - field exchange field .
solid line and circles : @xmath0 lattice ; dashed line and squares : @xmath71 lattice ; dotted line and diamonds : @xmath70 lattice .
the full symbols mark the energies for open boundary conditions .
@xmath51 . in order to compare the stability of skyrmion states with the vortex - antivortex solutions
, one has to take into account the far field contribution to the total energy .
considering again a @xmath0 system and @xmath51 the skyrmion binding energy with respect to the nel - type bipolaron ( cf .
4 ) is @xmath77 . including the far field energy ( taking again @xmath78 ) one obtains @xmath79 which is approximately half the value of the vortex - antivortex binding energy
the possibility that charge - spin coupling in correlated systems may induce the formation of elliptical domain walls was proposed by an analysis of the landau free - energy functional for coupled charge- and spin density waves @xcite .
these are coplanar spin structures where the spin components in the first harmonic are modulated as @xmath80 the eccentricity of the elliptical domain wall is determined by @xmath81 and @xmath82 correspond to the wave vectors of commensurate af and the domain wall periodicity , respectively .
the case @xmath83 describes an ideal spiral solution whereas @xmath84 reduces the spin structure to a collinear classical domain wall .
we have used ( non - self consistent ) hf states corresponding to eq .
( [ edw ] ) as starting fields for our minimization for different values of @xmath81 .
only vertical domain walls have been considered and periodic boundary conditions where applied in the x- and y - direction , respectively . in case of a completely filled domain wall ( i.e. one hole per site along the wall ) we only found the collinear solutions whereas coplanar structures become stable for half - filled walls .
5 . two possible spin structures for elliptical domain walls together with the corresponding spin currents .
the on - site repulsion is @xmath85 and periodic boundary conditions in x- and y - direction have been used .
shown are the results for a @xmath86 lattice doped with 4 holes .
this is shown in fig . 5 for a @xmath87 lattice with 68 particles where we plot two kinds of possible spin structures which are local minima of the energy functional eq . ( [ e1 ] ) .
also shown are the respective spin currents ( only z - components since the magnetization vector is completely in the xy - plane ) .
spin fields and currents display a quadrupled structure along the wall which is a necessary condition for stability within any mean - field approach @xcite . due to the stripe charge structure
the current flows are more complex than for the elliptical solution eq .
( [ edw ] ) which predicts currents flowing in a single direction orthogonal to the wall .
instead we observe also currents along the wall ( fig .
5a ) and a vortex - antivortex structure in fig . 5b .
although the elliptical stripes are local minima of the energy functional eq .
( [ e1 ] ) they are slightly higher in energy ( @xmath88 ) than collinear domain walls . these have been shown to correspond to the ground state when one takes long - range coulomb interactions into account @xcite .
however , we do not expect significant differences of a long - range contribution to collinear and elliptical stripe solutions .
the structures shown in fig . 5 correspond to systems with hole doping @xmath89 and we could not obtain elliptical solutions for higher doping
. however , one can also study the very low doping limit upon using open boundaries in the x - direction . indeed in this case
elliptical half - filled stripes become favored with repect to collinear domain walls for not too large values of the on - site repulsion u ( @xmath90 ) . fig .
the same as in fig . 5 but now for open boundaries in x - direction . in fig
6 we show the same spin structures as in fig . 5 but for open boundaries in x - direction .
the main difference between these two figures concerns the angle of spin rotation @xmath91 across the domain wall which is only @xmath92 of the expected value of @xmath4 according to eq .
( [ edw ] ) .
this is due to the fact that the system now can acquire a state which has zero total spin current , whereas for periodic boundaries the spiral component always requires a net flow in x - direction .
however , since for a regular array of stripes the charge periodicity and the spin modulation have to be related by @xmath93 @xcite the domain wall induced kink type spin rotation has to be supplemented by an additional spiral field .
assuming an exponential relaxation of the spin rotation from @xmath91 to @xmath4 by this spiral field gives an additional energy per site of @xmath94 where @xmath95 is the spin stiffness , @xmath62 defines the length scale of relaxation and l is the stripe separation .
consequently this additional energy can become small enough in the low doping regime so that elliptical stripe configurations are more stable than collinear solutions for small hole concentrations .
summarizing , we have presented the structure of spin textures which we obtained by applying an unrestricted slave - boson mean - field approximation in its spin - rotation invariant form to the 2d hubbard model .
this approach is suited for calculating the charge and spin distribution of electrons ( holes ) in inhomogeneous and strongly correlated systems since it incorporates correlation effects beyond the standard unrestricted hf theory .
these correlation effects turn out to be especially important for the interaction among holes in the 2-d hubbard model where the hf approximation strongly underestimates their attractive potential @xcite . including the effect of transversal degrees of freedom we have shown that within our slave - boson mean - field approach two holes in the half - filled two - dimensional hubbard model are bound by forming a vortex - antivortex pair , oriented along the diagonal direction .
this texture has significantly lower energy than a conventional collinear bipolaron , also when the far field contribution is taken into account .
additionally we have found that skyrmion states can be stable even on discrete lattices .
we attribute this to the inclusion of correlation effects within our approach , since unrestricted hartree - fock theory can not account for skyrmions as self - consistent solutions ( or local minima of energy ) .
indeed it has been also observed by the authors of ref .
@xcite that within the tj - model a semiclassical description can not account for the occurence of skyrmions but that it is the quantum fluctuations which stabilize this texture .
considering the formation of elliptical domain walls it turned out that these structures only appear for half - filled walls in the low doping regime .
similar to the collinear stripes they are stabilized by a quadrupling of the period along the wall .
this can be realized either by alternating on - wall spin currents ( fig .
5a ) or by forming a vortex - antivortex structure ( fig .
5b ) .
our purpose is to calculate the matrix elements of the hopping matrices @xmath96 by transforming to a diagonal representation of the matrix @xmath31 ( eq . ( [ pi ] ) ) according to @xmath97 where the eigenvalues are given by @xmath98 .
the transformation matrix @xmath99 reads as @xmath100 applied to the hopping matrix this transformation yields @xmath101 and since @xmath102 is diagonal it is straightforward to evaluate @xmath103 and @xmath104 as @xmath105 g. seibold , e. sigmund , and v. hizhnyakov , phys .
b*57 * , 6937 ( 1998 ) .
m. fleck , a. i. liechtenstein , a. m. ole , l. hedin , and v. i. anisimov , phys .
lett . * 80 * , 2393 ( 1998 ) .
r. frsard , and p. wlfle , j. phys .
c*4 * , 3625 ( 1992 ) .
j. a. vergs , e. louis , p. s. lomdahl , f. guinea , and a. r. bishop , phys .
rev . b*43 * , 6099 ( 1991 ) .
j. zaanen and o. gunnarsson , phys .
rev . b*40 * , 7391 ( 1989 ) .
a. a. belavin , and a. m. polyakov , jetp lett .
* 22 * ( 10 ) 245 ( 1975 ) .
b. i. shraiman , e. d. siggia , phys .
lett . * 61 * , 467 ( 1988 ) .
r. j. gooding , phys .
lett . * 66 * , 2266 ( 1991 ) .
s. haas , f - c .
zhang , f. mila , t. m. rice , phys .
lett . * 77 * , 3021 ( 1996 ) .
j. m. tranquada , d. j. buttrey , v. sachan , and j. e. lorenzo , phys .
lett . * 73 * , 1003 ( 1994 ) ; j. m. tranquada , b. j. sternlieb , j. d. axe , y. nakamura , and s. uchida , nature * 375 * , 561 ( 1995 ) ; j. m. tranquada , j. d. axe , n. ichikawa , a. r. moodenbaugh , y. nakamura , and s. uchida , phys . rev
. lett . * 78 * , 338 ( 1997 )
. j. m. tranquada , j. d. axe , n. ichikawa , y. nakamura , s. uchida , and b. nachumi , phys .
rev . b*54 * , 7489 ( 1996 ) .
j. zaanen and p. b. littlewood , phys .
b*50 * , 7222 ( 1994 ) ; z. g. yu , j. zang , j. t. gammel , and a. r. bishop , phys .
b*57 * , 3241 ( 1998 ) .
j. zaanen and m. ole , ann .
physik * 5 * , 224 ( 1996 ) .
g. seibold , c. castellani , c. di castro , and m. grilli , cond - mat/9803184 .
s. r. white and d. j. scalapino , cond - mat/9705128 ; s. r. white and d. j. scalapino , phys .
80 * , 1272 ( 1998 ) .
o. zachar , s. a. kivelson , and v. j. emery , phys .
rev . b*57 * , 1422 ( 1998 ) . t. li , p. wlfle , and p. j. hirschfeld , phys .
rev . b*40 * , 6817 ( 1989 ) ; r. frsard , and p. wlfle , int .
b*6 * , 237 ( 1992 ) .
g. kotliar and a. e. ruckenstein , phys .
lett . * 57 * , 1362 ( 1986 ) .[/INST] the spin and charge texture around doped holes in the two - dimensional hubbard model is calculated within an unrestricted spin rotational invariant slave - boson approach . in the first part
we examine in detail the spin structure around two holes doped in the half - filled system where we have studied cluster sizes up to @xmath0 .
it turns out that the most stable configuration corresponds to a vortex - antivortex pair which has lower energy than the nel - type bipolaron even when one takes the far field contribution into account .
we also obtain skyrmions as local minima of the energy functional but with higher total energy than the vortex solutions .
additionally we have investigated the stability of elliptical domain walls for commensurate hole concentrations .
we find that ( i ) these phases correspond to local minima of the energy functional only in case of partially filled walls , ( ii ) elliptical domain walls are only stable in the low doping regime .
pacs numbers : 71.27.+a,71.10.fd,75.10.-b,75.60.ch 2 </s> |
the pharmacokinetics of a single oral dose of two polymorphic forms ( form a versus form c ) of ponesimod in capsules and a tablet formulation ( form c ) were compared.comparison between the two polymorphic forms and comparison between the capsule and tablet formulations did not reveal relevant differences in pharmacokinetic and safety properties.capsules can be substituted with tablets , from which ponesimod is absorbed slightly more rapidly .
sphingosine-1-phosphate ( s1p ) is a phospholipid displaying a wide range of physiological roles [ 13 ] .
s1p effects are mediated by the activation of five g - protein - coupled receptors , s1p1 to s1p5 . among them , the s1p1 receptors , which are expressed in many cell types ( e.g. , lymphocytes , cardiomyocytes , and endothelial cells ) , induce gi protein - mediated signaling and play a role in the immune and cardiovascular systems .
recent studies have revealed that functional antagonism of the s1p1 receptor leads to inhibition of the egress of lymphocytes from secondary lymphoid organs and a low lymphocyte count in peripheral blood .
ponesimod ( act-128800 ) is a potent , orally active , selective , reversible s1p1 receptor modulator currently in clinical development for the treatment of autoimmune diseases and has successfully reached its study end points in recent phase ii trials in patients with chronic plaque psoriasis or relapsing remitting multiple sclerosis .
single- and multiple - dose administration of ponesimod results in a dose - dependent decrease in circulating lymphocytes in healthy subjects and is associated with heart rate reduction , a delay in atrioventricular conduction , and pulmonary effects [ 913 ] .
the maximum plasma concentration ( cmax ) is achieved approximately 24 h after dosing ( tmax ) , and the terminal half - life ( t ) is approximately 32 h. steady - state conditions are attained within 45 days when ponesimod is administered once daily at any given dose .
increases in cmax are dose proportional , while increases in the area under the curve ( auc ) are slightly greater than dose proportional [ 911 ] .
a previous study revealed low variability in pharmacokinetic parameters ( inter - subject variability < 36 % ) .
previous clinical trials were performed with polymorph form a ( a hydrated crystalline form ) of ponesimod capsules . during the development of the drug , solid - state investigations revealed the existence of distinct polymorphic forms of ponesimod .
form c ( an anhydrous polymorphic form)the thermodynamically most stable form at room temperature so far known was identified .
moreover , a tablet formulation of form c with a smaller size , compared with the capsules , was developed .
the aim of this study was to compare the two polymorphic forms ( form a and form c in capsules ) , as well as the capsule and tablet formulations of form c of ponesimod , in terms of their pharmacokinetics , safety , and tolerability , in order to bridge the results obtained in early clinical studies using capsules of form a with those of later studies .
healthy male and female subjects aged between 18 and 65 years were included in this study .
the health of the subjects was assessed at the screening visit , which included recording of the medical history , medications taken during the 3 months preceding the screening visit , a physical examination , measurement of body weight and height , clinical laboratory tests , recording of vital signs , and a standard electrocardiogram ( ecg ) . because of the teratogenic potential of ponesimod , women of childbearing potential were required to use two reliable and protocol - approved methods of contraception from screening until 2 months after the last study drug intake . at screening , subjects had to have a pr interval of < 200 ms , a heart rate of > 55 beats per minute ( bpm ) , and a total lymphocyte count of > 1000 lymphocytes/l . written informed consent was obtained from each individual participating in the study prior to any study procedure and after adequate explanation of the aims , methods , objectives , and potential hazards of the studies .
these studies were conducted at different centers and at different times . the comit de protection des
personnes ( paris , france ) approved the protocol of study 1 , and the aspire institutional review board ( la mesa , ca , usa ) approved the protocol of study 2 .
these studies were performed according to good clinical practice and in accordance with the principles of the declaration of helsinki .
this work was performed at two centers , one in france for the comparison of polymorphic form a and form c in capsules ( study 1 ) and one in the usa for the comparison between capsules and tablets of form c ( study 2 ) .
each study was a single - center , randomized , open - label , two - period , two - treatment , crossover , biocomparison study .
a total of 26 subjects ( 12 healthy male subjects in study 1 : age 31.3 [ 12.8 ] years , body weight 75.4 [ 11.3 ] kg ; 14 healthy male and female subjects [ ratio 1:1 ] in study 2 : age 31.1 [ 14.9 ] years , body weight 69.0 [ 14.5 ] kg ) were enrolled , and all subjects received active treatment . a power of 80 % was estimated with a sample size of 12 subjects ( in study 1 ) and 14 subjects ( in study 2 ) , based on an intra - subject coefficient of variation of the tablet formulation of ~12 % observed in previous clinical trials of ponesimod .
the treatment consisted of two treatment periods of a single dose of ponesimod 20 mg as one form a or form c capsule ( in study 1 ) or two treatment periods of a single dose of ponesimod 40 mg either as one capsule or one tablet ( in study 2 ) .
all treatments were administered in the morning with approximately 240 ml of water , and the two treatment periods were separated by a wash - out period of 815 days in study 1 and 1415 days in study 2 .
the subjects remained fasted from at least 10 h prior to drug intake until 4 h afterward .
the subjects remained in the clinic from day 1 ( i.e. , the day prior to study drug administration ) until day 2 , 24 h after study drug administration , and they could then be discharged if this was allowed on the basis of their medical condition at the end of each treatment period .
an end - of - study visit comprising the same examinations as those performed at the screening visit was conducted 6 days or 22 ( + 2 ) days after the last study drug administration in study 1 and study 2 , respectively .
safety and tolerability were evaluated by monitoring of adverse events and vital signs ( supine blood pressure and heart rate ) , a cardiodynamic assessment ( a 12-lead ecg recording ) , pulmonary function tests , clinical laboratory tests , and physical and neurological examinations .
vital signs were recorded from subjects in the supine position after they had rested for at least a 5-min period pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both study 1 and study 2 . in study 1 ,
vital signs were , in addition , recorded 0.5 , 1.5 , 6 , 36 , 72 , 96 , and 120 h after study drug administration .
a standard 12-lead ecg was recorded at rest in the supine position pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both studies . clinical laboratory tests and a physical examination
were done prior to study drug administration and during the end - of - study visit .
a lymphocyte count was only performed pre - dose and 144 h after ponesimod administration in study 2 . two additional assessments ( 24 and 48 h after study drug administration )
blood samples of about 3 ml were collected in ethylenediaminetetraacetic acid ( edta ) tubes just before study drug administration and 0.5 , 1 , 1.5 , 2.5 , 4 , 6 , 10 , 16 , 24 , 36 , 48 , 72 , 96 , 120 , and 144 h after study drug administration in both study 1 and study 2 .
after centrifugation , plasma was transferred into a labeled polypropylene tube and stored at 21 c ( 5 c ) pending analysis .
plasma concentrations of ponesimod were determined using a validated liquid chromatography tandem mass spectrometry ( lc ms / ms ) assay with a lower limit of quantification of 1 ng / ml . analysis of quality - control samples of all runs showed that the inter - day coefficients of variation were < 12.2 % , whereas the average intra - day inaccuracy was in the range of 6.0 to 3.3 % .
time profiles , auc from time zero to the time of the last measurable concentration ( auc0t ) was calculated using the trapezoidal method , and t was calculated as ln 2/z , where z is the terminal elimination rate constant estimated by log - linear regression analysis .
pharmacokinetic variables were analyzed descriptively , providing geometric means and 95 % confidence intervals ( cis ) for cmax , auc from time zero to infinity ( auc0inf ) , auc0t ( i.e. , auc from time zero to 144 h [ auc0144h ] ) , and t. for tmax , the median with minimum and maximum values were calculated and reported . safety and tolerability data were analyzed descriptively .
bioequivalence was explored , and the geometric mean ratios of auc and cmax of form c / form a and tablet / capsule , as well as their 90 % cis , were derived from mixed - effect models with treatment , sequence , and period as fixed effects and subjects as random effects , and by a linear model with treatment and subjects as fixed effects .
sas software versions 8.2 and 9.1 ( sas institute , cary , nc , usa ) were used for the statistical analysis and the reporting of safety and tolerability data . for the pharmacokinetics ,
the statistical package r ( r foundation for statistical computing version 2.6.1 , lme function ) was used .
cardiodynamic and pharmacodynamic data are expressed as mean standard deviation ( sd ) .
the student s t test was used to analyze the effects of ponesimod on the heart rate and blood pressure .
healthy male and female subjects aged between 18 and 65 years were included in this study .
the health of the subjects was assessed at the screening visit , which included recording of the medical history , medications taken during the 3 months preceding the screening visit , a physical examination , measurement of body weight and height , clinical laboratory tests , recording of vital signs , and a standard electrocardiogram ( ecg ) . because of the teratogenic potential of ponesimod , women of childbearing potential were required to use two reliable and protocol - approved methods of contraception from screening until 2 months after the last study drug intake . at screening , subjects had to have a pr interval of < 200 ms , a heart rate of > 55 beats per minute ( bpm ) , and a total lymphocyte count of > 1000 lymphocytes/l . written informed consent was obtained from each individual participating in the study prior to any study procedure and after adequate explanation of the aims , methods , objectives , and potential hazards of the studies .
these studies were conducted at different centers and at different times . the comit de protection des
personnes ( paris , france ) approved the protocol of study 1 , and the aspire institutional review board ( la mesa , ca , usa ) approved the protocol of study 2 .
these studies were performed according to good clinical practice and in accordance with the principles of the declaration of helsinki .
this work was performed at two centers , one in france for the comparison of polymorphic form a and form c in capsules ( study 1 ) and one in the usa for the comparison between capsules and tablets of form c ( study 2 ) .
each study was a single - center , randomized , open - label , two - period , two - treatment , crossover , biocomparison study .
a total of 26 subjects ( 12 healthy male subjects in study 1 : age 31.3 [ 12.8 ] years , body weight 75.4 [ 11.3 ] kg ; 14 healthy male and female subjects [ ratio 1:1 ] in study 2 : age 31.1 [ 14.9 ] years , body weight 69.0 [ 14.5 ] kg ) were enrolled , and all subjects received active treatment . a power of 80 % was estimated with a sample size of 12 subjects ( in study 1 ) and 14 subjects ( in study 2 ) , based on an intra - subject coefficient of variation of the tablet formulation of ~12 % observed in previous clinical trials of ponesimod .
the treatment consisted of two treatment periods of a single dose of ponesimod 20 mg as one form a or form c capsule ( in study 1 ) or two treatment periods of a single dose of ponesimod 40 mg either as one capsule or one tablet ( in study 2 ) .
all treatments were administered in the morning with approximately 240 ml of water , and the two treatment periods were separated by a wash - out period of 815 days in study 1 and 1415 days in study 2 .
the subjects remained fasted from at least 10 h prior to drug intake until 4 h afterward .
the subjects remained in the clinic from day 1 ( i.e. , the day prior to study drug administration ) until day 2 , 24 h after study drug administration , and they could then be discharged if this was allowed on the basis of their medical condition at the end of each treatment period .
an end - of - study visit comprising the same examinations as those performed at the screening visit was conducted 6 days or 22 ( + 2 ) days after the last study drug administration in study 1 and study 2 , respectively .
safety and tolerability were evaluated by monitoring of adverse events and vital signs ( supine blood pressure and heart rate ) , a cardiodynamic assessment ( a 12-lead ecg recording ) , pulmonary function tests , clinical laboratory tests , and physical and neurological examinations .
vital signs were recorded from subjects in the supine position after they had rested for at least a 5-min period pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both study 1 and study 2 . in study 1 ,
vital signs were , in addition , recorded 0.5 , 1.5 , 6 , 36 , 72 , 96 , and 120 h after study drug administration .
a standard 12-lead ecg was recorded at rest in the supine position pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both studies . clinical laboratory tests and a physical examination
were done prior to study drug administration and during the end - of - study visit .
a lymphocyte count was only performed pre - dose and 144 h after ponesimod administration in study 2 . two additional assessments ( 24 and 48 h after study drug administration )
blood samples of about 3 ml were collected in ethylenediaminetetraacetic acid ( edta ) tubes just before study drug administration and 0.5 , 1 , 1.5 , 2.5 , 4 , 6 , 10 , 16 , 24 , 36 , 48 , 72 , 96 , 120 , and 144 h after study drug administration in both study 1 and study 2 .
after centrifugation , plasma was transferred into a labeled polypropylene tube and stored at 21 c ( 5 c ) pending analysis .
plasma concentrations of ponesimod were determined using a validated liquid chromatography tandem mass spectrometry ( lc ms / ms ) assay with a lower limit of quantification of 1 ng / ml . analysis of quality - control samples of all runs showed that the inter - day coefficients of variation were < 12.2 % , whereas the average intra - day inaccuracy was in the range of 6.0 to 3.3 % .
time profiles , auc from time zero to the time of the last measurable concentration ( auc0t ) was calculated using the trapezoidal method , and t was calculated as ln 2/z , where z is the terminal elimination rate constant estimated by log - linear regression analysis .
pharmacokinetic variables were analyzed descriptively , providing geometric means and 95 % confidence intervals ( cis ) for cmax , auc from time zero to infinity ( auc0inf ) , auc0t ( i.e. , auc from time zero to 144 h [ auc0144h ] ) , and t. for tmax , the median with minimum and maximum values were calculated and reported .
bioequivalence was explored , and the geometric mean ratios of auc and cmax of form c / form a and tablet / capsule , as well as their 90 % cis , were derived from mixed - effect models with treatment , sequence , and period as fixed effects and subjects as random effects , and by a linear model with treatment and subjects as fixed effects .
sas software versions 8.2 and 9.1 ( sas institute , cary , nc , usa ) were used for the statistical analysis and the reporting of safety and tolerability data . for the pharmacokinetics , the statistical package r (
cardiodynamic and pharmacodynamic data are expressed as mean standard deviation ( sd ) .
the student s t test was used to analyze the effects of ponesimod on the heart rate and blood pressure .
in study 1 , the plasma concentration time profiles of ponesimod were characterized by a median tmax of 4 h for both polymorphic forms in capsules ( fig .
table 1 reveals that following ponesimod 20 mg , the observed total exposure , cmax , and t were similar with form a and form c. when bioequivalence was explored by mixed - effect and linear models , the geometric mean ratios ( and 90 % cis ) of cmax and auc for form c versus form a capsules were all within the 0.801.25 bioequivalence interval ( fig . 2 ; table 1).fig .
1arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14)table 1comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 )
n
c
max ( ng / ml )
t
max ( h )
auc0t ( ngh / ml)auc0inf ( ngh / ml )
t
( h)study 1 ( 20 mg ) form a1295.0 ( 82.0110)4.0 ( 2.56.0)3006 ( 27183325)3091 ( 28063404)26.3 ( 23.629.4 ) form c1289.4 ( 70.7113)4.0 ( 2.510.0)3064 ( 26493544)3150 ( 27253641)27.4 ( 25.129.9 ) form c versus form a
120.94 ( 0.811.10)nc1.02 ( 0.931.12)1.02 ( 0.931.12)ncstudy 2 ( 40 mg ) capsule14201 ( 160251)5.0 ( 2.516.0)7542 ( 61229290)7912 ( 63919795)31.2 ( 26.436.9 ) tablet14255 ( 212307)4.0 ( 3.95.3)8146 ( 66419991)8431 ( 682110,421)28.0 ( 24.831.7 ) tablet versus capsule
141.27 ( 1.151.40)nc1.08 ( 0.961.22)1.07 ( 0.951.19)0.90 ( 0.771.05)the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval)fig .
2geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14 ) comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 ) the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval ) geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) in study 2 , subjects received ponesimod 40 mg as either a tablet or a capsule of form c. when both formulations were compared , total exposure and t were similar ( table 1 ) .
cmax was slightly higher and reached earlier with the tablet than with the capsule ( fig .
1b ; table 1 ) , indicating more rapid absorption of ponesimod when administered in the tablet formulation .
the 90 % cis of the estimated geometric mean ratios of auc0t ( auc0144h ) and auc0inf were contained within the 0.801.25 bioequivalence interval .
the estimated geometric mean ratio for cmax was 27 % higher ( i.e. , ratio 1.27 ) with the tablet than with the capsule formulation ( 90 % ci 1.151.40 ) , and t tended to be slightly shorter with the tablet formulation ( ratio 0.90 , 90 % ci 0.771.05 ) ( fig . 2 ) . in study 2 ,
both male and female subjects ( ratio 1:1 ) were enrolled . the observed cmax was greater in female subjects ( geometric means [ 95 % cis ] 251.4 [ 176.6357.8 ] ng / ml and 326.8 [ 272.7391.7 ] ng / ml for capsules and tablets , respectively ) than in male subjects ( 160.1 [ 127.2201.7 ] ng / ml and 199.4 [ 165.4240.0 ] ng / ml for capsules and tablets , respectively ) .
moreover , exposure to ponesimod ( auc0inf ) was greater in female subjects ( 9841 [ 729213,280 ] ngh / ml and 10,864 [ 882613,372 ] ngh / ml for capsules and tablets , respectively ) than in male subjects ( 6361 [ 48968264 ] ngh / ml and 6543 [ 49478654 ] ngh / ml for capsules and tablets , respectively ) , and t was slightly longer in female subjects ( 37.1 [ 27.849.5 ] h and 31.2 [ 24.639.5 ] h for capsules and tablets , respectively ) than in male subjects ( 26.3 [ 23.229.7 ] h and 25.2 [ 23.327.3 ] h for capsules and tablets , respectively ) .
there was no marked difference in the nature , severity , and incidence of adverse events reported for the different formulations in study 1 ( form a and form c capsules ) and study 2 ( form c capsule and tablet ) ( table 2 ) .
all reported adverse events were of mild to moderate intensity , were considered by the investigators to be related to the study drug , and were reported as being resolved by the end of the studies . in both studies ,
the most frequently observed adverse events were headache , dizziness , nausea , and sinus bradycardia ( defined as a heart rate below 40 bpm ) , and three subjects ( one in study 1 and two in study 2 ) displayed an event of first - degree atrioventricular block ( defined as a pr interval above 200 ms ) . when comparing study 1 and study 2 ( table 2 ) , the incidence of adverse events ( i.e. , the number of subjects with at least one adverse event ) was higher following administration of ponesimod 40 mg ( 85.7 % ) than following ponesimod 20 mg ( 33.3 % ) .table 2treatment - emergent adverse events ( aes ) in study 1 and study 2study 1 ( 20 mg)study 2 ( 40 mg)form aform ccapsuletablettreatment number of subjects dosed12121414 number of subjects with at least one ae ( % ) 4 ( 33.3)4 ( 33.3)12 ( 85.7)12 ( 85.7 ) total number of aes654043number of subjects reporting an event ( % ) headache2 ( 16.7)1 ( 8.3)4 ( 28.6)6 ( 42.9 ) dizziness9 ( 64.3)7 ( 50.0 ) sinus bradycardia2 ( 16.7)1 ( 8.3)6 ( 42.9)6 ( 42.9 ) first - degree atrioventricular block1 ( 8.3)1 ( 8.3)1 ( 7.1)1 ( 7.1 ) nausea1 ( 8.3)1 ( 8.3)2 ( 14.3)2 ( 14.3 ) vomiting1 ( 8.3)1 ( 7.1 ) treatment - emergent adverse events ( aes ) in study 1 and study 2 in study 1 , maximum heart rate changes of ( mean sd ) 20.2 6.0 bpm ( t = 9.2 , p < 0.001 ) and 18.8 5.6 bpm ( t = 10.7 , p < 0.001 ) 2.5 h after administration of form a and form c , respectively , were observed ( fig
there was no relevant difference between the two polymorphic forms of ponesimod ( t = 0.6 , p = 0.6).fig .
3arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute in study 2 , the maximum heart rate changes were ( mean sd ) 15.6 10.6 bpm ( t = 4.9 , p < 0.0001 ) and 16.2 6.4 bpm ( t = 5.0 , p < 0.0001 ) 2.5 h after administration of the capsule and tablet formulations , respectively ( fig .
there was no relevant difference between the capsule and tablet formulations of form c ( t = 0.2 , p = 0.9 ) ( fig .
a reduction in blood pressure , compared with baseline , following administration of both polymorphic forms of ponesimod ( 20 mg ) was observed .
however , no relevant differences were observed in the decrease in systolic and diastolic blood pressure between form a ( systolic : 7 11 mmhg ; diastolic : 10 7 mmhg ) and form c ( systolic : 6 14 mmhg , t = 0.2 , p = 0.8 ; diastolic : 8 5 mmhg , t = 0.8 , p = 0.4 ) . in study 2 , both the capsule ( systolic : 7 9 mmhg ; diastolic : 9 8 mmhg ) and the tablet ( systolic : 6 6 mmhg , t = 0.4 , p = 0.7 ; diastolic : 7 11 mmhg , t = 0.7 , p = 0.5 ) formulations triggered similar decreases in blood pressure .
the maximum decrease in blood pressure was observed 2.5 h after ponesimod administration in both study 1 and study 2 . in both studies , administration of ponesimod 20 or 40
mg did not alter other safety parameters , such as ecg variables ( including the qtcb and qtcf intervals ) and body weight .
there were no marked differences regarding the number of ecg abnormalities in study 1 ( three ecg abnormalities were observed with each polymorphic form ) or study 2 ( 16 and 20 abnormalities were observed with the capsule and tablet , respectively ) .
thus , the frequency of abnormalities was higher following administration of ponesimod 40 mg than following ponesimod 20 mg . as expected , a single administration of ponesimod 20 mg ( mean sd decreases in the number of lymphocytes : 1.05 0.50
10 cells / l for form a and form c , respectively ) or 40 mg ( 0.30 0.51
10 cells / l and 0.23 0.27 10 cells / l for the capsule and tablet , respectively ) led to a reduction in the lymphocyte count ( not shown ) .
this effect was not considered to be an adverse event , as it is an anticipated pharmacodynamic effect of the drug .
in study 1 , the plasma concentration time profiles of ponesimod were characterized by a median tmax of 4 h for both polymorphic forms in capsules ( fig .
table 1 reveals that following ponesimod 20 mg , the observed total exposure , cmax , and t were similar with form a and form c. when bioequivalence was explored by mixed - effect and linear models , the geometric mean ratios ( and 90 % cis ) of cmax and auc for form c versus form a capsules were all within the 0.801.25 bioequivalence interval ( fig . 2 ; table 1).fig .
1arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14)table 1comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 )
n
c
max ( ng / ml )
t
max ( h )
auc0t ( ngh / ml)auc0inf ( ngh / ml )
t
( h)study 1 ( 20 mg ) form a1295.0 ( 82.0110)4.0 ( 2.56.0)3006 ( 27183325)3091 ( 28063404)26.3 ( 23.629.4 ) form c1289.4 ( 70.7113)4.0 ( 2.510.0)3064 ( 26493544)3150 ( 27253641)27.4 ( 25.129.9 ) form c versus form a
120.94 ( 0.811.10)nc1.02 ( 0.931.12)1.02 ( 0.931.12)ncstudy 2 ( 40 mg ) capsule14201 ( 160251)5.0 ( 2.516.0)7542 ( 61229290)7912 ( 63919795)31.2 ( 26.436.9 ) tablet14255 ( 212307)4.0 ( 3.95.3)8146 ( 66419991)8431 ( 682110,421)28.0 ( 24.831.7 ) tablet versus capsule
141.27 ( 1.151.40)nc1.08 ( 0.961.22)1.07 ( 0.951.19)0.90 ( 0.771.05)the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval)fig .
2geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14 ) comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 ) the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval ) geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) in study 2 , subjects received ponesimod 40 mg as either a tablet or a capsule of form c. when both formulations were compared , total exposure and t were similar ( table 1 ) .
cmax was slightly higher and reached earlier with the tablet than with the capsule ( fig .
1b ; table 1 ) , indicating more rapid absorption of ponesimod when administered in the tablet formulation .
the 90 % cis of the estimated geometric mean ratios of auc0t ( auc0144h ) and auc0inf were contained within the 0.801.25 bioequivalence interval .
the estimated geometric mean ratio for cmax was 27 % higher ( i.e. , ratio 1.27 ) with the tablet than with the capsule formulation ( 90 % ci 1.151.40 ) , and t tended to be slightly shorter with the tablet formulation ( ratio 0.90 , 90 % ci 0.771.05 ) ( fig . 2 ) . in study 2 ,
both male and female subjects ( ratio 1:1 ) were enrolled . the observed cmax was greater in female subjects ( geometric means [ 95 % cis ] 251.4 [ 176.6357.8 ] ng / ml and 326.8 [ 272.7391.7 ] ng / ml for capsules and tablets , respectively ) than in male subjects ( 160.1 [ 127.2201.7 ] ng / ml and 199.4 [ 165.4240.0 ] ng / ml for capsules and tablets , respectively ) .
moreover , exposure to ponesimod ( auc0inf ) was greater in female subjects ( 9841 [ 729213,280 ] ngh / ml and 10,864 [ 882613,372 ] ngh / ml for capsules and tablets , respectively ) than in male subjects ( 6361 [ 48968264 ] ngh / ml and 6543 [ 49478654 ] ngh / ml for capsules and tablets , respectively ) , and t was slightly longer in female subjects ( 37.1 [ 27.849.5 ] h and 31.2 [ 24.639.5 ] h for capsules and tablets , respectively ) than in male subjects ( 26.3 [ 23.229.7 ] h and 25.2 [ 23.327.3 ] h for capsules and tablets , respectively ) .
there was no marked difference in the nature , severity , and incidence of adverse events reported for the different formulations in study 1 ( form a and form c capsules ) and study 2 ( form c capsule and tablet ) ( table 2 ) .
all reported adverse events were of mild to moderate intensity , were considered by the investigators to be related to the study drug , and were reported as being resolved by the end of the studies . in both studies ,
the most frequently observed adverse events were headache , dizziness , nausea , and sinus bradycardia ( defined as a heart rate below 40 bpm ) , and three subjects ( one in study 1 and two in study 2 ) displayed an event of first - degree atrioventricular block ( defined as a pr interval above 200 ms ) . when comparing study 1 and study 2 ( table 2 ) , the incidence of adverse events ( i.e. , the number of subjects with at least one adverse event ) was higher following administration of ponesimod 40 mg ( 85.7 % ) than following ponesimod 20 mg ( 33.3 % ) .table 2treatment - emergent adverse events ( aes ) in study 1 and study 2study 1 ( 20 mg)study 2 ( 40 mg)form aform ccapsuletablettreatment number of subjects dosed12121414 number of subjects with at least one ae ( % ) 4 ( 33.3)4 ( 33.3)12 ( 85.7)12 ( 85.7 ) total number of aes654043number of subjects reporting an event ( % ) headache2 ( 16.7)1 ( 8.3)4 ( 28.6)6 ( 42.9 ) dizziness9 ( 64.3)7 ( 50.0 ) sinus bradycardia2 ( 16.7)1 ( 8.3)6 ( 42.9)6 ( 42.9 ) first - degree atrioventricular block1 ( 8.3)1 ( 8.3)1 ( 7.1)1 ( 7.1 ) nausea1 ( 8.3)1 ( 8.3)2 ( 14.3)2 ( 14.3 ) vomiting1 ( 8.3)1 ( 7.1 ) treatment - emergent adverse events ( aes ) in study 1 and study 2 in study 1 , maximum heart rate changes of ( mean sd ) 20.2 6.0 bpm ( t = 9.2 , p < 0.001 ) and 18.8 5.6 bpm ( t = 10.7 , p < 0.001 ) 2.5 h after administration of form a and form c , respectively , were observed ( fig
there was no relevant difference between the two polymorphic forms of ponesimod ( t = 0.6 , p = 0.6).fig .
3arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects . the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute in study 2 , the maximum heart rate changes were ( mean sd ) 15.6 10.6 bpm ( t = 4.9 , p < 0.0001 ) and 16.2 6.4 bpm ( t = 5.0 , p < 0.0001 ) 2.5 h after administration of the capsule and tablet formulations , respectively ( fig .
there was no relevant difference between the capsule and tablet formulations of form c ( t = 0.2 , p = 0.9 ) ( fig .
a reduction in blood pressure , compared with baseline , following administration of both polymorphic forms of ponesimod ( 20 mg ) was observed .
however , no relevant differences were observed in the decrease in systolic and diastolic blood pressure between form a ( systolic : 7 11 mmhg ; diastolic : 10 7 mmhg ) and form c ( systolic : 6 14 mmhg , t = 0.2 , p = 0.8 ; diastolic : 8 5 mmhg , t = 0.8 , p = 0.4 ) . in study 2 , both the capsule ( systolic : 7 9 mmhg ; diastolic : 9 8 mmhg ) and the tablet ( systolic : 6 6 mmhg , t = 0.4 , p = 0.7 ; diastolic : 7 11 mmhg , t = 0.7 , p = 0.5 ) formulations triggered similar decreases in blood pressure .
the maximum decrease in blood pressure was observed 2.5 h after ponesimod administration in both study 1 and study 2 . in both studies , administration of ponesimod 20 or 40
mg did not alter other safety parameters , such as ecg variables ( including the qtcb and qtcf intervals ) and body weight .
there were no marked differences regarding the number of ecg abnormalities in study 1 ( three ecg abnormalities were observed with each polymorphic form ) or study 2 ( 16 and 20 abnormalities were observed with the capsule and tablet , respectively ) .
thus , the frequency of abnormalities was higher following administration of ponesimod 40 mg than following ponesimod 20 mg . as expected , a single administration of ponesimod 20 mg ( mean sd decreases in the number of lymphocytes : 1.05 0.50
10 cells / l and 0.95 0.47 10 cells / l for form a and form c , respectively ) or 40 mg ( 0.30 0.51
10 cells / l for the capsule and tablet , respectively ) led to a reduction in the lymphocyte count ( not shown ) .
this effect was not considered to be an adverse event , as it is an anticipated pharmacodynamic effect of the drug .
the aim of the present study was to compare two polymorphic capsule forms , as well as comparing tablet and capsule formulations ( of the same polymorphic form ) of ponesimod , a potent s1p1 modulator .
the capsule and tablet formulations of ponesimod have similar concentration time profiles and exposure , as well as t values , though absorption of ponesimod from the tablet formulation was slightly more rapid , with a higher cmax than that seen with the capsule formulation .
previous clinical studies were performed with ponesimod polymorphic form a. this form is a crystalline solid obtained by rapid precipitation , whereas another formulation obtained by slow crystallization has been developed .
this form c is thermodynamically more stable than form a. in addition , the slow crystallization of form c in the final step of the synthesis is easier to control and more reproducible , especially on a large manufacturing scale , than the rapid precipitation that yields form a. in addition , a tablet formulation has been developed , which is preferred to the capsule formulation , since the tablets are smaller and easier to swallow , which may improve patient compliance .
it is worth noting that difficulties in swallowing are relatively frequent in patients with multiple sclerosis .
more importantly , tablets are generally more stable than capsules . in the present work ,
we have shown bioequivalence between the two polymorphic forms of ponesimod , and we observed slightly more rapid absorption of ponesimod when it was administered as tablet formulation .
therefore , ponesimod capsules can be substituted with tablets without any dose adjustment . between study 1 and study 2 ,
the increases in cmax were dose proportional and the increases in auc were slightly greater than dose proportional , which is in line with the findings of previous clinical studies performed with ponesimod [ 811 ] . whereas similar exposure in male and female subjects has been seen previously ,
the findings of a recent study are in good agreement with the greater exposure in female subjects that was observed in the present work .
this finding could be related to differences in body weight , requiring dose adjustment [ 16 , 17 ] . in terms of safety and tolerability , a similar incidence and nature of adverse events
the incidence of adverse events and the percentage of subjects displaying adverse events were dose dependent .
in current phase ii studies , an up - titration scheme ( a first dose of 10 mg ) is applied in patients to improve the safety and tolerability of ponesimod treatment [ 7 , 8 ] .
the lymphocyte nadir ( maximum observed decrease ) was higher following administration of ponesimod 20 mg than following 40 mg .
this might have been related to the timing of the assessments . indeed , in study 2 , the lymphocyte count was assessed pre - dose and 144 h after ponesimod administration . in study 1 ,
additional assessments were performed daily . in good agreement with previous studies , we observed transient significant reductions in the heart rate and blood pressure following administration of ponesimod , which were induced by the activation of s1p1 .
the maximum decrease was observed 2.5 h after ponesimod administration , and the heart rate returned to baseline within 10 h , as previously observed [ 911 ] .
when comparing study 1 and study 2 , no clear dose - dependent effect was observed .
this was also the case in a previous study , in which the decrease in the heart rate was similar in the 20 and 50 mg dose groups .
while comparison across studies has limitations , we may assume that the effect on the heart rate reaches a plateau with ponesimod 20 mg .
this reduction in the heart rate following ponesimod administration is explained by the internalization of the s1p1 receptors and their desensitization .
the two polymorphic forms of ponesimod and the tablet and capsule formulations were similar in terms of their pharmacokinetics , except for more rapid absorption of the tablet formulation than the capsule formulation . at the same dose ,
therefore , form a can be substituted with form c , and capsules can be substituted with tablets .
actelion pharmaceuticals ltd provided funding for these clinical trials . at the time of the study conduct and reporting , pierre - eric juif , matthias hoch , daniele dambrosio , and jasper dingemanse were fulltime employees of actelion pharmaceuticals ltd .
sgs aster sas and the hawaii clinical research center received financial compensation for the clinical conduct of study 1 and study 2 , respectively .
the study investigators were m. guillaume ( at sgs aster sas ) and j. ruckle ( at hawaii clinical research center ) . | backgroundponesimod is a potent selective sphingosine-1-phosphate receptor 1 ( s1p1 ) modulator , which leads to a reduction in circulating lymphocytes , reflecting their sequestration within lymphoid organs .
modulation of the s1p1 receptor has been previously described to be an effective treatment of autoimmune diseases ( e.g. , multiple sclerosis).objectivesthe aim of this study was to compare the relative bioavailability of two polymorphic forms of ponesimod in capsules ( form a versus form c ; study 1 ) and the relative bioavailability of a capsule formulation and a tablet formulation ( both polymorphic form c ; study 2).methodstwo open - label , randomized , two - way crossover studies in healthy subjects were performed . in study 1 , 12 male subjects received a single dose of 20 mg of polymorphic form a or form c of ponesimod in a capsule . in study 2 , 14 male and female subjects ( ratio 1:1 ) received a single dose of 40 mg of polymorphic form c of ponesimod in either a capsule or a tablet formulation .
pharmacokinetic and safety variables ( clinical laboratory test results , vital signs , and an electrocardiogram ) were assessed.resultscomparison of the exposure to ponesimod following administration of the formulations in study 1 showed that the 90 % confidence intervals of the geometric mean ratios for the area under the curve from time zero to infinity ( auc0inf ) , the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the terminal half - life ( t ) , and the maximum plasma concentration ( cmax ) were all within the 0.801.25 bioequivalence interval . in study 2 ,
more rapid absorption of ponesimod was observed from the tablet formulation than from the capsule formulation .
there were no relevant differences in the safety and tolerability profiles between the different formulations.conclusionthe two polymorphic forms of ponesimod and tablet versus capsule formulations were similar in terms of pharmacokinetics , safety , and tolerability . | <s>[INST]the pharmacokinetics of a single oral dose of two polymorphic forms ( form a versus form c ) of ponesimod in capsules and a tablet formulation ( form c ) were compared.comparison between the two polymorphic forms and comparison between the capsule and tablet formulations did not reveal relevant differences in pharmacokinetic and safety properties.capsules can be substituted with tablets , from which ponesimod is absorbed slightly more rapidly .
sphingosine-1-phosphate ( s1p ) is a phospholipid displaying a wide range of physiological roles [ 13 ] .
s1p effects are mediated by the activation of five g - protein - coupled receptors , s1p1 to s1p5 . among them , the s1p1 receptors , which are expressed in many cell types ( e.g. , lymphocytes , cardiomyocytes , and endothelial cells ) , induce gi protein - mediated signaling and play a role in the immune and cardiovascular systems .
recent studies have revealed that functional antagonism of the s1p1 receptor leads to inhibition of the egress of lymphocytes from secondary lymphoid organs and a low lymphocyte count in peripheral blood .
ponesimod ( act-128800 ) is a potent , orally active , selective , reversible s1p1 receptor modulator currently in clinical development for the treatment of autoimmune diseases and has successfully reached its study end points in recent phase ii trials in patients with chronic plaque psoriasis or relapsing remitting multiple sclerosis .
single- and multiple - dose administration of ponesimod results in a dose - dependent decrease in circulating lymphocytes in healthy subjects and is associated with heart rate reduction , a delay in atrioventricular conduction , and pulmonary effects [ 913 ] .
the maximum plasma concentration ( cmax ) is achieved approximately 24 h after dosing ( tmax ) , and the terminal half - life ( t ) is approximately 32 h. steady - state conditions are attained within 45 days when ponesimod is administered once daily at any given dose .
increases in cmax are dose proportional , while increases in the area under the curve ( auc ) are slightly greater than dose proportional [ 911 ] .
a previous study revealed low variability in pharmacokinetic parameters ( inter - subject variability < 36 % ) .
previous clinical trials were performed with polymorph form a ( a hydrated crystalline form ) of ponesimod capsules . during the development of the drug , solid - state investigations revealed the existence of distinct polymorphic forms of ponesimod .
form c ( an anhydrous polymorphic form)the thermodynamically most stable form at room temperature so far known was identified .
moreover , a tablet formulation of form c with a smaller size , compared with the capsules , was developed .
the aim of this study was to compare the two polymorphic forms ( form a and form c in capsules ) , as well as the capsule and tablet formulations of form c of ponesimod , in terms of their pharmacokinetics , safety , and tolerability , in order to bridge the results obtained in early clinical studies using capsules of form a with those of later studies .
healthy male and female subjects aged between 18 and 65 years were included in this study .
the health of the subjects was assessed at the screening visit , which included recording of the medical history , medications taken during the 3 months preceding the screening visit , a physical examination , measurement of body weight and height , clinical laboratory tests , recording of vital signs , and a standard electrocardiogram ( ecg ) . because of the teratogenic potential of ponesimod , women of childbearing potential were required to use two reliable and protocol - approved methods of contraception from screening until 2 months after the last study drug intake . at screening , subjects had to have a pr interval of < 200 ms , a heart rate of > 55 beats per minute ( bpm ) , and a total lymphocyte count of > 1000 lymphocytes/l . written informed consent was obtained from each individual participating in the study prior to any study procedure and after adequate explanation of the aims , methods , objectives , and potential hazards of the studies .
these studies were conducted at different centers and at different times . the comit de protection des
personnes ( paris , france ) approved the protocol of study 1 , and the aspire institutional review board ( la mesa , ca , usa ) approved the protocol of study 2 .
these studies were performed according to good clinical practice and in accordance with the principles of the declaration of helsinki .
this work was performed at two centers , one in france for the comparison of polymorphic form a and form c in capsules ( study 1 ) and one in the usa for the comparison between capsules and tablets of form c ( study 2 ) .
each study was a single - center , randomized , open - label , two - period , two - treatment , crossover , biocomparison study .
a total of 26 subjects ( 12 healthy male subjects in study 1 : age 31.3 [ 12.8 ] years , body weight 75.4 [ 11.3 ] kg ; 14 healthy male and female subjects [ ratio 1:1 ] in study 2 : age 31.1 [ 14.9 ] years , body weight 69.0 [ 14.5 ] kg ) were enrolled , and all subjects received active treatment . a power of 80 % was estimated with a sample size of 12 subjects ( in study 1 ) and 14 subjects ( in study 2 ) , based on an intra - subject coefficient of variation of the tablet formulation of ~12 % observed in previous clinical trials of ponesimod .
the treatment consisted of two treatment periods of a single dose of ponesimod 20 mg as one form a or form c capsule ( in study 1 ) or two treatment periods of a single dose of ponesimod 40 mg either as one capsule or one tablet ( in study 2 ) .
all treatments were administered in the morning with approximately 240 ml of water , and the two treatment periods were separated by a wash - out period of 815 days in study 1 and 1415 days in study 2 .
the subjects remained fasted from at least 10 h prior to drug intake until 4 h afterward .
the subjects remained in the clinic from day 1 ( i.e. , the day prior to study drug administration ) until day 2 , 24 h after study drug administration , and they could then be discharged if this was allowed on the basis of their medical condition at the end of each treatment period .
an end - of - study visit comprising the same examinations as those performed at the screening visit was conducted 6 days or 22 ( + 2 ) days after the last study drug administration in study 1 and study 2 , respectively .
safety and tolerability were evaluated by monitoring of adverse events and vital signs ( supine blood pressure and heart rate ) , a cardiodynamic assessment ( a 12-lead ecg recording ) , pulmonary function tests , clinical laboratory tests , and physical and neurological examinations .
vital signs were recorded from subjects in the supine position after they had rested for at least a 5-min period pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both study 1 and study 2 . in study 1 ,
vital signs were , in addition , recorded 0.5 , 1.5 , 6 , 36 , 72 , 96 , and 120 h after study drug administration .
a standard 12-lead ecg was recorded at rest in the supine position pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both studies . clinical laboratory tests and a physical examination
were done prior to study drug administration and during the end - of - study visit .
a lymphocyte count was only performed pre - dose and 144 h after ponesimod administration in study 2 . two additional assessments ( 24 and 48 h after study drug administration )
blood samples of about 3 ml were collected in ethylenediaminetetraacetic acid ( edta ) tubes just before study drug administration and 0.5 , 1 , 1.5 , 2.5 , 4 , 6 , 10 , 16 , 24 , 36 , 48 , 72 , 96 , 120 , and 144 h after study drug administration in both study 1 and study 2 .
after centrifugation , plasma was transferred into a labeled polypropylene tube and stored at 21 c ( 5 c ) pending analysis .
plasma concentrations of ponesimod were determined using a validated liquid chromatography tandem mass spectrometry ( lc ms / ms ) assay with a lower limit of quantification of 1 ng / ml . analysis of quality - control samples of all runs showed that the inter - day coefficients of variation were < 12.2 % , whereas the average intra - day inaccuracy was in the range of 6.0 to 3.3 % .
time profiles , auc from time zero to the time of the last measurable concentration ( auc0t ) was calculated using the trapezoidal method , and t was calculated as ln 2/z , where z is the terminal elimination rate constant estimated by log - linear regression analysis .
pharmacokinetic variables were analyzed descriptively , providing geometric means and 95 % confidence intervals ( cis ) for cmax , auc from time zero to infinity ( auc0inf ) , auc0t ( i.e. , auc from time zero to 144 h [ auc0144h ] ) , and t. for tmax , the median with minimum and maximum values were calculated and reported . safety and tolerability data were analyzed descriptively .
bioequivalence was explored , and the geometric mean ratios of auc and cmax of form c / form a and tablet / capsule , as well as their 90 % cis , were derived from mixed - effect models with treatment , sequence , and period as fixed effects and subjects as random effects , and by a linear model with treatment and subjects as fixed effects .
sas software versions 8.2 and 9.1 ( sas institute , cary , nc , usa ) were used for the statistical analysis and the reporting of safety and tolerability data . for the pharmacokinetics ,
the statistical package r ( r foundation for statistical computing version 2.6.1 , lme function ) was used .
cardiodynamic and pharmacodynamic data are expressed as mean standard deviation ( sd ) .
the student s t test was used to analyze the effects of ponesimod on the heart rate and blood pressure .
healthy male and female subjects aged between 18 and 65 years were included in this study .
the health of the subjects was assessed at the screening visit , which included recording of the medical history , medications taken during the 3 months preceding the screening visit , a physical examination , measurement of body weight and height , clinical laboratory tests , recording of vital signs , and a standard electrocardiogram ( ecg ) . because of the teratogenic potential of ponesimod , women of childbearing potential were required to use two reliable and protocol - approved methods of contraception from screening until 2 months after the last study drug intake . at screening , subjects had to have a pr interval of < 200 ms , a heart rate of > 55 beats per minute ( bpm ) , and a total lymphocyte count of > 1000 lymphocytes/l . written informed consent was obtained from each individual participating in the study prior to any study procedure and after adequate explanation of the aims , methods , objectives , and potential hazards of the studies .
these studies were conducted at different centers and at different times . the comit de protection des
personnes ( paris , france ) approved the protocol of study 1 , and the aspire institutional review board ( la mesa , ca , usa ) approved the protocol of study 2 .
these studies were performed according to good clinical practice and in accordance with the principles of the declaration of helsinki .
this work was performed at two centers , one in france for the comparison of polymorphic form a and form c in capsules ( study 1 ) and one in the usa for the comparison between capsules and tablets of form c ( study 2 ) .
each study was a single - center , randomized , open - label , two - period , two - treatment , crossover , biocomparison study .
a total of 26 subjects ( 12 healthy male subjects in study 1 : age 31.3 [ 12.8 ] years , body weight 75.4 [ 11.3 ] kg ; 14 healthy male and female subjects [ ratio 1:1 ] in study 2 : age 31.1 [ 14.9 ] years , body weight 69.0 [ 14.5 ] kg ) were enrolled , and all subjects received active treatment . a power of 80 % was estimated with a sample size of 12 subjects ( in study 1 ) and 14 subjects ( in study 2 ) , based on an intra - subject coefficient of variation of the tablet formulation of ~12 % observed in previous clinical trials of ponesimod .
the treatment consisted of two treatment periods of a single dose of ponesimod 20 mg as one form a or form c capsule ( in study 1 ) or two treatment periods of a single dose of ponesimod 40 mg either as one capsule or one tablet ( in study 2 ) .
all treatments were administered in the morning with approximately 240 ml of water , and the two treatment periods were separated by a wash - out period of 815 days in study 1 and 1415 days in study 2 .
the subjects remained fasted from at least 10 h prior to drug intake until 4 h afterward .
the subjects remained in the clinic from day 1 ( i.e. , the day prior to study drug administration ) until day 2 , 24 h after study drug administration , and they could then be discharged if this was allowed on the basis of their medical condition at the end of each treatment period .
an end - of - study visit comprising the same examinations as those performed at the screening visit was conducted 6 days or 22 ( + 2 ) days after the last study drug administration in study 1 and study 2 , respectively .
safety and tolerability were evaluated by monitoring of adverse events and vital signs ( supine blood pressure and heart rate ) , a cardiodynamic assessment ( a 12-lead ecg recording ) , pulmonary function tests , clinical laboratory tests , and physical and neurological examinations .
vital signs were recorded from subjects in the supine position after they had rested for at least a 5-min period pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both study 1 and study 2 . in study 1 ,
vital signs were , in addition , recorded 0.5 , 1.5 , 6 , 36 , 72 , 96 , and 120 h after study drug administration .
a standard 12-lead ecg was recorded at rest in the supine position pre - dose and 1 , 2.5 , 4 , 10 , 24 , 48 , and 144 h after study drug administration in both studies . clinical laboratory tests and a physical examination
were done prior to study drug administration and during the end - of - study visit .
a lymphocyte count was only performed pre - dose and 144 h after ponesimod administration in study 2 . two additional assessments ( 24 and 48 h after study drug administration )
blood samples of about 3 ml were collected in ethylenediaminetetraacetic acid ( edta ) tubes just before study drug administration and 0.5 , 1 , 1.5 , 2.5 , 4 , 6 , 10 , 16 , 24 , 36 , 48 , 72 , 96 , 120 , and 144 h after study drug administration in both study 1 and study 2 .
after centrifugation , plasma was transferred into a labeled polypropylene tube and stored at 21 c ( 5 c ) pending analysis .
plasma concentrations of ponesimod were determined using a validated liquid chromatography tandem mass spectrometry ( lc ms / ms ) assay with a lower limit of quantification of 1 ng / ml . analysis of quality - control samples of all runs showed that the inter - day coefficients of variation were < 12.2 % , whereas the average intra - day inaccuracy was in the range of 6.0 to 3.3 % .
time profiles , auc from time zero to the time of the last measurable concentration ( auc0t ) was calculated using the trapezoidal method , and t was calculated as ln 2/z , where z is the terminal elimination rate constant estimated by log - linear regression analysis .
pharmacokinetic variables were analyzed descriptively , providing geometric means and 95 % confidence intervals ( cis ) for cmax , auc from time zero to infinity ( auc0inf ) , auc0t ( i.e. , auc from time zero to 144 h [ auc0144h ] ) , and t. for tmax , the median with minimum and maximum values were calculated and reported .
bioequivalence was explored , and the geometric mean ratios of auc and cmax of form c / form a and tablet / capsule , as well as their 90 % cis , were derived from mixed - effect models with treatment , sequence , and period as fixed effects and subjects as random effects , and by a linear model with treatment and subjects as fixed effects .
sas software versions 8.2 and 9.1 ( sas institute , cary , nc , usa ) were used for the statistical analysis and the reporting of safety and tolerability data . for the pharmacokinetics , the statistical package r (
cardiodynamic and pharmacodynamic data are expressed as mean standard deviation ( sd ) .
the student s t test was used to analyze the effects of ponesimod on the heart rate and blood pressure .
in study 1 , the plasma concentration time profiles of ponesimod were characterized by a median tmax of 4 h for both polymorphic forms in capsules ( fig .
table 1 reveals that following ponesimod 20 mg , the observed total exposure , cmax , and t were similar with form a and form c. when bioequivalence was explored by mixed - effect and linear models , the geometric mean ratios ( and 90 % cis ) of cmax and auc for form c versus form a capsules were all within the 0.801.25 bioequivalence interval ( fig . 2 ; table 1).fig .
1arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14)table 1comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 )
n
c
max ( ng / ml )
t
max ( h )
auc0t ( ngh / ml)auc0inf ( ngh / ml )
t
( h)study 1 ( 20 mg ) form a1295.0 ( 82.0110)4.0 ( 2.56.0)3006 ( 27183325)3091 ( 28063404)26.3 ( 23.629.4 ) form c1289.4 ( 70.7113)4.0 ( 2.510.0)3064 ( 26493544)3150 ( 27253641)27.4 ( 25.129.9 ) form c versus form a
120.94 ( 0.811.10)nc1.02 ( 0.931.12)1.02 ( 0.931.12)ncstudy 2 ( 40 mg ) capsule14201 ( 160251)5.0 ( 2.516.0)7542 ( 61229290)7912 ( 63919795)31.2 ( 26.436.9 ) tablet14255 ( 212307)4.0 ( 3.95.3)8146 ( 66419991)8431 ( 682110,421)28.0 ( 24.831.7 ) tablet versus capsule
141.27 ( 1.151.40)nc1.08 ( 0.961.22)1.07 ( 0.951.19)0.90 ( 0.771.05)the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval)fig .
2geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14 ) comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 ) the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval ) geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) in study 2 , subjects received ponesimod 40 mg as either a tablet or a capsule of form c. when both formulations were compared , total exposure and t were similar ( table 1 ) .
cmax was slightly higher and reached earlier with the tablet than with the capsule ( fig .
1b ; table 1 ) , indicating more rapid absorption of ponesimod when administered in the tablet formulation .
the 90 % cis of the estimated geometric mean ratios of auc0t ( auc0144h ) and auc0inf were contained within the 0.801.25 bioequivalence interval .
the estimated geometric mean ratio for cmax was 27 % higher ( i.e. , ratio 1.27 ) with the tablet than with the capsule formulation ( 90 % ci 1.151.40 ) , and t tended to be slightly shorter with the tablet formulation ( ratio 0.90 , 90 % ci 0.771.05 ) ( fig . 2 ) . in study 2 ,
both male and female subjects ( ratio 1:1 ) were enrolled . the observed cmax was greater in female subjects ( geometric means [ 95 % cis ] 251.4 [ 176.6357.8 ] ng / ml and 326.8 [ 272.7391.7 ] ng / ml for capsules and tablets , respectively ) than in male subjects ( 160.1 [ 127.2201.7 ] ng / ml and 199.4 [ 165.4240.0 ] ng / ml for capsules and tablets , respectively ) .
moreover , exposure to ponesimod ( auc0inf ) was greater in female subjects ( 9841 [ 729213,280 ] ngh / ml and 10,864 [ 882613,372 ] ngh / ml for capsules and tablets , respectively ) than in male subjects ( 6361 [ 48968264 ] ngh / ml and 6543 [ 49478654 ] ngh / ml for capsules and tablets , respectively ) , and t was slightly longer in female subjects ( 37.1 [ 27.849.5 ] h and 31.2 [ 24.639.5 ] h for capsules and tablets , respectively ) than in male subjects ( 26.3 [ 23.229.7 ] h and 25.2 [ 23.327.3 ] h for capsules and tablets , respectively ) .
there was no marked difference in the nature , severity , and incidence of adverse events reported for the different formulations in study 1 ( form a and form c capsules ) and study 2 ( form c capsule and tablet ) ( table 2 ) .
all reported adverse events were of mild to moderate intensity , were considered by the investigators to be related to the study drug , and were reported as being resolved by the end of the studies . in both studies ,
the most frequently observed adverse events were headache , dizziness , nausea , and sinus bradycardia ( defined as a heart rate below 40 bpm ) , and three subjects ( one in study 1 and two in study 2 ) displayed an event of first - degree atrioventricular block ( defined as a pr interval above 200 ms ) . when comparing study 1 and study 2 ( table 2 ) , the incidence of adverse events ( i.e. , the number of subjects with at least one adverse event ) was higher following administration of ponesimod 40 mg ( 85.7 % ) than following ponesimod 20 mg ( 33.3 % ) .table 2treatment - emergent adverse events ( aes ) in study 1 and study 2study 1 ( 20 mg)study 2 ( 40 mg)form aform ccapsuletablettreatment number of subjects dosed12121414 number of subjects with at least one ae ( % ) 4 ( 33.3)4 ( 33.3)12 ( 85.7)12 ( 85.7 ) total number of aes654043number of subjects reporting an event ( % ) headache2 ( 16.7)1 ( 8.3)4 ( 28.6)6 ( 42.9 ) dizziness9 ( 64.3)7 ( 50.0 ) sinus bradycardia2 ( 16.7)1 ( 8.3)6 ( 42.9)6 ( 42.9 ) first - degree atrioventricular block1 ( 8.3)1 ( 8.3)1 ( 7.1)1 ( 7.1 ) nausea1 ( 8.3)1 ( 8.3)2 ( 14.3)2 ( 14.3 ) vomiting1 ( 8.3)1 ( 7.1 ) treatment - emergent adverse events ( aes ) in study 1 and study 2 in study 1 , maximum heart rate changes of ( mean sd ) 20.2 6.0 bpm ( t = 9.2 , p < 0.001 ) and 18.8 5.6 bpm ( t = 10.7 , p < 0.001 ) 2.5 h after administration of form a and form c , respectively , were observed ( fig
there was no relevant difference between the two polymorphic forms of ponesimod ( t = 0.6 , p = 0.6).fig .
3arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute in study 2 , the maximum heart rate changes were ( mean sd ) 15.6 10.6 bpm ( t = 4.9 , p < 0.0001 ) and 16.2 6.4 bpm ( t = 5.0 , p < 0.0001 ) 2.5 h after administration of the capsule and tablet formulations , respectively ( fig .
there was no relevant difference between the capsule and tablet formulations of form c ( t = 0.2 , p = 0.9 ) ( fig .
a reduction in blood pressure , compared with baseline , following administration of both polymorphic forms of ponesimod ( 20 mg ) was observed .
however , no relevant differences were observed in the decrease in systolic and diastolic blood pressure between form a ( systolic : 7 11 mmhg ; diastolic : 10 7 mmhg ) and form c ( systolic : 6 14 mmhg , t = 0.2 , p = 0.8 ; diastolic : 8 5 mmhg , t = 0.8 , p = 0.4 ) . in study 2 , both the capsule ( systolic : 7 9 mmhg ; diastolic : 9 8 mmhg ) and the tablet ( systolic : 6 6 mmhg , t = 0.4 , p = 0.7 ; diastolic : 7 11 mmhg , t = 0.7 , p = 0.5 ) formulations triggered similar decreases in blood pressure .
the maximum decrease in blood pressure was observed 2.5 h after ponesimod administration in both study 1 and study 2 . in both studies , administration of ponesimod 20 or 40
mg did not alter other safety parameters , such as ecg variables ( including the qtcb and qtcf intervals ) and body weight .
there were no marked differences regarding the number of ecg abnormalities in study 1 ( three ecg abnormalities were observed with each polymorphic form ) or study 2 ( 16 and 20 abnormalities were observed with the capsule and tablet , respectively ) .
thus , the frequency of abnormalities was higher following administration of ponesimod 40 mg than following ponesimod 20 mg . as expected , a single administration of ponesimod 20 mg ( mean sd decreases in the number of lymphocytes : 1.05 0.50
10 cells / l for form a and form c , respectively ) or 40 mg ( 0.30 0.51
10 cells / l and 0.23 0.27 10 cells / l for the capsule and tablet , respectively ) led to a reduction in the lymphocyte count ( not shown ) .
this effect was not considered to be an adverse event , as it is an anticipated pharmacodynamic effect of the drug .
in study 1 , the plasma concentration time profiles of ponesimod were characterized by a median tmax of 4 h for both polymorphic forms in capsules ( fig .
table 1 reveals that following ponesimod 20 mg , the observed total exposure , cmax , and t were similar with form a and form c. when bioequivalence was explored by mixed - effect and linear models , the geometric mean ratios ( and 90 % cis ) of cmax and auc for form c versus form a capsules were all within the 0.801.25 bioequivalence interval ( fig . 2 ; table 1).fig .
1arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14)table 1comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 )
n
c
max ( ng / ml )
t
max ( h )
auc0t ( ngh / ml)auc0inf ( ngh / ml )
t
( h)study 1 ( 20 mg ) form a1295.0 ( 82.0110)4.0 ( 2.56.0)3006 ( 27183325)3091 ( 28063404)26.3 ( 23.629.4 ) form c1289.4 ( 70.7113)4.0 ( 2.510.0)3064 ( 26493544)3150 ( 27253641)27.4 ( 25.129.9 ) form c versus form a
120.94 ( 0.811.10)nc1.02 ( 0.931.12)1.02 ( 0.931.12)ncstudy 2 ( 40 mg ) capsule14201 ( 160251)5.0 ( 2.516.0)7542 ( 61229290)7912 ( 63919795)31.2 ( 26.436.9 ) tablet14255 ( 212307)4.0 ( 3.95.3)8146 ( 66419991)8431 ( 682110,421)28.0 ( 24.831.7 ) tablet versus capsule
141.27 ( 1.151.40)nc1.08 ( 0.961.22)1.07 ( 0.951.19)0.90 ( 0.771.05)the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval)fig .
2geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) arithmetic mean ( with standard deviation ) plasma concentration time profiles of ponesimod ( left graphs from 0 to 144 h [ with linear scales and semi - logarithmic scales shown as insets ] ; right graphs from 0 to 8 h ) in healthy subjects after a single dose of a 20 mg as a form a or form c capsule ( n = 12 ) or b 40 mg as a form c capsule or tablet ( n = 14 ) comparison of pharmacokinetic parameters of the two polymorphic forms ( study 1 ) and the tablet versus capsule formulations ( study 2 ) the data are expressed as geometric mean ( 95 % confidence interval ) , except where indicated otherwise
auc
0inf area under the curve from time zero to infinity , auc
0t area under the curve from time zero to the time of the last measurable concentration , c
max maximum plasma concentration , nc not calculated , t
terminal half - life , t
max time to maximum plasma concentration
the data are expressed as median ( range )
the data are expressed as geometric mean ratio ( 90 % confidence interval ) geometric mean ratios ( with 90 % confidence intervals ) derived from mixed - effect models of the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the area under the curve from time zero to infinity ( auc0inf ) , and the maximum plasma concentration ( c
max ) in study 1 ( comparison of the two polymorphic forms c and a ; n = 12 ) and in study 2 ( comparison of the tablet and capsule formulations ; n = 14 ) .
the dotted lines represent the lower and upper bounds of the bioequivalence interval ( 0.801.25 ) in study 2 , subjects received ponesimod 40 mg as either a tablet or a capsule of form c. when both formulations were compared , total exposure and t were similar ( table 1 ) .
cmax was slightly higher and reached earlier with the tablet than with the capsule ( fig .
1b ; table 1 ) , indicating more rapid absorption of ponesimod when administered in the tablet formulation .
the 90 % cis of the estimated geometric mean ratios of auc0t ( auc0144h ) and auc0inf were contained within the 0.801.25 bioequivalence interval .
the estimated geometric mean ratio for cmax was 27 % higher ( i.e. , ratio 1.27 ) with the tablet than with the capsule formulation ( 90 % ci 1.151.40 ) , and t tended to be slightly shorter with the tablet formulation ( ratio 0.90 , 90 % ci 0.771.05 ) ( fig . 2 ) . in study 2 ,
both male and female subjects ( ratio 1:1 ) were enrolled . the observed cmax was greater in female subjects ( geometric means [ 95 % cis ] 251.4 [ 176.6357.8 ] ng / ml and 326.8 [ 272.7391.7 ] ng / ml for capsules and tablets , respectively ) than in male subjects ( 160.1 [ 127.2201.7 ] ng / ml and 199.4 [ 165.4240.0 ] ng / ml for capsules and tablets , respectively ) .
moreover , exposure to ponesimod ( auc0inf ) was greater in female subjects ( 9841 [ 729213,280 ] ngh / ml and 10,864 [ 882613,372 ] ngh / ml for capsules and tablets , respectively ) than in male subjects ( 6361 [ 48968264 ] ngh / ml and 6543 [ 49478654 ] ngh / ml for capsules and tablets , respectively ) , and t was slightly longer in female subjects ( 37.1 [ 27.849.5 ] h and 31.2 [ 24.639.5 ] h for capsules and tablets , respectively ) than in male subjects ( 26.3 [ 23.229.7 ] h and 25.2 [ 23.327.3 ] h for capsules and tablets , respectively ) .
there was no marked difference in the nature , severity , and incidence of adverse events reported for the different formulations in study 1 ( form a and form c capsules ) and study 2 ( form c capsule and tablet ) ( table 2 ) .
all reported adverse events were of mild to moderate intensity , were considered by the investigators to be related to the study drug , and were reported as being resolved by the end of the studies . in both studies ,
the most frequently observed adverse events were headache , dizziness , nausea , and sinus bradycardia ( defined as a heart rate below 40 bpm ) , and three subjects ( one in study 1 and two in study 2 ) displayed an event of first - degree atrioventricular block ( defined as a pr interval above 200 ms ) . when comparing study 1 and study 2 ( table 2 ) , the incidence of adverse events ( i.e. , the number of subjects with at least one adverse event ) was higher following administration of ponesimod 40 mg ( 85.7 % ) than following ponesimod 20 mg ( 33.3 % ) .table 2treatment - emergent adverse events ( aes ) in study 1 and study 2study 1 ( 20 mg)study 2 ( 40 mg)form aform ccapsuletablettreatment number of subjects dosed12121414 number of subjects with at least one ae ( % ) 4 ( 33.3)4 ( 33.3)12 ( 85.7)12 ( 85.7 ) total number of aes654043number of subjects reporting an event ( % ) headache2 ( 16.7)1 ( 8.3)4 ( 28.6)6 ( 42.9 ) dizziness9 ( 64.3)7 ( 50.0 ) sinus bradycardia2 ( 16.7)1 ( 8.3)6 ( 42.9)6 ( 42.9 ) first - degree atrioventricular block1 ( 8.3)1 ( 8.3)1 ( 7.1)1 ( 7.1 ) nausea1 ( 8.3)1 ( 8.3)2 ( 14.3)2 ( 14.3 ) vomiting1 ( 8.3)1 ( 7.1 ) treatment - emergent adverse events ( aes ) in study 1 and study 2 in study 1 , maximum heart rate changes of ( mean sd ) 20.2 6.0 bpm ( t = 9.2 , p < 0.001 ) and 18.8 5.6 bpm ( t = 10.7 , p < 0.001 ) 2.5 h after administration of form a and form c , respectively , were observed ( fig
there was no relevant difference between the two polymorphic forms of ponesimod ( t = 0.6 , p = 0.6).fig .
3arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects . the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute arithmetic mean ( with standard deviation ) heart rates from 0 to 144 h after administration of ponesimod at a dose of a 20 mg ( study 1 ; n = 12 ) or b 40 mg ( study 2 ; n = 14 ) in healthy subjects .
the insets show the arithmetic mean heart rates ( with standard deviations ) from 0 to 10 h. bpm beats per minute in study 2 , the maximum heart rate changes were ( mean sd ) 15.6 10.6 bpm ( t = 4.9 , p < 0.0001 ) and 16.2 6.4 bpm ( t = 5.0 , p < 0.0001 ) 2.5 h after administration of the capsule and tablet formulations , respectively ( fig .
there was no relevant difference between the capsule and tablet formulations of form c ( t = 0.2 , p = 0.9 ) ( fig .
a reduction in blood pressure , compared with baseline , following administration of both polymorphic forms of ponesimod ( 20 mg ) was observed .
however , no relevant differences were observed in the decrease in systolic and diastolic blood pressure between form a ( systolic : 7 11 mmhg ; diastolic : 10 7 mmhg ) and form c ( systolic : 6 14 mmhg , t = 0.2 , p = 0.8 ; diastolic : 8 5 mmhg , t = 0.8 , p = 0.4 ) . in study 2 , both the capsule ( systolic : 7 9 mmhg ; diastolic : 9 8 mmhg ) and the tablet ( systolic : 6 6 mmhg , t = 0.4 , p = 0.7 ; diastolic : 7 11 mmhg , t = 0.7 , p = 0.5 ) formulations triggered similar decreases in blood pressure .
the maximum decrease in blood pressure was observed 2.5 h after ponesimod administration in both study 1 and study 2 . in both studies , administration of ponesimod 20 or 40
mg did not alter other safety parameters , such as ecg variables ( including the qtcb and qtcf intervals ) and body weight .
there were no marked differences regarding the number of ecg abnormalities in study 1 ( three ecg abnormalities were observed with each polymorphic form ) or study 2 ( 16 and 20 abnormalities were observed with the capsule and tablet , respectively ) .
thus , the frequency of abnormalities was higher following administration of ponesimod 40 mg than following ponesimod 20 mg . as expected , a single administration of ponesimod 20 mg ( mean sd decreases in the number of lymphocytes : 1.05 0.50
10 cells / l and 0.95 0.47 10 cells / l for form a and form c , respectively ) or 40 mg ( 0.30 0.51
10 cells / l for the capsule and tablet , respectively ) led to a reduction in the lymphocyte count ( not shown ) .
this effect was not considered to be an adverse event , as it is an anticipated pharmacodynamic effect of the drug .
the aim of the present study was to compare two polymorphic capsule forms , as well as comparing tablet and capsule formulations ( of the same polymorphic form ) of ponesimod , a potent s1p1 modulator .
the capsule and tablet formulations of ponesimod have similar concentration time profiles and exposure , as well as t values , though absorption of ponesimod from the tablet formulation was slightly more rapid , with a higher cmax than that seen with the capsule formulation .
previous clinical studies were performed with ponesimod polymorphic form a. this form is a crystalline solid obtained by rapid precipitation , whereas another formulation obtained by slow crystallization has been developed .
this form c is thermodynamically more stable than form a. in addition , the slow crystallization of form c in the final step of the synthesis is easier to control and more reproducible , especially on a large manufacturing scale , than the rapid precipitation that yields form a. in addition , a tablet formulation has been developed , which is preferred to the capsule formulation , since the tablets are smaller and easier to swallow , which may improve patient compliance .
it is worth noting that difficulties in swallowing are relatively frequent in patients with multiple sclerosis .
more importantly , tablets are generally more stable than capsules . in the present work ,
we have shown bioequivalence between the two polymorphic forms of ponesimod , and we observed slightly more rapid absorption of ponesimod when it was administered as tablet formulation .
therefore , ponesimod capsules can be substituted with tablets without any dose adjustment . between study 1 and study 2 ,
the increases in cmax were dose proportional and the increases in auc were slightly greater than dose proportional , which is in line with the findings of previous clinical studies performed with ponesimod [ 811 ] . whereas similar exposure in male and female subjects has been seen previously ,
the findings of a recent study are in good agreement with the greater exposure in female subjects that was observed in the present work .
this finding could be related to differences in body weight , requiring dose adjustment [ 16 , 17 ] . in terms of safety and tolerability , a similar incidence and nature of adverse events
the incidence of adverse events and the percentage of subjects displaying adverse events were dose dependent .
in current phase ii studies , an up - titration scheme ( a first dose of 10 mg ) is applied in patients to improve the safety and tolerability of ponesimod treatment [ 7 , 8 ] .
the lymphocyte nadir ( maximum observed decrease ) was higher following administration of ponesimod 20 mg than following 40 mg .
this might have been related to the timing of the assessments . indeed , in study 2 , the lymphocyte count was assessed pre - dose and 144 h after ponesimod administration . in study 1 ,
additional assessments were performed daily . in good agreement with previous studies , we observed transient significant reductions in the heart rate and blood pressure following administration of ponesimod , which were induced by the activation of s1p1 .
the maximum decrease was observed 2.5 h after ponesimod administration , and the heart rate returned to baseline within 10 h , as previously observed [ 911 ] .
when comparing study 1 and study 2 , no clear dose - dependent effect was observed .
this was also the case in a previous study , in which the decrease in the heart rate was similar in the 20 and 50 mg dose groups .
while comparison across studies has limitations , we may assume that the effect on the heart rate reaches a plateau with ponesimod 20 mg .
this reduction in the heart rate following ponesimod administration is explained by the internalization of the s1p1 receptors and their desensitization .
the two polymorphic forms of ponesimod and the tablet and capsule formulations were similar in terms of their pharmacokinetics , except for more rapid absorption of the tablet formulation than the capsule formulation . at the same dose ,
therefore , form a can be substituted with form c , and capsules can be substituted with tablets .
actelion pharmaceuticals ltd provided funding for these clinical trials . at the time of the study conduct and reporting , pierre - eric juif , matthias hoch , daniele dambrosio , and jasper dingemanse were fulltime employees of actelion pharmaceuticals ltd .
sgs aster sas and the hawaii clinical research center received financial compensation for the clinical conduct of study 1 and study 2 , respectively .
the study investigators were m. guillaume ( at sgs aster sas ) and j. ruckle ( at hawaii clinical research center ) .[/INST]backgroundponesimod is a potent selective sphingosine-1-phosphate receptor 1 ( s1p1 ) modulator , which leads to a reduction in circulating lymphocytes , reflecting their sequestration within lymphoid organs .
modulation of the s1p1 receptor has been previously described to be an effective treatment of autoimmune diseases ( e.g. , multiple sclerosis).objectivesthe aim of this study was to compare the relative bioavailability of two polymorphic forms of ponesimod in capsules ( form a versus form c ; study 1 ) and the relative bioavailability of a capsule formulation and a tablet formulation ( both polymorphic form c ; study 2).methodstwo open - label , randomized , two - way crossover studies in healthy subjects were performed . in study 1 , 12 male subjects received a single dose of 20 mg of polymorphic form a or form c of ponesimod in a capsule . in study 2 , 14 male and female subjects ( ratio 1:1 ) received a single dose of 40 mg of polymorphic form c of ponesimod in either a capsule or a tablet formulation .
pharmacokinetic and safety variables ( clinical laboratory test results , vital signs , and an electrocardiogram ) were assessed.resultscomparison of the exposure to ponesimod following administration of the formulations in study 1 showed that the 90 % confidence intervals of the geometric mean ratios for the area under the curve from time zero to infinity ( auc0inf ) , the area under the curve from time zero to the time of the last measurable concentration ( auc0t ) , the terminal half - life ( t ) , and the maximum plasma concentration ( cmax ) were all within the 0.801.25 bioequivalence interval . in study 2 ,
more rapid absorption of ponesimod was observed from the tablet formulation than from the capsule formulation .
there were no relevant differences in the safety and tolerability profiles between the different formulations.conclusionthe two polymorphic forms of ponesimod and tablet versus capsule formulations were similar in terms of pharmacokinetics , safety , and tolerability .</s> |
the motivation for this work has been a renewed interest of theoretical physicists in basic statistical physics models , the ising and the dimer models .
let us mention two such recent promising works .
the first one is a new relation ( duality ) of topological strings and the dimer model , see e.g. @xcite .
the second one is a relation of the theory of discrete riemann surfaces @xcite and theta functions with criticality of the ising problem @xcite . in this paper
we present new formulas for the finite 3d dimer and 3d ising problems .
the formulas are obtained in a combinatorial way .
we hope that a profitable relation with the work mentioned above may be found .
a model we consider here is the _ ising version of the edwards - anderson model_. it can be described as follows .
a _ coupling constant _
@xmath0 is assigned to each bond @xmath1 of a given lattice graph g ; the coupling constant characterizes the interaction between the particles represented by sites @xmath2 and @xmath3 .
a physical state of the system is an assignment of spin @xmath4 to each site @xmath2 .
the _ hamiltonian _ ( or energy function ) is defined as @xmath5 .
the distribution of physical states over all possible energy levels is encapsulated in the _ partition function _
@xmath6 from which all fundamental physical quantities may be derived .
we may reformulate the ising problem in graph theoretic terms as follows .
a graph is a pair @xmath7 where @xmath8 is a set of _ vertices _ and @xmath9 is now the set of edges ( not the energy ) .
a graph with some regularity properties may be called a _
lattice graph_. we associate with each edge @xmath10 of @xmath11 a weight @xmath12 and for a subset of edges @xmath13 , @xmath14 will denote the sum of the weights @xmath12 associated with the edges in @xmath15 .
an _ even subgraph _ of a graph @xmath7 is a set of edges @xmath16 such that each vertex of @xmath8 is incident with an even number of edges from @xmath17 .
the _ generating function of even subgraphs _
@xmath18 equals the sum of @xmath19 over all even subgraphs @xmath17 of @xmath11 .
a classic relation between the ising partition function and the generating function of even subgraphs of the same graph states that @xmath20 a subset of edges @xmath21 is called a _ perfect matching _ or _ dimer arrangement _ if each vertex belongs to exactly one element of @xmath22 .
the _ dimer partition function _ on graph @xmath11 may be viewed as a polynomial @xmath23 which equals the sum of @xmath24 over all perfect matchings @xmath22 of @xmath11 .
this polynomial is also called the _ generating function of perfect matchings_. the generating functions of even subgraphs and perfect matchings may be defined in a more general way as follows : associate a variable @xmath25 with each edge @xmath10 of graph @xmath11 , let @xmath26 and let e.g. the generating function of perfect matchings be the sum of @xmath27 , @xmath22 perfect matching of @xmath11 .
all results introduced in this paper also hold in this more general setting ; however the presentation using weights rather than variables is perhaps more natural .
this paper studies properties of finite cubic lattices .
let us now fix some notation for them .
illustration of the linear order of vertices on a lattice @xmath28.,width=245 ] let @xmath29 be positive integers , where @xmath30 is even and @xmath31 and @xmath32 odd .
the cubic lattice @xmath33 is the following graph : + the vertices are : + @xmath34 , @xmath35 , @xmath36 , @xmath37 .
+ the edges are : * the _ vertical _ edges @xmath38 , + @xmath39 , * the _ width _ edges @xmath40 , + @xmath41 , * the _ horizontal _ edges @xmath42 , + @xmath43 . [ lin_order ]
we now fix as in fig .
[ fig - orde ] a _ linear order _
@xmath44 on the set of the vertices of @xmath45 as @xmath46 where @xmath47 and @xmath48 denotes the reversal of @xmath49 . for fixed @xmath10 ( @xmath50 is even ) in a given layer @xmath51
are marked all possible @xmath52 ( @xmath53 is odd ) to be in pair with @xmath10.,width=226 ] [ r(q ) ] let us now define a _ set of pairs of edges _ @xmath54 .
we let @xmath55 be the set of all horizontal edges . for each @xmath56
we let @xmath57 consist of all width edges with their x - coordinate equal to @xmath58 .
we call sets @xmath55 and @xmath57 _ layers _ of @xmath45 .
it is convenient to depict the edges of a layer as the horizontal edges of a square grid , where lower left corner is the smallest in the fixed ordering of vertices .
the first column of the layer @xmath55 is ordered according to the fixed ordering of vertices .
size of layer @xmath55 is @xmath59 , sizes of all @xmath57 are @xmath60 .
if @xmath10 is an edge of such a layer @xmath51 then let @xmath50 ( @xmath61 respectively ) denote the horizontal ( vertical respectively ) coordinate of the first vertex of @xmath10 in @xmath51 .
for a layer @xmath51 we let @xmath62 be the set of all pairs @xmath63 of edges of @xmath51 such that @xmath64 , and @xmath50 is even while @xmath53 is odd , example on fig .
[ fig - sign ] .
finally we let @xmath54 to be the union of @xmath62 over all layers of @xmath45 .
our result here is a simplification of the main result of @xcite .
the reader is heartily encouraged to check the original statement for a comparison . before we write the main theorems
let us introduce some necessary notation .
@xmath45 is a bipartite graph , which means that its vertices may be partitioned into two sets @xmath65 such that if @xmath10 is an edge of @xmath45 then @xmath66 . we have @xmath67 .
let @xmath68 be the square @xmath69 matrix defined by @xmath70 if @xmath71 is not any edge of @xmath45 .
if @xmath72 is an edge of @xmath45 ( @xmath73 , @xmath74 ) then @xmath75 if @xmath76 ( in fixed linear order ) and @xmath77 if @xmath78 .
we will consider matrix @xmath68 with its rows and columns ordered in agreement with the fixed ordering and we will assume that @xmath79 . a _
signing _ of a matrix is obtained by multiplying some of the entries of the matrix by @xmath80 .
an orientation of a graph @xmath7 is a _
digraph _ @xmath81 obtained from @xmath11 by assigning an orientation to each edge of @xmath11 , i.e. by ordering the elements of each edge of @xmath11 .
the elements of @xmath15 are called _
arcs_. we say that signing @xmath82 of @xmath68 corresponds to orientation @xmath83 of @xmath45 if @xmath84 for @xmath85 and @xmath78 .
for arc @xmath86 of orientation @xmath83 of @xmath45 we let @xmath87 if @xmath76 , and @xmath88 otherwise .
[ thm.uno ] the dimer partition function @xmath89 is @xmath90 where the sum is over all orientations of @xmath45 with all vertical edges positive , and @xmath91 .
knowing the proof theorem [ thm.uno ] can be easily rewritten as [ thm.dos ] @xmath92 where @xmath93 is the unique perfect matching of @xmath45 consisting of vertical edges only and @xmath94 equals the average of @xmath95 over all orientations @xmath83 of @xmath45 satisfying : @xmath96 is even ( and again all vertical edges are positive ) .
there are @xmath97 orientations to be sum over in theorem [ thm.uno ] and @xmath98 terms in theorem [ thm.dos ] to be averaged over .
therefore the exact numerical analysis is probably not possible .
we just tested theorem [ thm.uno ] for small planar lattices .
however it could be interesting to study statistical properties of determinants @xmath95 .
let us remark here also that theorem [ thm.uno ] for a planar graph ( 2d ising model , @xmath99 ) is still nontrivial , a question remains how to reduce it to the kasteleyn s one determinant . and
would it be possible to apply similar reduction even for the non - planar graph ?
the theory described in section [ sec.draw ] combined with the results of @xcite yields an expression of the 3d ising partition function as a linear combination of products over aperiodic closed walks on @xmath45 . we get a remarkably simple formula , analogous to the statement for the dimer partition function .
let @xmath7 be a planar graph embedded in the plane and for each edge @xmath10 let @xmath25 be an associate variable .
let @xmath100 be an arbitrary orientation of @xmath11 .
if @xmath101 then @xmath102 will denote the orientation of @xmath10 in @xmath103 and @xmath104 will be the reversed directed edge to @xmath105 .
we let @xmath106 .
a circular sequence @xmath107 is called _ non - periodic closed walk _ if the following conditions are satisfied : @xmath108 , @xmath109 and @xmath110 for some sequence @xmath82 and @xmath111 .
we let @xmath112 .
we further let @xmath113 , where @xmath114 is a _ rotation number _ of @xmath115 , i.e. the number of integral revolutions of the tangent vector .
finally let @xmath116
. now assume @xmath115 is a closed aperiodic walk in 3d cubic lattice @xmath45
. can we define its rotation number ?
the following construction provides a solution .
assume some vertices of planar graph @xmath11 embedded in the plane of degree @xmath117 are marked .
then we call a walk @xmath115 _ correct _ if it satisfies the crossover condition at each marked vertex , i.e. it never enters and exits a marked vertex in a pair of neighbouring edges along the vertex .
we naturally get a planar graph from @xmath45 if we consider @xmath45 drawn as bold @xmath118 in figure [ cube ] and put a new vertex to each edge - crossing .
these new vertices will form the set of the marked vertices .
clearly there is a natural bijection which associates to each walk @xmath115 of @xmath45 the corresponding correct walk @xmath119 in the new graph and we define rotation of @xmath115 to be equal to rotation of @xmath119 .
this defines @xmath120 for each closed aperiodic walk @xmath115 in @xmath45 . there is a natural equivalence on non - periodic closed walks :
@xmath115 is equivalent with reversed @xmath115 .
each equivalence class has two elements and will be denoted by @xmath121 $ ] .
we let @xmath122)=w(p)$ ] and note that this definition is correct since equivalent walks have the same sign .
we denote by @xmath123)$ ] the formal infinite product of @xmath124)$ ] over all equivalence classes of non - periodic closed walks of @xmath11 .
let @xmath83 be an orientation of @xmath45 .
we further let @xmath125)= \prod(1+w([p])|_{x_e= \sign(d , e)\alpha^{w_e}}.\ ] ] [ thm.tres ] generating function of even subgraphs is @xmath126),\ ] ] where the sum is over the orientations of @xmath45 with all the vertical edges positive .
* theorem [ thm.tres ] expresses the 3d ising partition function as a linear combination of infinite products over aperiodic closed walks . for planar lattice
this reduces to just one infinite product ( conjectured by feynman , proved in @xcite ) which provides an equivalence of planar ising model with the quantum field theory of free fermion .
there have been several attempts to generalize this equivalence for 3d .
earlier papers ( e.g. @xcite ) attempt to replace closed aperiodic walks by 2d surfaces .
recent promising development mentioned in the introduction deals with discrete riemann surfaces and the theta function : it is known that the planar ising partition function in the thermodynamical limit behaves like a common term times a riemann theta function . for torus
, @xcite asserts that in the thermodynamic limit and near to criticality , the ising partition function behaves like a common term times a linear combination of four riemann theta functions corresponding to torus . in @xcite and @xcite
, there is evidence that for the critical ising model , the dependence of the determinants of adjacency matrices on the kasteleyn orientations is exactly the same as the dependence of the determinants of the dirac operator , of the corresponding conformal field theory , on the spin structures of the 2d riemann surface ; this is given in terms of theta functions of half - integer characteristics .
we believe that theorem [ thm.tres ] may provide a new insight into these efforts .
in this section we describe how we draw cubic lattices on 2-dimensional surfaces .
[ def.surface ] a _ surface polygonal representation _ @xmath127 of an orientable 2d surface of genus @xmath128 consists of a _ base _ @xmath129 and @xmath130 _ bridges _
@xmath131 , @xmath132 and @xmath133 , where * @xmath129 is a convex @xmath134-gon with vertices @xmath135 numbered clockwise ; * @xmath136 , @xmath137 , is a @xmath117-gon with vertices @xmath138 numbered clockwise .
it is glued with @xmath129 so that the edge @xmath139 $ ] of @xmath136 is identified with the edge @xmath140 $ ] of @xmath129 and the edge @xmath141 $ ] of @xmath136 is identified with the edge @xmath142 $ ] of @xmath129 ; * @xmath143 , @xmath137 , is a @xmath117-gon with vertices @xmath144 numbered clockwise .
it is glued with @xmath129 so that the edge @xmath145 $ ] of @xmath143 is identified with the edge @xmath146 $ ] of @xmath129 and the edge @xmath147 $ ] of @xmath143 is identified with the edge @xmath148 $ ] of @xmath129 .
indexing is @xmath149 .
[ def.embed ] a graph @xmath11 is called a _ @xmath128-graph _ if it is embedded on @xmath127 so that all the vertices belong to the base @xmath129 , and the embedding of each edge uses at most one bridge .
we denote the set of the edges embedded entirely on the base by @xmath150 and the set of the edges embedded on each bridge @xmath131 by @xmath151 , @xmath152 @xmath133 .
moreover the following conditions need to be satisfied . 1 .
the outer face of @xmath153 is a cycle , and it is embedded on the boundary of @xmath129 , 2 . if @xmath154 then @xmath10 is embedded entirely on @xmath136 with one end - vertex belonging to @xmath139 $ ] and the other one to @xmath141 $ ] .
analogously for @xmath155 .
we need a generalization of the notion of a @xmath128-graph .
[ def.geng ] any graph @xmath11 obtained by the following construction will be called _
generalized g - graph_. 1 .
let @xmath156 be a partition of @xmath128 into positive integers .
2 . let @xmath157 be a polygonal representation of a surface of genus @xmath158 , @xmath159 .
let us denote the basis and the bridges of @xmath157 by @xmath160 and @xmath161 , @xmath159 , @xmath162 and @xmath163 .
3 . for @xmath159
let @xmath164 be a @xmath158-graph with the property that the subgraph of @xmath164 embedded on @xmath165 is a cycle , embedded on the boundary of @xmath165 .
let us denote it by @xmath166 .
4 . let @xmath167 be a @xmath168-connected graph properly embedded on the plane and let @xmath169 be a subset of the faces of @xmath167 .
let @xmath170 be the cycle bounding @xmath171 , @xmath159 .
let each @xmath170 be isomorphic to @xmath166 .
then @xmath11 is obtained by gluing the @xmath164 s into @xmath167 so that each @xmath170 is identified with @xmath172 .
* orientations .
* let @xmath11 be a @xmath128-graph and let @xmath173 .
an orientation @xmath174 of @xmath167 such that each inner face of each @xmath168-connected component of @xmath167 is clockwise odd in @xmath174 is called a _ basic orientation _ of @xmath167 .
note that a basic orientation always exists for a planar graph .
further we define the orientation @xmath175 of each @xmath176 as follows : we consider @xmath176 embedded on the plane by the planar projection of @xmath151 outside @xmath129 , and complete the basic orientation @xmath174 of @xmath167 to an orientation of @xmath176 so that each inner face of each @xmath168-connected component of @xmath176 is clockwise odd . the orientation @xmath177 is defined by complete reversing of the orientation @xmath175 of @xmath176 .
observe that after fixing a basic orientation @xmath174 , the orientation @xmath175 is uniquely determined for each @xmath178 .
[ def.r ] let @xmath11 be a @xmath128-graph , @xmath179 .
an orientation @xmath83 of @xmath11 which equals the _ basic orientation _
@xmath174 on @xmath167 and which equals @xmath175 or @xmath177 on @xmath151 is called _
relevant_. we define its _ type _ @xmath180 as follows : for @xmath181 and @xmath182 , @xmath183 equals @xmath184 or @xmath80 according to the sign of @xmath185 in @xmath83
. moreover we let @xmath186 equal the product of @xmath187 , @xmath188 , where @xmath189 and @xmath190 and @xmath191 .
observe that @xmath192 , where @xmath193 .
for each generalized g - graph @xmath11 we can define @xmath194 relevant orientations @xmath195 with respect to a fixed basic orientation of @xmath167 , and coefficients @xmath196 , @xmath159 in the same way as for a g - graph .
now we write theorem proved in @xcite which will be essential in proof of theorem [ thm.uno ] .
[ thm_gl ] let g be a generalized g - graph with a perfect matching @xmath197 of @xmath167 .
let @xmath174 be a basic orientation of @xmath167 . if we order the vertexes of @xmath11 so that @xmath198 is positive then @xmath199 where @xmath200 are all the relevant orientations of @xmath11 .
definition of @xmath198 follows from definition of _
pfaffian_. let @xmath7 be a graph with @xmath201 vertices and @xmath83 an orientation of @xmath11 . denote by @xmath202 the skew - symmetric matrix with the rows and the columns indexed by @xmath8 , where @xmath203 in case @xmath204 is an arc of @xmath83 , @xmath205 in case @xmath206 is an arc of @xmath83 , and @xmath207 otherwise . [ def_pf ] the _ pfaffian _ is defined as @xmath208 where @xmath209 is a partition of the set @xmath210 into pairs , @xmath211 for @xmath212 , and @xmath213 equals the sign of the permutation @xmath214 of @xmath215 . each nonzero term of the expansion of the pfaffian equals @xmath24 or @xmath216 where @xmath22 is a perfect matching of @xmath11 . if @xmath217 denote the sign of the term @xmath24 in the expansion , we may write @xmath218 in this subsection we will describe how to realize @xmath219 as a subgraph of a generalized g - graph .
let us denote by @xmath220 the larger lattice @xmath221 .
+ * how to draw @xmath220 on the plane .
* first draw the paths @xmath49 along a cycle in the linear order as in def .
[ lin_order ] .
next , draw the horizontal edges inside this cycle , and the width edges outside of this cycle as depicted in fig .
[ cube ] below where @xmath222 is properly drawn .
the figure also shows how @xmath223 is embeded in @xmath224 .
we keep the following rule : the interiors of the curves representing @xmath225 and @xmath226 ( @xmath227 and @xmath228 respectively ) intersect if and only if @xmath229 is even .
we denote by @xmath230 the curve representing edge @xmath10 .
drawing of a cube @xmath231 in a plane.,width=340 ] * now we modify @xmath220 into a generalized g - graph @xmath232 .
* we introduce new vertices to some edge - crossings of @xmath220 and delete and subdivide some edges . in this way
we obtain a generalised g - graph @xmath232 with an even subdivision of @xmath233 as its subgraph .
the construction is analogous and independent for each plane , and so we describe it only for a plane @xmath57 .
the construction is described by fig .
[ cons_q ] for the edges between @xmath234 and between @xmath235 , for @xmath58 odd and @xmath236 even .
construction of @xmath232 for part of the plane @xmath57 ( @xmath58 odd ) , @xmath237 ( @xmath238 even).,width=415 ] 1 .
for each @xmath238 even let @xmath239 odd @xmath240 .
for each edge @xmath10 of @xmath241 introduce a new vertex to each intersection of @xmath230 with the curves representing the edges of @xmath242 , where @xmath243 in case @xmath244 and @xmath245 otherwise . by this operation ,
each @xmath246 is replaced by a path .
call each edge of this path _ auxiliary_. 2 . for
each @xmath238 even let @xmath247 , where @xmath248 in case @xmath244 and @xmath249 otherwise .
for each edge @xmath10 of @xmath250 introduce a new vertex to each intersection of @xmath230 with the curves representing the edges of @xmath251 .
hence each @xmath252 is replaced by a path .
call each edge of this path _ auxiliary_. for each @xmath238 even the edges @xmath253 and also @xmath254 will also be called _
auxiliary_. in figure [ cons_q ] , the auxiliary edges are represented by dashed lines .
the edges @xmath227 , @xmath238 even and @xmath229 even will be called _ relevant _ for @xmath45 . if @xmath244 then the relevant edges are subdivided by two vertices ( added in 2 . ) into three edges of @xmath232 . the middle one will be called _ special _ and the other two _
long_. if @xmath255 then the relevant edge @xmath227 is subdivided by one vertex into two edges of @xmath232 .
the one incident to @xmath256 will be called _ special _ and the other one _
long_. if @xmath10 is a relevant edge of @xmath45 , then we choose a initial long edge @xmath257 and we let @xmath258 .
we let the weight of the special edge and of the remaining long edge be equal to 0 .
the edges of @xmath259 also got subdivided by new vertices introduced in step 1 and step 2 .
we delete all edges of the paths obtained from @xmath260 and @xmath228 , @xmath261 odd , as well as we delete all vertexes in intersections of those edges with auxiliary edges . in figure
[ cons_q ] , the deleted edges are represented by dotted lines .
each edge @xmath262 even @xmath240 , is subdivided by new vertices introduced in step 1 into a path .
we let the weights assigned to the edges of the path equal 0 except of one initial edge whose weight is let equal @xmath12 .
the edge @xmath10 of this path such that the interior of @xmath230 does not intersect interior of any curve representing a long edge will also be _ special_. the others are called _
short_. 7 .
all vertical edges which are not auxiliary ( see fig.[cons_q ] ) will be called _
special_. in figure [ cons_q ] , the special edges are represented by normal lines .
let @xmath263 denote the set of all auxiliary edges .
then deletion of @xmath263 results in a subdivision of @xmath264 .
we subdivide some special edges ( vertical and border width ones ) so that the graph @xmath265 is an even subdivision of @xmath264 .
all these new edges will be special , and we set their weights equal 0 .
this finishes the construction . in figure
[ cons_q ] , the long and short edges are represented by fat lines .
* @xmath232 is a generalised g - graph . *
its planar part @xmath266 is set of all the auxiliary and special edges .
other edges ( i.e. the short and long ) are drawn on a face of @xmath266 and they may be drawn onto a pair of bridges above this face .
one bridge contains one long edge , and the other bridge contains all the short edges .
now let us set appropriate weights to all the auxiliary edges . in order to do that first subdivide and add some auxiliary edges and vertices to @xmath266 in such a way that there exists a matching @xmath267 of @xmath268 consisting of auxiliary edges , and a perfect matching @xmath197 of @xmath266 .
we set weights of edges from @xmath267 as @xmath269 .
weights of other auxiliary edges @xmath270 . with such properties of @xmath232
we have an important result : @xmath271 .
now we introduce a _ basic orientation _
@xmath272 of @xmath266 in order to prepare our stage to use the theorem [ thm_gl ] for the generalised g - graph @xmath232 .
orientation @xmath272 has the following properties : 1 .
@xmath272 on special edges is in agreement with the natural ordering ( def .
[ lin_order ] ) .
all the signs @xmath273 in pfaffian @xmath274 ( def .
[ def_pf ] ) are positive .
the orientation of edges on a bridge has positive sign if and only if it is in agreement with the natural ordering ( def .
[ lin_order ] ) .
the construction of such a @xmath272 is possible according to kasteleyn @xcite .
we use theorem [ thm_gl ] for the graph @xmath232 .
then we may write @xmath275 where the first equality is the result of previous section .
the second equality holds because of the theorem [ thm_gl ] .
the third equality holds because of the setting of the weights of edges in @xmath232 in the previous section . and
finally , orientation @xmath276 being induced on @xmath45 by @xmath200 on @xmath277 , the fourth equality follows from the three facts : setting of the weights of edges , @xmath277 is even subdivision of @xmath45 , it is possible to permute vertexes covered by @xmath267 so that the sign is correct . in section [ sub.det ]
we have defined for a bipartite graph @xmath11 a matrix @xmath278 depending on a orientation @xmath83 .
it is easy to check that for @xmath45 holds @xmath279 . to proceed in proof of theorem [ thm.uno ] we have to establish the dependence of @xmath196 on the orientation @xmath276 of @xmath45 and specify the orientations we sum over in the language of @xmath45 not @xmath232 .
each relevant orientation @xmath200 of @xmath232 is determined by the fixed basic orientation @xmath272 of @xmath266 , and by a pair of signs for each pair of bridges .
each pair of bridges is associated with one long edge and set of short edges of @xmath232 .
hence these signs may be given by specifying @xmath280 , for each long edge @xmath10 , where @xmath281 denotes the sign of the bridge containing @xmath10 , and @xmath282 denotes the sign of the other bridge containing the set of short edges .
the relevant edges @xmath283 and @xmath284 are associated with only one long edge of @xmath232 .
if @xmath10 is such relevant edge of @xmath45 , we will call it _ border edge _ , and we denote by @xmath285 the corresponding long edge .
we let @xmath286 .
each relevant non - border edge @xmath10 of @xmath45 has two long edges @xmath287 associated with it .
we let @xmath288 .
a _ relevant vector _ is any element @xmath289 of @xmath290^{\mathcal r}$ ] such that @xmath291 for each relevant border edge @xmath10 of @xmath45
. from the definition of @xmath196 and from properties of the generalized g - graph @xmath232 of genus @xmath128 follows that @xmath292 , where @xmath293 is number of faces of @xmath266 above them edges on both bridges are oriented in negative sense , i.e. against fixed ordering .
there is a natural bijection between relevant orientations of @xmath232 and relevant vectors .
if @xmath289 is a relevant vector , then let @xmath294 denote the corresponding relevant orientation of @xmath232 and let @xmath295 of a relevant vector @xmath289 be calculated as follows : @xmath296 .
there is @xmath297 relevant edges and @xmath298 border edges .
genus of @xmath232 is therefore @xmath299 .
there are @xmath300 relevant vectors .
let us consider a set @xmath301 of relevant orientations @xmath200 such that there is at least one relevant non - border edge @xmath10 with @xmath302 , i.e. orientation of bridges with short edges incident to @xmath10 are different .
[ sum_zero ] sum of contribution of all orientations from @xmath301 to @xmath303 is zero .
* proof : * for given orientation @xmath304 define a set @xmath305 .
now let fix a set o relevant edges @xmath306 and consider all orientations @xmath307 such that @xmath308 .
fix also one relevant edge @xmath309 .
remark : @xmath310 if @xmath311 and @xmath312 differs only in one relevant edge @xmath10 in such a way that @xmath313 and
@xmath314 , @xmath315 .
it is also that induced orientations @xmath316 .
using this remark for @xmath317 we have for every @xmath306 : @xmath318 the claim in proposition [ sum_zero ] follows directly .
@xmath319 let us call all @xmath320 _ useful orientations _ and from now we sum only over such orientations .
there is @xmath321 of useful orientations .
similarly we define useful relevant vectors .
[ all_d ] each orientation @xmath83 of @xmath45 , which agrees with the fixed order on vertical edges , corresponds to @xmath322 of useful orientations @xmath200 of @xmath232 and all those @xmath200 have the same sign @xmath196 .
* proof : * let @xmath289 be a useful vector . then @xmath323 determines uniquely @xmath324 and @xmath325 for each relevant edge @xmath10 and also @xmath326 for each relevant border edge @xmath257 .
hence @xmath323 determines uniquely @xmath327 for each relevant border edge @xmath257 .
moreover @xmath323 determines uniquely the product @xmath328 for each relevant non - border edge @xmath10 .
since there are @xmath329 relevant non - border edges , there is @xmath322 orientations @xmath200 corresponding to it .
let @xmath330 be useful and both lead to the same @xmath83 of @xmath45 .
then @xmath331 for each relevant non - border edge @xmath10 and @xmath332 and @xmath333 for each relevant border edge .
this implies that @xmath334 .
@xmath319 concluding from what we did till now we can write the dimer partition function as @xmath335 where the sum is over all orientations of @xmath45 with all vertical edges positive . at this point the only thing missing in proof of theorem [ thm.uno ]
is to concretize @xmath336 .
[ sgn_d ] @xmath337 , where the set of edges @xmath54 is defined in [ r(q ) ] .
* proof : * let us remind that @xmath338 where @xmath293 is number of faces with both bridges above them negative .
each non - border relevant edge @xmath10 corresponds to two faces with bridges .
the contribution of the two corresponding faces to sign could be negative only if orientation of @xmath10 is negative ( @xmath339 ) . and moreover if orientation of corresponding shot edges is negative ( @xmath340 ) .
it follows from the construction that this happen only if product of orientation of all @xmath52 ( as defined in [ r(q ) ] ) is negative .
considering all the relevant edges we get the claim of proposition [ sgn_d ] @xmath319 [ av ] the average of @xmath95 over all orientations of @xmath45 with all vertical edges fixed positive equals @xmath341 , where @xmath93 is perfect matching of @xmath45 consisting only from vertical edges .
* proof : * by the linearity of expectation the contribution of other than vertical edges cancel out when we calculate the average of @xmath95 .
since @xmath342 has exactly one perfect matching consisting of vertical edges only , proposition [ av ] follows .
@xmath319 there is @xmath97 orientation d in [ thm.uno ] to be summed over . and @xmath343 of them have positive sign .
proof : looking at figure [ fig - sign ] we can see that as soon as there is at least one relevant ( shaded ) edge negative there is so many orientation with positive as with negative sign . only if all the relevant edges are positive the sign is also positive .
it means there is @xmath344 more positive orientation then negative . by theorem [ thm.uno ] and proposition [ av ]
we have then @xmath345= -2^{c } \alpha^{w(m ) } + \mathcal e ( 2^{c}+1),\ ] ] where @xmath346 equals the average of @xmath95 over all @xmath83 of @xmath45 with positive sign . and theorem [ thm.dos ] is proved .
@xmath319 we use a straightforward reformulation of a theorem of @xcite : [ thm.prd ] let g be a generalized g - graph .
then @xmath347 ) , \ ] ] where @xmath200 are all the relevant orientations of @xmath11 , and rotation of @xmath115 and @xmath348)$ ] are defined in the same way as described for @xmath45 in section [ sub.prod ] .
proof of this theorem could be found in @xcite and for planar graphs in @xcite .
let @xmath349 be the relevant orientations of generalised g - graph @xmath232 .
if we apply theorem [ thm.prd ] to @xmath232 , from the choice of weights we get @xmath350).\ ] ] the same analysis as in the previous section finishes the proof of theorem [ thm.tres ] .
we express the finite 3d dimer partition function as a linear combination of determinants of oriented adjacency matrices in theorem [ thm.uno ] , and the finite 3d ising partition function as a linear combination of products over aperiodic closed walks in theorem [ thm.tres ] .
the methodology we use is embedding of cubic lattice on 2d surfaces of large genus . by this embedding cubic lattice
is transformed to a generalized g - graph
. then we use theorems from @xcite , which generalize approach of @xcite .
we believe this approach may relate to recent developments in conformal field theory @xcite and topological string theory @xcite , and ultimately teach us something about 3d basic statistical physics problems . | we express the finite 3d dimer partition function as a linear combination of determinants of oriented adjacency matrices , and the finite 3d ising partition sum as a linear combination of products over aperiodic closed walks .
the methodology we use is embedding of cubic lattice on 2d surfaces of large genus . | <s>[INST]the motivation for this work has been a renewed interest of theoretical physicists in basic statistical physics models , the ising and the dimer models .
let us mention two such recent promising works .
the first one is a new relation ( duality ) of topological strings and the dimer model , see e.g. @xcite .
the second one is a relation of the theory of discrete riemann surfaces @xcite and theta functions with criticality of the ising problem @xcite . in this paper
we present new formulas for the finite 3d dimer and 3d ising problems .
the formulas are obtained in a combinatorial way .
we hope that a profitable relation with the work mentioned above may be found .
a model we consider here is the _ ising version of the edwards - anderson model_. it can be described as follows .
a _ coupling constant _
@xmath0 is assigned to each bond @xmath1 of a given lattice graph g ; the coupling constant characterizes the interaction between the particles represented by sites @xmath2 and @xmath3 .
a physical state of the system is an assignment of spin @xmath4 to each site @xmath2 .
the _ hamiltonian _ ( or energy function ) is defined as @xmath5 .
the distribution of physical states over all possible energy levels is encapsulated in the _ partition function _
@xmath6 from which all fundamental physical quantities may be derived .
we may reformulate the ising problem in graph theoretic terms as follows .
a graph is a pair @xmath7 where @xmath8 is a set of _ vertices _ and @xmath9 is now the set of edges ( not the energy ) .
a graph with some regularity properties may be called a _
lattice graph_. we associate with each edge @xmath10 of @xmath11 a weight @xmath12 and for a subset of edges @xmath13 , @xmath14 will denote the sum of the weights @xmath12 associated with the edges in @xmath15 .
an _ even subgraph _ of a graph @xmath7 is a set of edges @xmath16 such that each vertex of @xmath8 is incident with an even number of edges from @xmath17 .
the _ generating function of even subgraphs _
@xmath18 equals the sum of @xmath19 over all even subgraphs @xmath17 of @xmath11 .
a classic relation between the ising partition function and the generating function of even subgraphs of the same graph states that @xmath20 a subset of edges @xmath21 is called a _ perfect matching _ or _ dimer arrangement _ if each vertex belongs to exactly one element of @xmath22 .
the _ dimer partition function _ on graph @xmath11 may be viewed as a polynomial @xmath23 which equals the sum of @xmath24 over all perfect matchings @xmath22 of @xmath11 .
this polynomial is also called the _ generating function of perfect matchings_. the generating functions of even subgraphs and perfect matchings may be defined in a more general way as follows : associate a variable @xmath25 with each edge @xmath10 of graph @xmath11 , let @xmath26 and let e.g. the generating function of perfect matchings be the sum of @xmath27 , @xmath22 perfect matching of @xmath11 .
all results introduced in this paper also hold in this more general setting ; however the presentation using weights rather than variables is perhaps more natural .
this paper studies properties of finite cubic lattices .
let us now fix some notation for them .
illustration of the linear order of vertices on a lattice @xmath28.,width=245 ] let @xmath29 be positive integers , where @xmath30 is even and @xmath31 and @xmath32 odd .
the cubic lattice @xmath33 is the following graph : + the vertices are : + @xmath34 , @xmath35 , @xmath36 , @xmath37 .
+ the edges are : * the _ vertical _ edges @xmath38 , + @xmath39 , * the _ width _ edges @xmath40 , + @xmath41 , * the _ horizontal _ edges @xmath42 , + @xmath43 . [ lin_order ]
we now fix as in fig .
[ fig - orde ] a _ linear order _
@xmath44 on the set of the vertices of @xmath45 as @xmath46 where @xmath47 and @xmath48 denotes the reversal of @xmath49 . for fixed @xmath10 ( @xmath50 is even ) in a given layer @xmath51
are marked all possible @xmath52 ( @xmath53 is odd ) to be in pair with @xmath10.,width=226 ] [ r(q ) ] let us now define a _ set of pairs of edges _ @xmath54 .
we let @xmath55 be the set of all horizontal edges . for each @xmath56
we let @xmath57 consist of all width edges with their x - coordinate equal to @xmath58 .
we call sets @xmath55 and @xmath57 _ layers _ of @xmath45 .
it is convenient to depict the edges of a layer as the horizontal edges of a square grid , where lower left corner is the smallest in the fixed ordering of vertices .
the first column of the layer @xmath55 is ordered according to the fixed ordering of vertices .
size of layer @xmath55 is @xmath59 , sizes of all @xmath57 are @xmath60 .
if @xmath10 is an edge of such a layer @xmath51 then let @xmath50 ( @xmath61 respectively ) denote the horizontal ( vertical respectively ) coordinate of the first vertex of @xmath10 in @xmath51 .
for a layer @xmath51 we let @xmath62 be the set of all pairs @xmath63 of edges of @xmath51 such that @xmath64 , and @xmath50 is even while @xmath53 is odd , example on fig .
[ fig - sign ] .
finally we let @xmath54 to be the union of @xmath62 over all layers of @xmath45 .
our result here is a simplification of the main result of @xcite .
the reader is heartily encouraged to check the original statement for a comparison . before we write the main theorems
let us introduce some necessary notation .
@xmath45 is a bipartite graph , which means that its vertices may be partitioned into two sets @xmath65 such that if @xmath10 is an edge of @xmath45 then @xmath66 . we have @xmath67 .
let @xmath68 be the square @xmath69 matrix defined by @xmath70 if @xmath71 is not any edge of @xmath45 .
if @xmath72 is an edge of @xmath45 ( @xmath73 , @xmath74 ) then @xmath75 if @xmath76 ( in fixed linear order ) and @xmath77 if @xmath78 .
we will consider matrix @xmath68 with its rows and columns ordered in agreement with the fixed ordering and we will assume that @xmath79 . a _
signing _ of a matrix is obtained by multiplying some of the entries of the matrix by @xmath80 .
an orientation of a graph @xmath7 is a _
digraph _ @xmath81 obtained from @xmath11 by assigning an orientation to each edge of @xmath11 , i.e. by ordering the elements of each edge of @xmath11 .
the elements of @xmath15 are called _
arcs_. we say that signing @xmath82 of @xmath68 corresponds to orientation @xmath83 of @xmath45 if @xmath84 for @xmath85 and @xmath78 .
for arc @xmath86 of orientation @xmath83 of @xmath45 we let @xmath87 if @xmath76 , and @xmath88 otherwise .
[ thm.uno ] the dimer partition function @xmath89 is @xmath90 where the sum is over all orientations of @xmath45 with all vertical edges positive , and @xmath91 .
knowing the proof theorem [ thm.uno ] can be easily rewritten as [ thm.dos ] @xmath92 where @xmath93 is the unique perfect matching of @xmath45 consisting of vertical edges only and @xmath94 equals the average of @xmath95 over all orientations @xmath83 of @xmath45 satisfying : @xmath96 is even ( and again all vertical edges are positive ) .
there are @xmath97 orientations to be sum over in theorem [ thm.uno ] and @xmath98 terms in theorem [ thm.dos ] to be averaged over .
therefore the exact numerical analysis is probably not possible .
we just tested theorem [ thm.uno ] for small planar lattices .
however it could be interesting to study statistical properties of determinants @xmath95 .
let us remark here also that theorem [ thm.uno ] for a planar graph ( 2d ising model , @xmath99 ) is still nontrivial , a question remains how to reduce it to the kasteleyn s one determinant . and
would it be possible to apply similar reduction even for the non - planar graph ?
the theory described in section [ sec.draw ] combined with the results of @xcite yields an expression of the 3d ising partition function as a linear combination of products over aperiodic closed walks on @xmath45 . we get a remarkably simple formula , analogous to the statement for the dimer partition function .
let @xmath7 be a planar graph embedded in the plane and for each edge @xmath10 let @xmath25 be an associate variable .
let @xmath100 be an arbitrary orientation of @xmath11 .
if @xmath101 then @xmath102 will denote the orientation of @xmath10 in @xmath103 and @xmath104 will be the reversed directed edge to @xmath105 .
we let @xmath106 .
a circular sequence @xmath107 is called _ non - periodic closed walk _ if the following conditions are satisfied : @xmath108 , @xmath109 and @xmath110 for some sequence @xmath82 and @xmath111 .
we let @xmath112 .
we further let @xmath113 , where @xmath114 is a _ rotation number _ of @xmath115 , i.e. the number of integral revolutions of the tangent vector .
finally let @xmath116
. now assume @xmath115 is a closed aperiodic walk in 3d cubic lattice @xmath45
. can we define its rotation number ?
the following construction provides a solution .
assume some vertices of planar graph @xmath11 embedded in the plane of degree @xmath117 are marked .
then we call a walk @xmath115 _ correct _ if it satisfies the crossover condition at each marked vertex , i.e. it never enters and exits a marked vertex in a pair of neighbouring edges along the vertex .
we naturally get a planar graph from @xmath45 if we consider @xmath45 drawn as bold @xmath118 in figure [ cube ] and put a new vertex to each edge - crossing .
these new vertices will form the set of the marked vertices .
clearly there is a natural bijection which associates to each walk @xmath115 of @xmath45 the corresponding correct walk @xmath119 in the new graph and we define rotation of @xmath115 to be equal to rotation of @xmath119 .
this defines @xmath120 for each closed aperiodic walk @xmath115 in @xmath45 . there is a natural equivalence on non - periodic closed walks :
@xmath115 is equivalent with reversed @xmath115 .
each equivalence class has two elements and will be denoted by @xmath121 $ ] .
we let @xmath122)=w(p)$ ] and note that this definition is correct since equivalent walks have the same sign .
we denote by @xmath123)$ ] the formal infinite product of @xmath124)$ ] over all equivalence classes of non - periodic closed walks of @xmath11 .
let @xmath83 be an orientation of @xmath45 .
we further let @xmath125)= \prod(1+w([p])|_{x_e= \sign(d , e)\alpha^{w_e}}.\ ] ] [ thm.tres ] generating function of even subgraphs is @xmath126),\ ] ] where the sum is over the orientations of @xmath45 with all the vertical edges positive .
* theorem [ thm.tres ] expresses the 3d ising partition function as a linear combination of infinite products over aperiodic closed walks . for planar lattice
this reduces to just one infinite product ( conjectured by feynman , proved in @xcite ) which provides an equivalence of planar ising model with the quantum field theory of free fermion .
there have been several attempts to generalize this equivalence for 3d .
earlier papers ( e.g. @xcite ) attempt to replace closed aperiodic walks by 2d surfaces .
recent promising development mentioned in the introduction deals with discrete riemann surfaces and the theta function : it is known that the planar ising partition function in the thermodynamical limit behaves like a common term times a riemann theta function . for torus
, @xcite asserts that in the thermodynamic limit and near to criticality , the ising partition function behaves like a common term times a linear combination of four riemann theta functions corresponding to torus . in @xcite and @xcite
, there is evidence that for the critical ising model , the dependence of the determinants of adjacency matrices on the kasteleyn orientations is exactly the same as the dependence of the determinants of the dirac operator , of the corresponding conformal field theory , on the spin structures of the 2d riemann surface ; this is given in terms of theta functions of half - integer characteristics .
we believe that theorem [ thm.tres ] may provide a new insight into these efforts .
in this section we describe how we draw cubic lattices on 2-dimensional surfaces .
[ def.surface ] a _ surface polygonal representation _ @xmath127 of an orientable 2d surface of genus @xmath128 consists of a _ base _ @xmath129 and @xmath130 _ bridges _
@xmath131 , @xmath132 and @xmath133 , where * @xmath129 is a convex @xmath134-gon with vertices @xmath135 numbered clockwise ; * @xmath136 , @xmath137 , is a @xmath117-gon with vertices @xmath138 numbered clockwise .
it is glued with @xmath129 so that the edge @xmath139 $ ] of @xmath136 is identified with the edge @xmath140 $ ] of @xmath129 and the edge @xmath141 $ ] of @xmath136 is identified with the edge @xmath142 $ ] of @xmath129 ; * @xmath143 , @xmath137 , is a @xmath117-gon with vertices @xmath144 numbered clockwise .
it is glued with @xmath129 so that the edge @xmath145 $ ] of @xmath143 is identified with the edge @xmath146 $ ] of @xmath129 and the edge @xmath147 $ ] of @xmath143 is identified with the edge @xmath148 $ ] of @xmath129 .
indexing is @xmath149 .
[ def.embed ] a graph @xmath11 is called a _ @xmath128-graph _ if it is embedded on @xmath127 so that all the vertices belong to the base @xmath129 , and the embedding of each edge uses at most one bridge .
we denote the set of the edges embedded entirely on the base by @xmath150 and the set of the edges embedded on each bridge @xmath131 by @xmath151 , @xmath152 @xmath133 .
moreover the following conditions need to be satisfied . 1 .
the outer face of @xmath153 is a cycle , and it is embedded on the boundary of @xmath129 , 2 . if @xmath154 then @xmath10 is embedded entirely on @xmath136 with one end - vertex belonging to @xmath139 $ ] and the other one to @xmath141 $ ] .
analogously for @xmath155 .
we need a generalization of the notion of a @xmath128-graph .
[ def.geng ] any graph @xmath11 obtained by the following construction will be called _
generalized g - graph_. 1 .
let @xmath156 be a partition of @xmath128 into positive integers .
2 . let @xmath157 be a polygonal representation of a surface of genus @xmath158 , @xmath159 .
let us denote the basis and the bridges of @xmath157 by @xmath160 and @xmath161 , @xmath159 , @xmath162 and @xmath163 .
3 . for @xmath159
let @xmath164 be a @xmath158-graph with the property that the subgraph of @xmath164 embedded on @xmath165 is a cycle , embedded on the boundary of @xmath165 .
let us denote it by @xmath166 .
4 . let @xmath167 be a @xmath168-connected graph properly embedded on the plane and let @xmath169 be a subset of the faces of @xmath167 .
let @xmath170 be the cycle bounding @xmath171 , @xmath159 .
let each @xmath170 be isomorphic to @xmath166 .
then @xmath11 is obtained by gluing the @xmath164 s into @xmath167 so that each @xmath170 is identified with @xmath172 .
* orientations .
* let @xmath11 be a @xmath128-graph and let @xmath173 .
an orientation @xmath174 of @xmath167 such that each inner face of each @xmath168-connected component of @xmath167 is clockwise odd in @xmath174 is called a _ basic orientation _ of @xmath167 .
note that a basic orientation always exists for a planar graph .
further we define the orientation @xmath175 of each @xmath176 as follows : we consider @xmath176 embedded on the plane by the planar projection of @xmath151 outside @xmath129 , and complete the basic orientation @xmath174 of @xmath167 to an orientation of @xmath176 so that each inner face of each @xmath168-connected component of @xmath176 is clockwise odd . the orientation @xmath177 is defined by complete reversing of the orientation @xmath175 of @xmath176 .
observe that after fixing a basic orientation @xmath174 , the orientation @xmath175 is uniquely determined for each @xmath178 .
[ def.r ] let @xmath11 be a @xmath128-graph , @xmath179 .
an orientation @xmath83 of @xmath11 which equals the _ basic orientation _
@xmath174 on @xmath167 and which equals @xmath175 or @xmath177 on @xmath151 is called _
relevant_. we define its _ type _ @xmath180 as follows : for @xmath181 and @xmath182 , @xmath183 equals @xmath184 or @xmath80 according to the sign of @xmath185 in @xmath83
. moreover we let @xmath186 equal the product of @xmath187 , @xmath188 , where @xmath189 and @xmath190 and @xmath191 .
observe that @xmath192 , where @xmath193 .
for each generalized g - graph @xmath11 we can define @xmath194 relevant orientations @xmath195 with respect to a fixed basic orientation of @xmath167 , and coefficients @xmath196 , @xmath159 in the same way as for a g - graph .
now we write theorem proved in @xcite which will be essential in proof of theorem [ thm.uno ] .
[ thm_gl ] let g be a generalized g - graph with a perfect matching @xmath197 of @xmath167 .
let @xmath174 be a basic orientation of @xmath167 . if we order the vertexes of @xmath11 so that @xmath198 is positive then @xmath199 where @xmath200 are all the relevant orientations of @xmath11 .
definition of @xmath198 follows from definition of _
pfaffian_. let @xmath7 be a graph with @xmath201 vertices and @xmath83 an orientation of @xmath11 . denote by @xmath202 the skew - symmetric matrix with the rows and the columns indexed by @xmath8 , where @xmath203 in case @xmath204 is an arc of @xmath83 , @xmath205 in case @xmath206 is an arc of @xmath83 , and @xmath207 otherwise . [ def_pf ] the _ pfaffian _ is defined as @xmath208 where @xmath209 is a partition of the set @xmath210 into pairs , @xmath211 for @xmath212 , and @xmath213 equals the sign of the permutation @xmath214 of @xmath215 . each nonzero term of the expansion of the pfaffian equals @xmath24 or @xmath216 where @xmath22 is a perfect matching of @xmath11 . if @xmath217 denote the sign of the term @xmath24 in the expansion , we may write @xmath218 in this subsection we will describe how to realize @xmath219 as a subgraph of a generalized g - graph .
let us denote by @xmath220 the larger lattice @xmath221 .
+ * how to draw @xmath220 on the plane .
* first draw the paths @xmath49 along a cycle in the linear order as in def .
[ lin_order ] .
next , draw the horizontal edges inside this cycle , and the width edges outside of this cycle as depicted in fig .
[ cube ] below where @xmath222 is properly drawn .
the figure also shows how @xmath223 is embeded in @xmath224 .
we keep the following rule : the interiors of the curves representing @xmath225 and @xmath226 ( @xmath227 and @xmath228 respectively ) intersect if and only if @xmath229 is even .
we denote by @xmath230 the curve representing edge @xmath10 .
drawing of a cube @xmath231 in a plane.,width=340 ] * now we modify @xmath220 into a generalized g - graph @xmath232 .
* we introduce new vertices to some edge - crossings of @xmath220 and delete and subdivide some edges . in this way
we obtain a generalised g - graph @xmath232 with an even subdivision of @xmath233 as its subgraph .
the construction is analogous and independent for each plane , and so we describe it only for a plane @xmath57 .
the construction is described by fig .
[ cons_q ] for the edges between @xmath234 and between @xmath235 , for @xmath58 odd and @xmath236 even .
construction of @xmath232 for part of the plane @xmath57 ( @xmath58 odd ) , @xmath237 ( @xmath238 even).,width=415 ] 1 .
for each @xmath238 even let @xmath239 odd @xmath240 .
for each edge @xmath10 of @xmath241 introduce a new vertex to each intersection of @xmath230 with the curves representing the edges of @xmath242 , where @xmath243 in case @xmath244 and @xmath245 otherwise . by this operation ,
each @xmath246 is replaced by a path .
call each edge of this path _ auxiliary_. 2 . for
each @xmath238 even let @xmath247 , where @xmath248 in case @xmath244 and @xmath249 otherwise .
for each edge @xmath10 of @xmath250 introduce a new vertex to each intersection of @xmath230 with the curves representing the edges of @xmath251 .
hence each @xmath252 is replaced by a path .
call each edge of this path _ auxiliary_. for each @xmath238 even the edges @xmath253 and also @xmath254 will also be called _
auxiliary_. in figure [ cons_q ] , the auxiliary edges are represented by dashed lines .
the edges @xmath227 , @xmath238 even and @xmath229 even will be called _ relevant _ for @xmath45 . if @xmath244 then the relevant edges are subdivided by two vertices ( added in 2 . ) into three edges of @xmath232 . the middle one will be called _ special _ and the other two _
long_. if @xmath255 then the relevant edge @xmath227 is subdivided by one vertex into two edges of @xmath232 .
the one incident to @xmath256 will be called _ special _ and the other one _
long_. if @xmath10 is a relevant edge of @xmath45 , then we choose a initial long edge @xmath257 and we let @xmath258 .
we let the weight of the special edge and of the remaining long edge be equal to 0 .
the edges of @xmath259 also got subdivided by new vertices introduced in step 1 and step 2 .
we delete all edges of the paths obtained from @xmath260 and @xmath228 , @xmath261 odd , as well as we delete all vertexes in intersections of those edges with auxiliary edges . in figure
[ cons_q ] , the deleted edges are represented by dotted lines .
each edge @xmath262 even @xmath240 , is subdivided by new vertices introduced in step 1 into a path .
we let the weights assigned to the edges of the path equal 0 except of one initial edge whose weight is let equal @xmath12 .
the edge @xmath10 of this path such that the interior of @xmath230 does not intersect interior of any curve representing a long edge will also be _ special_. the others are called _
short_. 7 .
all vertical edges which are not auxiliary ( see fig.[cons_q ] ) will be called _
special_. in figure [ cons_q ] , the special edges are represented by normal lines .
let @xmath263 denote the set of all auxiliary edges .
then deletion of @xmath263 results in a subdivision of @xmath264 .
we subdivide some special edges ( vertical and border width ones ) so that the graph @xmath265 is an even subdivision of @xmath264 .
all these new edges will be special , and we set their weights equal 0 .
this finishes the construction . in figure
[ cons_q ] , the long and short edges are represented by fat lines .
* @xmath232 is a generalised g - graph . *
its planar part @xmath266 is set of all the auxiliary and special edges .
other edges ( i.e. the short and long ) are drawn on a face of @xmath266 and they may be drawn onto a pair of bridges above this face .
one bridge contains one long edge , and the other bridge contains all the short edges .
now let us set appropriate weights to all the auxiliary edges . in order to do that first subdivide and add some auxiliary edges and vertices to @xmath266 in such a way that there exists a matching @xmath267 of @xmath268 consisting of auxiliary edges , and a perfect matching @xmath197 of @xmath266 .
we set weights of edges from @xmath267 as @xmath269 .
weights of other auxiliary edges @xmath270 . with such properties of @xmath232
we have an important result : @xmath271 .
now we introduce a _ basic orientation _
@xmath272 of @xmath266 in order to prepare our stage to use the theorem [ thm_gl ] for the generalised g - graph @xmath232 .
orientation @xmath272 has the following properties : 1 .
@xmath272 on special edges is in agreement with the natural ordering ( def .
[ lin_order ] ) .
all the signs @xmath273 in pfaffian @xmath274 ( def .
[ def_pf ] ) are positive .
the orientation of edges on a bridge has positive sign if and only if it is in agreement with the natural ordering ( def .
[ lin_order ] ) .
the construction of such a @xmath272 is possible according to kasteleyn @xcite .
we use theorem [ thm_gl ] for the graph @xmath232 .
then we may write @xmath275 where the first equality is the result of previous section .
the second equality holds because of the theorem [ thm_gl ] .
the third equality holds because of the setting of the weights of edges in @xmath232 in the previous section . and
finally , orientation @xmath276 being induced on @xmath45 by @xmath200 on @xmath277 , the fourth equality follows from the three facts : setting of the weights of edges , @xmath277 is even subdivision of @xmath45 , it is possible to permute vertexes covered by @xmath267 so that the sign is correct . in section [ sub.det ]
we have defined for a bipartite graph @xmath11 a matrix @xmath278 depending on a orientation @xmath83 .
it is easy to check that for @xmath45 holds @xmath279 . to proceed in proof of theorem [ thm.uno ] we have to establish the dependence of @xmath196 on the orientation @xmath276 of @xmath45 and specify the orientations we sum over in the language of @xmath45 not @xmath232 .
each relevant orientation @xmath200 of @xmath232 is determined by the fixed basic orientation @xmath272 of @xmath266 , and by a pair of signs for each pair of bridges .
each pair of bridges is associated with one long edge and set of short edges of @xmath232 .
hence these signs may be given by specifying @xmath280 , for each long edge @xmath10 , where @xmath281 denotes the sign of the bridge containing @xmath10 , and @xmath282 denotes the sign of the other bridge containing the set of short edges .
the relevant edges @xmath283 and @xmath284 are associated with only one long edge of @xmath232 .
if @xmath10 is such relevant edge of @xmath45 , we will call it _ border edge _ , and we denote by @xmath285 the corresponding long edge .
we let @xmath286 .
each relevant non - border edge @xmath10 of @xmath45 has two long edges @xmath287 associated with it .
we let @xmath288 .
a _ relevant vector _ is any element @xmath289 of @xmath290^{\mathcal r}$ ] such that @xmath291 for each relevant border edge @xmath10 of @xmath45
. from the definition of @xmath196 and from properties of the generalized g - graph @xmath232 of genus @xmath128 follows that @xmath292 , where @xmath293 is number of faces of @xmath266 above them edges on both bridges are oriented in negative sense , i.e. against fixed ordering .
there is a natural bijection between relevant orientations of @xmath232 and relevant vectors .
if @xmath289 is a relevant vector , then let @xmath294 denote the corresponding relevant orientation of @xmath232 and let @xmath295 of a relevant vector @xmath289 be calculated as follows : @xmath296 .
there is @xmath297 relevant edges and @xmath298 border edges .
genus of @xmath232 is therefore @xmath299 .
there are @xmath300 relevant vectors .
let us consider a set @xmath301 of relevant orientations @xmath200 such that there is at least one relevant non - border edge @xmath10 with @xmath302 , i.e. orientation of bridges with short edges incident to @xmath10 are different .
[ sum_zero ] sum of contribution of all orientations from @xmath301 to @xmath303 is zero .
* proof : * for given orientation @xmath304 define a set @xmath305 .
now let fix a set o relevant edges @xmath306 and consider all orientations @xmath307 such that @xmath308 .
fix also one relevant edge @xmath309 .
remark : @xmath310 if @xmath311 and @xmath312 differs only in one relevant edge @xmath10 in such a way that @xmath313 and
@xmath314 , @xmath315 .
it is also that induced orientations @xmath316 .
using this remark for @xmath317 we have for every @xmath306 : @xmath318 the claim in proposition [ sum_zero ] follows directly .
@xmath319 let us call all @xmath320 _ useful orientations _ and from now we sum only over such orientations .
there is @xmath321 of useful orientations .
similarly we define useful relevant vectors .
[ all_d ] each orientation @xmath83 of @xmath45 , which agrees with the fixed order on vertical edges , corresponds to @xmath322 of useful orientations @xmath200 of @xmath232 and all those @xmath200 have the same sign @xmath196 .
* proof : * let @xmath289 be a useful vector . then @xmath323 determines uniquely @xmath324 and @xmath325 for each relevant edge @xmath10 and also @xmath326 for each relevant border edge @xmath257 .
hence @xmath323 determines uniquely @xmath327 for each relevant border edge @xmath257 .
moreover @xmath323 determines uniquely the product @xmath328 for each relevant non - border edge @xmath10 .
since there are @xmath329 relevant non - border edges , there is @xmath322 orientations @xmath200 corresponding to it .
let @xmath330 be useful and both lead to the same @xmath83 of @xmath45 .
then @xmath331 for each relevant non - border edge @xmath10 and @xmath332 and @xmath333 for each relevant border edge .
this implies that @xmath334 .
@xmath319 concluding from what we did till now we can write the dimer partition function as @xmath335 where the sum is over all orientations of @xmath45 with all vertical edges positive . at this point the only thing missing in proof of theorem [ thm.uno ]
is to concretize @xmath336 .
[ sgn_d ] @xmath337 , where the set of edges @xmath54 is defined in [ r(q ) ] .
* proof : * let us remind that @xmath338 where @xmath293 is number of faces with both bridges above them negative .
each non - border relevant edge @xmath10 corresponds to two faces with bridges .
the contribution of the two corresponding faces to sign could be negative only if orientation of @xmath10 is negative ( @xmath339 ) . and moreover if orientation of corresponding shot edges is negative ( @xmath340 ) .
it follows from the construction that this happen only if product of orientation of all @xmath52 ( as defined in [ r(q ) ] ) is negative .
considering all the relevant edges we get the claim of proposition [ sgn_d ] @xmath319 [ av ] the average of @xmath95 over all orientations of @xmath45 with all vertical edges fixed positive equals @xmath341 , where @xmath93 is perfect matching of @xmath45 consisting only from vertical edges .
* proof : * by the linearity of expectation the contribution of other than vertical edges cancel out when we calculate the average of @xmath95 .
since @xmath342 has exactly one perfect matching consisting of vertical edges only , proposition [ av ] follows .
@xmath319 there is @xmath97 orientation d in [ thm.uno ] to be summed over . and @xmath343 of them have positive sign .
proof : looking at figure [ fig - sign ] we can see that as soon as there is at least one relevant ( shaded ) edge negative there is so many orientation with positive as with negative sign . only if all the relevant edges are positive the sign is also positive .
it means there is @xmath344 more positive orientation then negative . by theorem [ thm.uno ] and proposition [ av ]
we have then @xmath345= -2^{c } \alpha^{w(m ) } + \mathcal e ( 2^{c}+1),\ ] ] where @xmath346 equals the average of @xmath95 over all @xmath83 of @xmath45 with positive sign . and theorem [ thm.dos ] is proved .
@xmath319 we use a straightforward reformulation of a theorem of @xcite : [ thm.prd ] let g be a generalized g - graph .
then @xmath347 ) , \ ] ] where @xmath200 are all the relevant orientations of @xmath11 , and rotation of @xmath115 and @xmath348)$ ] are defined in the same way as described for @xmath45 in section [ sub.prod ] .
proof of this theorem could be found in @xcite and for planar graphs in @xcite .
let @xmath349 be the relevant orientations of generalised g - graph @xmath232 .
if we apply theorem [ thm.prd ] to @xmath232 , from the choice of weights we get @xmath350).\ ] ] the same analysis as in the previous section finishes the proof of theorem [ thm.tres ] .
we express the finite 3d dimer partition function as a linear combination of determinants of oriented adjacency matrices in theorem [ thm.uno ] , and the finite 3d ising partition function as a linear combination of products over aperiodic closed walks in theorem [ thm.tres ] .
the methodology we use is embedding of cubic lattice on 2d surfaces of large genus . by this embedding cubic lattice
is transformed to a generalized g - graph
. then we use theorems from @xcite , which generalize approach of @xcite .
we believe this approach may relate to recent developments in conformal field theory @xcite and topological string theory @xcite , and ultimately teach us something about 3d basic statistical physics problems .[/INST] we express the finite 3d dimer partition function as a linear combination of determinants of oriented adjacency matrices , and the finite 3d ising partition sum as a linear combination of products over aperiodic closed walks .
the methodology we use is embedding of cubic lattice on 2d surfaces of large genus . </s> |
the number of dialysis patients is increasing worldwide as a consequence of treatment to prevent progression of chronic kidney disease ( ckd ) remaining largely unresolved . to prevent ckd progression from an early stage ,
many clinical studies have suggested that disease progression may be curbed by controlling dietary factors , blood pressure , lipids , anemia , and mineral balance
. however , management of protein and salt restriction along with blood pressure is not always effective in patients using a multidisciplinary approach , including the use of angiotensin - converting enzyme inhibitors ( aceis ) and angiotensin receptor blockers ( arbs ) , that forms the basic strategy currently used to control ckd progression [ 1 , 3 ] .
ast-120 ( kremezin , kureha corporation , tokyo , japan ) is an oral adsorbent consisting of microspheres made from porous carbon material . by adsorbing uremic toxins , including indoxyl sulfate ,
the drug has been clinically used in japan since 1991 and is covered by health insurance [ 5 , 6 ] . although large - scale multicenter trials have shown the effect of ast-120 to delay dialysis initiation in cdk patients , these reports were published in the late 1980s . updating data on the ast-120 efficacy for delaying dialysis initiation
these studies used the propensity score matching method to compare the efficacy of ast-120 , although the number of patients studied was relatively small .
the importance of early diagnosis and treatment of ckd patients is well established as cardiovascular disease is known to be the primary cause of high mortality in these patients .
recently , ueda et al . reported improved prognosis in ckd patients who had been administered ast-120 during the predialysis period .
however , further evidence is required to elucidate the effect of ast-120 on the prognosis of dialysis patients . in the present study
, we performed a retrospective examination on the therapeutic effect of ast-120 in combination with current basic treatment regimens in ckd patients . to guarantee the validity of the retrospective analysis we used the propensity score method to identify a matched - control group .
between january 1991 and december 2010 , 872 of ckd patients were followed until dialysis initiation at oyokyo kidney research institute , hirosaki . of the 872 patients , 363 had a history of using ast-120 , and 509 patients had never received ast-120 . by applying the propensity score matching method , 560 patients were pair - matched ( n = 280 of each group ) and enrolled in the study . dialysis initiation was determined based on scores consisting of ( 1 ) clinical symptom ( fluid retention , electrolyte abnormality , gastrointestinal symptoms , circulatory symptoms , neurological symptoms , hematological disorders , and vision disorders ) , ( 2 ) remnant kidney function ( serum creatinine or creatinine clearance ) , ( 3 ) impairment level of daily living , ( 4 ) age ( 10 years or less , and 65 or older ) , and ( 5 ) existence of systemic vascular disorder according to the guidelines for introducing patients to dialysis issued by the ministry of health , labour and welfare of japan . patients with sum total 60 or higher were indication for dialysis initiation ( table 1 ) .
this study was approved by the institutional ethical committee of oyokyo kidney research institute . to guarantee the validity of this retrospective analysis ,
the data used in the analyses included age , gender , blood pressure , biochemistry , concomitant drugs ( activated vitamin - d , aceis , arbs , and calcium blockers ) , estimated glomerular filtration rate ( egfr ) , presence of diabetes mellitus , and cardiovascular disease ( heart failure , myocardial infarction and angina pectoris ) at the initial visit .
the egfr was calculated using age , gender , and serum creatinine ( scr ) by the equation shown below .
this egfr equation for japanese patients is a modified version of the abbreviated modification of diet in renal disease study formula .
[ egfr ml / min/1.73 m = 194 scr age ( 0.739 , if female ) ] .
based on the scores of each patient , two patients with a score within 0.03 were selected as a pair . for the ast-120 group ,
baseline for patients in the control group was defined as the date of measurement of egfr that was closest to the baseline egfr level of their counterpart in the ast-120 group .
we compared the effect of ast-120 to delay dialysis initiation in patients taking ast-120 ( ast-120 group ) with pair - matched patients not taking ast-120 ( non - ast-120 group ) . because all patients received dialysis , the 12- and 24-month dialysis initiation free rate was assessed as primary endpoints between the pair - matched ast-120-treated and non - ast-120 treated groups .
the 3- , 5- , and 10-year survival rate after administration of ast-120 was assessed as a secondary endpoint .
the background clinical data and concomitant drugs of the two groups were compared using the chi - square test .
age and other biochemical parameters were expressed as mean sd , and statistical differences were calculated by student 's t - test .
the level of urinary protein excretion was expressed as median and tested by mann - whitney 's u - test .
cumulative dialysis initiation free rate and survival rate were plotted by the kaplan - meier method , and intergroup differences were tested by the log - rank test .
the baseline characteristics of the matched patients are summarized in table 2 . after matching ,
no significant differences were observed in patients ' background between the two groups . at the time of dialysis initiation ,
the effect of ast-120 on blood pressure , blood , and serum data were compared between ast-120 and non - ast-120 group ( table 3 ) .
there was no difference in blood and serum data but systolic and diastolic blood pressure showed significant difference between two groups ( p = 0.0217 and p = 0.0180 , resp . ) the effect of ast-120 on dialysis initiation in the pair - matched patients is shown in figure 1 .
the 12- and 24-month dialysis initiation free rate was significantly higher in the ast-120 group ( 25.0% and 13.7% , resp . ) than in the non - ast-120 group ( 10.5% and 5.7% , resp . )
, we evaluated the efficacy of ast-120 in patients with diabetic nephropathy or nondiabetic renal disease , and also with or without cardiovascular disease . for patients with diabetic nephropathy or cardiovascular disease ,
the 12- and 24-month dialysis initiation free rate was significantly higher in the ast-120 group than in the non - ast-120 group ( figure 2 , table 4 ) .
this delay in dialysis initiation was longer in patients with cardiovascular disease or those without diabetic nephropathy .
we performed a cox 's proportional hazard model based on uni- and multivariate analysis to determine the independent factors for dialysis initiation in the pair - matched patients . for univariate analysis we selected egfr and
similarly , for multivariate analysis we selected anemic status , egfr , and not receiving ast-120 as independent factors associated with a significant increase in risk of dialysis initiation ( table 5 ) . to examine whether or not the use of ast-120 in the predialysis period influenced prognosis after dialysis initiation , we compared the 3- , 5- , and 10-year survival rate from administration of ast-120 by the kaplan - meier method with a log - rank test .
we found that there was no significant difference in survival rates between the ast-120 and non - ast-120 groups ( p = 0.0664 ) ( table 6 , figure 3 ) .
ckd is recognized as a disease that increases the risk of many adverse events closely associated with death , such as cardiovascular disease .
ast-120 is an oral adsorbent that slows the progression of ckd by decreasing serum nephrotoxic substances such as indoxyl sulfate .
recently , the cap - kd study was conducted to evaluate the usefulness of ast-120 in patients with moderate to severe ckd .
this study showed no significant difference in the composite primary endpoints ( doubling of scr level , increase in scr level 6.0 mg / dl , need for dialysis or transplantation , and death ) , but revealed a significant suppression in the decrease of estimated gfr over 56 weeks in the ast-120 group .
however , because of the short follow - up period , the cap - kd study could not clarify the impact of ast-120 on the development of end - stage renal disease . in the present study , we retrospectively analyzed the effects of ast-120 to delay dialysis initiation and survival in the context of current treatment regimens .
this indicated that ast-120 is a useful treatment and supports recent retrospective studies by ueda et al . and maeda et al . that also showed ast-120 delayed dialysis initiation
furthermore , maeda et al . reported long - term treatment of chronic renal failure with ast-120 from early ckd stage has potential to slowing progression of renal failure and delaying initiation of dialysis . in this present study ,
our result has limitation because main patients were at the late stage of ckd ( ckd stage 5 ) and half of patients are initiated to hemodialysis within half year .
these results suggest that ast-120 administration from early ckd stage has potential to improve the progression of renal failure effectively .
although the pair - matching method minimizes imbalances in patient background , the finding that ast-120 delayed dialysis initiation is not definitive , given that this was a retrospective study on a relatively small number of patients from a single institute .
it is possible that the better outcomes in the ast-120 group may be due to selection bias , and therefore a prospective , randomized trial with long - term followup is essential to evaluate the effectiveness of ast-120 . in addition , we could not evaluate the effects of ast-120 on blood and serum data from ast-120 administration to dialysis initiation .
our data showed significant decrease in blood pressures at the time of dialysis initiation , but we could not conclude the effect of ast-120 on blood pressures because of retrospective limitations .
recently , nakamura et al . published ast-120 effects on scr , egfr , serum interleukin-6 ( il-6 ) , proteinuria , and urinary excretion levels of 8-hydoxydeoxyguanosine ( 8-ohdg ) and l - fatty acid binding protein ( l - fabp ) , markers of oxidative stress and tubular injury . in their prospective study ,
50 patients were divided in to 2 groups ( ast-120 and non - ast-120 group , n = 25 each ) and followed up for 12 months .
they showed ast-120 treatment significantly reduced scr , egfr , il-6 , proteinuria 8-ohdg , and l - fabp , but no effect on blood pressure .
in addition to its known effect of delaying dialysis initiation , the influence of ast-120 on subsequent prognosis requires further study .
recent studies suggested that high levels of serum indoxyl sulfate , one of the substances known to enhance progression of atherosclerotic lesions , increase the risk of a cardiovascular event or death in dialysis patients .
these studies showed an association between the serum levels of indoxyl sulfate and mortality in ckd patients , indicating that this nephrotoxic compound may be involved in ckd progression and vascular disease .
ueda et al . suggested that patients receiving ast-120 before dialysis initiation tend to have an improved prognosis . in their report ,
the 5-year survival rate was significantly higher in the ast-120 group ( 72.6% in the ast-120 group and 52.6% in the non - ast-120 group ) . however , our results showed no significant difference in survival rates between the pair - matched ast-120 and non - ast-120 groups .
this conflict result might be caused by the initial ckd stage difference in ast-120 administration . in the present study ,
94% of patients were stage 5 ( egfr , 8.0 5.7 ml / min ) but ckd stage of study population in ueda et al .
was stage 4 ( average of egfr , 24 - 25 ml / min ) .
yu et al . prospectively investigated the role of indoxyl sulfate in endothelial dysfunction in ckd stage 4 patients and reported that ast-120 administration improved endothelial dysfunction associated with a decrease in indoxyl sulfate and a restoration of antioxidant reserve .
h. shibahara and n. shibahara reported ast-120 administration contributed to the improvement of cardiac and renal function in moderate ckd patients ( scr , 1.32.0 mg / dl ) in their prospective study .
in addition , nakamura et al . evaluated ast-120 effects for tubular damage through the reduction of proteinuria and oxidative stress generation in ckd stage 4 patients . from these observations , we speculate that long - term ast-120 administration from early ckd stage might be essential to improve patient survival after dialysis initiation .
however , this contradictory result suggests that multiple factors may have a considerable impact on patient survival and also that there may be difficulties with retrospective analysis of ckd patients with heterogeneous backgrounds .
prospective trials are therefore necessary to confirm the beneficial effects of ast-120 on patient survival after dialysis initiation .
although the present study is retrospective and has some limitations , our results support the evidence that ast-120 treatment is associated with significant delays in the cumulative dialysis initiation rate . | the oral adsorbent ast-120 has the potential to delay dialysis initiation and improve survival of patients on dialysis .
we evaluated the effect of ast-120 on dialysis initiation and its potential to improve survival in patients with chronic kidney disease .
the present retrospective pair - matched study included 560 patients , grouped according to whether or not they received ast-120 before dialysis ( ast-120 and non - ast-120 groups ) .
the cumulative dialysis initiation free rate and survival rate were compared by the kaplan - meier method .
multivariate analysis was used to determine the impact of ast-120 on dialysis initiation .
our results showed significant differences in the 12- and 24-month dialysis initiation free rate ( p < 0.001 ) , although no significant difference was observed in the survival rate between the two groups . in conclusion , ast-120 delays dialysis initiation in chronic kidney disease ( ckd ) patients but has no effect on survival .
ast-120 is an effective therapy for delaying the progression of ckd . | <s>[INST]the number of dialysis patients is increasing worldwide as a consequence of treatment to prevent progression of chronic kidney disease ( ckd ) remaining largely unresolved . to prevent ckd progression from an early stage ,
many clinical studies have suggested that disease progression may be curbed by controlling dietary factors , blood pressure , lipids , anemia , and mineral balance
. however , management of protein and salt restriction along with blood pressure is not always effective in patients using a multidisciplinary approach , including the use of angiotensin - converting enzyme inhibitors ( aceis ) and angiotensin receptor blockers ( arbs ) , that forms the basic strategy currently used to control ckd progression [ 1 , 3 ] .
ast-120 ( kremezin , kureha corporation , tokyo , japan ) is an oral adsorbent consisting of microspheres made from porous carbon material . by adsorbing uremic toxins , including indoxyl sulfate ,
the drug has been clinically used in japan since 1991 and is covered by health insurance [ 5 , 6 ] . although large - scale multicenter trials have shown the effect of ast-120 to delay dialysis initiation in cdk patients , these reports were published in the late 1980s . updating data on the ast-120 efficacy for delaying dialysis initiation
these studies used the propensity score matching method to compare the efficacy of ast-120 , although the number of patients studied was relatively small .
the importance of early diagnosis and treatment of ckd patients is well established as cardiovascular disease is known to be the primary cause of high mortality in these patients .
recently , ueda et al . reported improved prognosis in ckd patients who had been administered ast-120 during the predialysis period .
however , further evidence is required to elucidate the effect of ast-120 on the prognosis of dialysis patients . in the present study
, we performed a retrospective examination on the therapeutic effect of ast-120 in combination with current basic treatment regimens in ckd patients . to guarantee the validity of the retrospective analysis we used the propensity score method to identify a matched - control group .
between january 1991 and december 2010 , 872 of ckd patients were followed until dialysis initiation at oyokyo kidney research institute , hirosaki . of the 872 patients , 363 had a history of using ast-120 , and 509 patients had never received ast-120 . by applying the propensity score matching method , 560 patients were pair - matched ( n = 280 of each group ) and enrolled in the study . dialysis initiation was determined based on scores consisting of ( 1 ) clinical symptom ( fluid retention , electrolyte abnormality , gastrointestinal symptoms , circulatory symptoms , neurological symptoms , hematological disorders , and vision disorders ) , ( 2 ) remnant kidney function ( serum creatinine or creatinine clearance ) , ( 3 ) impairment level of daily living , ( 4 ) age ( 10 years or less , and 65 or older ) , and ( 5 ) existence of systemic vascular disorder according to the guidelines for introducing patients to dialysis issued by the ministry of health , labour and welfare of japan . patients with sum total 60 or higher were indication for dialysis initiation ( table 1 ) .
this study was approved by the institutional ethical committee of oyokyo kidney research institute . to guarantee the validity of this retrospective analysis ,
the data used in the analyses included age , gender , blood pressure , biochemistry , concomitant drugs ( activated vitamin - d , aceis , arbs , and calcium blockers ) , estimated glomerular filtration rate ( egfr ) , presence of diabetes mellitus , and cardiovascular disease ( heart failure , myocardial infarction and angina pectoris ) at the initial visit .
the egfr was calculated using age , gender , and serum creatinine ( scr ) by the equation shown below .
this egfr equation for japanese patients is a modified version of the abbreviated modification of diet in renal disease study formula .
[ egfr ml / min/1.73 m = 194 scr age ( 0.739 , if female ) ] .
based on the scores of each patient , two patients with a score within 0.03 were selected as a pair . for the ast-120 group ,
baseline for patients in the control group was defined as the date of measurement of egfr that was closest to the baseline egfr level of their counterpart in the ast-120 group .
we compared the effect of ast-120 to delay dialysis initiation in patients taking ast-120 ( ast-120 group ) with pair - matched patients not taking ast-120 ( non - ast-120 group ) . because all patients received dialysis , the 12- and 24-month dialysis initiation free rate was assessed as primary endpoints between the pair - matched ast-120-treated and non - ast-120 treated groups .
the 3- , 5- , and 10-year survival rate after administration of ast-120 was assessed as a secondary endpoint .
the background clinical data and concomitant drugs of the two groups were compared using the chi - square test .
age and other biochemical parameters were expressed as mean sd , and statistical differences were calculated by student 's t - test .
the level of urinary protein excretion was expressed as median and tested by mann - whitney 's u - test .
cumulative dialysis initiation free rate and survival rate were plotted by the kaplan - meier method , and intergroup differences were tested by the log - rank test .
the baseline characteristics of the matched patients are summarized in table 2 . after matching ,
no significant differences were observed in patients ' background between the two groups . at the time of dialysis initiation ,
the effect of ast-120 on blood pressure , blood , and serum data were compared between ast-120 and non - ast-120 group ( table 3 ) .
there was no difference in blood and serum data but systolic and diastolic blood pressure showed significant difference between two groups ( p = 0.0217 and p = 0.0180 , resp . ) the effect of ast-120 on dialysis initiation in the pair - matched patients is shown in figure 1 .
the 12- and 24-month dialysis initiation free rate was significantly higher in the ast-120 group ( 25.0% and 13.7% , resp . ) than in the non - ast-120 group ( 10.5% and 5.7% , resp . )
, we evaluated the efficacy of ast-120 in patients with diabetic nephropathy or nondiabetic renal disease , and also with or without cardiovascular disease . for patients with diabetic nephropathy or cardiovascular disease ,
the 12- and 24-month dialysis initiation free rate was significantly higher in the ast-120 group than in the non - ast-120 group ( figure 2 , table 4 ) .
this delay in dialysis initiation was longer in patients with cardiovascular disease or those without diabetic nephropathy .
we performed a cox 's proportional hazard model based on uni- and multivariate analysis to determine the independent factors for dialysis initiation in the pair - matched patients . for univariate analysis we selected egfr and
similarly , for multivariate analysis we selected anemic status , egfr , and not receiving ast-120 as independent factors associated with a significant increase in risk of dialysis initiation ( table 5 ) . to examine whether or not the use of ast-120 in the predialysis period influenced prognosis after dialysis initiation , we compared the 3- , 5- , and 10-year survival rate from administration of ast-120 by the kaplan - meier method with a log - rank test .
we found that there was no significant difference in survival rates between the ast-120 and non - ast-120 groups ( p = 0.0664 ) ( table 6 , figure 3 ) .
ckd is recognized as a disease that increases the risk of many adverse events closely associated with death , such as cardiovascular disease .
ast-120 is an oral adsorbent that slows the progression of ckd by decreasing serum nephrotoxic substances such as indoxyl sulfate .
recently , the cap - kd study was conducted to evaluate the usefulness of ast-120 in patients with moderate to severe ckd .
this study showed no significant difference in the composite primary endpoints ( doubling of scr level , increase in scr level 6.0 mg / dl , need for dialysis or transplantation , and death ) , but revealed a significant suppression in the decrease of estimated gfr over 56 weeks in the ast-120 group .
however , because of the short follow - up period , the cap - kd study could not clarify the impact of ast-120 on the development of end - stage renal disease . in the present study , we retrospectively analyzed the effects of ast-120 to delay dialysis initiation and survival in the context of current treatment regimens .
this indicated that ast-120 is a useful treatment and supports recent retrospective studies by ueda et al . and maeda et al . that also showed ast-120 delayed dialysis initiation
furthermore , maeda et al . reported long - term treatment of chronic renal failure with ast-120 from early ckd stage has potential to slowing progression of renal failure and delaying initiation of dialysis . in this present study ,
our result has limitation because main patients were at the late stage of ckd ( ckd stage 5 ) and half of patients are initiated to hemodialysis within half year .
these results suggest that ast-120 administration from early ckd stage has potential to improve the progression of renal failure effectively .
although the pair - matching method minimizes imbalances in patient background , the finding that ast-120 delayed dialysis initiation is not definitive , given that this was a retrospective study on a relatively small number of patients from a single institute .
it is possible that the better outcomes in the ast-120 group may be due to selection bias , and therefore a prospective , randomized trial with long - term followup is essential to evaluate the effectiveness of ast-120 . in addition , we could not evaluate the effects of ast-120 on blood and serum data from ast-120 administration to dialysis initiation .
our data showed significant decrease in blood pressures at the time of dialysis initiation , but we could not conclude the effect of ast-120 on blood pressures because of retrospective limitations .
recently , nakamura et al . published ast-120 effects on scr , egfr , serum interleukin-6 ( il-6 ) , proteinuria , and urinary excretion levels of 8-hydoxydeoxyguanosine ( 8-ohdg ) and l - fatty acid binding protein ( l - fabp ) , markers of oxidative stress and tubular injury . in their prospective study ,
50 patients were divided in to 2 groups ( ast-120 and non - ast-120 group , n = 25 each ) and followed up for 12 months .
they showed ast-120 treatment significantly reduced scr , egfr , il-6 , proteinuria 8-ohdg , and l - fabp , but no effect on blood pressure .
in addition to its known effect of delaying dialysis initiation , the influence of ast-120 on subsequent prognosis requires further study .
recent studies suggested that high levels of serum indoxyl sulfate , one of the substances known to enhance progression of atherosclerotic lesions , increase the risk of a cardiovascular event or death in dialysis patients .
these studies showed an association between the serum levels of indoxyl sulfate and mortality in ckd patients , indicating that this nephrotoxic compound may be involved in ckd progression and vascular disease .
ueda et al . suggested that patients receiving ast-120 before dialysis initiation tend to have an improved prognosis . in their report ,
the 5-year survival rate was significantly higher in the ast-120 group ( 72.6% in the ast-120 group and 52.6% in the non - ast-120 group ) . however , our results showed no significant difference in survival rates between the pair - matched ast-120 and non - ast-120 groups .
this conflict result might be caused by the initial ckd stage difference in ast-120 administration . in the present study ,
94% of patients were stage 5 ( egfr , 8.0 5.7 ml / min ) but ckd stage of study population in ueda et al .
was stage 4 ( average of egfr , 24 - 25 ml / min ) .
yu et al . prospectively investigated the role of indoxyl sulfate in endothelial dysfunction in ckd stage 4 patients and reported that ast-120 administration improved endothelial dysfunction associated with a decrease in indoxyl sulfate and a restoration of antioxidant reserve .
h. shibahara and n. shibahara reported ast-120 administration contributed to the improvement of cardiac and renal function in moderate ckd patients ( scr , 1.32.0 mg / dl ) in their prospective study .
in addition , nakamura et al . evaluated ast-120 effects for tubular damage through the reduction of proteinuria and oxidative stress generation in ckd stage 4 patients . from these observations , we speculate that long - term ast-120 administration from early ckd stage might be essential to improve patient survival after dialysis initiation .
however , this contradictory result suggests that multiple factors may have a considerable impact on patient survival and also that there may be difficulties with retrospective analysis of ckd patients with heterogeneous backgrounds .
prospective trials are therefore necessary to confirm the beneficial effects of ast-120 on patient survival after dialysis initiation .
although the present study is retrospective and has some limitations , our results support the evidence that ast-120 treatment is associated with significant delays in the cumulative dialysis initiation rate .[/INST]the oral adsorbent ast-120 has the potential to delay dialysis initiation and improve survival of patients on dialysis .
we evaluated the effect of ast-120 on dialysis initiation and its potential to improve survival in patients with chronic kidney disease .
the present retrospective pair - matched study included 560 patients , grouped according to whether or not they received ast-120 before dialysis ( ast-120 and non - ast-120 groups ) .
the cumulative dialysis initiation free rate and survival rate were compared by the kaplan - meier method .
multivariate analysis was used to determine the impact of ast-120 on dialysis initiation .
our results showed significant differences in the 12- and 24-month dialysis initiation free rate ( p < 0.001 ) , although no significant difference was observed in the survival rate between the two groups . in conclusion , ast-120 delays dialysis initiation in chronic kidney disease ( ckd ) patients but has no effect on survival .
ast-120 is an effective therapy for delaying the progression of ckd .</s> |
Criminal record of driver in deadly immigrant case dates to 1997
The driver of a tractor-trailer in which several immigrants died has a criminal record that dates to 1997 and a life as mobile as his job.
James Matthew βBearβ Bradley Jr., 60, said little when informed by U.S. Magistrate Judge Elizabeth Chestney that the human trafficking charge he faces carries a maximum life sentence and the possibility of death.
Bradley was scheduled for a bail hearing Thursday, when his criminal history could come into play and keep him jailed, as prosecutors are expected to argue that he is a danger to the community and a flight risk because he faces a possible stiff sentence and has a record of not appearing at scheduled court hearings or not complying with the law.
RELATED: Survivor connects Zetas Cartel to bodies found inside trailer
What we know about James Matthew Bradley, Jr., 60, Bradley, the driver of a tractor-trailer in which 10 immigrants were found dead and several more injured, made his first court appearance Monday July 24, 2017. Bradley has claimed the he was unaware that people were in the trailer until he stopped at a San Antonio Walmart and heard noise coming from the back. less What we know about James Matthew Bradley, Jr., 60, Bradley, the driver of a tractor-trailer in which 10 immigrants were found dead and several more injured, made his first court appearance Monday July 24, 2017. ... more Photo: John Davenport, STAFF / San Antonio Express-News Photo: John Davenport, STAFF / San Antonio Express-News Image 1 of / 57 Caption Close Criminal record of driver in deadly immigrant case dates to 1997 1 / 57 Back to Gallery
According to public records, Bradley has compiled a criminal record at least since 1997, with arrests in multiple states on charges including menacing others, assault, grand theft, escape and several traffic offenses.
Most recently, he lived in Louisville, Kentucky, according to public records and his recent employer, Pyle Transportation of Iowa.
Bradleyβs fiancee, Darnisha Rose, also of Louisville, told the Associated Press that Bradley had no idea how the immigrants got into his trailer.
βI just canβt believe it. Iβm stunned, shocked. He is too good a person to do anything like this,β Rose said. βHe helps people, he doesnβt hurt people.β
RELATED: Statement: Walmart employees' 'quick actions' saved lives
Neighbors said Bradley lives with a relative but that they keep to themselves. For more than a month, a truck matching the description of the one located at the deadly scene in San Antonio had been parked outside the house.
βTheyβre just not very friendly,β said one of his Louisville neighbors, Irene Poynter. βThey donβt talk to you or have anything to say to you.β
Court records show that Bradley was arrested in 1997 in Arapahoe County, Colorado, on charges of felony menacing, menacing with a deadly weapon and third-degree assault. He pleaded guilty in 1998 to the felony menacing charge, and the others were dropped, records show. He was sentenced to 60 days in jail and two years of probation.
The probation was revoked in 2003 and he was arrested a year later on a felony escape warrant while in Hillsborough County, Florida. He was also charged in Florida with grand theft, but the charge was dropped after he spent more than a month in jail. He was then extradited to Colorado, where he received one year in prison on the escape charge.
His probation was revoked again, in 2005, and he was again sent to prison in Colorado, court records show.
He has also been convicted of several driving offenses in various states, including speeding, being over weight on his axles, misuse of equipment and driving without evidence of financial responsibility (insurance), according to court records.
Though public records and his latest employer say Bradley, who has been married twice, most recently lived in Louisville, federal agents and prosecutors identified him as being from Clearwater, Florida.
He has also lived in Sacramento and Rancho Cordova, California, along with Denver, Aurora and Broomfield, Colorado.
Bradley has been a truck driver for several years, according to court records. When he was arrested in 2004 in Florida, he listed his employment as a trucker for IBS Transportation. His Florida driverβs license information page also said he has endorsements to haul dual trailers.
According to federal records, he was one of 15 drivers for Pyle Transportation, which is authorized to haul general freight, fresh produce, meat, refrigerated foods and paper products.
Pyle company officials have described Bradley as an owner-operator, who made his own decisions and bought his own fuel, though he was covered under the companyβs insurance.
[email protected]
Twitter: @gmaninfedland
Staff Writer Caleb Downs contributed to this report. ||||| Brian Pyle, owner of Pyle Transportation, the Iowa trucking company linked to the deadly case of immigrant smuggling in Texas, is interviewed by a television reporter Monday in Schaller, Iowa. (Scott McFetridge/AP)
Pyle Transportation β the Schaller, Iowa-based trucking company whose name was on a trailer found to be carrying dozens of undocumented immigrants in San Antonio on Sunday β has a history of legal trouble and unpaid taxes, according to records.
Owner Brian Pyle told an Iowa news station that truck driver James Bradley, who has been charged with smuggling immigrants for financial gain, had worked with Pyle Transportation on and off for about five years. But Pyle said he did not know what Bradley was hauling when the trailer was discovered in a Walmart parking lot Sunday with eight of the migrants inside dead.
The federal government charged in March 2015 that Pyle Transportation Inc. had avoided tax obligations βby continually neglecting to timely file employment tax returnsβ since at least 2009, according to the complaint. Though the family-owned company withheld federal tax payments from its employees, it did not send that money to the federal government, the government alleged. The complaint also claimed that the company failed to pay taxes for heavy highway vehicle use. As of May 13, 2014, the government claimed that the company owed $151,223 in unpaid taxes.
βAbsent an injunction, based on its past tax history, it is reasonable to expect that PTIβs noncompliance with the tax laws will continue,β the complaint reads.
βIn fact, the individual defendants previously operated two other trucking businesses, Horizon Logistics and Pyle Truck Line,β which did the same thing, the complaint continues, referring to Brian Pyle and other Pyles listed as officers or employees of the company. βAfter accruing and failing to pay those tax liabilities, the operations and customers of the previous businesses were transferred to [Pyle Transportation].β
[19-year-old who died on truck in Texas grew up in Northern Va., was deported]
Pyle Truck Lines also faced felony charges in 2000 for falsifying a report or records to the secretary of transportation. A federal judge ordered the company to serve five years of probation and pay $42,254 in restitution, according to federal court documents.
Reached on the phone Monday, Pyle said, βMy lawyer just told me not talk to anyone anymore.β
Federal prosecutors say Bradley carried dozens of undocumented immigrants in a trailer with no cooling or ventilation. By the time Bradley stopped the trailer in a Walmart parking lot early Sunday, eight of the migrants inside were dead and many others were suffering from the critical effects of heat stroke, the government said. Two of them died later at hospitals.
Mexicoβs Foreign Ministry has said that 25 of 39 migrants were Mexican nationals, based on preliminary information from its consulate in San Antonio.
Bradley could face the death penalty because people died while in transit. Bradley told investigators that he was traveling from Iowa at the request of his boss to deliver the trailer to Brownsville, Tex., and didnβt know what was inside. He had said that his boss, who wasnβt named in the document, had sold the trailer to a person in Brownsville.
Reached Sunday by a reporter, Brian Pyle said Bradley was an owner-operator involved in a standard trucking practice in which Bradley owned the truck and managed his own deliveries but used Pyleβs insurance and company name and paid Pyle a percentage of his earnings.
Without naming Bradley, Pyle had told a Washington Post reporter on Sunday that this was the truck driverβs βvery first tripβ and that he didnβt know what he was hauling. However, Pyle told an Iowa television news station Monday that he had worked with Bradley for years and had hired Bradley to deliver a trailer he had sold in May. He said Bradley was scheduled to drop it off in Brownsville, Texas on Friday.
[After deadly smuggling case, officials charge truck driver and decry βcrime against humanityβ]
βHe has worked here before,β Pyle told the reporter. βHe is an owner-operator now, or he was at the time. . . . He did everything on his own β bought his own fuel, made his own decisions.β
The WHO-TV reporter said Pyle regretted not taking the logo off his trailer before selling it.
Bradley is pictured in his Facebook profile photo wearing a Pyle T-shirt and was Facebook friends with Pyle, whose Facebook page has now been removed, and other Pyle employees and truck drivers.
Pyle Transportation has 18 trucks and 15 drivers, according to the Federal Motor Carrier Safety Administration. Authorized for hire and interstate driving, Pyle is listed as a carrier of general freight, refrigerated food and beverages, meat, fresh produce and paper products.
[Horrific episode of human smuggling fuels both sides of immigration debate]
Owner-operator trucking can be a financially challenging job, said Norita Taylor, a spokeswoman for the Owner Operator Independent Drivers Association, a trade association with more than 150,000 truck-driver members. The average annual income for such drivers is around $43,000, she said, and while drivers operate with considerably more discretion over their hours and assignments than company drivers, they are also responsible for a wider range of costs.
βThe long and short of it is being a small business trucker entails not just the cost of your equipment but also the insurance and taxes and fees,β Taylor said. βAnd fuel is like the number-one expense after equipment.β
Bradley bought the truck β a 1999 Peterbilt model that had been refurbished and given a new paint job β in March for $90,000, said Justin McDaniel of Outlaw Iron in West Bend, Wis., who sold him the truck. Bradley had taken out a pair of loans earlier this year to buy a truck and trailer for which he needed to make payments of almost $2,000 a month, according to records.
Avi Selk and Todd Frankel contributed to this report.
Editorβs note: A previous version of this story included complaints about Pyle Transportation left on a Facebook page. Because the allegations in those complaints could not be corroborated, they have been removed. ||||| James Mathew Bradley Jr., 60, of Clearwater, Fla., left, arrives at the federal courthouse for a hearing, Monday, July 24, 2017, in San Antonio. Bradley was taken into custody and is expected to be charged... (Associated Press)
SAN ANTONIO (AP) β The Latest on the deaths of 10 people whose bodies were found in a broiling tractor-trailer in a Walmart parking lot in San Antonio (all times local):
2:30 p.m.
The state of Florida had suspended commercial driving privileges for a truck driver three months before he was arrested for driving a tractor-trailer so hot and so crammed with immigrants that 10 people died.
Alexis Bakofsky, a spokeswoman for the Florida Department of Highway Safety and Motor Vehicles, confirmed Tuesday that the agency disqualified 60-year-old James Matthew Bradley Jr.'s commercial driving privileges in April when he failed to file an updated medical card. Federal law requires commercial drivers supply the card to show they are physically fit for the road.
Bradley's driving record shows he was issued a commercial driver's license in Florida in 2004. Bakofsky confirmed the Florida license was disqualified indefinitely. Bakofsky also says it would have been illegal for him to have held a second license from another state.
Bradley faces charges of illegally transporting immigrants for financial gain resulting in death. The immigrants were found inside his truck at a Walmart in San Antonio.
___
2 p.m.
Court records show that a long-haul truck driver charged in the deaths of 10 immigrants found inside his sweltering tractor-trailer in San Antonio had been cited repeatedly for violating federal motor carrier safety regulations in Iowa dating back to 1995.
At least two of the tickets were for logging more hours than allowed.
James Matthew Bradley Jr.'s most recent infraction came in April 2013. He was ticketed for violating a rule that bars truckers from driving longer than 14 hours without a break. The citation shows that he was driving for Pyle Transportation. He was fined $127.50.
The records show Bradley also received tickets for violations of federal safety rules following stops or inspections in 2011, 2010 and 1995. They included a "maximum hours of service violation" for driving too much without rest in 2010.
___
12:15 a.m.
A long-haul truck driver charged in the deaths of 10 immigrants found inside his sweltering tractor-trailer called his fiancee Sunday from a jail more than 1,000 miles from home and briefly described the gruesome events.
Darnisha Rose says James Matthew Bradley Jr., who she called a generous person, claimed he had no idea how so many people came to be crammed inside his trailer in the Texas heat.
The 60-year-old Bradley, a diabetic whose criminal history includes a conviction in a felony domestic violence case, told Rose that he'd stopped his truck at a San Antonio Walmart and went inside to use the bathroom. He claimed that when he returned to his truck, he noticed the trailer rocking back and forth.
He said he'd heard nothing before that.
___
12:02 a.m.
Mexico's foreign ministry says 25 of the migrants found inside a sweltering tractor-trailer found parked outside a Texas Walmart were Mexican.
In a statement Monday night, the ministry says that based on interviews by Mexican consulate personnel and contact with local authorities, "we can say that of the 10 people who lost their lives ... four were of Mexican nationality."
The statement also says that of the 29 people hospitalized, 21 are Mexican.
Also Monday, the man charged with driving the rig appeared in federal court in San Antonio.
James Matthew Bradley Jr. faces charges of illegally transporting immigrants for financial gain, resulting in death. The judge explained to Bradley that he could face the death penalty, if convicted.
In the federal complaint, Bradley told authorities he didn't realize anyone was inside the 18-wheeler. | β The truck driver facing human trafficking charges in the deaths of 10 undocumented immigrants being transported in the back of a sweltering tractor-trailer in Texas had his commercial driving privileges suspended three months ago, the AP reports. The state of Florida suspended 60-year-old James Bradley Jr.'s privileges after he failed to submit a new medical card meant to show he was physically fit enough to drive. In addition, Bradley has numerous citations for violating federal safety rules dating back to 1995, including two tickets for logging more driving hours than allowed. Outside of his driving history, Bradley has a criminal record that goes back to 1997, My San Antonio reports. That history includes arrests and charges in multiple states for menacing others, assault, escape, grand theft, and traffic offenses. He was convicted of felony domestic violence and sent to prison multiple times for violating parole. Bradley's criminal history could keep him locked up as a flight risk. According to the Washington Post, Pyle Transportation, the trucking company with which Bradley worked, also has a checkered history. It owed more than $150,000 in back taxes as of May 2014 and was charged with a felony for falsifying reports or records in 2000. | <s>[INST]Criminal record of driver in deadly immigrant case dates to 1997
The driver of a tractor-trailer in which several immigrants died has a criminal record that dates to 1997 and a life as mobile as his job.
James Matthew βBearβ Bradley Jr., 60, said little when informed by U.S. Magistrate Judge Elizabeth Chestney that the human trafficking charge he faces carries a maximum life sentence and the possibility of death.
Bradley was scheduled for a bail hearing Thursday, when his criminal history could come into play and keep him jailed, as prosecutors are expected to argue that he is a danger to the community and a flight risk because he faces a possible stiff sentence and has a record of not appearing at scheduled court hearings or not complying with the law.
RELATED: Survivor connects Zetas Cartel to bodies found inside trailer
What we know about James Matthew Bradley, Jr., 60, Bradley, the driver of a tractor-trailer in which 10 immigrants were found dead and several more injured, made his first court appearance Monday July 24, 2017. Bradley has claimed the he was unaware that people were in the trailer until he stopped at a San Antonio Walmart and heard noise coming from the back. less What we know about James Matthew Bradley, Jr., 60, Bradley, the driver of a tractor-trailer in which 10 immigrants were found dead and several more injured, made his first court appearance Monday July 24, 2017. ... more Photo: John Davenport, STAFF / San Antonio Express-News Photo: John Davenport, STAFF / San Antonio Express-News Image 1 of / 57 Caption Close Criminal record of driver in deadly immigrant case dates to 1997 1 / 57 Back to Gallery
According to public records, Bradley has compiled a criminal record at least since 1997, with arrests in multiple states on charges including menacing others, assault, grand theft, escape and several traffic offenses.
Most recently, he lived in Louisville, Kentucky, according to public records and his recent employer, Pyle Transportation of Iowa.
Bradleyβs fiancee, Darnisha Rose, also of Louisville, told the Associated Press that Bradley had no idea how the immigrants got into his trailer.
βI just canβt believe it. Iβm stunned, shocked. He is too good a person to do anything like this,β Rose said. βHe helps people, he doesnβt hurt people.β
RELATED: Statement: Walmart employees' 'quick actions' saved lives
Neighbors said Bradley lives with a relative but that they keep to themselves. For more than a month, a truck matching the description of the one located at the deadly scene in San Antonio had been parked outside the house.
βTheyβre just not very friendly,β said one of his Louisville neighbors, Irene Poynter. βThey donβt talk to you or have anything to say to you.β
Court records show that Bradley was arrested in 1997 in Arapahoe County, Colorado, on charges of felony menacing, menacing with a deadly weapon and third-degree assault. He pleaded guilty in 1998 to the felony menacing charge, and the others were dropped, records show. He was sentenced to 60 days in jail and two years of probation.
The probation was revoked in 2003 and he was arrested a year later on a felony escape warrant while in Hillsborough County, Florida. He was also charged in Florida with grand theft, but the charge was dropped after he spent more than a month in jail. He was then extradited to Colorado, where he received one year in prison on the escape charge.
His probation was revoked again, in 2005, and he was again sent to prison in Colorado, court records show.
He has also been convicted of several driving offenses in various states, including speeding, being over weight on his axles, misuse of equipment and driving without evidence of financial responsibility (insurance), according to court records.
Though public records and his latest employer say Bradley, who has been married twice, most recently lived in Louisville, federal agents and prosecutors identified him as being from Clearwater, Florida.
He has also lived in Sacramento and Rancho Cordova, California, along with Denver, Aurora and Broomfield, Colorado.
Bradley has been a truck driver for several years, according to court records. When he was arrested in 2004 in Florida, he listed his employment as a trucker for IBS Transportation. His Florida driverβs license information page also said he has endorsements to haul dual trailers.
According to federal records, he was one of 15 drivers for Pyle Transportation, which is authorized to haul general freight, fresh produce, meat, refrigerated foods and paper products.
Pyle company officials have described Bradley as an owner-operator, who made his own decisions and bought his own fuel, though he was covered under the companyβs insurance.
[email protected]
Twitter: @gmaninfedland
Staff Writer Caleb Downs contributed to this report. ||||| Brian Pyle, owner of Pyle Transportation, the Iowa trucking company linked to the deadly case of immigrant smuggling in Texas, is interviewed by a television reporter Monday in Schaller, Iowa. (Scott McFetridge/AP)
Pyle Transportation β the Schaller, Iowa-based trucking company whose name was on a trailer found to be carrying dozens of undocumented immigrants in San Antonio on Sunday β has a history of legal trouble and unpaid taxes, according to records.
Owner Brian Pyle told an Iowa news station that truck driver James Bradley, who has been charged with smuggling immigrants for financial gain, had worked with Pyle Transportation on and off for about five years. But Pyle said he did not know what Bradley was hauling when the trailer was discovered in a Walmart parking lot Sunday with eight of the migrants inside dead.
The federal government charged in March 2015 that Pyle Transportation Inc. had avoided tax obligations βby continually neglecting to timely file employment tax returnsβ since at least 2009, according to the complaint. Though the family-owned company withheld federal tax payments from its employees, it did not send that money to the federal government, the government alleged. The complaint also claimed that the company failed to pay taxes for heavy highway vehicle use. As of May 13, 2014, the government claimed that the company owed $151,223 in unpaid taxes.
βAbsent an injunction, based on its past tax history, it is reasonable to expect that PTIβs noncompliance with the tax laws will continue,β the complaint reads.
βIn fact, the individual defendants previously operated two other trucking businesses, Horizon Logistics and Pyle Truck Line,β which did the same thing, the complaint continues, referring to Brian Pyle and other Pyles listed as officers or employees of the company. βAfter accruing and failing to pay those tax liabilities, the operations and customers of the previous businesses were transferred to [Pyle Transportation].β
[19-year-old who died on truck in Texas grew up in Northern Va., was deported]
Pyle Truck Lines also faced felony charges in 2000 for falsifying a report or records to the secretary of transportation. A federal judge ordered the company to serve five years of probation and pay $42,254 in restitution, according to federal court documents.
Reached on the phone Monday, Pyle said, βMy lawyer just told me not talk to anyone anymore.β
Federal prosecutors say Bradley carried dozens of undocumented immigrants in a trailer with no cooling or ventilation. By the time Bradley stopped the trailer in a Walmart parking lot early Sunday, eight of the migrants inside were dead and many others were suffering from the critical effects of heat stroke, the government said. Two of them died later at hospitals.
Mexicoβs Foreign Ministry has said that 25 of 39 migrants were Mexican nationals, based on preliminary information from its consulate in San Antonio.
Bradley could face the death penalty because people died while in transit. Bradley told investigators that he was traveling from Iowa at the request of his boss to deliver the trailer to Brownsville, Tex., and didnβt know what was inside. He had said that his boss, who wasnβt named in the document, had sold the trailer to a person in Brownsville.
Reached Sunday by a reporter, Brian Pyle said Bradley was an owner-operator involved in a standard trucking practice in which Bradley owned the truck and managed his own deliveries but used Pyleβs insurance and company name and paid Pyle a percentage of his earnings.
Without naming Bradley, Pyle had told a Washington Post reporter on Sunday that this was the truck driverβs βvery first tripβ and that he didnβt know what he was hauling. However, Pyle told an Iowa television news station Monday that he had worked with Bradley for years and had hired Bradley to deliver a trailer he had sold in May. He said Bradley was scheduled to drop it off in Brownsville, Texas on Friday.
[After deadly smuggling case, officials charge truck driver and decry βcrime against humanityβ]
βHe has worked here before,β Pyle told the reporter. βHe is an owner-operator now, or he was at the time. . . . He did everything on his own β bought his own fuel, made his own decisions.β
The WHO-TV reporter said Pyle regretted not taking the logo off his trailer before selling it.
Bradley is pictured in his Facebook profile photo wearing a Pyle T-shirt and was Facebook friends with Pyle, whose Facebook page has now been removed, and other Pyle employees and truck drivers.
Pyle Transportation has 18 trucks and 15 drivers, according to the Federal Motor Carrier Safety Administration. Authorized for hire and interstate driving, Pyle is listed as a carrier of general freight, refrigerated food and beverages, meat, fresh produce and paper products.
[Horrific episode of human smuggling fuels both sides of immigration debate]
Owner-operator trucking can be a financially challenging job, said Norita Taylor, a spokeswoman for the Owner Operator Independent Drivers Association, a trade association with more than 150,000 truck-driver members. The average annual income for such drivers is around $43,000, she said, and while drivers operate with considerably more discretion over their hours and assignments than company drivers, they are also responsible for a wider range of costs.
βThe long and short of it is being a small business trucker entails not just the cost of your equipment but also the insurance and taxes and fees,β Taylor said. βAnd fuel is like the number-one expense after equipment.β
Bradley bought the truck β a 1999 Peterbilt model that had been refurbished and given a new paint job β in March for $90,000, said Justin McDaniel of Outlaw Iron in West Bend, Wis., who sold him the truck. Bradley had taken out a pair of loans earlier this year to buy a truck and trailer for which he needed to make payments of almost $2,000 a month, according to records.
Avi Selk and Todd Frankel contributed to this report.
Editorβs note: A previous version of this story included complaints about Pyle Transportation left on a Facebook page. Because the allegations in those complaints could not be corroborated, they have been removed. ||||| James Mathew Bradley Jr., 60, of Clearwater, Fla., left, arrives at the federal courthouse for a hearing, Monday, July 24, 2017, in San Antonio. Bradley was taken into custody and is expected to be charged... (Associated Press)
SAN ANTONIO (AP) β The Latest on the deaths of 10 people whose bodies were found in a broiling tractor-trailer in a Walmart parking lot in San Antonio (all times local):
2:30 p.m.
The state of Florida had suspended commercial driving privileges for a truck driver three months before he was arrested for driving a tractor-trailer so hot and so crammed with immigrants that 10 people died.
Alexis Bakofsky, a spokeswoman for the Florida Department of Highway Safety and Motor Vehicles, confirmed Tuesday that the agency disqualified 60-year-old James Matthew Bradley Jr.'s commercial driving privileges in April when he failed to file an updated medical card. Federal law requires commercial drivers supply the card to show they are physically fit for the road.
Bradley's driving record shows he was issued a commercial driver's license in Florida in 2004. Bakofsky confirmed the Florida license was disqualified indefinitely. Bakofsky also says it would have been illegal for him to have held a second license from another state.
Bradley faces charges of illegally transporting immigrants for financial gain resulting in death. The immigrants were found inside his truck at a Walmart in San Antonio.
___
2 p.m.
Court records show that a long-haul truck driver charged in the deaths of 10 immigrants found inside his sweltering tractor-trailer in San Antonio had been cited repeatedly for violating federal motor carrier safety regulations in Iowa dating back to 1995.
At least two of the tickets were for logging more hours than allowed.
James Matthew Bradley Jr.'s most recent infraction came in April 2013. He was ticketed for violating a rule that bars truckers from driving longer than 14 hours without a break. The citation shows that he was driving for Pyle Transportation. He was fined $127.50.
The records show Bradley also received tickets for violations of federal safety rules following stops or inspections in 2011, 2010 and 1995. They included a "maximum hours of service violation" for driving too much without rest in 2010.
___
12:15 a.m.
A long-haul truck driver charged in the deaths of 10 immigrants found inside his sweltering tractor-trailer called his fiancee Sunday from a jail more than 1,000 miles from home and briefly described the gruesome events.
Darnisha Rose says James Matthew Bradley Jr., who she called a generous person, claimed he had no idea how so many people came to be crammed inside his trailer in the Texas heat.
The 60-year-old Bradley, a diabetic whose criminal history includes a conviction in a felony domestic violence case, told Rose that he'd stopped his truck at a San Antonio Walmart and went inside to use the bathroom. He claimed that when he returned to his truck, he noticed the trailer rocking back and forth.
He said he'd heard nothing before that.
___
12:02 a.m.
Mexico's foreign ministry says 25 of the migrants found inside a sweltering tractor-trailer found parked outside a Texas Walmart were Mexican.
In a statement Monday night, the ministry says that based on interviews by Mexican consulate personnel and contact with local authorities, "we can say that of the 10 people who lost their lives ... four were of Mexican nationality."
The statement also says that of the 29 people hospitalized, 21 are Mexican.
Also Monday, the man charged with driving the rig appeared in federal court in San Antonio.
James Matthew Bradley Jr. faces charges of illegally transporting immigrants for financial gain, resulting in death. The judge explained to Bradley that he could face the death penalty, if convicted.
In the federal complaint, Bradley told authorities he didn't realize anyone was inside the 18-wheeler.[/INST]β The truck driver facing human trafficking charges in the deaths of 10 undocumented immigrants being transported in the back of a sweltering tractor-trailer in Texas had his commercial driving privileges suspended three months ago, the AP reports. The state of Florida suspended 60-year-old James Bradley Jr.'s privileges after he failed to submit a new medical card meant to show he was physically fit enough to drive. In addition, Bradley has numerous citations for violating federal safety rules dating back to 1995, including two tickets for logging more driving hours than allowed. Outside of his driving history, Bradley has a criminal record that goes back to 1997, My San Antonio reports. That history includes arrests and charges in multiple states for menacing others, assault, escape, grand theft, and traffic offenses. He was convicted of felony domestic violence and sent to prison multiple times for violating parole. Bradley's criminal history could keep him locked up as a flight risk. According to the Washington Post, Pyle Transportation, the trucking company with which Bradley worked, also has a checkered history. It owed more than $150,000 in back taxes as of May 2014 and was charged with a felony for falsifying reports or records in 2000.</s> |
That section 315(a) of
the Communications Act of 1934 (47 U.S.C. 315) is amended to read as
follows:
``(a) Allowance of Television Broadcast Time for certain
Candidates; Censorship Prohibition.--Each licensee operating a
television broadcasting station shall make available without charge to
any legally qualified candidate in the general election for the office
of United States Senator an amount of broadcast time, determined by the
Commission under subsection (d), for use in his or her campaign for
election, subject to the conditions and limitations of subsection (e).
No licensee shall have power of censorship over the material broadcast
under the provisions of this section.
``(b) Equal Opportunities Requirement; Censorship Prohibition;
Allowance of Station Use.--Except in those circumstances to which
subsection (a) applies, if any licensee shall permit any person who is
a legally qualified candidate for any public office to use a
broadcasting station, he or she shall afford equal opportunities to all
other such candidates for the office in the use of such broadcasting
station: Provided, That such licensee shall have no power of censorship
over the material broadcast under the provisions of this section. No
obligation is imposed under this subsection upon any licensee to allow
the use of its station by any such candidate.
``(c) News Appearances Exception; Public Interest; Public Issues
Discussion Opportunities.--Appearance by a legally qualified candidate
on any--
``(1) bona fide newscast;
``(2) bona fide news interview;
``(3) bona fide news documentary (if the appearance of the
candidate is incidental to the presentation of the subject or
subjects covered by the news documentary); or
``(4) on-the-spot coverage of bona fide events (including
but not limited to political conventions and activities
incidental thereto);
shall not be deemed to be use of a broadcasting station within the
meaning of subsections (a) or (b). Nothing in the foregoing sentence
shall be construed as relieving broadcasters, in connection with the
presentation of newscast, news interviews, new documentaries, and on-
the-spot coverage of news events, from the obligation imposed upon them
under this chapter to operate in the public interest and to afford
reasonable opportunity for the discussion of conflicting views on
issues of public importance.
``(d) Rules and Regulations Regarding Allowance of Television
Broadcast Time for Certain Candidates.--The Commission shall, after
consultation with the Federal Election Commission, determine the amount
of television broadcast time that legally qualified major-party
candidates for a Senate office may receive under subsection (a) on the
basis of the amount of television broadcast time used by major-party
candidates in the previous election for the United States Senate,
provided that at a minimum such candidates be provided an amount of
television broadcast time necessary to make a complete presentation of
views to the electorate in the pending election. The amount of
television broadcast time that each candidate is eligible to receive
and the amount of such time that each licensee must make available to
each eligible candidate by name shall be published prior to each Senate
election in the Federal Register by the Commission on a date
established by regulation. The broadcast time made available under
subsection (a) shall be made available during the forty-five-day period
preceding the general election for such office. The Commission shall
ensure that the television broadcast time made available under
subsection (a) shall be made available fairly and equitably, through
licensees commonly used by candidates seeking the particular United
States Senate office, and at hours of the day which reflect television
viewing habits and contemporaneous campaign practices. A legally
qualified candidate of a party other than a party which obtained 5
percent or more of the popular vote in the last presidential election
shall, by regulation of the Commission, be granted an allocation of
broadcast time in proportion to the amount of contributions under $250
such a candidate has received when compared to such contributions
received by candidates of the major parties, provided that such
proportion exceeds 5 percent. The Commission shall require licensees
operating television broadcasting stations to enter into a pooling
agreement to ameliorate any disproportionate financial impact on
particular licensees. For purposes of this subsection, a major party is
a party which obtained more than 5 percent of the popular vote in the
previous presidential election.
``(e) Conditions and Limitations.--The entitlement of any legally
qualified candidate to television broadcast time under subsection (a)
is conditional upon (1) signing an agreement to forgo both the purchase
of any additional amount of television broadcast time, and the
acceptance of any additional amount of television broadcast time
purchased by another, during the period that such time is made
available with respect to such candidacy pursuant to subsection (a) and
the Commission's regulations, and (2) filing a copy of such agreement
with the Commission.
``(f) Penalties and Remedies.--Any candidate who purchases or
accepts purchased television broadcast time in violation of such
agreement shall be subject, upon conviction, to imprisonment of up to
one year or a fine of up to $10,000, or both. Any licensee who sells
television broadcast time to a candidate, who has filed an agreement,
in excess of the time to be provided by such licensee to such candidate
pursuant to subsection (a) and the Commission's regulations shall be
subject to appropriate disciplinary action by the Commission, including
(1) an order requiring the licensee to provide an equal amount of time
to other candidates for the same office, or (2) an order revoking the
licensee's license.''.
Sec. 2. Section 315 of the Communications Act of 1934 is further
amended as follows: (1) in subsection (b) by striking the phrase ``The
charges'' and inserting in lieu thereof ``Except to the extent that the
provisions of subsection (a) apply, the charges''; (2) by redesignating
subsections (b), (c), and (d) as (f), (g), and (h) respectively; and
(3) by adding ``generally'' after ``Rules and regulations'' in
redesignated subsection (h).
Sec. 3. Subsection (a)(7) of section 312 of the Communications Act
of 1934, as amended, is amended to read as follows: ``(7) for willful
or repeated failure to comply with the provisions of section 315 of
this title.''
Sec. 4. Subsection (8) of section 301 of the Federal Election
Campaign Act of 1971 (2 U.S.C. 431), as amended, relating to exclusions
from the definition of contributions, is amended as follows: (1) at the
end of paragraph (B)(xiii) by striking the semicolon; (2) at the end of
paragraph (B)(xiv) by striking the period and inserting ``; and'' in
lieu thereof; and (3) at the end of paragraph (B) by adding the
following: ``(xv) the value of any television broadcast time provided
without charge by a licensee pursuant to section 315(a) of the
Communications Act of 1934, as amended.''
Sec. 5. Subsection (9) of section 301 of the Federal Election
Campaign Act of 1971, as amended, relating to exclusions from the
definition of expenditures, is amended as follows: (1) by inserting
after paragraph (B)(i) the following: ``(ii) the provision without
charge of any television broadcast time by a licensee pursuant to
section 315(a) of the Communications Act of 1934, as amended;'' and (2)
by redesignating subsequent subparagraphs accordingly.
Sec. 6. The Federal Communications Commission shall study the
application of section 315(a) of the Communications Act of 1934, as
amended by this Act, to the first general election campaign conducted
under the provisions of that section and shall report the results of
that study, together with recommendations, including recommendations
for legislation, not later than the first day of March following such
general election. The study shall also evaluate the desirability and
feasibility of extending the provisions of section 315(a) of the
Communications Act of 1934 to primary and other election campaigns.
Sec. 7. The Federal Communications Commission shall promulgate
rules and regulations to implement this Act no later than one hundred
and eighty days after the date of enactment of this Act. Sections 1 and
2 of this Act shall not take effect until the first day of July
following the promulgation of such rules and regulations. | Amends the Communications Act of 1934 to require each licensee operating a television (TV) broadcasting station to make available without charge to any legally qualified candidate for the Senate an amount of broadcast time as determined by the Federal Communications Commission (FCC) during the 45-day period preceding such election.
Directs the FCC to: (1) determine the amount of TV broadcast time that such candidates may receive on the basis of the amount of broadcast time used by major party candidates in the previous Senate election, provided that at a minimum such candidates be provided sufficient time to make a complete presentation of views; and (2) ensure that such TV broadcast time be made available fairly and equitably and at hours of the day which reflect TV viewing habits and contemporaneous campaign practices.
Requires that a legally qualified candidate of a party other than a party which obtained five percent or more of the popular vote in the last presidential election be granted an allocation of broadcast time in proportion to the amount of contributions under $250 such candidate has received when compared to such contributions received by candidates of the major parties, provided such proportion exceeds five percent. Directs the FCC to require licensees operating TV broadcasting stations to enter into a pooling agreement to ameliorate any disproportionate financial impact on particular licensees.
Conditions the entitlement to TV broadcast time under this Act upon the candidate's: (1) signing an agreement to forego both the purchase of any additional amount of broadcast time and any additional time purchased by another candidate during the period that such time is made available; and (2) filing a copy of such agreement with the FCC.
Sets forth penalties for any candidate who purchases or accepts purchased TV broadcast time in violation of such agreement. Subjects licensees to appropriate disciplinary action by the FCC.
Amends the Federal Election Campaign Act of 1971 to exclude from the definitions of "contributions" and "expenditures" the value of TV broadcast time provided without charge by a licensee pursuant to the Communications Act of 1934.
Directs the FCC to study the provision of free TV broadcast time to Senate candidates and evaluate the feasibility of extending such provision to primary and other election campaigns. | <s>[INST]That section 315(a) of
the Communications Act of 1934 (47 U.S.C. 315) is amended to read as
follows:
``(a) Allowance of Television Broadcast Time for certain
Candidates; Censorship Prohibition.--Each licensee operating a
television broadcasting station shall make available without charge to
any legally qualified candidate in the general election for the office
of United States Senator an amount of broadcast time, determined by the
Commission under subsection (d), for use in his or her campaign for
election, subject to the conditions and limitations of subsection (e).
No licensee shall have power of censorship over the material broadcast
under the provisions of this section.
``(b) Equal Opportunities Requirement; Censorship Prohibition;
Allowance of Station Use.--Except in those circumstances to which
subsection (a) applies, if any licensee shall permit any person who is
a legally qualified candidate for any public office to use a
broadcasting station, he or she shall afford equal opportunities to all
other such candidates for the office in the use of such broadcasting
station: Provided, That such licensee shall have no power of censorship
over the material broadcast under the provisions of this section. No
obligation is imposed under this subsection upon any licensee to allow
the use of its station by any such candidate.
``(c) News Appearances Exception; Public Interest; Public Issues
Discussion Opportunities.--Appearance by a legally qualified candidate
on any--
``(1) bona fide newscast;
``(2) bona fide news interview;
``(3) bona fide news documentary (if the appearance of the
candidate is incidental to the presentation of the subject or
subjects covered by the news documentary); or
``(4) on-the-spot coverage of bona fide events (including
but not limited to political conventions and activities
incidental thereto);
shall not be deemed to be use of a broadcasting station within the
meaning of subsections (a) or (b). Nothing in the foregoing sentence
shall be construed as relieving broadcasters, in connection with the
presentation of newscast, news interviews, new documentaries, and on-
the-spot coverage of news events, from the obligation imposed upon them
under this chapter to operate in the public interest and to afford
reasonable opportunity for the discussion of conflicting views on
issues of public importance.
``(d) Rules and Regulations Regarding Allowance of Television
Broadcast Time for Certain Candidates.--The Commission shall, after
consultation with the Federal Election Commission, determine the amount
of television broadcast time that legally qualified major-party
candidates for a Senate office may receive under subsection (a) on the
basis of the amount of television broadcast time used by major-party
candidates in the previous election for the United States Senate,
provided that at a minimum such candidates be provided an amount of
television broadcast time necessary to make a complete presentation of
views to the electorate in the pending election. The amount of
television broadcast time that each candidate is eligible to receive
and the amount of such time that each licensee must make available to
each eligible candidate by name shall be published prior to each Senate
election in the Federal Register by the Commission on a date
established by regulation. The broadcast time made available under
subsection (a) shall be made available during the forty-five-day period
preceding the general election for such office. The Commission shall
ensure that the television broadcast time made available under
subsection (a) shall be made available fairly and equitably, through
licensees commonly used by candidates seeking the particular United
States Senate office, and at hours of the day which reflect television
viewing habits and contemporaneous campaign practices. A legally
qualified candidate of a party other than a party which obtained 5
percent or more of the popular vote in the last presidential election
shall, by regulation of the Commission, be granted an allocation of
broadcast time in proportion to the amount of contributions under $250
such a candidate has received when compared to such contributions
received by candidates of the major parties, provided that such
proportion exceeds 5 percent. The Commission shall require licensees
operating television broadcasting stations to enter into a pooling
agreement to ameliorate any disproportionate financial impact on
particular licensees. For purposes of this subsection, a major party is
a party which obtained more than 5 percent of the popular vote in the
previous presidential election.
``(e) Conditions and Limitations.--The entitlement of any legally
qualified candidate to television broadcast time under subsection (a)
is conditional upon (1) signing an agreement to forgo both the purchase
of any additional amount of television broadcast time, and the
acceptance of any additional amount of television broadcast time
purchased by another, during the period that such time is made
available with respect to such candidacy pursuant to subsection (a) and
the Commission's regulations, and (2) filing a copy of such agreement
with the Commission.
``(f) Penalties and Remedies.--Any candidate who purchases or
accepts purchased television broadcast time in violation of such
agreement shall be subject, upon conviction, to imprisonment of up to
one year or a fine of up to $10,000, or both. Any licensee who sells
television broadcast time to a candidate, who has filed an agreement,
in excess of the time to be provided by such licensee to such candidate
pursuant to subsection (a) and the Commission's regulations shall be
subject to appropriate disciplinary action by the Commission, including
(1) an order requiring the licensee to provide an equal amount of time
to other candidates for the same office, or (2) an order revoking the
licensee's license.''.
Sec. 2. Section 315 of the Communications Act of 1934 is further
amended as follows: (1) in subsection (b) by striking the phrase ``The
charges'' and inserting in lieu thereof ``Except to the extent that the
provisions of subsection (a) apply, the charges''; (2) by redesignating
subsections (b), (c), and (d) as (f), (g), and (h) respectively; and
(3) by adding ``generally'' after ``Rules and regulations'' in
redesignated subsection (h).
Sec. 3. Subsection (a)(7) of section 312 of the Communications Act
of 1934, as amended, is amended to read as follows: ``(7) for willful
or repeated failure to comply with the provisions of section 315 of
this title.''
Sec. 4. Subsection (8) of section 301 of the Federal Election
Campaign Act of 1971 (2 U.S.C. 431), as amended, relating to exclusions
from the definition of contributions, is amended as follows: (1) at the
end of paragraph (B)(xiii) by striking the semicolon; (2) at the end of
paragraph (B)(xiv) by striking the period and inserting ``; and'' in
lieu thereof; and (3) at the end of paragraph (B) by adding the
following: ``(xv) the value of any television broadcast time provided
without charge by a licensee pursuant to section 315(a) of the
Communications Act of 1934, as amended.''
Sec. 5. Subsection (9) of section 301 of the Federal Election
Campaign Act of 1971, as amended, relating to exclusions from the
definition of expenditures, is amended as follows: (1) by inserting
after paragraph (B)(i) the following: ``(ii) the provision without
charge of any television broadcast time by a licensee pursuant to
section 315(a) of the Communications Act of 1934, as amended;'' and (2)
by redesignating subsequent subparagraphs accordingly.
Sec. 6. The Federal Communications Commission shall study the
application of section 315(a) of the Communications Act of 1934, as
amended by this Act, to the first general election campaign conducted
under the provisions of that section and shall report the results of
that study, together with recommendations, including recommendations
for legislation, not later than the first day of March following such
general election. The study shall also evaluate the desirability and
feasibility of extending the provisions of section 315(a) of the
Communications Act of 1934 to primary and other election campaigns.
Sec. 7. The Federal Communications Commission shall promulgate
rules and regulations to implement this Act no later than one hundred
and eighty days after the date of enactment of this Act. Sections 1 and
2 of this Act shall not take effect until the first day of July
following the promulgation of such rules and regulations.[/INST]Amends the Communications Act of 1934 to require each licensee operating a television (TV) broadcasting station to make available without charge to any legally qualified candidate for the Senate an amount of broadcast time as determined by the Federal Communications Commission (FCC) during the 45-day period preceding such election.
Directs the FCC to: (1) determine the amount of TV broadcast time that such candidates may receive on the basis of the amount of broadcast time used by major party candidates in the previous Senate election, provided that at a minimum such candidates be provided sufficient time to make a complete presentation of views; and (2) ensure that such TV broadcast time be made available fairly and equitably and at hours of the day which reflect TV viewing habits and contemporaneous campaign practices.
Requires that a legally qualified candidate of a party other than a party which obtained five percent or more of the popular vote in the last presidential election be granted an allocation of broadcast time in proportion to the amount of contributions under $250 such candidate has received when compared to such contributions received by candidates of the major parties, provided such proportion exceeds five percent. Directs the FCC to require licensees operating TV broadcasting stations to enter into a pooling agreement to ameliorate any disproportionate financial impact on particular licensees.
Conditions the entitlement to TV broadcast time under this Act upon the candidate's: (1) signing an agreement to forego both the purchase of any additional amount of broadcast time and any additional time purchased by another candidate during the period that such time is made available; and (2) filing a copy of such agreement with the FCC.
Sets forth penalties for any candidate who purchases or accepts purchased TV broadcast time in violation of such agreement. Subjects licensees to appropriate disciplinary action by the FCC.
Amends the Federal Election Campaign Act of 1971 to exclude from the definitions of "contributions" and "expenditures" the value of TV broadcast time provided without charge by a licensee pursuant to the Communications Act of 1934.
Directs the FCC to study the provision of free TV broadcast time to Senate candidates and evaluate the feasibility of extending such provision to primary and other election campaigns.</s> |
Daily News Headlines & Events Newsletter Would you like to receive a digest of each day's headlines & events from The Daily News by email? Signup today!
The Amplifier Headlines & Events Newsletter Would you like to receive a weekly digest of headlines & events from The Amplifier by email? Signup today! ||||| Kentucky Little League All-Star Keenan Briggs hasnβt always had the easiest life. He was born with a congenital upper limb difference in the form of being born without a left hand, but the Warren County, Kentucky native never let that keep him from participating in any of the sports or activities that his friends and classmates did.
That includes baseball, where he has eventually become a bona fide all-star for the Warren County South Little League 10-and-11All-Stars. Batting right handed to keep his right hand as the bottom base for his swing, Briggs has always been a talented contact hitter, if not a slugger.
For at least one at-bat, that changed in the District 1 Little League All-Star Tournament on July 1. Thatβs when and where Briggs accomplished what you see below:
Keenan Briggs hits 2 run dinger in 11 yr old district all-star tourney! Born with only one hand but kid has a huge heart and drive #SCtop10 pic.twitter.com/kn6KZSSTlk β Chuck Owsley (@OwsleyChuck) July 2, 2017
That, friends, is one-handed Keenan Briggs drilling a two-run homer right out of the park as Warren County South raced to a 20-7 rout of Bowling Green East in both teamsβ opening games of the District 1 settee.
The best part of the deep ball? Briggs knew it was gone as soon as it hit his bat. | β Keenan Briggs was born without a left hand, but that doesn't seem to have had a negative impact on the 11-year-old's baseball career. He's a Kentucky Little League All-Star who, per USA Today, has "always been a talented contact hitter." And on Saturday, he hit a home run in his district's All-Star tournament. The two-run homer went out of the park, helping Briggs' team win the game. "It felt great," he told the Bowling Green Daily News. "Once I hit it, I just knew it was going. It was amazing." | <s>[INST]Daily News Headlines & Events Newsletter Would you like to receive a digest of each day's headlines & events from The Daily News by email? Signup today!
The Amplifier Headlines & Events Newsletter Would you like to receive a weekly digest of headlines & events from The Amplifier by email? Signup today! ||||| Kentucky Little League All-Star Keenan Briggs hasnβt always had the easiest life. He was born with a congenital upper limb difference in the form of being born without a left hand, but the Warren County, Kentucky native never let that keep him from participating in any of the sports or activities that his friends and classmates did.
That includes baseball, where he has eventually become a bona fide all-star for the Warren County South Little League 10-and-11All-Stars. Batting right handed to keep his right hand as the bottom base for his swing, Briggs has always been a talented contact hitter, if not a slugger.
For at least one at-bat, that changed in the District 1 Little League All-Star Tournament on July 1. Thatβs when and where Briggs accomplished what you see below:
Keenan Briggs hits 2 run dinger in 11 yr old district all-star tourney! Born with only one hand but kid has a huge heart and drive #SCtop10 pic.twitter.com/kn6KZSSTlk β Chuck Owsley (@OwsleyChuck) July 2, 2017
That, friends, is one-handed Keenan Briggs drilling a two-run homer right out of the park as Warren County South raced to a 20-7 rout of Bowling Green East in both teamsβ opening games of the District 1 settee.
The best part of the deep ball? Briggs knew it was gone as soon as it hit his bat.[/INST]β Keenan Briggs was born without a left hand, but that doesn't seem to have had a negative impact on the 11-year-old's baseball career. He's a Kentucky Little League All-Star who, per USA Today, has "always been a talented contact hitter." And on Saturday, he hit a home run in his district's All-Star tournament. The two-run homer went out of the park, helping Briggs' team win the game. "It felt great," he told the Bowling Green Daily News. "Once I hit it, I just knew it was going. It was amazing."</s> |
suppression of charmonium production in high energy heavy ion collisions is a possible signature for the quark - gluon plasma ( qgp ) formed in ultra - relativistic heavy ion collisions @xcite .
recent data from the pb+pb collision at @xmath5 gev@xmath6 in the na50 experiment at cern @xcite have shown an anomalously large @xmath0 suppression in high @xmath7 events . while there are suggestions that this anomalous suppression may be due to the formation of the qgp @xcite , more conventional mechanisms based on @xmath0 absorption by comoving hadrons
have also been proposed as a possible explanation @xcite .
since the latter scenario depends on the value of @xmath0 absorption cross sections by hadrons , it is important to have better knowledge of these cross sections in order to understand the observed anomalous charmonium suppression @xcite . even in heavy ion collisions at the relativistic heavy ion collider ( rhic ) , where the qgp is most likely to be formed ,
the effect of hadronic absorption of @xmath0 is still non - negligible @xcite .
furthermore , one needs to know if @xmath0 can also be produced from the hot hadronic matter in the later stage of heavy ion collisions @xcite .
also , charm mesons such as @xmath1 and @xmath2 are expected to be abundantly produced in heavy ion collisions at rhic energies and beyond .
it has been shown that the high mass ( @xmath8 gev ) dilepton spectrum at rhic may be dominated by decays from charm and bottom hadrons @xcite .
since charm quarks may lose appreciable energies in a quark - gluon plasma via gluon radiations , study of charm meson spectrum in heavy ion collisions could provide useful information on the properties of the qgp @xcite .
however , charm mesons may interact strongly with hadrons during later stage of heavy ion collisions , leading to possible changes in their final spectra . as a result ,
the dilepton spectrum from the decay of charm meson pairs could also be modified @xcite . to study the energy loss of charm quarks in the qgp
thus requires the understanding of charm meson interactions in hadronic matter .
various approaches have been used in evaluating the charmonium absorption cross sections by hadrons . in the quark - exchange model ,
an earlier study @xcite has shown that the @xmath0 absorption cross section by pion , @xmath9 , has a peak value of about @xmath10 mb at @xmath11 gev , but a recent study @xcite gives a peak value of only @xmath12 mb at the same @xmath13 region .
on the other hand , the perturbative qcd approach @xcite predicts that the @xmath0 dissociation cross section increases monotonously with @xmath13 and has a value of only about @xmath14 mb around @xmath15 gev .
charmonium absorption cross sections by hadrons have also been studied in meson - exchange models based on effective hadronic lagrangians .
using pseudoscalar - pseudoscalar - vector - meson ( ppv ) couplings and without form factors at the interaction vertices , matinyan and mller @xcite have found @xmath16 mb at @xmath17 gev . in a recent study ,
haglin @xcite has included also the three - vector - meson ( vvv ) and four - point couplings ( or contact terms ) , and obtained much larger values for the @xmath0 absorption cross sections .
large discrepancies in the magnitude of @xmath9 ( as well as @xmath18 ) thus exist among the predictions from these three approaches . in this study
, we use a meson - exchange model as in @xcite but treat differently the vvv and four - point couplings in the effective lagrangian . for charm
meson scattering cross sections with pion and rho meson , previous studies from the meson - exchange model include only the ppv interactions @xcite .
we now also use the extended hadronic lagrangian to study these cross sections .
the free lagrangian for pseudoscalar and vector mesons in the limit of su(4 ) invariance can be written as @xmath19 , where @xmath20 , and @xmath21 and @xmath22 denote , respectively , the @xmath23 pseudoscalar and vector meson matrices in su(4 ) @xcite . to obtain the couplings between pseudoscalar and vector mesons
, we introduce the minimal substitution @xmath24,~ f_{\mu \nu } \rightarrow \partial_\mu v_\nu-\partial_\nu v_\mu -\frac{ig}{2 } \left [ v_\mu , v_\nu \right ] .\ ] ] the effective lagrangian is then given by @xmath25 \right ) -\frac{g^2}{4 } { \rm tr } \left ( \left [ p , v_\mu \right ] ^2 \right ) \nonumber \\ & + & ig { \rm tr } \left ( \partial^\mu v^\nu \left [ v_\mu , v_\nu \right ] \right ) + \frac{g^2}{8 } { \rm tr } \left ( \left [ v_\mu , v_\nu \right ] ^2 \right ) ~. \label{lagn2}\end{aligned}\ ] ] since the su(4 ) symmetry is explicitly broken by hadron masses , terms involving hadron masses are added to eq.([lagn2 ] ) using the experimentally determined values . the effective lagrangian in eq . ( [ lagn2 ] )
is generated by minimal substitution , which is equivalent to treating vector mesons as gauge particles .
the gauge invariance leads to the current conservation ; i.e. , in the limit of zero vector meson masses , degenerate pseudoscalar meson masses , and su(4 ) invariant coupling constants , one has @xmath26 for any given process , where the index @xmath27 denotes the external vector meson @xmath28 .
we have checked that all the amplitudes without form factors satisfy the requirement of current conservation .
the above effective lagrangian allows us to study various interactions of charm mesons and @xmath0 with hadrons .
these include the charm meson scattering such as @xmath29 , the charm meson production and annihilation such as @xmath30 , and the charmonium absorption and annihilation such as @xmath31 .
this effective hadronic lagrangian has also been extended to su(5 ) to study @xmath32 absorption in hadronic matter @xcite . in the following ,
we show the results for @xmath0 absorption and charm meson scattering by pion and rho meson .
for @xmath0 absorption by @xmath3 and @xmath4 mesons , we study the following processes : @xmath33 the full amplitudes for these processes can be found in @xcite . from the @xmath2 decay width @xcite , the coupling constant @xmath34 is found to be @xmath35 . using the vector meson dominance ( vmd ) model , we determine other three - point coupling constants as @xcite @xmath36 for the four - point coupling constants , there is no empirical information , and we thus use the su(4 ) relations to determine their values as @xmath37 form factors are introduced at interaction vertices to take into account the composite nature of hadrons . unfortunately , there is no empirical information on form factors involving charmoniums and charm mesons .
we thus take the form factors as the usual monopole form at the three - point @xmath38 and @xmath39 channel vertices , i.e. , @xmath40 , where @xmath41 is a cutoff parameter , and @xmath42 is the squared three momentum transfer in the c.m .
frame , given by @xmath43 and @xmath44 for @xmath38 and @xmath39 channel processes , respectively . for simplicity
, we use the same value for all cutoff parameters , i.e. , @xmath45 , and choose @xmath41 as either @xmath46 or @xmath47 gev to study the uncertainties due to form factors .
we also assume that the form factor at four - point vertices is given by @xmath48 ^ 2 $ ] , where @xmath49 is the average value of the squared three momentum transfers in @xmath38 and @xmath39 channels , @xmath50 .
[ cols= " < , > " , ] the charm meson scattering cross sections and their thermal averages are shown in figure 2a and 2b , respectively .
as expected , the magnitude of the cross sections decreases with decreasing cutoff parameter . for the cutoff parameters used here , the cross sections for @xmath51 and @xmath52 scattering are all roughly between 10 and 20 mb .
we note that form factors only suppress modestly ( by a factor of two and less ) these total cross sections and their thermal averages .
this is due to the fact that these cross sections are dominated by elastic processes , which involve small momentum transfer near the threshold .
in contrast , the process @xmath53 has a large threshold , and form factors suppress its cross section by as much as a factor of 8 .
in summary , we have introduced an effective hadronic lagrangian , that includes the charm mesons , to study the interactions of charmed mesons and @xmath0 in hadronic matter . in particular , we have calculated the absorption cross sections of @xmath0 and scattering cross sections of charmed mesons by @xmath3 and @xmath4 mesons .
we find that the @xmath0 absorption cross sections are much larger than those in a previous study , where only pseudoscalar - pseudoscalar - vector - meson couplings were considered .
including form factors at the interaction vertices , the values for @xmath9 and @xmath18 are about @xmath10 mb and @xmath54 mb , respectively , and their thermal averages at the temperature of @xmath55 mev are roughly @xmath46 mb and @xmath47 mb , respectively .
these values suggest that the absorption of @xmath0 by comoving hadrons may play an important role in @xmath0 suppression in relativistic heavy ion collisions .
we also find that the scattering cross sections of @xmath1 or @xmath2 by @xmath3 or @xmath4 mesons are all about @xmath56 mb and thus expect these scatterings to significantly modify the charm meson spectra in heavy ion collisions .
this work was supported in part by the national science foundation under grant no .
phy-9870038 , the welch foundation under grant no
. a-1358 , and the texas advanced research program under grant no .
fy99 - 010366 - 0081 .
99 matsui t and satz h .
gonin m _ et al _ ( na50 collaboration ) ; abreu m c _ et al _ ( na50 collaboration ) .
blaizot j p and ollitrault j y .
cassing w and ko c m ; cassing w and bratkovskaya e l .
armesto n and capella a . for recent reviews , see , e.g. , vogt r ; satz h .
zhang b , ko c m , li b a , lin z and sa b h .
ko c m , wang x n , zhang b and zhang x f .
braun - munzinger b and redlich k .
vogt r , jacak b v , mcgaughey p l and ruuskanen p v .
shuryak e .
lin z , vogt r and wang x n .
lin z and wang x n .
martins k , blaschke d and quack e . wong c y , swanson e s and barnes t .
kharzeev d and satz h .
matinyan s g and mller b .
haglin k and gale c .
lin z , ko c m and zhang b .
lin z and ko c m .
lin z and ko c m .
colangelo p , de fazio f and nardulli g ; belyaev v m , braun v m , khodjamirian a and ruckl r .
kahana d e and kahana s h ; sa b h , tai a , wang h and liu f h ; spieles c , vogt r , gerland l , bass s a , bleicher m , stcker h and greiner w .
lin z , di t g and ko c m .
brown g e , ko c m , wu z g and xia l h ; ko c m and seibert d .
tsushima k , huang s w and faessler a ; bratkovskaya e l and ko c m . | an effective hadronic lagrangian including the charm mesons is introduced to study their interactions in hadronic matter . using coupling constants that are determined either empirically or by the su(4 ) symmetry ,
we have evaluated the absorption cross sections of @xmath0 and the scattering cross sections of @xmath1 and @xmath2 by @xmath3 and @xmath4 mesons . | <s>[INST]suppression of charmonium production in high energy heavy ion collisions is a possible signature for the quark - gluon plasma ( qgp ) formed in ultra - relativistic heavy ion collisions @xcite .
recent data from the pb+pb collision at @xmath5 gev@xmath6 in the na50 experiment at cern @xcite have shown an anomalously large @xmath0 suppression in high @xmath7 events . while there are suggestions that this anomalous suppression may be due to the formation of the qgp @xcite , more conventional mechanisms based on @xmath0 absorption by comoving hadrons
have also been proposed as a possible explanation @xcite .
since the latter scenario depends on the value of @xmath0 absorption cross sections by hadrons , it is important to have better knowledge of these cross sections in order to understand the observed anomalous charmonium suppression @xcite . even in heavy ion collisions at the relativistic heavy ion collider ( rhic ) , where the qgp is most likely to be formed ,
the effect of hadronic absorption of @xmath0 is still non - negligible @xcite .
furthermore , one needs to know if @xmath0 can also be produced from the hot hadronic matter in the later stage of heavy ion collisions @xcite .
also , charm mesons such as @xmath1 and @xmath2 are expected to be abundantly produced in heavy ion collisions at rhic energies and beyond .
it has been shown that the high mass ( @xmath8 gev ) dilepton spectrum at rhic may be dominated by decays from charm and bottom hadrons @xcite .
since charm quarks may lose appreciable energies in a quark - gluon plasma via gluon radiations , study of charm meson spectrum in heavy ion collisions could provide useful information on the properties of the qgp @xcite .
however , charm mesons may interact strongly with hadrons during later stage of heavy ion collisions , leading to possible changes in their final spectra . as a result ,
the dilepton spectrum from the decay of charm meson pairs could also be modified @xcite . to study the energy loss of charm quarks in the qgp
thus requires the understanding of charm meson interactions in hadronic matter .
various approaches have been used in evaluating the charmonium absorption cross sections by hadrons . in the quark - exchange model ,
an earlier study @xcite has shown that the @xmath0 absorption cross section by pion , @xmath9 , has a peak value of about @xmath10 mb at @xmath11 gev , but a recent study @xcite gives a peak value of only @xmath12 mb at the same @xmath13 region .
on the other hand , the perturbative qcd approach @xcite predicts that the @xmath0 dissociation cross section increases monotonously with @xmath13 and has a value of only about @xmath14 mb around @xmath15 gev .
charmonium absorption cross sections by hadrons have also been studied in meson - exchange models based on effective hadronic lagrangians .
using pseudoscalar - pseudoscalar - vector - meson ( ppv ) couplings and without form factors at the interaction vertices , matinyan and mller @xcite have found @xmath16 mb at @xmath17 gev . in a recent study ,
haglin @xcite has included also the three - vector - meson ( vvv ) and four - point couplings ( or contact terms ) , and obtained much larger values for the @xmath0 absorption cross sections .
large discrepancies in the magnitude of @xmath9 ( as well as @xmath18 ) thus exist among the predictions from these three approaches . in this study
, we use a meson - exchange model as in @xcite but treat differently the vvv and four - point couplings in the effective lagrangian . for charm
meson scattering cross sections with pion and rho meson , previous studies from the meson - exchange model include only the ppv interactions @xcite .
we now also use the extended hadronic lagrangian to study these cross sections .
the free lagrangian for pseudoscalar and vector mesons in the limit of su(4 ) invariance can be written as @xmath19 , where @xmath20 , and @xmath21 and @xmath22 denote , respectively , the @xmath23 pseudoscalar and vector meson matrices in su(4 ) @xcite . to obtain the couplings between pseudoscalar and vector mesons
, we introduce the minimal substitution @xmath24,~ f_{\mu \nu } \rightarrow \partial_\mu v_\nu-\partial_\nu v_\mu -\frac{ig}{2 } \left [ v_\mu , v_\nu \right ] .\ ] ] the effective lagrangian is then given by @xmath25 \right ) -\frac{g^2}{4 } { \rm tr } \left ( \left [ p , v_\mu \right ] ^2 \right ) \nonumber \\ & + & ig { \rm tr } \left ( \partial^\mu v^\nu \left [ v_\mu , v_\nu \right ] \right ) + \frac{g^2}{8 } { \rm tr } \left ( \left [ v_\mu , v_\nu \right ] ^2 \right ) ~. \label{lagn2}\end{aligned}\ ] ] since the su(4 ) symmetry is explicitly broken by hadron masses , terms involving hadron masses are added to eq.([lagn2 ] ) using the experimentally determined values . the effective lagrangian in eq . ( [ lagn2 ] )
is generated by minimal substitution , which is equivalent to treating vector mesons as gauge particles .
the gauge invariance leads to the current conservation ; i.e. , in the limit of zero vector meson masses , degenerate pseudoscalar meson masses , and su(4 ) invariant coupling constants , one has @xmath26 for any given process , where the index @xmath27 denotes the external vector meson @xmath28 .
we have checked that all the amplitudes without form factors satisfy the requirement of current conservation .
the above effective lagrangian allows us to study various interactions of charm mesons and @xmath0 with hadrons .
these include the charm meson scattering such as @xmath29 , the charm meson production and annihilation such as @xmath30 , and the charmonium absorption and annihilation such as @xmath31 .
this effective hadronic lagrangian has also been extended to su(5 ) to study @xmath32 absorption in hadronic matter @xcite . in the following ,
we show the results for @xmath0 absorption and charm meson scattering by pion and rho meson .
for @xmath0 absorption by @xmath3 and @xmath4 mesons , we study the following processes : @xmath33 the full amplitudes for these processes can be found in @xcite . from the @xmath2 decay width @xcite , the coupling constant @xmath34 is found to be @xmath35 . using the vector meson dominance ( vmd ) model , we determine other three - point coupling constants as @xcite @xmath36 for the four - point coupling constants , there is no empirical information , and we thus use the su(4 ) relations to determine their values as @xmath37 form factors are introduced at interaction vertices to take into account the composite nature of hadrons . unfortunately , there is no empirical information on form factors involving charmoniums and charm mesons .
we thus take the form factors as the usual monopole form at the three - point @xmath38 and @xmath39 channel vertices , i.e. , @xmath40 , where @xmath41 is a cutoff parameter , and @xmath42 is the squared three momentum transfer in the c.m .
frame , given by @xmath43 and @xmath44 for @xmath38 and @xmath39 channel processes , respectively . for simplicity
, we use the same value for all cutoff parameters , i.e. , @xmath45 , and choose @xmath41 as either @xmath46 or @xmath47 gev to study the uncertainties due to form factors .
we also assume that the form factor at four - point vertices is given by @xmath48 ^ 2 $ ] , where @xmath49 is the average value of the squared three momentum transfers in @xmath38 and @xmath39 channels , @xmath50 .
[ cols= " < , > " , ] the charm meson scattering cross sections and their thermal averages are shown in figure 2a and 2b , respectively .
as expected , the magnitude of the cross sections decreases with decreasing cutoff parameter . for the cutoff parameters used here , the cross sections for @xmath51 and @xmath52 scattering are all roughly between 10 and 20 mb .
we note that form factors only suppress modestly ( by a factor of two and less ) these total cross sections and their thermal averages .
this is due to the fact that these cross sections are dominated by elastic processes , which involve small momentum transfer near the threshold .
in contrast , the process @xmath53 has a large threshold , and form factors suppress its cross section by as much as a factor of 8 .
in summary , we have introduced an effective hadronic lagrangian , that includes the charm mesons , to study the interactions of charmed mesons and @xmath0 in hadronic matter . in particular , we have calculated the absorption cross sections of @xmath0 and scattering cross sections of charmed mesons by @xmath3 and @xmath4 mesons .
we find that the @xmath0 absorption cross sections are much larger than those in a previous study , where only pseudoscalar - pseudoscalar - vector - meson couplings were considered .
including form factors at the interaction vertices , the values for @xmath9 and @xmath18 are about @xmath10 mb and @xmath54 mb , respectively , and their thermal averages at the temperature of @xmath55 mev are roughly @xmath46 mb and @xmath47 mb , respectively .
these values suggest that the absorption of @xmath0 by comoving hadrons may play an important role in @xmath0 suppression in relativistic heavy ion collisions .
we also find that the scattering cross sections of @xmath1 or @xmath2 by @xmath3 or @xmath4 mesons are all about @xmath56 mb and thus expect these scatterings to significantly modify the charm meson spectra in heavy ion collisions .
this work was supported in part by the national science foundation under grant no .
phy-9870038 , the welch foundation under grant no
. a-1358 , and the texas advanced research program under grant no .
fy99 - 010366 - 0081 .
99 matsui t and satz h .
gonin m _ et al _ ( na50 collaboration ) ; abreu m c _ et al _ ( na50 collaboration ) .
blaizot j p and ollitrault j y .
cassing w and ko c m ; cassing w and bratkovskaya e l .
armesto n and capella a . for recent reviews , see , e.g. , vogt r ; satz h .
zhang b , ko c m , li b a , lin z and sa b h .
ko c m , wang x n , zhang b and zhang x f .
braun - munzinger b and redlich k .
vogt r , jacak b v , mcgaughey p l and ruuskanen p v .
shuryak e .
lin z , vogt r and wang x n .
lin z and wang x n .
martins k , blaschke d and quack e . wong c y , swanson e s and barnes t .
kharzeev d and satz h .
matinyan s g and mller b .
haglin k and gale c .
lin z , ko c m and zhang b .
lin z and ko c m .
lin z and ko c m .
colangelo p , de fazio f and nardulli g ; belyaev v m , braun v m , khodjamirian a and ruckl r .
kahana d e and kahana s h ; sa b h , tai a , wang h and liu f h ; spieles c , vogt r , gerland l , bass s a , bleicher m , stcker h and greiner w .
lin z , di t g and ko c m .
brown g e , ko c m , wu z g and xia l h ; ko c m and seibert d .
tsushima k , huang s w and faessler a ; bratkovskaya e l and ko c m .[/INST] an effective hadronic lagrangian including the charm mesons is introduced to study their interactions in hadronic matter . using coupling constants that are determined either empirically or by the su(4 ) symmetry ,
we have evaluated the absorption cross sections of @xmath0 and the scattering cross sections of @xmath1 and @xmath2 by @xmath3 and @xmath4 mesons . </s> |
over the past eons , tidal interaction produced a major evolution of the earth - moon system , producing a relatively slowly rotating planet down from about one - third of centrifugal break - up at birth , very similar then to jupiter s state today .
for a detailed discussion on the break - up angular velocity @xmath11 of a planet of mass @xmath12 and radius @xmath13 , see , e.g. , @xcite .
tidal interactions are inherently dissipative , determined by a phase - lag between tidal deformation and position of the perturber , i.e. , a misalignment of tidal bulge relative to the earth - moon direction . for the earth , dissipation is primarily in the ocean tidal flows , more so than viscoelastic deformation of the earth s mantle ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) , whose seismic frequencies are relative high compared to the tidal frequency @xcite with the exception of those driven by ocean waves @xcite .
however , a detailed quantitative account for the overall moon s migration time due to various nonlinear dissipation channels @xcite , remains to be identified .
tidal dissipation @xcite has various mechanisms in shallow water wave theory , some of which have recently been highlighted in detailed numerical simulations on ocean dynamics and dissipation covering relatively short initial and present epochs ( e.g * ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
dissipation generally occurs when nonlinear steepening exceeds the mitigating effect of dispersion . determining the net global result from detailed modeling of tidal dissipation is particularly challenging by the diversity of oceans and coastal regions , where most of the dissipation is expected to occur @xcite . here , we focus on scaling in both amplitude and frequency of global tidal dissipation to account for the earth - moon history over the past 4.52 gyr .
this approach aims at providing an effective description of an otherwise complex spatio - temperal distribution of dissipation in broadband ocean waves . for a confrontation with data , the moon s migration time is computed by numerical integration of angular momentum transfer backwards in time , to the instant of its formation from the earth or a surrounding proto - lunar disk
this approach enables taking into account variations in tidal implitude over a few orders of magnitude , the effect of which seems not to have been computed before .
the evolution by coupling to the earth s spin ( e.g. * ? ? ?
* ) is conveniently described by the orbital angular momentum @xmath14 with semi - major axis @xmath15 , where @xmath16 g and @xmath17 g denote the mass of the moon and , respectively , earth .
the orbital ellipticity @xmath18 is presently about @xmath19 .
a large dynamic range in tidal interaction strength arises from the tidal amplitude @xmath20 by which the moon s specific angular momentum at radius @xmath21 evolves according to @xmath22 where @xmath23 is the phase - lag of the moon s orbit relative to the tide raised on the earth , and @xmath24 is the mutual interaction strength for a given @xmath5 . as a result , @xmath25 ( cf . * ? ? ?
* ) . to begin , we first recall some general conditions for dissipation in ocean tidal flows ( 2 ) . in 3 , we formulate our scaling of dissipation in tidal amplitude and frequency .
it serves to parameterize damping in our model based on ( [ eqn_j ] ) and the pendulum equation ( 4 ) .
this model is explored numerically in 5 . in 6 , we summarize the results .
while the theory of linear shallow water waves is dissipationless , finite amplitude waves can steepen to dissipative bores , provided that steeping exceeds the mitigating effect of dispersion .
the degree of nonlinearity over dispersion is expressed by ursell number @xmath26 , by the amplitude @xmath5 and wave length @xmath27 @xcite @xmath28 here specialized to shallow water waves with propagation speed @xmath29 in oceans of depth @xmath30 at tidal period @xmath31 , where @xmath32ms@xmath33 is the earth s gravitational acceleration . while , a large ursell number is suggestive of a general tendency for wave breaking , it does not directly define scaling of dissipation . for breaking to occur
, steepening must be sufficiently fast ( e.g. * ? ? ?
* ) ( see @xcite for a discussion in burgers equation with time - dependent forcing ) . in nonlinear wave motion ( cf .
* ) , it results from steepening after a time @xmath34 ( for a more detailed discussion , see @xcite . ) here , ( [ eqn_wb ] ) is relaxed by an additional @xmath8-factor of the oceans with reflection of tidal waves off coastal regions . with @xmath35
, however , wave breaking is unlikely to occur in the open oceans even at present - day values of @xmath8 ( 3 below ) .
instead , it believed to occur in shallow seas , in run - up waves in shoaling shelf regions with slopes @xmath36 satisfying @xcite @xmath37 the dissipation rate of bores produced by wave breaking satisfies entropy creation in shocks of compressible gas dynamics , i.e. , scaling with the cube of their amplitude . by aforementioned @xmath20 , wave breaking , by either ( [ eqn_ursell ] ) or ( [ eqn_surf ] ) ,
provides a time rate of dissipation effectively described by damping proportional to @xmath5 , possibly including tidal frequency in light of broadband wave spectra .
our approach is focused on scaling in global dissipation described by ( [ eqn_epsd0 ] ) , to capture the net result of an otherwise complex spatio - temporal distribution of dissipation in the earth s oceans .
we set out model global tidal dissipation in the earth s oceans by ( [ eqn_j ] ) in dimensionless variables , normalized by today s moon migration data and age .
the tidal amplitude @xmath5 is described by a damped linear pendulum equation with eigenfrequency @xmath38 , forced at semi - diurnal tidal frequency @xmath39 by the action of the moon at orbital angular velocity @xmath40 , @xmath41 where @xmath42 denotes the angular velocity of the earth . the damping coefficient @xmath43 in the pendulum equation represents dissipation with associated phase lag @xmath23 and @xmath8-factor @xmath44 . to study the net result over the entire history of the earth - moon system
, we consider the general scaling in amplitude @xmath5 and dimensionless tidal frequency @xmath6 , @xmath45 and its confrontation with data for various choices of @xmath46 . with ( [ eqn_epsd0 ] ) , we aim to capture the net result of tidal amplitude - frequency dependence that covers weak and strong interactions at present and , respectively , back in the distant past . in the stokes limit @xmath47 , for instance , and ignoring resonances , integration of ( [ eqn_j ] ) backwards in time obtains a migration time on the order of 1 gyr at odds with the moon s age ( cf . * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
this suggests that tidal dissipation is anomalously high at present .
( equivalently , the @xmath8-factor was higher in the past , e.g. , @xcite . ) taking into account the inertial range off - resonance in the past ( fig .
1 ) , however , one is led to the opposite conclusion with a previously _ low _
@xmath8-factor , here revisited by numerical integration of ( [ eqn_j ] ) with ( [ eqn_epsd0 ] ) in the forced pendulum equation .
the moon migrated to its present mean distance @xmath48 cm with a radial velocity @xmath2 cm yr@xmath3 @xcite .
it defines a characteristic migration time scale @xmath49 that will serve to express the equation of motion ( [ eqn_j ] ) in terms of a dimensionless time @xmath50 ( 3 below ) .
being tidally locked , the moon spins slowly with negligible angular momentum . by now ,
the earth s spin has effectively been transferred to the earth - moon orbit , since @xmath51 based on the moon s mass @xmath52 , the earth s angular momentum @xmath53 , radius @xmath54 and moment of inertia @xmath55 , $ ] @xmath56 @xcite .
the present - day tidal deformation @xmath57 ( in cm ) has a characteristic scale defined by the zero - frequency perturbation of the newtonian binding energy @xmath58 of self - gravity and @xmath59 in the moon s tidal field , @xmath60 , @xmath61 which recovers the familiar scaling @xmath62 with @xmath63 erg , consistent with existing estimates on ocean tide energies @xcite and measured mean values of the dynamical tidal amplitude @xmath5 to about 20% @xcite .
consistency of @xmath57 with dynamical tidal amplitude is somewhat coincidental in view of the relatively minor deformation of the earth s mantle @xcite and an appreciable @xmath8-factor in the ocean tides ( e.g. * ? ? ?
[ cols="<,<,<,<,<",options="header " , ] the trajectory of ( [ eqn_r4e ] ) , illustrated in fig .
[ figa ] , with amplitude - frequency scaling ( [ eqn_epsd0 ] ) with @xmath64 shows that most of the moon s migration time is associated with the last 40% of its current distance .
the first 60% is marked by a transition starting with a sharp spike , denoting rapid eviction of the moon from @xmath65 .
it results from an anomalously large tidal wave amplitude of a few km ( essentially the current ocean depths ) , defined by @xmath66 in units of the present - day amplitue scale @xmath57 .
thus , @xmath67 , giving an eviction time scale of about one hundred years out to tens of @xmath68 .
while this is unlikely accurate , e.g. , tidal heating may have prevented water to condensate and may , instead , derive from a magma ocean @xcite , the idea seems valid that , once oceans form , eviction is swift .
the migration time of the moon is determined by the rate of tidal dissipation , predominantly in tidal waves . in the past , forcing was mostly off - resonance in the inertial range above the resonance frequency @xmath38 in ( [ eqn_pe ] ) .
linear theory of dissipation described by the stokes limit @xmath69 falls short of explaining a migration time equal to the moon s age .
nonlinear dissipation mechanisms pointed to by ( [ eqn_ursell ] ) are important , now and even more so during off - resonance in the past .
dissipation in bores is similar to that in shocks of compressible gas dynamics .
the same is expected to feature spectral broadening and hardening by dispersion ( e.g. * ? ? ?
* ; * ? ? ?
damping representing total tidal dissipation hereby is expected to scale both with tidal amplitude and frequency proposed in ( [ eqn_epsd ] ) .
total dissipation in the ocean tides contains also a component of internal dissipation by flows over non - smooth surfaces @xcite .
it scales effectively with the cube of horizontal tidal flows @xcite , akin to high reynolds number flows past solid objects .
according to the theory of shallow water wave equations , column height and height - averaged horizontal velocity satisfy the same wave equation in the linearized limit , the latter with amplitude @xmath70 for harmonic perturbations , internal dissipation is equivalently described by damping proportional to @xmath71 , and hence by @xmath5 as a consequence of ( [ eqn_uh ] ) . in table 2 , this is included in the scaling by tidal amplitude . in scaling damping of ocean waves by @xmath72 , the same would be included approximately to within 30% . in considering ( [ eqn_r4e ] ) as an effective description of the dominant dissipation in semidiurnal tidal interactions , higher order tidal modes @xcite are neglected with generally complex dependence on ocean basin geometry @xcite . in a linearized approximation
, one might contemplate including damping by higher harmonics .
however , the latter are difficult to constrain observationally based on data of the moon s migration velocity .
even if known , evolution of ocean basins on the geological time scale of @xmath73 myr ( e.g. * ? ? ?
* ; * ? ? ?
* ) makes estimation of time - averages over a recent epoch highly uncertain . for this reason and the expectation that dissipation in the semi - diurnal tides
are dominant , these higher order perturbations fall outside the scope of the present approach . numerical integration of ( [ eqn_r4e ] ) with ( [ eqn_epsd ] ) reproduces a moon migration time equal to its age for a present @xmath8-factor ( [ eqn_qer ] ) in excellent agreement with the observational constraint ( [ eqn_qe ] ) . by ( [ eqn_epsd ] )
, it introduces a dynamic @xmath8-factor @xmath74 that was substantially below @xmath75 in the past .
its trajectory features a startingly fast eviction of the moon at or close to the initial , unstable synchronous orbit at @xmath76 . a protolunar disk with the same composition as the earth ( e.g. * ?
* ) might require even higher earth spin rates prior , to facilitate its ejection by a giant impact @xcite .
if so , the moon is even more pertinent as a deposit of the earth s initial spin angular momentum .
some uncertainty in the formulation of our model arises from the fact that the ocean eigenfrequency @xmath38 ( closest to the semidiurnal tidal frequency ) is that of the atlantic ocean . by continental drift
, it evolves on aforementioned geological time scale that , in particular , might include intermittent closure @xcite . in our numerical formulation ,
the present state then represents a time - average of a recent epoch , small relative to the moon s age of 4.5 gyr , probably satisfying @xmath77 where the right hand side refers to today s instantaneous value .
here , we assume that during closure , @xmath38 is determined by the remaining oceans , also since @xmath8 of the atlantic near closure is probably suppressed by inversion ( uplift of the ocean basin ; * ? ? ?
* ) ) . in fig .
[ figke ] , ( [ eqn_ave ] ) corresponds to moving along the ordinate to the right . by the relative flatness of the curves shown ,
our main conclusions hold , provided ( [ eqn_ave ] ) remains in the window @xmath78 for solutions to exist .
implications of larger perturbations fall outside the scope of the present formulation .
once oceans form , eviction of the moon was swift with steep spindown of the earth from what was very similar to that of jupiter today .
in contrast to jupiter s extreme weather patterns @xcite , our dramatically reduced spin with small coriolis forces today facilitates a clement global climate . it is tempting to consider application of ( [ eqn_epsd ] ) further to exoplanet - moon systems @xcite , whose selection is currently based on temperature , mass and size @xcite .
relatively distant moons may be indirect evidence for effective tidal interaction with oceans , further favoring a potentially clement climate conducive to advanced life .
* acknowledgments . *
the author gratefully thanks the reviewer for constructive comments and pointing out several pertinent references .
this report was supported in part by the national research foundation of korea under grant no .
2015r1d1a1a01059793 and 2016r1a5a1013277 .
99 barnes , j.j .
, tartse , r. , anand , m. , mccubbin , f. , franchi , i.a . , et al . , 2014 ,
earth and plan .
lett . , 390 , 244 barthlemy , e. , 2004 , surv .
, 25 , 315 bills , b.g . , & ray , r.d . , 1999 , geophysical res .
lett . , 26 , 3045 canup , r.m . , asphaug , e. , 2001 , nature , 412 , 708 cheng , w.h . ,
lee , m.h . , & peale , s.j .
, 2014 , icarus , 233 , 242 cuk , m. , & stewart , s. , 2012 , science , 338 , 1047 dahlen , f.a .
, 1974 , geophys .
j. r. astr .
, 36 , 461 davidsson , b.j.r . , 1999 , icarus , 142 , 525 dickey , j.o . ,
bender , p.l . ,
faller , j.e . , et al . , 1994 , science , 265 , 482 doodson , a.t . , 1921 , proc .
soc . , 100 , 305 egbert , g.d . , & ray , r.d . , 2000 , nature , 405 , 775 egbert , g.d
, & ray , r.d . , 2001 , j. geophys .
res . , 106 , 22 , 475 egbert , g.d . , & ray , r.d . , bills , b.g . , 2004 , j. geophys .
res . , 109 , c03003 efroimsky , m. , & williams , j.g . , 2009 ,
astr . , 104 , 257 efroimsky , m. , 2012 , celest .
mech . dyn .
astr . , 112 , 283 efroimsky , m. , , 2015 , apj , 150 , 98 nasa exoplanet archive , 2016 , http://exoplanetarchive.ipac.caltech.edu farinella , p. , milani , a. , nobili , a.m. , & valsecchi , g.b . , 1979 ,
moon & planets , 20 , 415 ford , e.b .
, rowe , , j.f . , fabrycky , d. , carter , j.a . ,
holman , m.j .
, et al . , 2011 , apjss , 197 , 2 frouard , fouchard , m. , & vienne , a. , 2010 , a&a , 515 , a54 garret , c.j.r . ,
& munk , w.h . , 1971 , deep - sea res . , 18 , 493 gerstenkorn , h. , z. astrophys . , 36 , 245 goldreich , p. , & , soter , s. , 1966 , icarus , 5 , 375 goldreich , p. , 1966
geophys . , 4 , 411 gemmrich , j. , & klymak , j.m . , 2015 , jpo , 45 , 2221 hansen , k.s . , 1982 , rev .
geophys . , 20 , 457 hendershott , m.c . , & munk , w.h . , 1970 ,
fluid mech . , 2 , 205 kleine , t. , palme , h. , mezger , k. , halliday , a.n . , 2005 , science , 310 , 5754 , 1671 halliday , a.n .
, 2008 , phil .
royal society a , 2008 , 366 , 4163 kipping , d.m . , 2009 ,
mnras , 396 , 1797 love , a.e.h . , 1911 , some problems in geodynamics , " cambridge university press lambeck , k. , phil .
a287 , 545 levinson , a. , & van putten , m.h.p.m .
, 1997 , apj , 488 , 69 macdonald , g.j.f .
, 1964 , rev .
geophys . 2 , 467 mndez , _ in _ 37@xmath79 ann .
lunar planetary sc .
, march 13 - 17 , texas , # 2396 miller , g.r . , 1966 , j. geophys .
, 71 , 2485 munk , w.h . , & macdonald , g.j.f .
, 1960 , the rotation of the earth " , cambridge univ .
press munk , & cartwright , 1966 , phil . , trans .
london , 259 , 533 munk , w.h . , 1968 , q. j. astr .
9 , 352 pekeris , c.l . , & accad , y. , 1969 , phil .
( a ) , 259 , 533 platzman , g.w . ,
curtis , g.a . , hansen , k.s .
, & slater , r.d . , j. phys .
ocean , 11 , 579 ray , r. d. _ in _ the oceans , eds .
majumdar , s. k. et al .
( pennsylvania academy of science , easton , 1994 ) , p.171 ray , r.d . ,
eanes , r.j .
, & chao , b.f . , 1996 , nature , 381 , 595 romanowicz & dambeck , 1977 , phys . earth plan .
, 15 , 1 schneider , j. , dedieu , c. , le sidaner , p. , savalle , r. , & zolotukhin , i. , 2011 , a&a , 532 , a79 salmon , r. , 2016 , http://www-pord.ucsd.edu/(tilde)rsalmon/111.textbook.pdf seabra - santos , f. j. , 1985 , contribution ltude des ondes de gravit bidimensionnelles en eau peu profonde , " ph.d .
thesis , institut national polytechnique de grenoble et universit scientifique et mdicle de grenoble 1 .
sommeria , j. , meyers , s.d . , & swinney , h.l . , 1998 ,
nature , 331 , 689 stammer , d. , ray , r.d . , anderson , o.b . , et al . , 2014 , rev .
geophys . , 52 , 243 stoker , j.j . , 1948 , commun .
pure appl .
, 1 , 1 stoker , j.j . , 1957 ,
_ water waves _ , interscience , new york taylor , p.a . , &
margot , j .-
l . , 2011 ,
icarus , 212 , 661 taylor , p.a . , & margot , j .-
l . , 2014 ,
icarus , 229 , 418 touma , j. , & wisdom , j. , 1994 , astron . j. , 1994 , 108 , 1943 touma , j. , & wisdom , j. , 1998 , astron . j. , 115 , 1653 tyler , r.h . , 2008 , nature , 456 , 770 ursell , 1953 , proc .
camb . philos . soc . , 49 , 685 wahr , 1995 , _ in _ global earth physics , a handbook of physical constants , agu reference shelf , 1 , , p.40 - 46 webb , d.j . , 1973 ,
deep sea res . , 20 , 847 webb , d.j . , 1982 ,
soc . , 70 , 261 webb , s.c .
, 2007 , nature , 445 , 754 whitham , g.b .
, 1974 , _ linear and nonlinear waves _ , john wiley & sons , ch
. 2 wilson , j.t .
, 1966 , nature , 211 , 676 wilson , j.t .
, 1975 , epsl , 25 , 33 zahnle , k. , lupu , r. , dobrovolskis , a. , & sleep , n.h . , 2015 ,
earth plan .
lett . , 427 , 74 | the moon migrated to @xmath0 cm over a characteristic time @xmath1 gyr by tidal interaction with the earth s oceans at a present velocity of @xmath2 cm yr@xmath3 . we derive scaling of global dissipation that covers the entire history over the past 4.52 gyr .
off - resonance tidal interactions at relatively short tidal periods in the past reveal the need for scaling with amplitude .
the global properties of the complex spatio - temporal dynamics and dissipation in broad spectrum ocean waves is modeled by damping @xmath4 , where @xmath5 is the tidal wave amplitude , @xmath6 is the tidal frequency , and @xmath7 is the @xmath8-factor at the present time .
it satisfies @xmath9 for consistency of migration time and age of the moon consistent with observations for a near - resonance state today .
it shows a startingly fast eviction of the moon from an unstable near - synchronous orbit close to the roche limit , probably in a protolunar disk .
rapid spin down of the earth from an intial @xmath10 of break - up by the moon favored early formation of a clement global climate .
our theory suggests moons may be similarly advantageous to potentially habitable exoplanets .
[ firstpage ] earth moon planets and satellites : oceans | <s>[INST]over the past eons , tidal interaction produced a major evolution of the earth - moon system , producing a relatively slowly rotating planet down from about one - third of centrifugal break - up at birth , very similar then to jupiter s state today .
for a detailed discussion on the break - up angular velocity @xmath11 of a planet of mass @xmath12 and radius @xmath13 , see , e.g. , @xcite .
tidal interactions are inherently dissipative , determined by a phase - lag between tidal deformation and position of the perturber , i.e. , a misalignment of tidal bulge relative to the earth - moon direction . for the earth , dissipation is primarily in the ocean tidal flows , more so than viscoelastic deformation of the earth s mantle ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) , whose seismic frequencies are relative high compared to the tidal frequency @xcite with the exception of those driven by ocean waves @xcite .
however , a detailed quantitative account for the overall moon s migration time due to various nonlinear dissipation channels @xcite , remains to be identified .
tidal dissipation @xcite has various mechanisms in shallow water wave theory , some of which have recently been highlighted in detailed numerical simulations on ocean dynamics and dissipation covering relatively short initial and present epochs ( e.g * ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
dissipation generally occurs when nonlinear steepening exceeds the mitigating effect of dispersion . determining the net global result from detailed modeling of tidal dissipation is particularly challenging by the diversity of oceans and coastal regions , where most of the dissipation is expected to occur @xcite . here , we focus on scaling in both amplitude and frequency of global tidal dissipation to account for the earth - moon history over the past 4.52 gyr .
this approach aims at providing an effective description of an otherwise complex spatio - temperal distribution of dissipation in broadband ocean waves . for a confrontation with data , the moon s migration time is computed by numerical integration of angular momentum transfer backwards in time , to the instant of its formation from the earth or a surrounding proto - lunar disk
this approach enables taking into account variations in tidal implitude over a few orders of magnitude , the effect of which seems not to have been computed before .
the evolution by coupling to the earth s spin ( e.g. * ? ? ?
* ) is conveniently described by the orbital angular momentum @xmath14 with semi - major axis @xmath15 , where @xmath16 g and @xmath17 g denote the mass of the moon and , respectively , earth .
the orbital ellipticity @xmath18 is presently about @xmath19 .
a large dynamic range in tidal interaction strength arises from the tidal amplitude @xmath20 by which the moon s specific angular momentum at radius @xmath21 evolves according to @xmath22 where @xmath23 is the phase - lag of the moon s orbit relative to the tide raised on the earth , and @xmath24 is the mutual interaction strength for a given @xmath5 . as a result , @xmath25 ( cf . * ? ? ?
* ) . to begin , we first recall some general conditions for dissipation in ocean tidal flows ( 2 ) . in 3 , we formulate our scaling of dissipation in tidal amplitude and frequency .
it serves to parameterize damping in our model based on ( [ eqn_j ] ) and the pendulum equation ( 4 ) .
this model is explored numerically in 5 . in 6 , we summarize the results .
while the theory of linear shallow water waves is dissipationless , finite amplitude waves can steepen to dissipative bores , provided that steeping exceeds the mitigating effect of dispersion .
the degree of nonlinearity over dispersion is expressed by ursell number @xmath26 , by the amplitude @xmath5 and wave length @xmath27 @xcite @xmath28 here specialized to shallow water waves with propagation speed @xmath29 in oceans of depth @xmath30 at tidal period @xmath31 , where @xmath32ms@xmath33 is the earth s gravitational acceleration . while , a large ursell number is suggestive of a general tendency for wave breaking , it does not directly define scaling of dissipation . for breaking to occur
, steepening must be sufficiently fast ( e.g. * ? ? ?
* ) ( see @xcite for a discussion in burgers equation with time - dependent forcing ) . in nonlinear wave motion ( cf .
* ) , it results from steepening after a time @xmath34 ( for a more detailed discussion , see @xcite . ) here , ( [ eqn_wb ] ) is relaxed by an additional @xmath8-factor of the oceans with reflection of tidal waves off coastal regions . with @xmath35
, however , wave breaking is unlikely to occur in the open oceans even at present - day values of @xmath8 ( 3 below ) .
instead , it believed to occur in shallow seas , in run - up waves in shoaling shelf regions with slopes @xmath36 satisfying @xcite @xmath37 the dissipation rate of bores produced by wave breaking satisfies entropy creation in shocks of compressible gas dynamics , i.e. , scaling with the cube of their amplitude . by aforementioned @xmath20 , wave breaking , by either ( [ eqn_ursell ] ) or ( [ eqn_surf ] ) ,
provides a time rate of dissipation effectively described by damping proportional to @xmath5 , possibly including tidal frequency in light of broadband wave spectra .
our approach is focused on scaling in global dissipation described by ( [ eqn_epsd0 ] ) , to capture the net result of an otherwise complex spatio - temporal distribution of dissipation in the earth s oceans .
we set out model global tidal dissipation in the earth s oceans by ( [ eqn_j ] ) in dimensionless variables , normalized by today s moon migration data and age .
the tidal amplitude @xmath5 is described by a damped linear pendulum equation with eigenfrequency @xmath38 , forced at semi - diurnal tidal frequency @xmath39 by the action of the moon at orbital angular velocity @xmath40 , @xmath41 where @xmath42 denotes the angular velocity of the earth . the damping coefficient @xmath43 in the pendulum equation represents dissipation with associated phase lag @xmath23 and @xmath8-factor @xmath44 . to study the net result over the entire history of the earth - moon system
, we consider the general scaling in amplitude @xmath5 and dimensionless tidal frequency @xmath6 , @xmath45 and its confrontation with data for various choices of @xmath46 . with ( [ eqn_epsd0 ] ) , we aim to capture the net result of tidal amplitude - frequency dependence that covers weak and strong interactions at present and , respectively , back in the distant past . in the stokes limit @xmath47 , for instance , and ignoring resonances , integration of ( [ eqn_j ] ) backwards in time obtains a migration time on the order of 1 gyr at odds with the moon s age ( cf . * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
this suggests that tidal dissipation is anomalously high at present .
( equivalently , the @xmath8-factor was higher in the past , e.g. , @xcite . ) taking into account the inertial range off - resonance in the past ( fig .
1 ) , however , one is led to the opposite conclusion with a previously _ low _
@xmath8-factor , here revisited by numerical integration of ( [ eqn_j ] ) with ( [ eqn_epsd0 ] ) in the forced pendulum equation .
the moon migrated to its present mean distance @xmath48 cm with a radial velocity @xmath2 cm yr@xmath3 @xcite .
it defines a characteristic migration time scale @xmath49 that will serve to express the equation of motion ( [ eqn_j ] ) in terms of a dimensionless time @xmath50 ( 3 below ) .
being tidally locked , the moon spins slowly with negligible angular momentum . by now ,
the earth s spin has effectively been transferred to the earth - moon orbit , since @xmath51 based on the moon s mass @xmath52 , the earth s angular momentum @xmath53 , radius @xmath54 and moment of inertia @xmath55 , $ ] @xmath56 @xcite .
the present - day tidal deformation @xmath57 ( in cm ) has a characteristic scale defined by the zero - frequency perturbation of the newtonian binding energy @xmath58 of self - gravity and @xmath59 in the moon s tidal field , @xmath60 , @xmath61 which recovers the familiar scaling @xmath62 with @xmath63 erg , consistent with existing estimates on ocean tide energies @xcite and measured mean values of the dynamical tidal amplitude @xmath5 to about 20% @xcite .
consistency of @xmath57 with dynamical tidal amplitude is somewhat coincidental in view of the relatively minor deformation of the earth s mantle @xcite and an appreciable @xmath8-factor in the ocean tides ( e.g. * ? ? ?
[ cols="<,<,<,<,<",options="header " , ] the trajectory of ( [ eqn_r4e ] ) , illustrated in fig .
[ figa ] , with amplitude - frequency scaling ( [ eqn_epsd0 ] ) with @xmath64 shows that most of the moon s migration time is associated with the last 40% of its current distance .
the first 60% is marked by a transition starting with a sharp spike , denoting rapid eviction of the moon from @xmath65 .
it results from an anomalously large tidal wave amplitude of a few km ( essentially the current ocean depths ) , defined by @xmath66 in units of the present - day amplitue scale @xmath57 .
thus , @xmath67 , giving an eviction time scale of about one hundred years out to tens of @xmath68 .
while this is unlikely accurate , e.g. , tidal heating may have prevented water to condensate and may , instead , derive from a magma ocean @xcite , the idea seems valid that , once oceans form , eviction is swift .
the migration time of the moon is determined by the rate of tidal dissipation , predominantly in tidal waves . in the past , forcing was mostly off - resonance in the inertial range above the resonance frequency @xmath38 in ( [ eqn_pe ] ) .
linear theory of dissipation described by the stokes limit @xmath69 falls short of explaining a migration time equal to the moon s age .
nonlinear dissipation mechanisms pointed to by ( [ eqn_ursell ] ) are important , now and even more so during off - resonance in the past .
dissipation in bores is similar to that in shocks of compressible gas dynamics .
the same is expected to feature spectral broadening and hardening by dispersion ( e.g. * ? ? ?
* ; * ? ? ?
damping representing total tidal dissipation hereby is expected to scale both with tidal amplitude and frequency proposed in ( [ eqn_epsd ] ) .
total dissipation in the ocean tides contains also a component of internal dissipation by flows over non - smooth surfaces @xcite .
it scales effectively with the cube of horizontal tidal flows @xcite , akin to high reynolds number flows past solid objects .
according to the theory of shallow water wave equations , column height and height - averaged horizontal velocity satisfy the same wave equation in the linearized limit , the latter with amplitude @xmath70 for harmonic perturbations , internal dissipation is equivalently described by damping proportional to @xmath71 , and hence by @xmath5 as a consequence of ( [ eqn_uh ] ) . in table 2 , this is included in the scaling by tidal amplitude . in scaling damping of ocean waves by @xmath72 , the same would be included approximately to within 30% . in considering ( [ eqn_r4e ] ) as an effective description of the dominant dissipation in semidiurnal tidal interactions , higher order tidal modes @xcite are neglected with generally complex dependence on ocean basin geometry @xcite . in a linearized approximation
, one might contemplate including damping by higher harmonics .
however , the latter are difficult to constrain observationally based on data of the moon s migration velocity .
even if known , evolution of ocean basins on the geological time scale of @xmath73 myr ( e.g. * ? ? ?
* ; * ? ? ?
* ) makes estimation of time - averages over a recent epoch highly uncertain . for this reason and the expectation that dissipation in the semi - diurnal tides
are dominant , these higher order perturbations fall outside the scope of the present approach . numerical integration of ( [ eqn_r4e ] ) with ( [ eqn_epsd ] ) reproduces a moon migration time equal to its age for a present @xmath8-factor ( [ eqn_qer ] ) in excellent agreement with the observational constraint ( [ eqn_qe ] ) . by ( [ eqn_epsd ] )
, it introduces a dynamic @xmath8-factor @xmath74 that was substantially below @xmath75 in the past .
its trajectory features a startingly fast eviction of the moon at or close to the initial , unstable synchronous orbit at @xmath76 . a protolunar disk with the same composition as the earth ( e.g. * ?
* ) might require even higher earth spin rates prior , to facilitate its ejection by a giant impact @xcite .
if so , the moon is even more pertinent as a deposit of the earth s initial spin angular momentum .
some uncertainty in the formulation of our model arises from the fact that the ocean eigenfrequency @xmath38 ( closest to the semidiurnal tidal frequency ) is that of the atlantic ocean . by continental drift
, it evolves on aforementioned geological time scale that , in particular , might include intermittent closure @xcite . in our numerical formulation ,
the present state then represents a time - average of a recent epoch , small relative to the moon s age of 4.5 gyr , probably satisfying @xmath77 where the right hand side refers to today s instantaneous value .
here , we assume that during closure , @xmath38 is determined by the remaining oceans , also since @xmath8 of the atlantic near closure is probably suppressed by inversion ( uplift of the ocean basin ; * ? ? ?
* ) ) . in fig .
[ figke ] , ( [ eqn_ave ] ) corresponds to moving along the ordinate to the right . by the relative flatness of the curves shown ,
our main conclusions hold , provided ( [ eqn_ave ] ) remains in the window @xmath78 for solutions to exist .
implications of larger perturbations fall outside the scope of the present formulation .
once oceans form , eviction of the moon was swift with steep spindown of the earth from what was very similar to that of jupiter today .
in contrast to jupiter s extreme weather patterns @xcite , our dramatically reduced spin with small coriolis forces today facilitates a clement global climate . it is tempting to consider application of ( [ eqn_epsd ] ) further to exoplanet - moon systems @xcite , whose selection is currently based on temperature , mass and size @xcite .
relatively distant moons may be indirect evidence for effective tidal interaction with oceans , further favoring a potentially clement climate conducive to advanced life .
* acknowledgments . *
the author gratefully thanks the reviewer for constructive comments and pointing out several pertinent references .
this report was supported in part by the national research foundation of korea under grant no .
2015r1d1a1a01059793 and 2016r1a5a1013277 .
99 barnes , j.j .
, tartse , r. , anand , m. , mccubbin , f. , franchi , i.a . , et al . , 2014 ,
earth and plan .
lett . , 390 , 244 barthlemy , e. , 2004 , surv .
, 25 , 315 bills , b.g . , & ray , r.d . , 1999 , geophysical res .
lett . , 26 , 3045 canup , r.m . , asphaug , e. , 2001 , nature , 412 , 708 cheng , w.h . ,
lee , m.h . , & peale , s.j .
, 2014 , icarus , 233 , 242 cuk , m. , & stewart , s. , 2012 , science , 338 , 1047 dahlen , f.a .
, 1974 , geophys .
j. r. astr .
, 36 , 461 davidsson , b.j.r . , 1999 , icarus , 142 , 525 dickey , j.o . ,
bender , p.l . ,
faller , j.e . , et al . , 1994 , science , 265 , 482 doodson , a.t . , 1921 , proc .
soc . , 100 , 305 egbert , g.d . , & ray , r.d . , 2000 , nature , 405 , 775 egbert , g.d
, & ray , r.d . , 2001 , j. geophys .
res . , 106 , 22 , 475 egbert , g.d . , & ray , r.d . , bills , b.g . , 2004 , j. geophys .
res . , 109 , c03003 efroimsky , m. , & williams , j.g . , 2009 ,
astr . , 104 , 257 efroimsky , m. , 2012 , celest .
mech . dyn .
astr . , 112 , 283 efroimsky , m. , , 2015 , apj , 150 , 98 nasa exoplanet archive , 2016 , http://exoplanetarchive.ipac.caltech.edu farinella , p. , milani , a. , nobili , a.m. , & valsecchi , g.b . , 1979 ,
moon & planets , 20 , 415 ford , e.b .
, rowe , , j.f . , fabrycky , d. , carter , j.a . ,
holman , m.j .
, et al . , 2011 , apjss , 197 , 2 frouard , fouchard , m. , & vienne , a. , 2010 , a&a , 515 , a54 garret , c.j.r . ,
& munk , w.h . , 1971 , deep - sea res . , 18 , 493 gerstenkorn , h. , z. astrophys . , 36 , 245 goldreich , p. , & , soter , s. , 1966 , icarus , 5 , 375 goldreich , p. , 1966
geophys . , 4 , 411 gemmrich , j. , & klymak , j.m . , 2015 , jpo , 45 , 2221 hansen , k.s . , 1982 , rev .
geophys . , 20 , 457 hendershott , m.c . , & munk , w.h . , 1970 ,
fluid mech . , 2 , 205 kleine , t. , palme , h. , mezger , k. , halliday , a.n . , 2005 , science , 310 , 5754 , 1671 halliday , a.n .
, 2008 , phil .
royal society a , 2008 , 366 , 4163 kipping , d.m . , 2009 ,
mnras , 396 , 1797 love , a.e.h . , 1911 , some problems in geodynamics , " cambridge university press lambeck , k. , phil .
a287 , 545 levinson , a. , & van putten , m.h.p.m .
, 1997 , apj , 488 , 69 macdonald , g.j.f .
, 1964 , rev .
geophys . 2 , 467 mndez , _ in _ 37@xmath79 ann .
lunar planetary sc .
, march 13 - 17 , texas , # 2396 miller , g.r . , 1966 , j. geophys .
, 71 , 2485 munk , w.h . , & macdonald , g.j.f .
, 1960 , the rotation of the earth " , cambridge univ .
press munk , & cartwright , 1966 , phil . , trans .
london , 259 , 533 munk , w.h . , 1968 , q. j. astr .
9 , 352 pekeris , c.l . , & accad , y. , 1969 , phil .
( a ) , 259 , 533 platzman , g.w . ,
curtis , g.a . , hansen , k.s .
, & slater , r.d . , j. phys .
ocean , 11 , 579 ray , r. d. _ in _ the oceans , eds .
majumdar , s. k. et al .
( pennsylvania academy of science , easton , 1994 ) , p.171 ray , r.d . ,
eanes , r.j .
, & chao , b.f . , 1996 , nature , 381 , 595 romanowicz & dambeck , 1977 , phys . earth plan .
, 15 , 1 schneider , j. , dedieu , c. , le sidaner , p. , savalle , r. , & zolotukhin , i. , 2011 , a&a , 532 , a79 salmon , r. , 2016 , http://www-pord.ucsd.edu/(tilde)rsalmon/111.textbook.pdf seabra - santos , f. j. , 1985 , contribution ltude des ondes de gravit bidimensionnelles en eau peu profonde , " ph.d .
thesis , institut national polytechnique de grenoble et universit scientifique et mdicle de grenoble 1 .
sommeria , j. , meyers , s.d . , & swinney , h.l . , 1998 ,
nature , 331 , 689 stammer , d. , ray , r.d . , anderson , o.b . , et al . , 2014 , rev .
geophys . , 52 , 243 stoker , j.j . , 1948 , commun .
pure appl .
, 1 , 1 stoker , j.j . , 1957 ,
_ water waves _ , interscience , new york taylor , p.a . , &
margot , j .-
l . , 2011 ,
icarus , 212 , 661 taylor , p.a . , & margot , j .-
l . , 2014 ,
icarus , 229 , 418 touma , j. , & wisdom , j. , 1994 , astron . j. , 1994 , 108 , 1943 touma , j. , & wisdom , j. , 1998 , astron . j. , 115 , 1653 tyler , r.h . , 2008 , nature , 456 , 770 ursell , 1953 , proc .
camb . philos . soc . , 49 , 685 wahr , 1995 , _ in _ global earth physics , a handbook of physical constants , agu reference shelf , 1 , , p.40 - 46 webb , d.j . , 1973 ,
deep sea res . , 20 , 847 webb , d.j . , 1982 ,
soc . , 70 , 261 webb , s.c .
, 2007 , nature , 445 , 754 whitham , g.b .
, 1974 , _ linear and nonlinear waves _ , john wiley & sons , ch
. 2 wilson , j.t .
, 1966 , nature , 211 , 676 wilson , j.t .
, 1975 , epsl , 25 , 33 zahnle , k. , lupu , r. , dobrovolskis , a. , & sleep , n.h . , 2015 ,
earth plan .
lett . , 427 , 74[/INST] the moon migrated to @xmath0 cm over a characteristic time @xmath1 gyr by tidal interaction with the earth s oceans at a present velocity of @xmath2 cm yr@xmath3 . we derive scaling of global dissipation that covers the entire history over the past 4.52 gyr .
off - resonance tidal interactions at relatively short tidal periods in the past reveal the need for scaling with amplitude .
the global properties of the complex spatio - temporal dynamics and dissipation in broad spectrum ocean waves is modeled by damping @xmath4 , where @xmath5 is the tidal wave amplitude , @xmath6 is the tidal frequency , and @xmath7 is the @xmath8-factor at the present time .
it satisfies @xmath9 for consistency of migration time and age of the moon consistent with observations for a near - resonance state today .
it shows a startingly fast eviction of the moon from an unstable near - synchronous orbit close to the roche limit , probably in a protolunar disk .
rapid spin down of the earth from an intial @xmath10 of break - up by the moon favored early formation of a clement global climate .
our theory suggests moons may be similarly advantageous to potentially habitable exoplanets .
[ firstpage ] earth moon planets and satellites : oceans </s> |
SECTION 1. RISK ASSESSMENT AND COST-BENEFIT ANALYSIS.
(a) Requirement.--Except as provided in subsection (b), in
promulgating any proposed or final major regulation relating to human
health or the environment, the Administrator of the Environmental
Protection Agency shall publish in the Federal Register along with the
regulation a clear and concise statement that--
(1) describes and, to the extent practicable, quantifies
the risks to human health or the environment to be addressed by
the regulation (including, where applicable and practicable,
the human health risks to significant subpopulations who are
disproportionately exposed or particularly sensitive);
(2) compares the human health or environmental risks to be
addressed by the regulation to other risks chosen by the
Administrator, including--
(A) at least three other risks regulated by the
Environmental Protection Agency or another Federal
agency; and
(B) at least three other risks that are not
directly regulated by the Federal Government;
(3) estimates--
(A) the costs to the United States Government,
State and local governments, and the private sector of
implementing and complying with the regulation; and
(B) the benefits of the regulation;
including both quantifiable measures of costs and benefits, to
the fullest extent that they can be estimated, and qualitative
measures that are difficult to quantify; and
(4) contains a certification by the Administrator that--
(A) the analyses performed under paragraphs (1)
through (3) are based on the best reasonably obtainable
scientific information;
(B) the regulation is likely to significantly
reduce the human health or environmental risks to be
addressed;
(C) there is no regulatory alternative that is
allowed by the statute under which the regulation is
promulgated and that would achieve an equivalent
reduction in risk in a more cost-effective manner,
along with a brief explanation of why other such
regulatory alternatives that were considered by the
Administrator were found to be less cost-effective; and
(D) the regulation is likely to produce benefits to
human health or the environment that will justify the
costs to the United States Government, State and local
governments, and the private sector of implementing and
complying with the regulation.
(b) Substantially Similar Final Regulations.--If the Administrator
determines that a final major regulation is substantially similar to
the proposed version of the regulation with respect to each of the
matters referred to in subsection (a), the Administrator may publish in
the Federal Register a reference to the statement published under
subsection (a) for the proposed regulation in lieu of publishing a new
statement for the final regulation.
(c) Reporting.--If the Administrator cannot certify with respect to
one or more of the matters addressed in subsection (a)(4), the
Administrator shall identify those matters for which certification
cannot be made, and shall include a statement of the reasons therefor
in the Federal Register along with the regulation. Not later than March
1 of each year, the Administrator shall submit a report to Congress
identifying those major regulations promulgated during the previous
calendar year for which complete certification was not made, and
summarizing the reasons therefor.
(d) Other Requirements.--Nothing in this section affects any other
provision of Federal law, or changes the factors that the Administrator
is authorized to consider in promulgating a regulation pursuant to any
statute, or shall delay any action required to meet a deadline imposed
by statute or a court.
(e) Judicial Review.--Nothing in this section creates any right to
judicial or administrative review, nor creates any right or benefit,
substantive or procedural, enforceable at law or equity by a party
against the United States, its agencies or instrumentalities, its
officers or employees, or any other person. If a major regulation is
subject to judicial or administrative review under any other provision
of law, the adequacy of the certification prepared pursuant to this
section, and any alleged failure to comply with this section, may not
be used as grounds for affecting or invalidating such major regulation,
although the statements and information prepared pursuant to this
section, including statements contained in the certification, may be
considered as part of the record for judicial or administrative review
conducted under such other provision of law.
(f) Definition of Major Regulation.--For purposes of this section,
``major regulation'' means a regulation that the Administrator
determines may have an effect on the economy of $100,000,000 or more in
any one year.
(g) Effective Date.--This section shall take effect 180 days after
the date of enactment of this Act. | Directs the Administrator of the Environmental Protection Agency, in promulgating any proposed or final major regulation relating to human health or the environment, to publish in the Federal Register, along with the regulation, a statement that: (1) describes and quantifies the risks to human health and the environment to be addressed by the regulation; (2) compares such risks to other risks chosen by the Administrator; (3) estimates the costs to the U.S. Government, State and local governments, and the private sector of implementing and complying with the regulation and the benefits of the regulation; and (4) contains a certification that analyses performed are based on the best obtainable scientific information, the regulation is likely to reduce the risks to be addressed, there is no regulatory alternative that would achieve an equivalent reduction in risk in a more cost-effective manner, and the regulation is likely to produce benefits to human health or the environment that will justify the costs of compliance.
Defines a "major regulation" as one that may have an effect on the economy of $100 million or more in any one year.
Authorizes the Administrator, if a final regulation is substantially similar to the proposed version, to publish a reference to the statement of the proposed regulation in lieu of publishing a new statement for the final regulation. | <s>[INST]SECTION 1. RISK ASSESSMENT AND COST-BENEFIT ANALYSIS.
(a) Requirement.--Except as provided in subsection (b), in
promulgating any proposed or final major regulation relating to human
health or the environment, the Administrator of the Environmental
Protection Agency shall publish in the Federal Register along with the
regulation a clear and concise statement that--
(1) describes and, to the extent practicable, quantifies
the risks to human health or the environment to be addressed by
the regulation (including, where applicable and practicable,
the human health risks to significant subpopulations who are
disproportionately exposed or particularly sensitive);
(2) compares the human health or environmental risks to be
addressed by the regulation to other risks chosen by the
Administrator, including--
(A) at least three other risks regulated by the
Environmental Protection Agency or another Federal
agency; and
(B) at least three other risks that are not
directly regulated by the Federal Government;
(3) estimates--
(A) the costs to the United States Government,
State and local governments, and the private sector of
implementing and complying with the regulation; and
(B) the benefits of the regulation;
including both quantifiable measures of costs and benefits, to
the fullest extent that they can be estimated, and qualitative
measures that are difficult to quantify; and
(4) contains a certification by the Administrator that--
(A) the analyses performed under paragraphs (1)
through (3) are based on the best reasonably obtainable
scientific information;
(B) the regulation is likely to significantly
reduce the human health or environmental risks to be
addressed;
(C) there is no regulatory alternative that is
allowed by the statute under which the regulation is
promulgated and that would achieve an equivalent
reduction in risk in a more cost-effective manner,
along with a brief explanation of why other such
regulatory alternatives that were considered by the
Administrator were found to be less cost-effective; and
(D) the regulation is likely to produce benefits to
human health or the environment that will justify the
costs to the United States Government, State and local
governments, and the private sector of implementing and
complying with the regulation.
(b) Substantially Similar Final Regulations.--If the Administrator
determines that a final major regulation is substantially similar to
the proposed version of the regulation with respect to each of the
matters referred to in subsection (a), the Administrator may publish in
the Federal Register a reference to the statement published under
subsection (a) for the proposed regulation in lieu of publishing a new
statement for the final regulation.
(c) Reporting.--If the Administrator cannot certify with respect to
one or more of the matters addressed in subsection (a)(4), the
Administrator shall identify those matters for which certification
cannot be made, and shall include a statement of the reasons therefor
in the Federal Register along with the regulation. Not later than March
1 of each year, the Administrator shall submit a report to Congress
identifying those major regulations promulgated during the previous
calendar year for which complete certification was not made, and
summarizing the reasons therefor.
(d) Other Requirements.--Nothing in this section affects any other
provision of Federal law, or changes the factors that the Administrator
is authorized to consider in promulgating a regulation pursuant to any
statute, or shall delay any action required to meet a deadline imposed
by statute or a court.
(e) Judicial Review.--Nothing in this section creates any right to
judicial or administrative review, nor creates any right or benefit,
substantive or procedural, enforceable at law or equity by a party
against the United States, its agencies or instrumentalities, its
officers or employees, or any other person. If a major regulation is
subject to judicial or administrative review under any other provision
of law, the adequacy of the certification prepared pursuant to this
section, and any alleged failure to comply with this section, may not
be used as grounds for affecting or invalidating such major regulation,
although the statements and information prepared pursuant to this
section, including statements contained in the certification, may be
considered as part of the record for judicial or administrative review
conducted under such other provision of law.
(f) Definition of Major Regulation.--For purposes of this section,
``major regulation'' means a regulation that the Administrator
determines may have an effect on the economy of $100,000,000 or more in
any one year.
(g) Effective Date.--This section shall take effect 180 days after
the date of enactment of this Act.[/INST]Directs the Administrator of the Environmental Protection Agency, in promulgating any proposed or final major regulation relating to human health or the environment, to publish in the Federal Register, along with the regulation, a statement that: (1) describes and quantifies the risks to human health and the environment to be addressed by the regulation; (2) compares such risks to other risks chosen by the Administrator; (3) estimates the costs to the U.S. Government, State and local governments, and the private sector of implementing and complying with the regulation and the benefits of the regulation; and (4) contains a certification that analyses performed are based on the best obtainable scientific information, the regulation is likely to reduce the risks to be addressed, there is no regulatory alternative that would achieve an equivalent reduction in risk in a more cost-effective manner, and the regulation is likely to produce benefits to human health or the environment that will justify the costs of compliance.
Defines a "major regulation" as one that may have an effect on the economy of $100 million or more in any one year.
Authorizes the Administrator, if a final regulation is substantially similar to the proposed version, to publish a reference to the statement of the proposed regulation in lieu of publishing a new statement for the final regulation.</s> |
several lines of evidence indicate that the progenitors of short - duration , hard - spectrum gamma - ray bursts ( grbs ) are related to an old stellar population .
these include the localization of grb050724 @xcite , and most likely grb050509b @xcite , to bright elliptical galaxies , the lack of supernova emission in several low redshift short grbs @xcite , and the location of grb050709 outside of any star forming region in its host galaxy @xcite .
while this supports the popular notion that the progenitors are compact objects binaries ( dns or ns - bh ; e.g. , @xcite ) , the lack of direct observations ( e.g. , gravitational waves or a sub - relativistic , radioactive component : @xcite ) , suggests that a more detailed understanding of the progenitor population has to rely on statistical studies . in this vein ,
@xcite and @xcite argue that the redshift and luminosity distributions of and batse short grbs , are inconsistent with the nominal merger time distribution of dns binaries in the milky way , @xmath19 @xcite .
they further conclude that the typical age of the progenitors is old , @xmath20 gyr @xcite .
similarly , @xcite and @xcite propose that the relative fractions of short grbs in early- and late - type galaxies should constrain the progenitor lifetime distribution .
this test derives from the fact that , on average , stars in early - type galaxies form earlier than in late - type galaxies . an an extension of this idea , the preponderance of short grbs in galaxy clusters can also be used to constrain the age distribution and nature of the progenitor population . in the framework of @xmath21cdm cosmology ,
high - resolution numerical simulations suggest that the oldest stars reside in dense galaxy cluster environments , typically within @xmath22 kpc of the cluster center @xcite .
this is supported by observations , which indicate that the difference in formation epochs for stars in cluster and field ellipticals is @xmath23 gyr ( e.g. , @xcite ) .
since @xmath24 * in clusters is larger than in the field ( e.g. , @xcite ) , this leads to an even more pronounced difference in star formation history than just the difference between early- and late - type galaxies discussed in @xcite .
in addition , the early - type fraction in clusters , @xmath25 , is twice as high as in the field @xcite , suggesting that the fraction of short grbs in clusters is intimately related to their rate in early - type galaxies .
this is of particular importance in cases where the positional accuracy of the burst is not sufficient to associate it with a particular galaxy , but may be sufficient to associate it with a galaxy cluster .
finally , the specific frequency of globular clusters is at least a factor of a few higher in bright cluster ellipticals than in field galaxies @xcite .
thus , the fraction of short bursts in galaxy clusters may shed light on whether globular clusters are an efficient site for the formation of short grb progenitors , as proposed by @xcite .
a complete search for clusters is also important from an observational point of view .
these associations can be made at high significance based on the prompt @xmath26-ray positions alone ( typically , @xmath27 ) , whereas associations with individual galaxies require accurate positions ( @xmath28 ) from the optical , radio , or x - ray afterglow .
since the afterglow brightness correlates with the circumburst density the latter approach may produce an observational bias in favor of gas - rich or disk galaxies . to date , three associations of short grbs with galaxy clusters have been claimed .
grb050509b appears to reside in the cluster zwcl 1234.0 + 02916 at @xmath29 @xcite , grb050813 is apparently associated with a cluster at @xmath30 ( @xcite ; gladders et al . in prep . ) , and grb790613 may be associated with the cluster abell 1892 at @xmath31 @xcite .
the statistical significance of these associations is @xmath32 . motivated by these considerations we began the first systematic search for galaxy clusters hosting short grbs , using multi - slit optical spectroscopy and archival x - ray observations
this is part of a long - term program to constrain the age distribution of the progenitors using the properties of their large - scale environments . here
we present spectroscopy in the fields of grbs 050709 , 050724 , 050911 , and 051221a .
we also re - analyze all of the available x - ray observations of short grb fields to search for diffuse emission from hot intracluster gas associated with potential clusters .
the layout of the paper is as follows .
the optical observations are described in [
sec : spec ] , and the x - ray analysis in presented in [ sec : xray ] . in
[ sec : res ] we summarize the results of our search , including a determination of the optical and x - ray properties of the cluster edcc 493 , which coincides with grb050911 .
we draw initial conclusions in [ sec : disc ] . throughout the paper
we use the standard @xmath21cdm cosmology with @xmath33 km s@xmath2 mpc@xmath2 , @xmath34 , and @xmath35 .
for a detailed discussion of the four bursts studied in this paper we refer the reader to the following publications .
grb050709 : @xcite , @xcite , and @xcite .
grb050724 : @xcite , @xcite , and @xcite .
grb050911 : @xcite .
grb051221a : @xcite and @xcite .
we note that the classification of is somewhat ambiguous .
formally , @xmath36 for this burst is @xmath37 s @xcite , but the light curve is dominated by an initial pair of short pulses with a total duration of about 1.5 s , followed by a softer component with a slow rise and decay .
the latter component may be similar to the soft tails observed in grbs 050709 @xcite and 050724 @xcite , and moreover would have been missed by batse @xcite . in this framework , would be classified as a short grb .
we selected targets for spectroscopy based on imaging observations from the _ hubble space telescope _
( 050709 ) , the magellan / clay low dispersion survey spectrograph ( 050724 ) , the gemini multi - object spectrograph ( 051221a ) , and the du pont 100-inch telescope at las campanas observatory ( 050911 ) .
we used the program sextractor @xcite to estimate source magnitudes and to separate stars and galaxies ( using a stellarity index of @xmath38 for galaxies ) . from the spectroscopy
we find a star interloper fraction of @xmath39 for grb050911 , @xmath40 for grb051221a , and zero for grbs 050724 and 050709 .
the objects range in brightness from @xmath41 to @xmath42 mag ( 050709 ; @xmath43 mag ) , @xmath44 to @xmath45 mag ( 050724 ; @xmath46 mag ) , @xmath47 to @xmath48 mag ( 050911 ) , and @xmath49 to @xmath50 mag ( 051221a ; @xmath51 mag ) .
the final source catalogs ( not including stars ) contain 33 objects ( 050709 ) , 21 objects ( 050724 ) , 79 objects ( 051221a ) , and 38 objects ( 051109 ) .
all spectra were obtained with the low dispersion survey spectrograph ( ldss3 ) mounted on the magellan / clay 6.5-m telescope using a 300 lines mm@xmath2 grism , which provides a resolution of about @xmath52 .
for grb050724 we also used a volume - phase holographic grism , which provides a resolution of about 2 .
the log of the observations is provided in table [ tab : obs ] .
we reduced the data with the cosmos software package , using flat and henear arc exposures obtained following each mask exposure .
the data were bias - subtracted , flat - fielded with a response - corrected flat , and sky - subtracted using a 2-d spline fit .
the spectra were then extracted and combined following cosmic - ray rejection .
redshifts were determined manually using the iraf task splot to measure the absorption and/or emission line positions .
we obtained redshifts for a total of 151 galaxies in the four grb fields , or an overall success rate of @xmath53 .
we retrieved from the high energy astrophysics science archive research center all publicly available observations of short grbs taken with the x - ray telescope ( xrt ) and the _ chandra x - ray observatory_. a summary of the observations and exposure times for the sixteen available grbs is given in table [ tab : xray ] .
we processed the xrt data with the xrtpipeline script packaged within the heasoft software , using the default grade selection and screening parameters .
for the _ chandra _ data we used the evt2 files provided by heasarc .
all event files were further filtered for the energy range @xmath54 kev using xselect .
we searched for diffuse emission at the positions of the short grbs visually using the ciao routine csmooth to construct smoothed images .
we show the results of our spectroscopic observations overlaid on images of each of the four fields in figures [ fig:050709][fig:051221a ] .
the redshift distributions are presented in figure [ fig : grbsz ] .
for grb050724 we do not find any galaxies in the @xmath55 diameter field , within @xmath56 km s@xmath2 of the host redshift of @xmath57 .
a possible background galaxy group or cluster is located at @xmath58 , but we do not detect any coincident x - ray emission with a limit of @xmath59 erg s@xmath2 ( at @xmath12 ) .
this indicates that this background structure is at most a poor cluster .
similarly , of the 21 galaxies with spectroscopic redshifts in the @xmath60 field of grb050709 , we find only two within @xmath61 km s@xmath2 of the burst redshift , @xmath62 .
this is unlikely to constitute a significant structure , and in fact we place a limit of @xmath63 erg s@xmath2 on diffuse x - ray emission associated with the burst environment . in the field of grb051221a
we find a nearly uniform redshift distribution between @xmath64 and @xmath65 , with only two galaxies in the @xmath66 field located within 2000 km s@xmath2 of the burst redshift , @xmath67 .
however , these galaxies , at @xmath68 and @xmath69 , are situated about @xmath70 ( 1.2 mpc ) and @xmath71 ( 1.1 mpc ) away from the grb host galaxy , respectively , suggesting that this is not likely to be a significantly overdense structure .
the limit on diffuse x - ray emission coincident with the burst position is @xmath72 erg s@xmath2 , or about @xmath73 fainter than the x - ray luminosity of the cluster associated with grb050509b ( @xcite ; table [ tab : xray ] ) .
the bat error circle of , centered on @xmath74 , @xmath75 ( j2000 ) with an uncertainty of @xmath71 radius @xcite , intersects the galaxy cluster edcc 493 @xcite .
this cluster has an abell radius of about @xmath76 @xcite . our spectroscopic observations in this field
quantify the properties of the cluster .
we obtain redshifts for fourteen cluster members , including the brightest elliptical galaxy .
the properties of the cluster galaxies are summarized in table [ fig:050911 ] .
we estimate the cluster velocity dispersion using the rostat package @xcite .
we consider all galaxies within @xmath77 km s@xmath2 of the mean cluster redshift , and calculate the biweight estimators of the location ( mean velocity ) and scale ( velocity dispersion )
. objects with velocities greater than three times the velocity dispersion are removed from the sample and a new location and scale are calculated iteratively until no more objects are clipped . in this particular system , no objects were clipped from the original list .
we find @xmath78 km s@xmath2 and a redshift of @xmath0 ( figure [ fig : grbsz ] ) .
the early - type fraction in our sample of fourteen cluster members is @xmath79 , at the high end of the distribution for groups / clusters with a similar velocity dispersion @xcite .
this suggests that was most likely associated with an early - type galaxy .
another potential implication is that edcc 493 is more evolved than a typical cluster of the same mass , perhaps a reflection of the old age of the grb progenitor system . the determination of the early - type fraction for a larger sample of cluster members will show whether this effect is real .
we also detect diffuse x - ray emission in the xrt data coincident with the optical cluster position , at @xmath74 , @xmath75 ( j2000 ) , with an uncertainty of about @xmath80 in each coordinate ( figure [ fig:050911xray ] ) .
this position is @xmath81 west and @xmath82 south of the optical position of the bright cluster elliptical . to determine the source x - ray properties we extract counts for each individual observation in an elliptical aperture with semi - major and semi - minor axes of @xmath83 and @xmath84 , respectively , selected to match the scale at which the cluster diffuse emission matches the background level .
we then bin the extracted counts in energy such that each bin contains at least ten counts . using a mekal model fit to the energy range of @xmath54 kev with an abundance fixed at @xmath85 z@xmath6 @xcite and an absorbing column density of @xmath86 @xmath10 @xmath10 @xcite , we find @xmath87 kev , and @xmath88 erg s@xmath2 ( @xmath89 for 19 degrees of freedom ) .
the data and model fit are shown in figure [ fig : g050911spec ] .
the measured velocity dispersion and x - ray luminosity are in good agreement with values measured for galaxy groups and poor clusters from the rosat deep cluster survey @xcite , but the temperature is somewhat lower than expected in comparison to the compilation of @xcite from which we estimate @xmath90 kev . using the cluster mass - temperature relation @xcite we estimate a mass of @xmath91 m@xmath6 , or about a factor of six times lower than the cluster zwcl 1234.0 + 02916 in the field of grb050509b ( see [ sec : xdata ] ) .
we next assess the probability that is associated with edcc 493 . from the @xmath92 relation for x - ray clusters in the rosat deep cluster survey
we find that for a flux of @xmath93 erg @xmath2 @xmath10 the surface density of sources is about 1.4 deg@xmath94 @xcite .
the probability of chance coincidence with the @xmath71 radius error circle is therefore @xmath95 .
thus , we conclude that the association between and edcc 493 is significant at the @xmath96 confidence level .
we note that taking into account the thirteen additional searches ( excluding grb050509b ; see [ sec : xdata ] ) the probability of finding such a cluster in any of the bat error circles is about @xmath40 ( or , @xmath97 ) . of course , of the other fourteen short bursts , eleven have much more accurate positions from x - ray , optical , and/or radio afterglow observations .
if we consider the x - ray luminosity of the cluster , we find that the volume density of clusters with @xmath98 erg s@xmath2 is @xmath99 mpc@xmath100 ( @xmath101 erg s@xmath2)@xmath2 @xcite . integrating the x - ray luminosity function with @xmath102 @xcite we find @xmath103 mpc@xmath100 , or @xmath104 arcmin@xmath94 within the distance to edcc 493 .
the probability of finding such a cluster within the error circle is therefore @xmath105 , or a @xmath106 significance level for an association with .
turning to the brightest cluster galaxy ( bcg ) , we find from the 2mass catalog that it has @xmath107 mag in a @xmath108 aperture , or @xmath109 mag compared to our @xmath110-band photometry .
the surface density of sources with equal or greater brightness is about 18 deg@xmath94 , or a probability of @xmath111 of finding such an object within the error circle .
the rest - frame @xmath112-band absolute magnitude of the bcg is @xmath113 mag , or @xmath114 * in comparison to the luminosity function from the 2df galaxy redshift survey and 2mass @xcite . integrating the @xmath112-band luminosity function
we find that the number density of such galaxies is @xmath115 mpc@xmath100 , or @xmath116 arcmin@xmath94 within the distance to edcc 493 .
thus , the probability to find such a luminous galaxy within the bat error circle of is about 0.01 ( @xmath96 confidence level ) .
we therefore conclude that the probability of chance association is only 0.1 - 1@xmath117 , and it is therefore likely that occurred within the cluster . at the redshift of edcc 493 ,
the isotropic - equivalent @xmath26-ray energy release of the burst was @xmath118 erg , similar to that of other short grbs @xcite . in figure
[ fig : xray ] we show smoothed xrt and _ chandra _ x - ray images of the fields of the fifteen short grbs . with the exception of the previously detected diffuse x - ray emission from the cluster zwcl 1234.0 + 02916 coincident with grb050509b @xcite
, we do not detect clear diffuse x - ray emission in coincidence with any of other short grbs .
we calculate upper limits on the x - ray flux using @xmath119 within a @xmath120 radius circle centered on each grb position , where @xmath121 is the total number of counts within the circle in the @xmath54 kev range ( effectively the background level ) , and @xmath122 is the total exposure time . to convert from count rate to flux we assume a thermal bremsstrahlung model with @xmath123 kev and an absorbing column given by the @xcite value for each burst .
the typical upper limits are @xmath124 erg s@xmath2 @xmath10 , or about a factor two lower than for edcc 493 . assuming a typical redshift , @xmath125
, the corresponding luminosity limit is @xmath126 erg s@xmath2 , or roughly @xmath127 m@xmath6 . for the cluster
zwcl 1234.0 + 02916 associated with grb050509b we derive a temperature of @xmath128 kev and an unabsorbed luminosity of @xmath129 erg s@xmath2 ( @xmath130 for 12 degrees of freedom ) .
the absorbing column density is @xmath131 @xmath10 , about an order of magnitude larger than the @xcite value for the galactic column .
here we used a mekal model with the abundance fixed to @xmath85 z@xmath6 .
we note that our derived temperature is in good agreement with the value of about 3.65 kev found by @xcite , but is lower than the value of 5.25 kev found by @xcite .
our derived luminosity is about @xmath73 higher than that of @xcite .
the inferred cluster mass is @xmath132 m@xmath6 .
we present the first systematic search for galaxy clusters hosting short grbs using multi - slit optical spectroscopy in the fields of grbs 050709 , 050724 , 050911 , and 051221a , and a re - analysis of all publicly available x - ray observations .
future papers in this series will present optical spectroscopy of additional short grb fields and a detailed analysis of the galaxy cluster statistics .
no apparent clusters are found in the fields of grbs 050709 , 050724 , and 051221a from optical and x - ray observations . in the error circle of the putative short burst
we show that the cluster edcc 493 has a mean redshift , @xmath0 , a velocity dispersion , @xmath133 km s@xmath2 , an x - ray temperature , @xmath134 kev , and a luminosity , @xmath98 erg s@xmath2 . these values are typical for poor clusters , and the inferred mass is about @xmath5 m@xmath6 .
we estimate that the chance probability of finding such a galaxy cluster in the bat error circle of is about 0.1 - 1@xmath117 .
this result highlights the ability to associate short grbs with galaxy clusters based on @xmath26-ray positions alone , thus removing a potential bias in favor of associations with gas - rich galaxies when relying on afterglow positions .
it has been suggested that the relative fraction of early- and late - type host galaxies of short grbs can be used to constrain the age distribution of the progenitor population @xcite . making the association between and edcc 493 , and using all of the available observations to date
, we find that of the short grbs five appear to be associated with early - type galaxies ( 050509b , 050724 , 050813 , 050911 , 060502b ) and two are associated with late - type galaxies ( 050709 , 051221a ) .
taken at face value , this would argue for an age distribution , @xmath135 with @xmath136 @xcite . naturally , in making a more accurate derivation of this value , one has to take into account the respective probability of association for each burst .
in fact if we consider only secure associations , the relative numbers are @xmath137 instead of @xmath138 , leading to @xmath139 .
independent of associations with individual galaxies , the fraction of short grbs in clusters is also of interest in assessing the age distribution . of the sixteen available bursts ,
three have claimed cluster associations ( 050509b , 050813 , 050911 ) . within the uncertainty
, this fraction is in rough agreement with the value of @xmath140 for the overall fraction of stellar mass in galaxy clusters @xcite , or roughly @xmath13 in clusters equal to or more massive than edcc 493 @xcite . of course , not all stars are capable of producing short grbs , but assuming that the initial mass function and binary fractions are independent of galaxy properties , the total stellar mass provides a good proxy for the mass in short grb progenitors .
thus , at the present there is reasonable agreement between the fraction of short grbs and the baseline fraction of stellar mass in galaxy clusters .
finally , we note that the frequency of short grbs in galaxy clusters may reflect a potential association with globular clusters .
the latter are thought to provide an efficient environment for the production of dns binaries , and may account for a substantial fraction of all short grb progenitors @xcite . in particular , the specific frequency of globular clusters increases significantly from a value of @xmath141 for s+irr galaxies to @xmath142 for e+s0 galaxies , and @xmath143 for cd galaxies @xcite . given that massive ellipticals are over - represented in galaxy clusters compared to the field , we expect that an association with globular clusters will increase the fraction of galaxy cluster associations compared to the baseline level of @xmath144 indicated above .
thus , continued searches for galaxy clusters hosting short grbs , and more detailed predictions for the expected fraction as a function of cluster mass and redshift , may hold the key to a clearer understanding of the progenitor population .
we thank a. dressler , a. gal - yam , m. gladders , d. kawata , f. schweizer , and a. soderberg for helpful discussions .
e.b . is supported by nasa through hubble fellowship grant hst-01171.01 awarded by the space telescope science institute , which is operated by aura , inc . for nasa under contract nas 5 - 26555 .
s. acknowledges support from the observatories of the carnegie institution of washington and korean science and engineering foundation grant kosef-2005 - 215-c00056 funded by the korean government ( most ) .
, s. d. m. , & springel , v. 2000 , in the first stars : proceedings of the mpa / eso workshop held at garching , germany , 4 - 6 august 1999 , eso astrophysics symposia .
isbn 3 - 540 - 67222 - 2 . edited by a. weiss , t.g .
abel , and v. hill .
springer - verlag , 2000 , p. 327
a. weiss , t. g. abel , & v. hill , 327 llcccclcc 0.05 in 050709 & 2006 june 28.23 & 300 & og590 & 4800 & 1.47 & @xmath145 & 15 & 10 + & 2006 june 28.30 & 300 & og590 & 4800 & 1.12 & @xmath145 & 11 & 5 + & 2006 june 28.39 & 300 & og590 & 4000 & 1.02 & @xmath145 & 7 & 6 + 050724 & 2006 june 28.96 & 300 & w4800 - 7800 & 4800 & 1.47 & @xmath146 & 21 & 18 + & 2006 june 29.02 & 1090 & none & 3600 & 1.13 & @xmath147 & 21 & 19 + 051221a & 2006 june 29.28 & 300 & w4800 - 7800 & 6000 & 1.59 & @xmath146 & 41 & 34 + & 2006 june 29.36 & 300 & w4800 - 7800 & 6900 & 1.44 & @xmath146 & 38 & 27 + 050911 & 2006 june 30.28 & 300 & none & 6000 & 1.70 & @xmath148 & 25 & 21 + & 2006 june 30.36 & 300 & none & 5800 & 1.18 & @xmath148 & 13 & 11 lllcccccc 0.05 in 050509b & 0.226 & 2005 may 9.17 & xrt & @xmath149 & 1.27 & 0.0092 & @xmath150 & @xmath151 + 050709 & 0.161 & 2005 jul . 11.55 & xrt & 17316 & & & & + & & 2005 jul . 12.43 & xrt & 4977 & & & & + & & 2005 jul . 13.11 & xrt & 7035 & 1.23 & @xmath152 & @xmath153 & @xmath154 + & & 2005 jul . 25.86 & cxo & 18284 & & @xmath155 & @xmath156 & @xmath157 + 050724 & 0.257 & 2005 jul . 29.02
& xrt & 24880 & & & & + & & 2005 jul .
30.02 & xrt & 21128 & 14.5 & @xmath152 & @xmath156 & @xmath158 + & & 2005 jul .
26.84 & cxo & 49955 & & @xmath159 & @xmath160 & @xmath161 + 050813 & 1.8 ?
& 2005 aug . 13.28 & xrt & 14210 & & & & + & & 2005 aug . 16.03 & xrt & 11438 & & & & + & & 2005 aug . 19.04 & xrt & 9265 & & & & + & & 2005 aug . 21.65 & xrt & 13985 & 4.08 & @xmath162 & @xmath163 & @xmath164 + 050906 & & 2005 sep . 6.44
& xrt & 5687 & 5.60 & @xmath165 & @xmath166 & + 050911 & 0.165 & 2005 sep . 11.86 & xrt & 6225 & & & & + & & 2005 sep . 12.59 & xrt & 9755 & & & & + & & 2005 sep . 14.06 & xrt & 12983 & & & & + & & 2005 sep . 18.27 & xrt & 16723 & 2.70 & 0.0033 & @xmath167 & @xmath168 + 050925@xmath169 & & 2005 sep .
25.38 & xrt & 37152 & & & & + & & 2006 apr . 6.03 & xrt & 14841 & & & & + & & 2006 may 8.76 & xrt & 8735 & 114 & @xmath170 & @xmath171 & + 051105a & & 2005 nov . 5.27 & xrt & 55846 & 2.89 & @xmath172 & @xmath173 & + 051114 & & 2005 nov . 15.64 & xrt & 4750 & & & & + & & 2005 nov .
15.91 & xrt & 10753 & 1.66 & @xmath162 & @xmath174 & + 051210 & & 2005 dec . 10.24 & xrt & 37401 & 2.14 & @xmath170 & @xmath175 & + 051221a & 0.546 & 2006 jan . 2.09 & xrt & 56663 & 6.58 & @xmath172 & @xmath176 & @xmath177 + 051227 & & 2005 dec .
30.03 & xrt & 45913 & & & & + & & 2006 jan . 1.02 & xrt & 10216 & & & & + & & 2006 jan . 2.11 & xrt & 27203 & 4.20 & @xmath178 & @xmath179 & + 060121 & & 2006 jan . 28.01 & xrt & 25272 & & & & + & & 2006 feb . 2.04 & xrt & 18420 & 1.66 & @xmath172 & @xmath180 & + 060313 & & 2006 mar . 15.00 & xrt & 40463 & 4.65 & @xmath181 & @xmath182 & + 060502b & 0.287 ?
& 2006 may 2.73 & xrt & 29630 & 4.32 & @xmath152 & @xmath174 & @xmath158 + 060801 & 1.131 & 2006 aug . 2.04 & xrt & 20942 & & & & + & & 2006 aug . 3.05 & xrt & 38051 & 1.54 & @xmath172 & @xmath180 & @xmath183 llllc 0.2 in & & 20.48 & @xmath184 & abs+em + & & 20.76 & @xmath185 & abs+em + & & 21.62 & @xmath186 & abs + & & 20.00 & @xmath187 & abs + & & 20.36 & @xmath188 & abs + & & 20.36 & @xmath189 & abs + & & 17.57 & @xmath190 & abs + & & 20.53 & @xmath191 & abs+em + & & 18.98 & @xmath192 & abs + & & 18.90 & @xmath193 & abs + & & 19.08 & @xmath194 & abs + & & 21.14 & @xmath195 & abs + & & 20.80 & @xmath184 & abs + & & 20.03 & @xmath196 & abs ) .
the data are binned with at least ten counts per bin .
we use a mekal model fit with an abundance fixed at @xmath85 z@xmath6 and an absorbing column density of @xmath198 @xmath10 @xmath10 @xcite .
the best - fit parameters are @xmath87 kev , and @xmath88 erg s@xmath2 ( @xmath89 for 19 degrees of freedom ) .
[ fig : g050911spec],width=720 ] z@xmath6 . the best - fit parameters are @xmath128 kev , an unabsorbed luminosity of @xmath129 erg s@xmath2 , and an absorbing column density of @xmath199 @xmath10 ( @xmath130 for 12 degrees of freedom ) .
[ fig : g050509bspec],width=720 ] | we present a search for galaxy clusters in the fields of three bona - fide short grbs ( 050709 , 050724 , and 051221a ) and the putative short burst grb050911 using multi - slit optical spectroscopy .
these observations are part of a long - term program to constrain the progenitor age distribution based on the fraction of short grbs in galaxy clusters and early - type galaxies .
we find no evidence for cluster associations at the redshifts of the first three bursts , but we confirm the presence of the cluster edcc 493 within the error circle of grb050911 and determine its redshift , @xmath0 , and velocity dispersion , @xmath1 km s@xmath2 .
in addition , our analysis of /xrt observations of this burst reveals diffuse x - ray emission coincident with the optical cluster position , with a luminosity , @xmath3 erg s@xmath2 , and a temperature , @xmath4 kev .
the inferred mass of the cluster is @xmath5 m@xmath6 , and the probability of chance coincidence is about @xmath7 , indicating an association with at the 2.6 - 3.2@xmath8 confidence level .
a search for diffuse x - ray emission in coincidence with the fifteen other short grbs observed with xrt and _ chandra _ reveals that with the exception of the previously - noted cluster zwcl 1234.0 + 02916 likely associated with grb050509b , no additional associations are evident to a typical limit of @xmath9 erg s@xmath2 @xmath10 , or @xmath11 m@xmath6 assuming a typical @xmath12 .
the resulting fraction of short grbs hosted by galaxy clusters of about @xmath13 is in rough agreement with the fraction of stellar mass in clusters of @xmath14 .
# 1#2#3#1@xmath15#2@xmath16#3@xmath17 # 1#2#3@xmath18 | <s>[INST]several lines of evidence indicate that the progenitors of short - duration , hard - spectrum gamma - ray bursts ( grbs ) are related to an old stellar population .
these include the localization of grb050724 @xcite , and most likely grb050509b @xcite , to bright elliptical galaxies , the lack of supernova emission in several low redshift short grbs @xcite , and the location of grb050709 outside of any star forming region in its host galaxy @xcite .
while this supports the popular notion that the progenitors are compact objects binaries ( dns or ns - bh ; e.g. , @xcite ) , the lack of direct observations ( e.g. , gravitational waves or a sub - relativistic , radioactive component : @xcite ) , suggests that a more detailed understanding of the progenitor population has to rely on statistical studies . in this vein ,
@xcite and @xcite argue that the redshift and luminosity distributions of and batse short grbs , are inconsistent with the nominal merger time distribution of dns binaries in the milky way , @xmath19 @xcite .
they further conclude that the typical age of the progenitors is old , @xmath20 gyr @xcite .
similarly , @xcite and @xcite propose that the relative fractions of short grbs in early- and late - type galaxies should constrain the progenitor lifetime distribution .
this test derives from the fact that , on average , stars in early - type galaxies form earlier than in late - type galaxies . an an extension of this idea , the preponderance of short grbs in galaxy clusters can also be used to constrain the age distribution and nature of the progenitor population . in the framework of @xmath21cdm cosmology ,
high - resolution numerical simulations suggest that the oldest stars reside in dense galaxy cluster environments , typically within @xmath22 kpc of the cluster center @xcite .
this is supported by observations , which indicate that the difference in formation epochs for stars in cluster and field ellipticals is @xmath23 gyr ( e.g. , @xcite ) .
since @xmath24 * in clusters is larger than in the field ( e.g. , @xcite ) , this leads to an even more pronounced difference in star formation history than just the difference between early- and late - type galaxies discussed in @xcite .
in addition , the early - type fraction in clusters , @xmath25 , is twice as high as in the field @xcite , suggesting that the fraction of short grbs in clusters is intimately related to their rate in early - type galaxies .
this is of particular importance in cases where the positional accuracy of the burst is not sufficient to associate it with a particular galaxy , but may be sufficient to associate it with a galaxy cluster .
finally , the specific frequency of globular clusters is at least a factor of a few higher in bright cluster ellipticals than in field galaxies @xcite .
thus , the fraction of short bursts in galaxy clusters may shed light on whether globular clusters are an efficient site for the formation of short grb progenitors , as proposed by @xcite .
a complete search for clusters is also important from an observational point of view .
these associations can be made at high significance based on the prompt @xmath26-ray positions alone ( typically , @xmath27 ) , whereas associations with individual galaxies require accurate positions ( @xmath28 ) from the optical , radio , or x - ray afterglow .
since the afterglow brightness correlates with the circumburst density the latter approach may produce an observational bias in favor of gas - rich or disk galaxies . to date , three associations of short grbs with galaxy clusters have been claimed .
grb050509b appears to reside in the cluster zwcl 1234.0 + 02916 at @xmath29 @xcite , grb050813 is apparently associated with a cluster at @xmath30 ( @xcite ; gladders et al . in prep . ) , and grb790613 may be associated with the cluster abell 1892 at @xmath31 @xcite .
the statistical significance of these associations is @xmath32 . motivated by these considerations we began the first systematic search for galaxy clusters hosting short grbs , using multi - slit optical spectroscopy and archival x - ray observations
this is part of a long - term program to constrain the age distribution of the progenitors using the properties of their large - scale environments . here
we present spectroscopy in the fields of grbs 050709 , 050724 , 050911 , and 051221a .
we also re - analyze all of the available x - ray observations of short grb fields to search for diffuse emission from hot intracluster gas associated with potential clusters .
the layout of the paper is as follows .
the optical observations are described in [
sec : spec ] , and the x - ray analysis in presented in [ sec : xray ] . in
[ sec : res ] we summarize the results of our search , including a determination of the optical and x - ray properties of the cluster edcc 493 , which coincides with grb050911 .
we draw initial conclusions in [ sec : disc ] . throughout the paper
we use the standard @xmath21cdm cosmology with @xmath33 km s@xmath2 mpc@xmath2 , @xmath34 , and @xmath35 .
for a detailed discussion of the four bursts studied in this paper we refer the reader to the following publications .
grb050709 : @xcite , @xcite , and @xcite .
grb050724 : @xcite , @xcite , and @xcite .
grb050911 : @xcite .
grb051221a : @xcite and @xcite .
we note that the classification of is somewhat ambiguous .
formally , @xmath36 for this burst is @xmath37 s @xcite , but the light curve is dominated by an initial pair of short pulses with a total duration of about 1.5 s , followed by a softer component with a slow rise and decay .
the latter component may be similar to the soft tails observed in grbs 050709 @xcite and 050724 @xcite , and moreover would have been missed by batse @xcite . in this framework , would be classified as a short grb .
we selected targets for spectroscopy based on imaging observations from the _ hubble space telescope _
( 050709 ) , the magellan / clay low dispersion survey spectrograph ( 050724 ) , the gemini multi - object spectrograph ( 051221a ) , and the du pont 100-inch telescope at las campanas observatory ( 050911 ) .
we used the program sextractor @xcite to estimate source magnitudes and to separate stars and galaxies ( using a stellarity index of @xmath38 for galaxies ) . from the spectroscopy
we find a star interloper fraction of @xmath39 for grb050911 , @xmath40 for grb051221a , and zero for grbs 050724 and 050709 .
the objects range in brightness from @xmath41 to @xmath42 mag ( 050709 ; @xmath43 mag ) , @xmath44 to @xmath45 mag ( 050724 ; @xmath46 mag ) , @xmath47 to @xmath48 mag ( 050911 ) , and @xmath49 to @xmath50 mag ( 051221a ; @xmath51 mag ) .
the final source catalogs ( not including stars ) contain 33 objects ( 050709 ) , 21 objects ( 050724 ) , 79 objects ( 051221a ) , and 38 objects ( 051109 ) .
all spectra were obtained with the low dispersion survey spectrograph ( ldss3 ) mounted on the magellan / clay 6.5-m telescope using a 300 lines mm@xmath2 grism , which provides a resolution of about @xmath52 .
for grb050724 we also used a volume - phase holographic grism , which provides a resolution of about 2 .
the log of the observations is provided in table [ tab : obs ] .
we reduced the data with the cosmos software package , using flat and henear arc exposures obtained following each mask exposure .
the data were bias - subtracted , flat - fielded with a response - corrected flat , and sky - subtracted using a 2-d spline fit .
the spectra were then extracted and combined following cosmic - ray rejection .
redshifts were determined manually using the iraf task splot to measure the absorption and/or emission line positions .
we obtained redshifts for a total of 151 galaxies in the four grb fields , or an overall success rate of @xmath53 .
we retrieved from the high energy astrophysics science archive research center all publicly available observations of short grbs taken with the x - ray telescope ( xrt ) and the _ chandra x - ray observatory_. a summary of the observations and exposure times for the sixteen available grbs is given in table [ tab : xray ] .
we processed the xrt data with the xrtpipeline script packaged within the heasoft software , using the default grade selection and screening parameters .
for the _ chandra _ data we used the evt2 files provided by heasarc .
all event files were further filtered for the energy range @xmath54 kev using xselect .
we searched for diffuse emission at the positions of the short grbs visually using the ciao routine csmooth to construct smoothed images .
we show the results of our spectroscopic observations overlaid on images of each of the four fields in figures [ fig:050709][fig:051221a ] .
the redshift distributions are presented in figure [ fig : grbsz ] .
for grb050724 we do not find any galaxies in the @xmath55 diameter field , within @xmath56 km s@xmath2 of the host redshift of @xmath57 .
a possible background galaxy group or cluster is located at @xmath58 , but we do not detect any coincident x - ray emission with a limit of @xmath59 erg s@xmath2 ( at @xmath12 ) .
this indicates that this background structure is at most a poor cluster .
similarly , of the 21 galaxies with spectroscopic redshifts in the @xmath60 field of grb050709 , we find only two within @xmath61 km s@xmath2 of the burst redshift , @xmath62 .
this is unlikely to constitute a significant structure , and in fact we place a limit of @xmath63 erg s@xmath2 on diffuse x - ray emission associated with the burst environment . in the field of grb051221a
we find a nearly uniform redshift distribution between @xmath64 and @xmath65 , with only two galaxies in the @xmath66 field located within 2000 km s@xmath2 of the burst redshift , @xmath67 .
however , these galaxies , at @xmath68 and @xmath69 , are situated about @xmath70 ( 1.2 mpc ) and @xmath71 ( 1.1 mpc ) away from the grb host galaxy , respectively , suggesting that this is not likely to be a significantly overdense structure .
the limit on diffuse x - ray emission coincident with the burst position is @xmath72 erg s@xmath2 , or about @xmath73 fainter than the x - ray luminosity of the cluster associated with grb050509b ( @xcite ; table [ tab : xray ] ) .
the bat error circle of , centered on @xmath74 , @xmath75 ( j2000 ) with an uncertainty of @xmath71 radius @xcite , intersects the galaxy cluster edcc 493 @xcite .
this cluster has an abell radius of about @xmath76 @xcite . our spectroscopic observations in this field
quantify the properties of the cluster .
we obtain redshifts for fourteen cluster members , including the brightest elliptical galaxy .
the properties of the cluster galaxies are summarized in table [ fig:050911 ] .
we estimate the cluster velocity dispersion using the rostat package @xcite .
we consider all galaxies within @xmath77 km s@xmath2 of the mean cluster redshift , and calculate the biweight estimators of the location ( mean velocity ) and scale ( velocity dispersion )
. objects with velocities greater than three times the velocity dispersion are removed from the sample and a new location and scale are calculated iteratively until no more objects are clipped . in this particular system , no objects were clipped from the original list .
we find @xmath78 km s@xmath2 and a redshift of @xmath0 ( figure [ fig : grbsz ] ) .
the early - type fraction in our sample of fourteen cluster members is @xmath79 , at the high end of the distribution for groups / clusters with a similar velocity dispersion @xcite .
this suggests that was most likely associated with an early - type galaxy .
another potential implication is that edcc 493 is more evolved than a typical cluster of the same mass , perhaps a reflection of the old age of the grb progenitor system . the determination of the early - type fraction for a larger sample of cluster members will show whether this effect is real .
we also detect diffuse x - ray emission in the xrt data coincident with the optical cluster position , at @xmath74 , @xmath75 ( j2000 ) , with an uncertainty of about @xmath80 in each coordinate ( figure [ fig:050911xray ] ) .
this position is @xmath81 west and @xmath82 south of the optical position of the bright cluster elliptical . to determine the source x - ray properties we extract counts for each individual observation in an elliptical aperture with semi - major and semi - minor axes of @xmath83 and @xmath84 , respectively , selected to match the scale at which the cluster diffuse emission matches the background level .
we then bin the extracted counts in energy such that each bin contains at least ten counts . using a mekal model fit to the energy range of @xmath54 kev with an abundance fixed at @xmath85 z@xmath6 @xcite and an absorbing column density of @xmath86 @xmath10 @xmath10 @xcite , we find @xmath87 kev , and @xmath88 erg s@xmath2 ( @xmath89 for 19 degrees of freedom ) .
the data and model fit are shown in figure [ fig : g050911spec ] .
the measured velocity dispersion and x - ray luminosity are in good agreement with values measured for galaxy groups and poor clusters from the rosat deep cluster survey @xcite , but the temperature is somewhat lower than expected in comparison to the compilation of @xcite from which we estimate @xmath90 kev . using the cluster mass - temperature relation @xcite we estimate a mass of @xmath91 m@xmath6 , or about a factor of six times lower than the cluster zwcl 1234.0 + 02916 in the field of grb050509b ( see [ sec : xdata ] ) .
we next assess the probability that is associated with edcc 493 . from the @xmath92 relation for x - ray clusters in the rosat deep cluster survey
we find that for a flux of @xmath93 erg @xmath2 @xmath10 the surface density of sources is about 1.4 deg@xmath94 @xcite .
the probability of chance coincidence with the @xmath71 radius error circle is therefore @xmath95 .
thus , we conclude that the association between and edcc 493 is significant at the @xmath96 confidence level .
we note that taking into account the thirteen additional searches ( excluding grb050509b ; see [ sec : xdata ] ) the probability of finding such a cluster in any of the bat error circles is about @xmath40 ( or , @xmath97 ) . of course , of the other fourteen short bursts , eleven have much more accurate positions from x - ray , optical , and/or radio afterglow observations .
if we consider the x - ray luminosity of the cluster , we find that the volume density of clusters with @xmath98 erg s@xmath2 is @xmath99 mpc@xmath100 ( @xmath101 erg s@xmath2)@xmath2 @xcite . integrating the x - ray luminosity function with @xmath102 @xcite we find @xmath103 mpc@xmath100 , or @xmath104 arcmin@xmath94 within the distance to edcc 493 .
the probability of finding such a cluster within the error circle is therefore @xmath105 , or a @xmath106 significance level for an association with .
turning to the brightest cluster galaxy ( bcg ) , we find from the 2mass catalog that it has @xmath107 mag in a @xmath108 aperture , or @xmath109 mag compared to our @xmath110-band photometry .
the surface density of sources with equal or greater brightness is about 18 deg@xmath94 , or a probability of @xmath111 of finding such an object within the error circle .
the rest - frame @xmath112-band absolute magnitude of the bcg is @xmath113 mag , or @xmath114 * in comparison to the luminosity function from the 2df galaxy redshift survey and 2mass @xcite . integrating the @xmath112-band luminosity function
we find that the number density of such galaxies is @xmath115 mpc@xmath100 , or @xmath116 arcmin@xmath94 within the distance to edcc 493 .
thus , the probability to find such a luminous galaxy within the bat error circle of is about 0.01 ( @xmath96 confidence level ) .
we therefore conclude that the probability of chance association is only 0.1 - 1@xmath117 , and it is therefore likely that occurred within the cluster . at the redshift of edcc 493 ,
the isotropic - equivalent @xmath26-ray energy release of the burst was @xmath118 erg , similar to that of other short grbs @xcite . in figure
[ fig : xray ] we show smoothed xrt and _ chandra _ x - ray images of the fields of the fifteen short grbs . with the exception of the previously detected diffuse x - ray emission from the cluster zwcl 1234.0 + 02916 coincident with grb050509b @xcite
, we do not detect clear diffuse x - ray emission in coincidence with any of other short grbs .
we calculate upper limits on the x - ray flux using @xmath119 within a @xmath120 radius circle centered on each grb position , where @xmath121 is the total number of counts within the circle in the @xmath54 kev range ( effectively the background level ) , and @xmath122 is the total exposure time . to convert from count rate to flux we assume a thermal bremsstrahlung model with @xmath123 kev and an absorbing column given by the @xcite value for each burst .
the typical upper limits are @xmath124 erg s@xmath2 @xmath10 , or about a factor two lower than for edcc 493 . assuming a typical redshift , @xmath125
, the corresponding luminosity limit is @xmath126 erg s@xmath2 , or roughly @xmath127 m@xmath6 . for the cluster
zwcl 1234.0 + 02916 associated with grb050509b we derive a temperature of @xmath128 kev and an unabsorbed luminosity of @xmath129 erg s@xmath2 ( @xmath130 for 12 degrees of freedom ) .
the absorbing column density is @xmath131 @xmath10 , about an order of magnitude larger than the @xcite value for the galactic column .
here we used a mekal model with the abundance fixed to @xmath85 z@xmath6 .
we note that our derived temperature is in good agreement with the value of about 3.65 kev found by @xcite , but is lower than the value of 5.25 kev found by @xcite .
our derived luminosity is about @xmath73 higher than that of @xcite .
the inferred cluster mass is @xmath132 m@xmath6 .
we present the first systematic search for galaxy clusters hosting short grbs using multi - slit optical spectroscopy in the fields of grbs 050709 , 050724 , 050911 , and 051221a , and a re - analysis of all publicly available x - ray observations .
future papers in this series will present optical spectroscopy of additional short grb fields and a detailed analysis of the galaxy cluster statistics .
no apparent clusters are found in the fields of grbs 050709 , 050724 , and 051221a from optical and x - ray observations . in the error circle of the putative short burst
we show that the cluster edcc 493 has a mean redshift , @xmath0 , a velocity dispersion , @xmath133 km s@xmath2 , an x - ray temperature , @xmath134 kev , and a luminosity , @xmath98 erg s@xmath2 . these values are typical for poor clusters , and the inferred mass is about @xmath5 m@xmath6 .
we estimate that the chance probability of finding such a galaxy cluster in the bat error circle of is about 0.1 - 1@xmath117 .
this result highlights the ability to associate short grbs with galaxy clusters based on @xmath26-ray positions alone , thus removing a potential bias in favor of associations with gas - rich galaxies when relying on afterglow positions .
it has been suggested that the relative fraction of early- and late - type host galaxies of short grbs can be used to constrain the age distribution of the progenitor population @xcite . making the association between and edcc 493 , and using all of the available observations to date
, we find that of the short grbs five appear to be associated with early - type galaxies ( 050509b , 050724 , 050813 , 050911 , 060502b ) and two are associated with late - type galaxies ( 050709 , 051221a ) .
taken at face value , this would argue for an age distribution , @xmath135 with @xmath136 @xcite . naturally , in making a more accurate derivation of this value , one has to take into account the respective probability of association for each burst .
in fact if we consider only secure associations , the relative numbers are @xmath137 instead of @xmath138 , leading to @xmath139 .
independent of associations with individual galaxies , the fraction of short grbs in clusters is also of interest in assessing the age distribution . of the sixteen available bursts ,
three have claimed cluster associations ( 050509b , 050813 , 050911 ) . within the uncertainty
, this fraction is in rough agreement with the value of @xmath140 for the overall fraction of stellar mass in galaxy clusters @xcite , or roughly @xmath13 in clusters equal to or more massive than edcc 493 @xcite . of course , not all stars are capable of producing short grbs , but assuming that the initial mass function and binary fractions are independent of galaxy properties , the total stellar mass provides a good proxy for the mass in short grb progenitors .
thus , at the present there is reasonable agreement between the fraction of short grbs and the baseline fraction of stellar mass in galaxy clusters .
finally , we note that the frequency of short grbs in galaxy clusters may reflect a potential association with globular clusters .
the latter are thought to provide an efficient environment for the production of dns binaries , and may account for a substantial fraction of all short grb progenitors @xcite . in particular , the specific frequency of globular clusters increases significantly from a value of @xmath141 for s+irr galaxies to @xmath142 for e+s0 galaxies , and @xmath143 for cd galaxies @xcite . given that massive ellipticals are over - represented in galaxy clusters compared to the field , we expect that an association with globular clusters will increase the fraction of galaxy cluster associations compared to the baseline level of @xmath144 indicated above .
thus , continued searches for galaxy clusters hosting short grbs , and more detailed predictions for the expected fraction as a function of cluster mass and redshift , may hold the key to a clearer understanding of the progenitor population .
we thank a. dressler , a. gal - yam , m. gladders , d. kawata , f. schweizer , and a. soderberg for helpful discussions .
e.b . is supported by nasa through hubble fellowship grant hst-01171.01 awarded by the space telescope science institute , which is operated by aura , inc . for nasa under contract nas 5 - 26555 .
s. acknowledges support from the observatories of the carnegie institution of washington and korean science and engineering foundation grant kosef-2005 - 215-c00056 funded by the korean government ( most ) .
, s. d. m. , & springel , v. 2000 , in the first stars : proceedings of the mpa / eso workshop held at garching , germany , 4 - 6 august 1999 , eso astrophysics symposia .
isbn 3 - 540 - 67222 - 2 . edited by a. weiss , t.g .
abel , and v. hill .
springer - verlag , 2000 , p. 327
a. weiss , t. g. abel , & v. hill , 327 llcccclcc 0.05 in 050709 & 2006 june 28.23 & 300 & og590 & 4800 & 1.47 & @xmath145 & 15 & 10 + & 2006 june 28.30 & 300 & og590 & 4800 & 1.12 & @xmath145 & 11 & 5 + & 2006 june 28.39 & 300 & og590 & 4000 & 1.02 & @xmath145 & 7 & 6 + 050724 & 2006 june 28.96 & 300 & w4800 - 7800 & 4800 & 1.47 & @xmath146 & 21 & 18 + & 2006 june 29.02 & 1090 & none & 3600 & 1.13 & @xmath147 & 21 & 19 + 051221a & 2006 june 29.28 & 300 & w4800 - 7800 & 6000 & 1.59 & @xmath146 & 41 & 34 + & 2006 june 29.36 & 300 & w4800 - 7800 & 6900 & 1.44 & @xmath146 & 38 & 27 + 050911 & 2006 june 30.28 & 300 & none & 6000 & 1.70 & @xmath148 & 25 & 21 + & 2006 june 30.36 & 300 & none & 5800 & 1.18 & @xmath148 & 13 & 11 lllcccccc 0.05 in 050509b & 0.226 & 2005 may 9.17 & xrt & @xmath149 & 1.27 & 0.0092 & @xmath150 & @xmath151 + 050709 & 0.161 & 2005 jul . 11.55 & xrt & 17316 & & & & + & & 2005 jul . 12.43 & xrt & 4977 & & & & + & & 2005 jul . 13.11 & xrt & 7035 & 1.23 & @xmath152 & @xmath153 & @xmath154 + & & 2005 jul . 25.86 & cxo & 18284 & & @xmath155 & @xmath156 & @xmath157 + 050724 & 0.257 & 2005 jul . 29.02
& xrt & 24880 & & & & + & & 2005 jul .
30.02 & xrt & 21128 & 14.5 & @xmath152 & @xmath156 & @xmath158 + & & 2005 jul .
26.84 & cxo & 49955 & & @xmath159 & @xmath160 & @xmath161 + 050813 & 1.8 ?
& 2005 aug . 13.28 & xrt & 14210 & & & & + & & 2005 aug . 16.03 & xrt & 11438 & & & & + & & 2005 aug . 19.04 & xrt & 9265 & & & & + & & 2005 aug . 21.65 & xrt & 13985 & 4.08 & @xmath162 & @xmath163 & @xmath164 + 050906 & & 2005 sep . 6.44
& xrt & 5687 & 5.60 & @xmath165 & @xmath166 & + 050911 & 0.165 & 2005 sep . 11.86 & xrt & 6225 & & & & + & & 2005 sep . 12.59 & xrt & 9755 & & & & + & & 2005 sep . 14.06 & xrt & 12983 & & & & + & & 2005 sep . 18.27 & xrt & 16723 & 2.70 & 0.0033 & @xmath167 & @xmath168 + 050925@xmath169 & & 2005 sep .
25.38 & xrt & 37152 & & & & + & & 2006 apr . 6.03 & xrt & 14841 & & & & + & & 2006 may 8.76 & xrt & 8735 & 114 & @xmath170 & @xmath171 & + 051105a & & 2005 nov . 5.27 & xrt & 55846 & 2.89 & @xmath172 & @xmath173 & + 051114 & & 2005 nov . 15.64 & xrt & 4750 & & & & + & & 2005 nov .
15.91 & xrt & 10753 & 1.66 & @xmath162 & @xmath174 & + 051210 & & 2005 dec . 10.24 & xrt & 37401 & 2.14 & @xmath170 & @xmath175 & + 051221a & 0.546 & 2006 jan . 2.09 & xrt & 56663 & 6.58 & @xmath172 & @xmath176 & @xmath177 + 051227 & & 2005 dec .
30.03 & xrt & 45913 & & & & + & & 2006 jan . 1.02 & xrt & 10216 & & & & + & & 2006 jan . 2.11 & xrt & 27203 & 4.20 & @xmath178 & @xmath179 & + 060121 & & 2006 jan . 28.01 & xrt & 25272 & & & & + & & 2006 feb . 2.04 & xrt & 18420 & 1.66 & @xmath172 & @xmath180 & + 060313 & & 2006 mar . 15.00 & xrt & 40463 & 4.65 & @xmath181 & @xmath182 & + 060502b & 0.287 ?
& 2006 may 2.73 & xrt & 29630 & 4.32 & @xmath152 & @xmath174 & @xmath158 + 060801 & 1.131 & 2006 aug . 2.04 & xrt & 20942 & & & & + & & 2006 aug . 3.05 & xrt & 38051 & 1.54 & @xmath172 & @xmath180 & @xmath183 llllc 0.2 in & & 20.48 & @xmath184 & abs+em + & & 20.76 & @xmath185 & abs+em + & & 21.62 & @xmath186 & abs + & & 20.00 & @xmath187 & abs + & & 20.36 & @xmath188 & abs + & & 20.36 & @xmath189 & abs + & & 17.57 & @xmath190 & abs + & & 20.53 & @xmath191 & abs+em + & & 18.98 & @xmath192 & abs + & & 18.90 & @xmath193 & abs + & & 19.08 & @xmath194 & abs + & & 21.14 & @xmath195 & abs + & & 20.80 & @xmath184 & abs + & & 20.03 & @xmath196 & abs ) .
the data are binned with at least ten counts per bin .
we use a mekal model fit with an abundance fixed at @xmath85 z@xmath6 and an absorbing column density of @xmath198 @xmath10 @xmath10 @xcite .
the best - fit parameters are @xmath87 kev , and @xmath88 erg s@xmath2 ( @xmath89 for 19 degrees of freedom ) .
[ fig : g050911spec],width=720 ] z@xmath6 . the best - fit parameters are @xmath128 kev , an unabsorbed luminosity of @xmath129 erg s@xmath2 , and an absorbing column density of @xmath199 @xmath10 ( @xmath130 for 12 degrees of freedom ) .
[ fig : g050509bspec],width=720 ][/INST] we present a search for galaxy clusters in the fields of three bona - fide short grbs ( 050709 , 050724 , and 051221a ) and the putative short burst grb050911 using multi - slit optical spectroscopy .
these observations are part of a long - term program to constrain the progenitor age distribution based on the fraction of short grbs in galaxy clusters and early - type galaxies .
we find no evidence for cluster associations at the redshifts of the first three bursts , but we confirm the presence of the cluster edcc 493 within the error circle of grb050911 and determine its redshift , @xmath0 , and velocity dispersion , @xmath1 km s@xmath2 .
in addition , our analysis of /xrt observations of this burst reveals diffuse x - ray emission coincident with the optical cluster position , with a luminosity , @xmath3 erg s@xmath2 , and a temperature , @xmath4 kev .
the inferred mass of the cluster is @xmath5 m@xmath6 , and the probability of chance coincidence is about @xmath7 , indicating an association with at the 2.6 - 3.2@xmath8 confidence level .
a search for diffuse x - ray emission in coincidence with the fifteen other short grbs observed with xrt and _ chandra _ reveals that with the exception of the previously - noted cluster zwcl 1234.0 + 02916 likely associated with grb050509b , no additional associations are evident to a typical limit of @xmath9 erg s@xmath2 @xmath10 , or @xmath11 m@xmath6 assuming a typical @xmath12 .
the resulting fraction of short grbs hosted by galaxy clusters of about @xmath13 is in rough agreement with the fraction of stellar mass in clusters of @xmath14 .
# 1#2#3#1@xmath15#2@xmath16#3@xmath17 # 1#2#3@xmath18 </s> |
osteochondroma is the most common benign tumour of the bone and is considered as developmental lesion of the bone .
common site of osteochondroma presentation is around the knee but calcaneal osteochondroma as such is a rare entity .
osteochondromas grow during childhood through adolescence , but usually the growth of osteochondroma ends when the epiphyseal plates close . in an adult , growth of an osteochondroma suggests the diagnosis of a malignant transformation . however , it can also present as pressure symptom in later phase of life . here
, we presented a case of retrocalcaneal bursitis in late phase of life of a male farmer due to late growth of osteochondroma .
we report a case of calcaneal osteochondroma which is an extremely rare site of occurrence with painful swelling of ankle causing limitation of walking in a 58-year - old male . surgical excision of tumour followed by a histological confirmation reported negative for any malignant changes .
it is possible of late detection of benign osteochondromas which show symptomatic growth and pressure effect in skeletally mature patients without malignant transformation .
osteochondroma is the most common benign tumour of the bone which is better known as skeletal developmental lesion .
it usually arises from the metaphyseal or metadiaphyseal region of long bones of the appendicular skeleton and are most commonly seen around the knee [ 1 , 2 ] .
osteochondromas grow during childhood through adolescence , but usuallytheir growth ends when the epiphyseal plates close [ 1 , 3 ] . they are typically described in patients younger than 20 year - old and extensive osteochondroma growth into adulthood is rarely reported [ 3 , 4 ] . in an adult , growth of an osteochondroma suggests the diagnosis of malignant transformation to a chondrosarcoma [ 3 , 5 ] . however , krieg et al and nogier et al reported extensive growth of an osteochondroma in a skeletally mature patient whose tumour had no evidence of malignancy in histological examination .
calcaneus is one of the most unusual region for an osteochondroma . in this study , we describe the clinical presentation of calcaneal osteochondroma with retrocalcaneal bursitis in a skeletally mature male .
a 58-year - old male patient who belongs to jharkhand was admitted to our hospital with painful swelling and stiffness in his right ankle .
the swelling was present in a smaller form for many years but past three to four years there was progressive swelling at the back of ankle joint and now he was unable to walk properly .
he was not able to walk more than 200 - 300 metre at a stretch .
he ignored the symptoms many a times , and had been taking analgesics as prescribed by the local doctor but was never investigated properly before except an x - ray of ankle joint . since last two weeks , the pain had increased tremendously without any precipitating reason along with inflammatory sign over the ankle joint . at the time of presentation ,
pain was severe and he was unable to stand , and there was enough pain at rest also .
no past history of trauma or any other illness which can affect its course was observed . on physical examination
, about 3.5 2 cm stiff , immobile , painful mass placed between tendoachilis and plafond of tibia was palpated .
the antero- posterior and lateral view plain x - ray radiography and plane computed tomography ( ct ) revealed a bony prominence 31 17 mm ( cartilage cap thickness : 5 mm app ) in size raising from superior part of the calcaneus near posterior margin of talo calcaneus joint and reported as a higher possibility of an osteochondroma ( fig . 1 , 2 , 3 )
in addition , retrocalcanealbursitis features were observed . as the pain was of moderate to severe grade and caused major limitation in activities of daily living , it was decided to excise the osseous mass .
intraoperatively , it was observed that the lesion rose from the posteromedial side of the calcaneus and grew through the surface pushing the soft tissues more posteromedially .
posterolateral approach chosen as it was safer and mass was pushing all the soft tissue on lateral side and it was easy to remove adhesion on posterolateral approach .
the bony mass was excised as much as possible from its attachment to calcaneus ; stalk was not differentiated as this was very compressed .
bony material along with soft tissue was sent for pathologic examination , inflamed bursa was also removed .
histopathological examination of the bony mass reported it as osteochondroma ( cartilage cap 4 mm ) but there was no evidence of malignancy .
after surgery , patient was put on below knee slab which was removed after 21 days to get adequate soft tissue healing .
follow up , there was no recurrence of lesion and patient was comfortably walking without pain .
currently , the patient is asymptomatic and has no pain , but there is limitation of motion at the ankle joint .
a preoperative radiograph of the foot shows a bony prominence ( arrows ) raising from posteromedial of the calcaneus .
a preoperative axial ct scan with 3d reconstruction of the foot shows the osteochondroma lesion raising from posteromedial of the calcaneus ( 31 * 17 mm in size , cartilage cap thickness : 5 mm ) axial ct scan taken at the 1-month postoperative of the foot shows an exofitic lesion ( arrow ) detected posteromedially to the calcaneus ( 31 * 17 mm in size with cartilage cap thickness of 5 mm ) .
osteochondromas are developmental lesions rather than true neoplasms and they may occur solitary or as multiple lesions , associated with the syndrome multiple hereditary exostoses .
osteochondroma is seen in 2% to 3% of the general population and represents approximately 36% to 41% of benign bone tumours [ 7 , 8 ] .
post operative clinical photograph of excised mass of bone from calcaneus post operative x - ray ap and lat of ankle joint after removal of osteochondroma of calcaneus follow up x - ray of ankle at 6 month after surgical removal of osteochondroma from calcaneus the evaluation of osteochondromas can generally help clinical findings , and imaging methods such as plain radiography , ultrasonography , ct , mr imaging and bone scanning [ 1 , 3 ] .
the most common symptom is a non - tender , painless cosmetic deformity secondary to the slowly enlarging exophytic mass .
additional complications that cause symptoms include osseous deformity , fracture , vascular - nerve compression , neurologic sequelae , bursa formation , and malignant transformation [ 3 , 7 ] .
malignant transformation is seen in less than 1% to 2% of patients of solitary osteochondroma [ 2 , 9 ] and in 5%-25% of patients with multiple hereditary exostoses [ 1 , 2 , 10 ] .
clinical features suspicious for malignant transformation comprise new onset of pain in a previously stable lesion , rapid or new growth , growth after skeletal maturity , and/or large lesions [ 2 , 11 ] .
these lesions are usually a low - grade chondrosarcoma or less often a secondary osteosarcoma [ 12 , 13 ] . in our case , the first complaint was pain that was progressively increasing with limitation of movement .
although , radiography alone is often diagnostic , other imaging modalities may be necessary for surgical planning and to exclude sarcomatous degeneration . the radiographic appearance of this tumour is often diagnostic and reflects its pathologic characteristics
. the lesion is composed of native cortical and medullar bone protruding from and continuous with the underlying bone and they appear as sessile or pedunculated [ 1 , 2 ] . however , if there is no extensive mineralization , the thickness of the cartilage cap is usually not well evaluated with radiography . in our case , because of the unusual posteroinferior placement to calcaneus , ap and lateral radiographies did not reveal a satisfactory view .
ultrasonography can be used in the measurement of the hyaline cartilage cap thickness [ 14 , 15 ] .
however , it is an operator - dependent examination with often limited value in obese patients and lack of evaluation of the osseous components of the lesion .
bone scanning is directly correlated with the degree of enchondral bone formation [ 16 , 17 ] .
it also important for visualizing the effect of the lesion on surrounding structures and shows cortical and medullary continuity between the parent bone and osteochondroma .
multiplanar reconstruction and three - dimensional imaging features of ct give important information about determining these lesions .
it allows optimal demonstration of the pathognomonic cortical and medullary continuity of the lesion and parent bone as in our case .
murphey et al believed that very thin sections available with ct are often superior to mr imaging , especially in complex areas of anatomy , in osteochondroma cases .
however , it can be very difficult to correctly measure the thickness of a totally nonmineralized cartilage cap because it can not be easily differentiated from surrounding muscle or bursa .
cartilage cap thickness greater than 1 to 2 cm in adults and 2 to 3 cm in growing children suggests malignant transformation [ 1 , 2 ] .
if the lesion is painful and growing after skeletal maturity and exhibits signs of malignant transformation , it should be treated surgically .
any remaining cartilage cap may result in recurrence , especially in growing lesions . in our case
, osteochondroma was slowly growing in size , there was only minimal increase in size of swelling in due course of time .
but there was progressive increase in intensity of pain as well limitation of movement at ankle joint radiograph and ct scan showing osteochondroma with cartilage cap but there was no obvious sign of any malignancy .
in conclusion , we should keep in mind that benign osteochondromas can represent as symptomatic growth in skeletally mature patients even in 5th or 6th decade without a malignant transformation .
calcaneal osteochondroma is a rare condition , which can present as retro calcaneal bursitis due to growth without malignant change in late phase of life . | introduction : osteochondroma is the most common benign tumour of the bone and is considered as developmental lesion of the bone .
common site of osteochondroma presentation is around the knee but calcaneal osteochondroma as such is a rare entity .
osteochondromas grow during childhood through adolescence , but usually the growth of osteochondroma ends when the epiphyseal plates close . in an adult , growth of an osteochondroma suggests the diagnosis of a malignant transformation . however , it can also present as pressure symptom in later phase of life . here
, we presented a case of retrocalcaneal bursitis in late phase of life of a male farmer due to late growth of osteochondroma.case presentation : we report a case of calcaneal osteochondroma which is an extremely rare site of occurrence with painful swelling of ankle causing limitation of walking in a 58-year - old male .
surgical excision of tumour followed by a histological confirmation reported negative for any malignant changes.conclusion:there may be chances of osteochondroma being a reason for retrocalcaneal bursitis .
it is possible of late detection of benign osteochondromas which show symptomatic growth and pressure effect in skeletally mature patients without malignant transformation . | <s>[INST]osteochondroma is the most common benign tumour of the bone and is considered as developmental lesion of the bone .
common site of osteochondroma presentation is around the knee but calcaneal osteochondroma as such is a rare entity .
osteochondromas grow during childhood through adolescence , but usually the growth of osteochondroma ends when the epiphyseal plates close . in an adult , growth of an osteochondroma suggests the diagnosis of a malignant transformation . however , it can also present as pressure symptom in later phase of life . here
, we presented a case of retrocalcaneal bursitis in late phase of life of a male farmer due to late growth of osteochondroma .
we report a case of calcaneal osteochondroma which is an extremely rare site of occurrence with painful swelling of ankle causing limitation of walking in a 58-year - old male . surgical excision of tumour followed by a histological confirmation reported negative for any malignant changes .
it is possible of late detection of benign osteochondromas which show symptomatic growth and pressure effect in skeletally mature patients without malignant transformation .
osteochondroma is the most common benign tumour of the bone which is better known as skeletal developmental lesion .
it usually arises from the metaphyseal or metadiaphyseal region of long bones of the appendicular skeleton and are most commonly seen around the knee [ 1 , 2 ] .
osteochondromas grow during childhood through adolescence , but usuallytheir growth ends when the epiphyseal plates close [ 1 , 3 ] . they are typically described in patients younger than 20 year - old and extensive osteochondroma growth into adulthood is rarely reported [ 3 , 4 ] . in an adult , growth of an osteochondroma suggests the diagnosis of malignant transformation to a chondrosarcoma [ 3 , 5 ] . however , krieg et al and nogier et al reported extensive growth of an osteochondroma in a skeletally mature patient whose tumour had no evidence of malignancy in histological examination .
calcaneus is one of the most unusual region for an osteochondroma . in this study , we describe the clinical presentation of calcaneal osteochondroma with retrocalcaneal bursitis in a skeletally mature male .
a 58-year - old male patient who belongs to jharkhand was admitted to our hospital with painful swelling and stiffness in his right ankle .
the swelling was present in a smaller form for many years but past three to four years there was progressive swelling at the back of ankle joint and now he was unable to walk properly .
he was not able to walk more than 200 - 300 metre at a stretch .
he ignored the symptoms many a times , and had been taking analgesics as prescribed by the local doctor but was never investigated properly before except an x - ray of ankle joint . since last two weeks , the pain had increased tremendously without any precipitating reason along with inflammatory sign over the ankle joint . at the time of presentation ,
pain was severe and he was unable to stand , and there was enough pain at rest also .
no past history of trauma or any other illness which can affect its course was observed . on physical examination
, about 3.5 2 cm stiff , immobile , painful mass placed between tendoachilis and plafond of tibia was palpated .
the antero- posterior and lateral view plain x - ray radiography and plane computed tomography ( ct ) revealed a bony prominence 31 17 mm ( cartilage cap thickness : 5 mm app ) in size raising from superior part of the calcaneus near posterior margin of talo calcaneus joint and reported as a higher possibility of an osteochondroma ( fig . 1 , 2 , 3 )
in addition , retrocalcanealbursitis features were observed . as the pain was of moderate to severe grade and caused major limitation in activities of daily living , it was decided to excise the osseous mass .
intraoperatively , it was observed that the lesion rose from the posteromedial side of the calcaneus and grew through the surface pushing the soft tissues more posteromedially .
posterolateral approach chosen as it was safer and mass was pushing all the soft tissue on lateral side and it was easy to remove adhesion on posterolateral approach .
the bony mass was excised as much as possible from its attachment to calcaneus ; stalk was not differentiated as this was very compressed .
bony material along with soft tissue was sent for pathologic examination , inflamed bursa was also removed .
histopathological examination of the bony mass reported it as osteochondroma ( cartilage cap 4 mm ) but there was no evidence of malignancy .
after surgery , patient was put on below knee slab which was removed after 21 days to get adequate soft tissue healing .
follow up , there was no recurrence of lesion and patient was comfortably walking without pain .
currently , the patient is asymptomatic and has no pain , but there is limitation of motion at the ankle joint .
a preoperative radiograph of the foot shows a bony prominence ( arrows ) raising from posteromedial of the calcaneus .
a preoperative axial ct scan with 3d reconstruction of the foot shows the osteochondroma lesion raising from posteromedial of the calcaneus ( 31 * 17 mm in size , cartilage cap thickness : 5 mm ) axial ct scan taken at the 1-month postoperative of the foot shows an exofitic lesion ( arrow ) detected posteromedially to the calcaneus ( 31 * 17 mm in size with cartilage cap thickness of 5 mm ) .
osteochondromas are developmental lesions rather than true neoplasms and they may occur solitary or as multiple lesions , associated with the syndrome multiple hereditary exostoses .
osteochondroma is seen in 2% to 3% of the general population and represents approximately 36% to 41% of benign bone tumours [ 7 , 8 ] .
post operative clinical photograph of excised mass of bone from calcaneus post operative x - ray ap and lat of ankle joint after removal of osteochondroma of calcaneus follow up x - ray of ankle at 6 month after surgical removal of osteochondroma from calcaneus the evaluation of osteochondromas can generally help clinical findings , and imaging methods such as plain radiography , ultrasonography , ct , mr imaging and bone scanning [ 1 , 3 ] .
the most common symptom is a non - tender , painless cosmetic deformity secondary to the slowly enlarging exophytic mass .
additional complications that cause symptoms include osseous deformity , fracture , vascular - nerve compression , neurologic sequelae , bursa formation , and malignant transformation [ 3 , 7 ] .
malignant transformation is seen in less than 1% to 2% of patients of solitary osteochondroma [ 2 , 9 ] and in 5%-25% of patients with multiple hereditary exostoses [ 1 , 2 , 10 ] .
clinical features suspicious for malignant transformation comprise new onset of pain in a previously stable lesion , rapid or new growth , growth after skeletal maturity , and/or large lesions [ 2 , 11 ] .
these lesions are usually a low - grade chondrosarcoma or less often a secondary osteosarcoma [ 12 , 13 ] . in our case , the first complaint was pain that was progressively increasing with limitation of movement .
although , radiography alone is often diagnostic , other imaging modalities may be necessary for surgical planning and to exclude sarcomatous degeneration . the radiographic appearance of this tumour is often diagnostic and reflects its pathologic characteristics
. the lesion is composed of native cortical and medullar bone protruding from and continuous with the underlying bone and they appear as sessile or pedunculated [ 1 , 2 ] . however , if there is no extensive mineralization , the thickness of the cartilage cap is usually not well evaluated with radiography . in our case , because of the unusual posteroinferior placement to calcaneus , ap and lateral radiographies did not reveal a satisfactory view .
ultrasonography can be used in the measurement of the hyaline cartilage cap thickness [ 14 , 15 ] .
however , it is an operator - dependent examination with often limited value in obese patients and lack of evaluation of the osseous components of the lesion .
bone scanning is directly correlated with the degree of enchondral bone formation [ 16 , 17 ] .
it also important for visualizing the effect of the lesion on surrounding structures and shows cortical and medullary continuity between the parent bone and osteochondroma .
multiplanar reconstruction and three - dimensional imaging features of ct give important information about determining these lesions .
it allows optimal demonstration of the pathognomonic cortical and medullary continuity of the lesion and parent bone as in our case .
murphey et al believed that very thin sections available with ct are often superior to mr imaging , especially in complex areas of anatomy , in osteochondroma cases .
however , it can be very difficult to correctly measure the thickness of a totally nonmineralized cartilage cap because it can not be easily differentiated from surrounding muscle or bursa .
cartilage cap thickness greater than 1 to 2 cm in adults and 2 to 3 cm in growing children suggests malignant transformation [ 1 , 2 ] .
if the lesion is painful and growing after skeletal maturity and exhibits signs of malignant transformation , it should be treated surgically .
any remaining cartilage cap may result in recurrence , especially in growing lesions . in our case
, osteochondroma was slowly growing in size , there was only minimal increase in size of swelling in due course of time .
but there was progressive increase in intensity of pain as well limitation of movement at ankle joint radiograph and ct scan showing osteochondroma with cartilage cap but there was no obvious sign of any malignancy .
in conclusion , we should keep in mind that benign osteochondromas can represent as symptomatic growth in skeletally mature patients even in 5th or 6th decade without a malignant transformation .
calcaneal osteochondroma is a rare condition , which can present as retro calcaneal bursitis due to growth without malignant change in late phase of life .[/INST]introduction : osteochondroma is the most common benign tumour of the bone and is considered as developmental lesion of the bone .
common site of osteochondroma presentation is around the knee but calcaneal osteochondroma as such is a rare entity .
osteochondromas grow during childhood through adolescence , but usually the growth of osteochondroma ends when the epiphyseal plates close . in an adult , growth of an osteochondroma suggests the diagnosis of a malignant transformation . however , it can also present as pressure symptom in later phase of life . here
, we presented a case of retrocalcaneal bursitis in late phase of life of a male farmer due to late growth of osteochondroma.case presentation : we report a case of calcaneal osteochondroma which is an extremely rare site of occurrence with painful swelling of ankle causing limitation of walking in a 58-year - old male .
surgical excision of tumour followed by a histological confirmation reported negative for any malignant changes.conclusion:there may be chances of osteochondroma being a reason for retrocalcaneal bursitis .
it is possible of late detection of benign osteochondromas which show symptomatic growth and pressure effect in skeletally mature patients without malignant transformation .</s> |
metabolic syndrome ( mets ) is a conglomeration of abnormalities relating metabolism to cardiovascular risk .
factors involved with this syndrome include atherogenic dyslipidemias , central obesity , increased blood pressure , and impaired fasting glucose levels .
individuals diagnosed with mets have a 5-fold risk for type 2 diabetes mellitus ( t2 dm ) and a 2-fold risk for cardiovascular disease ( cvd ) .
risk factors for mets are concordant with each other and have been defined by many groups .
the national cholesterol education program - adult treatment panel iii ( ncep - atp iii ) guidelines have identified mets as a multiplex risk factor for cvd that deserves more clinical attention .
the skeleton , which is typically considered a static structure that is important for providing the necessary framework of the body , has recently been found to play an important role in the maintenance of energy homeostasis .
the bones , adipose tissue , and brain interact with one another to control body weight and to regulate energy expenditure and glucose metabolism through the actions of a hormone that is secreted specifically by the osteoblasts , namely , osteocalcin [ 2 , 3 ] .
osteocalcin ( oc ) , or bone gla protein , is the major noncollagenous protein that acts locally in the bone mineralization .
oc is synthesized by the osteoblasts as the pre - pro - form and is cleaved to the mature protein with subsequent enzymatic posttranslational carboxylation .
this molecule is present in the circulation in the carboxylated ( coc ) form and , to a lesser degree , in the undercarboxylated ( uoc ) form .
total serum oc ( toc ) , which comprises both the carboxylated and the undercarboxylated forms , has been utilized traditionally as a marker of bone formation or bone turnover .
studies using animal models have demonstrated that oc is involved in the regulation of body energy by modulating fat and glucose metabolism .
the uoc acts directly on the -cells to increase their mass and proliferation and therefore increases insulin secretion .
moreover , it influences white adipocytes to induce the expression of genes involved in energy expenditure and to enhance the secretion of adiponectin , thus increasing insulin sensitivity .
apart from its secretion from the osteoblasts , oc is also secreted locally by adipocytes and megakaryocytes [ 7 , 8 ] . combining these actions ,
oc is capable of enhancing the secretion of insulin and increasing insulin sensitivity in both fat and muscle .
consistent with the animal studies , oc levels have been reported to be decreased in patients with t2 dm and to be inversely related to the levels of insulin resistance and adiposity in humans [ 9 , 10 ] .
cross - sectional analyses have extended these observations to apply the mets criteria in examining the association between oc level and cardiovascular risk ; the results have revealed that oc is inversely related to the number of mets components [ 1 , 2 ] .
shea et al . reported that the carboxylated fraction is inversely related to impaired glucose metabolism indices .
by contrast , kanazawa et al . demonstrated that serum uoc and toc levels are inversely related to impaired glucose levels .
the same group also found that the uoc / toc ratio is not related to the fasting plasma glucose or the diabetic status . in their formen study , iki et al . reported that the total , carboxylated and undercarboxylated forms are all proportional to one another . considering these studies in combination , it appears that the role of the various oc fractions in humans is still unclear .
to date , one of the main limitations of the studies on this subject is that they have measured one or two fractions of oc , and no study has measured all three fractions together . because prior studies have demonstrated that the undercarboxylated fraction is implicated in the pathophysiology of insulin sensitivity , further investigations in this area should include a direct measurement of this fraction . in an attempt to fill this gap , we measured the carboxylated , undercarboxylated , and total oc in a population of patients with t2 dm who were either positive or negative for mets .
our objective was to determine whether uoc is related to mets and/or its individual components and other cardiovascular risk factors in patients with t2 dm , and whether toc and uoc have utility in predicting cardiovascular risk .
in this cross - sectional study , 203 consecutive patients with t2 dm followed regularly at a diabetes outpatient clinic were studied .
all the patients were 40 years of age , were not taking any lipid - lowering drugs , and had serum triglyceride levels of < 3.38
the exclusion criteria included the presence of any significant liver disease , renal failure requiring renal - replacement therapy , and the usage of oral contraceptives , hormone replacement therapy , or other drugs that could influence bone metabolism .
this study was performed at the obesity research center , college of medicine , king saud university , riyadh , saudi arabia .
the institutional review board approved this study , and all the participants gave their informed consent .
anthropometric measurements ( including height and weight ) were taken , and the body mass index ( bmi ) was calculated .
the waist circumference was determined as the minimum value between the iliac crest and the lateral costal margin .
serum toc was measured using an n - mid osteocalcin elisa kit ( elecsys , roche diagnostic ltd . ,
the serum uoc and serum coc were measured using eia kits ( takara bio inc . ,
the undercarboxylated eia kit uses a set of monoclonal antibodies that are reactive to uoc and less reactive to coc at amino acid positions 17 , 21 , and 24 .
the carboxylated eia kit uses a set of monoclonal antibodies that are reactive to coc at amino acid position 17 .
the intraassay and inter - assay variabilities were , respectively , 5.7% and 6.2% for coc , 10.2% and 9.8% for uoc , and 3.4% and 3.6% for toc .
the total cholesterol and triglycerides were determined by enzymatic techniques , whereas apolipoprotein a-1 ( apo a-1 ) and apolipoprotein b ( apo b ) were determined by immune - turbidimetric assays ( kone instruments , espoo , finland ) .
hdl cholesterol was measured after precipitation of vldl and ldl with phosphotungstic acid and magnesium chloride .
we used the definition of mets according to the ncep - atp iii . within this definition ,
three or more of the following criteria must be fulfilled : fasting blood glucose level 5.6 mmol / l , blood pressure 130/85 mmhg , triglycerides 1.7 mmol / l , hdl cholesterol < 1.03 mmol / l for men and < 1.29 mmol / l for women , and waist circumference > 102 cm for men and > 88 cm for women .
the statistical analysis was performed using spss version 17 ( chicago , illinois , usa ) .
all the data are presented either as the mean sd ( for symmetric variables ) or median with inter quartile range ( for skewed variables ) .
independent student 's t - test and mann - whitney u test were used to compare the means and mean ranks between the groups .
kruskal - wallis test was used to compare the mean ranks of toc , uoc , and coc across the three groups of mets components .
logarithmic transformations for skewed outcome variables ( toc , uoc , and coc ) were done so as to carry out the regression analysis .
karl pearson 's correlation analysis was performed to determine the relationships between two continuous variables of interest .
a multiple linear regression analysis was performed to test the independent linear relationship between the logarithmic transformed serum oc level and the markers of lipid metabolism by adjusting the effect of confounding variables , including age , bmi , waist circumference , and hba1c .
the levels of the three different forms of oc ( table 1 ) were lower than what has been reported in normal individuals .
the three different forms of oc were measured independently and were significantly correlated with each other ( p = 0.00 , data not shown ) .
the measured toc was inversely related to the markers of adiposity , as assessed via bmi ( r = 0.16 , p = 0.02 ) and glycemia ( indicated by the hba1c : r = 0.2 , p = 0.01 ) , as shown in table 2 .
the serum uoc was significantly and positively correlated with hdl - cholesterol ( r = 0.15 , p = 0.03 ) and negatively correlated with apo b / apo a-1 ratio ( r = 0.16 , p = 0.02 ) .
subsequently , the study population was divided based on the presence or absence of mets , according to the ncep - atp iii criteria .
individuals with mets , when compared to those subjects without mets , exhibited significantly higher bmis , waist circumferences , triglycerides levels , apo b levels , and apo b / apo a-1 ratios ( p = 0.00 ) , as presented in table 1 .
individuals without mets had higher levels of hdl - cholesterol ( p = 0.00 ) .
the group with mets had lower levels of toc and uoc , compared with those subjects without mets ( p = 0.01 and p = 0.03 , resp . ) .
a significant decrease in toc levels was observed with a higher number of mets components ( p = 0.02 ) .
a similar trend was observed with the uocs but this did not reach statistical significance ( figure 1 ) . to further investigate whether the serums toc and uoc levels in patients with mets were related to markers of dyslipidemia independently of other risk factors , multiple regression analyses adjusted for age , bmi , waist circumference , and hba1c were performed between toc and uoc versus the lipid parameters .
the serum toc was significantly and negatively correlated with serum triglycerides ( r = 0.032 , p = 0.049 ) , whereas uoc significantly correlated with serum hdl - cholesterol levels ( r = 0.05 , p = 0.023 ) as shown in figure 2 .
to our knowledge , the present study is the first to measure all the different forms of oc . for the first time
, we established an association between the uoc fraction and the lipidemic status in individuals with mets . in agreement with other studies
, we found that toc is related to the glycemic control and markers of adiposity in patients with t2 dm .
previous studies have demonstrated that toc levels are significantly and negatively correlated with the fasting blood glucose and hba1c levels [ 10 , 16 , 17 ] .
an inverse association between the toc level and hba1c was also observed in the present study .
this finding indicates that among our patients with t2 dm those individuals with better glycemic control are more likely to exhibit higher toc levels .
this result would also indicate that prolonged hyperglycemia and uncontrolled diabetes negatively affect the toc level .
by contrast , we did not determine an association between uoc and the measures of glycemia .
it is possible that the antidiabetic medications received by our patients could affect the levels of uoc ; thus , further studies are necessary to clarify this point . in our study , toc was significantly and negatively correlated with bmi .
this finding confirms other investigations demonstrating that toc is negatively associated with bmi and fat mass .
the uoc was significantly and positively correlated with hdl - cholesterol but was negatively correlated with the apo b / apo a-1 ratio .
this finding confirms a prior report of lee et al . , who demonstrated this relationship in animals .
to our knowledge , the present study is the first to establish a relationship between uoc and the apo b / apo a-1 ratio in humans , suggesting that a low uoc is closely related to an atherogenic , dyslipidemic profile that would otherwise increase the cardiovascular risk . individuals with t2 dm
are known to exhibit a classic lipid triad that includes high triglyceride levels , low hdl - cholesterol levels , and normal ldl - cholesterol levels . however , this triad is not sufficient to predict an untoward cardiovascular event .
the apo b / apo a-1 ratio is superior to any other cholesterol measurement for predicting cardiovascular risk [ 1820 ] .
as determined in a large prospective amoris study , higher apo b levels , an increased apo b / apo a-1 ratio , and low levels of apo a-1 are highly predictive of risk of fatal myocardial infarction [ 19 , 21 ] .
the inverse association of uoc with the apob / apo a-1 ratio that was reported in our study suggests the possible role of uoc in cardiovascular risk assessment in patients with t2 dm .
although it would be premature to conclude a causal effect of uoc on these parameters , it would be of interest to explore whether interventions that specifically raise uoc levels would decrease cardiovascular risk .
the goal of identifying mets is to prevent the occurrence of these diseases . to investigate whether the presence of mets increases the relationship between uoc and the prediction of cvd risk , we divided our population ( based on the ncep - atp iii guidelines ) into those subjects with and those without mets .
patients with mets had a higher bmi , waist circumference , triglyceride level , apo b level and apo b / apo a-1 ratio , and lower hdl - cholesterol level .
we also found that the toc and the uoc , but not the coc , were significantly lower in patients with mets in comparison to those without mets .
these differences point toward an association between these forms of oc and the dyslipidemia that is found in patients with mets .
previous studies mainly focused on determining the role of circulating toc , but they did not differentiate between the different forms of oc . to resolve this issue , we measured all the oc fractions independently , thus overcoming the problem associated with either calculating the coc levels by subtracting the uoc from the toc or adding the coc and uoc fractions to obtain the total oc , as has been done by polgreen et al . . in our study
, we found that the measured toc value was higher than the value obtained by summing up the two individual fractions ( data not shown ) . to study how the uoc and toc are associated with cvd risk
, we compared the relationship between the mets components and other cardiovascular risk factors and the different forms of oc .
there was an inverse association between the toc and the waist circumference values and serum triglycerides levels , although the former did not reach statistical significance .
saleem et al . determined that serum toc is negatively associated with mets in both blacks and non - hispanic whites .
found that plasma oc was inversely associated with mets in a community - dwelling cohort of older persons in the netherlands ; the authors reported that the subjects with the lowest quartile of oc concentrations had an approximately 3.7-fold higher risk of mets than did the subjects with the highest quartile .
first , the study population is comprised of subjects who were followed for t2 dm at a tertiary care hospital and thus might not have been representative of the general population .
second , this cross - sectional study could not determine a causal relationship between the fractions of oc and mets .
third , we did not measure sex steroids and vitamin k intake which could influence oc and bone metabolism .
the present study measured the three independent forms of oc in patients with t2 dm . we found that the toc level was associated with the degree of glycemic control , independently of the carboxylated or undercarboxylated forms .
we have established a new relationship between the uoc and lipid indices ( particularly the hdl - cholesterol and apo b / apoa-1 ratio ) , and we therefore suggest that uoc could play a role in the evaluation of the cardiovascular risk in patients with t2 dm . if serum osteocalcin is employed to determine the cardiovascular risk in patients with t2 dm , then the measured uoc would be a better predictor than the toc .
nonetheless , prospective studies are necessary to investigate further the utility of uoc for cardiovascular risk prediction . | studies have demonstrated that total osteocalcin ( toc ) is associated with metabolic syndrome ( mets ) and therefore might influence the risk of cardiovascular disease in humans .
undercarboxylated osteocalcin ( uoc ) regulates insulin secretion and sensitivity in mice , but its relation to mets in humans is unclear .
we aimed to determine whether uoc is related to mets and/or its individual components and other cardiovascular risk factors in patients with type 2 diabetes mellitus ( t2 dm ) , and whether toc and uoc have utility in predicting the cardiovascular risk .
we studied 203 t2 dm patients with and without mets .
mets was defined based on the ncep - atp iii criteria .
a correlation analysis was performed between the three outcome variables : ( i ) toc , ( ii ) uoc , and ( iii ) carboxylated osteocalcin ( coc ) and mets components and other cardiovascular risk factors .
both toc and uoc were significantly lower in patients with mets compared to those without mets , independent of body mass index . in patients with mets ,
uoc was significantly and positively correlated with hdl cholesterol , while toc was significantly and negatively correlated with serum triglycerides .
we report for the first time that uoc is related to lipid indices in patients with t2 dm . further studies are necessary to determine whether uoc can be utilized for cardiovascular risk assessments in these patients . | <s>[INST]metabolic syndrome ( mets ) is a conglomeration of abnormalities relating metabolism to cardiovascular risk .
factors involved with this syndrome include atherogenic dyslipidemias , central obesity , increased blood pressure , and impaired fasting glucose levels .
individuals diagnosed with mets have a 5-fold risk for type 2 diabetes mellitus ( t2 dm ) and a 2-fold risk for cardiovascular disease ( cvd ) .
risk factors for mets are concordant with each other and have been defined by many groups .
the national cholesterol education program - adult treatment panel iii ( ncep - atp iii ) guidelines have identified mets as a multiplex risk factor for cvd that deserves more clinical attention .
the skeleton , which is typically considered a static structure that is important for providing the necessary framework of the body , has recently been found to play an important role in the maintenance of energy homeostasis .
the bones , adipose tissue , and brain interact with one another to control body weight and to regulate energy expenditure and glucose metabolism through the actions of a hormone that is secreted specifically by the osteoblasts , namely , osteocalcin [ 2 , 3 ] .
osteocalcin ( oc ) , or bone gla protein , is the major noncollagenous protein that acts locally in the bone mineralization .
oc is synthesized by the osteoblasts as the pre - pro - form and is cleaved to the mature protein with subsequent enzymatic posttranslational carboxylation .
this molecule is present in the circulation in the carboxylated ( coc ) form and , to a lesser degree , in the undercarboxylated ( uoc ) form .
total serum oc ( toc ) , which comprises both the carboxylated and the undercarboxylated forms , has been utilized traditionally as a marker of bone formation or bone turnover .
studies using animal models have demonstrated that oc is involved in the regulation of body energy by modulating fat and glucose metabolism .
the uoc acts directly on the -cells to increase their mass and proliferation and therefore increases insulin secretion .
moreover , it influences white adipocytes to induce the expression of genes involved in energy expenditure and to enhance the secretion of adiponectin , thus increasing insulin sensitivity .
apart from its secretion from the osteoblasts , oc is also secreted locally by adipocytes and megakaryocytes [ 7 , 8 ] . combining these actions ,
oc is capable of enhancing the secretion of insulin and increasing insulin sensitivity in both fat and muscle .
consistent with the animal studies , oc levels have been reported to be decreased in patients with t2 dm and to be inversely related to the levels of insulin resistance and adiposity in humans [ 9 , 10 ] .
cross - sectional analyses have extended these observations to apply the mets criteria in examining the association between oc level and cardiovascular risk ; the results have revealed that oc is inversely related to the number of mets components [ 1 , 2 ] .
shea et al . reported that the carboxylated fraction is inversely related to impaired glucose metabolism indices .
by contrast , kanazawa et al . demonstrated that serum uoc and toc levels are inversely related to impaired glucose levels .
the same group also found that the uoc / toc ratio is not related to the fasting plasma glucose or the diabetic status . in their formen study , iki et al . reported that the total , carboxylated and undercarboxylated forms are all proportional to one another . considering these studies in combination , it appears that the role of the various oc fractions in humans is still unclear .
to date , one of the main limitations of the studies on this subject is that they have measured one or two fractions of oc , and no study has measured all three fractions together . because prior studies have demonstrated that the undercarboxylated fraction is implicated in the pathophysiology of insulin sensitivity , further investigations in this area should include a direct measurement of this fraction . in an attempt to fill this gap , we measured the carboxylated , undercarboxylated , and total oc in a population of patients with t2 dm who were either positive or negative for mets .
our objective was to determine whether uoc is related to mets and/or its individual components and other cardiovascular risk factors in patients with t2 dm , and whether toc and uoc have utility in predicting cardiovascular risk .
in this cross - sectional study , 203 consecutive patients with t2 dm followed regularly at a diabetes outpatient clinic were studied .
all the patients were 40 years of age , were not taking any lipid - lowering drugs , and had serum triglyceride levels of < 3.38
the exclusion criteria included the presence of any significant liver disease , renal failure requiring renal - replacement therapy , and the usage of oral contraceptives , hormone replacement therapy , or other drugs that could influence bone metabolism .
this study was performed at the obesity research center , college of medicine , king saud university , riyadh , saudi arabia .
the institutional review board approved this study , and all the participants gave their informed consent .
anthropometric measurements ( including height and weight ) were taken , and the body mass index ( bmi ) was calculated .
the waist circumference was determined as the minimum value between the iliac crest and the lateral costal margin .
serum toc was measured using an n - mid osteocalcin elisa kit ( elecsys , roche diagnostic ltd . ,
the serum uoc and serum coc were measured using eia kits ( takara bio inc . ,
the undercarboxylated eia kit uses a set of monoclonal antibodies that are reactive to uoc and less reactive to coc at amino acid positions 17 , 21 , and 24 .
the carboxylated eia kit uses a set of monoclonal antibodies that are reactive to coc at amino acid position 17 .
the intraassay and inter - assay variabilities were , respectively , 5.7% and 6.2% for coc , 10.2% and 9.8% for uoc , and 3.4% and 3.6% for toc .
the total cholesterol and triglycerides were determined by enzymatic techniques , whereas apolipoprotein a-1 ( apo a-1 ) and apolipoprotein b ( apo b ) were determined by immune - turbidimetric assays ( kone instruments , espoo , finland ) .
hdl cholesterol was measured after precipitation of vldl and ldl with phosphotungstic acid and magnesium chloride .
we used the definition of mets according to the ncep - atp iii . within this definition ,
three or more of the following criteria must be fulfilled : fasting blood glucose level 5.6 mmol / l , blood pressure 130/85 mmhg , triglycerides 1.7 mmol / l , hdl cholesterol < 1.03 mmol / l for men and < 1.29 mmol / l for women , and waist circumference > 102 cm for men and > 88 cm for women .
the statistical analysis was performed using spss version 17 ( chicago , illinois , usa ) .
all the data are presented either as the mean sd ( for symmetric variables ) or median with inter quartile range ( for skewed variables ) .
independent student 's t - test and mann - whitney u test were used to compare the means and mean ranks between the groups .
kruskal - wallis test was used to compare the mean ranks of toc , uoc , and coc across the three groups of mets components .
logarithmic transformations for skewed outcome variables ( toc , uoc , and coc ) were done so as to carry out the regression analysis .
karl pearson 's correlation analysis was performed to determine the relationships between two continuous variables of interest .
a multiple linear regression analysis was performed to test the independent linear relationship between the logarithmic transformed serum oc level and the markers of lipid metabolism by adjusting the effect of confounding variables , including age , bmi , waist circumference , and hba1c .
the levels of the three different forms of oc ( table 1 ) were lower than what has been reported in normal individuals .
the three different forms of oc were measured independently and were significantly correlated with each other ( p = 0.00 , data not shown ) .
the measured toc was inversely related to the markers of adiposity , as assessed via bmi ( r = 0.16 , p = 0.02 ) and glycemia ( indicated by the hba1c : r = 0.2 , p = 0.01 ) , as shown in table 2 .
the serum uoc was significantly and positively correlated with hdl - cholesterol ( r = 0.15 , p = 0.03 ) and negatively correlated with apo b / apo a-1 ratio ( r = 0.16 , p = 0.02 ) .
subsequently , the study population was divided based on the presence or absence of mets , according to the ncep - atp iii criteria .
individuals with mets , when compared to those subjects without mets , exhibited significantly higher bmis , waist circumferences , triglycerides levels , apo b levels , and apo b / apo a-1 ratios ( p = 0.00 ) , as presented in table 1 .
individuals without mets had higher levels of hdl - cholesterol ( p = 0.00 ) .
the group with mets had lower levels of toc and uoc , compared with those subjects without mets ( p = 0.01 and p = 0.03 , resp . ) .
a significant decrease in toc levels was observed with a higher number of mets components ( p = 0.02 ) .
a similar trend was observed with the uocs but this did not reach statistical significance ( figure 1 ) . to further investigate whether the serums toc and uoc levels in patients with mets were related to markers of dyslipidemia independently of other risk factors , multiple regression analyses adjusted for age , bmi , waist circumference , and hba1c were performed between toc and uoc versus the lipid parameters .
the serum toc was significantly and negatively correlated with serum triglycerides ( r = 0.032 , p = 0.049 ) , whereas uoc significantly correlated with serum hdl - cholesterol levels ( r = 0.05 , p = 0.023 ) as shown in figure 2 .
to our knowledge , the present study is the first to measure all the different forms of oc . for the first time
, we established an association between the uoc fraction and the lipidemic status in individuals with mets . in agreement with other studies
, we found that toc is related to the glycemic control and markers of adiposity in patients with t2 dm .
previous studies have demonstrated that toc levels are significantly and negatively correlated with the fasting blood glucose and hba1c levels [ 10 , 16 , 17 ] .
an inverse association between the toc level and hba1c was also observed in the present study .
this finding indicates that among our patients with t2 dm those individuals with better glycemic control are more likely to exhibit higher toc levels .
this result would also indicate that prolonged hyperglycemia and uncontrolled diabetes negatively affect the toc level .
by contrast , we did not determine an association between uoc and the measures of glycemia .
it is possible that the antidiabetic medications received by our patients could affect the levels of uoc ; thus , further studies are necessary to clarify this point . in our study , toc was significantly and negatively correlated with bmi .
this finding confirms other investigations demonstrating that toc is negatively associated with bmi and fat mass .
the uoc was significantly and positively correlated with hdl - cholesterol but was negatively correlated with the apo b / apo a-1 ratio .
this finding confirms a prior report of lee et al . , who demonstrated this relationship in animals .
to our knowledge , the present study is the first to establish a relationship between uoc and the apo b / apo a-1 ratio in humans , suggesting that a low uoc is closely related to an atherogenic , dyslipidemic profile that would otherwise increase the cardiovascular risk . individuals with t2 dm
are known to exhibit a classic lipid triad that includes high triglyceride levels , low hdl - cholesterol levels , and normal ldl - cholesterol levels . however , this triad is not sufficient to predict an untoward cardiovascular event .
the apo b / apo a-1 ratio is superior to any other cholesterol measurement for predicting cardiovascular risk [ 1820 ] .
as determined in a large prospective amoris study , higher apo b levels , an increased apo b / apo a-1 ratio , and low levels of apo a-1 are highly predictive of risk of fatal myocardial infarction [ 19 , 21 ] .
the inverse association of uoc with the apob / apo a-1 ratio that was reported in our study suggests the possible role of uoc in cardiovascular risk assessment in patients with t2 dm .
although it would be premature to conclude a causal effect of uoc on these parameters , it would be of interest to explore whether interventions that specifically raise uoc levels would decrease cardiovascular risk .
the goal of identifying mets is to prevent the occurrence of these diseases . to investigate whether the presence of mets increases the relationship between uoc and the prediction of cvd risk , we divided our population ( based on the ncep - atp iii guidelines ) into those subjects with and those without mets .
patients with mets had a higher bmi , waist circumference , triglyceride level , apo b level and apo b / apo a-1 ratio , and lower hdl - cholesterol level .
we also found that the toc and the uoc , but not the coc , were significantly lower in patients with mets in comparison to those without mets .
these differences point toward an association between these forms of oc and the dyslipidemia that is found in patients with mets .
previous studies mainly focused on determining the role of circulating toc , but they did not differentiate between the different forms of oc . to resolve this issue , we measured all the oc fractions independently , thus overcoming the problem associated with either calculating the coc levels by subtracting the uoc from the toc or adding the coc and uoc fractions to obtain the total oc , as has been done by polgreen et al . . in our study
, we found that the measured toc value was higher than the value obtained by summing up the two individual fractions ( data not shown ) . to study how the uoc and toc are associated with cvd risk
, we compared the relationship between the mets components and other cardiovascular risk factors and the different forms of oc .
there was an inverse association between the toc and the waist circumference values and serum triglycerides levels , although the former did not reach statistical significance .
saleem et al . determined that serum toc is negatively associated with mets in both blacks and non - hispanic whites .
found that plasma oc was inversely associated with mets in a community - dwelling cohort of older persons in the netherlands ; the authors reported that the subjects with the lowest quartile of oc concentrations had an approximately 3.7-fold higher risk of mets than did the subjects with the highest quartile .
first , the study population is comprised of subjects who were followed for t2 dm at a tertiary care hospital and thus might not have been representative of the general population .
second , this cross - sectional study could not determine a causal relationship between the fractions of oc and mets .
third , we did not measure sex steroids and vitamin k intake which could influence oc and bone metabolism .
the present study measured the three independent forms of oc in patients with t2 dm . we found that the toc level was associated with the degree of glycemic control , independently of the carboxylated or undercarboxylated forms .
we have established a new relationship between the uoc and lipid indices ( particularly the hdl - cholesterol and apo b / apoa-1 ratio ) , and we therefore suggest that uoc could play a role in the evaluation of the cardiovascular risk in patients with t2 dm . if serum osteocalcin is employed to determine the cardiovascular risk in patients with t2 dm , then the measured uoc would be a better predictor than the toc .
nonetheless , prospective studies are necessary to investigate further the utility of uoc for cardiovascular risk prediction .[/INST]studies have demonstrated that total osteocalcin ( toc ) is associated with metabolic syndrome ( mets ) and therefore might influence the risk of cardiovascular disease in humans .
undercarboxylated osteocalcin ( uoc ) regulates insulin secretion and sensitivity in mice , but its relation to mets in humans is unclear .
we aimed to determine whether uoc is related to mets and/or its individual components and other cardiovascular risk factors in patients with type 2 diabetes mellitus ( t2 dm ) , and whether toc and uoc have utility in predicting the cardiovascular risk .
we studied 203 t2 dm patients with and without mets .
mets was defined based on the ncep - atp iii criteria .
a correlation analysis was performed between the three outcome variables : ( i ) toc , ( ii ) uoc , and ( iii ) carboxylated osteocalcin ( coc ) and mets components and other cardiovascular risk factors .
both toc and uoc were significantly lower in patients with mets compared to those without mets , independent of body mass index . in patients with mets ,
uoc was significantly and positively correlated with hdl cholesterol , while toc was significantly and negatively correlated with serum triglycerides .
we report for the first time that uoc is related to lipid indices in patients with t2 dm . further studies are necessary to determine whether uoc can be utilized for cardiovascular risk assessments in these patients .</s> |
cataract surgery techniques and technologies have improved the surgery from a procedure that could prevent blindness to a procedure that maximizes visual performance.13 the overwhelming majority of intraocular lens ( iol ) implants after phacoemulsification surgery and cataract removal are monofocal iols , which have been specifically designed to improve the distance of optical resolution and have very few complications associated with the material or the technology.13 however , most of the patients will still require spectacles for near and intermediate tasks , including computer work .
the ongoing need for spectacle use after surgery has , in turn , decreased the overall patient satisfaction and perceived quality of life,14 especially in younger patients who typically have more demands for spectacle - free vision for their lifestyle , reading , and computer work.5 the advent of multifocal iols introduced an effective solution for spectacle independence after cataract surgery and added to the surgical options for the correction of presbyopia.1,610 compared with monofocal iol capabilities , multifocal iols have been shown to increase the depth of vision , maintain distance vision , and improve near vision.1,3,6,7,11 the first - generation multifocal iols are apodized diffractive lenses that send energy to two focal points in small pupils and only to distance points in larger pupils , using the zero and first diffraction orders for distance and near foci , respectively . because of their design , multifocal iols are generally ineffective in improving intermediate vision tasks.6,9,10 also , these lenses have been associated with halos , reduced contrast sensitivity , and increased dysphotopsia , which can lead to ongoing patient dissatisfaction.1,7,12,13 whether the potential visual complications from multifocal lenses outweigh the gain of additional spectacle independence depends on patient preference and adaptability .
trifocality in iol designs has been found to provide good near , intermediate , and distance visual performances and increase spectacle independence.14 acrysof iq panoptix presbyopia correcting iols ( panoptix ; alcon research , fort worth , tx , usa ) are trifocal iols that have been ce mark - approved in europe .
the lens is made up of the same hydrophobic and ultraviolet- and blue light - filtering acrylate / methacrylate copolymer material used in the acrysof family of lenses ( alcon research ) .
the lens design is intended to improve the intermediate vision tasks and increase patient satisfaction , with a third focal point at an optimal intermediate distance of 60 cm .
panoptix is a nonapodized diffractive trifocal iol that distributes light energy to three focal points in both small and large pupil conditions .
it uses zeroth , second , and third nonsequential diffraction orders for distance , intermediate , and near foci , respectively , and the energy at the first diffractive order is redistributed to optimize the performance at three other focal points .
this novel diffractive structure produces high light utilization , transmitting 88% of light at the simulated 3.0 mm pupil size to the retina.15 the light is split into two with one half allocated to the distance focus and the other half split between the near and intermediate focus .
panoptix is also designed with an intermediary 4.5 mm diffractive zone , making its performance less dependent on pupil size .
optical bench evaluation is a well - known method to determine the optical quality of iols.9,11,16,17 this study compared the results of various bench simulations of visual performance : through - focus modulation transfer function ( mtf ) , through - focus badal image testing , and headlight image testing for panoptix and restor + 3.0 d. restor + 3.0 d was selected as the comparator lens because it is a multifocal iol with established good distance and near visual acuity ( va).18 this study chose those particular bench tests on the basis of their specificity : through - focus badal images to test optical resolution , headlight images to assess the photic phenomena associated with iols , and through - focus mtf curves to assess image quality by quantifying the contrast passing through a system at a given spatial frequency.5,6,9
restor + 3.0 d iols ( model sn6ad1 ; alcon research ) and panoptix iols that are used in this study had a 21.0 d base power .
restor + 3.0 d is an apodized diffractive multifocal iol , whereas panoptix is a nonapodized diffractive trifocal iol .
restor + 3.0 d and panoptix have aspherical designs and aspheric corrections for a corneal spherical aberration of 0.1 m.19
table 1 lists the optical specifications of restor + 3.0 d and panoptix .
restor + 3.0 d has active diffraction orders of the zeroth and first magnitude , and panoptix iol has active diffraction orders of the zeroth , second , and third magnitude .
the optical technology of panoptix uses nonsequential diffractive orders to create near ( 42 cm ) , distance , and intermediate ( 60 cm ) foci.20 in panoptix , energy at the first diffractive order is redistributed to optimize the performance at the other focal points.20 a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models .
the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera . through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
restor + 3.0 d iols ( model sn6ad1 ; alcon research ) and panoptix iols that are used in this study had a 21.0 d base power .
restor + 3.0 d is an apodized diffractive multifocal iol , whereas panoptix is a nonapodized diffractive trifocal iol .
restor + 3.0 d and panoptix have aspherical designs and aspheric corrections for a corneal spherical aberration of 0.1 m.19
table 1 lists the optical specifications of restor + 3.0 d and panoptix .
restor + 3.0 d has active diffraction orders of the zeroth and first magnitude , and panoptix iol has active diffraction orders of the zeroth , second , and third magnitude .
the optical technology of panoptix uses nonsequential diffractive orders to create near ( 42 cm ) , distance , and intermediate ( 60 cm ) foci.20 in panoptix , energy at the first diffractive order is redistributed to optimize the performance at the other focal points.20
a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models .
the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera . through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models . the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera .
through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
through - focus badal images captured at defocus distances of infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) are shown in figure 1a .
the trifocal iol provided equivalent distance and near performance compared with the multifocal iol , with a photopic pupil size of 3.0 mm .
the intermediate visual performance was improved in the trifocal over the multifocal iol , with approximately three lines of improvement at 60 and 80 cm defocus distances .
the best panoptix intermediate focus distance was 60 cm , whereas restor + 3.0 d lacks an intermediate focus .
figure 1b shows the 3.0 mm pupil badal images taken at the best near focus of restor + 3.0 d and panoptix , which were 44 cm ( 2.25 d ) and 42 cm ( 2.37 d ) , respectively .
results were similar for panoptix in badal images taken at infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) using the 4.5 mm pupil in figure 2 , whereas restor + 3.0 d had less image quality at the 60 and 80 cm defocus positions .
the bench - simulated badal images that were used to assess the resolution of restor + 3.0 d and panoptix iols were taken at defocus distances from 0.0 d to + 3.5 d using the 3.0 mm pupil size .
the following video s1 shows the badal images from restor + 3.0 d ( left ) and panoptix ( right ) over these defocus distances .
the 20/40 line in panoptix was resolvable in the 2.50 d ( 40 cm ) to 1.25 d ( 80 cm ) images .
representative simulated headlight images for the study lenses taken at the distance focus of the lenses using a 5.0 mm pupil are illustrated in figure 3 .
the halos surrounding the headlight target diminished at a shorter distance from the central spot with the multifocal iol compared with the trifocal iol .
the difference in halos can be explained by the difference in apodization between the lenses . in restor
+ 3.0 d , apodization helps to direct most of the light energy ( ~85% by design ) to distance focus in large pupil diameters . on the other hand ,
the nonapodized panoptix design consistently splits the light energy to the three foci ( distance , intermediate , and near ) independent of the pupil diameter .
mtf measurements were taken at the designated foci of the two lens models with a 3.0 mm aperture and at spatial frequencies of 100 ( figure 4a ) and 50 lp / mm ( figure 4b ) .
distance - focus and near - focus values were greater for restor + 3.0 d than for panoptix , but panoptix had considerably higher intermediate mtf values . at 100 and 50 lp / mm , the restor + 3.0 d iols had distance mtf values of 35.2% and 47.6% , respectively , and the trifocal iols had distance mtf values of 30.9% and 40.2% , respectively .
near - focus mtf values at 100 and 50 lp / mm were 17.5% and 22.8% , respectively , for restor + 3.0 d and 15.3% and 18.1% , respectively , for panoptix .
the intermediate - focus mtf values for panoptix were higher than those for restor + 3.0 d , as expected with the design of the trifocal iol .
intermediate - focus mtf at 100 and 50 lp / mm were 2.9% and 4.4% , respectively , for restor + 3.0 d and 13.3% and 15.3% , respectively , for panoptix .
the through - focus mtf curves at spatial frequencies of 100 and 50 lp / mm using a 3.0 mm pupil are shown in figure 5 .
the distance - focus mtf peak was greater for the multifocal iol than the trifocal iol .
restor + 3.0 d had a slightly greater near - focus mtf peak than panoptix ; the intermediate - focus peak was located at 60 cm , and restor + 3.0 d did not possess an intermediate - focus peak .
through - focus badal images captured at defocus distances of infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) are shown in figure 1a .
the trifocal iol provided equivalent distance and near performance compared with the multifocal iol , with a photopic pupil size of 3.0 mm .
the intermediate visual performance was improved in the trifocal over the multifocal iol , with approximately three lines of improvement at 60 and 80 cm defocus distances .
the best panoptix intermediate focus distance was 60 cm , whereas restor + 3.0 d lacks an intermediate focus .
figure 1b shows the 3.0 mm pupil badal images taken at the best near focus of restor + 3.0 d and panoptix , which were 44 cm ( 2.25 d ) and 42 cm ( 2.37 d ) , respectively .
results were similar for panoptix in badal images taken at infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) using the 4.5 mm pupil in figure 2 , whereas restor + 3.0 d had less image quality at the 60 and 80 cm defocus positions .
the bench - simulated badal images that were used to assess the resolution of restor + 3.0 d and panoptix iols were taken at defocus distances from 0.0 d to + 3.5 d using the 3.0 mm pupil size .
the following video s1 shows the badal images from restor + 3.0 d ( left ) and panoptix ( right ) over these defocus distances .
the 20/40 line in panoptix was resolvable in the 2.50 d ( 40 cm ) to 1.25 d ( 80 cm ) images .
representative simulated headlight images for the study lenses taken at the distance focus of the lenses using a 5.0 mm pupil are illustrated in figure 3 .
the halos surrounding the headlight target diminished at a shorter distance from the central spot with the multifocal iol compared with the trifocal iol .
the difference in halos can be explained by the difference in apodization between the lenses . in restor
+ 3.0 d , apodization helps to direct most of the light energy ( ~85% by design ) to distance focus in large pupil diameters . on the other hand ,
the nonapodized panoptix design consistently splits the light energy to the three foci ( distance , intermediate , and near ) independent of the pupil diameter .
mtf measurements were taken at the designated foci of the two lens models with a 3.0 mm aperture and at spatial frequencies of 100 ( figure 4a ) and 50 lp / mm ( figure 4b ) .
distance - focus and near - focus values were greater for restor + 3.0 d than for panoptix , but panoptix had considerably higher intermediate mtf values . at 100 and 50 lp / mm , the restor + 3.0 d iols had distance mtf values of 35.2% and 47.6% , respectively , and the trifocal iols had distance mtf values of 30.9% and 40.2% , respectively .
near - focus mtf values at 100 and 50 lp / mm were 17.5% and 22.8% , respectively , for restor + 3.0 d and 15.3% and 18.1% , respectively , for panoptix .
the intermediate - focus mtf values for panoptix were higher than those for restor + 3.0 d , as expected with the design of the trifocal iol .
intermediate - focus mtf at 100 and 50 lp / mm were 2.9% and 4.4% , respectively , for restor + 3.0 d and 13.3% and 15.3% , respectively , for panoptix .
the through - focus mtf curves at spatial frequencies of 100 and 50 lp / mm using a 3.0 mm pupil are shown in figure 5 .
the distance - focus mtf peak was greater for the multifocal iol than the trifocal iol .
restor + 3.0 d had a slightly greater near - focus mtf peak than panoptix ; the intermediate - focus peak was located at 60 cm , and restor + 3.0 d did not possess an intermediate - focus peak .
in this study , the new panoptix trifocal iol design was evaluated with standard bench measurements such as through - focus badal images for resolution , through - focus mtf curves for image quality , and headlight images for photic phenomena ( halo propensity ) , all compared with its multifocal counterpart , restor + 3.0 d. the results showed that the panoptix iol had improved performance at an intermediate distance range of 6080 cm and showed a greater than three lines of improvement in resolution at 60 , 70 , and 80 cm compared with the restor + 3.0 d iol .
laboratory testing also showed that distance and near resolution for the trifocal iol is likely to be comparable to restor + 3.0 d for photopic pupil ( 3.0 mm ) .
the bench simulation that was used to measure image contrast showed equivalent distance and near performance for panoptix and restor + 3.0 d iols , but panoptix fared much better in intermediate vision .
monofocal iols have traditionally higher contrast sensitivity than their multifocal counterparts because the light from the out - of - focus image reduces the sharpness of the in - focus image in multifocal designs.23 however , monofocal lenses are not designed to provide spectacle - free vision in situations outside of distance vision , creating a challenge for patients who need good intermediate vision ( eg , computer work ) and near vision ( eg , reading ) .
diffractive multifocal iols have compensated for this by decreasing near add powers,24 as in the case of the restor + 3.0 d , which has a decreased near add power compared with its predecessor , the restor + 4.0 d. however , in this study , panoptix was shown to produce clearer images from 60 to 80 cm than even the restor + 3.0 d , potentially overcoming the ongoing intermediate vision and contrast sensitivity issues associated with other bifocal lenses.5 the higher energy usage of panoptix allowed the iol to provide equivalent simulated distance vision to restor + 3.0 d in this study .
de vries et al25 and alfonso et al26 found that the reduced near add power of the restor + 3.0 d , compared with the restor + 4.0 d or other multifocal iols , produced better intermediate vision , but gatinel and houbrechts11 maintained that true intermediate va can only be achieved by adding a third focal point . additionally , the intermediate and near performances of panoptix are independent of pupil size .
the through - focus mtf curves confirmed a distance and near focus for each lens , but the curve for panoptix also had an intermediate focus at 60 cm .
other studies have found restor + 3.0 d to have higher mtf values at near and distance focal points compared with other commercialized trifocal lenses.5 of interest , the 60 cm intermediate focal point achieved by the panoptix lens , as indicated by its mtf peak , was within the preferred viewing distance range , 45.761.0 cm , for computer terminals.2729 in addition , restor + 3.0 d demonstrated slightly lowered haloing effects compared with panoptix .
the slight differences in haloing effects between the two lenses can be accounted for by the central apodized diffractive zone of the multifocal iol that ends at 3.6 mm diameter with a refractive outer zone.30 this allows the iol to be more strongly distance - dominant with larger pupil sizes . in the nonapodized panoptix lens ,
the addition of a third focus , by itself may increase halos . in large pupils
, most of the light energy of restor + 3.0 d ( ~85% by design ) goes to distance focus , which may account for the variability between the two designs .
it is not known whether this difference in halos between the study lenses is expected to be clinically significant , and future studies may be necessary to understand the clinical significance .
other commercially available trifocal iols provide intermediate add powers at about 80 cm.17,3134 however , this study showed that panoptix provides an intermediate add power of about 60 cm in a unilateral bench test , which was intended to achieve the most suitable and comfortable intermediate distance for most patients.2729 this study is limited by its laboratory nature ; extrapolating the results into clinical practice may not be straightforward , and the findings can not guarantee that the lenses will perform the same in vivo
this novel , presbyopia - correcting lens is equivalent to restor + 3.0 d in photopic near and distance performance but provides a substantial range of intermediate foci with an optimal intermediate focus at 60 cm .
although additional clinical studies are necessary , these bench analyses have shown that panoptix may be a viable choice for patients who require optimal vision across all distances and minimal use of spectacle correction .
| purposethe purpose of this study is to compare the optical characteristics of the novel panoptix presbyopia - correcting trifocal intraocular lens ( iol ) and the multifocal restor + 3.0 d iol , through in vitro bench investigations.methodsthe optical characteristics of acrysof iq panoptix ( panoptix ) and acrysof iq restor + 3.0 d ( restor + 3.0 d ) iols were evaluated by through - focus badal images , simulated headlight images , and modulation transfer function ( mtf ) measurements which determine resolution , photic phenomena , and image quality . through - focus badal images of an early treatment of diabetic retinopathy study chart were recorded at both photopic and mesopic pupil sizes .
simulated headlight images were taken on an mtf bench with a 50-m pinhole target and a 5.0 mm pupil at the distance focus of the iol .
mtf curves were measured with a 3.0 mm pupil , and spatial frequencies equivalent to 20/40 and 20/20 visual acuities were recorded to illustrate the through - focus mtf curves .
far- , intermediate- , and near - focus mtf values were obtained.resultsbench badal image testing and mtf measurements showed that panoptix has a near focus at a distance of 42 cm and an additional intermediate focus at a distance of about 60 cm . the near focus for restor
+ 3.0 d is at 45 cm .
panoptix and restor + 3.0 d have comparable photopic distances and near mtf values .
additionally , panoptix provided a substantial continuous range of vision from distance to intermediate and to near compared with restor + 3.0 d. the halo propensity for panoptix was slightly higher than that for restor + 3.0 d.conclusionlaboratory-based in vitro simulations showed that panoptix trifocal iol has comparable resolution and image quality performance in distance and near foci compared with restor + 3.0 d iol .
panoptix showed better resolution and image quality performance at the intermediate focus than restor + 3.0 d iol . | <s>[INST]cataract surgery techniques and technologies have improved the surgery from a procedure that could prevent blindness to a procedure that maximizes visual performance.13 the overwhelming majority of intraocular lens ( iol ) implants after phacoemulsification surgery and cataract removal are monofocal iols , which have been specifically designed to improve the distance of optical resolution and have very few complications associated with the material or the technology.13 however , most of the patients will still require spectacles for near and intermediate tasks , including computer work .
the ongoing need for spectacle use after surgery has , in turn , decreased the overall patient satisfaction and perceived quality of life,14 especially in younger patients who typically have more demands for spectacle - free vision for their lifestyle , reading , and computer work.5 the advent of multifocal iols introduced an effective solution for spectacle independence after cataract surgery and added to the surgical options for the correction of presbyopia.1,610 compared with monofocal iol capabilities , multifocal iols have been shown to increase the depth of vision , maintain distance vision , and improve near vision.1,3,6,7,11 the first - generation multifocal iols are apodized diffractive lenses that send energy to two focal points in small pupils and only to distance points in larger pupils , using the zero and first diffraction orders for distance and near foci , respectively . because of their design , multifocal iols are generally ineffective in improving intermediate vision tasks.6,9,10 also , these lenses have been associated with halos , reduced contrast sensitivity , and increased dysphotopsia , which can lead to ongoing patient dissatisfaction.1,7,12,13 whether the potential visual complications from multifocal lenses outweigh the gain of additional spectacle independence depends on patient preference and adaptability .
trifocality in iol designs has been found to provide good near , intermediate , and distance visual performances and increase spectacle independence.14 acrysof iq panoptix presbyopia correcting iols ( panoptix ; alcon research , fort worth , tx , usa ) are trifocal iols that have been ce mark - approved in europe .
the lens is made up of the same hydrophobic and ultraviolet- and blue light - filtering acrylate / methacrylate copolymer material used in the acrysof family of lenses ( alcon research ) .
the lens design is intended to improve the intermediate vision tasks and increase patient satisfaction , with a third focal point at an optimal intermediate distance of 60 cm .
panoptix is a nonapodized diffractive trifocal iol that distributes light energy to three focal points in both small and large pupil conditions .
it uses zeroth , second , and third nonsequential diffraction orders for distance , intermediate , and near foci , respectively , and the energy at the first diffractive order is redistributed to optimize the performance at three other focal points .
this novel diffractive structure produces high light utilization , transmitting 88% of light at the simulated 3.0 mm pupil size to the retina.15 the light is split into two with one half allocated to the distance focus and the other half split between the near and intermediate focus .
panoptix is also designed with an intermediary 4.5 mm diffractive zone , making its performance less dependent on pupil size .
optical bench evaluation is a well - known method to determine the optical quality of iols.9,11,16,17 this study compared the results of various bench simulations of visual performance : through - focus modulation transfer function ( mtf ) , through - focus badal image testing , and headlight image testing for panoptix and restor + 3.0 d. restor + 3.0 d was selected as the comparator lens because it is a multifocal iol with established good distance and near visual acuity ( va).18 this study chose those particular bench tests on the basis of their specificity : through - focus badal images to test optical resolution , headlight images to assess the photic phenomena associated with iols , and through - focus mtf curves to assess image quality by quantifying the contrast passing through a system at a given spatial frequency.5,6,9
restor + 3.0 d iols ( model sn6ad1 ; alcon research ) and panoptix iols that are used in this study had a 21.0 d base power .
restor + 3.0 d is an apodized diffractive multifocal iol , whereas panoptix is a nonapodized diffractive trifocal iol .
restor + 3.0 d and panoptix have aspherical designs and aspheric corrections for a corneal spherical aberration of 0.1 m.19
table 1 lists the optical specifications of restor + 3.0 d and panoptix .
restor + 3.0 d has active diffraction orders of the zeroth and first magnitude , and panoptix iol has active diffraction orders of the zeroth , second , and third magnitude .
the optical technology of panoptix uses nonsequential diffractive orders to create near ( 42 cm ) , distance , and intermediate ( 60 cm ) foci.20 in panoptix , energy at the first diffractive order is redistributed to optimize the performance at the other focal points.20 a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models .
the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera . through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
restor + 3.0 d iols ( model sn6ad1 ; alcon research ) and panoptix iols that are used in this study had a 21.0 d base power .
restor + 3.0 d is an apodized diffractive multifocal iol , whereas panoptix is a nonapodized diffractive trifocal iol .
restor + 3.0 d and panoptix have aspherical designs and aspheric corrections for a corneal spherical aberration of 0.1 m.19
table 1 lists the optical specifications of restor + 3.0 d and panoptix .
restor + 3.0 d has active diffraction orders of the zeroth and first magnitude , and panoptix iol has active diffraction orders of the zeroth , second , and third magnitude .
the optical technology of panoptix uses nonsequential diffractive orders to create near ( 42 cm ) , distance , and intermediate ( 60 cm ) foci.20 in panoptix , energy at the first diffractive order is redistributed to optimize the performance at the other focal points.20
a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models .
the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera . through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
a custom model eye was assembled as a badal optometer , as previously described by carson et al.5 the model eye used for testing both the study lenses was modified with 0.1 m spherical aberration according to the design of the lenses .
a bench simulation of visual performance using through - focus badal image testing of an early treatment of diabetic retinopathy study chart from 1.0 d to + 3.0 d at 0.25 d increments was performed , and images simulating viewing distances from infinity to 40 cm were evaluated .
an additional image was also taken at the best near focus of each lens in order to account for the differences in near add power .
badal images taken with the letter chart target placed at the simulated depth of foci of infinity , 80 , 60 , 40 cm , and best near focus were depicted to demonstrate the difference between the two lens models .
the iols were positioned within a model eye containing deionized water and a convex plano model cornea lens with a matching spherical aberration , as described previously;5 the iol was held on a paddle that contained a 3.0 mm pupil .
the target was a chrome - on - glass , 25 mm diameter early treatment of diabetic retinopathy study va chart that depicted nine rows , with the smallest row corresponding to a va of 20/12 .
va difference of no more than two letters is considered equivalent at a given focus distance ( less than one - half of the clinically relevant value of 0.1 logarithm of the minimum angle of resolution ) .
photic phenomena of the two iols in the form of halo propensity assessment were measured using the optikos mtf system ( optikos corp . , wakefield , ma , usa ) with optest software ( version 5.2.2 ; optikos corp . ) in a pseudophakic eye model with a spherical aberration matching international organization of standardizations model eye as previously described by carson et al.5 an illuminated pinhole with a 50 m aperture was used to simulate a car headlight viewed at a distance of ~250 m.21 all the images were taken at the distance foci of the specific iol model with 5.0 mm pupil on the iol under white light conditions by illumination on one side using a fiber - lite dc-950 fiber optic illuminator ( dolan - jenner industries , boxborough , ma , usa ) .
test conditions , including the light intensity and the position of the iol relative to the aperture and cornea , were the same for both iol models . the light intensity level was adjusted until the halo structure could be clearly seen on a charge - coupled device camera .
through - focus mtf is an established method to determine the amount of contrast passed through a system at a given spatial frequency.22 the iols were used following iso 11979 - 2 requirements and test methods in order to assess the optical properties of the multifocal iols using a validated optikos mtf system according to the conditions described by carson et al.5 mtf measurement was performed on the iols with spherical aberration - matching corneas to yield the best optical performance .
testing was conducted with a 3.0 mm lens aperture that corresponds to average photopic pupil size .
slit targets illuminated by a light source with a 550 nm narrow - band filter were imaged at infinity .
each target image was obtained from the iols , was relayed to the charge - coupled device camera , and was analyzed .
mtf curves were generated from the mean vertical- and horizontal - slit values . through - focus mtf curves at two spatial frequencies of 50 and 100 line pairs per millimeter ( lp / mm ) were used to determine the best foci for distance , near distance , and intermediate distance .
the two frequencies correspond to cycle widths of 4 and 2 minutes , respectively , conventionally equated to acuities of 20/40 and 20/20 , respectively , at least for a square - wave grating.23
through - focus badal images captured at defocus distances of infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) are shown in figure 1a .
the trifocal iol provided equivalent distance and near performance compared with the multifocal iol , with a photopic pupil size of 3.0 mm .
the intermediate visual performance was improved in the trifocal over the multifocal iol , with approximately three lines of improvement at 60 and 80 cm defocus distances .
the best panoptix intermediate focus distance was 60 cm , whereas restor + 3.0 d lacks an intermediate focus .
figure 1b shows the 3.0 mm pupil badal images taken at the best near focus of restor + 3.0 d and panoptix , which were 44 cm ( 2.25 d ) and 42 cm ( 2.37 d ) , respectively .
results were similar for panoptix in badal images taken at infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) using the 4.5 mm pupil in figure 2 , whereas restor + 3.0 d had less image quality at the 60 and 80 cm defocus positions .
the bench - simulated badal images that were used to assess the resolution of restor + 3.0 d and panoptix iols were taken at defocus distances from 0.0 d to + 3.5 d using the 3.0 mm pupil size .
the following video s1 shows the badal images from restor + 3.0 d ( left ) and panoptix ( right ) over these defocus distances .
the 20/40 line in panoptix was resolvable in the 2.50 d ( 40 cm ) to 1.25 d ( 80 cm ) images .
representative simulated headlight images for the study lenses taken at the distance focus of the lenses using a 5.0 mm pupil are illustrated in figure 3 .
the halos surrounding the headlight target diminished at a shorter distance from the central spot with the multifocal iol compared with the trifocal iol .
the difference in halos can be explained by the difference in apodization between the lenses . in restor
+ 3.0 d , apodization helps to direct most of the light energy ( ~85% by design ) to distance focus in large pupil diameters . on the other hand ,
the nonapodized panoptix design consistently splits the light energy to the three foci ( distance , intermediate , and near ) independent of the pupil diameter .
mtf measurements were taken at the designated foci of the two lens models with a 3.0 mm aperture and at spatial frequencies of 100 ( figure 4a ) and 50 lp / mm ( figure 4b ) .
distance - focus and near - focus values were greater for restor + 3.0 d than for panoptix , but panoptix had considerably higher intermediate mtf values . at 100 and 50 lp / mm , the restor + 3.0 d iols had distance mtf values of 35.2% and 47.6% , respectively , and the trifocal iols had distance mtf values of 30.9% and 40.2% , respectively .
near - focus mtf values at 100 and 50 lp / mm were 17.5% and 22.8% , respectively , for restor + 3.0 d and 15.3% and 18.1% , respectively , for panoptix .
the intermediate - focus mtf values for panoptix were higher than those for restor + 3.0 d , as expected with the design of the trifocal iol .
intermediate - focus mtf at 100 and 50 lp / mm were 2.9% and 4.4% , respectively , for restor + 3.0 d and 13.3% and 15.3% , respectively , for panoptix .
the through - focus mtf curves at spatial frequencies of 100 and 50 lp / mm using a 3.0 mm pupil are shown in figure 5 .
the distance - focus mtf peak was greater for the multifocal iol than the trifocal iol .
restor + 3.0 d had a slightly greater near - focus mtf peak than panoptix ; the intermediate - focus peak was located at 60 cm , and restor + 3.0 d did not possess an intermediate - focus peak .
through - focus badal images captured at defocus distances of infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) are shown in figure 1a .
the trifocal iol provided equivalent distance and near performance compared with the multifocal iol , with a photopic pupil size of 3.0 mm .
the intermediate visual performance was improved in the trifocal over the multifocal iol , with approximately three lines of improvement at 60 and 80 cm defocus distances .
the best panoptix intermediate focus distance was 60 cm , whereas restor + 3.0 d lacks an intermediate focus .
figure 1b shows the 3.0 mm pupil badal images taken at the best near focus of restor + 3.0 d and panoptix , which were 44 cm ( 2.25 d ) and 42 cm ( 2.37 d ) , respectively .
results were similar for panoptix in badal images taken at infinity ( 0.0 d ) , 80 cm ( 1.25 d ) , 60 cm ( 1.67 d ) , and 40 cm ( 2.50 d ) using the 4.5 mm pupil in figure 2 , whereas restor + 3.0 d had less image quality at the 60 and 80 cm defocus positions .
the bench - simulated badal images that were used to assess the resolution of restor + 3.0 d and panoptix iols were taken at defocus distances from 0.0 d to + 3.5 d using the 3.0 mm pupil size .
the following video s1 shows the badal images from restor + 3.0 d ( left ) and panoptix ( right ) over these defocus distances .
the 20/40 line in panoptix was resolvable in the 2.50 d ( 40 cm ) to 1.25 d ( 80 cm ) images .
representative simulated headlight images for the study lenses taken at the distance focus of the lenses using a 5.0 mm pupil are illustrated in figure 3 .
the halos surrounding the headlight target diminished at a shorter distance from the central spot with the multifocal iol compared with the trifocal iol .
the difference in halos can be explained by the difference in apodization between the lenses . in restor
+ 3.0 d , apodization helps to direct most of the light energy ( ~85% by design ) to distance focus in large pupil diameters . on the other hand ,
the nonapodized panoptix design consistently splits the light energy to the three foci ( distance , intermediate , and near ) independent of the pupil diameter .
mtf measurements were taken at the designated foci of the two lens models with a 3.0 mm aperture and at spatial frequencies of 100 ( figure 4a ) and 50 lp / mm ( figure 4b ) .
distance - focus and near - focus values were greater for restor + 3.0 d than for panoptix , but panoptix had considerably higher intermediate mtf values . at 100 and 50 lp / mm , the restor + 3.0 d iols had distance mtf values of 35.2% and 47.6% , respectively , and the trifocal iols had distance mtf values of 30.9% and 40.2% , respectively .
near - focus mtf values at 100 and 50 lp / mm were 17.5% and 22.8% , respectively , for restor + 3.0 d and 15.3% and 18.1% , respectively , for panoptix .
the intermediate - focus mtf values for panoptix were higher than those for restor + 3.0 d , as expected with the design of the trifocal iol .
intermediate - focus mtf at 100 and 50 lp / mm were 2.9% and 4.4% , respectively , for restor + 3.0 d and 13.3% and 15.3% , respectively , for panoptix .
the through - focus mtf curves at spatial frequencies of 100 and 50 lp / mm using a 3.0 mm pupil are shown in figure 5 .
the distance - focus mtf peak was greater for the multifocal iol than the trifocal iol .
restor + 3.0 d had a slightly greater near - focus mtf peak than panoptix ; the intermediate - focus peak was located at 60 cm , and restor + 3.0 d did not possess an intermediate - focus peak .
in this study , the new panoptix trifocal iol design was evaluated with standard bench measurements such as through - focus badal images for resolution , through - focus mtf curves for image quality , and headlight images for photic phenomena ( halo propensity ) , all compared with its multifocal counterpart , restor + 3.0 d. the results showed that the panoptix iol had improved performance at an intermediate distance range of 6080 cm and showed a greater than three lines of improvement in resolution at 60 , 70 , and 80 cm compared with the restor + 3.0 d iol .
laboratory testing also showed that distance and near resolution for the trifocal iol is likely to be comparable to restor + 3.0 d for photopic pupil ( 3.0 mm ) .
the bench simulation that was used to measure image contrast showed equivalent distance and near performance for panoptix and restor + 3.0 d iols , but panoptix fared much better in intermediate vision .
monofocal iols have traditionally higher contrast sensitivity than their multifocal counterparts because the light from the out - of - focus image reduces the sharpness of the in - focus image in multifocal designs.23 however , monofocal lenses are not designed to provide spectacle - free vision in situations outside of distance vision , creating a challenge for patients who need good intermediate vision ( eg , computer work ) and near vision ( eg , reading ) .
diffractive multifocal iols have compensated for this by decreasing near add powers,24 as in the case of the restor + 3.0 d , which has a decreased near add power compared with its predecessor , the restor + 4.0 d. however , in this study , panoptix was shown to produce clearer images from 60 to 80 cm than even the restor + 3.0 d , potentially overcoming the ongoing intermediate vision and contrast sensitivity issues associated with other bifocal lenses.5 the higher energy usage of panoptix allowed the iol to provide equivalent simulated distance vision to restor + 3.0 d in this study .
de vries et al25 and alfonso et al26 found that the reduced near add power of the restor + 3.0 d , compared with the restor + 4.0 d or other multifocal iols , produced better intermediate vision , but gatinel and houbrechts11 maintained that true intermediate va can only be achieved by adding a third focal point . additionally , the intermediate and near performances of panoptix are independent of pupil size .
the through - focus mtf curves confirmed a distance and near focus for each lens , but the curve for panoptix also had an intermediate focus at 60 cm .
other studies have found restor + 3.0 d to have higher mtf values at near and distance focal points compared with other commercialized trifocal lenses.5 of interest , the 60 cm intermediate focal point achieved by the panoptix lens , as indicated by its mtf peak , was within the preferred viewing distance range , 45.761.0 cm , for computer terminals.2729 in addition , restor + 3.0 d demonstrated slightly lowered haloing effects compared with panoptix .
the slight differences in haloing effects between the two lenses can be accounted for by the central apodized diffractive zone of the multifocal iol that ends at 3.6 mm diameter with a refractive outer zone.30 this allows the iol to be more strongly distance - dominant with larger pupil sizes . in the nonapodized panoptix lens ,
the addition of a third focus , by itself may increase halos . in large pupils
, most of the light energy of restor + 3.0 d ( ~85% by design ) goes to distance focus , which may account for the variability between the two designs .
it is not known whether this difference in halos between the study lenses is expected to be clinically significant , and future studies may be necessary to understand the clinical significance .
other commercially available trifocal iols provide intermediate add powers at about 80 cm.17,3134 however , this study showed that panoptix provides an intermediate add power of about 60 cm in a unilateral bench test , which was intended to achieve the most suitable and comfortable intermediate distance for most patients.2729 this study is limited by its laboratory nature ; extrapolating the results into clinical practice may not be straightforward , and the findings can not guarantee that the lenses will perform the same in vivo
this novel , presbyopia - correcting lens is equivalent to restor + 3.0 d in photopic near and distance performance but provides a substantial range of intermediate foci with an optimal intermediate focus at 60 cm .
although additional clinical studies are necessary , these bench analyses have shown that panoptix may be a viable choice for patients who require optimal vision across all distances and minimal use of spectacle correction .
[/INST]purposethe purpose of this study is to compare the optical characteristics of the novel panoptix presbyopia - correcting trifocal intraocular lens ( iol ) and the multifocal restor + 3.0 d iol , through in vitro bench investigations.methodsthe optical characteristics of acrysof iq panoptix ( panoptix ) and acrysof iq restor + 3.0 d ( restor + 3.0 d ) iols were evaluated by through - focus badal images , simulated headlight images , and modulation transfer function ( mtf ) measurements which determine resolution , photic phenomena , and image quality . through - focus badal images of an early treatment of diabetic retinopathy study chart were recorded at both photopic and mesopic pupil sizes .
simulated headlight images were taken on an mtf bench with a 50-m pinhole target and a 5.0 mm pupil at the distance focus of the iol .
mtf curves were measured with a 3.0 mm pupil , and spatial frequencies equivalent to 20/40 and 20/20 visual acuities were recorded to illustrate the through - focus mtf curves .
far- , intermediate- , and near - focus mtf values were obtained.resultsbench badal image testing and mtf measurements showed that panoptix has a near focus at a distance of 42 cm and an additional intermediate focus at a distance of about 60 cm . the near focus for restor
+ 3.0 d is at 45 cm .
panoptix and restor + 3.0 d have comparable photopic distances and near mtf values .
additionally , panoptix provided a substantial continuous range of vision from distance to intermediate and to near compared with restor + 3.0 d. the halo propensity for panoptix was slightly higher than that for restor + 3.0 d.conclusionlaboratory-based in vitro simulations showed that panoptix trifocal iol has comparable resolution and image quality performance in distance and near foci compared with restor + 3.0 d iol .
panoptix showed better resolution and image quality performance at the intermediate focus than restor + 3.0 d iol .</s> |
Sign up! Β» Welcome to Spaceport Sweden Spaceport Sweden is a pioneering initiative to establish commercial human spaceflight in Kiruna and become Europeβs gateway to space. We welcome you to join our journey towards the future and offer you space experiences already now β your next adventure starts here; Over a hundred kilometers above the Arctic Circle, in the land of the midnight sun and the northern lights, a project is underway that has the potential to change the way people relate to their planet and the universe beyond. Here, in the last wilderness of Europe, Spaceport Sweden is working to establish a state of the art facility worthy of being Europeβs gateway into space. Active in the development of commercial manned space flight since 2005, Spaceport Sweden is today one of the more established players in the dynamic international space industry. Kiruna in Swedish Lapland will be home to a world-class spaceport, which will feature a wide-array of educational experiences, training and development programs, and will literally be the launching off point for a range of products and services connected to space tourism. Many of these are currently in development alongside the most cutting-edge technological innovations. Kiruna is already one of the worldβs premier space cities. Since 1957, the Swedish Institute of Space Physics has conducted extensive research here, and Esrange Space Center, a rocket range and research facility built by the European Space Agency and managed by the SSC Group, has been active in the area since 1966. Spaceport Sweden is proud to be a part of Kirunaβs space heritage and is enormously excited to be contributing to its next phase. Kiruna is Swedenβs principal mining town and the combination of high-tech industry, sophisticated research facilities, and natural, unspoiled beauty is turning this city on the edge of the continent into one of the most dynamic locations in Europe. Come join us and see just how close the future is.
Sign up! Β» Talks and Technical Visits Spaceport Sweden is proud to be one of the pioneers working to make commercial space travel a reality. With our Talks and Technical Visits you will be able to discover first hand the work of establishing a space tourism as a new industry and developing new innovative products and adventures working across industries. Traveling to space stands as one of humanityβs greatest accomplishments. Leaving the atmosphere of the earth and flying into space is a feat built on decades of hard work, involving enormous amounts of ingenuity, knowledge, and bravery. Spaceport Sweden is honored to be a part of this tradition and proud to be one of the pioneers working to make commercial space travel a reality. With our Talks and Technical Visits you will be able to see and listen for yourself the incredible strides that weβve made and discover first hand the latest developments in space exploration. We are extremely excited to tell you the story of Spaceport Sweden and have you witness the incredible determination we bring to realizing our vision of becoming one of the worldβs leading spaceports and Europeβs gateway to space. Talks With our Talks, the future comes to you. Many of the primary figures within Spaceport Sweden are sought after lecturers, with years of experience participating in conferences, future forums, industry days, and holding inspirational sessions. Hear about the work of establishing Spaceport Sweden and the continual developments that make the future seem closer than ever. Learn from the experience of figures who have been involved in global collaborations and who are in continuous dialogue with people in the forefront of their industries, government agencies, researchers, and trade councils. Technical Visits Technical Visits will take place on location at the future facilities of Spaceport Sweden and our partners. With these in-depth visits, you can learn from the experts about space travel, as well as the past, present and future role of Kiruna in this process. Meet some of the greatest minds in science, engineering, and tourism and see the technologies that will be sending civilians into space. At Spaceport Sweden we could not be more passionately committed to our goals and relish the opportunity to share our incredible journey with you. Please contact us to find out more about how you as a private person, student, researcher, company or organization can be a part of this exciting enterprise, which is changing the way people around the globe think about their planet and the universe around them. [email protected] Click on the picture to watch the clip.
Sign up! Β» Meetings and Incentives Spaceport Sweden, with its exotic location in Kiruna and the Arctic climate of Swedish Lapland, provides the ideal setting for a wide range of exceptional meetings, incentives and conferences β creating an unforgettable experience. The immense expanse of the universe and our place within it is endlessly fascinating. The mere possibility of one day ascending through Earthβs atmosphere into space is enough to grab the attention of the most seasoned adventurer. Whether you come to Kiruna in the summer under the midnight sun, or in the middle of the Arctic winter with the northern lights pulsating overhead, with the romance of space and the stunning nature of Kiruna as your backdrop, all the ingredients are present to create an unforgettable experience. Our facilities have been outfitted to surpass the demands of our business customers and there is no better environment in which to focus the mind, gain perspective, and think creatively. Conferences on the ski slopes, team building exercises in micro-gravity, and aurora reconnaissance excursions are organized with the same creativity and precision with which an aircraft hangar is transformed into the ultimate post-conference party locale. After a management meeting, travel with your colleagues, a Sami guide, and a pack of Siberian huskies through snow-covered forests, stopping at your destination to build a quinzhee, a snow cave in which youβll spend the night, while drinking hot lemonade beside a roaring fire. Put aside some time during a conference to play on one of the worldβs northernmost golf courses, which has been specially designed to accommodate snow golf in the winter. Spaceport Sweden acts as a node, catalyst and development corporation for new innovative ideas and approaches. Having recently hosted the Swedish Space Forum and TEDxKiruna, we are excited to meet and organize events with other innovators throughout the worlds of business, academy, and government and beyond. Come to simultaneously experience relaxation and stimulation, advanced technology and traditional culture, comfort and adventure. Leave refreshed and inspired, ready to take your work to ever-greater heights. Contact us and together we will put together a package that exceeds your needs and desires. [email protected]
Sign up! Β» Spaceflight preparation program This is where your space adventure begins. Spaceport Sweden has partnered with QinetiQ to develop and deliver a world-class spaceflight preparation program together, where future space travelers will emerge prepared, confident and relaxed, ready to maximise their journey to space. The Flight Physiological Centre in LinkΓΆping, Sweden, is one of the worldβs advanced Dynamic Flight Simulators (DFS), combining a man-rated, long-arm centrifuge and flight simulator. The DFS provides a safe and highly controllable environment in which passengers can experience the sustained periods of increased acceleration present during launch and re-entry and allows for the precise re-creation of the complex and unique βGβ profiles generated by future commercial space vehicles. Spaceport Sweden together with QinetiQ offers courses at the Flight Physiological Centre that will prepare passengers and crew of future space vehicles for the unique acceleration environment they will experience. When it comes to preparing for a new experience, we believe that knowledge is as important as familiarity, and our courses are geared to empower people with both. Extensive experience combined with state-of-the-art facilities, QinetiQβs highly experienced team of doctors and scientists will guide clients through the world of G forces, utilizing a mixture of lectures, practical demonstrations and one-on-one tuition on the DFS itself. Clients will learn about the effects of +Gz and +Gx, gain practical experience of the symptoms they are likely to experience and the actions they can take, if required, to effectively counter these symptoms. Culminating in an experience of the complete launch-to-landing, vehicle-specific G profile precisely recreated on the DFS, QinetiQβs courses will provide clients with a unique insight into the space flight environment. By understanding the effects of +Gz and +Gx, and having practical experience of their personal symptoms, any anxieties will be transformed into anticipation and clients will emerge, confident, relaxed and ready to absorb every detail of what will prove to be an extraordinary space experience. Irrespective of whether or not you decide to venture into space, Spaceflight Training will provide you with unforgettable experiences. Are you ready to take the first step of an extraordinary adventure? Optional programs available very soon. Sign up and weβll keep you posted: [email protected] Space camp Everyone has dreamt of making the journey into space. While in the past it was inevitable that very few people would actually turn this dream into a reality, contemporary advances in space tourism are dramatically increasing everyoneβs chances of one day looking down on Earth from space. The future is here now and Spaceport Sweden is delighted to be able to introduce the newest generations of earthlings to the wonders of space with our Space Camp. Children attend an educational and inspirational camp where they meet astronauts, test the laws of gravity, understand our solar system, and learn to work as a team as they simulate an entire space mission. Space Camp is about more than just a one-off experience. The excitement of space coupled with the possibility of space travel will inspire more children to learn and study the natural sciences, thereby contributing to a more sustainable future and increasing the likelihood of further innovation. Space Camp is the ultimate adventure for your ultimate adventurer. ||||| Arctic town eyes future as gateway to space
KIRUNA, Sweden β Sweden's small Arctic town of Kiruna has a surprisingly international airport with regular flights to London and Tokyo, but it has even bigger plans: to offer commercial space flights.
Spaceport Sweden, a company founded in 2007, hopes to be able to provide the first flights within a decade from Kiruna's airport.
"We're working on establishing commercial flights from Sweden to space for tourism and research, and to create a launching pad at the airport," explained the company's enthusiastic director, Karin Nilsdotter, seated in her office at the Swedish Institute of Space Physics (IRF).
The idea is that space tourists would take off for a maximum two-hour trip into space aboard futuristic spacecraft currently undergoing testing, which resemble a cross between an airplane and a space shuttle and which can carry between one and six passengers.
The sub-orbital flights will send passengers 100 kilometres (60 miles) above Earth and allow them to experience five minutes of weightlessness.
Kiruna's location in the far north of Sweden, and Europe, makes it a prime location for space flights, Nilsdotter said.
The space flights would not be disturbed by heavy air traffic, nor is the region a densely populated area. The wide-open spaces within Sweden's borders also mean no bureaucratic red-tape to be resolved with other countries.
Kiruna also has 60 years experience of space research to its credit. IRF was founded in 1957 and the Swedish space research and rocket centre Esrange, located in the town, was founded in 1966.
"We have to use this knowledge to create a unique adventure with global impact: space travel," Nilsdotter insisted.
"Even if it's too early to give any figures, market studies show there is potential for 14,000 travellers after 10 years of business," she added.
Spaceport Sweden is not building its own spacecraft, but will instead collaborate with a company that is doing so, she says, refusing to disclose how many spacecraft it will operate nor the identity of its partner.
In the United States, several companies are already developing aircraft capable of carrying space tourists, such as Richard Branson's Virgin Galactic.
"The technology isn't fully developed yet," Nilsdotter said, adding that the companies were currently carrying out test flights in the United States.
The first commercial space flights are expected to take place in the United States in 2014 and a few years after that in Sweden.
The head of the Esrange space research and rocket site, Lennart Poromaa, is meanwhile more measured in his enthusiasm for the project.
"In a few years there may be commercial space flights, but it will take longer than people think," he said.
Esrange pulled out of the project "because we're not about creating adventure", he explained.
But "we could help them if they need help in the field of research, possibly", the aerospace engineer said.
According to Nilsdotter, space flights could take off four times a day. Esrange meanwhile launches four rockets a year.
"Researchers who want to test their experiments in microgravity may be able to fly with us and then adjust their projects," she said.
In the United States, more than 1,000 tickets for space flights have already been reserved, at around $200,000 (153,000 euros) apiece.
For adventure-seekers who can't wait to visit space, Spaceport Sweden already offers flights from Kiruna airport to view the northern lights, a spectacular phenomenon of colourful lights that streak across the night sky, for the tidy sum of 6,990 kronor (810 euros, $1,059).
Copyright Β© 2013 AFP. All rights reserved. More Β» | β A company in a tiny Arctic town plans to launch people into space like clockwork, on two-hour trips four times a day. But a little more workβor even a lotβis required first, AFP reports. The company, Spaceport Sweden, is building a unique vessel that combines a space shuttle with an airplane. And director Karin Nilsdotter is already counting the customers who will trek to the town of Kiruna: "Even if it's too early to give any figures, market studies show there is potential for 14,000 travellers after 10 years of business," she says. But she says the technology "isn't fully developed yet" and competitors like Virgin Atlantic are already launching test flights in the US. A few things are going for her, however: Kiruna has a 60-year history of space research, there's little air traffic to clutter things up, and wide-open spaces within Sweden ensure there's no red tape with other countries. Still, the head of a space research and rocket site in town offers a cautionary note: "In a few years there may be commercial space flights, but it will take longer than people think." | <s>[INST]Sign up! Β» Welcome to Spaceport Sweden Spaceport Sweden is a pioneering initiative to establish commercial human spaceflight in Kiruna and become Europeβs gateway to space. We welcome you to join our journey towards the future and offer you space experiences already now β your next adventure starts here; Over a hundred kilometers above the Arctic Circle, in the land of the midnight sun and the northern lights, a project is underway that has the potential to change the way people relate to their planet and the universe beyond. Here, in the last wilderness of Europe, Spaceport Sweden is working to establish a state of the art facility worthy of being Europeβs gateway into space. Active in the development of commercial manned space flight since 2005, Spaceport Sweden is today one of the more established players in the dynamic international space industry. Kiruna in Swedish Lapland will be home to a world-class spaceport, which will feature a wide-array of educational experiences, training and development programs, and will literally be the launching off point for a range of products and services connected to space tourism. Many of these are currently in development alongside the most cutting-edge technological innovations. Kiruna is already one of the worldβs premier space cities. Since 1957, the Swedish Institute of Space Physics has conducted extensive research here, and Esrange Space Center, a rocket range and research facility built by the European Space Agency and managed by the SSC Group, has been active in the area since 1966. Spaceport Sweden is proud to be a part of Kirunaβs space heritage and is enormously excited to be contributing to its next phase. Kiruna is Swedenβs principal mining town and the combination of high-tech industry, sophisticated research facilities, and natural, unspoiled beauty is turning this city on the edge of the continent into one of the most dynamic locations in Europe. Come join us and see just how close the future is.
Sign up! Β» Talks and Technical Visits Spaceport Sweden is proud to be one of the pioneers working to make commercial space travel a reality. With our Talks and Technical Visits you will be able to discover first hand the work of establishing a space tourism as a new industry and developing new innovative products and adventures working across industries. Traveling to space stands as one of humanityβs greatest accomplishments. Leaving the atmosphere of the earth and flying into space is a feat built on decades of hard work, involving enormous amounts of ingenuity, knowledge, and bravery. Spaceport Sweden is honored to be a part of this tradition and proud to be one of the pioneers working to make commercial space travel a reality. With our Talks and Technical Visits you will be able to see and listen for yourself the incredible strides that weβve made and discover first hand the latest developments in space exploration. We are extremely excited to tell you the story of Spaceport Sweden and have you witness the incredible determination we bring to realizing our vision of becoming one of the worldβs leading spaceports and Europeβs gateway to space. Talks With our Talks, the future comes to you. Many of the primary figures within Spaceport Sweden are sought after lecturers, with years of experience participating in conferences, future forums, industry days, and holding inspirational sessions. Hear about the work of establishing Spaceport Sweden and the continual developments that make the future seem closer than ever. Learn from the experience of figures who have been involved in global collaborations and who are in continuous dialogue with people in the forefront of their industries, government agencies, researchers, and trade councils. Technical Visits Technical Visits will take place on location at the future facilities of Spaceport Sweden and our partners. With these in-depth visits, you can learn from the experts about space travel, as well as the past, present and future role of Kiruna in this process. Meet some of the greatest minds in science, engineering, and tourism and see the technologies that will be sending civilians into space. At Spaceport Sweden we could not be more passionately committed to our goals and relish the opportunity to share our incredible journey with you. Please contact us to find out more about how you as a private person, student, researcher, company or organization can be a part of this exciting enterprise, which is changing the way people around the globe think about their planet and the universe around them. [email protected] Click on the picture to watch the clip.
Sign up! Β» Meetings and Incentives Spaceport Sweden, with its exotic location in Kiruna and the Arctic climate of Swedish Lapland, provides the ideal setting for a wide range of exceptional meetings, incentives and conferences β creating an unforgettable experience. The immense expanse of the universe and our place within it is endlessly fascinating. The mere possibility of one day ascending through Earthβs atmosphere into space is enough to grab the attention of the most seasoned adventurer. Whether you come to Kiruna in the summer under the midnight sun, or in the middle of the Arctic winter with the northern lights pulsating overhead, with the romance of space and the stunning nature of Kiruna as your backdrop, all the ingredients are present to create an unforgettable experience. Our facilities have been outfitted to surpass the demands of our business customers and there is no better environment in which to focus the mind, gain perspective, and think creatively. Conferences on the ski slopes, team building exercises in micro-gravity, and aurora reconnaissance excursions are organized with the same creativity and precision with which an aircraft hangar is transformed into the ultimate post-conference party locale. After a management meeting, travel with your colleagues, a Sami guide, and a pack of Siberian huskies through snow-covered forests, stopping at your destination to build a quinzhee, a snow cave in which youβll spend the night, while drinking hot lemonade beside a roaring fire. Put aside some time during a conference to play on one of the worldβs northernmost golf courses, which has been specially designed to accommodate snow golf in the winter. Spaceport Sweden acts as a node, catalyst and development corporation for new innovative ideas and approaches. Having recently hosted the Swedish Space Forum and TEDxKiruna, we are excited to meet and organize events with other innovators throughout the worlds of business, academy, and government and beyond. Come to simultaneously experience relaxation and stimulation, advanced technology and traditional culture, comfort and adventure. Leave refreshed and inspired, ready to take your work to ever-greater heights. Contact us and together we will put together a package that exceeds your needs and desires. [email protected]
Sign up! Β» Spaceflight preparation program This is where your space adventure begins. Spaceport Sweden has partnered with QinetiQ to develop and deliver a world-class spaceflight preparation program together, where future space travelers will emerge prepared, confident and relaxed, ready to maximise their journey to space. The Flight Physiological Centre in LinkΓΆping, Sweden, is one of the worldβs advanced Dynamic Flight Simulators (DFS), combining a man-rated, long-arm centrifuge and flight simulator. The DFS provides a safe and highly controllable environment in which passengers can experience the sustained periods of increased acceleration present during launch and re-entry and allows for the precise re-creation of the complex and unique βGβ profiles generated by future commercial space vehicles. Spaceport Sweden together with QinetiQ offers courses at the Flight Physiological Centre that will prepare passengers and crew of future space vehicles for the unique acceleration environment they will experience. When it comes to preparing for a new experience, we believe that knowledge is as important as familiarity, and our courses are geared to empower people with both. Extensive experience combined with state-of-the-art facilities, QinetiQβs highly experienced team of doctors and scientists will guide clients through the world of G forces, utilizing a mixture of lectures, practical demonstrations and one-on-one tuition on the DFS itself. Clients will learn about the effects of +Gz and +Gx, gain practical experience of the symptoms they are likely to experience and the actions they can take, if required, to effectively counter these symptoms. Culminating in an experience of the complete launch-to-landing, vehicle-specific G profile precisely recreated on the DFS, QinetiQβs courses will provide clients with a unique insight into the space flight environment. By understanding the effects of +Gz and +Gx, and having practical experience of their personal symptoms, any anxieties will be transformed into anticipation and clients will emerge, confident, relaxed and ready to absorb every detail of what will prove to be an extraordinary space experience. Irrespective of whether or not you decide to venture into space, Spaceflight Training will provide you with unforgettable experiences. Are you ready to take the first step of an extraordinary adventure? Optional programs available very soon. Sign up and weβll keep you posted: [email protected] Space camp Everyone has dreamt of making the journey into space. While in the past it was inevitable that very few people would actually turn this dream into a reality, contemporary advances in space tourism are dramatically increasing everyoneβs chances of one day looking down on Earth from space. The future is here now and Spaceport Sweden is delighted to be able to introduce the newest generations of earthlings to the wonders of space with our Space Camp. Children attend an educational and inspirational camp where they meet astronauts, test the laws of gravity, understand our solar system, and learn to work as a team as they simulate an entire space mission. Space Camp is about more than just a one-off experience. The excitement of space coupled with the possibility of space travel will inspire more children to learn and study the natural sciences, thereby contributing to a more sustainable future and increasing the likelihood of further innovation. Space Camp is the ultimate adventure for your ultimate adventurer. ||||| Arctic town eyes future as gateway to space
KIRUNA, Sweden β Sweden's small Arctic town of Kiruna has a surprisingly international airport with regular flights to London and Tokyo, but it has even bigger plans: to offer commercial space flights.
Spaceport Sweden, a company founded in 2007, hopes to be able to provide the first flights within a decade from Kiruna's airport.
"We're working on establishing commercial flights from Sweden to space for tourism and research, and to create a launching pad at the airport," explained the company's enthusiastic director, Karin Nilsdotter, seated in her office at the Swedish Institute of Space Physics (IRF).
The idea is that space tourists would take off for a maximum two-hour trip into space aboard futuristic spacecraft currently undergoing testing, which resemble a cross between an airplane and a space shuttle and which can carry between one and six passengers.
The sub-orbital flights will send passengers 100 kilometres (60 miles) above Earth and allow them to experience five minutes of weightlessness.
Kiruna's location in the far north of Sweden, and Europe, makes it a prime location for space flights, Nilsdotter said.
The space flights would not be disturbed by heavy air traffic, nor is the region a densely populated area. The wide-open spaces within Sweden's borders also mean no bureaucratic red-tape to be resolved with other countries.
Kiruna also has 60 years experience of space research to its credit. IRF was founded in 1957 and the Swedish space research and rocket centre Esrange, located in the town, was founded in 1966.
"We have to use this knowledge to create a unique adventure with global impact: space travel," Nilsdotter insisted.
"Even if it's too early to give any figures, market studies show there is potential for 14,000 travellers after 10 years of business," she added.
Spaceport Sweden is not building its own spacecraft, but will instead collaborate with a company that is doing so, she says, refusing to disclose how many spacecraft it will operate nor the identity of its partner.
In the United States, several companies are already developing aircraft capable of carrying space tourists, such as Richard Branson's Virgin Galactic.
"The technology isn't fully developed yet," Nilsdotter said, adding that the companies were currently carrying out test flights in the United States.
The first commercial space flights are expected to take place in the United States in 2014 and a few years after that in Sweden.
The head of the Esrange space research and rocket site, Lennart Poromaa, is meanwhile more measured in his enthusiasm for the project.
"In a few years there may be commercial space flights, but it will take longer than people think," he said.
Esrange pulled out of the project "because we're not about creating adventure", he explained.
But "we could help them if they need help in the field of research, possibly", the aerospace engineer said.
According to Nilsdotter, space flights could take off four times a day. Esrange meanwhile launches four rockets a year.
"Researchers who want to test their experiments in microgravity may be able to fly with us and then adjust their projects," she said.
In the United States, more than 1,000 tickets for space flights have already been reserved, at around $200,000 (153,000 euros) apiece.
For adventure-seekers who can't wait to visit space, Spaceport Sweden already offers flights from Kiruna airport to view the northern lights, a spectacular phenomenon of colourful lights that streak across the night sky, for the tidy sum of 6,990 kronor (810 euros, $1,059).
Copyright Β© 2013 AFP. All rights reserved. More Β»[/INST]β A company in a tiny Arctic town plans to launch people into space like clockwork, on two-hour trips four times a day. But a little more workβor even a lotβis required first, AFP reports. The company, Spaceport Sweden, is building a unique vessel that combines a space shuttle with an airplane. And director Karin Nilsdotter is already counting the customers who will trek to the town of Kiruna: "Even if it's too early to give any figures, market studies show there is potential for 14,000 travellers after 10 years of business," she says. But she says the technology "isn't fully developed yet" and competitors like Virgin Atlantic are already launching test flights in the US. A few things are going for her, however: Kiruna has a 60-year history of space research, there's little air traffic to clutter things up, and wide-open spaces within Sweden ensure there's no red tape with other countries. Still, the head of a space research and rocket site in town offers a cautionary note: "In a few years there may be commercial space flights, but it will take longer than people think."</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Stonewall National Historic Site
Establishment Act''.
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--The Congress finds that--
(1) the Stonewall National Historic Landmark in New York
City, designated in 2000, commemorates the site of the citizen
uprising of June 28-July 3, 1969, that inspired the modern
Lesbian, Gay, Bisexual, and Transgender (LGBT) civil rights
movement in America;
(2) the Stonewall uprising became the major catalyst for
change in the self-awareness of the LGBT community, as well as
in the perception and acceptance of LGBT individuals within the
United States, and now represents to the Nation and the world
the struggle for LGBT civil rights; and
(3) the Stonewall National Historic Landmark, within the
Greenwich Village Historic District, consists of the former
Stonewall Inn at 51-53 Christopher Street, that was raided by
police on June 28, 1969, as well as Christopher Park,
Christopher Street, Grove Street, Gay Street, Waverly Place,
Greenwich Avenue, Sixth Avenue, and West 10th Street between
Sixth Avenue and Seventh Avenue South, which are all associated
with the uprising.
(b) Purpose.--The purposes of this Act are--
(1) to help preserve, protect, and interpret the site of
the Stonewall uprising for the benefit of present and future
generations; and
(2) to enhance understanding of the discrimination against
LGBT individuals that led to the Stonewall uprising and of the
ongoing struggle to achieve civil rights.
SEC. 3. DEFINITIONS.
In this Act:
(1) National historic site.--The term ``National Historic
Site'' means the Stonewall National Historic Site in New York
City, New York, authorized to be established as a unit of the
National Park System under section 4(a) of this Act.
(2) Map.--The term ``Map'' means the map entitled
``Stonewall National Historic Site, Proposed Boundary'',
numbered 668/129,921, and dated September 2015.
(3) City of new york.--The term ``City'' means the
government of the City of New York in the State of New York.
(4) Secretary.--The term ``Secretary'' means the Secretary
of the Interior.
(5) State.--The term ``State'' means the State of New York.
SEC. 4. STONEWALL NATIONAL HISTORIC SITE.
(a) Establishment.--
(1) In general.--Subject to paragraph (2), there is
established in the State a unit of the National Park System to
be known as the ``Stonewall National Historic Site''.
(2) Conditions for establishment.--The National Historic
Site shall not be established as a unit of the National Park
System until the date on which the Secretary has determined
that--
(A) the Secretary has acquired sufficient land or
an interest in land within the boundary of the National
Historic Site to constitute a manageable unit, as
determined by the Secretary; and
(B) the Secretary has entered into a written
agreement with the City, as authorized and described in
subsection (c).
(b) Boundary.--
(1) In general.--The boundary of the National Historic Site
shall be identical to the boundary of the Stonewall National
Historic Landmark, as generally depicted on the Map.
(2) Availability of map.--The Map shall be available for
public inspection in the appropriate offices of the National
Park Service, Department of the Interior.
(c) Agreement.--The Secretary is authorized to enter into an
agreement with the City that delineates the respective roles and
responsibilities of the National Park Service and the City in the
operation, maintenance, and interpretation of the National Historic
Site.
(d) Publication of Notice.--Not later than 60 days after the date
on which the conditions in subsection (a)(2) are satisfied, the
Secretary shall publish in the Federal Register notice of the
establishment of the National Historic Site as a unit of the National
Park System.
(e) Land Acquisition.--The Secretary is authorized to acquire by
donation, purchase with donated or appropriated funds from a willing
seller, or exchange--
(1) lands or interests in land within the boundary of the
National Historic Site; and
(2) lands or interests in land in the vicinity of the
National Historic Site for the purpose of providing park
administration and visitor service facilities, as determined by
the Secretary.
(f) Administration.--
(1) In general.--The Secretary shall administer the
National Historic Site in accordance with this Act and with the
laws generally applicable to units of the National Park System,
including--
(A) the National Park Service Organic Act (section
100101(a), chapter 1003, and sections 100751(a),
100752, 100753 and 102101 of title 54, United States
Code); and
(B) chapter 3201 of title 54, United States Code.
(2) Cooperative agreements.--
(A) In general.--The Secretary may enter into
cooperative agreements with the State, City, units of
local government, organizations, or individuals to
further the purposes of this Act.
(B) Cost-sharing requirement.--
(i) Federal share.--The Federal share of
the total cost of any activity carried out
under this paragraph shall not exceed 50
percent.
(ii) Form of non-federal share.--The non-
Federal share of the cost of carrying out an
activity under this paragraph may be in the
form of in-kind contributions or goods or
services, fairly valued.
(g) General Management Plan.--Not later than 3 years after the date
on which funds are made available to carry out this section, the
Secretary, in consultation with the City, shall prepare a general
management plan for the National Historic Site in accordance with
section 100502 of title 54, United States Code. | Stonewall National Historic Site Establishment Act This bill establishes the Stonewall National Historic Site in New York as a unit of the National Park System. The boundary of the Historic Site shall be identical to that of the Stonewall National Historic Landmark. The Department of the Interior may enter into an agreement with New York City, New York, delineating the respective roles and responsibilities of the National Park Service and New York City in operating, maintaining, and interpreting the Historic Site. Interior shall prepare a general management plan for the Historic Site. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Stonewall National Historic Site
Establishment Act''.
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--The Congress finds that--
(1) the Stonewall National Historic Landmark in New York
City, designated in 2000, commemorates the site of the citizen
uprising of June 28-July 3, 1969, that inspired the modern
Lesbian, Gay, Bisexual, and Transgender (LGBT) civil rights
movement in America;
(2) the Stonewall uprising became the major catalyst for
change in the self-awareness of the LGBT community, as well as
in the perception and acceptance of LGBT individuals within the
United States, and now represents to the Nation and the world
the struggle for LGBT civil rights; and
(3) the Stonewall National Historic Landmark, within the
Greenwich Village Historic District, consists of the former
Stonewall Inn at 51-53 Christopher Street, that was raided by
police on June 28, 1969, as well as Christopher Park,
Christopher Street, Grove Street, Gay Street, Waverly Place,
Greenwich Avenue, Sixth Avenue, and West 10th Street between
Sixth Avenue and Seventh Avenue South, which are all associated
with the uprising.
(b) Purpose.--The purposes of this Act are--
(1) to help preserve, protect, and interpret the site of
the Stonewall uprising for the benefit of present and future
generations; and
(2) to enhance understanding of the discrimination against
LGBT individuals that led to the Stonewall uprising and of the
ongoing struggle to achieve civil rights.
SEC. 3. DEFINITIONS.
In this Act:
(1) National historic site.--The term ``National Historic
Site'' means the Stonewall National Historic Site in New York
City, New York, authorized to be established as a unit of the
National Park System under section 4(a) of this Act.
(2) Map.--The term ``Map'' means the map entitled
``Stonewall National Historic Site, Proposed Boundary'',
numbered 668/129,921, and dated September 2015.
(3) City of new york.--The term ``City'' means the
government of the City of New York in the State of New York.
(4) Secretary.--The term ``Secretary'' means the Secretary
of the Interior.
(5) State.--The term ``State'' means the State of New York.
SEC. 4. STONEWALL NATIONAL HISTORIC SITE.
(a) Establishment.--
(1) In general.--Subject to paragraph (2), there is
established in the State a unit of the National Park System to
be known as the ``Stonewall National Historic Site''.
(2) Conditions for establishment.--The National Historic
Site shall not be established as a unit of the National Park
System until the date on which the Secretary has determined
that--
(A) the Secretary has acquired sufficient land or
an interest in land within the boundary of the National
Historic Site to constitute a manageable unit, as
determined by the Secretary; and
(B) the Secretary has entered into a written
agreement with the City, as authorized and described in
subsection (c).
(b) Boundary.--
(1) In general.--The boundary of the National Historic Site
shall be identical to the boundary of the Stonewall National
Historic Landmark, as generally depicted on the Map.
(2) Availability of map.--The Map shall be available for
public inspection in the appropriate offices of the National
Park Service, Department of the Interior.
(c) Agreement.--The Secretary is authorized to enter into an
agreement with the City that delineates the respective roles and
responsibilities of the National Park Service and the City in the
operation, maintenance, and interpretation of the National Historic
Site.
(d) Publication of Notice.--Not later than 60 days after the date
on which the conditions in subsection (a)(2) are satisfied, the
Secretary shall publish in the Federal Register notice of the
establishment of the National Historic Site as a unit of the National
Park System.
(e) Land Acquisition.--The Secretary is authorized to acquire by
donation, purchase with donated or appropriated funds from a willing
seller, or exchange--
(1) lands or interests in land within the boundary of the
National Historic Site; and
(2) lands or interests in land in the vicinity of the
National Historic Site for the purpose of providing park
administration and visitor service facilities, as determined by
the Secretary.
(f) Administration.--
(1) In general.--The Secretary shall administer the
National Historic Site in accordance with this Act and with the
laws generally applicable to units of the National Park System,
including--
(A) the National Park Service Organic Act (section
100101(a), chapter 1003, and sections 100751(a),
100752, 100753 and 102101 of title 54, United States
Code); and
(B) chapter 3201 of title 54, United States Code.
(2) Cooperative agreements.--
(A) In general.--The Secretary may enter into
cooperative agreements with the State, City, units of
local government, organizations, or individuals to
further the purposes of this Act.
(B) Cost-sharing requirement.--
(i) Federal share.--The Federal share of
the total cost of any activity carried out
under this paragraph shall not exceed 50
percent.
(ii) Form of non-federal share.--The non-
Federal share of the cost of carrying out an
activity under this paragraph may be in the
form of in-kind contributions or goods or
services, fairly valued.
(g) General Management Plan.--Not later than 3 years after the date
on which funds are made available to carry out this section, the
Secretary, in consultation with the City, shall prepare a general
management plan for the National Historic Site in accordance with
section 100502 of title 54, United States Code.[/INST]Stonewall National Historic Site Establishment Act This bill establishes the Stonewall National Historic Site in New York as a unit of the National Park System. The boundary of the Historic Site shall be identical to that of the Stonewall National Historic Landmark. The Department of the Interior may enter into an agreement with New York City, New York, delineating the respective roles and responsibilities of the National Park Service and New York City in operating, maintaining, and interpreting the Historic Site. Interior shall prepare a general management plan for the Historic Site. </s> |
black holes @xcite are generally accepted as possible endpoints of gravitational collapse .
oppenheimer and snyder predicted the formation of black holes in some stellar collapses @xcite , and for some astrophysical situations there is no generally accepted mechanism to prevent the formation of a black hole .
indeed there are strong candidate objects to have reached this stage of compression among supernova remnants @xcite and galactic cores @xcite .
we wish to propose that there is a mechanism in the @xmath0 x @xmath0 and @xmath1 heterotic string theories which would avert horizon formation in all cases where no other mechanism comes into play , with regions of a hot string phase forming instead of black holes .
the scenario which is proposed would also resolve the recently noted ` firewall paradox ' @xcite , @xcite in a radical way . here
, quantum mechanics and the equivalence principle are both respected , but the black hole complementarity principle @xcite is abandoned .
an infalling observer would indeed encounter a kind of ` firewall ' as novel processes rooted in thermal duality are triggered .
+ the process of black hole formation in general relativity was shown to be generic in the penrose singularity theorem @xcite .
the scenario in general relativity is summarised by a penrose diagram with all world lines which cross the horizon meeting a spacelike singularity set within a finite time .
penrose identified @xcite a point of no return after which a singular endpoint can not be averted ( except possibly by invoking negative energy ) as the formation of a closed trapped surface @xcite .
it is just prior to the formation of such trapped surfaces that the mechanism proposed in this paper would come into play , circumventing the formation of horizons
. the causal structure of spacetime would then be isomorphic to that of minkowski space .
+ the necessity of a singularity within a black hole can be understood as follows .
if we look at a forming black hole as a particle accelerator , suppose that two particles ( e.g. electrons ) falling in from opposite sides could collide .
at the collision , since both particles have timelike worldlines , the centre of mass energy of the two particles would take some finite value @xmath2 .
however , in the reference frame of an observer at the centre of mass , the kinetic energy of the particles will already have exceeded @xmath2 ( and indeed any finite value ) during the collapse . to avoid the possibility of such a contradiction
, the causal structure of spacetime must make any such encounter impossible , and this is realised by the presence of the singularity which enforces a spacelike separation of the particle worldlines to their ends . + towards the singularity , an unboundedly large energy is compressed within an unboundedly small volume @xcite .
a natural conjecture would be that high energy effects ( perhaps related to string theory ) would intervene in this state of high compression to resolve the singularity , as the conditions are reminiscent of a time - reversed version of those prevailing in the early universe .
however , the mechanism which is thought to resolve the singularity at the beginning of time predicted by the hawking singularity theorem @xcite , namely inflation , relies on negative pressure filling boundaryless spatial hypersurfaces . as the collapsing object does not fill space , the negative pressure needed to support rapid deflation would have no support at the object s surface .
the best strategy for averting a singularity in the case of collapse thus seems to be to prevent the formation of a closed horizon .
+ can quantum mechanics , and in particular string theory provide such a mechanism ? near the horizon the temperature apparently diverges for a static observer held in place at a fixed distance from the horizon , due to the unruh effect @xcite .
however , string theory apparently implies that there is a maximum temperature ( the hagedorn temperature @xcite ) suggesting that horizon formation may be averted by string effects @xcite or be taken to be equivalent to a string theoretic picture @xcite . in themselves
, however , these observations do not provide the mechanism for braking the fall of matter during gravitational collapse which would be needed to avert horizon formation .
+ string and brane state counting for near critical holes @xcite , @xcite in type ii string theory gives agreement with the bekenstein - hawking entropy @xcite , and can be pictured as being due to string or d brane degrees of freedom near the horizon @xcite .
the analyses of @xcite , @xcite rely on counting d brane degrees of freedom , which are absent in the @xmath0 x @xmath0 heterotic string regime @xcite , due to the absence here of d branes and the unbreakable nature of e8 strings for topological reasons @xcite .
the suggested string - hole equivalence would thus have to be realised in a different way for @xmath3 x @xmath0 strings .
the possibility of such a connection seems worth studying for two reasons : the string - hole correspondence seems likely for reasons of consistency to hold for all regions of m theory , including @xmath0 x @xmath0 strings , and more pragmatically because this kind of string model is more likely to be relevant to astrophysical gravitational collapse . + a closer analysis of the hagedorn transition @xcite , @xcite
, @xcite indicates the possibility of a high temperature string phase for heterotic strings characterised by the formation of a condensate .
the heterotic nature of the strings is essential to this mechanism .
this phase was first noted for its possible relevance to gravitational collapse in @xcite . in @xcite
it was suggested that the endpoint of gravitational collapse would be a region of the high temperature phase , having a hyperbolic internal spatial geometry , allowing the entropy to be reconciled with the hawking value , which is related to the surface area rather than the euclidean volume .
a non - local quantum mechanical mechanism which would allow conversion of infalling matter to the high temperature string phase through the spontaneous formation of shells of the high temperature string phase was also proposed in @xcite .
it was conjectured that the nucleation of such shells would take place where the surface gravity reaches the duality temperature , giving a close relationship between nucleation sites and proximity to the point where penrose surfaces would otherwise form .
+ the purpose of this communication is to replace the shell nucleation mechanism of @xcite , which relies on no - local quantum correlations around the collapsing object with a process that works locally to convert the kinetic energy of infalling matter into thermal excitations of the string vacuum .
the conditions for thermalon excitation during an astrophysical gravitational collapse are identified , and the mechanism by which the kinetic energy of infalling matter is converted to the thermalized energy of the high temperature string phase is elucidated .
it will be shown that the conditions under which the conversion of energy to thermalon excitations and thence to high temperature string phase would occur only in final stages of gravitational collapse , and that the normal vacuum would be stable against such processes . a dissipative mechanism for the thermalisation of the kinetic energy of infalling matter is proposed , which could lead to a final state almost in thermal equilibrium with the surrounding vacuum ( with only hawking like radiation escaping ) and which would not have an event horizon . a possible relationship between thermodynamic thermalon entropy and an entropy of entanglement between short and long string sectors
will be proposed which could enable the generation of the hawking entropy to be reconciled with conventional quantum mechanical state evolution .
+ the thermal equilibrium between the high temperature string phase and normal vacuum indicates that the entropy of the high temperature string phase should agree with the hawking value to leading order in @xmath4 ( @xmath5 is the planck mass ) .
it thus seems that a microscopic model of the hawking entropy may also be possible for @xmath0 x @xmath0 strings .
the approach taken in this paper addresses the issue of string - hole correspondence in a different regime and with different methods to @xcite , @xcite .
the latter invoke supersymmetry to carry out an evaluation of the number of microstates by direct enumeration , in a way which is independent of thermodynamic arguments .
this takes place in a critical limit , where the hole becomes cold .
in contrast , the current paper relies on properties of the heterotic thermalon , which intrinsically breaks supersymmetry
supersymmetry is necessarily broken in a thermal ensemble , and indeed the thermalon does not even belong to a supersymmetry multiplet .
agreement with the hawking entropy value follows directly to leading order from the thermodynamic equilibrium between the hot phase and the ambient normal vacuum , although the counting of string microstates can only be inferred at this stage . again in contrast to the cases considered in @xcite , @xcite it is the approximately schwarzschild case which is easiest to analyse for the thermalon mechanism , rather than the critical ones .
the justification of the hawking entropy in such contrasting scenarios seems to support the conjecture that it should be valid for all m theory cases .
the partition sum @xmath6 at a finite temperature may be calculated by compactifying time in an imaginary direction .
this introduces a winding mode in string theory @xcite , which we will refer to as the thermalon .
this situation may be represented by a compactification of the string target space on a lorentzian lattice .
a change of @xmath7 is represented by a lorentzian transformation @xcite .
the critical points at which the thermalon becomes a tachyon are located where the lorentzian trajectory crosses the circle in the @xmath8 energy plane representing zero mass , and this gives a value for the hagedorn temperature @xcite which agrees with that found by counting string states . for free strings ,
the partition sum @xmath6 for a single string diverges at this temperature .
although the thermalon is , in itself , a fictitious particle it provides an effective theory which summarises the overall effect of the tower of excited string states .
when the continuation is made back to the physical minkowski regime , the interaction of the thermalon field with the background geometry presented below is intended to provide an effective theory which summarises interactions of strings with a condensate of string tower states . for interacting strings ,
the hagedorn temperature is marked by the formation of this condensate .
+ for heterotic strings , of either the @xmath0 x @xmath0 or @xmath1 types , the winding and momentum numbers @xmath9 of the thermalon state which may become a tachyon are @xmath10 .
this is possible because the gso projection is reversed for consistency for the winding state @xcite .
note that the combination of wrapping and momentum quantum numbers for the thermalon around the imaginary time circle is the same as that for left moving heterotic modes .
there is a contrast between the lorentzian trajectories for the thermalon in the non - heterotic and heterotic cases , with the heterotic case exhibiting thermal duality .
the thermalon is a tachyon where its trajectory lies inside the circle ( in the euclidean norm of conformal weights ) representing zero mass . in the non - heterotic case
, the trajectory follows a straight line towards the origin , and the thermalon becomes more tachyonic as the temperature is increased further ( see figure 1 ) .
+ in the heterotic case , the trajectory is a hyperbola , and there is a second critical temperature ( the upper hagedorn point ) with @xmath11 where the trajectory leaves this circle ( see figure 2 ) .
+ similarly to the higgs mechanism where the tachyon is modified by quartic or higher interactions , thermalon interactions may allow a condensate phase to form at high temperatures .
the thermalon would effectively have a positive mass in the condensate phase , so that there would be a finite density of string , string degrees of freedom and entropy in this phase .
+ for an abelian gauge field @xmath12 in a heterotic string theory , the right - moving component is represented by the spacetime index @xmath13 , while the left component is represented by @xmath14 , a left - heterotic winding direction . +
a frame field description of gravity is natural in heterotic string theory , with the graviton @xmath15 and gravitino @xmath16 described using left - moving world and right - moving frame indices .
consider the timelike component of the metric frame field @xmath17 . on wick rotation in the thermal geometry ,
the left index @xmath18 is a winding direction , and the thermalon carries momentum in this direction . at the self - dual point ( @xmath19 )
the combination of wrapping and momentum contributes only to the left - moving conformal weight . here
the relationship between @xmath20 and the thermalon field @xmath21 is the same as that between a @xmath22 gauge field and a charged scalar .
+ continuation to the imaginary time regime makes like charges for this @xmath22 repel .
this will allow us to make a comparison between the frame - thermalon system and a ginzburg - landau superconductor @xcite in the euclidean regime , which will be relevant in the case where @xmath23 is near a global minimum .
+ suppose that we introduce a gravitational gradient , producing a deviation from minkowski geometry but with a timelike killing vector that may be used to define energy and temperature .
the effect of the gravitational gradient is to make length of this killing vector vary , so that @xmath24 , the local size of compact dimension will vary accordingly .
note that although @xmath7 varies locally , its relationship with the gravitational gradient and killing vector length means that the temperature viewed by an external observer is constant . + we will explore the possibility of both strong and weak thermalon excitations in equilibrium with the vacuum .
the unruh effect @xcite , whereby an accelerating rindler observer measures a nonzero temperature proportional to the acceleration @xmath25 indicates that this is possible , as in principle the high temperatures needed for the hagedorn transition may be obtained from high accelerations .
we will show that there are solutions for the heterotic thermalon corresponding to accelerating excitations , which have zero overlap with the horizon .
these excitations would represent alternative thermal string ensembles with a nonzero thermalon condensate , in equilibrium with the normal vacuum .
these solutions are incompatible with a minkowski background , but would provide a way to interpolate between concentric exterior schwarzschild metrics.the possible relevance of these ensembles to gravitational collapse will be explored below .
two ( extreme ) cases will be examined below in detail , for @xmath21 small compared to the string tension scale , and for @xmath21 in the nonlinear region .
in this section , we will investigate the possibility of weak thermalon deformations of minkowski space .
essentially , we will show that there is an obstruction to the existence of such deformations , due to a warp in the transverse metric across a solution with nonzero @xmath21 . on gauging away the phase of @xmath21 in the euclidean regime and continuing to minkowski space
, the lagrangian for the thermalon takes the form @xcite for small @xmath21 @xmath26 where the squared mass @xmath27 is given by @xmath28 the higher order terms in @xmath21 describe the effects of string interactions . in general , the higher order terms can not be calculated in the absence of a string field theory formalism . however , at the critical points where @xmath29 a constant @xmath21 corresponds to on - shell thermalons .
now on - shell , the 4 thermalon scattering amplitude is accessible to perturbation theory , and takes a form similar to the virasoro - shapiro amplitude , giving a nonzero value for @xmath30 which is the same at the two critical points by @xmath31 duality .
the effective @xmath32 between the critical points will be relevant to the issue of thermalon condensation , and as long as this is non - zero a finite condensate will form .
+ in this section we will consider the case of of excitations with small values of @xmath33 in a flat minkowski background , for which the non - linear terms ( which are of higher order in @xmath33 ) may be neglected ( and so the uncertainty regarding their values is not relevant ) .
this we will call the regime of weak excitations .
the case for larger values of @xmath33 will be considered below , to build up a picture of how thermalon condensation may progress during gravitational collapse .
+ in this regime we will seek solutions which appear static to a rindler observer , which can be in thermal equilibrium with the surrounding vacuum at a position dependent unruh temperature .
it should be emphasised that we do not take such accelerated observers to have a privileged status beyond the accelerated excitation solutions taking a simple form in such frames . from the standpoint of general covariance , in such a frame
we can take @xmath21 to be a scalar , although it should be remembered that this is essentially a shorthand for the entity @xmath34 or equivalently @xmath35 , as @xmath36 is needed to define the local temperature and wick rotation .
if @xmath37 is the vector field dual to @xmath36 , then the local energy and temperature are defined relative to the killing vector @xmath38 .
+ note that in minkowski space the choice of @xmath37 is arbitrary due to lorentz invariance .
however , the conjecture that we will develop below is that thermalon deformations of the ordinary vacuum are only relevant where @xmath37 is parallel to a timelike killing vector , and in the case of interest here , of near spherically symmetric collapsed objects , this will be essentially unique .
+ using rindler coordinates @xmath39 @xcite for such an accelerated observer , the inverse temperature @xmath7 depends on the distance @xmath40 from the horizon as @xmath41 , and the effective squared mass of the thermalon @xmath27 varies accordingly , as @xmath42 for thermal equilibrium @xmath43 = 0 , and for a plane wave solution @xmath44 , and the differential equation for @xmath21 becomes @xmath45 near the horizon , @xmath46 , we have @xmath47 and ( [ de ] ) simplifies to a bessel form and the solution which is finite at @xmath48 has @xmath49 likewise it is easy to verify that @xmath21 will have a gaussian cut - off at large @xmath40 . in fact , the exact solution of ( [ de ] ) which is finite at @xmath48 is @xmath50 where @xmath51 is an arbitrary small parameter . here
@xmath51 has the same dimensions as @xmath21 ( energy ) , and the solution is shown in figure 3 .
the simple form of @xmath21 will enable us to evaluate various integrals of interest below .
+ note that for this solution , @xmath21 takes its maximum value at @xmath52 where @xmath53 , the self - dual value .
the solution for @xmath21 vanishes at the horizon , and the solution is essentially confined to @xmath54 , as @xmath21 diminishes rapidly beyond this point . + for comparison , let us compare this solution to the situation for a non - heterotic thermalon , for example that for the bosonic string . here , @xcite
@xmath55 and the solution which is finite for @xmath46 has @xmath56 which tends to a non - zero value as @xmath46 and the exact solution , with @xmath57 , may be given in terms of a laguerre polynomial of fractional order as @xmath58 whereas this solution has the same gaussian cut - off at large @xmath40 as for the heterotic case , the thermalon excitation is not now excluded from the horizon .
thus thermal duality can be seen to be responsible for confining the weak thermalon excitation solution away from the horizon ( the other independent solution diverges at horizon and is unphysical ) which would be relevant in the environment of a gravitationally collapsed object .
the heterotic thermalon excitation is thus kept from falling into the horizon .
an ` excitation trap ' effect is thus present in this case .
although the solution presented above was calculated using a special reference frame , the excitation would have properties such as the distortion of the metric produced by back reaction on which all observers would agree .
this back reaction will be seen to produce a transverse warp , presenting an obstruction to embedding in a minkowski background .
+ the thermalon excitation solution in the previous section apparently accelerates through minkowski spacetime
. this would be mechanically possible if the overall inertia of the solution vanished , with positive mass on the forward side , negative mass on the following side and positive pressure in between acting against the inertia ( positive and negative ) on either side .
we will now look in more detail at the back reaction of the thermalon excitation ` wall ' solution on the metric .
it will turn out that the excitation has a positive overall gravitational mass .
acceleration of a configuration with positive mass through minkowski space is clearly impossible , as the conservation of momentum and energy would be violated . rather than inhabiting a conventional minkowski background
, it will be shown that the thermalon excitation wall interpolates between two minkowski regions with a transverse warp factor between them .
+ the einstein field equations are given by @xmath59 where we have retained newton s constant @xmath60 as we are working in string tension units .
we will work to first order in @xmath51 , so that the solution above remains valid .
introducing notation for the @xmath21 kinetic term @xmath61 the einstein equations become , on implementing the thermal equilibrium constraints @xmath62 and re - arranging , as follows ( where v is the poential ) : @xmath63 @xmath64 and similarly for @xmath65 and @xmath66 .
+ now from ( [ rzz ] ) we have a local gravitational source @xmath67 given by , with @xmath68 @xmath69 and introducing @xmath70 gives @xmath71 and now @xmath72 as @xmath73 introducing a factor of @xmath74 to compensate for the redshift seen by an observer at the arbitrary location @xmath75 gives @xmath76 and @xmath77 which is finite and positive .
note that @xmath13 is zero at @xmath78 and is negative to the high temperature side of this point and positive to the low temperature side .
+ now the warp factor across the wall can be calculated by an application of the equivalence principle . if an area @xmath79 behind the wall matches an area @xmath80 ahead of the wall , and we define the warp factor @xmath81 by @xmath82 then with @xmath83 the acceleration due to gravity in the rindler frame , @xmath84 where the volume @xmath85 extends across the comparison surface and between @xmath86 and @xmath87 . now letting @xmath88 and @xmath89 gives @xmath90 and finally @xmath91 this warp factor is realised by a hyperbolic spatial geometry within the thermalon ` wall ' , which is another aspect of the back reaction , described by ( [ r11 ] ) .
this hyperbolic geometry is a feature that the weak thermalon wall solution shares with the strong @xmath21 solutions discussed below .
+ although the plane wave solution is not viable in an ordinary minkowski space background , where conservation of energy requires a counter - factual warp factor , this analysis does suggest the possibility of a standing wave solution in a strong gravitational field , which we will examine next .
the exterior schwarzschild metric is given by @xmath92 where @xmath93 is the schwarzschild radius , @xmath94 at which there is an event horizon . for large @xmath95
, we will assume that the background is sufficiently flat that the hagedorn transition points are not significantly affected ; the results below will be qulitatively similar even if these points are perturbed a little by the background
. we will use this exterior schwarzschild metric , but will work in a region excluding the horizon .
we will argue that in fact a closed horizon will never form due to thermalon effects .
+ for a thermalon deformation to be a viable solution , it must interpolate between concentric ( approximately ) schwarzschild solutions , with the thermalon wrapping aligned with ( the wick rotation of ) a timelike killing vector to give a standing thermalon excitation just outside the virtual horizon . for a large black hole ,
the surface is almost flat and the plane wave thermalon solution given above will locally be a good approximation to the true solution .
to leading order in @xmath96 , the area of a static surface at the self - dual temperature @xmath97 will differ from the area of the horizon by a fixed amount ( independent of @xmath95 ) of @xmath98 , due to the approximately hypercylindrical form of the spatial metric .
the area difference @xmath99 that comes from the warp factor @xmath81 of the static thermalon excitation will therefore provide an interpolation to another schwarzschild metric to the exterior .
the horizon area that would be predicted from the exterior solution is increased by @xmath99 compared to the actual horizon area .
this shows the possibility of thermalons shrinking the actual horizon area for a given mass .
we will argue below that in fact a closed horizon will never form as the energy present will be converted to thermalon form during collapse .
whereas this altered black hole solution can be seen as a deformed version of the conventional black hole , in the scenario below the black hole is replaced completely by a region of thermalon condensate .
+ the warp factor of the thermalon solution means that thermalon deformations of the minkowski vacuum are not possible . only in the near horizon geometry
will coherent and persistent thermalon excitations be possible .
the persistence of strongly accelerated thermalon traps in these solutions is the key to the possibility of persistent deformations , rather than simply the presence of curvature ( which is small for high mass backgrounds ) .
+ our basic conjecture is that a particle of energy @xmath100 ( measured from infinity ) falling through a schwarzschild geometry will begin to nucleate thermalons when the geometry to its outside locally acquires a timelike killing vector with critical acceleration .
thereafter , this condition will be maintained by kinetic energy being fed from the particle to increase the thermalon density in the static trap .
this process is thermodynamically favoured because of the large amount of entropy released , which we will show in the next section will be esentially the hawking entropy for an equivalent black hole .
the basis of hawking s analysis of the entropy of black holes is the relationship @xmath101 where @xmath7 is the vacuum temperature , which expresses the principle that energy emitted by a black hole is completely thermalised .
since the thermalon excitation is in thermal equilibrium with the vacuum , this relationship should also apply to our solution @xmath102 interpreted either as a static or a dynamic excitation . now
( [ s ] ) may be expressed in terms of the free energy as @xmath103 or equivalently @xmath104 now @xmath105 consists of a kinetic part and a potential part , which can be evaluated for the solution ( [ sol ] ) by direct integration .
first , the kinetic part per unit area is given by @xmath106 and inserting the solution ( [ sol2 ] ) we have @xmath107 the potential part of @xmath108 per unit area is @xmath109 and using @xmath110 we have @xmath111 and @xmath112 giving @xmath113 so that @xmath114 confirming the thermal nature of the excitation .
for a static excitation bounded by the horizon we will have a differential form of the hawking area law @xmath115 +
the process of conversion of kinetic to thermalon energy will proceed from the outside inwards . due to the large release of entropy in thermalon condensation outlined above , the motion of an infalling particle is essentially determined by the condition that the static surface gravity is regulated by thermalon condensation .
the kinetic energy of the particle reduces with the enclosed area to mainatin a constant static surface gravity , and the thermalon warp increases to compensate , so that the thermalon region continues to interpolate between the schwarzschild solutions to the inside and outside of the particle . note that the term involving the time derivative of @xmath21 in the thermalon action will be suppressed by a factor
@xmath116 compared to the other terms .
+ the distance to fall for a particle of mass @xmath100 between the start of thermalon nucleation and merger with an existing collapsed object of mass @xmath95 is @xmath117 , and during this the kinetic energy is reduced from @xmath118 to @xmath98 ( note the squared reduction factor , so that the particle undergoes a double deceleration compared to the local surface gravity ) . +
although the particle spectrum is lorentz invariant , the thermalon modes that they couple to during the conversion process are not , as the possibility of thermalon deformations is dependent on the formation of static traps , which are not lorentz invariant .
+ assume that the wavefunction for a particle of mass @xmath100 is spread out transverely over an area @xmath79 .
the change of the horizon area on adding the mass @xmath100 is @xmath119 .
and we assume that @xmath120 ( so that there is a small relative area change ) . the area change for thermalon parameter @xmath21 over the area @xmath79 scales like @xmath121 , so that @xmath122 and @xmath123 , and the weak thermalon regime applies , so that a consideration of higher order terms in @xmath21 is not necessary in dealing with the particle conversion process . + for the plane wave thermalon solution to be relevant , it is only necessary that the infalling particle wavefunction be spread out on a scale large compared to @xmath124 , which is roughly of nuclear dimensions for a stellar mass collapsing object , and of atomic scale for a galactic core object . if the infalling particle can not be assumed to be delocalised , then the following observation is relevant . during its fall from the initiation of thermalon condensation to an existing thermalon region , through a distance of @xmath125 , the thermalon green s function can spread over an area @xmath126 , comparable to the increase in surface area of the condensate region , so that the weak @xmath21 limit is valid for infalling particles through most of their trajectory .
+ the production of thermalons due to the deceleration of the nucleating particle may arise through a larmor like radiation process . the radiated power would in that case scale as @xmath127 which will equal @xmath128 for relativistic motion , so that @xmath129 .
interactions between thermalons and light particles that could generate thermalon bremsstrahlung are accessible on shell through conformal field theory , and a self - consistent interaction berween light particles and thermalons which would support the conversion process may be possible .
+ it may be noted that the interaction between matter falling through the excitation region is similar to that of particles moving through a detector e.g. a cloud chamber . in both cases a dissipative process converts part of the kinetic energy of the particle into a trace carrying information about the particle s trajectory . + a freely falling observer , on passing into the conversion region , would also be subject to these processes , and would effectively be converted into a rindler observer at a string tension scale acceleration and temperature and thus would experience an encounter with a kind of ` firewall ' in the conversion region .
once a closed static trap has formed within the collapsing body , the kinetic energy of infalling particles will undergo thermalon conversion and increase the value of @xmath21 there .
as @xmath21 strengthens , it is driven towards the non - linear region , where the small @xmath21 approximation used above no longer applies .
eventually a stationary point in the @xmath21 potential is approached and a phase transition should occur .
the region where @xmath21 approximates the stationary value will thereafter expand , rather than the value of @xmath21 increasing further .
we will first examine the bulk properties of this phase by looking for a space filling solution with constant @xmath21 .
for this space - filling solution , a low energy approximation is valid for the bulk region because there the space and time derivatives of @xmath21 are small .
+ if we assume the presence of higher order terms in the thermalon potential , there will be a minimum for a given @xmath7 .
further , for the heterotic models there will be a space filling solution with constant @xmath7 and @xmath21 .
let @xmath130 be the point in @xmath131 space where @xmath132 has its global minimum .
this will exist between the upper and lower hagedorn temperatures , by the mean value theorem .
then from ( [ rzz ] ) we have @xmath133 and also @xmath134 allowing a solution with @xmath135 .
for @xmath21 constant in space , and with @xmath136 we have from ( [ r11 ] ) @xmath137 where @xmath138 and similarly for @xmath65 and @xmath66 , giving a hyperbolic spatial geometry . @xmath139 and a space - time interval @xmath140 with @xmath141 + it
can be seen that the spatial geometry must undergo a radical radial deflation during the conversion to the high temperature string phase .
+ in the effective theory with real @xmath21 , if a gravitational gradient is introduced , it will produce a gradient in @xmath7 .
any gradient of @xmath7 around @xmath142 will produce a polarization of @xmath13 with positive source on the high @xmath7 side and negative source on the low @xmath7 side since @xmath143 has a maximum at the stable point @xmath144 .
this provides the gravitational london current required to expel gravitational gradients ( up to some breakdown point ) .
the london response is given by @xmath145 which changes sign at @xmath146 .
+ we conjecture that finite regions of this gravitationally superconducting phase can exist , with an outer boundary layer with a positive gravitational source , interpolating between the high temperature string phase and the surrounding vacuum , with which it will be in thermal equilibrium . any gravitational source in the exterior
is effectively screened so that it appears only in this boundary layer .
+ as well as the thermalon condensate , the high temperature phase will be expected to contain a finite density of string excitations , due to the positive mass of the thermalon mode around the ground state .
because of the short range of gravity , which is effectively restricted to the penetration depth , the gravitational field of these strings is screened , allowing them to exist without generating event horizons .
this indicates a basic role for the thermalon mechanism in maintaining dynamical consistency for the heterotic string models , as otherwise most string states would be hidden by event horizons @xcite .
the string spectrum is thereby restored , with long strings existing in an alternative phase in a way reminiscent of colour confinement in qcd . as explained below , the emergence of these long string excitations in the condensate phase opens the possibility of an entanglement between long and short string sectors being set up during collapse and conversion , which may allow a reconciliation between the generation of the hawking entropy and the principles of quantum mechanics .
+ due to the hyperbolic geometry of the high temperature string phase interior , the volume of the bulk is proportional to the surface area for high mass .
this makes the bulk thermodynamic properties of the high temperature string phase region , and particular the entropy , consistent with the area scaling of the hawking entropy .
the hilbert space for such a region might correspond to a field theory on a ` fuzzy sphere ' @xcite , @xcite .
a stringy collapsed state without a horizon or singularity was proposed in @xcite as a resolution of the black hole information paradox . + during a collapse , a shell region of the high temperature string phase once formed will expand both outwards , as infalling matter reaches the outer surface of the shell drawing an extended region of thermalon condensation in behind it , and inwards as the contracting inner surface of the shell engulfs matter to the inside .
+ in a realistic collapse , concentric shells may form , but these will merge as the collapse progresses . these processes will continue until a stable , near spherical configuration is attained , with the interior filled with the high temperature string phase .
+ the boundary region of a shell is almost completely transparent as the thermalon condensate does not carry electric , colour or other charges .
we conjecture that the effective opacity builds with shell thickness , as the excitation strings hosted by the shell will interact with normal matter .
the combination of exponential extinction with the logarithmic dependence of the shell thickness with area ratio indicates that the resulting transmission coefficient should be a power of @xmath147 , the ratio of its outer to inner surface areas . as the inner surface of the shell shrinks , the limit of a black body is approached .
+ overall , the conversion process of kinetic energy to thermalon excitations to high temperature string phase provides a dissipative mechanism by which the energy released by gravitational collapse produces a hot final state without horizons or singularities .
the entropy of this final state , relative to an observer to whom only short string states are available for measurement , matches the hawking entropy , which is here generated during the braking process .. the large hawking entropy in this context means that the relatively small number of ordered collapsing states will end up in final states whose bulk properties are the same as those of a very much larger number of other possible states in the high temperature string phase .
+ note that the thermalon has no supersymmetry partner , so the screening mechanism gives mass to the @xmath36 component of gravity , but not to the gravitino , illustrating that thermal effects do not respect supersymmetry .
reconciling the process of gravitational collapse with quantum mechanics and quantum information theory presents two problems : what happens to the information stored in the collapsing body , and where does the very large amount of apparently random information produced during the hawking evaporation process come from ? in our scenario , the first problem is easily resolved , as there is no singularity , and the infalling matter is simply transformed into another form .
however , our analysis of the thermalon indicates that the high temperature string phase will have esentially the same large area dependent entropy as in the hawking case .
what is the microscopic description of this entropy , and how can it arise in a way consistent with quantum mechanics ?
+ entropy is related to incomplete information , or access to only part of a complete system . in quantum mechanics ,
this can be expressed through the concept of entanglement entropy . if the state of the system under consideration is ideally isolated from its envionment
, we may write @xmath148 where @xmath149 represents the total state in hilbert space , @xmath150 the state of the system and @xmath151 the state of the environment .
in general , however there will be entanglement between the system and environment so that @xmath152 and if only the system @xmath153 is accessible to measurement , it has an effective density matrix @xmath154 and our incomplete knowlwdge of the pure state @xmath149 is quantified by the entropy @xmath155 . + the thermalon entropy calculated in thermodynamic terms above should have a microscopic quantum description , and in particular the large thermalon entropy generated during the conversion process should be consistent with the preservation of a pure overall state @xmath149 . before the conversion process begins ,
the short and long string sectors are essentially decoupled , and the long string sector is in the ground state so that @xmath156 where @xmath157 represent multiple tensor indices related to a fuzzy sphere related decomposition @xcite , @xcite into angular momentum modes , with the order of @xmath14 proportional to the inner surface area of the shell and @xmath158 to the difference between outer and inner surface areas - the orders of @xmath159 and @xmath160 together are proportional to the outer surface area .
if a similar decomposition is made for @xmath161 , the conversion process will be represented by a unitary transfromation @xmath162 on the states @xmath163 and @xmath164 .
the factorisation @xmath165 no longer holds , and the short string sector now has an entanglement entropy proportional to the difference in surface area between the inside and outside of the shell .
this will increase as the conversion process proceeds , eventually reaching a value proportional to the outer surface area .
this provides a mechanism by which the short string ( field ) sector can acquire an area related entanglement entropy which , for consistency with the thermodynamic analysis above , should coincide with the hawking entropy .
+ the long strings would provide the heat bath in the interior , which would interact with photons etc .
( via biquadratic and higher order interactions ) to maintain a temperature consistent with continuity with the external vacuum .
+ as the entropy apparently generated by the conversion process is mainly due to a conversion of entanglement , the form of the entropy is approximately universal and its thermal nature , as shown in the production of ( the equivalent of ) hawking radiation , has its origin in the entanglement entropy of the near ( virtual ) horizon region . in this way
, the evolution of the system does not require the generation of a large amount of new random information , and can be consistent with the general principles of quantum mechanics .
+ the thermalon scenario provides an information buffer for information to escape from the interior which gives a kind of ` firewall ' that will not fall into the hole , as there is a physical mechanism to support it against collapse . in the final state
, the interior space has been crushed into a hyperbolic geometry , effectively a hologram only a few hundred planck lengths thick which holds all the information from the collapsed object and the entanglement partners of hawking photons .
in this section we will identify various timescales associated with the conversion process outlined above , and make estimates for the width of the dynamic trap region for typical astrophysical scenarios of terminal gravitational collapse .
+ the timescale for external accumulation , in which the remaining outer part of the collapsing body undergoes conversion after the initiation of the conversion processl is @xmath166 , and the time taken ( as measured by an external observer ) for the conversion process to form a complete hyperbolic internal region is also @xmath166 .
this is much shorter than the time taken for the collapsed object to decay by hawking like radiation , which will be @xmath167
. the average rate at which string would be produced within a collapsing object against the clock of an external observer would have an average value of @xmath98 independent of the mass @xmath95 of the object .
+ the time taken for the distribution of string around a shell to relax to a uniform configuration will vary from @xmath168 to @xmath169 depending on the degree of anisotropy of the infalling matter .
+ for a ten solar mass object , we have @xmath170x@xmath171 kg , and the @xmath124 scale of the dynamic trap region is equivalent to @xmath172x@xmath173 m , while a ten million solar mass object has @xmath174x@xmath175 m .
in this paper we have identified an accelerating excitation ( the`thermalon excitation ' ) of the heterotic string vacuum , which could propagate consistently in a spacetime background of the kind that would be found in gravitational collapse , allowing the formation of a configuration without a closed horizon .
+ there appears to be a viable mechanism by which the energy released in extreme gravitational collapse may be converted to thermalons , which would accumulate to produce a region of a high temperature string phase in the @xmath0 x @xmath0 and @xmath1 string models
. this would provide away of braking the motion of infalling matter and leading to an endpoint free of event horizons or singularities .
+ a possible resoultion of the apparent conflict between quantum mechanics and the generation of the hawking entropy through an entanglement between the short and long string sectors has been proposed .
+ the mechanism proposed may also give other benefits in confirming the dynamical consistency of string theory by making the string spectrum stable against horizon formation .
bearing in mind the fictitious nature of the thermalon , and the dependence of thermal effects upon the observer , this may be summarised as proposing that the resolution of the horizon problem raised in @xcite is that the consistency of string theory is related to the emergence of coherent string tower effects in strong gravitational fields . + as no event horizon
is formed , the problems of cross horizon entanglement arising from conventional gravitational collapses are avoided @xcite .
+ the scenario presented here would also avoid the radical violation of time reversal symmetry that is involved in admitting conventional black holes but not their time reversed counterparts .
+ although we have concentrated on the schwarzschild case in 4 dimensions , similar results should apply without spherical symmetry and in different numbers of uncompactified dimensions .
in particular , the shell formation mechanism does not rely on strict spherical symmetry and should be a robust and generic feature of extreme gravitational collapse in heterotic string models .
the author would like to thank dan waldram for useful discussions , and nick mavromatos and steven duplij for helpful comments and suggestions .
+ r. m. wald , `` general relativity '' , university of chicago press ( 1984 ) .
+ j. r. oppenheimer and h. snyder , on continued gravitational contraction " , physical review 56 ( 5 ) , 455 ( 1939 ) .
+ j. a. orosz et al . ,
`` the mass of the black hole in cygnus x-1 '' , astrophysical journal 742 , 84 ( 2011 ) .
+ r. bender et al . ,
hst stis spectroscopy of the triple nucleus of m31 : two nested disks in keplerian rotation around a supermassive black hole " .
astrophysical journal 631 ( 1 ) , 280 ( 2005 ) .
+ a. almheiri , d. marolf , j.polchinski and j. sully ,
black holes : complementarity or firewalls ? " , arxiv:1207.3123 ( 2103 ) .
+ l. braunstein ,
black hole entropy as entropy of entanglement , or it s curtains for the equivalence principle " , arxiv:0907.1190v1 [ quant - ph ] . s. l. braunstein , s. pirandola and k. z.yczkowski , entangled black holes as ciphers of hidden information , " phys
110 , 101301 ( 2013 ) [ arxiv:0907.1190 [ quant - ph ] ] .
+ l. susskind , `` some seculations about black hole entropy in string theory '' , arxiv : hep - th/9309145 ( 1993 ) .
+ r. penrose , gravitational collapse and space - time singularities " , physical review letters 14 ( 3 ) , 57 ( 1965 ) .
+ s. w. hawking and g. f. r. ellis , `` the large scale structure of space time '' , cambridge university press ( 1973 ) .
+ w. g. unruh ,
notes on black - hole evaporation " , physical review d 14 ( 4 ) : 870 ( 1976 ) .
+ r. hagedorn , `` statistical thermodynamics of strong interactions at high energies '' , nuovo cimento suppl .
3 , 147186 ( 1965 ) .
+ m. hewitt , `` strings and gravitational collapse '' , physics letters b309 264 ( 1993 ) .
+ a. strominger and c. vafa , `` microscopic origin of the bekenstein - hawking entropy '' , physics letters b 379 ( 14 ) , 99 ( 1996 ) .
+ j. maldacena , `` black holes in string theory '' , arxiv : hep - th/9607235 ( 1996 ) .
+ s. w. hawking , `` black holes and thermodynamics '' , physical review d13 , 191 - 197 ( 1976 ) .
+ d. j. gross , j. a. harvey , e. j. martinec and r. rohm , `` heterotic string theory .
1 . the free heterotic string , '' nuclear physics b 256 , 253 ( 1985 ) .
+ j. polchinski , `` open heterotic strings '' , arxiv : hep - th/0510033 ( 2005 ) .
+ j. j. atick and e. witten , `` the hagedorn transition and the number of degrees of freedom of string theory '' , nuclear physics b 310 , 291 ( 1988 ) .
+ b. sathiapalan , `` vortices on the string world sheet and constraints on toral compactification '' , physical review d35 , 3277 ( 1987 )
. + k.h . obrien and c.i .
tan , `` modular invariance of thermopartition function and global phase structure of heterotic string '' , physical review d36 , 1184(1987 ) .
+ m. hewitt , `` vacuum instability and gravitational collapse '' , arxiv : hep - th/0211037(2002 ) .
ginzburg and l.d .
landau , zh .
20 , 1064 ( 1950 ) + n.d .
birrell and p.c.w .
davies , quantum fields in curved space " , cambridge university press ( 1984 ) .
+ j. madore , the fuzzzy sphere " , classical and quantum gravity 9 , 69 ( 1992 ) .
+ g. thooft , quantization of point particles in ( 2 + 1)-dimensional gravity and spacetime discreteness " , classical and quantum gravity 13 , 1023 ( 1996 ) .
+ o.lunin and s.d.mathur , ads / cft duality and the black hole information paradox " , nuclear physics b623 , 342 ( 2002 ) . | the thermal duality of @xmath0 x @xmath0 and @xmath1 heterotic string theories may underpin a mechanism that would convert the kinetic energy of infalling matter during gravitational collapse to form a region of a hot string phase that would expel gravitational gradients .
this phase would be the continuation of a ginzburg - landau like superconductor in the euclidean regime . in this scenario , there would be no event horizon or singularity produced in gravitational collapse .
solutions are presented for excitations of the string vacuum that may form during gravitational collapse and drive the transition to the hot phase .
the proposed mechanism is developed here for the case of approximately spherical gravitational collapse in 4 uncompactified spacetime dimensions . a way to reconcile the large entropy apparently produced in this process with quantum mechanics
is briefly discussed . in this scenario ,
astrophysical objects such as stellar or galactic cores which have undergone extreme gravitational collapse would have converted to regions of this hot string phase .
the relationship of this proposal to the ` firewall paradox ' is noted .
+ pacs numbers : 11.25.sq , 11.25.mj , 04.70dy . | <s>[INST]black holes @xcite are generally accepted as possible endpoints of gravitational collapse .
oppenheimer and snyder predicted the formation of black holes in some stellar collapses @xcite , and for some astrophysical situations there is no generally accepted mechanism to prevent the formation of a black hole .
indeed there are strong candidate objects to have reached this stage of compression among supernova remnants @xcite and galactic cores @xcite .
we wish to propose that there is a mechanism in the @xmath0 x @xmath0 and @xmath1 heterotic string theories which would avert horizon formation in all cases where no other mechanism comes into play , with regions of a hot string phase forming instead of black holes .
the scenario which is proposed would also resolve the recently noted ` firewall paradox ' @xcite , @xcite in a radical way . here
, quantum mechanics and the equivalence principle are both respected , but the black hole complementarity principle @xcite is abandoned .
an infalling observer would indeed encounter a kind of ` firewall ' as novel processes rooted in thermal duality are triggered .
+ the process of black hole formation in general relativity was shown to be generic in the penrose singularity theorem @xcite .
the scenario in general relativity is summarised by a penrose diagram with all world lines which cross the horizon meeting a spacelike singularity set within a finite time .
penrose identified @xcite a point of no return after which a singular endpoint can not be averted ( except possibly by invoking negative energy ) as the formation of a closed trapped surface @xcite .
it is just prior to the formation of such trapped surfaces that the mechanism proposed in this paper would come into play , circumventing the formation of horizons
. the causal structure of spacetime would then be isomorphic to that of minkowski space .
+ the necessity of a singularity within a black hole can be understood as follows .
if we look at a forming black hole as a particle accelerator , suppose that two particles ( e.g. electrons ) falling in from opposite sides could collide .
at the collision , since both particles have timelike worldlines , the centre of mass energy of the two particles would take some finite value @xmath2 .
however , in the reference frame of an observer at the centre of mass , the kinetic energy of the particles will already have exceeded @xmath2 ( and indeed any finite value ) during the collapse . to avoid the possibility of such a contradiction
, the causal structure of spacetime must make any such encounter impossible , and this is realised by the presence of the singularity which enforces a spacelike separation of the particle worldlines to their ends . + towards the singularity , an unboundedly large energy is compressed within an unboundedly small volume @xcite .
a natural conjecture would be that high energy effects ( perhaps related to string theory ) would intervene in this state of high compression to resolve the singularity , as the conditions are reminiscent of a time - reversed version of those prevailing in the early universe .
however , the mechanism which is thought to resolve the singularity at the beginning of time predicted by the hawking singularity theorem @xcite , namely inflation , relies on negative pressure filling boundaryless spatial hypersurfaces . as the collapsing object does not fill space , the negative pressure needed to support rapid deflation would have no support at the object s surface .
the best strategy for averting a singularity in the case of collapse thus seems to be to prevent the formation of a closed horizon .
+ can quantum mechanics , and in particular string theory provide such a mechanism ? near the horizon the temperature apparently diverges for a static observer held in place at a fixed distance from the horizon , due to the unruh effect @xcite .
however , string theory apparently implies that there is a maximum temperature ( the hagedorn temperature @xcite ) suggesting that horizon formation may be averted by string effects @xcite or be taken to be equivalent to a string theoretic picture @xcite . in themselves
, however , these observations do not provide the mechanism for braking the fall of matter during gravitational collapse which would be needed to avert horizon formation .
+ string and brane state counting for near critical holes @xcite , @xcite in type ii string theory gives agreement with the bekenstein - hawking entropy @xcite , and can be pictured as being due to string or d brane degrees of freedom near the horizon @xcite .
the analyses of @xcite , @xcite rely on counting d brane degrees of freedom , which are absent in the @xmath0 x @xmath0 heterotic string regime @xcite , due to the absence here of d branes and the unbreakable nature of e8 strings for topological reasons @xcite .
the suggested string - hole equivalence would thus have to be realised in a different way for @xmath3 x @xmath0 strings .
the possibility of such a connection seems worth studying for two reasons : the string - hole correspondence seems likely for reasons of consistency to hold for all regions of m theory , including @xmath0 x @xmath0 strings , and more pragmatically because this kind of string model is more likely to be relevant to astrophysical gravitational collapse . + a closer analysis of the hagedorn transition @xcite , @xcite
, @xcite indicates the possibility of a high temperature string phase for heterotic strings characterised by the formation of a condensate .
the heterotic nature of the strings is essential to this mechanism .
this phase was first noted for its possible relevance to gravitational collapse in @xcite . in @xcite
it was suggested that the endpoint of gravitational collapse would be a region of the high temperature phase , having a hyperbolic internal spatial geometry , allowing the entropy to be reconciled with the hawking value , which is related to the surface area rather than the euclidean volume .
a non - local quantum mechanical mechanism which would allow conversion of infalling matter to the high temperature string phase through the spontaneous formation of shells of the high temperature string phase was also proposed in @xcite .
it was conjectured that the nucleation of such shells would take place where the surface gravity reaches the duality temperature , giving a close relationship between nucleation sites and proximity to the point where penrose surfaces would otherwise form .
+ the purpose of this communication is to replace the shell nucleation mechanism of @xcite , which relies on no - local quantum correlations around the collapsing object with a process that works locally to convert the kinetic energy of infalling matter into thermal excitations of the string vacuum .
the conditions for thermalon excitation during an astrophysical gravitational collapse are identified , and the mechanism by which the kinetic energy of infalling matter is converted to the thermalized energy of the high temperature string phase is elucidated .
it will be shown that the conditions under which the conversion of energy to thermalon excitations and thence to high temperature string phase would occur only in final stages of gravitational collapse , and that the normal vacuum would be stable against such processes . a dissipative mechanism for the thermalisation of the kinetic energy of infalling matter is proposed , which could lead to a final state almost in thermal equilibrium with the surrounding vacuum ( with only hawking like radiation escaping ) and which would not have an event horizon . a possible relationship between thermodynamic thermalon entropy and an entropy of entanglement between short and long string sectors
will be proposed which could enable the generation of the hawking entropy to be reconciled with conventional quantum mechanical state evolution .
+ the thermal equilibrium between the high temperature string phase and normal vacuum indicates that the entropy of the high temperature string phase should agree with the hawking value to leading order in @xmath4 ( @xmath5 is the planck mass ) .
it thus seems that a microscopic model of the hawking entropy may also be possible for @xmath0 x @xmath0 strings .
the approach taken in this paper addresses the issue of string - hole correspondence in a different regime and with different methods to @xcite , @xcite .
the latter invoke supersymmetry to carry out an evaluation of the number of microstates by direct enumeration , in a way which is independent of thermodynamic arguments .
this takes place in a critical limit , where the hole becomes cold .
in contrast , the current paper relies on properties of the heterotic thermalon , which intrinsically breaks supersymmetry
supersymmetry is necessarily broken in a thermal ensemble , and indeed the thermalon does not even belong to a supersymmetry multiplet .
agreement with the hawking entropy value follows directly to leading order from the thermodynamic equilibrium between the hot phase and the ambient normal vacuum , although the counting of string microstates can only be inferred at this stage . again in contrast to the cases considered in @xcite , @xcite it is the approximately schwarzschild case which is easiest to analyse for the thermalon mechanism , rather than the critical ones .
the justification of the hawking entropy in such contrasting scenarios seems to support the conjecture that it should be valid for all m theory cases .
the partition sum @xmath6 at a finite temperature may be calculated by compactifying time in an imaginary direction .
this introduces a winding mode in string theory @xcite , which we will refer to as the thermalon .
this situation may be represented by a compactification of the string target space on a lorentzian lattice .
a change of @xmath7 is represented by a lorentzian transformation @xcite .
the critical points at which the thermalon becomes a tachyon are located where the lorentzian trajectory crosses the circle in the @xmath8 energy plane representing zero mass , and this gives a value for the hagedorn temperature @xcite which agrees with that found by counting string states . for free strings ,
the partition sum @xmath6 for a single string diverges at this temperature .
although the thermalon is , in itself , a fictitious particle it provides an effective theory which summarises the overall effect of the tower of excited string states .
when the continuation is made back to the physical minkowski regime , the interaction of the thermalon field with the background geometry presented below is intended to provide an effective theory which summarises interactions of strings with a condensate of string tower states . for interacting strings ,
the hagedorn temperature is marked by the formation of this condensate .
+ for heterotic strings , of either the @xmath0 x @xmath0 or @xmath1 types , the winding and momentum numbers @xmath9 of the thermalon state which may become a tachyon are @xmath10 .
this is possible because the gso projection is reversed for consistency for the winding state @xcite .
note that the combination of wrapping and momentum quantum numbers for the thermalon around the imaginary time circle is the same as that for left moving heterotic modes .
there is a contrast between the lorentzian trajectories for the thermalon in the non - heterotic and heterotic cases , with the heterotic case exhibiting thermal duality .
the thermalon is a tachyon where its trajectory lies inside the circle ( in the euclidean norm of conformal weights ) representing zero mass . in the non - heterotic case
, the trajectory follows a straight line towards the origin , and the thermalon becomes more tachyonic as the temperature is increased further ( see figure 1 ) .
+ in the heterotic case , the trajectory is a hyperbola , and there is a second critical temperature ( the upper hagedorn point ) with @xmath11 where the trajectory leaves this circle ( see figure 2 ) .
+ similarly to the higgs mechanism where the tachyon is modified by quartic or higher interactions , thermalon interactions may allow a condensate phase to form at high temperatures .
the thermalon would effectively have a positive mass in the condensate phase , so that there would be a finite density of string , string degrees of freedom and entropy in this phase .
+ for an abelian gauge field @xmath12 in a heterotic string theory , the right - moving component is represented by the spacetime index @xmath13 , while the left component is represented by @xmath14 , a left - heterotic winding direction . +
a frame field description of gravity is natural in heterotic string theory , with the graviton @xmath15 and gravitino @xmath16 described using left - moving world and right - moving frame indices .
consider the timelike component of the metric frame field @xmath17 . on wick rotation in the thermal geometry ,
the left index @xmath18 is a winding direction , and the thermalon carries momentum in this direction . at the self - dual point ( @xmath19 )
the combination of wrapping and momentum contributes only to the left - moving conformal weight . here
the relationship between @xmath20 and the thermalon field @xmath21 is the same as that between a @xmath22 gauge field and a charged scalar .
+ continuation to the imaginary time regime makes like charges for this @xmath22 repel .
this will allow us to make a comparison between the frame - thermalon system and a ginzburg - landau superconductor @xcite in the euclidean regime , which will be relevant in the case where @xmath23 is near a global minimum .
+ suppose that we introduce a gravitational gradient , producing a deviation from minkowski geometry but with a timelike killing vector that may be used to define energy and temperature .
the effect of the gravitational gradient is to make length of this killing vector vary , so that @xmath24 , the local size of compact dimension will vary accordingly .
note that although @xmath7 varies locally , its relationship with the gravitational gradient and killing vector length means that the temperature viewed by an external observer is constant . + we will explore the possibility of both strong and weak thermalon excitations in equilibrium with the vacuum .
the unruh effect @xcite , whereby an accelerating rindler observer measures a nonzero temperature proportional to the acceleration @xmath25 indicates that this is possible , as in principle the high temperatures needed for the hagedorn transition may be obtained from high accelerations .
we will show that there are solutions for the heterotic thermalon corresponding to accelerating excitations , which have zero overlap with the horizon .
these excitations would represent alternative thermal string ensembles with a nonzero thermalon condensate , in equilibrium with the normal vacuum .
these solutions are incompatible with a minkowski background , but would provide a way to interpolate between concentric exterior schwarzschild metrics.the possible relevance of these ensembles to gravitational collapse will be explored below .
two ( extreme ) cases will be examined below in detail , for @xmath21 small compared to the string tension scale , and for @xmath21 in the nonlinear region .
in this section , we will investigate the possibility of weak thermalon deformations of minkowski space .
essentially , we will show that there is an obstruction to the existence of such deformations , due to a warp in the transverse metric across a solution with nonzero @xmath21 . on gauging away the phase of @xmath21 in the euclidean regime and continuing to minkowski space
, the lagrangian for the thermalon takes the form @xcite for small @xmath21 @xmath26 where the squared mass @xmath27 is given by @xmath28 the higher order terms in @xmath21 describe the effects of string interactions . in general , the higher order terms can not be calculated in the absence of a string field theory formalism . however , at the critical points where @xmath29 a constant @xmath21 corresponds to on - shell thermalons .
now on - shell , the 4 thermalon scattering amplitude is accessible to perturbation theory , and takes a form similar to the virasoro - shapiro amplitude , giving a nonzero value for @xmath30 which is the same at the two critical points by @xmath31 duality .
the effective @xmath32 between the critical points will be relevant to the issue of thermalon condensation , and as long as this is non - zero a finite condensate will form .
+ in this section we will consider the case of of excitations with small values of @xmath33 in a flat minkowski background , for which the non - linear terms ( which are of higher order in @xmath33 ) may be neglected ( and so the uncertainty regarding their values is not relevant ) .
this we will call the regime of weak excitations .
the case for larger values of @xmath33 will be considered below , to build up a picture of how thermalon condensation may progress during gravitational collapse .
+ in this regime we will seek solutions which appear static to a rindler observer , which can be in thermal equilibrium with the surrounding vacuum at a position dependent unruh temperature .
it should be emphasised that we do not take such accelerated observers to have a privileged status beyond the accelerated excitation solutions taking a simple form in such frames . from the standpoint of general covariance , in such a frame
we can take @xmath21 to be a scalar , although it should be remembered that this is essentially a shorthand for the entity @xmath34 or equivalently @xmath35 , as @xmath36 is needed to define the local temperature and wick rotation .
if @xmath37 is the vector field dual to @xmath36 , then the local energy and temperature are defined relative to the killing vector @xmath38 .
+ note that in minkowski space the choice of @xmath37 is arbitrary due to lorentz invariance .
however , the conjecture that we will develop below is that thermalon deformations of the ordinary vacuum are only relevant where @xmath37 is parallel to a timelike killing vector , and in the case of interest here , of near spherically symmetric collapsed objects , this will be essentially unique .
+ using rindler coordinates @xmath39 @xcite for such an accelerated observer , the inverse temperature @xmath7 depends on the distance @xmath40 from the horizon as @xmath41 , and the effective squared mass of the thermalon @xmath27 varies accordingly , as @xmath42 for thermal equilibrium @xmath43 = 0 , and for a plane wave solution @xmath44 , and the differential equation for @xmath21 becomes @xmath45 near the horizon , @xmath46 , we have @xmath47 and ( [ de ] ) simplifies to a bessel form and the solution which is finite at @xmath48 has @xmath49 likewise it is easy to verify that @xmath21 will have a gaussian cut - off at large @xmath40 . in fact , the exact solution of ( [ de ] ) which is finite at @xmath48 is @xmath50 where @xmath51 is an arbitrary small parameter . here
@xmath51 has the same dimensions as @xmath21 ( energy ) , and the solution is shown in figure 3 .
the simple form of @xmath21 will enable us to evaluate various integrals of interest below .
+ note that for this solution , @xmath21 takes its maximum value at @xmath52 where @xmath53 , the self - dual value .
the solution for @xmath21 vanishes at the horizon , and the solution is essentially confined to @xmath54 , as @xmath21 diminishes rapidly beyond this point . + for comparison , let us compare this solution to the situation for a non - heterotic thermalon , for example that for the bosonic string . here , @xcite
@xmath55 and the solution which is finite for @xmath46 has @xmath56 which tends to a non - zero value as @xmath46 and the exact solution , with @xmath57 , may be given in terms of a laguerre polynomial of fractional order as @xmath58 whereas this solution has the same gaussian cut - off at large @xmath40 as for the heterotic case , the thermalon excitation is not now excluded from the horizon .
thus thermal duality can be seen to be responsible for confining the weak thermalon excitation solution away from the horizon ( the other independent solution diverges at horizon and is unphysical ) which would be relevant in the environment of a gravitationally collapsed object .
the heterotic thermalon excitation is thus kept from falling into the horizon .
an ` excitation trap ' effect is thus present in this case .
although the solution presented above was calculated using a special reference frame , the excitation would have properties such as the distortion of the metric produced by back reaction on which all observers would agree .
this back reaction will be seen to produce a transverse warp , presenting an obstruction to embedding in a minkowski background .
+ the thermalon excitation solution in the previous section apparently accelerates through minkowski spacetime
. this would be mechanically possible if the overall inertia of the solution vanished , with positive mass on the forward side , negative mass on the following side and positive pressure in between acting against the inertia ( positive and negative ) on either side .
we will now look in more detail at the back reaction of the thermalon excitation ` wall ' solution on the metric .
it will turn out that the excitation has a positive overall gravitational mass .
acceleration of a configuration with positive mass through minkowski space is clearly impossible , as the conservation of momentum and energy would be violated . rather than inhabiting a conventional minkowski background
, it will be shown that the thermalon excitation wall interpolates between two minkowski regions with a transverse warp factor between them .
+ the einstein field equations are given by @xmath59 where we have retained newton s constant @xmath60 as we are working in string tension units .
we will work to first order in @xmath51 , so that the solution above remains valid .
introducing notation for the @xmath21 kinetic term @xmath61 the einstein equations become , on implementing the thermal equilibrium constraints @xmath62 and re - arranging , as follows ( where v is the poential ) : @xmath63 @xmath64 and similarly for @xmath65 and @xmath66 .
+ now from ( [ rzz ] ) we have a local gravitational source @xmath67 given by , with @xmath68 @xmath69 and introducing @xmath70 gives @xmath71 and now @xmath72 as @xmath73 introducing a factor of @xmath74 to compensate for the redshift seen by an observer at the arbitrary location @xmath75 gives @xmath76 and @xmath77 which is finite and positive .
note that @xmath13 is zero at @xmath78 and is negative to the high temperature side of this point and positive to the low temperature side .
+ now the warp factor across the wall can be calculated by an application of the equivalence principle . if an area @xmath79 behind the wall matches an area @xmath80 ahead of the wall , and we define the warp factor @xmath81 by @xmath82 then with @xmath83 the acceleration due to gravity in the rindler frame , @xmath84 where the volume @xmath85 extends across the comparison surface and between @xmath86 and @xmath87 . now letting @xmath88 and @xmath89 gives @xmath90 and finally @xmath91 this warp factor is realised by a hyperbolic spatial geometry within the thermalon ` wall ' , which is another aspect of the back reaction , described by ( [ r11 ] ) .
this hyperbolic geometry is a feature that the weak thermalon wall solution shares with the strong @xmath21 solutions discussed below .
+ although the plane wave solution is not viable in an ordinary minkowski space background , where conservation of energy requires a counter - factual warp factor , this analysis does suggest the possibility of a standing wave solution in a strong gravitational field , which we will examine next .
the exterior schwarzschild metric is given by @xmath92 where @xmath93 is the schwarzschild radius , @xmath94 at which there is an event horizon . for large @xmath95
, we will assume that the background is sufficiently flat that the hagedorn transition points are not significantly affected ; the results below will be qulitatively similar even if these points are perturbed a little by the background
. we will use this exterior schwarzschild metric , but will work in a region excluding the horizon .
we will argue that in fact a closed horizon will never form due to thermalon effects .
+ for a thermalon deformation to be a viable solution , it must interpolate between concentric ( approximately ) schwarzschild solutions , with the thermalon wrapping aligned with ( the wick rotation of ) a timelike killing vector to give a standing thermalon excitation just outside the virtual horizon . for a large black hole ,
the surface is almost flat and the plane wave thermalon solution given above will locally be a good approximation to the true solution .
to leading order in @xmath96 , the area of a static surface at the self - dual temperature @xmath97 will differ from the area of the horizon by a fixed amount ( independent of @xmath95 ) of @xmath98 , due to the approximately hypercylindrical form of the spatial metric .
the area difference @xmath99 that comes from the warp factor @xmath81 of the static thermalon excitation will therefore provide an interpolation to another schwarzschild metric to the exterior .
the horizon area that would be predicted from the exterior solution is increased by @xmath99 compared to the actual horizon area .
this shows the possibility of thermalons shrinking the actual horizon area for a given mass .
we will argue below that in fact a closed horizon will never form as the energy present will be converted to thermalon form during collapse .
whereas this altered black hole solution can be seen as a deformed version of the conventional black hole , in the scenario below the black hole is replaced completely by a region of thermalon condensate .
+ the warp factor of the thermalon solution means that thermalon deformations of the minkowski vacuum are not possible . only in the near horizon geometry
will coherent and persistent thermalon excitations be possible .
the persistence of strongly accelerated thermalon traps in these solutions is the key to the possibility of persistent deformations , rather than simply the presence of curvature ( which is small for high mass backgrounds ) .
+ our basic conjecture is that a particle of energy @xmath100 ( measured from infinity ) falling through a schwarzschild geometry will begin to nucleate thermalons when the geometry to its outside locally acquires a timelike killing vector with critical acceleration .
thereafter , this condition will be maintained by kinetic energy being fed from the particle to increase the thermalon density in the static trap .
this process is thermodynamically favoured because of the large amount of entropy released , which we will show in the next section will be esentially the hawking entropy for an equivalent black hole .
the basis of hawking s analysis of the entropy of black holes is the relationship @xmath101 where @xmath7 is the vacuum temperature , which expresses the principle that energy emitted by a black hole is completely thermalised .
since the thermalon excitation is in thermal equilibrium with the vacuum , this relationship should also apply to our solution @xmath102 interpreted either as a static or a dynamic excitation . now
( [ s ] ) may be expressed in terms of the free energy as @xmath103 or equivalently @xmath104 now @xmath105 consists of a kinetic part and a potential part , which can be evaluated for the solution ( [ sol ] ) by direct integration .
first , the kinetic part per unit area is given by @xmath106 and inserting the solution ( [ sol2 ] ) we have @xmath107 the potential part of @xmath108 per unit area is @xmath109 and using @xmath110 we have @xmath111 and @xmath112 giving @xmath113 so that @xmath114 confirming the thermal nature of the excitation .
for a static excitation bounded by the horizon we will have a differential form of the hawking area law @xmath115 +
the process of conversion of kinetic to thermalon energy will proceed from the outside inwards . due to the large release of entropy in thermalon condensation outlined above , the motion of an infalling particle is essentially determined by the condition that the static surface gravity is regulated by thermalon condensation .
the kinetic energy of the particle reduces with the enclosed area to mainatin a constant static surface gravity , and the thermalon warp increases to compensate , so that the thermalon region continues to interpolate between the schwarzschild solutions to the inside and outside of the particle . note that the term involving the time derivative of @xmath21 in the thermalon action will be suppressed by a factor
@xmath116 compared to the other terms .
+ the distance to fall for a particle of mass @xmath100 between the start of thermalon nucleation and merger with an existing collapsed object of mass @xmath95 is @xmath117 , and during this the kinetic energy is reduced from @xmath118 to @xmath98 ( note the squared reduction factor , so that the particle undergoes a double deceleration compared to the local surface gravity ) . +
although the particle spectrum is lorentz invariant , the thermalon modes that they couple to during the conversion process are not , as the possibility of thermalon deformations is dependent on the formation of static traps , which are not lorentz invariant .
+ assume that the wavefunction for a particle of mass @xmath100 is spread out transverely over an area @xmath79 .
the change of the horizon area on adding the mass @xmath100 is @xmath119 .
and we assume that @xmath120 ( so that there is a small relative area change ) . the area change for thermalon parameter @xmath21 over the area @xmath79 scales like @xmath121 , so that @xmath122 and @xmath123 , and the weak thermalon regime applies , so that a consideration of higher order terms in @xmath21 is not necessary in dealing with the particle conversion process . + for the plane wave thermalon solution to be relevant , it is only necessary that the infalling particle wavefunction be spread out on a scale large compared to @xmath124 , which is roughly of nuclear dimensions for a stellar mass collapsing object , and of atomic scale for a galactic core object . if the infalling particle can not be assumed to be delocalised , then the following observation is relevant . during its fall from the initiation of thermalon condensation to an existing thermalon region , through a distance of @xmath125 , the thermalon green s function can spread over an area @xmath126 , comparable to the increase in surface area of the condensate region , so that the weak @xmath21 limit is valid for infalling particles through most of their trajectory .
+ the production of thermalons due to the deceleration of the nucleating particle may arise through a larmor like radiation process . the radiated power would in that case scale as @xmath127 which will equal @xmath128 for relativistic motion , so that @xmath129 .
interactions between thermalons and light particles that could generate thermalon bremsstrahlung are accessible on shell through conformal field theory , and a self - consistent interaction berween light particles and thermalons which would support the conversion process may be possible .
+ it may be noted that the interaction between matter falling through the excitation region is similar to that of particles moving through a detector e.g. a cloud chamber . in both cases a dissipative process converts part of the kinetic energy of the particle into a trace carrying information about the particle s trajectory . + a freely falling observer , on passing into the conversion region , would also be subject to these processes , and would effectively be converted into a rindler observer at a string tension scale acceleration and temperature and thus would experience an encounter with a kind of ` firewall ' in the conversion region .
once a closed static trap has formed within the collapsing body , the kinetic energy of infalling particles will undergo thermalon conversion and increase the value of @xmath21 there .
as @xmath21 strengthens , it is driven towards the non - linear region , where the small @xmath21 approximation used above no longer applies .
eventually a stationary point in the @xmath21 potential is approached and a phase transition should occur .
the region where @xmath21 approximates the stationary value will thereafter expand , rather than the value of @xmath21 increasing further .
we will first examine the bulk properties of this phase by looking for a space filling solution with constant @xmath21 .
for this space - filling solution , a low energy approximation is valid for the bulk region because there the space and time derivatives of @xmath21 are small .
+ if we assume the presence of higher order terms in the thermalon potential , there will be a minimum for a given @xmath7 .
further , for the heterotic models there will be a space filling solution with constant @xmath7 and @xmath21 .
let @xmath130 be the point in @xmath131 space where @xmath132 has its global minimum .
this will exist between the upper and lower hagedorn temperatures , by the mean value theorem .
then from ( [ rzz ] ) we have @xmath133 and also @xmath134 allowing a solution with @xmath135 .
for @xmath21 constant in space , and with @xmath136 we have from ( [ r11 ] ) @xmath137 where @xmath138 and similarly for @xmath65 and @xmath66 , giving a hyperbolic spatial geometry . @xmath139 and a space - time interval @xmath140 with @xmath141 + it
can be seen that the spatial geometry must undergo a radical radial deflation during the conversion to the high temperature string phase .
+ in the effective theory with real @xmath21 , if a gravitational gradient is introduced , it will produce a gradient in @xmath7 .
any gradient of @xmath7 around @xmath142 will produce a polarization of @xmath13 with positive source on the high @xmath7 side and negative source on the low @xmath7 side since @xmath143 has a maximum at the stable point @xmath144 .
this provides the gravitational london current required to expel gravitational gradients ( up to some breakdown point ) .
the london response is given by @xmath145 which changes sign at @xmath146 .
+ we conjecture that finite regions of this gravitationally superconducting phase can exist , with an outer boundary layer with a positive gravitational source , interpolating between the high temperature string phase and the surrounding vacuum , with which it will be in thermal equilibrium . any gravitational source in the exterior
is effectively screened so that it appears only in this boundary layer .
+ as well as the thermalon condensate , the high temperature phase will be expected to contain a finite density of string excitations , due to the positive mass of the thermalon mode around the ground state .
because of the short range of gravity , which is effectively restricted to the penetration depth , the gravitational field of these strings is screened , allowing them to exist without generating event horizons .
this indicates a basic role for the thermalon mechanism in maintaining dynamical consistency for the heterotic string models , as otherwise most string states would be hidden by event horizons @xcite .
the string spectrum is thereby restored , with long strings existing in an alternative phase in a way reminiscent of colour confinement in qcd . as explained below , the emergence of these long string excitations in the condensate phase opens the possibility of an entanglement between long and short string sectors being set up during collapse and conversion , which may allow a reconciliation between the generation of the hawking entropy and the principles of quantum mechanics .
+ due to the hyperbolic geometry of the high temperature string phase interior , the volume of the bulk is proportional to the surface area for high mass .
this makes the bulk thermodynamic properties of the high temperature string phase region , and particular the entropy , consistent with the area scaling of the hawking entropy .
the hilbert space for such a region might correspond to a field theory on a ` fuzzy sphere ' @xcite , @xcite .
a stringy collapsed state without a horizon or singularity was proposed in @xcite as a resolution of the black hole information paradox . + during a collapse , a shell region of the high temperature string phase once formed will expand both outwards , as infalling matter reaches the outer surface of the shell drawing an extended region of thermalon condensation in behind it , and inwards as the contracting inner surface of the shell engulfs matter to the inside .
+ in a realistic collapse , concentric shells may form , but these will merge as the collapse progresses . these processes will continue until a stable , near spherical configuration is attained , with the interior filled with the high temperature string phase .
+ the boundary region of a shell is almost completely transparent as the thermalon condensate does not carry electric , colour or other charges .
we conjecture that the effective opacity builds with shell thickness , as the excitation strings hosted by the shell will interact with normal matter .
the combination of exponential extinction with the logarithmic dependence of the shell thickness with area ratio indicates that the resulting transmission coefficient should be a power of @xmath147 , the ratio of its outer to inner surface areas . as the inner surface of the shell shrinks , the limit of a black body is approached .
+ overall , the conversion process of kinetic energy to thermalon excitations to high temperature string phase provides a dissipative mechanism by which the energy released by gravitational collapse produces a hot final state without horizons or singularities .
the entropy of this final state , relative to an observer to whom only short string states are available for measurement , matches the hawking entropy , which is here generated during the braking process .. the large hawking entropy in this context means that the relatively small number of ordered collapsing states will end up in final states whose bulk properties are the same as those of a very much larger number of other possible states in the high temperature string phase .
+ note that the thermalon has no supersymmetry partner , so the screening mechanism gives mass to the @xmath36 component of gravity , but not to the gravitino , illustrating that thermal effects do not respect supersymmetry .
reconciling the process of gravitational collapse with quantum mechanics and quantum information theory presents two problems : what happens to the information stored in the collapsing body , and where does the very large amount of apparently random information produced during the hawking evaporation process come from ? in our scenario , the first problem is easily resolved , as there is no singularity , and the infalling matter is simply transformed into another form .
however , our analysis of the thermalon indicates that the high temperature string phase will have esentially the same large area dependent entropy as in the hawking case .
what is the microscopic description of this entropy , and how can it arise in a way consistent with quantum mechanics ?
+ entropy is related to incomplete information , or access to only part of a complete system . in quantum mechanics ,
this can be expressed through the concept of entanglement entropy . if the state of the system under consideration is ideally isolated from its envionment
, we may write @xmath148 where @xmath149 represents the total state in hilbert space , @xmath150 the state of the system and @xmath151 the state of the environment .
in general , however there will be entanglement between the system and environment so that @xmath152 and if only the system @xmath153 is accessible to measurement , it has an effective density matrix @xmath154 and our incomplete knowlwdge of the pure state @xmath149 is quantified by the entropy @xmath155 . + the thermalon entropy calculated in thermodynamic terms above should have a microscopic quantum description , and in particular the large thermalon entropy generated during the conversion process should be consistent with the preservation of a pure overall state @xmath149 . before the conversion process begins ,
the short and long string sectors are essentially decoupled , and the long string sector is in the ground state so that @xmath156 where @xmath157 represent multiple tensor indices related to a fuzzy sphere related decomposition @xcite , @xcite into angular momentum modes , with the order of @xmath14 proportional to the inner surface area of the shell and @xmath158 to the difference between outer and inner surface areas - the orders of @xmath159 and @xmath160 together are proportional to the outer surface area .
if a similar decomposition is made for @xmath161 , the conversion process will be represented by a unitary transfromation @xmath162 on the states @xmath163 and @xmath164 .
the factorisation @xmath165 no longer holds , and the short string sector now has an entanglement entropy proportional to the difference in surface area between the inside and outside of the shell .
this will increase as the conversion process proceeds , eventually reaching a value proportional to the outer surface area .
this provides a mechanism by which the short string ( field ) sector can acquire an area related entanglement entropy which , for consistency with the thermodynamic analysis above , should coincide with the hawking entropy .
+ the long strings would provide the heat bath in the interior , which would interact with photons etc .
( via biquadratic and higher order interactions ) to maintain a temperature consistent with continuity with the external vacuum .
+ as the entropy apparently generated by the conversion process is mainly due to a conversion of entanglement , the form of the entropy is approximately universal and its thermal nature , as shown in the production of ( the equivalent of ) hawking radiation , has its origin in the entanglement entropy of the near ( virtual ) horizon region . in this way
, the evolution of the system does not require the generation of a large amount of new random information , and can be consistent with the general principles of quantum mechanics .
+ the thermalon scenario provides an information buffer for information to escape from the interior which gives a kind of ` firewall ' that will not fall into the hole , as there is a physical mechanism to support it against collapse . in the final state
, the interior space has been crushed into a hyperbolic geometry , effectively a hologram only a few hundred planck lengths thick which holds all the information from the collapsed object and the entanglement partners of hawking photons .
in this section we will identify various timescales associated with the conversion process outlined above , and make estimates for the width of the dynamic trap region for typical astrophysical scenarios of terminal gravitational collapse .
+ the timescale for external accumulation , in which the remaining outer part of the collapsing body undergoes conversion after the initiation of the conversion processl is @xmath166 , and the time taken ( as measured by an external observer ) for the conversion process to form a complete hyperbolic internal region is also @xmath166 .
this is much shorter than the time taken for the collapsed object to decay by hawking like radiation , which will be @xmath167
. the average rate at which string would be produced within a collapsing object against the clock of an external observer would have an average value of @xmath98 independent of the mass @xmath95 of the object .
+ the time taken for the distribution of string around a shell to relax to a uniform configuration will vary from @xmath168 to @xmath169 depending on the degree of anisotropy of the infalling matter .
+ for a ten solar mass object , we have @xmath170x@xmath171 kg , and the @xmath124 scale of the dynamic trap region is equivalent to @xmath172x@xmath173 m , while a ten million solar mass object has @xmath174x@xmath175 m .
in this paper we have identified an accelerating excitation ( the`thermalon excitation ' ) of the heterotic string vacuum , which could propagate consistently in a spacetime background of the kind that would be found in gravitational collapse , allowing the formation of a configuration without a closed horizon .
+ there appears to be a viable mechanism by which the energy released in extreme gravitational collapse may be converted to thermalons , which would accumulate to produce a region of a high temperature string phase in the @xmath0 x @xmath0 and @xmath1 string models
. this would provide away of braking the motion of infalling matter and leading to an endpoint free of event horizons or singularities .
+ a possible resoultion of the apparent conflict between quantum mechanics and the generation of the hawking entropy through an entanglement between the short and long string sectors has been proposed .
+ the mechanism proposed may also give other benefits in confirming the dynamical consistency of string theory by making the string spectrum stable against horizon formation .
bearing in mind the fictitious nature of the thermalon , and the dependence of thermal effects upon the observer , this may be summarised as proposing that the resolution of the horizon problem raised in @xcite is that the consistency of string theory is related to the emergence of coherent string tower effects in strong gravitational fields . + as no event horizon
is formed , the problems of cross horizon entanglement arising from conventional gravitational collapses are avoided @xcite .
+ the scenario presented here would also avoid the radical violation of time reversal symmetry that is involved in admitting conventional black holes but not their time reversed counterparts .
+ although we have concentrated on the schwarzschild case in 4 dimensions , similar results should apply without spherical symmetry and in different numbers of uncompactified dimensions .
in particular , the shell formation mechanism does not rely on strict spherical symmetry and should be a robust and generic feature of extreme gravitational collapse in heterotic string models .
the author would like to thank dan waldram for useful discussions , and nick mavromatos and steven duplij for helpful comments and suggestions .
+ r. m. wald , `` general relativity '' , university of chicago press ( 1984 ) .
+ j. r. oppenheimer and h. snyder , on continued gravitational contraction " , physical review 56 ( 5 ) , 455 ( 1939 ) .
+ j. a. orosz et al . ,
`` the mass of the black hole in cygnus x-1 '' , astrophysical journal 742 , 84 ( 2011 ) .
+ r. bender et al . ,
hst stis spectroscopy of the triple nucleus of m31 : two nested disks in keplerian rotation around a supermassive black hole " .
astrophysical journal 631 ( 1 ) , 280 ( 2005 ) .
+ a. almheiri , d. marolf , j.polchinski and j. sully ,
black holes : complementarity or firewalls ? " , arxiv:1207.3123 ( 2103 ) .
+ l. braunstein ,
black hole entropy as entropy of entanglement , or it s curtains for the equivalence principle " , arxiv:0907.1190v1 [ quant - ph ] . s. l. braunstein , s. pirandola and k. z.yczkowski , entangled black holes as ciphers of hidden information , " phys
110 , 101301 ( 2013 ) [ arxiv:0907.1190 [ quant - ph ] ] .
+ l. susskind , `` some seculations about black hole entropy in string theory '' , arxiv : hep - th/9309145 ( 1993 ) .
+ r. penrose , gravitational collapse and space - time singularities " , physical review letters 14 ( 3 ) , 57 ( 1965 ) .
+ s. w. hawking and g. f. r. ellis , `` the large scale structure of space time '' , cambridge university press ( 1973 ) .
+ w. g. unruh ,
notes on black - hole evaporation " , physical review d 14 ( 4 ) : 870 ( 1976 ) .
+ r. hagedorn , `` statistical thermodynamics of strong interactions at high energies '' , nuovo cimento suppl .
3 , 147186 ( 1965 ) .
+ m. hewitt , `` strings and gravitational collapse '' , physics letters b309 264 ( 1993 ) .
+ a. strominger and c. vafa , `` microscopic origin of the bekenstein - hawking entropy '' , physics letters b 379 ( 14 ) , 99 ( 1996 ) .
+ j. maldacena , `` black holes in string theory '' , arxiv : hep - th/9607235 ( 1996 ) .
+ s. w. hawking , `` black holes and thermodynamics '' , physical review d13 , 191 - 197 ( 1976 ) .
+ d. j. gross , j. a. harvey , e. j. martinec and r. rohm , `` heterotic string theory .
1 . the free heterotic string , '' nuclear physics b 256 , 253 ( 1985 ) .
+ j. polchinski , `` open heterotic strings '' , arxiv : hep - th/0510033 ( 2005 ) .
+ j. j. atick and e. witten , `` the hagedorn transition and the number of degrees of freedom of string theory '' , nuclear physics b 310 , 291 ( 1988 ) .
+ b. sathiapalan , `` vortices on the string world sheet and constraints on toral compactification '' , physical review d35 , 3277 ( 1987 )
. + k.h . obrien and c.i .
tan , `` modular invariance of thermopartition function and global phase structure of heterotic string '' , physical review d36 , 1184(1987 ) .
+ m. hewitt , `` vacuum instability and gravitational collapse '' , arxiv : hep - th/0211037(2002 ) .
ginzburg and l.d .
landau , zh .
20 , 1064 ( 1950 ) + n.d .
birrell and p.c.w .
davies , quantum fields in curved space " , cambridge university press ( 1984 ) .
+ j. madore , the fuzzzy sphere " , classical and quantum gravity 9 , 69 ( 1992 ) .
+ g. thooft , quantization of point particles in ( 2 + 1)-dimensional gravity and spacetime discreteness " , classical and quantum gravity 13 , 1023 ( 1996 ) .
+ o.lunin and s.d.mathur , ads / cft duality and the black hole information paradox " , nuclear physics b623 , 342 ( 2002 ) .[/INST] the thermal duality of @xmath0 x @xmath0 and @xmath1 heterotic string theories may underpin a mechanism that would convert the kinetic energy of infalling matter during gravitational collapse to form a region of a hot string phase that would expel gravitational gradients .
this phase would be the continuation of a ginzburg - landau like superconductor in the euclidean regime . in this scenario , there would be no event horizon or singularity produced in gravitational collapse .
solutions are presented for excitations of the string vacuum that may form during gravitational collapse and drive the transition to the hot phase .
the proposed mechanism is developed here for the case of approximately spherical gravitational collapse in 4 uncompactified spacetime dimensions . a way to reconcile the large entropy apparently produced in this process with quantum mechanics
is briefly discussed . in this scenario ,
astrophysical objects such as stellar or galactic cores which have undergone extreme gravitational collapse would have converted to regions of this hot string phase .
the relationship of this proposal to the ` firewall paradox ' is noted .
+ pacs numbers : 11.25.sq , 11.25.mj , 04.70dy . </s> |
the study of couette flow in a rectangular channel of an electrically conducting viscous fluid under the action of a transversely applied magnetic field has immediate applications in many devices such as magnetohydrodynamic ( mhd ) power generators , mhd pumps , accelerators , aerodynamics heating , electrostatic precipitation , polymer technology , petroleum industry , purification of crude oil and fluid droplets sprays .
channel flows of a newtonian fluid with heat transfer were studied with or without hall currents by many authors @xcite .
the effects of : injection / suction through the injection / suction parameter number , hartmann number , permeability or darcy parameter on the stability of the fluids flows were studied by many researchers @xcite with different approch .
the heat source and the soret effects on an oscillatory hydromagnetic flow through a porous medium bounded by two vertical parallel porous plates is analyzed by k. chand et al.@xcite , where one plate of the channel is kept stationary and the other is moving with uniform velocity .
the plates of the channel are subjected to constant injection and suction velocities respectively .
a. nayak et al.@xcite have studied an oscillatory effects on magneto - hydrodynamic flow and heat transfer in rotating horizontal porous channel .
n. v. r. v. prasad et al .
@xcite have considered the unsteady hydromagnetic incompressible viscous fluid flow through a porous medium in a horizontal channel under prescribed discharge , under the influence of inclined magnetic field .
das et al .
@xcite analyze the effects of constant suction and sinusoidal injection on three dimensional couette flow of a viscous incompressible electrically conducting fluid through a porous medium between two infinite horizontal parallel porous flat plates in presence of a transverse magnetic field .
the stationary plate and the plate in uniform motion are , respectively , subjected to a transverse sinusoidal injection and uniform suction of the fluid .
shalini et al.@xcite have studied the effects of variable viscosity and heat source on unsteady laminar flow of dusty conducting fluid between parallel porous plates through porous medium with temperature dependent viscosity.it is assumed that the parallel plates are porous and subjected to a uniform suction from above and injection from below .
the objective of the present paper is to study the effects of the injection / suction reynods number , hartmann number , permeability parameter on the linear temporal stability of the flow of a viscous incompressible electrically conducting fluid in a couette horizontal porous channel in the presence of a uniform transverse magnetic field when it is fixed relative to the fluid through the modified orr - sommerfeld equation .
the plates of the channel are considered porous and flow within the channel is due to the uniform motion of the upper plate . such linear temporal stability analysis through a modified orr - sommerfeld equation has been made earlier by a. v. monwanou and j. b. chabi orou @xcite in a poiseuille flow without injection / suction .
the same problem with a viscous incompressible no - conduction fluid but with small injection/ suction in medium through the porous plates fat has been made by l.hinvi et al .
@xcite.the paper is organized as follows . in the second section the modified orr - sommerfeld equation governing
the stability analysis in the couette horizontal porous plates flow is checked . in the third section an analysis of the effects of small injection / suction reynolds number @xmath0 , hartmann number@xmath1 and permeability parameter @xmath2 on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel linear stability will be invertigated with the help of figures and tables . .
the conclusions is presented in the final section .
we considered a poiseuille viscous incompressilbe and electrically conduction fluid flow between two porous parallel plates of infinite lengh , distant @xmath3 apart in the presence of uniform transverse constant magnetic field @xmath4 applied parallel to @xmath5 axis which is normal to the planes of the plates .
we considered the simple case where , @xmath4 is fixed relative to the fluid .
we work at constant temperature , the heat transfert aspect of the flow is not studied .
we applied a small constant injection @xmath6 , at the lower plate and a same small constant suction @xmath6 , at the upper plate.the upper plate is allowed to mouve with non - zero uniform velocity @xmath7 in flow direction and the lower plate is kept at rest .
we choose the origine on the plane @xmath8 such as @xmath9 and @xmath10 parallel to the direction of the motion of the upper plate .
we assumed the magnetic reynolds number very small for metallic liquids and neglected the induced magnetic field in comparison with the applied one @xcite .
initially , @xmath11 , both the fluid and plates are assumed to be at rest .
when @xmath12 , the upper plate starts moving with a constant velocity @xmath13 in coordinate system with the fluid .
the equations of continuity , motion for the viscous incompressible electically conduction fluid in vector form are : @xmath14 they are continuity , newton s second law , ampere s law , faraday s law , maxwell s law and gauss law equations respectively , with @xmath15 where @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 the velocity , the magnetic field , the electric field , the current density vector , the fluid electrical conductivity and the magnetic permeability of the fluid respectively and @xmath22 denotes time .
the physical model of the problem is illustrated in figure [ fig : 0 ] below , where @xmath16 is the velocity vector in the @xmath23 directions respectively .
@xmath24 where @xmath4 is a constant .
we assumed that no applied and polarization voltage exists ( i.e. , @xmath25 )
. then @xmath26 and ( [ eq6 ] ) yields @xmath27 we introduced the following non - dimensional quantities @xmath28 , @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 , @xmath36 ( hydrodynamic reynolds number ) @xmath37 ( reynods injection / suction number ) , @xmath38 ( hartmann number ) , @xmath39 ( permeability parameter ) and the equations ( [ eq1 ] ) and ( [ eq2 ] ) become @xmath40 @xmath41 for the stability analysis , the flow is decomposed into the mean flow and the disturbance according to @xmath42 studied and analyzed with the help of figures and tables .
we take the dimensional base flow for small suction and injection @xcite @xmath43 by scaling these velocities as above , we obtain with @xmath44 ( @xmath45 ) the no - dimensional base flow @xmath46 to obtain the stability equations for the spatial evolution of three - dimensional , we take the dependent on time disturbances @xmath47 which are scaled in the same way as above . + we replace the equations ( [ eq17 ] ) - ( [ eq25 ] ) in the equations ( [ eq14])-([eq16 ] ) , after linearization and neglection of quadratic terms we find @xmath48 the pressure terms can be eliminated from navier - stokes equations .
for such a mean profile ( base flow ) , the divergence of navier - stokes equations and continuity , gives @xmath49 the equations @xmath50 and ( [ eq29 ] ) after linearization give @xmath51 { \bigtriangledown}^{2}{v } - \frac{d^{2}u}{{dy}^{2}}\frac{\partial{v}}{\partial{x}}+ \frac{m^{2}}{r_{e}}\frac{\partial^{2}{v}}{{\partial{y}}^{2 } } & = & 0 .
\label{eq30}\end{aligned}\ ] ] the disturbances are taken to be periodic in the streamwise , spanwise directions and time , which allow us to assume solutions of the form @xmath52 where @xmath53 represents either one of the disturbances @xmath54 , @xmath55 , @xmath56 or @xmath57 and @xmath58 the amplitude function , @xmath59 , @xmath60 and @xmath61 are the wave numbers , @xmath62 the pulsation of the wave . with @xmath63 , @xmath64 , @xmath65 wave velocity which is taken to be complex ,
@xmath66 and @xmath67 are real because of temporal stability analysis consideration . then with the equation ( [ eq31 ] ) ,
the equation ( [ eq30 ] ) becomes @xmath68 where @xmath69 ; with boundary conditions for all @xmath70 @xmath71 taking @xmath72 the equation ( [ eq32 ] ) , the boundary conditions ( [ eq34 ] ) and ( [ eq37 ] ) , take the forms @xmath73 @xmath74 the equation ( [ eq40 ] ) is a flow equation modified by the small injection / suction reynolds number @xmath75 , the hartmann number @xmath76 , and permeability parameter ( @xmath39 ) which we call modified orr - sommerfeld equation , rewritten as an eigenvalue problem , where @xmath77 is the eigenvalue and @xmath78 the eigenfunction .
@xmath79\nonumber \end{aligned}\ ] ] and @xmath80 are the operators .
we consider our three - dimensional disturbances .
we use a temporal stability analysis as mentioned above . with @xmath77 complex as we have defined above , when @xmath81 we have stability , @xmath82 we have neutral stability and elsewhere we have instability .
we employ matlab @xmath83 in all our numerical computations to find the eigenvalues .
the couette horizontal porous plates flow with the basic velocity profile @xmath84 for @xmath0 small ( i.e. small suction ) is considered .
the eigenvalue problem ( [ eq40 ] ) is solved numerically with the suitable boundary conditions .
the solutions are found in a layer bounded at @xmath85 with @xmath86 .
the results of calculations are presented in the figures below .
we present the figures related to the eigenvalue problem ( [ eq40 ] ) . for all these figures the black , red , green and blue colors are respectively , the curves @xmath87 and the yellow color is for @xmath82 . for all frame
@xmath88 we have fixed free parameters and we gave the curves @xmath89vs.@xmath90 for sequential values of other parameters .
figure [ fig : 1 ] presents the effect of reynods injection / suction number @xmath0 on linear temporal stability of viscous incompressible non electrically conduction fluid ( @xmath91 ) flow for different values of wave number .
it is observed that for @xmath92 and @xmath93 ( see figure [ fig : 1 ] frames a and b ) , the stability is not affected by @xmath0 and the flow is instable but for @xmath94 and @xmath95 ( see figure [ fig : 1 ] frames c and d ) , @xmath0 affecte it and the flow stays stable , also increase of @xmath0 does nt contribute to the satability .
figure [ fig : 2 ] exhibits the effect of permeability parameter @xmath2 on linear temporal stability of viscous incompressible non electrically conduction fluid flow for different values of wave number .
it is observed that @xmath2 affectes the stability . for @xmath92 and @xmath93 , the frames @xmath96 and @xmath97 show that for @xmath98 the flow is instable ( see curves @xmath99 ) and stable for @xmath100 ( see curves @xmath101 ) but for @xmath102 and @xmath103 ( see curves @xmath104 ) , we have the transition of the flow ( seen tabular below for the criticals reynoldsnumber values ) . for @xmath94 and @xmath95 ( see frames @xmath77 and @xmath105 ) the flow is completely stable .
on careful observation , we remark that for @xmath106 , @xmath2 s increase contributes to the stability in frame @xmath105 case and the opposite is noticed in the frame @xmath77 case , but when @xmath107 , @xmath2 s increase contributes in the two cases .
thus , it may be concluded that except the frame @xmath77 case where , the @xmath2 s increase does nt contribute to stability for @xmath106 , the permeability parameter increasing contributes to the flow stability .
figure [ fig : 3 ] shows the effect of hartmann number @xmath1 on linear temporal stability of viscous incompressible electrically conduction fluid flow for different values of wave number .
it is observed that @xmath1 affectes the stability . for @xmath92 and @xmath93 ,
the frames @xmath96 and @xmath97 show that for @xmath108 the flow is instable ( see curves @xmath99 ) and stable for @xmath109 ( see curves @xmath101 ) but for @xmath110 and @xmath111 ( see curves @xmath104 ) , we have the transition of the flow ( seen tabular below for the criticals reynoldsnumber values ) . for @xmath94 and @xmath95 ( see frames @xmath77 and @xmath105 ) the flow is completely stable .
thus , we may concluded that the hartmann number increasing contribute more to the flow stability .
figure [ fig : 4 ] depicts the effet of phase angle @xmath112 for different values of the wave number on the flow stability . for @xmath92 and @xmath93 , the frames @xmath96 and
@xmath97 show that the flow is instable and the instability increases when the angle @xmath112 increases .
but , for @xmath94 and @xmath95 the flow is completely stable except the curve @xmath113 frame @xmath114 , which presents a transition initialy and stays instable after .
finaly , the figures [ fig : 5 ] , [ fig : 6 ] and [ fig : 7 ] ( @xmath115 , electically conduction fluid ) show that for @xmath92 and @xmath116 the small injection / suction has no effect on the linear temporal stability of the flow .
but for @xmath94 and @xmath117 , we remark a little influence of the small injection / suction on the stability only in a little interval of @xmath118 .
[ cols="<,<,<,<,<,<",options="header " , ]
fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] + fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] + fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] + fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] + fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] + fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] + fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ] + fixed and @xmath124 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ]
the conclusions of the study are : * the small injection / suction reynolds number has a little effect on the linear temporal stability of the couette flow only for the high waves numbers ( @xmath125 ) . *
the permeability parameter i.e. darcy number , the lorentz force parameter i.e. the hartmann number and the wave number contribute to the linear temporal stability of the couette flow .
* for the small wave number @xmath126 , @xmath112 does nt contribute to the stability of the couette flow but for @xmath127 his effect is opposite . 100 fluid mechanics , @xmath128 , @xmath129 september @xmath130 , @xmath131 .
a. v. monwanou and j. b. chabi orou .
, _ the inviscid instability in an electrically conducting fluid affected by a parallel magnetic field _ ( the african review of physics ( @xmath132 ) @xmath133 ) .
k. chand , r. kumar and s. sharma . , _
hydromagnetic oscillatory flow through a porous medium bounded by two vertical porous plates with heat source and soret effect _
( advances in applied science research , @xmath132 , @xmath134 ) .
a. nayak , g.c .
, _ oscillatory effect on magneto - hydrodynamic flow and heat transfer in a rotating horizontal porous channel _ ( annals of faculty engineering hunedoara - international journal of engineering : p@xmath135-tome @xmath136 ( year @xmath137 ) .
fascicule @xmath138 .
issn @xmath139 ) . n. v. r. v. prasad , g. s. s. raju , s. venkataraman . , _ unsteaedy hydromagnetic flow through a porous medium in a horizontal channel under prescribed discharge with inclined magnetic field _
( international journal of emerging technology and advanced engineering issn @xmath140 , volume @xmath141 , issue @xmath142 , july @xmath132 ) .
s. s. das , m. mohanty , s. k. panigrahi , r. k. padhy , m. sahu .
, _ radiative heat and mass transfer effects on natural convection couette flow through a porous medium in the slip flow regime _ ( international journal of renewable energy technology research vol .
@xmath138 , no.@xmath138 , pp : @xmath143 , december @xmath132 , issn : @xmath144 ( online ) ) .
shalini , prof .
m. s. saroa , prof .
rajeev jha . , _ unsteady flow of a dusty conducting fluid through porous medium between parallel porous plates with temperature dependent viscosity and heat source _ ( international journal of scientific research engineering and technology ( ijsret ) volume @xmath138 issue@xmath117 pp @xmath145 june @xmath132 ) .
m. e. sayed - ahmed , hazem a. attia , karem m. ewis . , _ time dependent pressure gradient effect on unsteady mhd couette flow and heat transfer of a casson fluid _
( engineering , @xmath146 , @xmath117 , @xmath147-@xmath148 doi : @xmath149/eng.@xmath150 published online january @xmath146 ( http : //www.scirp.org / journal / eng ) ) .
l. hinvi , a. v. monwanou , j. b. chabi orou . , _ linear stability analysis of fluid flow between two parallel porous stationary plates with small suction and injection _ ( arxiv : @xmath151v@xmath138 [ physics.flu-dyn]@xmath152 apr @xmath137 ) .
j. m. mcdonough .
, _ lectures in elementary fluid dynamics : physics , mathematics and applications _ ( departments of mechanical engineering and mathematics .
university of kentucky , lexington , ky @xmath153 ) .
s. o. ajadi . ,
_ a note on unsteady flow of dusty viscous fluid between two parallel plates _ ( j. appl
. math . and
computing vol .
@xmath155 , no .
@xmath138 - @xmath141 , pp .
@xmath156 ) . | this paper analyses the effects of small injection / suction reynolds number , hartmann number , permeability parameter and wave number on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel .
the plates of the channel with small constant injection / suction , have constant temperature .
the upper plate is allowed to mouve in flow direction and the lower plate is kept at rest . a magnetic field of uniform strength
is also applied normally to the plates what are parallel .
the originality of the paper is to study the effect of the above parameter in temporal linear stabilty analysis of the flow through the modified orr - sommerfeld equation .
* keywords : * temporal linear stability , small injection / injection reynolds number , modified orr - sommerfeld equation , hydromagnetic poiseulle flow . | <s>[INST]the study of couette flow in a rectangular channel of an electrically conducting viscous fluid under the action of a transversely applied magnetic field has immediate applications in many devices such as magnetohydrodynamic ( mhd ) power generators , mhd pumps , accelerators , aerodynamics heating , electrostatic precipitation , polymer technology , petroleum industry , purification of crude oil and fluid droplets sprays .
channel flows of a newtonian fluid with heat transfer were studied with or without hall currents by many authors @xcite .
the effects of : injection / suction through the injection / suction parameter number , hartmann number , permeability or darcy parameter on the stability of the fluids flows were studied by many researchers @xcite with different approch .
the heat source and the soret effects on an oscillatory hydromagnetic flow through a porous medium bounded by two vertical parallel porous plates is analyzed by k. chand et al.@xcite , where one plate of the channel is kept stationary and the other is moving with uniform velocity .
the plates of the channel are subjected to constant injection and suction velocities respectively .
a. nayak et al.@xcite have studied an oscillatory effects on magneto - hydrodynamic flow and heat transfer in rotating horizontal porous channel .
n. v. r. v. prasad et al .
@xcite have considered the unsteady hydromagnetic incompressible viscous fluid flow through a porous medium in a horizontal channel under prescribed discharge , under the influence of inclined magnetic field .
das et al .
@xcite analyze the effects of constant suction and sinusoidal injection on three dimensional couette flow of a viscous incompressible electrically conducting fluid through a porous medium between two infinite horizontal parallel porous flat plates in presence of a transverse magnetic field .
the stationary plate and the plate in uniform motion are , respectively , subjected to a transverse sinusoidal injection and uniform suction of the fluid .
shalini et al.@xcite have studied the effects of variable viscosity and heat source on unsteady laminar flow of dusty conducting fluid between parallel porous plates through porous medium with temperature dependent viscosity.it is assumed that the parallel plates are porous and subjected to a uniform suction from above and injection from below .
the objective of the present paper is to study the effects of the injection / suction reynods number , hartmann number , permeability parameter on the linear temporal stability of the flow of a viscous incompressible electrically conducting fluid in a couette horizontal porous channel in the presence of a uniform transverse magnetic field when it is fixed relative to the fluid through the modified orr - sommerfeld equation .
the plates of the channel are considered porous and flow within the channel is due to the uniform motion of the upper plate . such linear temporal stability analysis through a modified orr - sommerfeld equation has been made earlier by a. v. monwanou and j. b. chabi orou @xcite in a poiseuille flow without injection / suction .
the same problem with a viscous incompressible no - conduction fluid but with small injection/ suction in medium through the porous plates fat has been made by l.hinvi et al .
@xcite.the paper is organized as follows . in the second section the modified orr - sommerfeld equation governing
the stability analysis in the couette horizontal porous plates flow is checked . in the third section an analysis of the effects of small injection / suction reynolds number @xmath0 , hartmann number@xmath1 and permeability parameter @xmath2 on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel linear stability will be invertigated with the help of figures and tables . .
the conclusions is presented in the final section .
we considered a poiseuille viscous incompressilbe and electrically conduction fluid flow between two porous parallel plates of infinite lengh , distant @xmath3 apart in the presence of uniform transverse constant magnetic field @xmath4 applied parallel to @xmath5 axis which is normal to the planes of the plates .
we considered the simple case where , @xmath4 is fixed relative to the fluid .
we work at constant temperature , the heat transfert aspect of the flow is not studied .
we applied a small constant injection @xmath6 , at the lower plate and a same small constant suction @xmath6 , at the upper plate.the upper plate is allowed to mouve with non - zero uniform velocity @xmath7 in flow direction and the lower plate is kept at rest .
we choose the origine on the plane @xmath8 such as @xmath9 and @xmath10 parallel to the direction of the motion of the upper plate .
we assumed the magnetic reynolds number very small for metallic liquids and neglected the induced magnetic field in comparison with the applied one @xcite .
initially , @xmath11 , both the fluid and plates are assumed to be at rest .
when @xmath12 , the upper plate starts moving with a constant velocity @xmath13 in coordinate system with the fluid .
the equations of continuity , motion for the viscous incompressible electically conduction fluid in vector form are : @xmath14 they are continuity , newton s second law , ampere s law , faraday s law , maxwell s law and gauss law equations respectively , with @xmath15 where @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 the velocity , the magnetic field , the electric field , the current density vector , the fluid electrical conductivity and the magnetic permeability of the fluid respectively and @xmath22 denotes time .
the physical model of the problem is illustrated in figure [ fig : 0 ] below , where @xmath16 is the velocity vector in the @xmath23 directions respectively .
@xmath24 where @xmath4 is a constant .
we assumed that no applied and polarization voltage exists ( i.e. , @xmath25 )
. then @xmath26 and ( [ eq6 ] ) yields @xmath27 we introduced the following non - dimensional quantities @xmath28 , @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 , @xmath36 ( hydrodynamic reynolds number ) @xmath37 ( reynods injection / suction number ) , @xmath38 ( hartmann number ) , @xmath39 ( permeability parameter ) and the equations ( [ eq1 ] ) and ( [ eq2 ] ) become @xmath40 @xmath41 for the stability analysis , the flow is decomposed into the mean flow and the disturbance according to @xmath42 studied and analyzed with the help of figures and tables .
we take the dimensional base flow for small suction and injection @xcite @xmath43 by scaling these velocities as above , we obtain with @xmath44 ( @xmath45 ) the no - dimensional base flow @xmath46 to obtain the stability equations for the spatial evolution of three - dimensional , we take the dependent on time disturbances @xmath47 which are scaled in the same way as above . + we replace the equations ( [ eq17 ] ) - ( [ eq25 ] ) in the equations ( [ eq14])-([eq16 ] ) , after linearization and neglection of quadratic terms we find @xmath48 the pressure terms can be eliminated from navier - stokes equations .
for such a mean profile ( base flow ) , the divergence of navier - stokes equations and continuity , gives @xmath49 the equations @xmath50 and ( [ eq29 ] ) after linearization give @xmath51 { \bigtriangledown}^{2}{v } - \frac{d^{2}u}{{dy}^{2}}\frac{\partial{v}}{\partial{x}}+ \frac{m^{2}}{r_{e}}\frac{\partial^{2}{v}}{{\partial{y}}^{2 } } & = & 0 .
\label{eq30}\end{aligned}\ ] ] the disturbances are taken to be periodic in the streamwise , spanwise directions and time , which allow us to assume solutions of the form @xmath52 where @xmath53 represents either one of the disturbances @xmath54 , @xmath55 , @xmath56 or @xmath57 and @xmath58 the amplitude function , @xmath59 , @xmath60 and @xmath61 are the wave numbers , @xmath62 the pulsation of the wave . with @xmath63 , @xmath64 , @xmath65 wave velocity which is taken to be complex ,
@xmath66 and @xmath67 are real because of temporal stability analysis consideration . then with the equation ( [ eq31 ] ) ,
the equation ( [ eq30 ] ) becomes @xmath68 where @xmath69 ; with boundary conditions for all @xmath70 @xmath71 taking @xmath72 the equation ( [ eq32 ] ) , the boundary conditions ( [ eq34 ] ) and ( [ eq37 ] ) , take the forms @xmath73 @xmath74 the equation ( [ eq40 ] ) is a flow equation modified by the small injection / suction reynolds number @xmath75 , the hartmann number @xmath76 , and permeability parameter ( @xmath39 ) which we call modified orr - sommerfeld equation , rewritten as an eigenvalue problem , where @xmath77 is the eigenvalue and @xmath78 the eigenfunction .
@xmath79\nonumber \end{aligned}\ ] ] and @xmath80 are the operators .
we consider our three - dimensional disturbances .
we use a temporal stability analysis as mentioned above . with @xmath77 complex as we have defined above , when @xmath81 we have stability , @xmath82 we have neutral stability and elsewhere we have instability .
we employ matlab @xmath83 in all our numerical computations to find the eigenvalues .
the couette horizontal porous plates flow with the basic velocity profile @xmath84 for @xmath0 small ( i.e. small suction ) is considered .
the eigenvalue problem ( [ eq40 ] ) is solved numerically with the suitable boundary conditions .
the solutions are found in a layer bounded at @xmath85 with @xmath86 .
the results of calculations are presented in the figures below .
we present the figures related to the eigenvalue problem ( [ eq40 ] ) . for all these figures the black , red , green and blue colors are respectively , the curves @xmath87 and the yellow color is for @xmath82 . for all frame
@xmath88 we have fixed free parameters and we gave the curves @xmath89vs.@xmath90 for sequential values of other parameters .
figure [ fig : 1 ] presents the effect of reynods injection / suction number @xmath0 on linear temporal stability of viscous incompressible non electrically conduction fluid ( @xmath91 ) flow for different values of wave number .
it is observed that for @xmath92 and @xmath93 ( see figure [ fig : 1 ] frames a and b ) , the stability is not affected by @xmath0 and the flow is instable but for @xmath94 and @xmath95 ( see figure [ fig : 1 ] frames c and d ) , @xmath0 affecte it and the flow stays stable , also increase of @xmath0 does nt contribute to the satability .
figure [ fig : 2 ] exhibits the effect of permeability parameter @xmath2 on linear temporal stability of viscous incompressible non electrically conduction fluid flow for different values of wave number .
it is observed that @xmath2 affectes the stability . for @xmath92 and @xmath93 , the frames @xmath96 and @xmath97 show that for @xmath98 the flow is instable ( see curves @xmath99 ) and stable for @xmath100 ( see curves @xmath101 ) but for @xmath102 and @xmath103 ( see curves @xmath104 ) , we have the transition of the flow ( seen tabular below for the criticals reynoldsnumber values ) . for @xmath94 and @xmath95 ( see frames @xmath77 and @xmath105 ) the flow is completely stable .
on careful observation , we remark that for @xmath106 , @xmath2 s increase contributes to the stability in frame @xmath105 case and the opposite is noticed in the frame @xmath77 case , but when @xmath107 , @xmath2 s increase contributes in the two cases .
thus , it may be concluded that except the frame @xmath77 case where , the @xmath2 s increase does nt contribute to stability for @xmath106 , the permeability parameter increasing contributes to the flow stability .
figure [ fig : 3 ] shows the effect of hartmann number @xmath1 on linear temporal stability of viscous incompressible electrically conduction fluid flow for different values of wave number .
it is observed that @xmath1 affectes the stability . for @xmath92 and @xmath93 ,
the frames @xmath96 and @xmath97 show that for @xmath108 the flow is instable ( see curves @xmath99 ) and stable for @xmath109 ( see curves @xmath101 ) but for @xmath110 and @xmath111 ( see curves @xmath104 ) , we have the transition of the flow ( seen tabular below for the criticals reynoldsnumber values ) . for @xmath94 and @xmath95 ( see frames @xmath77 and @xmath105 ) the flow is completely stable .
thus , we may concluded that the hartmann number increasing contribute more to the flow stability .
figure [ fig : 4 ] depicts the effet of phase angle @xmath112 for different values of the wave number on the flow stability . for @xmath92 and @xmath93 , the frames @xmath96 and
@xmath97 show that the flow is instable and the instability increases when the angle @xmath112 increases .
but , for @xmath94 and @xmath95 the flow is completely stable except the curve @xmath113 frame @xmath114 , which presents a transition initialy and stays instable after .
finaly , the figures [ fig : 5 ] , [ fig : 6 ] and [ fig : 7 ] ( @xmath115 , electically conduction fluid ) show that for @xmath92 and @xmath116 the small injection / suction has no effect on the linear temporal stability of the flow .
but for @xmath94 and @xmath117 , we remark a little influence of the small injection / suction on the stability only in a little interval of @xmath118 .
[ cols="<,<,<,<,<,<",options="header " , ]
fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] + fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] + fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath120 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] + fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath121 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] + fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath122 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] + fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath123 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] + fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath119 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ] + fixed and @xmath124 variable , title="fig:",width=226 ] fixed and @xmath124 variable , title="fig:",width=226 ]
the conclusions of the study are : * the small injection / suction reynolds number has a little effect on the linear temporal stability of the couette flow only for the high waves numbers ( @xmath125 ) . *
the permeability parameter i.e. darcy number , the lorentz force parameter i.e. the hartmann number and the wave number contribute to the linear temporal stability of the couette flow .
* for the small wave number @xmath126 , @xmath112 does nt contribute to the stability of the couette flow but for @xmath127 his effect is opposite . 100 fluid mechanics , @xmath128 , @xmath129 september @xmath130 , @xmath131 .
a. v. monwanou and j. b. chabi orou .
, _ the inviscid instability in an electrically conducting fluid affected by a parallel magnetic field _ ( the african review of physics ( @xmath132 ) @xmath133 ) .
k. chand , r. kumar and s. sharma . , _
hydromagnetic oscillatory flow through a porous medium bounded by two vertical porous plates with heat source and soret effect _
( advances in applied science research , @xmath132 , @xmath134 ) .
a. nayak , g.c .
, _ oscillatory effect on magneto - hydrodynamic flow and heat transfer in a rotating horizontal porous channel _ ( annals of faculty engineering hunedoara - international journal of engineering : p@xmath135-tome @xmath136 ( year @xmath137 ) .
fascicule @xmath138 .
issn @xmath139 ) . n. v. r. v. prasad , g. s. s. raju , s. venkataraman . , _ unsteaedy hydromagnetic flow through a porous medium in a horizontal channel under prescribed discharge with inclined magnetic field _
( international journal of emerging technology and advanced engineering issn @xmath140 , volume @xmath141 , issue @xmath142 , july @xmath132 ) .
s. s. das , m. mohanty , s. k. panigrahi , r. k. padhy , m. sahu .
, _ radiative heat and mass transfer effects on natural convection couette flow through a porous medium in the slip flow regime _ ( international journal of renewable energy technology research vol .
@xmath138 , no.@xmath138 , pp : @xmath143 , december @xmath132 , issn : @xmath144 ( online ) ) .
shalini , prof .
m. s. saroa , prof .
rajeev jha . , _ unsteady flow of a dusty conducting fluid through porous medium between parallel porous plates with temperature dependent viscosity and heat source _ ( international journal of scientific research engineering and technology ( ijsret ) volume @xmath138 issue@xmath117 pp @xmath145 june @xmath132 ) .
m. e. sayed - ahmed , hazem a. attia , karem m. ewis . , _ time dependent pressure gradient effect on unsteady mhd couette flow and heat transfer of a casson fluid _
( engineering , @xmath146 , @xmath117 , @xmath147-@xmath148 doi : @xmath149/eng.@xmath150 published online january @xmath146 ( http : //www.scirp.org / journal / eng ) ) .
l. hinvi , a. v. monwanou , j. b. chabi orou . , _ linear stability analysis of fluid flow between two parallel porous stationary plates with small suction and injection _ ( arxiv : @xmath151v@xmath138 [ physics.flu-dyn]@xmath152 apr @xmath137 ) .
j. m. mcdonough .
, _ lectures in elementary fluid dynamics : physics , mathematics and applications _ ( departments of mechanical engineering and mathematics .
university of kentucky , lexington , ky @xmath153 ) .
s. o. ajadi . ,
_ a note on unsteady flow of dusty viscous fluid between two parallel plates _ ( j. appl
. math . and
computing vol .
@xmath155 , no .
@xmath138 - @xmath141 , pp .
@xmath156 ) .[/INST] this paper analyses the effects of small injection / suction reynolds number , hartmann number , permeability parameter and wave number on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel .
the plates of the channel with small constant injection / suction , have constant temperature .
the upper plate is allowed to mouve in flow direction and the lower plate is kept at rest . a magnetic field of uniform strength
is also applied normally to the plates what are parallel .
the originality of the paper is to study the effect of the above parameter in temporal linear stabilty analysis of the flow through the modified orr - sommerfeld equation .
* keywords : * temporal linear stability , small injection / injection reynolds number , modified orr - sommerfeld equation , hydromagnetic poiseulle flow . </s> |
thz - frequency radiation is sensitive to the frequency - dependent intraband conductivity of mos@xmath0 , @xmath10 , which contains information about carrier scattering and mobility . using a thz time - domain spectrometer@xcite
, we measure the amplitude and phase of broadband thz pulses transmitted through our 4 @xmath11 m thick natural mos@xmath0 samples . in a static transmission measurement , where the conductivity is time - independent , the thin - film ( @xmath12 ) amplitude transmission for thz pulses is ( see supplementary information ) , @xmath13^{-1 } \label{eq : tr}\ ] ] where @xmath14 is the frequency
, @xmath15 is the sample thickness , @xmath16 is the speed of light , @xmath17 is the impedance of free space , @xmath18 is the sample refractive index . using equation [ eq : tr ] and the measured spectra of thz pulses transmitted through an unpumped multilayer mos@xmath0 sample
, we obtained a constant value of refractive index @xmath19 in the 0.2 - 2.0 thz frequency range .
further , the unpumped dc conductivity @xmath20 was found to be in the range 10 - 20 s m@xmath2 indicating that the sample was very mildly doped .
electrical measurements on similar single - layer and multilayer samples have indicated that these mos@xmath4 samples tend to be n - doped@xcite .
given the large value of the refractive index and the small value of @xmath20 , this unpumped transmission measurement could not reliably determine the frequency dependence of the conductivity and thereby the mobility .
in contrast , since the change in thz transmission , @xmath21 , between pumped and unpumped samples is directly proportional to the change in the conductivity @xmath22 , optical - pump thz - probe spectroscopy is a highly - sensitive method to extract the frequency - dependent conductivity . in the optical - pump thz - probe scheme , depicted in figure [ fig : deltae](a - b ) , 780 nm center wavelength ( 1.58 ev ) , sub-100 fs optical pulses excite electron and hole distributions at the six @xmath23 points and the @xmath24 point , respectively , after which the distributions cool and recombine .
the field of the thz pulse transmitted through the pumped sample , @xmath25 , is sensitive to the evolving conductivity and , therefore , depends on the pump - probe delay @xmath26 . in our experiments ,
the incident optical and thz pulses are mechanically chopped at different frequencies and the transmitted thz pulse is measured at the sum frequency .
we therefore measure the change in the transmitted thz pulse , @xmath27 , in the presence ( @xmath28 ) and absence ( @xmath29 ) of optical pumping . in this paper ,
the symbol @xmath30 signifies the change in a quantity due to optical pumping .
figure [ fig : deltae](c ) shows the measured @xmath5 for a fixed delay of @xmath6 ps at different temperatures .
we also display @xmath31 , which was essentially temperature - independent .
@xmath5 contains information of both the amplitude and phase changes of @xmath31 upon pumping .
comparison of @xmath5 and @xmath31 shows a trend of increasing phase shifts with decreasing temperatures due to photoexcited carriers .
thus , both the amplitude and the phase of the transmitted thz pulse are needed to determine the sample response .
the sample response can be determined from the measured change in the transmitted thz pulse , @xmath5 , as follows .
we scan the pump - probe delay simultaneously with the transmitted thz pulse in the time - domain thz spectrometer such that each measured point of the transmitted thz pulse is at the same delay , @xmath26 , from the pump@xcite .
the measured pulse , @xmath32 , satisfies ( see supplementary information ) , @xmath33 where @xmath34 is the permittivity of free - space .
equation [ eq : deltaj ] describes the effect of the free - carrier and polarization current densities on the thz pulse .
the change in the free - carrier current density , @xmath35 , in the sample can be written approximately as ( see supplementary information ) , @xmath36 \label{eq : j}\ ] ] here , @xmath37 is the change in the dc conductivity and @xmath38 is the normalized current impulse response ( @xmath39 ) . in fourier domain , we define @xmath40 as @xmath41 .
techniques to extract @xmath40 from the measured @xmath42 are described in the methods section
. plotted versus frequency for various temperatures . in each case , the probe delay is @xmath6 ps , and the pump fluence is @xmath91.2 @xmath11j @xmath43 .
( dashed lines )
drude model fits to the measured conductivity spectra used to extract @xmath44 . ]
figure [ fig : drudefits ] shows the real and imaginary parts of the photoexcited conductivity @xmath45 measured at four different temperatures in mos@xmath0 .
we find that the measured conductivity spectra closely follow the drude form , @xmath46 , which is the simplest conductivity model in the relaxation time approximation .
therefore , the current impulse response @xmath47 is @xmath48 .
we fit the real and imaginary parts of the data simultaneously with a weighted least - squares regression and extract the photoexcited dc conductivity @xmath49 and the carrier momentum scattering time @xmath44 .
weights were the data variance at each frequency point over twenty scans .
the high quality of fits to the data obtained at all temperatures , as shown in figure [ fig : drudefits ] , is strong evidence of the fact that the change in thz transmission we measure indeed originates from the intraband conductivity of the photoexcited carriers .
also , at all temperatures we find no significant variation in the extracted value of @xmath44 for any value of @xmath26 in the range 5 ps @xmath50 12 ns .
since one expects very hot carriers to have average momentum scattering times different from that of cold carriers@xcite , this observation suggests that the carrier distributions after photoexcitation cool down on time scales shorter than a few picoseconds .
we further discuss carrier cooling times below .
carrier in - plane ( @xmath51 to c - axis ) mobility is related to the momentum scattering time by @xmath52 , where @xmath53 is the in - plane conductivity effective mass .
multilayer mos@xmath4 has six electron pockets in the brillouin zone , each with an anisotropic effective mass tensor@xcite .
the one hole pocket has an isotropic effective mass tensor . using dft values for the electron and hole effective mass tensors@xcite
, we find the conductivity effective masses for both electrons and holes to be @xmath90.61@xmath54 . in figure [ fig : mobility](a ) , we plot the electron mobilities corresponding to the measured momentum scattering times at different temperatures ( @xmath55 = 30 , 45 , 100 , 200 , 300 k ) .
we find a mobility of 257 @xmath1v@xmath2s@xmath2 at 300 k , increasing to 4200 @xmath1v@xmath2s@xmath2 at 30 k. for 300 k , the measured mobility is consistent with recent electronic transport measurements in multilayer mos@xmath0@xcite . but
the mobilities we find below 200 k in this contact - free measurement are significantly higher than the values previously reported for mos@xmath0 .
k. the @xmath56 dependence at low temperatures suggests acoustic phonon scattering as the dominant scattering mechanism .
meascured mobility reaches @xmath94200 @xmath1v@xmath2s@xmath2 at 30 k. ] in figure [ fig : mobility](b ) , we plot the carrier momentum scattering rate , @xmath57 , versus temperature .
the scattering rate for @xmath58 k increases linearly with temperature .
this linear temperature dependence is expected for quasi - elastic acoustic phonon scattering in 2d and layered materials in the equipartition regime@xcite .
other scattering mechanisms , such as impurity scattering , have a different temperature dependence for layered materials@xcite .
the larger scattering rate observed at the highest temperature ( 300 k ) likely indicates an optical phonon scattering contribution@xcite . in the deformation - potential approximation , the energy - independent acoustic - phonon - limited momentum scattering rate in 2d and layered materials is related to the temperature by@xcite , @xmath59 where @xmath60 is the deformation potential , @xmath61 is the 2d mass density , @xmath62 is the la phonon velocity , and @xmath63 is the carrier density of states effective mass . from the data in figure [
fig : mobility](b ) , we find @xmath64 ns@xmath2k@xmath2 for @xmath65 k. using @xmath66 m s@xmath2@xcite , @xmath67 kg m@xmath68 , @xmath69 ( ab - initio values for @xmath63 are almost identical for electrons and holes@xcite ) , we find @xmath70 ev . this value compares well with previously experimentally and theoretically determined values , generally in the 2 - 10 ev range , for the deformation potentials in single - layer and multilayer mos@xmath4@xcite . knowing @xmath47 and @xmath45 , we determine the photoexcited dc conductivity , @xmath49 ( see methods ) . the temporal resolution in our experiments is set by the measurement bandwidth of @xmath45 , @xmath91.8 thz , and is approximately @xmath71 ps .
since the in - plane conductivity effective masses for electrons and holes are approximately the same in multilayer mos@xmath4@xcite , one can write the dc conductivity as @xmath72 , where @xmath73 is the total mobile carrier density and equals the sum of the mobile electron density , @xmath18 , and the mobile hole density , @xmath74 .
the change in the carrier density @xmath75 can be determined from the measurement of @xmath76 .
, versus pump - probe delay on short time scales ( -2 @xmath50 5 ps ) .
we show data for two representative temperatures ( ( a ) 300 k and ( b ) 45 k ) , each with a pump fluence of @xmath91.2 @xmath11j @xmath43 . immediately after the pump pulse , the conductivity increases , reaching its maximum value within 5 ps at all temperatures .
the rise time is slower at 45 k than at 300 k. ] figure [ fig : tempdynamics ] shows the measured change in the conductivity @xmath77 on short time scales ( @xmath78 ps ) for two different representative temperatures .
the pump fluence in each case is @xmath91.2 @xmath11j/@xmath3 . immediately after photoexcitation ( @xmath79 ) , the conductivity increases , reaching its maximum value within 5 ps at all temperatures .
the error - range displayed for each data point represents a 95% confidence interval for the fitting parameter @xmath77 .
the dashed lines superimposed on the data represent fittings using exponential curves with 0.7 ps and 1.2 ps time constants at 300 k and 45 k , respectively .
our data suggests that the conductivity reaches its peak value faster at higher temperatures .
as we discuss below , we attribute these short - time - scale dynamics to picosecond cooling of the electron and hole distributions .
as depicted in figure [ fig : deltae](b ) , the 1.58 ev pump photons excite electrons from the valence band maximum at the @xmath24 point to the conduction band minima at the @xmath23 point by a phonon - assisted ( or impurity - assisted ) indirect absorption process . since the indirect bandgap in multilayer mos@xmath4 is around 1.29 ev@xcite ,
the photoexcited electrons and holes are at an elevated temperature compared to the lattice immediately after photoexcitation and thermalization@xcite .
if the photon energy in excess of the indirect bandgap contributes to the kinetic energy of the carriers , we estimate the carrier temperature immediately after photoexcitation to be around 1100 k. at this high temperature , the electron and hole distributions would be spread out in energy , with fast momentum scattering rates and reduced mobility due to optical phonons@xcite . as the carrier distributions relax towards the band extrema and cool via optical phonon emission , the carrier momentum scattering rates decrease and the conductivity increases .
the rise in the conductivity following photoexcitation observed in our experiments is therefore indicative of carrier cooling .
the slower cooling observed at lower lattice temperatures can be attributed to a number of factors .
for example , the carrier cooling rates due to optical phonon emission are proportional to @xmath80 , where @xmath81 , the bose occupation factor for phonons , is aproximately 20% larger at 300 k compared to 45 k. in addition , the heat capacity of optical phonons is around three orders of magnitude larger at 300 k compared to 45 k and , therefore , carrier cooling bottleneck due to the generation of hot phonons is much reduced at higher lattice temepratures@xcite .
plotted on a log scale as a function of probe delay .
shown are transients for four pump fluences ( 0.2 , 0.4 , 0.8 , and 1.2 @xmath11j @xmath43 ) at 45 k. ( blue dot - dash ) initial exponential relaxation corresponding to the estimated @xmath82 .
( red dash ) full transient simulations using equations [ eq : model ] .
( b ) measured @xmath83 ( circles ) and @xmath84 ( diamonds ) versus pump fluence at 45 k. ( solid ) curves obtained from simulations of equations [ eq : model ] .
( c ) the measured inverse decay time @xmath85 at 45 k versus @xmath86 .
the slope of the line estimates the electron capture rate @xmath87 .
] figure [ fig : powerdynamics](a ) shows the change in the mobile carrier density @xmath88 at 45 k for various pump fluences , determined from measured @xmath77 on long time scales ( @xmath89 ps ) .
as expected , the carrier density decays after reaching a peak value in the first few picoseconds after photoexcitation .
we attribute this relaxation to carrier trapping and recombination by defects .
the carrier density decay rate is relatively fast in the first @xmath9100 ps after photoexcitation , after which the decay occurs on much longer time scales .
the maximum probe delay allowed by our setup , 400 ps , is unable to resolve these long time scales .
but the non - zero carrier densities observed at negative probe delays show that the photoexcited carrier density does not completely decay in the time interval , around 12.3 ns , between two successive optical pulses .
the carrier densities immediately before and after photoexcitation , as a function of pump fluence , reveal the carrier density dependence of the long term ( @xmath90100 ps ) recombination rates .
figure [ fig : powerdynamics](b ) shows the change in carrier density immediately before , @xmath91 , and after , @xmath92 , photoexcitation .
both @xmath93 and @xmath94 increase with the pump fluence in a nonlinear fashion , so carrier - density - independent recombination times can be ruled out .
we also estimate the initial recombination rate , @xmath95 , versus pump fluence from the slope of the blue dash - dot lines in figure [ fig : powerdynamics](a ) .
figure [ fig : powerdynamics](c ) shows that @xmath85 increases approximately linearly with @xmath94 .
any physical model that describes the observed carrier dynamics must account for the transition from the fast decay rates in the first @xmath9100 ps to the slow decay rates thereafter .
in addition , the model must account for the severe nonlinearity of @xmath96 and @xmath86 versus pump fluence .
here , we present a model of carrier relaxation based on trapping and recombination by optically - active defect states .
this model explains all features of the observed carrier dynamics at 45 k. the natural mos@xmath0 used in our work is known to have defects such as vacancies , grain boundaries , and impurities@xcite .
many of these defects are optically active in the near - ir wavelength region and appear in the optical absorption spectra@xcite .
we assume that the initial fast decay of the photoexcited carrier density is due to the capture of electrons by defect states in the bandgap@xcite ( see figure [ fig : deltae](b ) ) . as these defect
states become full of electrons , the decay rate decreases ( due to pauli blocking ) and becomes limited by the capture of photoexcited holes from the valence band .
the optical pump pulse excites electrons to the conduction band from both the valence band and also the defect states , and we assume that the defect states become empty immediately after the pump pulse@xcite .
our final assumption is that the defect states are assumed to be occupied by electrons in thermal equilibrium in our n - doped sample .
ignoring thermal generation of electrons and holes from defect states , the rate equations for the decay of the electron and hole densities in our model are ( see supplementary information ) , @xmath97 here , @xmath18 and @xmath74 are the total mobile electron and hole densities , respectively , and @xmath98 ( @xmath99 ) is the rate constant for electron capture ( hole capture ) by the defect states via the dominant auger mechanisms in a n - doped semiconductor@xcite .
the value @xmath18 is the sum of the equilibrium electron density , @xmath100 , and the excess photoexcited electron density .
@xmath101 is the density of defect states , and @xmath102 is the electron occupation of the defect states , assumed to be unity in equilibrium . note that a phonon - assisted carrier trapping process would not have the carrier density dependence consistent with the observed decay rates@xcite .
we varied the values of the fitting parameters @xmath98 , @xmath99 , @xmath103 , and @xmath100 in simulations to fit the data in figures [ fig : powerdynamics](a ) and [ fig : powerdynamics](b ) .
the simulations involved time - stepping the rate equations over many ( 1 - 5@xmath104 ) pump pulse cycles until a steady state was achieved .
the difference @xmath105 @xmath106 per @xmath11j @xmath43 determined the mobile carrier density created by the pump pulse in our simulations .
the data in figure [ fig : powerdynamics ] can inform the search for appropriate values of the fitting parameters . immediately after photoexcitation , since @xmath18 varies as @xmath107 , the slope of the line in figure [ fig : powerdynamics](c ) estimates the product @xmath108 . since the long term decay of the photoexcited density is limited by the capture of holes in defects , the values of @xmath96 estimate the product @xmath109 .
finally , the density of defect states governs how quickly they fill with electrons , therefore @xmath101 is determined from the time at which the initial fast decay transitions to the slower decay , as measured in figure [ fig : powerdynamics](a ) .
the values of fitting parameters that best fit the data are : @xmath110 @xmath111 s@xmath2 , @xmath112 @xmath111 s@xmath2 , @xmath113 @xmath106 , and @xmath114 @xmath106 . this value of @xmath100 corresponds to a dc conductivity of 12 s m@xmath2 , which compares well with the value of conductivity obtained from thz transmission measurements of the unpumped sample , @xmath115 s m@xmath2 .
the model presented here closely agrees with the data , accurately reproducing the values of @xmath96 , the relaxation curves , and the nonlinearity of @xmath75 versus pump fluence .
in this paper , we presented measurements of the mobility of photoexcited carriers in multilayer mos@xmath0 using thz time - domain spectroscopy .
the observed temperature dependence of the mobility for @xmath116 k indicates acoustic phonon scattering as the dominant mobility - limiting mechanism .
the measured carrier momentum scattering rates are comparable to theoretical predictions based on phonon - scattering - limited transport@xcite .
in contrast , previously reported dc electrical measurements have suggested impurity or defect scattering as the dominant mobility - limiting mechanism in multilayer mos@xmath0@xcite .
given the prevalence of defects and impurities in mos@xmath0@xcite , it is intriguing that we observe mobilities limited by acoustic phonon scattering .
the observed high mobilities at low temperatures in our experiments could be related to the fact that our measurements were performed at very high frequencies .
it is well known theoretically and experimentally that ac conductivity in disordered materials increases with the ac frequency@xcite .
this phenomenon appears in the microscopic models of hopping conduction@xcite as well as in the classical models of the ac conductivity in inhomogeneous materials@xcite .
since we did not see signatures of ac hopping conduction in our sample at any temperature , we believe models that describe the ac conductivity in inhomogeneous materials are more relevant to our observations@xcite . accordingly , we believe that the mos@xmath4 atomic layers in our sample consist of interspersed high and low mobility regions ( due to grain boundaries , crystal defects , impurities , etc.@xcite ) and the conductivity of the layers is determined by the resistive and capacitive couplings of these regions@xcite . even a small fraction of low mobility regions can significantly affect the dc conductivity in lower dimensions .
the high mobility regions have a conductivity given by the drude form .
the ac conductivity of the sample is then expected to increase with the frequency until the low mobility regions are capacitively shorted out and the conductivity of the sample is then limited by the drude conductivity of the high mobility regions .
although this model qualitatively explains the observation of the long momentum scattering times in our experiments , investigation of the frequency dependence of the sample conductivity in the low frequency region ( @xmath117 thz ) is needed to fully understand the nature of the transport and determine which model , if any , best describes the nature of the conduction .
carrier relaxation and recombination dynamics directly affect the performance of almost all electronic and optoelectronic devices .
we have observed several time scales in the dynamics associated with carrier relaxation and recombination .
the initial intraband relaxation ( or carrier cooling ) occurs within 5 ps .
carrier interband recombination appears to result from carrier trapping in optically active defect states , with recombination lasting over tens of nanoseconds due to slow hole capture in the defect states .
it is important to mention that simple bimolecular recombination ( proportional to @xmath118 ) and direct interband auger recombination ( proportional to @xmath119 ) are not sufficiently nonlinear to account for the density dependence seen in figure [ fig : powerdynamics](b ) .
although our data shows that the recombination times in multilayer mos@xmath4 are long , they are short in comparison with other indirect bandgap semiconductors , such as high - quality si or ge , which have recombination times in excess of one microsecond at room temperature@xcite .
we note here that our measurements might not have detected charge trapping dynamics occurring on much longer time scales ( @xmath12010 ns ) recently observed in mos@xmath4 photoconductive devices@xcite .
the authors would like to acknowledge helpful discussions with haining wang , michael g. spencer , and paul l. mceuen , as well as support from ccmr under nsf grant number dmr-1120296 , afosr - muri under grant number fa9550 - 09 - 1 - 0705 , onr under grant number n00014 - 12 - 1 - 0072 , and the cornell center for nanoscale systems funded by nsf .
the multilayer mos@xmath0 sample used in this study was cleaved from a large piece of natural mos@xmath0 ( spi supplies ) .
we adhered the resulting flake to completely cover a 2 mm clear aperture and mounted the sample in a cryostat . by measuring the broadband optical transmission interference fringes and using existing index of refraction data@xcite
, we determined that the average thickness of the flake was 4 @xmath11 m , with variations of @xmath121 @xmath11 m across the aperture .
electron - hole pairs were optically excited in the mos@xmath0 using sub-100 fs pulses from a ti : sapphire oscillator with a center frequency of 785 nm , pulse repetition rate of 81 mhz , and maximum fluence of 1.2 @xmath11j @xmath43 .
we used synchronized , few - cycle thz pulses , generated and detected with photoconductive switches in a thz time - domain spectrometer@xcite , to probe the excited carrier distribution .
optical pump and thz probe beams were mechanically chopped at 400 and 333 hz , respectively , and the detected photocurrent was demodulated with a lock - in amplifier at the sum frequency .
the fourier transform of equation [ eq : j ] is , @xmath122 where , @xmath123 equals @xmath124 $ ] . here , @xmath125 is the fourier transform operator with respect to @xmath126 .
measurement of @xmath42 enables one to obtain @xmath127 using equation [ eq : deltaj ] , and then @xmath123 can be obtained using the above equation . in general
, @xmath123 does not equal @xmath128@xcite . however ,
if the dc conductivity is changing slowly compared to the duration of the current impulse response @xmath38 then @xmath129 .
since the carrier density , and therefore the dc conductivity , varies slowly for @xmath130 ps in all of our measurements , we have extracted @xmath45 using this simple relation for @xmath131 ps . but extracting @xmath45 from @xmath123 for cases when the dc conductivity varies rapidly , such as in figure [ fig : tempdynamics](b ) , requires two transformations@xcite : first , @xmath132 $ ] , followed by , @xmath133 $ ] .
these transformations can add considerable noise , and we have employed them only to extract the dc conductivity changes for small pump - probe delays , @xmath134 ps , and low temperatures .
56 natexlab#1#1bibnamefont # 1#1bibfnamefont # 1#1citenamefont # 1#1url # 1`#1`urlprefix[2]#2 [ 2][]#2 , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/84/17/10.1063/1.1723695 . , , , , , , , , * * , ( ) , , , http://pubs.acs.org/doi/abs/10.1021/nl903868w . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevlett.105.136805 . , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl201874w . , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl2018178 .
, , , , , , , , , , , * * , ( ) , http://www.nature.com/ncomms/journal/v3/n6/full/ncomms1882.html . , , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/101/221907/1 . , , , , , , , , , , p. ( ) , http://www.nature.com/nmat/journal/v12/n6/full/nmat3633.html .
, , , , , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl4007479 . , , , , , _ _ ( ) , http://www.nature.com/nnano/journal/v7/n11/full/nnano.2012.193.html . , , , , , , , ,
, , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl302015v .
, , , , , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/102/25/10.1063/1.4811410 . , , , , , * * , ( ) , http://www.nature.com/nnano/journal/v8/n7/full/nnano.2013.100.html .
, , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl3043079 . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.87.201401 . , , , , , , , , * * , ( ) , http://www.nature.com/ncomms/2014/140117/ncomms4087/full/ncomms4087.html .
( ) , http://arxiv.org/abs/1403.5039 . , , , ,
* * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl303583v . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/102/042104/1 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrev.163.743 . , , , , , , , , , p. ( ) , http://www.nature.com/ncomms/journal/v3/n8/full/ncomms2018.html .
, , , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/102/123105/1 . , p. ( ) , http://www.nature.com/nmat/journal/v12/n9/full/nmat3687.html .
, , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?jap/113/133702/1 . , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.85.115317 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevx.4.011043 . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/99/102109/1 . , * * , ( ) . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.89.205436 . , * * , ( ) , http://link.aip.org/link/?jcp/110/8589/1 . , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.62.15764 . ,
* * , ( ) , http://link.aps.org/doi/10.1103/physrevb.71.235110 . , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl303988q .
, * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.86.241401 . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?adv/3/052111/1 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.45.3612 . , * * , ( ) .
, , , , * * , ( ) . , , , , * * , ( ) . , , , , , , , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/96/8/10.1063/1.3291615 . , _
_ ( , , ) , ed . , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.90.041402 . , , , , , , , , * * , ( ) , issn , http://dx.doi.org/10.1002/adma.201306322 . , , , , , , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nn403886t . , , ,
, ( ) , http://arxiv.org/abs/1406.5640 . ,
_ _ ( , , ) , ed . , * * , ( ) , http://link.aps.org/doi/10.1103/physrev.122.1742 . , pp . ( ) . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.6.1572 . , * * , ( ) , http://scitation.aip.org/content/aip/journal/jap/23/7/10.1063/1.1702301
, , , , * * , ( ) , , http://dx.doi.org/10.1080/00018739000101501 . , , , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevlett.83.4880 . , , , ,
* * , ( ) . , , , , , , , , , * * , ( ) , http://iopscience.iop.org/0957 - 4484/25/15/155201/. , * * , ( ) , , http://rspa.royalsocietypublishing.org/content/284/1398/402.abstract . ,
_ _ ( , , ) , ed .
we use equation 1 of the main text to estimate the frequency - dependent transmission of thz pulses through the mos@xmath0 sample .
equation 1 can be derived as follows .
we start with the exact solution for the transmission of light through an etalon with a refractive index @xmath135 and thickness @xmath15 , surrounded by air ( @xmath136 ) , @xmath137 in the limit , @xmath138 , @xmath139^{-1 } \label{eq : approx}\ ] ] for the measured thz refractive index of mos@xmath4 , @xmath140 , and the thickness of our sample , @xmath141 @xmath11 m , the approximation in the above expression is extremely good , as illustrated in figure [ fig : trans ] . in the case of a conductive medium , with conductivity @xmath10 , the complex refractive index is , @xmath143 . here , @xmath18 is the frequency - independent refractive index and @xmath144 is the permittivity of free space .
the inverse fourier transform of the relation in equation [ eq : approx ] gives , @xmath145 - \frac{1}{\epsilon_0(n^{2}-1 ) } j(t)\ ] ] subtracting versions of the above equation in the presence and absence of optical pumping one obtains , @xmath146 equation 2 in the text follows directly from the above relation following the substitution @xmath147 . in this section ,
we wish to establish equations 3 and 6 of the main text .
we assume that the current density @xmath148 in the sample for pump - probe delay @xmath26 in the presence of the field @xmath149 of a thz pulse and a time - dependent dc conductivity @xmath150 is@xcite , @xmath151 \otimes j(t ) \label{eq : js}\ ] ] here , @xmath38 is the normalized current impulse response ( @xmath39 ) and @xmath152 is the convolution operator with respect to @xmath126 .
this is the most general way of writing the current response if the current density obeys the operator equation , @xmath153 where , @xmath154 is a linear - time - invariant ( lti ) differential operator .
equation [ eq : js ] gives , @xmath155 = \tilde{e}(t , u ) \otimes \tilde{\sigma}(t , u)\ ] ] the change @xmath127 in the current density in the presence and absence of pumping is @xmath156 . here ,
the subscripts p and 0 indicate the value with and without optical pumping , respectively
. therefore , one obtains , @xmath157 by applying a fourier transform with respect to @xmath126 to each term , we have , @xmath158 equations 3 and 6 of the main text will be valid provided the final two terms on the right hand side of equation [ eq : dj ] are negligibly small compared to the first term . in figure [ fig : ratio ] , we show a representative measured ratio of @xmath159 , which is at most on the order of @xmath160 for the highest pump fluence used in our experiments . at all other temperatures , pump fluences , and pump - probe delays ,
this ratio is either similar or smaller . since @xmath161 at all frequencies
, we can safely neglect @xmath162 compared to @xmath163 in equation [ eq : dj ] .
next , using equation 2 from the main text , we see that the ratio @xmath164 s m@xmath2 .
in contrast , the measured value of the unpumped dc conductivity @xmath165 is smaller than @xmath166 s m@xmath2 and , therefore , @xmath167 at all frequencies .
consequently , we can also neglect @xmath168 compared to @xmath163 in equation [ eq : dj ] . in this way
, we empirically verify that our use of the approximations in equations 3 and 6 in the main text is valid for our our experiments .
theoretically , it can be shown that , @xmath169 the second term in equation [ eq : dj ] can be neglected provided @xmath170 , which is indeed the case in our experiments .
there are essentially two main mechanisms for the capture / emission of electrons and holes at / from localized crystal defects@xcite : ( 1 ) phonon - assisted processes , and ( 2 ) auger processes .
phonon - assisted processes can be single - phonon processes or multi - phonon processes , including phonon - cascade processes@xcite . in phonon - assisted processes the capture rates ( units : @xmath106s@xmath2 ) ,
tend to go linearly with the carrier density ( i.e. the capture times are independent of the carrier density ) .
the capture times observed in our experiments are carrier density dependent ( inverse electron capture times increase linearly with the electron density ) , as shown in figure 5(c ) of the main text .
the capture times in auger processes are carrier density dependent .
figure [ fig : auger ] shows the four basic auger processes for the capture of electrons ( ( i ) and ( ii ) ) and holes ( ( iii ) and ( iv ) ) at defects .
the corresponding emission processes are the just the inverse of the capture processes .
the rate equations for each auger process ( and its inverse ) can be written using figure [ fig : auger ] .
for example , the electron density rate equation for process ( i ) and its inverse is , @xmath174 here , @xmath18 is the electron density , @xmath98 is the rate constant for electron capture by the defect state , @xmath175 is the defect density , and @xmath176 is the occupation of the defect state .
the first terms describes the capture process and the second term describes the emission process . the value of the constant @xmath177 can be determined by using the fact that in thermal equilibrium @xmath178 : @xmath179 where @xmath180 is the equilibrium electron density and @xmath181 is the equilibrium defect occupation . if in equilibrium @xmath182 , as is expected for defects deeper than a few @xmath183 in an n - doped material ,
then @xmath184 can be assumed to be negligibly small and electron generation from the defect states can be ignored in the above equation .
process ( i ) and process ( ii ) can have comparable magnitudes@xcite .
so , ignoring emission processes , the rate equation for the electron density becomes , @xmath185 @xmath98 and @xmath186 are the rate constants for electron capture by the defect state corresponding to processes ( i ) and ( ii ) in figure [ fig : auger ] , respectively . in our experiments , since our mos@xmath4 sample is n - doped , the first term of the right hand side is more important for small pump fluence values ( when the hole density is small ) compared to the second term . for large pump fluence values , both the electron and the hole densities can become comparable and the second term on the right hand side may not be ignored .
however , at large pump fluences the effect of the second term is indistinguishable from the first term in our pump - probe experiments ( since both terms would result in the inverse electron capture time to increase linearly with the photoexcited carrier density ) .
since the pump fluences used in our experiments are relatively small ( and the maximum photoexcited carrier density is in the low @xmath187 @xmath106 ) , we have chosen to ignore the second term , corresponding to process ( ii ) , in the above equation for simplicity .
similarly , ignoring emission processes , the rate equation for the hole density becomes , @xmath188 here , @xmath74 is the hole density . @xmath189 and @xmath99 are the rate constants for hole capture by the defect state corresponding to processes ( iii ) and ( iv ) in figure [ fig : auger ] , respectively .
again , since our mos@xmath4 sample is n - doped and the pump fluences used in our experiments are small , we have chosen to ignore the second term , corresponding to process ( iv ) , in the above equation for simplicity . | the ultimate limitations on carrier mobilities in metal dichalcogenides , and the dynamics associated with carrier relaxation , are unclear .
we present measurements of the frequency - dependent conductivity of multilayer dichalcogenide mos@xmath0 by optical - pump terahertz - probe spectroscopy .
we find mobilities in this material approaching 4200 @xmath1v@xmath2s@xmath2 at low temperatures .
the temperature dependence of scattering indicates that the mobility , an order of magnitude larger than previously reported for mos@xmath0 , is intrinsically limited by acoustic phonon scattering at thz frequencies .
our measurements of carrier relaxation reveal picosecond cooling times followed by recombination lasting tens of nanoseconds and dominated by auger scattering into defects .
our results provide a useful context in which to understand and evaluate the performance of mos@xmath0-based electronic and optoelectronic devices .
layered two - dimensional transition metal dichalcogenides have recently enjoyed a resurgence of interest from the scientific community both from a new science perspective and also for novel applications@xcite .
in contrast to graphene , metal dichalcogenides have non - zero bandgaps and are also efficient light emitters , making them attractive for electronics and optoelectronics@xcite .
the ability to synthesize atomically thin semiconducting crystals and their heterostructures and transfer them to arbitrary substrates has opened the possibility of transparent , flexible electronics and optoelectronics based on these material systems@xcite .
the best reported carrier mobilities in metal dichalcogenides , typically in the few hundred @xmath3v@xmath2s@xmath2 range for mos@xmath4@xcite , are not as large as in graphene . but the reported mobilities are large in comparison to those of organic materials often used for flexible electronics@xcite .
physical mechanisms limiting the mobility of monolayer and multilayer mos@xmath0 field effect transistors have been the subject of several experimental@xcite and theoretical@xcite investigations .
charged impurity scattering , electron - phonon interaction , and screening by the surrounding dielectric environment are all believed to affect the mobility .
due to the challenge of isolating these effects , the intrinsic mobility of mos@xmath0 , and the ultimate performance of electronic devices , remains unclear .
similarly , carrier intraband and interband scattering and relaxation rates , which determine the performance of almost all proposed and demonstrated electronic and optoelectronic metal dichalcogenide devices , remain poorly understood . depicting carrier photoexcitation and recombination .
( c ) ( solid ) measured @xmath5 in units of detector current for a fixed pump - probe delay @xmath6 ps . @xmath7
ps ) is subtracted for clarity .
( dashed ) the scaled reference thz pulse @xmath8 . ] in this report , we present optical - pump thz - probe measurements of the time- and frequency - dependent conductivity of multilayer mos@xmath0 .
previously reported electrical measurements@xcite have probed the mos@xmath0 dc carrier transport , and all - optical measurements@xcite have probed the exciton temporal dynamics .
in contrast , optical - pump thz - probe spectroscopy can measure the time development of the complex intraband conductivity in the 0.2 - 2.0 thz frequency range with a temporal resolution better than a few hundred femtoseconds .
the frequency dependence of the measured intraband conductivity leads to the direct extraction of the carrier momentum scattering rate , from which the carrier mobility can be determined in a contact - free way .
in addition , the temporal development of the intraband conductivity reveals carrier interband and intraband relaxation dynamics .
our results show that the momentum scattering times in multilayer mos@xmath0 vary from @xmath990 fs at 300 k to @xmath91.46 ps at 30 k , corresponding to carrier mobilities of @xmath9257 and @xmath94200 @xmath3v@xmath2s@xmath2 , respectively .
the temperature dependence of the momentum scattering rate reveals that the mobility is limited by acoustic phonon scattering and the measured scattering times agree well with the theoretical predictions@xcite .
the measured mobility values are almost an order of magnitude larger than the previously reported values in multilayer mos@xmath0 devices@xcite .
our results indicate that the mobilities in reported mos@xmath0 electronic devices@xcite are likely limited by extrinsic mechanisms ( defects , impurities , grain boundaries , etc . ) and point to the ultimate performance of metal dichalcogenide electronic devices .
our measurements of carrier relaxation reveal picosecond cooling times varying from @xmath90.7 ps at 300 k to @xmath91.2 ps at 45 k. subsequent density - dependent recombination of carriers occurs over 10 s of nanoseconds at low temperature .
we present a recombination model based on carrier capture into defect states which reproduces the measured nonlinearity of this recombination versus carrier density as well as the observed temporal dynamics . | <s>[INST]thz - frequency radiation is sensitive to the frequency - dependent intraband conductivity of mos@xmath0 , @xmath10 , which contains information about carrier scattering and mobility . using a thz time - domain spectrometer@xcite
, we measure the amplitude and phase of broadband thz pulses transmitted through our 4 @xmath11 m thick natural mos@xmath0 samples . in a static transmission measurement , where the conductivity is time - independent , the thin - film ( @xmath12 ) amplitude transmission for thz pulses is ( see supplementary information ) , @xmath13^{-1 } \label{eq : tr}\ ] ] where @xmath14 is the frequency
, @xmath15 is the sample thickness , @xmath16 is the speed of light , @xmath17 is the impedance of free space , @xmath18 is the sample refractive index . using equation [ eq : tr ] and the measured spectra of thz pulses transmitted through an unpumped multilayer mos@xmath0 sample
, we obtained a constant value of refractive index @xmath19 in the 0.2 - 2.0 thz frequency range .
further , the unpumped dc conductivity @xmath20 was found to be in the range 10 - 20 s m@xmath2 indicating that the sample was very mildly doped .
electrical measurements on similar single - layer and multilayer samples have indicated that these mos@xmath4 samples tend to be n - doped@xcite .
given the large value of the refractive index and the small value of @xmath20 , this unpumped transmission measurement could not reliably determine the frequency dependence of the conductivity and thereby the mobility .
in contrast , since the change in thz transmission , @xmath21 , between pumped and unpumped samples is directly proportional to the change in the conductivity @xmath22 , optical - pump thz - probe spectroscopy is a highly - sensitive method to extract the frequency - dependent conductivity . in the optical - pump thz - probe scheme , depicted in figure [ fig : deltae](a - b ) , 780 nm center wavelength ( 1.58 ev ) , sub-100 fs optical pulses excite electron and hole distributions at the six @xmath23 points and the @xmath24 point , respectively , after which the distributions cool and recombine .
the field of the thz pulse transmitted through the pumped sample , @xmath25 , is sensitive to the evolving conductivity and , therefore , depends on the pump - probe delay @xmath26 . in our experiments ,
the incident optical and thz pulses are mechanically chopped at different frequencies and the transmitted thz pulse is measured at the sum frequency .
we therefore measure the change in the transmitted thz pulse , @xmath27 , in the presence ( @xmath28 ) and absence ( @xmath29 ) of optical pumping . in this paper ,
the symbol @xmath30 signifies the change in a quantity due to optical pumping .
figure [ fig : deltae](c ) shows the measured @xmath5 for a fixed delay of @xmath6 ps at different temperatures .
we also display @xmath31 , which was essentially temperature - independent .
@xmath5 contains information of both the amplitude and phase changes of @xmath31 upon pumping .
comparison of @xmath5 and @xmath31 shows a trend of increasing phase shifts with decreasing temperatures due to photoexcited carriers .
thus , both the amplitude and the phase of the transmitted thz pulse are needed to determine the sample response .
the sample response can be determined from the measured change in the transmitted thz pulse , @xmath5 , as follows .
we scan the pump - probe delay simultaneously with the transmitted thz pulse in the time - domain thz spectrometer such that each measured point of the transmitted thz pulse is at the same delay , @xmath26 , from the pump@xcite .
the measured pulse , @xmath32 , satisfies ( see supplementary information ) , @xmath33 where @xmath34 is the permittivity of free - space .
equation [ eq : deltaj ] describes the effect of the free - carrier and polarization current densities on the thz pulse .
the change in the free - carrier current density , @xmath35 , in the sample can be written approximately as ( see supplementary information ) , @xmath36 \label{eq : j}\ ] ] here , @xmath37 is the change in the dc conductivity and @xmath38 is the normalized current impulse response ( @xmath39 ) . in fourier domain , we define @xmath40 as @xmath41 .
techniques to extract @xmath40 from the measured @xmath42 are described in the methods section
. plotted versus frequency for various temperatures . in each case , the probe delay is @xmath6 ps , and the pump fluence is @xmath91.2 @xmath11j @xmath43 .
( dashed lines )
drude model fits to the measured conductivity spectra used to extract @xmath44 . ]
figure [ fig : drudefits ] shows the real and imaginary parts of the photoexcited conductivity @xmath45 measured at four different temperatures in mos@xmath0 .
we find that the measured conductivity spectra closely follow the drude form , @xmath46 , which is the simplest conductivity model in the relaxation time approximation .
therefore , the current impulse response @xmath47 is @xmath48 .
we fit the real and imaginary parts of the data simultaneously with a weighted least - squares regression and extract the photoexcited dc conductivity @xmath49 and the carrier momentum scattering time @xmath44 .
weights were the data variance at each frequency point over twenty scans .
the high quality of fits to the data obtained at all temperatures , as shown in figure [ fig : drudefits ] , is strong evidence of the fact that the change in thz transmission we measure indeed originates from the intraband conductivity of the photoexcited carriers .
also , at all temperatures we find no significant variation in the extracted value of @xmath44 for any value of @xmath26 in the range 5 ps @xmath50 12 ns .
since one expects very hot carriers to have average momentum scattering times different from that of cold carriers@xcite , this observation suggests that the carrier distributions after photoexcitation cool down on time scales shorter than a few picoseconds .
we further discuss carrier cooling times below .
carrier in - plane ( @xmath51 to c - axis ) mobility is related to the momentum scattering time by @xmath52 , where @xmath53 is the in - plane conductivity effective mass .
multilayer mos@xmath4 has six electron pockets in the brillouin zone , each with an anisotropic effective mass tensor@xcite .
the one hole pocket has an isotropic effective mass tensor . using dft values for the electron and hole effective mass tensors@xcite
, we find the conductivity effective masses for both electrons and holes to be @xmath90.61@xmath54 . in figure [ fig : mobility](a ) , we plot the electron mobilities corresponding to the measured momentum scattering times at different temperatures ( @xmath55 = 30 , 45 , 100 , 200 , 300 k ) .
we find a mobility of 257 @xmath1v@xmath2s@xmath2 at 300 k , increasing to 4200 @xmath1v@xmath2s@xmath2 at 30 k. for 300 k , the measured mobility is consistent with recent electronic transport measurements in multilayer mos@xmath0@xcite . but
the mobilities we find below 200 k in this contact - free measurement are significantly higher than the values previously reported for mos@xmath0 .
k. the @xmath56 dependence at low temperatures suggests acoustic phonon scattering as the dominant scattering mechanism .
meascured mobility reaches @xmath94200 @xmath1v@xmath2s@xmath2 at 30 k. ] in figure [ fig : mobility](b ) , we plot the carrier momentum scattering rate , @xmath57 , versus temperature .
the scattering rate for @xmath58 k increases linearly with temperature .
this linear temperature dependence is expected for quasi - elastic acoustic phonon scattering in 2d and layered materials in the equipartition regime@xcite .
other scattering mechanisms , such as impurity scattering , have a different temperature dependence for layered materials@xcite .
the larger scattering rate observed at the highest temperature ( 300 k ) likely indicates an optical phonon scattering contribution@xcite . in the deformation - potential approximation , the energy - independent acoustic - phonon - limited momentum scattering rate in 2d and layered materials is related to the temperature by@xcite , @xmath59 where @xmath60 is the deformation potential , @xmath61 is the 2d mass density , @xmath62 is the la phonon velocity , and @xmath63 is the carrier density of states effective mass . from the data in figure [
fig : mobility](b ) , we find @xmath64 ns@xmath2k@xmath2 for @xmath65 k. using @xmath66 m s@xmath2@xcite , @xmath67 kg m@xmath68 , @xmath69 ( ab - initio values for @xmath63 are almost identical for electrons and holes@xcite ) , we find @xmath70 ev . this value compares well with previously experimentally and theoretically determined values , generally in the 2 - 10 ev range , for the deformation potentials in single - layer and multilayer mos@xmath4@xcite . knowing @xmath47 and @xmath45 , we determine the photoexcited dc conductivity , @xmath49 ( see methods ) . the temporal resolution in our experiments is set by the measurement bandwidth of @xmath45 , @xmath91.8 thz , and is approximately @xmath71 ps .
since the in - plane conductivity effective masses for electrons and holes are approximately the same in multilayer mos@xmath4@xcite , one can write the dc conductivity as @xmath72 , where @xmath73 is the total mobile carrier density and equals the sum of the mobile electron density , @xmath18 , and the mobile hole density , @xmath74 .
the change in the carrier density @xmath75 can be determined from the measurement of @xmath76 .
, versus pump - probe delay on short time scales ( -2 @xmath50 5 ps ) .
we show data for two representative temperatures ( ( a ) 300 k and ( b ) 45 k ) , each with a pump fluence of @xmath91.2 @xmath11j @xmath43 . immediately after the pump pulse , the conductivity increases , reaching its maximum value within 5 ps at all temperatures .
the rise time is slower at 45 k than at 300 k. ] figure [ fig : tempdynamics ] shows the measured change in the conductivity @xmath77 on short time scales ( @xmath78 ps ) for two different representative temperatures .
the pump fluence in each case is @xmath91.2 @xmath11j/@xmath3 . immediately after photoexcitation ( @xmath79 ) , the conductivity increases , reaching its maximum value within 5 ps at all temperatures .
the error - range displayed for each data point represents a 95% confidence interval for the fitting parameter @xmath77 .
the dashed lines superimposed on the data represent fittings using exponential curves with 0.7 ps and 1.2 ps time constants at 300 k and 45 k , respectively .
our data suggests that the conductivity reaches its peak value faster at higher temperatures .
as we discuss below , we attribute these short - time - scale dynamics to picosecond cooling of the electron and hole distributions .
as depicted in figure [ fig : deltae](b ) , the 1.58 ev pump photons excite electrons from the valence band maximum at the @xmath24 point to the conduction band minima at the @xmath23 point by a phonon - assisted ( or impurity - assisted ) indirect absorption process . since the indirect bandgap in multilayer mos@xmath4 is around 1.29 ev@xcite ,
the photoexcited electrons and holes are at an elevated temperature compared to the lattice immediately after photoexcitation and thermalization@xcite .
if the photon energy in excess of the indirect bandgap contributes to the kinetic energy of the carriers , we estimate the carrier temperature immediately after photoexcitation to be around 1100 k. at this high temperature , the electron and hole distributions would be spread out in energy , with fast momentum scattering rates and reduced mobility due to optical phonons@xcite . as the carrier distributions relax towards the band extrema and cool via optical phonon emission , the carrier momentum scattering rates decrease and the conductivity increases .
the rise in the conductivity following photoexcitation observed in our experiments is therefore indicative of carrier cooling .
the slower cooling observed at lower lattice temperatures can be attributed to a number of factors .
for example , the carrier cooling rates due to optical phonon emission are proportional to @xmath80 , where @xmath81 , the bose occupation factor for phonons , is aproximately 20% larger at 300 k compared to 45 k. in addition , the heat capacity of optical phonons is around three orders of magnitude larger at 300 k compared to 45 k and , therefore , carrier cooling bottleneck due to the generation of hot phonons is much reduced at higher lattice temepratures@xcite .
plotted on a log scale as a function of probe delay .
shown are transients for four pump fluences ( 0.2 , 0.4 , 0.8 , and 1.2 @xmath11j @xmath43 ) at 45 k. ( blue dot - dash ) initial exponential relaxation corresponding to the estimated @xmath82 .
( red dash ) full transient simulations using equations [ eq : model ] .
( b ) measured @xmath83 ( circles ) and @xmath84 ( diamonds ) versus pump fluence at 45 k. ( solid ) curves obtained from simulations of equations [ eq : model ] .
( c ) the measured inverse decay time @xmath85 at 45 k versus @xmath86 .
the slope of the line estimates the electron capture rate @xmath87 .
] figure [ fig : powerdynamics](a ) shows the change in the mobile carrier density @xmath88 at 45 k for various pump fluences , determined from measured @xmath77 on long time scales ( @xmath89 ps ) .
as expected , the carrier density decays after reaching a peak value in the first few picoseconds after photoexcitation .
we attribute this relaxation to carrier trapping and recombination by defects .
the carrier density decay rate is relatively fast in the first @xmath9100 ps after photoexcitation , after which the decay occurs on much longer time scales .
the maximum probe delay allowed by our setup , 400 ps , is unable to resolve these long time scales .
but the non - zero carrier densities observed at negative probe delays show that the photoexcited carrier density does not completely decay in the time interval , around 12.3 ns , between two successive optical pulses .
the carrier densities immediately before and after photoexcitation , as a function of pump fluence , reveal the carrier density dependence of the long term ( @xmath90100 ps ) recombination rates .
figure [ fig : powerdynamics](b ) shows the change in carrier density immediately before , @xmath91 , and after , @xmath92 , photoexcitation .
both @xmath93 and @xmath94 increase with the pump fluence in a nonlinear fashion , so carrier - density - independent recombination times can be ruled out .
we also estimate the initial recombination rate , @xmath95 , versus pump fluence from the slope of the blue dash - dot lines in figure [ fig : powerdynamics](a ) .
figure [ fig : powerdynamics](c ) shows that @xmath85 increases approximately linearly with @xmath94 .
any physical model that describes the observed carrier dynamics must account for the transition from the fast decay rates in the first @xmath9100 ps to the slow decay rates thereafter .
in addition , the model must account for the severe nonlinearity of @xmath96 and @xmath86 versus pump fluence .
here , we present a model of carrier relaxation based on trapping and recombination by optically - active defect states .
this model explains all features of the observed carrier dynamics at 45 k. the natural mos@xmath0 used in our work is known to have defects such as vacancies , grain boundaries , and impurities@xcite .
many of these defects are optically active in the near - ir wavelength region and appear in the optical absorption spectra@xcite .
we assume that the initial fast decay of the photoexcited carrier density is due to the capture of electrons by defect states in the bandgap@xcite ( see figure [ fig : deltae](b ) ) . as these defect
states become full of electrons , the decay rate decreases ( due to pauli blocking ) and becomes limited by the capture of photoexcited holes from the valence band .
the optical pump pulse excites electrons to the conduction band from both the valence band and also the defect states , and we assume that the defect states become empty immediately after the pump pulse@xcite .
our final assumption is that the defect states are assumed to be occupied by electrons in thermal equilibrium in our n - doped sample .
ignoring thermal generation of electrons and holes from defect states , the rate equations for the decay of the electron and hole densities in our model are ( see supplementary information ) , @xmath97 here , @xmath18 and @xmath74 are the total mobile electron and hole densities , respectively , and @xmath98 ( @xmath99 ) is the rate constant for electron capture ( hole capture ) by the defect states via the dominant auger mechanisms in a n - doped semiconductor@xcite .
the value @xmath18 is the sum of the equilibrium electron density , @xmath100 , and the excess photoexcited electron density .
@xmath101 is the density of defect states , and @xmath102 is the electron occupation of the defect states , assumed to be unity in equilibrium . note that a phonon - assisted carrier trapping process would not have the carrier density dependence consistent with the observed decay rates@xcite .
we varied the values of the fitting parameters @xmath98 , @xmath99 , @xmath103 , and @xmath100 in simulations to fit the data in figures [ fig : powerdynamics](a ) and [ fig : powerdynamics](b ) .
the simulations involved time - stepping the rate equations over many ( 1 - 5@xmath104 ) pump pulse cycles until a steady state was achieved .
the difference @xmath105 @xmath106 per @xmath11j @xmath43 determined the mobile carrier density created by the pump pulse in our simulations .
the data in figure [ fig : powerdynamics ] can inform the search for appropriate values of the fitting parameters . immediately after photoexcitation , since @xmath18 varies as @xmath107 , the slope of the line in figure [ fig : powerdynamics](c ) estimates the product @xmath108 . since the long term decay of the photoexcited density is limited by the capture of holes in defects , the values of @xmath96 estimate the product @xmath109 .
finally , the density of defect states governs how quickly they fill with electrons , therefore @xmath101 is determined from the time at which the initial fast decay transitions to the slower decay , as measured in figure [ fig : powerdynamics](a ) .
the values of fitting parameters that best fit the data are : @xmath110 @xmath111 s@xmath2 , @xmath112 @xmath111 s@xmath2 , @xmath113 @xmath106 , and @xmath114 @xmath106 . this value of @xmath100 corresponds to a dc conductivity of 12 s m@xmath2 , which compares well with the value of conductivity obtained from thz transmission measurements of the unpumped sample , @xmath115 s m@xmath2 .
the model presented here closely agrees with the data , accurately reproducing the values of @xmath96 , the relaxation curves , and the nonlinearity of @xmath75 versus pump fluence .
in this paper , we presented measurements of the mobility of photoexcited carriers in multilayer mos@xmath0 using thz time - domain spectroscopy .
the observed temperature dependence of the mobility for @xmath116 k indicates acoustic phonon scattering as the dominant mobility - limiting mechanism .
the measured carrier momentum scattering rates are comparable to theoretical predictions based on phonon - scattering - limited transport@xcite .
in contrast , previously reported dc electrical measurements have suggested impurity or defect scattering as the dominant mobility - limiting mechanism in multilayer mos@xmath0@xcite .
given the prevalence of defects and impurities in mos@xmath0@xcite , it is intriguing that we observe mobilities limited by acoustic phonon scattering .
the observed high mobilities at low temperatures in our experiments could be related to the fact that our measurements were performed at very high frequencies .
it is well known theoretically and experimentally that ac conductivity in disordered materials increases with the ac frequency@xcite .
this phenomenon appears in the microscopic models of hopping conduction@xcite as well as in the classical models of the ac conductivity in inhomogeneous materials@xcite .
since we did not see signatures of ac hopping conduction in our sample at any temperature , we believe models that describe the ac conductivity in inhomogeneous materials are more relevant to our observations@xcite . accordingly , we believe that the mos@xmath4 atomic layers in our sample consist of interspersed high and low mobility regions ( due to grain boundaries , crystal defects , impurities , etc.@xcite ) and the conductivity of the layers is determined by the resistive and capacitive couplings of these regions@xcite . even a small fraction of low mobility regions can significantly affect the dc conductivity in lower dimensions .
the high mobility regions have a conductivity given by the drude form .
the ac conductivity of the sample is then expected to increase with the frequency until the low mobility regions are capacitively shorted out and the conductivity of the sample is then limited by the drude conductivity of the high mobility regions .
although this model qualitatively explains the observation of the long momentum scattering times in our experiments , investigation of the frequency dependence of the sample conductivity in the low frequency region ( @xmath117 thz ) is needed to fully understand the nature of the transport and determine which model , if any , best describes the nature of the conduction .
carrier relaxation and recombination dynamics directly affect the performance of almost all electronic and optoelectronic devices .
we have observed several time scales in the dynamics associated with carrier relaxation and recombination .
the initial intraband relaxation ( or carrier cooling ) occurs within 5 ps .
carrier interband recombination appears to result from carrier trapping in optically active defect states , with recombination lasting over tens of nanoseconds due to slow hole capture in the defect states .
it is important to mention that simple bimolecular recombination ( proportional to @xmath118 ) and direct interband auger recombination ( proportional to @xmath119 ) are not sufficiently nonlinear to account for the density dependence seen in figure [ fig : powerdynamics](b ) .
although our data shows that the recombination times in multilayer mos@xmath4 are long , they are short in comparison with other indirect bandgap semiconductors , such as high - quality si or ge , which have recombination times in excess of one microsecond at room temperature@xcite .
we note here that our measurements might not have detected charge trapping dynamics occurring on much longer time scales ( @xmath12010 ns ) recently observed in mos@xmath4 photoconductive devices@xcite .
the authors would like to acknowledge helpful discussions with haining wang , michael g. spencer , and paul l. mceuen , as well as support from ccmr under nsf grant number dmr-1120296 , afosr - muri under grant number fa9550 - 09 - 1 - 0705 , onr under grant number n00014 - 12 - 1 - 0072 , and the cornell center for nanoscale systems funded by nsf .
the multilayer mos@xmath0 sample used in this study was cleaved from a large piece of natural mos@xmath0 ( spi supplies ) .
we adhered the resulting flake to completely cover a 2 mm clear aperture and mounted the sample in a cryostat . by measuring the broadband optical transmission interference fringes and using existing index of refraction data@xcite
, we determined that the average thickness of the flake was 4 @xmath11 m , with variations of @xmath121 @xmath11 m across the aperture .
electron - hole pairs were optically excited in the mos@xmath0 using sub-100 fs pulses from a ti : sapphire oscillator with a center frequency of 785 nm , pulse repetition rate of 81 mhz , and maximum fluence of 1.2 @xmath11j @xmath43 .
we used synchronized , few - cycle thz pulses , generated and detected with photoconductive switches in a thz time - domain spectrometer@xcite , to probe the excited carrier distribution .
optical pump and thz probe beams were mechanically chopped at 400 and 333 hz , respectively , and the detected photocurrent was demodulated with a lock - in amplifier at the sum frequency .
the fourier transform of equation [ eq : j ] is , @xmath122 where , @xmath123 equals @xmath124 $ ] . here , @xmath125 is the fourier transform operator with respect to @xmath126 .
measurement of @xmath42 enables one to obtain @xmath127 using equation [ eq : deltaj ] , and then @xmath123 can be obtained using the above equation . in general
, @xmath123 does not equal @xmath128@xcite . however ,
if the dc conductivity is changing slowly compared to the duration of the current impulse response @xmath38 then @xmath129 .
since the carrier density , and therefore the dc conductivity , varies slowly for @xmath130 ps in all of our measurements , we have extracted @xmath45 using this simple relation for @xmath131 ps . but extracting @xmath45 from @xmath123 for cases when the dc conductivity varies rapidly , such as in figure [ fig : tempdynamics](b ) , requires two transformations@xcite : first , @xmath132 $ ] , followed by , @xmath133 $ ] .
these transformations can add considerable noise , and we have employed them only to extract the dc conductivity changes for small pump - probe delays , @xmath134 ps , and low temperatures .
56 natexlab#1#1bibnamefont # 1#1bibfnamefont # 1#1citenamefont # 1#1url # 1`#1`urlprefix[2]#2 [ 2][]#2 , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/84/17/10.1063/1.1723695 . , , , , , , , , * * , ( ) , , , http://pubs.acs.org/doi/abs/10.1021/nl903868w . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevlett.105.136805 . , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl201874w . , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl2018178 .
, , , , , , , , , , , * * , ( ) , http://www.nature.com/ncomms/journal/v3/n6/full/ncomms1882.html . , , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/101/221907/1 . , , , , , , , , , , p. ( ) , http://www.nature.com/nmat/journal/v12/n6/full/nmat3633.html .
, , , , , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl4007479 . , , , , , _ _ ( ) , http://www.nature.com/nnano/journal/v7/n11/full/nnano.2012.193.html . , , , , , , , ,
, , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl302015v .
, , , , , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/102/25/10.1063/1.4811410 . , , , , , * * , ( ) , http://www.nature.com/nnano/journal/v8/n7/full/nnano.2013.100.html .
, , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl3043079 . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.87.201401 . , , , , , , , , * * , ( ) , http://www.nature.com/ncomms/2014/140117/ncomms4087/full/ncomms4087.html .
( ) , http://arxiv.org/abs/1403.5039 . , , , ,
* * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl303583v . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/102/042104/1 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrev.163.743 . , , , , , , , , , p. ( ) , http://www.nature.com/ncomms/journal/v3/n8/full/ncomms2018.html .
, , , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/102/123105/1 . , p. ( ) , http://www.nature.com/nmat/journal/v12/n9/full/nmat3687.html .
, , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?jap/113/133702/1 . , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.85.115317 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevx.4.011043 . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?apl/99/102109/1 . , * * , ( ) . , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.89.205436 . , * * , ( ) , http://link.aip.org/link/?jcp/110/8589/1 . , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.62.15764 . ,
* * , ( ) , http://link.aps.org/doi/10.1103/physrevb.71.235110 . , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nl303988q .
, * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.86.241401 . , , , , , * * , ( pages ) ( ) , http://link.aip.org/link/?adv/3/052111/1 . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.45.3612 . , * * , ( ) .
, , , , * * , ( ) . , , , , * * , ( ) . , , , , , , , , , , , * * , ( ) , http://scitation.aip.org/content/aip/journal/apl/96/8/10.1063/1.3291615 . , _
_ ( , , ) , ed . , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.90.041402 . , , , , , , , , * * , ( ) , issn , http://dx.doi.org/10.1002/adma.201306322 . , , , , , , , , , , , * * , ( ) , , http://pubs.acs.org/doi/abs/10.1021/nn403886t . , , ,
, ( ) , http://arxiv.org/abs/1406.5640 . ,
_ _ ( , , ) , ed . , * * , ( ) , http://link.aps.org/doi/10.1103/physrev.122.1742 . , pp . ( ) . , * * , ( ) , http://link.aps.org/doi/10.1103/physrevb.6.1572 . , * * , ( ) , http://scitation.aip.org/content/aip/journal/jap/23/7/10.1063/1.1702301
, , , , * * , ( ) , , http://dx.doi.org/10.1080/00018739000101501 . , , , , , , , * * , ( ) , http://link.aps.org/doi/10.1103/physrevlett.83.4880 . , , , ,
* * , ( ) . , , , , , , , , , * * , ( ) , http://iopscience.iop.org/0957 - 4484/25/15/155201/. , * * , ( ) , , http://rspa.royalsocietypublishing.org/content/284/1398/402.abstract . ,
_ _ ( , , ) , ed .
we use equation 1 of the main text to estimate the frequency - dependent transmission of thz pulses through the mos@xmath0 sample .
equation 1 can be derived as follows .
we start with the exact solution for the transmission of light through an etalon with a refractive index @xmath135 and thickness @xmath15 , surrounded by air ( @xmath136 ) , @xmath137 in the limit , @xmath138 , @xmath139^{-1 } \label{eq : approx}\ ] ] for the measured thz refractive index of mos@xmath4 , @xmath140 , and the thickness of our sample , @xmath141 @xmath11 m , the approximation in the above expression is extremely good , as illustrated in figure [ fig : trans ] . in the case of a conductive medium , with conductivity @xmath10 , the complex refractive index is , @xmath143 . here , @xmath18 is the frequency - independent refractive index and @xmath144 is the permittivity of free space .
the inverse fourier transform of the relation in equation [ eq : approx ] gives , @xmath145 - \frac{1}{\epsilon_0(n^{2}-1 ) } j(t)\ ] ] subtracting versions of the above equation in the presence and absence of optical pumping one obtains , @xmath146 equation 2 in the text follows directly from the above relation following the substitution @xmath147 . in this section ,
we wish to establish equations 3 and 6 of the main text .
we assume that the current density @xmath148 in the sample for pump - probe delay @xmath26 in the presence of the field @xmath149 of a thz pulse and a time - dependent dc conductivity @xmath150 is@xcite , @xmath151 \otimes j(t ) \label{eq : js}\ ] ] here , @xmath38 is the normalized current impulse response ( @xmath39 ) and @xmath152 is the convolution operator with respect to @xmath126 .
this is the most general way of writing the current response if the current density obeys the operator equation , @xmath153 where , @xmath154 is a linear - time - invariant ( lti ) differential operator .
equation [ eq : js ] gives , @xmath155 = \tilde{e}(t , u ) \otimes \tilde{\sigma}(t , u)\ ] ] the change @xmath127 in the current density in the presence and absence of pumping is @xmath156 . here ,
the subscripts p and 0 indicate the value with and without optical pumping , respectively
. therefore , one obtains , @xmath157 by applying a fourier transform with respect to @xmath126 to each term , we have , @xmath158 equations 3 and 6 of the main text will be valid provided the final two terms on the right hand side of equation [ eq : dj ] are negligibly small compared to the first term . in figure [ fig : ratio ] , we show a representative measured ratio of @xmath159 , which is at most on the order of @xmath160 for the highest pump fluence used in our experiments . at all other temperatures , pump fluences , and pump - probe delays ,
this ratio is either similar or smaller . since @xmath161 at all frequencies
, we can safely neglect @xmath162 compared to @xmath163 in equation [ eq : dj ] .
next , using equation 2 from the main text , we see that the ratio @xmath164 s m@xmath2 .
in contrast , the measured value of the unpumped dc conductivity @xmath165 is smaller than @xmath166 s m@xmath2 and , therefore , @xmath167 at all frequencies .
consequently , we can also neglect @xmath168 compared to @xmath163 in equation [ eq : dj ] . in this way
, we empirically verify that our use of the approximations in equations 3 and 6 in the main text is valid for our our experiments .
theoretically , it can be shown that , @xmath169 the second term in equation [ eq : dj ] can be neglected provided @xmath170 , which is indeed the case in our experiments .
there are essentially two main mechanisms for the capture / emission of electrons and holes at / from localized crystal defects@xcite : ( 1 ) phonon - assisted processes , and ( 2 ) auger processes .
phonon - assisted processes can be single - phonon processes or multi - phonon processes , including phonon - cascade processes@xcite . in phonon - assisted processes the capture rates ( units : @xmath106s@xmath2 ) ,
tend to go linearly with the carrier density ( i.e. the capture times are independent of the carrier density ) .
the capture times observed in our experiments are carrier density dependent ( inverse electron capture times increase linearly with the electron density ) , as shown in figure 5(c ) of the main text .
the capture times in auger processes are carrier density dependent .
figure [ fig : auger ] shows the four basic auger processes for the capture of electrons ( ( i ) and ( ii ) ) and holes ( ( iii ) and ( iv ) ) at defects .
the corresponding emission processes are the just the inverse of the capture processes .
the rate equations for each auger process ( and its inverse ) can be written using figure [ fig : auger ] .
for example , the electron density rate equation for process ( i ) and its inverse is , @xmath174 here , @xmath18 is the electron density , @xmath98 is the rate constant for electron capture by the defect state , @xmath175 is the defect density , and @xmath176 is the occupation of the defect state .
the first terms describes the capture process and the second term describes the emission process . the value of the constant @xmath177 can be determined by using the fact that in thermal equilibrium @xmath178 : @xmath179 where @xmath180 is the equilibrium electron density and @xmath181 is the equilibrium defect occupation . if in equilibrium @xmath182 , as is expected for defects deeper than a few @xmath183 in an n - doped material ,
then @xmath184 can be assumed to be negligibly small and electron generation from the defect states can be ignored in the above equation .
process ( i ) and process ( ii ) can have comparable magnitudes@xcite .
so , ignoring emission processes , the rate equation for the electron density becomes , @xmath185 @xmath98 and @xmath186 are the rate constants for electron capture by the defect state corresponding to processes ( i ) and ( ii ) in figure [ fig : auger ] , respectively . in our experiments , since our mos@xmath4 sample is n - doped , the first term of the right hand side is more important for small pump fluence values ( when the hole density is small ) compared to the second term . for large pump fluence values , both the electron and the hole densities can become comparable and the second term on the right hand side may not be ignored .
however , at large pump fluences the effect of the second term is indistinguishable from the first term in our pump - probe experiments ( since both terms would result in the inverse electron capture time to increase linearly with the photoexcited carrier density ) .
since the pump fluences used in our experiments are relatively small ( and the maximum photoexcited carrier density is in the low @xmath187 @xmath106 ) , we have chosen to ignore the second term , corresponding to process ( ii ) , in the above equation for simplicity .
similarly , ignoring emission processes , the rate equation for the hole density becomes , @xmath188 here , @xmath74 is the hole density . @xmath189 and @xmath99 are the rate constants for hole capture by the defect state corresponding to processes ( iii ) and ( iv ) in figure [ fig : auger ] , respectively .
again , since our mos@xmath4 sample is n - doped and the pump fluences used in our experiments are small , we have chosen to ignore the second term , corresponding to process ( iv ) , in the above equation for simplicity .[/INST] the ultimate limitations on carrier mobilities in metal dichalcogenides , and the dynamics associated with carrier relaxation , are unclear .
we present measurements of the frequency - dependent conductivity of multilayer dichalcogenide mos@xmath0 by optical - pump terahertz - probe spectroscopy .
we find mobilities in this material approaching 4200 @xmath1v@xmath2s@xmath2 at low temperatures .
the temperature dependence of scattering indicates that the mobility , an order of magnitude larger than previously reported for mos@xmath0 , is intrinsically limited by acoustic phonon scattering at thz frequencies .
our measurements of carrier relaxation reveal picosecond cooling times followed by recombination lasting tens of nanoseconds and dominated by auger scattering into defects .
our results provide a useful context in which to understand and evaluate the performance of mos@xmath0-based electronic and optoelectronic devices .
layered two - dimensional transition metal dichalcogenides have recently enjoyed a resurgence of interest from the scientific community both from a new science perspective and also for novel applications@xcite .
in contrast to graphene , metal dichalcogenides have non - zero bandgaps and are also efficient light emitters , making them attractive for electronics and optoelectronics@xcite .
the ability to synthesize atomically thin semiconducting crystals and their heterostructures and transfer them to arbitrary substrates has opened the possibility of transparent , flexible electronics and optoelectronics based on these material systems@xcite .
the best reported carrier mobilities in metal dichalcogenides , typically in the few hundred @xmath3v@xmath2s@xmath2 range for mos@xmath4@xcite , are not as large as in graphene . but the reported mobilities are large in comparison to those of organic materials often used for flexible electronics@xcite .
physical mechanisms limiting the mobility of monolayer and multilayer mos@xmath0 field effect transistors have been the subject of several experimental@xcite and theoretical@xcite investigations .
charged impurity scattering , electron - phonon interaction , and screening by the surrounding dielectric environment are all believed to affect the mobility .
due to the challenge of isolating these effects , the intrinsic mobility of mos@xmath0 , and the ultimate performance of electronic devices , remains unclear .
similarly , carrier intraband and interband scattering and relaxation rates , which determine the performance of almost all proposed and demonstrated electronic and optoelectronic metal dichalcogenide devices , remain poorly understood . depicting carrier photoexcitation and recombination .
( c ) ( solid ) measured @xmath5 in units of detector current for a fixed pump - probe delay @xmath6 ps . @xmath7
ps ) is subtracted for clarity .
( dashed ) the scaled reference thz pulse @xmath8 . ] in this report , we present optical - pump thz - probe measurements of the time- and frequency - dependent conductivity of multilayer mos@xmath0 .
previously reported electrical measurements@xcite have probed the mos@xmath0 dc carrier transport , and all - optical measurements@xcite have probed the exciton temporal dynamics .
in contrast , optical - pump thz - probe spectroscopy can measure the time development of the complex intraband conductivity in the 0.2 - 2.0 thz frequency range with a temporal resolution better than a few hundred femtoseconds .
the frequency dependence of the measured intraband conductivity leads to the direct extraction of the carrier momentum scattering rate , from which the carrier mobility can be determined in a contact - free way .
in addition , the temporal development of the intraband conductivity reveals carrier interband and intraband relaxation dynamics .
our results show that the momentum scattering times in multilayer mos@xmath0 vary from @xmath990 fs at 300 k to @xmath91.46 ps at 30 k , corresponding to carrier mobilities of @xmath9257 and @xmath94200 @xmath3v@xmath2s@xmath2 , respectively .
the temperature dependence of the momentum scattering rate reveals that the mobility is limited by acoustic phonon scattering and the measured scattering times agree well with the theoretical predictions@xcite .
the measured mobility values are almost an order of magnitude larger than the previously reported values in multilayer mos@xmath0 devices@xcite .
our results indicate that the mobilities in reported mos@xmath0 electronic devices@xcite are likely limited by extrinsic mechanisms ( defects , impurities , grain boundaries , etc . ) and point to the ultimate performance of metal dichalcogenide electronic devices .
our measurements of carrier relaxation reveal picosecond cooling times varying from @xmath90.7 ps at 300 k to @xmath91.2 ps at 45 k. subsequent density - dependent recombination of carriers occurs over 10 s of nanoseconds at low temperature .
we present a recombination model based on carrier capture into defect states which reproduces the measured nonlinearity of this recombination versus carrier density as well as the observed temporal dynamics . </s> |
in the last few years , an increasing attention has been paid to possible nonextensive effects in the fields of thermodynamics and statistical mechanics .
the main motivation is the lack of a comprehensive treatment including gravitational and coulombian fields for which the assumed additivity of the entropy present in the standard approach is not valid [ 1 - 2 ] .
inspired on such problems , as well as in the traditional ensemble theory , tsallis@xcite proposed a remarkable @xmath0-parameterized nonextensive entropic expression which reduces to the extensive gibbs - jaynes - shannon entropy in the limiting case @xmath4 ( see @xcite for a regularly updated bibliography on this subject ) .
later on , the first attempts exploring the kinetic route associated to this nonextensive approach appeared in the literature[5 - 10 ] . the original kinetic derivation advanced by maxwell@xcite was generalized to include power law distributions as required by this enlarged framework .
in particular , it was shown that the equilibrium velocity @xmath0-distribution @xmath5^{1/(1-q)},\ ] ] is uniquely determined from two simple requirements@xcite : ( i ) isotropy of the velocity space , and ( ii ) a suitable nonextensive generalization of the maxwell factorizability condition , or equivalently , the assumption that @xmath6 .
the quantity @xmath7 above denotes the @xmath0-dependent normalization constant whose expression on the interval @xmath8 is @xmath9 where @xmath10 is the particle number density , @xmath11 is the mass and @xmath12 is the temperature . as expected , in the limiting case @xmath4 , such expressions reduce to the standard maxwellian ones@xcite .
more recently , the kinetic foundations of the above distribution were investigated in a deeper level through the generalized boltzmann s transport equation@xcite @xmath13 where @xmath14 is the @xmath0-nonextensive integral source term measuring the change in @xmath15 due to collisions .
this boltzmannian like approach incorporated the nonextensive effects using two different ingredients .
first , a new functional form to the kinetic local gas entropy , and , second , a nonfactorizable distribution function for the colliding pairs of particles whose physical meaning is quite clear : the boltzmann chaos molecular hypothesis is not valid in this extended framework .
it was also shown that the kinetic version of the tsallis entropy satisfies an @xmath16-theorem , and more important still , the @xmath0-parameterized class of power law velocity distributions emerged as the unique nonextensive solution describing the equilibrium states . in this paper
we go one step further by computing the basic nonextensive transport coefficients for dilute gases and plasmas . due to the intricate form of the new collisional term ,
we adopt here the relaxation - time model proposed by bhatnager , gross and krook@xcite because it permits an exact mathematical treatment . in spite of its limitation , the relaxation - time model ( henceforth bgk model )
has been proved quite useful from a methodological viewpoint because it yields the correct answer to the problem in a first approximation , and as such , it can guide us to the correct nonextensive results which must rigorously be obtained using the full @xmath0-transport equation .
as we shall see , analytical expressions for the transport coefficients of a dilute gas are readily obtained with basis on the local @xmath0-nonextensive distribution . in particular , we show that the available experimental results to the ratio @xmath1/@xmath2 constrains the @xmath0-parameter on the interval @xmath3 . as expected , in the extensive limiting case , the classical expressions of the transport coefficients are readily recovered .
however , due to a surprising cancellation , the standard electric conductivity of a dilute neutral plasma is not modified .
the analysis presented here is also compared with independent calculations based on rather different approaches@xcite .
let us now consider a dilute gas whose particles are acted by external forces
. in the bgk approximation the @xmath0-transport equation ( [ beq ] ) reads : @xmath17 where @xmath18 is the external force and @xmath11 is the mass of the particles . in this approximation
, @xmath19 is the local equilibrium distribution function and @xmath20 is a relaxation time which is a number of the order of the collision time .
we recall that under stationary conditions the distribution function does not depend on time , however , the concentration , and the temperature , are local quantities .
the whole system is assumed to be out but close to the local stationary equilibrium state@xcite .
in particular , this means that the resulting nonequilibrium distribution , @xmath21 , is only slightly different from the equilibrium unperturbed stationary distribution , @xmath22 , and can be approximated as latexmath:[\[\label{oi } f({\bf r},{\bf v})=f_0({\bf v},{\bf r})+g({\bf v},{\bf r}),\quad nonextensive distribution on the thermal conductivity @xmath1 .
it will be assumed that the heat flux is macroscopically governed by the classical fourier law @xmath24 while , microscopically , it is expressed as the usual average value of the perturbed kinetic energy flow@xcite @xmath25 as one may check , in the absence of external forces , the bgk model leads to @xmath26 substituting ( [ g ] ) into ( [ eq17 ] ) , and rewriting the resulting expression in spherical coordinates @xmath27 , one obtains @xmath28 d\phi.\ ] ] before proceed further , we note that the orthogonality relation @xmath29 where @xmath30 , may be used to show that the angular integral can be written as @xmath31 d\phi = \frac{4\pi}{3}v^2 \frac{\partial { \it f_0}}{\partial{\bf r}},\ ] ] with equation ( [ eq19 ] ) simplifying to @xmath32 as remarked earlier , the concentration @xmath10 and the temperature @xmath12 in the local @xmath0-distribution are spatially dependent while the pressure remains constant .
thus , as a consequence of the extended virial theorem@xcite , one may write @xmath33 , and combining that with the spatial gradient of the unperturbed distribution , the heat flow can be rewritten as @xmath34^{q/(1-q)}\frac{mv^2}{2k_bt}\end{aligned}\ ] ] @xmath35^{1/(1-q)}\}\frac{\partial { \it t}}{\partial{\bf r}}dv.\ ] ] now , comparing with the fourier law ( [ eq26 ] ) , we obtain an integral expression for the nonextensive thermal conductivity @xmath36^{q/(1-q)}dv\end{aligned}\ ] ] @xmath37^{1/(1-q)}dv.\ ] ] the above integrals can easily be evaluated .
we find @xmath38^{q/(1-q)}dv=\end{aligned}\ ] ] @xmath39 and , @xmath40^{1/(1-q)}dv=\end{aligned}\ ] ] @xmath41 as one may check , inserting these integrals and the normalization constant @xmath7 into equation ( [ eq27 ] ) , we obtain @xmath42.\ ] ] the nonextensive parameter @xmath0 in the above expressions are restricted to positive values with @xmath43,@xmath44 .
note also that expression ( [ eq30 ] ) reduces to standard value in the extensive limiting case@xcite @xmath45 it thus follows that the ratio between the nonextensive thermal conductivity and the extensive value , @xmath46 , is dependent on the tsallis thermostatistics through parameter @xmath0 ( see fig .
1 ) . note that for values of @xmath0 smaller than unity , the corresponding coefficient @xmath1 can be much smaller than the standard result ( nearly @xmath47 for @xmath48 ) , while for @xmath49 it may increases without limit .
let us now consider the nonextensive effects on the viscosity coefficient . in this case , the particles of the gas do not move with the same velocity . in a simplified treatment ,
the particles have constant mean velocity @xmath50 in the @xmath51 direction with the magnitude of @xmath50 depending only on @xmath52 , that is , @xmath53 .
thus , neglecting bulk viscosity , the navier - stokes stress reduces to @xmath54 a complementary hypothesis is that the collisional state tend to produce a local equilibrium distribution relative to the moving gas with mean velocity @xmath50 . under such conditions ,
the stationary @xmath0-distribution becomes @xmath55^{1/(1-q)},\ ] ] where @xmath56 , @xmath57 , @xmath58 .
since the resulting distribution @xmath15 is stationary but also depends on @xmath52 ( the direction of the gradient velocity ) , the bgk equation ( [ eq1 ] ) now reads @xmath59 the perturbed distribution function obeys @xmath60 so that @xmath61 in order to calculate the component @xmath62 of the stress tensor , we consider its kinetic definition@xcite @xmath63 following standard lines we see that ( for details see ref .
@xcite ) @xmath64 and comparing this result with the macroscopic equation ( [ eq39 ] ) we find @xmath65 where @xmath66^{q/(1-q)}mu_x\ ] ] replacing ( [ eq41 ] ) into ( [ eq40 ] ) it follows that @xmath67^{q/(1-q)}u_z^2u_x^2,\ ] ] and performing the elementary integrals @xmath68 finally , substituting the expression of @xmath7 and cancelling out the common factors , the viscosity coefficient assumes the rather simple form @xmath69 this expression is valid only for @xmath70 , and as expected , in the limit @xmath71 it reduces to the standard extensive result@xcite @xmath72 in figure 2 we show the ratio @xmath73 as a function of the nonextensive parameter .
this plot is similar to what happens with the thermal conductivity ( see fig.1 ) , and as expected , only for @xmath4 the standard maxwellian result is recovered . note also that combining equations ( [ eq30 ] ) and ( [ eq44 ] ) we also obtain a quite simple expression to the dimensionless ratio , @xmath74 , involving the transport coefficients , @xmath1 and @xmath2 , namely @xmath75 such a quantity ( sometimes called eucken s ratio@xcite ) plays an important experimental role because the unknown collision time appearing in both transport coefficients cancels out in this ratio . in figure 3 , we plot @xmath74 as a function of @xmath0 . note that @xmath74 does not depend on the temperature , and for @xmath4 it reduces to the extensive result @xmath76@xcite . as widely known , this pure number lies experimentally within the range @xmath77@xcite .
therefore , the allowed values to the nonextensive parameter is restricted on the interval @xmath3 , thereby showing that the maxwellian result is only marginally compatible with such measurements .
it is worth mentioning that the departure from standard maxwellian prediction is usually taken as an indication that the energy of the molecules must include another forms than mere kinetic energy of translation , or equivalently , an anomalous specific heat@xcite .
however , as we have seen , a possible alternative explanation ( at least for monatomic gases ) is provided by the existence of nonextensive effects associated to tsallis thermostatistics . for completeness
, we now investigate the possible nonextensive effects on the electric conductivity of a dilute neutral plasma .
as before , we consider the bgk approximation assuming that the external electric field is uniform and points to the positive @xmath52 direction , that is , @xmath78 .
the relevant macroscopic equation is now the ohm s law @xmath79 where @xmath80 is the electric conductivity .
microscopically , the electric current density is defined as the statistical average@xcite @xmath81 where the subscript @xmath10 means that the charge flow is directed along the normal to the corresponding surface element .
note that only the component _
j@xmath82 _ does not vanish since for an homogeneous and isotropic medium the current * j * is parallel to the electric field .
as one may check , from equations ( [ eq0 ] ) , ( [ oi ] ) and ( [ eq9 ] ) it follows that @xmath83^{q/(1-q)}v_z^2.\ ] ] performing the integration and comparing to the ohm s law the resulting electric conductivity is @xmath84 or still , inserting the value of @xmath7 ( see eq .
( [ eq13 ] ) ) @xmath85 therefore , within the bgk approximation , the above cancellation results that the electric conductivity does not depend on the nonextensive @xmath0-parameter .
in this paper we discussed some possible nonextensive effects on the transport phenomena in gases and plasmas .
it was shown that the theoretical analysis based on the relaxation - time approximation lead to simple analytic expressions to the heat conduction and viscosity coefficients , while the electric conductivity was not modified .
it is interesting to compare our results ( and the overall approach ) with independent analyzes and some previous expressions to nonextensive transport coefficients appearing in the literature@xcite .
we first notice that our main results are quite different from that ones obtained by boghosian@xcite .
probably , the basic reason comes from the fact that in his paper it was advocated a different choice to the bgk operator , namely , @xmath86 .
note that it depends nonlinearly on the nonextensive parameter and should be compared with the standard bgk operator assumed in the present paper ( see our equation ( [ eq1 ] ) ) . in the treatment adopted here , the nonextensive effects appear only implicitly through the power law equilibrium distribution . in addition ,
boghosian ( and also the authors of ref .
@xcite ) assumed that the pressure in the perturbed gas does not remain constant thereby giving rise to an anomalous heat conduction ( @xmath87 in their notation ) . in this concern ,
our approach may be considered more conservative . as a matter of fact , using the extended virial theorem @xcite , we have assumed constant pressure as usually done in the bgk approximation so that the anomalous heat conduction coefficient , @xmath87 , is absent .
another crucial difference among these works is that three kinds of averaging methods has been considered .
boghosian@xcite and potiguar et al.@xcite employed unnormalized and normalized @xmath0-expectations values , respectively , while we have computed the averages in the usual manner . in this way , it is not surprising that although obtaining coefficients @xmath1 and @xmath2 proportional to the temperature , the behavior of the dimensionless ratio @xmath88 as a function of the @xmath0 parameter is quite different ( compare our equation ( [ ratio ] ) with equations ( 83 ) and ( 40 ) in the quoted papers ) .
since this ratio can be measured in laboratory , hopefully , these different approaches , as well as their basic underlying assumptions will be experimentally confronted in the near future .
* acknowledgments : * the authors are grateful to uriel costa for helpful discussions .
this work was supported by pronex / finep ( no .
41.96.0908.00 ) , fapesp ( 00/06695 - 0 ) , cnpq and capes ( brazilian research agencies ) .
p. t. landsberg , dover ( 1967 ) .
p. hertel and w. thirring , ann .
* 63 * , 520 ( 1971 ) . c. tsallis , j. stat
. phys . * 52 * , 479 ( 1988 ) .
r. silva , a. r. plastino and j. a. s. lima , phys .
lett . * a 249 * , 401 ( 1998 ) .
a. r. plastino and j. a. s. lima , phys .
a * 260 * , 46 ( 1999 ) .
b. m. boghosian , braz .
* 29 * , 91 ( 1999 ) .
j. a. s. lima , r. silva , and j. santos , phys .
e * 61 * , 3260 ( 2000 ) .
j. a. s. lima , r. silva , and a. r. plastino , phys .
* 86 * , 2938 ( 2001 ) .
f. q. potiguar and u. m. s. costa , physica a * 303 * , 457 ( 2002 ) .
j. c. maxwell , philos . mag
. ser . 4 , * 20 * , 21,(1860 ) .
p. l. bhatnagar , e. p. gross , and m. krook , phys .
, * 94 * , 511 ( 1954 ) .
s. r. de groot and p. mazur , non - equilibrium thermodynamics , dover , new york ( 1984 ) .
k. huang , _ statistical mechanics _ , john wiley & sons ( 1987 ) .
n. a. krall and trivelpiece , principles of plasma physics , mcgraw - hill , kogakusha ( 1973 ) .
f. reif , fundamentals of statistical and thermal physics , mcgraw - hill ( 1965 ) .
l. c. woods , an introduction to kinetic theory of gases and magneto plasmas , oxford up , new york ( 1993 ) . | we discuss the basic transport phenomena in gases and plasmas obeying the @xmath0-nonextensive velocity distribution ( power - law ) .
analytical expressions for the thermal conductivity ( @xmath1 ) and viscosity ( @xmath2 ) are derived by solving the boltzmann equation in the relaxation - time approximation .
the available experimental results to the ratio @xmath1/@xmath2 constrains the @xmath0-parameter on the interval @xmath3 . in the extensive limiting case ,
the standard transport coefficients based on the local gaussian distribution are recovered , and due to a surprising cancellation , the electric conductivity of a neutral plasma is not modified .
1.5 cm | <s>[INST]in the last few years , an increasing attention has been paid to possible nonextensive effects in the fields of thermodynamics and statistical mechanics .
the main motivation is the lack of a comprehensive treatment including gravitational and coulombian fields for which the assumed additivity of the entropy present in the standard approach is not valid [ 1 - 2 ] .
inspired on such problems , as well as in the traditional ensemble theory , tsallis@xcite proposed a remarkable @xmath0-parameterized nonextensive entropic expression which reduces to the extensive gibbs - jaynes - shannon entropy in the limiting case @xmath4 ( see @xcite for a regularly updated bibliography on this subject ) .
later on , the first attempts exploring the kinetic route associated to this nonextensive approach appeared in the literature[5 - 10 ] . the original kinetic derivation advanced by maxwell@xcite was generalized to include power law distributions as required by this enlarged framework .
in particular , it was shown that the equilibrium velocity @xmath0-distribution @xmath5^{1/(1-q)},\ ] ] is uniquely determined from two simple requirements@xcite : ( i ) isotropy of the velocity space , and ( ii ) a suitable nonextensive generalization of the maxwell factorizability condition , or equivalently , the assumption that @xmath6 .
the quantity @xmath7 above denotes the @xmath0-dependent normalization constant whose expression on the interval @xmath8 is @xmath9 where @xmath10 is the particle number density , @xmath11 is the mass and @xmath12 is the temperature . as expected , in the limiting case @xmath4 , such expressions reduce to the standard maxwellian ones@xcite .
more recently , the kinetic foundations of the above distribution were investigated in a deeper level through the generalized boltzmann s transport equation@xcite @xmath13 where @xmath14 is the @xmath0-nonextensive integral source term measuring the change in @xmath15 due to collisions .
this boltzmannian like approach incorporated the nonextensive effects using two different ingredients .
first , a new functional form to the kinetic local gas entropy , and , second , a nonfactorizable distribution function for the colliding pairs of particles whose physical meaning is quite clear : the boltzmann chaos molecular hypothesis is not valid in this extended framework .
it was also shown that the kinetic version of the tsallis entropy satisfies an @xmath16-theorem , and more important still , the @xmath0-parameterized class of power law velocity distributions emerged as the unique nonextensive solution describing the equilibrium states . in this paper
we go one step further by computing the basic nonextensive transport coefficients for dilute gases and plasmas . due to the intricate form of the new collisional term ,
we adopt here the relaxation - time model proposed by bhatnager , gross and krook@xcite because it permits an exact mathematical treatment . in spite of its limitation , the relaxation - time model ( henceforth bgk model )
has been proved quite useful from a methodological viewpoint because it yields the correct answer to the problem in a first approximation , and as such , it can guide us to the correct nonextensive results which must rigorously be obtained using the full @xmath0-transport equation .
as we shall see , analytical expressions for the transport coefficients of a dilute gas are readily obtained with basis on the local @xmath0-nonextensive distribution . in particular , we show that the available experimental results to the ratio @xmath1/@xmath2 constrains the @xmath0-parameter on the interval @xmath3 . as expected , in the extensive limiting case , the classical expressions of the transport coefficients are readily recovered .
however , due to a surprising cancellation , the standard electric conductivity of a dilute neutral plasma is not modified .
the analysis presented here is also compared with independent calculations based on rather different approaches@xcite .
let us now consider a dilute gas whose particles are acted by external forces
. in the bgk approximation the @xmath0-transport equation ( [ beq ] ) reads : @xmath17 where @xmath18 is the external force and @xmath11 is the mass of the particles . in this approximation
, @xmath19 is the local equilibrium distribution function and @xmath20 is a relaxation time which is a number of the order of the collision time .
we recall that under stationary conditions the distribution function does not depend on time , however , the concentration , and the temperature , are local quantities .
the whole system is assumed to be out but close to the local stationary equilibrium state@xcite .
in particular , this means that the resulting nonequilibrium distribution , @xmath21 , is only slightly different from the equilibrium unperturbed stationary distribution , @xmath22 , and can be approximated as latexmath:[\[\label{oi } f({\bf r},{\bf v})=f_0({\bf v},{\bf r})+g({\bf v},{\bf r}),\quad nonextensive distribution on the thermal conductivity @xmath1 .
it will be assumed that the heat flux is macroscopically governed by the classical fourier law @xmath24 while , microscopically , it is expressed as the usual average value of the perturbed kinetic energy flow@xcite @xmath25 as one may check , in the absence of external forces , the bgk model leads to @xmath26 substituting ( [ g ] ) into ( [ eq17 ] ) , and rewriting the resulting expression in spherical coordinates @xmath27 , one obtains @xmath28 d\phi.\ ] ] before proceed further , we note that the orthogonality relation @xmath29 where @xmath30 , may be used to show that the angular integral can be written as @xmath31 d\phi = \frac{4\pi}{3}v^2 \frac{\partial { \it f_0}}{\partial{\bf r}},\ ] ] with equation ( [ eq19 ] ) simplifying to @xmath32 as remarked earlier , the concentration @xmath10 and the temperature @xmath12 in the local @xmath0-distribution are spatially dependent while the pressure remains constant .
thus , as a consequence of the extended virial theorem@xcite , one may write @xmath33 , and combining that with the spatial gradient of the unperturbed distribution , the heat flow can be rewritten as @xmath34^{q/(1-q)}\frac{mv^2}{2k_bt}\end{aligned}\ ] ] @xmath35^{1/(1-q)}\}\frac{\partial { \it t}}{\partial{\bf r}}dv.\ ] ] now , comparing with the fourier law ( [ eq26 ] ) , we obtain an integral expression for the nonextensive thermal conductivity @xmath36^{q/(1-q)}dv\end{aligned}\ ] ] @xmath37^{1/(1-q)}dv.\ ] ] the above integrals can easily be evaluated .
we find @xmath38^{q/(1-q)}dv=\end{aligned}\ ] ] @xmath39 and , @xmath40^{1/(1-q)}dv=\end{aligned}\ ] ] @xmath41 as one may check , inserting these integrals and the normalization constant @xmath7 into equation ( [ eq27 ] ) , we obtain @xmath42.\ ] ] the nonextensive parameter @xmath0 in the above expressions are restricted to positive values with @xmath43,@xmath44 .
note also that expression ( [ eq30 ] ) reduces to standard value in the extensive limiting case@xcite @xmath45 it thus follows that the ratio between the nonextensive thermal conductivity and the extensive value , @xmath46 , is dependent on the tsallis thermostatistics through parameter @xmath0 ( see fig .
1 ) . note that for values of @xmath0 smaller than unity , the corresponding coefficient @xmath1 can be much smaller than the standard result ( nearly @xmath47 for @xmath48 ) , while for @xmath49 it may increases without limit .
let us now consider the nonextensive effects on the viscosity coefficient . in this case , the particles of the gas do not move with the same velocity . in a simplified treatment ,
the particles have constant mean velocity @xmath50 in the @xmath51 direction with the magnitude of @xmath50 depending only on @xmath52 , that is , @xmath53 .
thus , neglecting bulk viscosity , the navier - stokes stress reduces to @xmath54 a complementary hypothesis is that the collisional state tend to produce a local equilibrium distribution relative to the moving gas with mean velocity @xmath50 . under such conditions ,
the stationary @xmath0-distribution becomes @xmath55^{1/(1-q)},\ ] ] where @xmath56 , @xmath57 , @xmath58 .
since the resulting distribution @xmath15 is stationary but also depends on @xmath52 ( the direction of the gradient velocity ) , the bgk equation ( [ eq1 ] ) now reads @xmath59 the perturbed distribution function obeys @xmath60 so that @xmath61 in order to calculate the component @xmath62 of the stress tensor , we consider its kinetic definition@xcite @xmath63 following standard lines we see that ( for details see ref .
@xcite ) @xmath64 and comparing this result with the macroscopic equation ( [ eq39 ] ) we find @xmath65 where @xmath66^{q/(1-q)}mu_x\ ] ] replacing ( [ eq41 ] ) into ( [ eq40 ] ) it follows that @xmath67^{q/(1-q)}u_z^2u_x^2,\ ] ] and performing the elementary integrals @xmath68 finally , substituting the expression of @xmath7 and cancelling out the common factors , the viscosity coefficient assumes the rather simple form @xmath69 this expression is valid only for @xmath70 , and as expected , in the limit @xmath71 it reduces to the standard extensive result@xcite @xmath72 in figure 2 we show the ratio @xmath73 as a function of the nonextensive parameter .
this plot is similar to what happens with the thermal conductivity ( see fig.1 ) , and as expected , only for @xmath4 the standard maxwellian result is recovered . note also that combining equations ( [ eq30 ] ) and ( [ eq44 ] ) we also obtain a quite simple expression to the dimensionless ratio , @xmath74 , involving the transport coefficients , @xmath1 and @xmath2 , namely @xmath75 such a quantity ( sometimes called eucken s ratio@xcite ) plays an important experimental role because the unknown collision time appearing in both transport coefficients cancels out in this ratio . in figure 3 , we plot @xmath74 as a function of @xmath0 . note that @xmath74 does not depend on the temperature , and for @xmath4 it reduces to the extensive result @xmath76@xcite . as widely known , this pure number lies experimentally within the range @xmath77@xcite .
therefore , the allowed values to the nonextensive parameter is restricted on the interval @xmath3 , thereby showing that the maxwellian result is only marginally compatible with such measurements .
it is worth mentioning that the departure from standard maxwellian prediction is usually taken as an indication that the energy of the molecules must include another forms than mere kinetic energy of translation , or equivalently , an anomalous specific heat@xcite .
however , as we have seen , a possible alternative explanation ( at least for monatomic gases ) is provided by the existence of nonextensive effects associated to tsallis thermostatistics . for completeness
, we now investigate the possible nonextensive effects on the electric conductivity of a dilute neutral plasma .
as before , we consider the bgk approximation assuming that the external electric field is uniform and points to the positive @xmath52 direction , that is , @xmath78 .
the relevant macroscopic equation is now the ohm s law @xmath79 where @xmath80 is the electric conductivity .
microscopically , the electric current density is defined as the statistical average@xcite @xmath81 where the subscript @xmath10 means that the charge flow is directed along the normal to the corresponding surface element .
note that only the component _
j@xmath82 _ does not vanish since for an homogeneous and isotropic medium the current * j * is parallel to the electric field .
as one may check , from equations ( [ eq0 ] ) , ( [ oi ] ) and ( [ eq9 ] ) it follows that @xmath83^{q/(1-q)}v_z^2.\ ] ] performing the integration and comparing to the ohm s law the resulting electric conductivity is @xmath84 or still , inserting the value of @xmath7 ( see eq .
( [ eq13 ] ) ) @xmath85 therefore , within the bgk approximation , the above cancellation results that the electric conductivity does not depend on the nonextensive @xmath0-parameter .
in this paper we discussed some possible nonextensive effects on the transport phenomena in gases and plasmas .
it was shown that the theoretical analysis based on the relaxation - time approximation lead to simple analytic expressions to the heat conduction and viscosity coefficients , while the electric conductivity was not modified .
it is interesting to compare our results ( and the overall approach ) with independent analyzes and some previous expressions to nonextensive transport coefficients appearing in the literature@xcite .
we first notice that our main results are quite different from that ones obtained by boghosian@xcite .
probably , the basic reason comes from the fact that in his paper it was advocated a different choice to the bgk operator , namely , @xmath86 .
note that it depends nonlinearly on the nonextensive parameter and should be compared with the standard bgk operator assumed in the present paper ( see our equation ( [ eq1 ] ) ) . in the treatment adopted here , the nonextensive effects appear only implicitly through the power law equilibrium distribution . in addition ,
boghosian ( and also the authors of ref .
@xcite ) assumed that the pressure in the perturbed gas does not remain constant thereby giving rise to an anomalous heat conduction ( @xmath87 in their notation ) . in this concern ,
our approach may be considered more conservative . as a matter of fact , using the extended virial theorem @xcite , we have assumed constant pressure as usually done in the bgk approximation so that the anomalous heat conduction coefficient , @xmath87 , is absent .
another crucial difference among these works is that three kinds of averaging methods has been considered .
boghosian@xcite and potiguar et al.@xcite employed unnormalized and normalized @xmath0-expectations values , respectively , while we have computed the averages in the usual manner . in this way , it is not surprising that although obtaining coefficients @xmath1 and @xmath2 proportional to the temperature , the behavior of the dimensionless ratio @xmath88 as a function of the @xmath0 parameter is quite different ( compare our equation ( [ ratio ] ) with equations ( 83 ) and ( 40 ) in the quoted papers ) .
since this ratio can be measured in laboratory , hopefully , these different approaches , as well as their basic underlying assumptions will be experimentally confronted in the near future .
* acknowledgments : * the authors are grateful to uriel costa for helpful discussions .
this work was supported by pronex / finep ( no .
41.96.0908.00 ) , fapesp ( 00/06695 - 0 ) , cnpq and capes ( brazilian research agencies ) .
p. t. landsberg , dover ( 1967 ) .
p. hertel and w. thirring , ann .
* 63 * , 520 ( 1971 ) . c. tsallis , j. stat
. phys . * 52 * , 479 ( 1988 ) .
r. silva , a. r. plastino and j. a. s. lima , phys .
lett . * a 249 * , 401 ( 1998 ) .
a. r. plastino and j. a. s. lima , phys .
a * 260 * , 46 ( 1999 ) .
b. m. boghosian , braz .
* 29 * , 91 ( 1999 ) .
j. a. s. lima , r. silva , and j. santos , phys .
e * 61 * , 3260 ( 2000 ) .
j. a. s. lima , r. silva , and a. r. plastino , phys .
* 86 * , 2938 ( 2001 ) .
f. q. potiguar and u. m. s. costa , physica a * 303 * , 457 ( 2002 ) .
j. c. maxwell , philos . mag
. ser . 4 , * 20 * , 21,(1860 ) .
p. l. bhatnagar , e. p. gross , and m. krook , phys .
, * 94 * , 511 ( 1954 ) .
s. r. de groot and p. mazur , non - equilibrium thermodynamics , dover , new york ( 1984 ) .
k. huang , _ statistical mechanics _ , john wiley & sons ( 1987 ) .
n. a. krall and trivelpiece , principles of plasma physics , mcgraw - hill , kogakusha ( 1973 ) .
f. reif , fundamentals of statistical and thermal physics , mcgraw - hill ( 1965 ) .
l. c. woods , an introduction to kinetic theory of gases and magneto plasmas , oxford up , new york ( 1993 ) .[/INST] we discuss the basic transport phenomena in gases and plasmas obeying the @xmath0-nonextensive velocity distribution ( power - law ) .
analytical expressions for the thermal conductivity ( @xmath1 ) and viscosity ( @xmath2 ) are derived by solving the boltzmann equation in the relaxation - time approximation .
the available experimental results to the ratio @xmath1/@xmath2 constrains the @xmath0-parameter on the interval @xmath3 . in the extensive limiting case ,
the standard transport coefficients based on the local gaussian distribution are recovered , and due to a surprising cancellation , the electric conductivity of a neutral plasma is not modified .
1.5 cm </s> |
the goal of this article is to describe a general methodology guided by well - established quality attributes used in the development of the architecture of an integrated e - learning system which will be further referred as _ iels_. throughout the presentation we will refer to the reasons that led to various architectural decisions related to the division of the system into logical components and also to the interaction between the sub - systems involved in the development of the project . the objective of iels is to create an ( online ) integrated system that is to be used in the creation of educational content for standard _ lmss _ ( learning management systems ) .
we believe that the main obstacle in the use of lmss is the development of proper material on which learning sessions are based .
iels aims to fix this problem with intuitive and easy to use tools targeted towards the exact individuals that are going to guide the learners during the interactive lectures .
for start we set up five basic functionalities of iels : * a teacher will access the system to design a lesson , * he will be able to access the platform regardless on the operating system and the architecture of his machine , * the system will facilitate the development of attractive and intuitive educational content , * the system will be able to use existing content ( from integrated repositories ) , * system requirements for both client and server will be minimized , with the possibility of extension for the server side . using standard technologies and accessible tools
the teacher will be able to create , aggregate , reuse an publish educational content with ease .
+ the main actor is the content creator and one fundamental requirement of the system is that inexperienced users can be trained quickly referring to knowledge acquired using other tools .
the _ architecture _ of a software system refers to the structural presentation of the system as a grouping of components that are connected through relations with specific properties .
the software architecture also comprises the principles that conduct the design and development of the system .
the conceptual framework that lies at the foundations of the software architecture design is presented in figure [ fig : cf ] . a starting point in developing
a software system architecture lies in the definition of stakeholders and their concerns . in developing a software architecture
a _ stakeholder _ is an entity ( most often an individual , community or organization ) which is involved in the development or use of the system and shows interest in the decisions that are made during the entire development phase .
+ during the development of iels we have identified two classes of stakeholders : * people who will interact with the deployed system : customers , owners , operators , system engineers , * people who are an active part in the development of the system : architects , designers , developers , distributors .
the _ concerns _ of the stakeholders are generally focused on simplifying the development or use of the system . starting from concerns one can identify issues or functional requirements of the system specific to each stakeholder .
the _ architectural description _ includes those products which occur during the development of the system that reveal useful information about the architecture .
these products can have various uses in : * brief description of the system and its evolution , * communication between stakeholders , * assessment and comparison of architectures in a consistent way , * planning and execution of activities , * the degree of compatibility between the implementation and the architectural description . in order to reduce the complexity of the architectural description
one can identify _ views _
, i.e. small collections of concerns , mostly related , of one or more stakeholders . from this perspective we can say that the architectural description is a consistent collection of views , each of them contributing with new information to the description of the architecture .
each view is built on a set of resources and structuring rules well - defined by a _
viewpoint_. one can describe a viewpoint by specifying its name , the stakeholders and the concerns it addresses to and the modeling techniques used in building views .
software architecture focuses on general decisions about the elements of the system and the interactions between them , thus making abstraction of more specific issues such as data structures or algorithms .
based on the architecture one can derive a design plan that describes the hierarchical layout of the system and how elements of the system are integrated to form subsystems that meet requirements . also the design plan can be used to sketch the development of the system , deal with possible answers to concerns of stakeholders and to set expectations for the clients .
from the perspective of software engineering , in the analysis of a system one can identify two types of requirements : functional and non - functional . + in general ,
functional requirements define the functionality of the system or what system should do .
these requirements define the behavior of the system , referring to the transformations applied by components on some input data to get output data .
+ _ non - functional requirements _ are defined in terms of system properties or qualities .
in contrast to functional requirements , non - functional requirements do not describe what the system does but focus on some characteristics of how the system operates .
examples of non - functional requirements include external interface requirements , design restrictions and _ quality attributes_. due to their nature , the task of assessing the response to a non - functional requirement is difficult and mostly subjective .
depending on how their value is determined , quality attributes fall into two main categories : * attributes that can be evaluated by analyzing the static structure of the system : scalability , extensibility , maintenance , testing effort , etc .
* attributes that can be evaluated only while the system is running : performance , security , usability , etc . in general ,
quality attributes are not unique to a development stage and should be considered throughout the entire development process , from design to implementation and deployment .
some quality attributes are considered critical so their value is assessed at the level of the architecture .
other attributes are too particular and can be evaluated only by analyzing the implementation . in the development of iels
we have identified the following quality attributes : * system qualities : availability , adaptability , maintenance , performance , security , creating logs , usability , * business qualities : time to market , integration , platform independence .
we will formally specify quality attributes through _
scenarios_. for each quality attribute a scenario should include : source : : : the software system or actor that produces a trigger , trigger : : : the situation in which the quality attribute is evaluated , environment : : : the state of the system , artifact : : : the region of the system in which the assessment takes place , response : : : the behavior of the system , assessment : : : how the evaluation of the response is performed .
the _ performance _ of a system refers to the number of tasks performed by the system in relation to used resources .
the system performance is evaluated differently depending on context . in our project
we will refer to four types of measurements : * response time relative to a user s request , * rate of data processing , * utilization of computing resources , * volume of transmitted data . the general scenario for performance is presented in table [ table : gsp ] .
.general scenario for performance [ cols= " > , < " , ] _ architectural tactics _ are fundamental design decisions that significantly contribute to the design and analysis of the system architecture .
they are closely related to quality attributes and have a direct influence on the response to a single quality attribute .
architectural tactics are therefore sufficiently simple such that one could easily understand their properties and effects .
most design decision have side effects , meaning that they affect other quality attributes besides those directly concerned .
it follows that the use of an architectural tactic must be preceded by an estimation of both positive and negative impact of its implementation on other significant quality attributes .
we will further focus on architectural tactics aimed at the scenarios of three quality attributes described in the previous section : performance , security and usability .
_ performance _ targets various aspects of the system including computing time , response time , resource consumption , throughput and efficiency .
we will simplify the analysis and concentrate on the response time relative to the messages or requests submitted by users . from this restricted point of view
, performance related tactics can be classified as : * resource management tactics , * resource arbitration tactics . _ resource management tactics _ lead to improvement in the performance of the system by a better organization of the resources that have a major impact on the response time .
+ one such tactic is _ induced concurrency_. under this tactic threads or distinct processes are associated with resources .
thus concurrent accesses on resources translates into concurrent executions of threads . in this way the waiting time
can be reduced through techniques specific to concurrent processing , e.g. load balancing . +
another resource management tactic is _ targeted redundancy_.
it is achieved by maintaining multiple copies , in various and usually distant regions of the system , of the data that is frequently used .
the immediate consequence of the existence of multiple copies of the same resources is a weaker competition between the sub - systems that request access to those resources . in the case of raw data , using this tactic involves the existence of a data storage space with a cache and a cache manager .
the cache aims to retain the data that is most often required , while the cache manager has to update the cache such that it reflects frequently requested data .
it is also responsible with synchronizing the cache with the main storage space in situations when cached data gets changed . _ resource arbitration
_ is used to improve performance by scheduling requests to essential resources such as cpu or network .
there are two well known methods of scheduling requests : * _ fifo _
( first in first out ) tactics : all requests are treated equally in the order they are received , * tactics based on _ priorities _ : the order the requests are processed is determined by ( static or dynamic ) priorities associated with each request .
the _ security _ of the system deals with prevention of unauthorized access while providing services for legitimate users .
security related tactics can be tactics targeted towards resisting attacks , detecting attacks or recovering from attacks .
the first class of tactics offers several ways to protect the system during an attack .
one protective measure is _ user authentication _ , for example through ids and passwords .
in this case we have two possible tactics : * i d / password : the i d and the password are chosen by the user , * onetime password : the i d and the password are automatically generated by the system .
another method of protection is the use of an integrated _
authorization system_. under this tactic users access to data and services is restricted depending on their privileges .
these tactics are mostly used in combination with other user authentication tactics .
other ways to ensure safety increase the _ resistance _ of the system to attacks by using _ encrypted communication channels_. in such situations , specialized components are needed to efficiently encrypt / decrypt messages .
+ resistance to attacks is strongly related to the _ detection _ of attacks .
such tactics include limiting the attacker s possibilities , for example by disabling certain ports or through a firewall .
other methods consist of continuously monitoring network traffic and compare it with patterns calculated from records of previous attacks .
_ recovery tactics _ have applicability in situations in which it is necessary to restore the system after a successful attack is recorded or as an attempt to minimize the damage produced by a successful attack .
the basic restoration tactic consists of separating critical , security related data from ordinary data .
this is achieved in iels by separating the administrative data referring to the creators of educational content from actual data like the one used during learning sessions .
tactics targeted towards _ usability _ aim to develop a product with a low learning curve which users can use quickly and efficiently .
such tactics are divided into two categories : * _ run - time tactics _ : consist of interface design principles and are strongly influenced by customer feedback , * _ design - time tactics _
: focused on the user interface design phase and on developers involved in this process .
according to these tactics , a number of interface design principles were considered in the development of iels : * early focus on users and activities through direct interactions between the interface design team and the target group , * testing the system since the first stages of development , * constant evaluation of the learning curve of the system , * applying an iterative design process via a cycle of prototyping , testing , analyzing , and refining .
patterns and architectural styles are ways of managing the complexity and size of the design of software architecture .
their use greatly reduces the process of designing the architecture to understanding , selection , combination or adjustment of well - established architectural patterns . because architectural patterns retain much of the complexity of the system , the results of their interaction are generally difficult to predict . in order to have a high degree of applicability architectural patterns
are often specified generically .
for this reason , during the design process , the patterns are altered with system - specific information
. an _ architectural pattern _ shows an image of the system without being a complete architecture .
more specifically an architectural pattern describes some essential elements of the software system architecture .
similar to architectural tactics , an important characteristic of architectural patterns is that each pattern is related to a well - defined set of quality attributes .
it follows that the choice of architectural patterns that provide the best response to requirements determined by quality attributes must be done in the early stages of design . according to the notions presented in the previous sections ,
the description of a software architecture includes : * _ components _ responsible with computations or storing data : objects , filters , databases , etc . * _ connectors _ that ensure interaction between components : procedure calls , communication channels , events , etc . * _ attributes _ that provide the useful information in analysis and design of the architecture : signatures , pre - conditions , post - conditions , etc .
components are the basic elements used in the development of the architecture .
most of the times they are active entities of the system , with well - defined computational properties .
communication of a component with the environment is done through ports or interfaces .
a port may be a user interface , a shared variable , a reference to a procedure of another component , a collection of events that can be triggered , etc .
each component defines one or more interfaces that specify its communication capabilities .
each interface can connect to multiple interfaces of other components .
the analysis of the communication between components must consider a number of attributes like the direction of data flow , the existence of a buffer and its capacity , the supported communication protocols , etc . an _ architectural style _ defines a family of architectures that have a common architectural description , topology and other semantic constraints . in this context , the _ topology _ or configuration of an architectural style is a graph in which vertices and edges are the core elements of the architectural description : components and connectors .
thus the analysis of components and connectors extends to the analysis of topologies .
frequent tests are related to the overall performance of an architecture , concurrent and distributed computing properties , reliability , etc . in general the architecture of a system
is obtained by combining several architectural styles .
the architecture considered for iels falls into this category although the predominant model is the _ ria _ ( rich internet application ) client - server model .
_ rias _ are web applications with most of the features of regular desktop applications but generally run in a web browser or a virtual machine . among the most popular ria technologies we mention flex , ajax , javafx and silverlight .
applications developed using these technologies share a similar architecture based on a client module and a distinct level of services .
ria is more suited to a client - server development than to a traditional web development where the state of the system is part of the session . in a client - server approach
the client has its own state , it knows the data it needs and also the types of the data received from the server . among the immediate benefits of this approach we mention a well organized service level , simple requests to the server and a reduced computation demand on the server by running some calculations on the client side .
the global architecture of a _ client - server application _ includes a series of sub - architectures .
the system can be briefly described as the communication between the client and the server using a level of services .
each component of the global architecture has its own local architecture .
_ mvc _ ( model - view - controller ) is an architectural pattern in which the system is divided into a series of sub - systems responsible for data access , business logic and user interface .
the name of the pattern is given by the roles of its components : the model : : is a convenient representation of data on which the application runs .
when the state of a model changes the views associated with the model are automatically informed to update the interface .
generally it is assumed that the level of data access is integrated within the model .
the view : : is generally an element specific to the user interface that displays a particular model .
more insights on the model can be obtained using multiple views .
views are also responsible for interacting with the user .
the controller : : provides communication between views and models .
a control module receives input and generates a response after querying a model . in a ria application
one can identify two levels that implement the mvc architectural pattern : * an implementation at the client level , * an implementation at the service level . although both levels display features specific to mvcs , a complete functionality is rarely implemented .
the _ client mvc _ manages the interaction between user and user interface ( by invoking commands , loading data , updating the interface etc . ) .
the main objectives of a client mvc are maintaining the state of the application , mediating requests to the server and displaying control data .
the task of the _ server mvc _ is to manage the requests received from the client . for this
it processes the requests and triggers actions on the server
. these actions may include : * saving information in the database , * updating information , * returning requested information , * analytical calculations . the major difference compared to the corresponding client mvc is that in this situation there is no user interface .
instead , views consist in the format of the data returned to the client application .
common technologies appropriate to ria development can be : * java , php , rails , .net for the service level , * flex , ajax , javafx for the client .
this work was partially supported by the grant of the minsitry of education , research , youth and sports , no .
136/2007 , through the program `` innovation '' .
r. aust , designing network information services for educators , journal of machine - mediated learning . 4(2 - 3 ) , 1994 , 251 - 267 .
deniau , m.t swink , r aust , j.b .
evans , s. gauch , j. miller , d. niehaus , the unite system : distributed delivery and contribution of multimedia objects over the internet . proceedings of the internet society conference , 1995 ( www.isoc.org/hmp/paper/248/ ) .
internet society .
reston , virginia .
meyen , final report : online delivery model project
office of special education programs , u.s .
department of education ( lawrence , ks : center for research on learning , university of kansas , 2003 ) .
meyen , y.n .
bui , online academy : content validation through a juror process , journal of technology and teacher education , ii(3 ) , 2003 , 443- 454 .
j. neilson , designing web usability ( pp .
16 - 17 ) .
( indianapolis , in : new riders publishing , 2000 ) .
wiley , connecting learning objects to instructional design theory : a definition , a metaphor , and a taxonomy .
wiley ( ed . ) , the instructional use of learning objects : online version .
andriole , l. adelman , cognitive systems engineering for user - computer interface design , prototyping and evaluation ( pp . 4 - 6 )
( hillsdale , nj : lawrence erlbaum associates , 1995 ) .
kovitz , practical software requirements : a manual of content and style ( pp .
27 - 29 ) .
( greenwich , ct : manning publications co. , 1990 ) . m.m .
gardiner , b. christie , applying cognitive psychology to user - interface design ( pp.4 - 5 ) .
( rochester ; ny : wiley , 1987 ) .
t. mandel , the elements of user interface design ( new york : wiley , 1997 ) .
b. shneiderman , designing the user interface : strategies for effective human - computer - interaction ( 3rd ed . ) .
( reading , ma : addison wesley longman , 1998 ) .
l. rosenfeld , p. morville , information architecture for the world wide web .
( oriely , 1998 ) .
lynch , s. horton , web style guide : basic design principles for creating web sites ( new haven , ct : yale university press , 1999 ) .
r. aust , m.j .
kelly , w. roby , the use of hyperreference and conventional dictionaries educational technology research and development , 41(4 ) , 1993 , 63 - 73 .
meyen , r.j .
aust , y.n .
bui , e. ramp , s.j .
smith , the online academy formative evaluation approach to evaluating online instruction , the internet and higher education , 5 , 2002 , 89 - 108 . | this study presents a methodological approach to the development of integrated e - learning systems that is used in the creation of educational content for standard learning management systems . | <s>[INST]the goal of this article is to describe a general methodology guided by well - established quality attributes used in the development of the architecture of an integrated e - learning system which will be further referred as _ iels_. throughout the presentation we will refer to the reasons that led to various architectural decisions related to the division of the system into logical components and also to the interaction between the sub - systems involved in the development of the project . the objective of iels is to create an ( online ) integrated system that is to be used in the creation of educational content for standard _ lmss _ ( learning management systems ) .
we believe that the main obstacle in the use of lmss is the development of proper material on which learning sessions are based .
iels aims to fix this problem with intuitive and easy to use tools targeted towards the exact individuals that are going to guide the learners during the interactive lectures .
for start we set up five basic functionalities of iels : * a teacher will access the system to design a lesson , * he will be able to access the platform regardless on the operating system and the architecture of his machine , * the system will facilitate the development of attractive and intuitive educational content , * the system will be able to use existing content ( from integrated repositories ) , * system requirements for both client and server will be minimized , with the possibility of extension for the server side . using standard technologies and accessible tools
the teacher will be able to create , aggregate , reuse an publish educational content with ease .
+ the main actor is the content creator and one fundamental requirement of the system is that inexperienced users can be trained quickly referring to knowledge acquired using other tools .
the _ architecture _ of a software system refers to the structural presentation of the system as a grouping of components that are connected through relations with specific properties .
the software architecture also comprises the principles that conduct the design and development of the system .
the conceptual framework that lies at the foundations of the software architecture design is presented in figure [ fig : cf ] . a starting point in developing
a software system architecture lies in the definition of stakeholders and their concerns . in developing a software architecture
a _ stakeholder _ is an entity ( most often an individual , community or organization ) which is involved in the development or use of the system and shows interest in the decisions that are made during the entire development phase .
+ during the development of iels we have identified two classes of stakeholders : * people who will interact with the deployed system : customers , owners , operators , system engineers , * people who are an active part in the development of the system : architects , designers , developers , distributors .
the _ concerns _ of the stakeholders are generally focused on simplifying the development or use of the system . starting from concerns one can identify issues or functional requirements of the system specific to each stakeholder .
the _ architectural description _ includes those products which occur during the development of the system that reveal useful information about the architecture .
these products can have various uses in : * brief description of the system and its evolution , * communication between stakeholders , * assessment and comparison of architectures in a consistent way , * planning and execution of activities , * the degree of compatibility between the implementation and the architectural description . in order to reduce the complexity of the architectural description
one can identify _ views _
, i.e. small collections of concerns , mostly related , of one or more stakeholders . from this perspective we can say that the architectural description is a consistent collection of views , each of them contributing with new information to the description of the architecture .
each view is built on a set of resources and structuring rules well - defined by a _
viewpoint_. one can describe a viewpoint by specifying its name , the stakeholders and the concerns it addresses to and the modeling techniques used in building views .
software architecture focuses on general decisions about the elements of the system and the interactions between them , thus making abstraction of more specific issues such as data structures or algorithms .
based on the architecture one can derive a design plan that describes the hierarchical layout of the system and how elements of the system are integrated to form subsystems that meet requirements . also the design plan can be used to sketch the development of the system , deal with possible answers to concerns of stakeholders and to set expectations for the clients .
from the perspective of software engineering , in the analysis of a system one can identify two types of requirements : functional and non - functional . + in general ,
functional requirements define the functionality of the system or what system should do .
these requirements define the behavior of the system , referring to the transformations applied by components on some input data to get output data .
+ _ non - functional requirements _ are defined in terms of system properties or qualities .
in contrast to functional requirements , non - functional requirements do not describe what the system does but focus on some characteristics of how the system operates .
examples of non - functional requirements include external interface requirements , design restrictions and _ quality attributes_. due to their nature , the task of assessing the response to a non - functional requirement is difficult and mostly subjective .
depending on how their value is determined , quality attributes fall into two main categories : * attributes that can be evaluated by analyzing the static structure of the system : scalability , extensibility , maintenance , testing effort , etc .
* attributes that can be evaluated only while the system is running : performance , security , usability , etc . in general ,
quality attributes are not unique to a development stage and should be considered throughout the entire development process , from design to implementation and deployment .
some quality attributes are considered critical so their value is assessed at the level of the architecture .
other attributes are too particular and can be evaluated only by analyzing the implementation . in the development of iels
we have identified the following quality attributes : * system qualities : availability , adaptability , maintenance , performance , security , creating logs , usability , * business qualities : time to market , integration , platform independence .
we will formally specify quality attributes through _
scenarios_. for each quality attribute a scenario should include : source : : : the software system or actor that produces a trigger , trigger : : : the situation in which the quality attribute is evaluated , environment : : : the state of the system , artifact : : : the region of the system in which the assessment takes place , response : : : the behavior of the system , assessment : : : how the evaluation of the response is performed .
the _ performance _ of a system refers to the number of tasks performed by the system in relation to used resources .
the system performance is evaluated differently depending on context . in our project
we will refer to four types of measurements : * response time relative to a user s request , * rate of data processing , * utilization of computing resources , * volume of transmitted data . the general scenario for performance is presented in table [ table : gsp ] .
.general scenario for performance [ cols= " > , < " , ] _ architectural tactics _ are fundamental design decisions that significantly contribute to the design and analysis of the system architecture .
they are closely related to quality attributes and have a direct influence on the response to a single quality attribute .
architectural tactics are therefore sufficiently simple such that one could easily understand their properties and effects .
most design decision have side effects , meaning that they affect other quality attributes besides those directly concerned .
it follows that the use of an architectural tactic must be preceded by an estimation of both positive and negative impact of its implementation on other significant quality attributes .
we will further focus on architectural tactics aimed at the scenarios of three quality attributes described in the previous section : performance , security and usability .
_ performance _ targets various aspects of the system including computing time , response time , resource consumption , throughput and efficiency .
we will simplify the analysis and concentrate on the response time relative to the messages or requests submitted by users . from this restricted point of view
, performance related tactics can be classified as : * resource management tactics , * resource arbitration tactics . _ resource management tactics _ lead to improvement in the performance of the system by a better organization of the resources that have a major impact on the response time .
+ one such tactic is _ induced concurrency_. under this tactic threads or distinct processes are associated with resources .
thus concurrent accesses on resources translates into concurrent executions of threads . in this way the waiting time
can be reduced through techniques specific to concurrent processing , e.g. load balancing . +
another resource management tactic is _ targeted redundancy_.
it is achieved by maintaining multiple copies , in various and usually distant regions of the system , of the data that is frequently used .
the immediate consequence of the existence of multiple copies of the same resources is a weaker competition between the sub - systems that request access to those resources . in the case of raw data , using this tactic involves the existence of a data storage space with a cache and a cache manager .
the cache aims to retain the data that is most often required , while the cache manager has to update the cache such that it reflects frequently requested data .
it is also responsible with synchronizing the cache with the main storage space in situations when cached data gets changed . _ resource arbitration
_ is used to improve performance by scheduling requests to essential resources such as cpu or network .
there are two well known methods of scheduling requests : * _ fifo _
( first in first out ) tactics : all requests are treated equally in the order they are received , * tactics based on _ priorities _ : the order the requests are processed is determined by ( static or dynamic ) priorities associated with each request .
the _ security _ of the system deals with prevention of unauthorized access while providing services for legitimate users .
security related tactics can be tactics targeted towards resisting attacks , detecting attacks or recovering from attacks .
the first class of tactics offers several ways to protect the system during an attack .
one protective measure is _ user authentication _ , for example through ids and passwords .
in this case we have two possible tactics : * i d / password : the i d and the password are chosen by the user , * onetime password : the i d and the password are automatically generated by the system .
another method of protection is the use of an integrated _
authorization system_. under this tactic users access to data and services is restricted depending on their privileges .
these tactics are mostly used in combination with other user authentication tactics .
other ways to ensure safety increase the _ resistance _ of the system to attacks by using _ encrypted communication channels_. in such situations , specialized components are needed to efficiently encrypt / decrypt messages .
+ resistance to attacks is strongly related to the _ detection _ of attacks .
such tactics include limiting the attacker s possibilities , for example by disabling certain ports or through a firewall .
other methods consist of continuously monitoring network traffic and compare it with patterns calculated from records of previous attacks .
_ recovery tactics _ have applicability in situations in which it is necessary to restore the system after a successful attack is recorded or as an attempt to minimize the damage produced by a successful attack .
the basic restoration tactic consists of separating critical , security related data from ordinary data .
this is achieved in iels by separating the administrative data referring to the creators of educational content from actual data like the one used during learning sessions .
tactics targeted towards _ usability _ aim to develop a product with a low learning curve which users can use quickly and efficiently .
such tactics are divided into two categories : * _ run - time tactics _ : consist of interface design principles and are strongly influenced by customer feedback , * _ design - time tactics _
: focused on the user interface design phase and on developers involved in this process .
according to these tactics , a number of interface design principles were considered in the development of iels : * early focus on users and activities through direct interactions between the interface design team and the target group , * testing the system since the first stages of development , * constant evaluation of the learning curve of the system , * applying an iterative design process via a cycle of prototyping , testing , analyzing , and refining .
patterns and architectural styles are ways of managing the complexity and size of the design of software architecture .
their use greatly reduces the process of designing the architecture to understanding , selection , combination or adjustment of well - established architectural patterns . because architectural patterns retain much of the complexity of the system , the results of their interaction are generally difficult to predict . in order to have a high degree of applicability architectural patterns
are often specified generically .
for this reason , during the design process , the patterns are altered with system - specific information
. an _ architectural pattern _ shows an image of the system without being a complete architecture .
more specifically an architectural pattern describes some essential elements of the software system architecture .
similar to architectural tactics , an important characteristic of architectural patterns is that each pattern is related to a well - defined set of quality attributes .
it follows that the choice of architectural patterns that provide the best response to requirements determined by quality attributes must be done in the early stages of design . according to the notions presented in the previous sections ,
the description of a software architecture includes : * _ components _ responsible with computations or storing data : objects , filters , databases , etc . * _ connectors _ that ensure interaction between components : procedure calls , communication channels , events , etc . * _ attributes _ that provide the useful information in analysis and design of the architecture : signatures , pre - conditions , post - conditions , etc .
components are the basic elements used in the development of the architecture .
most of the times they are active entities of the system , with well - defined computational properties .
communication of a component with the environment is done through ports or interfaces .
a port may be a user interface , a shared variable , a reference to a procedure of another component , a collection of events that can be triggered , etc .
each component defines one or more interfaces that specify its communication capabilities .
each interface can connect to multiple interfaces of other components .
the analysis of the communication between components must consider a number of attributes like the direction of data flow , the existence of a buffer and its capacity , the supported communication protocols , etc . an _ architectural style _ defines a family of architectures that have a common architectural description , topology and other semantic constraints . in this context , the _ topology _ or configuration of an architectural style is a graph in which vertices and edges are the core elements of the architectural description : components and connectors .
thus the analysis of components and connectors extends to the analysis of topologies .
frequent tests are related to the overall performance of an architecture , concurrent and distributed computing properties , reliability , etc . in general the architecture of a system
is obtained by combining several architectural styles .
the architecture considered for iels falls into this category although the predominant model is the _ ria _ ( rich internet application ) client - server model .
_ rias _ are web applications with most of the features of regular desktop applications but generally run in a web browser or a virtual machine . among the most popular ria technologies we mention flex , ajax , javafx and silverlight .
applications developed using these technologies share a similar architecture based on a client module and a distinct level of services .
ria is more suited to a client - server development than to a traditional web development where the state of the system is part of the session . in a client - server approach
the client has its own state , it knows the data it needs and also the types of the data received from the server . among the immediate benefits of this approach we mention a well organized service level , simple requests to the server and a reduced computation demand on the server by running some calculations on the client side .
the global architecture of a _ client - server application _ includes a series of sub - architectures .
the system can be briefly described as the communication between the client and the server using a level of services .
each component of the global architecture has its own local architecture .
_ mvc _ ( model - view - controller ) is an architectural pattern in which the system is divided into a series of sub - systems responsible for data access , business logic and user interface .
the name of the pattern is given by the roles of its components : the model : : is a convenient representation of data on which the application runs .
when the state of a model changes the views associated with the model are automatically informed to update the interface .
generally it is assumed that the level of data access is integrated within the model .
the view : : is generally an element specific to the user interface that displays a particular model .
more insights on the model can be obtained using multiple views .
views are also responsible for interacting with the user .
the controller : : provides communication between views and models .
a control module receives input and generates a response after querying a model . in a ria application
one can identify two levels that implement the mvc architectural pattern : * an implementation at the client level , * an implementation at the service level . although both levels display features specific to mvcs , a complete functionality is rarely implemented .
the _ client mvc _ manages the interaction between user and user interface ( by invoking commands , loading data , updating the interface etc . ) .
the main objectives of a client mvc are maintaining the state of the application , mediating requests to the server and displaying control data .
the task of the _ server mvc _ is to manage the requests received from the client . for this
it processes the requests and triggers actions on the server
. these actions may include : * saving information in the database , * updating information , * returning requested information , * analytical calculations . the major difference compared to the corresponding client mvc is that in this situation there is no user interface .
instead , views consist in the format of the data returned to the client application .
common technologies appropriate to ria development can be : * java , php , rails , .net for the service level , * flex , ajax , javafx for the client .
this work was partially supported by the grant of the minsitry of education , research , youth and sports , no .
136/2007 , through the program `` innovation '' .
r. aust , designing network information services for educators , journal of machine - mediated learning . 4(2 - 3 ) , 1994 , 251 - 267 .
deniau , m.t swink , r aust , j.b .
evans , s. gauch , j. miller , d. niehaus , the unite system : distributed delivery and contribution of multimedia objects over the internet . proceedings of the internet society conference , 1995 ( www.isoc.org/hmp/paper/248/ ) .
internet society .
reston , virginia .
meyen , final report : online delivery model project
office of special education programs , u.s .
department of education ( lawrence , ks : center for research on learning , university of kansas , 2003 ) .
meyen , y.n .
bui , online academy : content validation through a juror process , journal of technology and teacher education , ii(3 ) , 2003 , 443- 454 .
j. neilson , designing web usability ( pp .
16 - 17 ) .
( indianapolis , in : new riders publishing , 2000 ) .
wiley , connecting learning objects to instructional design theory : a definition , a metaphor , and a taxonomy .
wiley ( ed . ) , the instructional use of learning objects : online version .
andriole , l. adelman , cognitive systems engineering for user - computer interface design , prototyping and evaluation ( pp . 4 - 6 )
( hillsdale , nj : lawrence erlbaum associates , 1995 ) .
kovitz , practical software requirements : a manual of content and style ( pp .
27 - 29 ) .
( greenwich , ct : manning publications co. , 1990 ) . m.m .
gardiner , b. christie , applying cognitive psychology to user - interface design ( pp.4 - 5 ) .
( rochester ; ny : wiley , 1987 ) .
t. mandel , the elements of user interface design ( new york : wiley , 1997 ) .
b. shneiderman , designing the user interface : strategies for effective human - computer - interaction ( 3rd ed . ) .
( reading , ma : addison wesley longman , 1998 ) .
l. rosenfeld , p. morville , information architecture for the world wide web .
( oriely , 1998 ) .
lynch , s. horton , web style guide : basic design principles for creating web sites ( new haven , ct : yale university press , 1999 ) .
r. aust , m.j .
kelly , w. roby , the use of hyperreference and conventional dictionaries educational technology research and development , 41(4 ) , 1993 , 63 - 73 .
meyen , r.j .
aust , y.n .
bui , e. ramp , s.j .
smith , the online academy formative evaluation approach to evaluating online instruction , the internet and higher education , 5 , 2002 , 89 - 108 .[/INST] this study presents a methodological approach to the development of integrated e - learning systems that is used in the creation of educational content for standard learning management systems . </s> |
the characterization of memory effects in non - markovian evolutions is a fundamental subject in the theory of open systems @xcite .
indeed , the markovian behavior is always an idealization in the description of the quantum dynamics , with non - markovianity being non - negligible in a number of different scenarios , such as biological @xcite or condensed matter systems @xcite . from an applied point of view , non - markovian dynamics may be a resource for quantum tasks through an increase in the capacities of quantum channels @xcite .
moreover , it also exhibits applications in fault - tolerant quantum computation @xcite .
rigorously , non - markovianity can be defined through the deviation of a dynamical evolution map from a _ divisible _ completely positive trace - preserving ( cptp ) map @xcite .
this behavior is manifested both in entanglement @xcite and in other correlation sources @xcite , providing an approach that takes advantage of quantum information tools in the open - systems realm .
more specifically , non - markovianity can be interpreted in this context as a flow of information back to the system due to its interaction with the environment , which may imply non - monotonic behavior of correlations as a function of time . here , we propose a general framework to characterize non - markovianity through multipartite measures of quantum , classical , and total correlations . recently , there has been growing interest in the investigation of correlation measures from a quantum information perspective @xcite . in particular ,
measures for quantum correlations such as those provided by discordlike quantities and their corresponding classical counterparts have been formulated , with these quantities used as resources for implementing a variety of quantum tasks ( see ref .
@xcite and references therein ) .
these measures were originally introduced in an entropic scenario by ollivier and zurek @xcite . in a geometric context , correlations can be defined based on the relative entropy @xcite , hilbert - schmidt norm @xcite , trace norm @xcite , and bures norm @xcite .
all of these distinct versions of correlation measures can be described by a unified framework in terms of a generalized distance ( or pseudo distance ) function @xcite .
our approach for non - markovianity includes all these measures as particular cases and characterizes the non - markovian behavior by taking into account the program introduced by rivas , huelga , and plenio @xcite , in which an ancilla is coupled to a system which interacts with an environment .
specifically , we provide a rigorous description of the hypotheses over local dynamical maps under which quantum , classical , and total correlations can be used as measures of non - markovianity .
we illustrate the results considering the dynamics of the trace - distance correlations in qubit systems under either local dephasing or generalized amplitude damping ( gad ) .
let us suppose a quantum process governed by a time - local master equation @xmath0 where the time - dependent generator @xmath1 is given by @xmath2 + \sum_i \gamma_i ( t ) \left ( a_i(t)\rho(t)a^\dagger_i(t ) \right .
\nonumber \\ & & \left .
- \frac{1}{2 } \left\{a^\dagger_i(t ) a_i(t),\rho(t)\right\}\right ) , \end{aligned}\ ] ] with @xmath3 denoting the effective system hamiltonian , @xmath4 denoting the lindblad operators , and @xmath5 denoting the relaxation rates . by taking the relaxation rates as positive functions ,
i.e. , @xmath6 , the generator @xmath1 assumes the lindblad form @xcite for each fixed @xmath7 .
the master equation describes the dynamics of the density operator through @xmath8 , with the cptp map @xmath9 given by @xmath10 , with @xmath11 denoting the chronological time - ordering operator .
the dynamical map @xmath9 then satisfies the divisibility condition @xmath12 @xmath13 ) , which characterizes the markovianity of the quantum process . on the other hand , for @xmath14 , the corresponding dynamical map @xmath9 may not be cptp for intermediate time intervals and the divisibility property of the overall cptp dynamics is violated , which characterizes a non - markovian behavior @xcite .
if a function @xmath15 is monotonically nonincreasing under divisible maps acting on @xmath16 , i.e. , @xmath17 when @xmath12 , then @xmath18 is monotonically nonincreasing with increasing time , namely , @xmath19 . however , this is not always true for a non - markovian process , in which the divisibility of the map is violated , with @xmath20 being a straightforward non - markovianity witness @xcite .
therefore , @xmath18 can be employed to point out the breakdown of markovianity and the degree of non - markovianity can be defined by @xmath21 with the maximization performed over all sets of possible initial states @xmath22 and the integration extended over all time intervals for which @xmath23 .
numerically , we can write @xmath24 , \label{nf2}\ ] ] where @xmath25 represents the set of all time intervals for which @xmath26 .
the maximization over @xmath27 is not a trivial task .
nevertheless , it is always possible to find out lower bounds to @xmath28 by optimizing over any class of initial states , which leads to a qualitative assessment of the non - markovianity of the map @xmath29 @xcite .
in the general approach introduced in refs .
@xcite , discordlike measures of quantum , classical , and total correlations of an @xmath30-partite system in a state @xmath16 are defined by the respective expressions @xmath31 , \label{mq}\\ c(\rho)&=&k\left[m^{+}\rho,\ , m^{+}\pi_{\rho}\right ] , \label{mc } \\
t(\rho)&=&k\left[\rho,\ , \pi_{\rho}\right],\label{mt}\end{aligned}\ ] ] where @xmath32 $ ] denotes a real and positive function that vanishes for @xmath33 , the operator @xmath34 represents the product of the local marginals of @xmath16 , and @xmath35 and @xmath36 are _ classical _ states obtained through measurement maps @xmath37 and @xmath38 that minimize @xmath39 and maximize @xmath40 , respectively .
in particular , they will be taken here as local @xmath30-partite maps @xmath41 , where @xmath42 or @xmath43 depending on whether the _ _ i__th partition is measured or unmeasured .
furthermore , we will define the measurements @xmath44 as optimized complete sets of local _ orthogonal projectors_.
since orthogonal projective measurements are adopted , we have @xmath45 . the correlation measures in eqs .
( [ mq])-([mt ] ) are expected to obey the following set of fundamental criteria @xcite : ( i ) product states have no correlations , ( ii ) all correlations are invariant under local unitary operations , ( iii ) all correlations are non - negative , ( iv ) total correlations are nonincreasing under local quantum channels ( cptp maps ) , ( v ) classical states have no quantum correlations , and ( vi ) quantum correlations are nonincreasing under local quantum channels over unmeasured subsystems @xcite .
in order to satisfy the requirements above , we restrict @xmath46 to be positive and unitary invariant .
moreover , we also require @xmath46 to be _
contractible _ under cptp maps @xmath29 @xcite , i.e. , @xmath47 \le k[\rho , \sigma ] \,\,\,\,\,\ , ( \forall \rho,\sigma).\ ] ] in particular , a variety of such functions @xmath46 can be adopted as , for instance , the trace distance @xmath48 . in this work
, we will consider multipartite correlated quantum systems , such as that illustrated in fig .
[ fig:1 ] .
in particular , we will consider local dynamical maps @xmath49 . in this scenario
, we can show that a non - monotonic behavior of the correlations @xmath50 , @xmath51 , and @xmath52 as a function of time may provide a direct measure of the degree of non - markovianity @xmath28 , with @xmath53 or @xmath54 .
this result is contained in theorem 1 below . via locally measured states . ]
consider a quantum evolution driven by a local dynamical map @xmath55 .
then , assuming that @xmath46 is contractible under cptp maps , it follows that ( i ) @xmath56 is a measure of non - markovianity and ( ii ) @xmath57 and @xmath58 are measures of non - markovianity for local measurements @xmath59 such that @xmath60 when @xmath61 .
we begin by using @xmath55 .
then , by adopting @xmath62 , we write @xmath63 .
moreover , for local cptp maps , we have the relation @xmath64 .
( i ) thus , let us consider @xmath56 .
a generalized total correlation measure can be written as @xmath65= k\left[\phi_{t,\tau}\rho(\tau),\ , \phi_{t,\tau}\pi_{\rho(\tau)}\right]$ ] . imposing the condition that @xmath46 is contractible under cptp maps , we have @xmath66 \leq k\left[\rho(\tau),\ , \pi_{\rho(\tau)}\right]= t(\tau)$ ] . hence , @xmath67 .
( ii ) let us now take @xmath57 and @xmath58 .
a generalized quantum correlation measure can be written as @xmath68 $ ] , where we are considering @xmath69 with @xmath70 when @xmath71 ( consequently , @xmath72 ) . as @xmath73 does not necessarily minimize @xmath74 , we can write @xmath75=k\left[\phi_{t,\tau}\rho(\tau),\phi_{t,\tau}m_{\tau}^{-}\rho(\tau)\right]$ ] . by taking @xmath76 as a cptp map and imposing the condition that @xmath46 is contractible under cptp maps , we obtain @xmath77\leq k\left[\rho(\tau),m_{\tau}^{-}\rho(\tau)\right]=q(\tau)$ ] .
hence , @xmath78 .
next , let us consider @xmath58 .
a generalized classical correlation measure can be written as @xmath79 $ ] , where we are considering @xmath80 with @xmath81 when @xmath71 ( consequently , @xmath82 ) . then , imposing the condition that @xmath46 is contractible under cptp maps , we can write @xmath83\leq k\left[m_{t}^{+}\rho(\tau ) , m_{t}^{+}\pi_{\rho(\tau)}\right]$ ] .
as @xmath84 does not necessarily maximize @xmath85 , then @xmath86\leq k\left[m_{\tau}^{+}\rho(\tau),m_{\tau}^{+}\pi_{\rho(\tau)}\right]=c(\tau)$ ] .
hence , @xmath87 .
we observe that theorem 1 ensures @xmath57 and @xmath58 as measures of non - markovianity by assuming that the subsystems under decoherence are unmeasured , i.e. , @xmath60 when @xmath71 .
the measurements are then performed over ancillary states that are effectively free of decoherence .
this requirement is unnecessary for @xmath56 since it is a measurement - independent quantifier .
an effective isolation of an ancilla to probe non - markovianity has been experimentally achieved in several scenarios ( see , e.g. , refs .
more generally , it can be approximately assumed when the relaxation times of the ancillary subsystem are much larger than those of the principal subsystem .
similarly , it also happens when the multi - local dynamical map can be written as an effective transformation where only part of the subsystems undergoes decoherence [ see eq .
( [ phi - eff - iva ] ) for a bipartite example in sec .
let us consider correlations based on the schatten 1-norm ( trace - norm ) and projective measurements operating over one qubit within a two - qubit system , i.e. , @xmath32=\mathrm{tr}|\rho-\sigma|$ ] and @xmath88 . by adopting these conditions , @xmath89 is then the trace - norm geometric quantum discord , as introduced in refs .
@xcite , with @xmath90 and @xmath91 being the corresponding classical and total correlations @xcite .
the trace - norm geometric quantum and classical correlations have been experimentally discussed in refs .
we will consider initial density operators restricted to the _ x _ states , i.e. , @xmath92,\ ] ] where @xmath93 represent the pauli matrices and @xmath94 are the initial correlation parameters .
these states represent , for example , the general form of reduced density operators of arbitrary quantum spin chains with @xmath95 ( parity ) symmetry ( for a review see , e.g. , ref .
the trace - norm correlation measures have been analytically developed for a general _ x _ state @xcite , reading @xmath96 where @xmath97 , @xmath98 , @xmath99 , and @xmath100 .
let us start by focusing on a dynamical map of the form @xmath101 , where @xmath102 with @xmath103 $ ] .
this represents a local dephasing channel acting over subsystem @xmath104 , which can be derived from eq .
( [ master ] ) by taking @xmath105 and @xmath106 ( @xmath107 ) . for simplicity
, the time - dependent decoherence rates associated with each subsystem will be chosen to be the same , namely , @xmath108 such that @xmath109 .
the map @xmath110 preserves the _ x _ state form of @xmath16 , with @xmath111 .
moreover , we can write @xmath112 where @xmath113 is an effective dephasing channel with @xmath114 $ ] , with @xmath115 , such that @xmath116 .
therefore , @xmath74 , @xmath117 , or @xmath118 can be used to characterize non - markovianity , as provided by theorem 1 . in the markovian regime , which takes place when @xmath119 for all @xmath120 , we have @xmath121 .
consequently , we have @xmath122 , @xmath123 , and @xmath124 . in order to quantify the non - markovianity of the dynamical map @xmath125
, we will first consider the classical correlation .
thus , we replace @xmath126 by @xmath117 in eq .
( [ nf ] ) .
the condition @xmath127 occurs only if @xmath128 and @xmath129 . under this condition , @xmath130 and the maximization in eq .
( [ nf ] ) is achieved when @xmath131 and @xmath132 .
thus , we find @xmath133 by taking @xmath27 as a maximally entangled state , we obtain the same estimation of the non - markovianity degree via total or quantum correlation .
in fact , we have for the four bell states @xmath134 and @xmath135 such that @xmath136 and @xmath137 . as @xmath138 and @xmath139
, we conclude that @xmath140 or @xmath141 is equivalent to @xmath129 . under this condition ,
@xmath142 and @xmath143 , which leads to @xmath144 the degree of non - markovianity found here via trace - distance correlation measures is then consistent with previous results for measures of non - markovianity @xcite .
let us now illustrate the signature of non - markovianity for two qubits under local gad , which will be described in the open - system framework developed in ref .
@xcite based on a lindblad rate equation . in this scenario , the density matrix in eq.([master ] ) is replaced by @xmath145 where each auxiliary ( unnormalized ) operator @xmath146 defines the system dynamics given that the reservoir is in the @xmath147-configurational bath state , with @xmath148 being the number of configurational states of the environment . the probability
that the environment is in a given state at time @xmath149 reads @xmath150 $ ] , and the set of states @xmath151 encodes both the system dynamics and the fluctuations of the environment @xcite .
then , we model the environment as being characterized by a two - dimensional configurational space ( @xmath152 ) , which only affects the decay rates of the system .
each state follows by itself a lindblad rate equation @xmath153 + \bar{\gamma}^{a}_1\mathcal { l}^{a}\rho_1(t ) + \bar{\gamma}^{b}_1\mathcal { l}^{b}\rho_1(t ) \\&- & \phi_{21}\rho_1(t)+\phi_{12}\rho_{2}(t ) , \\ \label{eq : rho2 } \nonumber \frac{d\rho_2(t)}{dt } & = & -i[h_2 , \rho_2(t ) ] + \bar{\gamma}^{a}_2 \mathcal { l}^{a}\rho_2(t ) + \bar{\gamma}^{b}_2 \mathcal { l}^{b}\rho_2(t ) \nonumber\\ & - & \phi_{21}\rho_2(t)+\phi_{12}\rho_{1}(t),\end{aligned}\ ] ] where the structure of the superoperator @xmath154 for the gad channel is given by @xmath155 the first lines of eqs .
( [ eq : rho1 ] ) and ( [ eq : rho2 ] ) define the unitary and dissipative dynamics for the two - qubit system , given that the bath is in configurational state 1 and configurational state 2 , respectively .
the constants @xmath156 are the natural decay rates of the system associated with each reservoir state .
the positivity of the density matrix will be ensured as long as these decoherence coefficients obey @xmath157 @xcite . on the other hand , the second line of eqs .
( [ eq : rho1 ] ) and ( [ eq : rho2 ] ) describes transitions between the configurational states of the environment ( with rates @xmath158 and @xmath159 ) @xcite . for simplicity
, the decay rates associated with each subsystem will be chosen to be the same , namely , @xmath160 and @xmath161 .
moreover , we define the characteristic dimensionless parameters @xmath162 where @xmath163 $ ] and @xmath164
. we will analyze the system in the limit of either fast or slow environmental fluctuations .
the fast limit of environmental fluctuations occurs when the reservoir fluctuations are much faster than the average decay rates of the system , namely , @xmath165 ( @xmath166 ) , which implies that the system exhibits markovian behavior . on the other hand ,
when the bath fluctuations are much slower than the average decay rate , namely , @xmath167 ( @xmath168 ) , the system is in the limit of slow environmental fluctuations .
the signatures of non - markovianity will be provided by the total correlation , which has the advantages of avoiding both extremization procedures and further requirements over the dynamical map .
the non - markovian behavior can then be witnessed in fig .
[ fig : gadvel ] , which shows the temporal evolution of the total correlation for several values of @xmath169 , where we have taken @xmath170 , @xmath171 , and an initial _ x _ state described by @xmath172 , and @xmath173 .
for a two - qubit system under a non - markovian gad channel .
the initial state is in the _ x _ form , with @xmath174 , @xmath175 , @xmath176 , @xmath177 , and @xmath173 .
we have also taken @xmath178 and @xmath179 .
the non - monotonic behavior gets pronounced as we decrease @xmath169 from the markovian regime ( @xmath180 ) towards the non - markovian regime . ] for the fast limit , the decay of the total correlation is a monotonically decreasing function , which corresponds to a markovian evolution .
otherwise , when the system is subject to a non - markovian evolution ( slow limit ) , the total correlation shows a non - monotonic evolution , which gets more pronounced as we decrease @xmath169 .
the degree of non - markovianity @xmath181 can be rigorously obtained from eq.([nf2 ] ) by a maximization over all initial states .
on the other hand , a lower bound for @xmath181 can be directly obtained from fig .
[ fig : gadvel ] through the height of the non - monotonic sector as a function of @xmath169 .
consider an @xmath30-partite system initially in the greenberger - horne - zeilinger ( ghz ) state , i.e. , a maximally entangled state of the form @xmath182 where @xmath183 @xmath184 . by applying a dynamical map @xmath185 over the ghz state and choosing @xmath186 as a local dephasing channel as in eq .
( [ local - dep ] ) , we get @xmath187 where @xmath188 $ ] , with @xmath189 denoting the sum of the time - dependent decoherence rates .
we will consider the multipartite total correlation as the non - markovianity quantifier and use the ghz state to provide a lower bound for @xmath190 .
the product of the local marginals of @xmath191 is given by @xmath192 , and the eigenvalues of the operator @xmath193 are @xmath194 therefore , @xmath195 or @xmath196 we have @xmath197 for @xmath198 and @xmath199 for @xmath200 . since @xmath139
, we conclude that @xmath201 is equivalent to the condition @xmath129 .
moreover , @xmath142 [ consequently , @xmath202 when @xmath129 .
thus , we find a generalization of the result in eq.([nc ] ) : @xmath203
we have introduced a unified framework based on generalized quantum , classical , and total correlation measures to characterize the non - markovianity of local dynamical maps over multipartite quantum systems .
this approach establishes sufficient conditions under which each class of correlation can be used to determine the degree of non - markovian behavior .
we illustrated our results for different master - equation methods and for different sources of decoherence .
we expect applications in experimental setups for which correlations may be accessible to the observer .
in addition , the vanishing of entanglement for high - temperature regimes @xcite or for distant neighbors within a composite system @xcite may also motivate the use of generalized correlations as a tool to characterize non - markovianity .
further applications include the assessment of other approaches beyond markovianity ( see , e.g. , ref .
@xcite ) and of additional axioms over correlation functions ( see , e.g. , refs .
these topics are left for future research .
m.s.s . thanks d. lidar for his hospitality at the university of southern california .
this work is supported by the brazilian agencies cnpq , capes , and faperj and the brazilian national institute for science and technology of quantum information ( inct - iq ) .
f. m. paula , i. a. silva , j. d. montealegre , a. m. souza , e. r. deazevedo , r. s. sarthour , a. saguia , i. s. oliveira , d. o. soares - pinto , g. adesso , and m. s. sarandy , phys.rev .
lett . * 111 * , 250401 ( 2013 ) . | we provide a characterization of memory effects in non - markovian system - bath interactions from a quantum information perspective .
more specifically , we establish sufficient conditions for which generalized measures of multipartite quantum , classical , and total correlations can be used to quantify the degree of non - markovianity of a local quantum decohering process .
we illustrate our results by considering the dynamical behavior of the trace - distance correlations in multi - qubit systems under local dephasing and generalized amplitude damping . | <s>[INST]the characterization of memory effects in non - markovian evolutions is a fundamental subject in the theory of open systems @xcite .
indeed , the markovian behavior is always an idealization in the description of the quantum dynamics , with non - markovianity being non - negligible in a number of different scenarios , such as biological @xcite or condensed matter systems @xcite . from an applied point of view , non - markovian dynamics may be a resource for quantum tasks through an increase in the capacities of quantum channels @xcite .
moreover , it also exhibits applications in fault - tolerant quantum computation @xcite .
rigorously , non - markovianity can be defined through the deviation of a dynamical evolution map from a _ divisible _ completely positive trace - preserving ( cptp ) map @xcite .
this behavior is manifested both in entanglement @xcite and in other correlation sources @xcite , providing an approach that takes advantage of quantum information tools in the open - systems realm .
more specifically , non - markovianity can be interpreted in this context as a flow of information back to the system due to its interaction with the environment , which may imply non - monotonic behavior of correlations as a function of time . here , we propose a general framework to characterize non - markovianity through multipartite measures of quantum , classical , and total correlations . recently , there has been growing interest in the investigation of correlation measures from a quantum information perspective @xcite . in particular ,
measures for quantum correlations such as those provided by discordlike quantities and their corresponding classical counterparts have been formulated , with these quantities used as resources for implementing a variety of quantum tasks ( see ref .
@xcite and references therein ) .
these measures were originally introduced in an entropic scenario by ollivier and zurek @xcite . in a geometric context , correlations can be defined based on the relative entropy @xcite , hilbert - schmidt norm @xcite , trace norm @xcite , and bures norm @xcite .
all of these distinct versions of correlation measures can be described by a unified framework in terms of a generalized distance ( or pseudo distance ) function @xcite .
our approach for non - markovianity includes all these measures as particular cases and characterizes the non - markovian behavior by taking into account the program introduced by rivas , huelga , and plenio @xcite , in which an ancilla is coupled to a system which interacts with an environment .
specifically , we provide a rigorous description of the hypotheses over local dynamical maps under which quantum , classical , and total correlations can be used as measures of non - markovianity .
we illustrate the results considering the dynamics of the trace - distance correlations in qubit systems under either local dephasing or generalized amplitude damping ( gad ) .
let us suppose a quantum process governed by a time - local master equation @xmath0 where the time - dependent generator @xmath1 is given by @xmath2 + \sum_i \gamma_i ( t ) \left ( a_i(t)\rho(t)a^\dagger_i(t ) \right .
\nonumber \\ & & \left .
- \frac{1}{2 } \left\{a^\dagger_i(t ) a_i(t),\rho(t)\right\}\right ) , \end{aligned}\ ] ] with @xmath3 denoting the effective system hamiltonian , @xmath4 denoting the lindblad operators , and @xmath5 denoting the relaxation rates . by taking the relaxation rates as positive functions ,
i.e. , @xmath6 , the generator @xmath1 assumes the lindblad form @xcite for each fixed @xmath7 .
the master equation describes the dynamics of the density operator through @xmath8 , with the cptp map @xmath9 given by @xmath10 , with @xmath11 denoting the chronological time - ordering operator .
the dynamical map @xmath9 then satisfies the divisibility condition @xmath12 @xmath13 ) , which characterizes the markovianity of the quantum process . on the other hand , for @xmath14 , the corresponding dynamical map @xmath9 may not be cptp for intermediate time intervals and the divisibility property of the overall cptp dynamics is violated , which characterizes a non - markovian behavior @xcite .
if a function @xmath15 is monotonically nonincreasing under divisible maps acting on @xmath16 , i.e. , @xmath17 when @xmath12 , then @xmath18 is monotonically nonincreasing with increasing time , namely , @xmath19 . however , this is not always true for a non - markovian process , in which the divisibility of the map is violated , with @xmath20 being a straightforward non - markovianity witness @xcite .
therefore , @xmath18 can be employed to point out the breakdown of markovianity and the degree of non - markovianity can be defined by @xmath21 with the maximization performed over all sets of possible initial states @xmath22 and the integration extended over all time intervals for which @xmath23 .
numerically , we can write @xmath24 , \label{nf2}\ ] ] where @xmath25 represents the set of all time intervals for which @xmath26 .
the maximization over @xmath27 is not a trivial task .
nevertheless , it is always possible to find out lower bounds to @xmath28 by optimizing over any class of initial states , which leads to a qualitative assessment of the non - markovianity of the map @xmath29 @xcite .
in the general approach introduced in refs .
@xcite , discordlike measures of quantum , classical , and total correlations of an @xmath30-partite system in a state @xmath16 are defined by the respective expressions @xmath31 , \label{mq}\\ c(\rho)&=&k\left[m^{+}\rho,\ , m^{+}\pi_{\rho}\right ] , \label{mc } \\
t(\rho)&=&k\left[\rho,\ , \pi_{\rho}\right],\label{mt}\end{aligned}\ ] ] where @xmath32 $ ] denotes a real and positive function that vanishes for @xmath33 , the operator @xmath34 represents the product of the local marginals of @xmath16 , and @xmath35 and @xmath36 are _ classical _ states obtained through measurement maps @xmath37 and @xmath38 that minimize @xmath39 and maximize @xmath40 , respectively .
in particular , they will be taken here as local @xmath30-partite maps @xmath41 , where @xmath42 or @xmath43 depending on whether the _ _ i__th partition is measured or unmeasured .
furthermore , we will define the measurements @xmath44 as optimized complete sets of local _ orthogonal projectors_.
since orthogonal projective measurements are adopted , we have @xmath45 . the correlation measures in eqs .
( [ mq])-([mt ] ) are expected to obey the following set of fundamental criteria @xcite : ( i ) product states have no correlations , ( ii ) all correlations are invariant under local unitary operations , ( iii ) all correlations are non - negative , ( iv ) total correlations are nonincreasing under local quantum channels ( cptp maps ) , ( v ) classical states have no quantum correlations , and ( vi ) quantum correlations are nonincreasing under local quantum channels over unmeasured subsystems @xcite .
in order to satisfy the requirements above , we restrict @xmath46 to be positive and unitary invariant .
moreover , we also require @xmath46 to be _
contractible _ under cptp maps @xmath29 @xcite , i.e. , @xmath47 \le k[\rho , \sigma ] \,\,\,\,\,\ , ( \forall \rho,\sigma).\ ] ] in particular , a variety of such functions @xmath46 can be adopted as , for instance , the trace distance @xmath48 . in this work
, we will consider multipartite correlated quantum systems , such as that illustrated in fig .
[ fig:1 ] .
in particular , we will consider local dynamical maps @xmath49 . in this scenario
, we can show that a non - monotonic behavior of the correlations @xmath50 , @xmath51 , and @xmath52 as a function of time may provide a direct measure of the degree of non - markovianity @xmath28 , with @xmath53 or @xmath54 .
this result is contained in theorem 1 below . via locally measured states . ]
consider a quantum evolution driven by a local dynamical map @xmath55 .
then , assuming that @xmath46 is contractible under cptp maps , it follows that ( i ) @xmath56 is a measure of non - markovianity and ( ii ) @xmath57 and @xmath58 are measures of non - markovianity for local measurements @xmath59 such that @xmath60 when @xmath61 .
we begin by using @xmath55 .
then , by adopting @xmath62 , we write @xmath63 .
moreover , for local cptp maps , we have the relation @xmath64 .
( i ) thus , let us consider @xmath56 .
a generalized total correlation measure can be written as @xmath65= k\left[\phi_{t,\tau}\rho(\tau),\ , \phi_{t,\tau}\pi_{\rho(\tau)}\right]$ ] . imposing the condition that @xmath46 is contractible under cptp maps , we have @xmath66 \leq k\left[\rho(\tau),\ , \pi_{\rho(\tau)}\right]= t(\tau)$ ] . hence , @xmath67 .
( ii ) let us now take @xmath57 and @xmath58 .
a generalized quantum correlation measure can be written as @xmath68 $ ] , where we are considering @xmath69 with @xmath70 when @xmath71 ( consequently , @xmath72 ) . as @xmath73 does not necessarily minimize @xmath74 , we can write @xmath75=k\left[\phi_{t,\tau}\rho(\tau),\phi_{t,\tau}m_{\tau}^{-}\rho(\tau)\right]$ ] . by taking @xmath76 as a cptp map and imposing the condition that @xmath46 is contractible under cptp maps , we obtain @xmath77\leq k\left[\rho(\tau),m_{\tau}^{-}\rho(\tau)\right]=q(\tau)$ ] .
hence , @xmath78 .
next , let us consider @xmath58 .
a generalized classical correlation measure can be written as @xmath79 $ ] , where we are considering @xmath80 with @xmath81 when @xmath71 ( consequently , @xmath82 ) . then , imposing the condition that @xmath46 is contractible under cptp maps , we can write @xmath83\leq k\left[m_{t}^{+}\rho(\tau ) , m_{t}^{+}\pi_{\rho(\tau)}\right]$ ] .
as @xmath84 does not necessarily maximize @xmath85 , then @xmath86\leq k\left[m_{\tau}^{+}\rho(\tau),m_{\tau}^{+}\pi_{\rho(\tau)}\right]=c(\tau)$ ] .
hence , @xmath87 .
we observe that theorem 1 ensures @xmath57 and @xmath58 as measures of non - markovianity by assuming that the subsystems under decoherence are unmeasured , i.e. , @xmath60 when @xmath71 .
the measurements are then performed over ancillary states that are effectively free of decoherence .
this requirement is unnecessary for @xmath56 since it is a measurement - independent quantifier .
an effective isolation of an ancilla to probe non - markovianity has been experimentally achieved in several scenarios ( see , e.g. , refs .
more generally , it can be approximately assumed when the relaxation times of the ancillary subsystem are much larger than those of the principal subsystem .
similarly , it also happens when the multi - local dynamical map can be written as an effective transformation where only part of the subsystems undergoes decoherence [ see eq .
( [ phi - eff - iva ] ) for a bipartite example in sec .
let us consider correlations based on the schatten 1-norm ( trace - norm ) and projective measurements operating over one qubit within a two - qubit system , i.e. , @xmath32=\mathrm{tr}|\rho-\sigma|$ ] and @xmath88 . by adopting these conditions , @xmath89 is then the trace - norm geometric quantum discord , as introduced in refs .
@xcite , with @xmath90 and @xmath91 being the corresponding classical and total correlations @xcite .
the trace - norm geometric quantum and classical correlations have been experimentally discussed in refs .
we will consider initial density operators restricted to the _ x _ states , i.e. , @xmath92,\ ] ] where @xmath93 represent the pauli matrices and @xmath94 are the initial correlation parameters .
these states represent , for example , the general form of reduced density operators of arbitrary quantum spin chains with @xmath95 ( parity ) symmetry ( for a review see , e.g. , ref .
the trace - norm correlation measures have been analytically developed for a general _ x _ state @xcite , reading @xmath96 where @xmath97 , @xmath98 , @xmath99 , and @xmath100 .
let us start by focusing on a dynamical map of the form @xmath101 , where @xmath102 with @xmath103 $ ] .
this represents a local dephasing channel acting over subsystem @xmath104 , which can be derived from eq .
( [ master ] ) by taking @xmath105 and @xmath106 ( @xmath107 ) . for simplicity
, the time - dependent decoherence rates associated with each subsystem will be chosen to be the same , namely , @xmath108 such that @xmath109 .
the map @xmath110 preserves the _ x _ state form of @xmath16 , with @xmath111 .
moreover , we can write @xmath112 where @xmath113 is an effective dephasing channel with @xmath114 $ ] , with @xmath115 , such that @xmath116 .
therefore , @xmath74 , @xmath117 , or @xmath118 can be used to characterize non - markovianity , as provided by theorem 1 . in the markovian regime , which takes place when @xmath119 for all @xmath120 , we have @xmath121 .
consequently , we have @xmath122 , @xmath123 , and @xmath124 . in order to quantify the non - markovianity of the dynamical map @xmath125
, we will first consider the classical correlation .
thus , we replace @xmath126 by @xmath117 in eq .
( [ nf ] ) .
the condition @xmath127 occurs only if @xmath128 and @xmath129 . under this condition , @xmath130 and the maximization in eq .
( [ nf ] ) is achieved when @xmath131 and @xmath132 .
thus , we find @xmath133 by taking @xmath27 as a maximally entangled state , we obtain the same estimation of the non - markovianity degree via total or quantum correlation .
in fact , we have for the four bell states @xmath134 and @xmath135 such that @xmath136 and @xmath137 . as @xmath138 and @xmath139
, we conclude that @xmath140 or @xmath141 is equivalent to @xmath129 . under this condition ,
@xmath142 and @xmath143 , which leads to @xmath144 the degree of non - markovianity found here via trace - distance correlation measures is then consistent with previous results for measures of non - markovianity @xcite .
let us now illustrate the signature of non - markovianity for two qubits under local gad , which will be described in the open - system framework developed in ref .
@xcite based on a lindblad rate equation . in this scenario , the density matrix in eq.([master ] ) is replaced by @xmath145 where each auxiliary ( unnormalized ) operator @xmath146 defines the system dynamics given that the reservoir is in the @xmath147-configurational bath state , with @xmath148 being the number of configurational states of the environment . the probability
that the environment is in a given state at time @xmath149 reads @xmath150 $ ] , and the set of states @xmath151 encodes both the system dynamics and the fluctuations of the environment @xcite .
then , we model the environment as being characterized by a two - dimensional configurational space ( @xmath152 ) , which only affects the decay rates of the system .
each state follows by itself a lindblad rate equation @xmath153 + \bar{\gamma}^{a}_1\mathcal { l}^{a}\rho_1(t ) + \bar{\gamma}^{b}_1\mathcal { l}^{b}\rho_1(t ) \\&- & \phi_{21}\rho_1(t)+\phi_{12}\rho_{2}(t ) , \\ \label{eq : rho2 } \nonumber \frac{d\rho_2(t)}{dt } & = & -i[h_2 , \rho_2(t ) ] + \bar{\gamma}^{a}_2 \mathcal { l}^{a}\rho_2(t ) + \bar{\gamma}^{b}_2 \mathcal { l}^{b}\rho_2(t ) \nonumber\\ & - & \phi_{21}\rho_2(t)+\phi_{12}\rho_{1}(t),\end{aligned}\ ] ] where the structure of the superoperator @xmath154 for the gad channel is given by @xmath155 the first lines of eqs .
( [ eq : rho1 ] ) and ( [ eq : rho2 ] ) define the unitary and dissipative dynamics for the two - qubit system , given that the bath is in configurational state 1 and configurational state 2 , respectively .
the constants @xmath156 are the natural decay rates of the system associated with each reservoir state .
the positivity of the density matrix will be ensured as long as these decoherence coefficients obey @xmath157 @xcite . on the other hand , the second line of eqs .
( [ eq : rho1 ] ) and ( [ eq : rho2 ] ) describes transitions between the configurational states of the environment ( with rates @xmath158 and @xmath159 ) @xcite . for simplicity
, the decay rates associated with each subsystem will be chosen to be the same , namely , @xmath160 and @xmath161 .
moreover , we define the characteristic dimensionless parameters @xmath162 where @xmath163 $ ] and @xmath164
. we will analyze the system in the limit of either fast or slow environmental fluctuations .
the fast limit of environmental fluctuations occurs when the reservoir fluctuations are much faster than the average decay rates of the system , namely , @xmath165 ( @xmath166 ) , which implies that the system exhibits markovian behavior . on the other hand ,
when the bath fluctuations are much slower than the average decay rate , namely , @xmath167 ( @xmath168 ) , the system is in the limit of slow environmental fluctuations .
the signatures of non - markovianity will be provided by the total correlation , which has the advantages of avoiding both extremization procedures and further requirements over the dynamical map .
the non - markovian behavior can then be witnessed in fig .
[ fig : gadvel ] , which shows the temporal evolution of the total correlation for several values of @xmath169 , where we have taken @xmath170 , @xmath171 , and an initial _ x _ state described by @xmath172 , and @xmath173 .
for a two - qubit system under a non - markovian gad channel .
the initial state is in the _ x _ form , with @xmath174 , @xmath175 , @xmath176 , @xmath177 , and @xmath173 .
we have also taken @xmath178 and @xmath179 .
the non - monotonic behavior gets pronounced as we decrease @xmath169 from the markovian regime ( @xmath180 ) towards the non - markovian regime . ] for the fast limit , the decay of the total correlation is a monotonically decreasing function , which corresponds to a markovian evolution .
otherwise , when the system is subject to a non - markovian evolution ( slow limit ) , the total correlation shows a non - monotonic evolution , which gets more pronounced as we decrease @xmath169 .
the degree of non - markovianity @xmath181 can be rigorously obtained from eq.([nf2 ] ) by a maximization over all initial states .
on the other hand , a lower bound for @xmath181 can be directly obtained from fig .
[ fig : gadvel ] through the height of the non - monotonic sector as a function of @xmath169 .
consider an @xmath30-partite system initially in the greenberger - horne - zeilinger ( ghz ) state , i.e. , a maximally entangled state of the form @xmath182 where @xmath183 @xmath184 . by applying a dynamical map @xmath185 over the ghz state and choosing @xmath186 as a local dephasing channel as in eq .
( [ local - dep ] ) , we get @xmath187 where @xmath188 $ ] , with @xmath189 denoting the sum of the time - dependent decoherence rates .
we will consider the multipartite total correlation as the non - markovianity quantifier and use the ghz state to provide a lower bound for @xmath190 .
the product of the local marginals of @xmath191 is given by @xmath192 , and the eigenvalues of the operator @xmath193 are @xmath194 therefore , @xmath195 or @xmath196 we have @xmath197 for @xmath198 and @xmath199 for @xmath200 . since @xmath139
, we conclude that @xmath201 is equivalent to the condition @xmath129 .
moreover , @xmath142 [ consequently , @xmath202 when @xmath129 .
thus , we find a generalization of the result in eq.([nc ] ) : @xmath203
we have introduced a unified framework based on generalized quantum , classical , and total correlation measures to characterize the non - markovianity of local dynamical maps over multipartite quantum systems .
this approach establishes sufficient conditions under which each class of correlation can be used to determine the degree of non - markovian behavior .
we illustrated our results for different master - equation methods and for different sources of decoherence .
we expect applications in experimental setups for which correlations may be accessible to the observer .
in addition , the vanishing of entanglement for high - temperature regimes @xcite or for distant neighbors within a composite system @xcite may also motivate the use of generalized correlations as a tool to characterize non - markovianity .
further applications include the assessment of other approaches beyond markovianity ( see , e.g. , ref .
@xcite ) and of additional axioms over correlation functions ( see , e.g. , refs .
these topics are left for future research .
m.s.s . thanks d. lidar for his hospitality at the university of southern california .
this work is supported by the brazilian agencies cnpq , capes , and faperj and the brazilian national institute for science and technology of quantum information ( inct - iq ) .
f. m. paula , i. a. silva , j. d. montealegre , a. m. souza , e. r. deazevedo , r. s. sarthour , a. saguia , i. s. oliveira , d. o. soares - pinto , g. adesso , and m. s. sarandy , phys.rev .
lett . * 111 * , 250401 ( 2013 ) .[/INST] we provide a characterization of memory effects in non - markovian system - bath interactions from a quantum information perspective .
more specifically , we establish sufficient conditions for which generalized measures of multipartite quantum , classical , and total correlations can be used to quantify the degree of non - markovianity of a local quantum decohering process .
we illustrate our results by considering the dynamical behavior of the trace - distance correlations in multi - qubit systems under local dephasing and generalized amplitude damping . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Chattahoochee-Oconee National Forest
Land Adjustment Act of 2015''.
SEC. 2. FINDINGS AND DEFINITION.
(a) Findings.--Congress finds that--
(1) certain National Forest System land in the State of
Georgia consists of isolated tracts that are inefficient to
manage or have lost their principal value for National Forest
purposes;
(2) the disposal of that land would be in the public
interest; and
(3) proceeds from the sale of land authorized by this Act
would be used best by the Forest Service to purchase land for
National Forest purposes in the State of Georgia.
(b) Definition of Secretary.--In this Act, the term ``Secretary''
means the Secretary of Agriculture.
SEC. 3. LAND CONVEYANCE AUTHORITY.
(a) In General.--The Secretary is authorized, under such terms and
conditions as the Secretary may prescribe, to sell or exchange any or
all rights, title, and interest of the United States in the National
Forest System land described in subsection (b).
(b) Land Authorized for Disposal.--
(1) In general.--The National Forest System land subject to
sale or exchange under this Act are 30 tracts of land totaling
approximately 3,841 acres, which are generally depicted on 2
maps entitled ``Priority Land Adjustments, State of Georgia,
U.S. Forest Service-Southern Region, Oconee and Chattahoochee
National Forests, U.S. Congressional Districts-8, 9, 10 & 14''
and dated September 24, 2013.
(2) Maps.--The maps described in paragraph (1) shall be on
file and available for public inspection in the Office of the
Forest Supervisor, Chattahoochee-Oconee National Forest, until
such time as the land is sold or exchanged.
(3) Modification of boundaries.--The Secretary may modify
the boundaries of the land described in paragraph (1) based on
land management considerations.
(c) Form of Conveyance.--
(1) Quitclaim deed.--The Secretary shall convey land sold
under this Act by quitclaim deed.
(2) Reservations.--The Secretary may reserve any rights-of-
way or other rights or interests in land sold or exchanged
under this Act that the Secretary considers necessary for
management purposes or to protect the public interest.
(d) Valuation.--
(1) Market value.--The Secretary may not sell or exchange
land under this Act for less than market value, as determined
by appraisal or through competitive bid.
(2) Appraisal requirements.--Any appraisal shall be--
(A) consistent with the Uniform Appraisal Standards
for Federal Land Acquisitions or the Uniform Standards
of Professional Appraisal Practice; and
(B) subject to the approval of the Secretary.
(e) Consideration.--
(1) Cash.--Consideration for a sale of land or equalization
of an exchange shall be paid in cash.
(2) Exchange.--Notwithstanding section 206(b) of the
Federal Land Policy and Management Act of 1976 (43 U.S.C.
1716(b)), the Secretary may accept a cash equalization payment
in excess of 25 percent of the value of any land exchanged.
(f) Method of Sale.--
(1) Options.--The Secretary may sell land under subsection
(a) at public or private sale, including competitive sale by
auction, bid, or otherwise, in accordance with such terms,
conditions, and procedures as the Secretary determines are in
the best interest of the United States.
(2) Solicitations.--The Secretary may--
(A) make public or private solicitations for the
sale or exchange of land authorized by this Act; and
(B) reject any offer that the Secretary determines
is not adequate or not in the public interest.
(g) Brokers.--The Secretary may--
(1) use brokers or other third parties in the disposition
of the land authorized by this Act; and
(2) from the proceeds of a sale, pay reasonable commissions
or fees.
SEC. 4. TREATMENT OF PROCEEDS.
(a) Deposit.--The Secretary shall deposit the proceeds of a sale
authorized by this Act in the fund established under Public Law 90-171
(commonly known as the ``Sisk Act'') (16 U.S.C. 484a).
(b) Availability.--Subject to subsection (c), amounts deposited
under subsection (a) shall be available to the Secretary until
expended, without further appropriation, for the acquisition of land
for National Forest purposes in the State of Georgia.
(c) Private Property Protection.--Nothing in this Act authorizes
the use of funds deposited under subsection (a) to be used to acquire
land without the written consent of the owner of the land. | . Chattahoochee-Oconee National Forest Land Adjustment Act of 2015 (Sec. 3) This bill authorizes the Department of Agriculture (USDA) to may sell or exchange any or all interest of the United States in 30 tracts of National Forest System land in Georgia totaling approximately 3,841 acres. USDA may modify the boundaries of such lands based on land management considerations. USDA shall convey by quitclaim deed land sold or exchanged under this bill. USDA may reserve any rights-of-way or other rights or interests in land sold or exchanged under this bill that are considered necessary for management purposes or to protect the public interest. USDA may not sell or exchange land under this bill for less than market value, as determined by an appraisal or through a competitive bid. Any such appraisal shall be: consistent with the Uniform Appraisal Standards for Federal Land Acquisitions or the Uniform Standards of Professional Appraisal Practice, and subject to USDA's approval. The consideration for sales of lands or equalization of exchanges under this bill shall be paid in cash. USDA may accept a cash equalization payment that exceeds 25% of the value of any of the land to be exchanged under this bill. USDA may sell lands under this bill at public or private sale, including competitive sale by auction, bid, or otherwise, according to such terms, conditions, and procedures that are in the best interest of the United States. USDA may: make public or private solicitations for the sale or exchange of land authorized by this bill, and reject any offer that is determined as not being adequate or not in the public interest. USDA may: use brokers or other third parties in disposing of the lands authorized by this bill; and from the proceeds of such a sale, pay reasonable commissions or fees. (Sec. 4) USDA shall deposit the proceeds of a sale authorized by this bill in the fund established under the Sisk Act. Amounts deposited into such fund shall be made available to USDA for the acquisition of land for national forest purposes in Georgia. Nothing in this bill authorizes the use of the amounts deposited into such fund for the acquisition of land without the written consent of the owner of that land. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Chattahoochee-Oconee National Forest
Land Adjustment Act of 2015''.
SEC. 2. FINDINGS AND DEFINITION.
(a) Findings.--Congress finds that--
(1) certain National Forest System land in the State of
Georgia consists of isolated tracts that are inefficient to
manage or have lost their principal value for National Forest
purposes;
(2) the disposal of that land would be in the public
interest; and
(3) proceeds from the sale of land authorized by this Act
would be used best by the Forest Service to purchase land for
National Forest purposes in the State of Georgia.
(b) Definition of Secretary.--In this Act, the term ``Secretary''
means the Secretary of Agriculture.
SEC. 3. LAND CONVEYANCE AUTHORITY.
(a) In General.--The Secretary is authorized, under such terms and
conditions as the Secretary may prescribe, to sell or exchange any or
all rights, title, and interest of the United States in the National
Forest System land described in subsection (b).
(b) Land Authorized for Disposal.--
(1) In general.--The National Forest System land subject to
sale or exchange under this Act are 30 tracts of land totaling
approximately 3,841 acres, which are generally depicted on 2
maps entitled ``Priority Land Adjustments, State of Georgia,
U.S. Forest Service-Southern Region, Oconee and Chattahoochee
National Forests, U.S. Congressional Districts-8, 9, 10 & 14''
and dated September 24, 2013.
(2) Maps.--The maps described in paragraph (1) shall be on
file and available for public inspection in the Office of the
Forest Supervisor, Chattahoochee-Oconee National Forest, until
such time as the land is sold or exchanged.
(3) Modification of boundaries.--The Secretary may modify
the boundaries of the land described in paragraph (1) based on
land management considerations.
(c) Form of Conveyance.--
(1) Quitclaim deed.--The Secretary shall convey land sold
under this Act by quitclaim deed.
(2) Reservations.--The Secretary may reserve any rights-of-
way or other rights or interests in land sold or exchanged
under this Act that the Secretary considers necessary for
management purposes or to protect the public interest.
(d) Valuation.--
(1) Market value.--The Secretary may not sell or exchange
land under this Act for less than market value, as determined
by appraisal or through competitive bid.
(2) Appraisal requirements.--Any appraisal shall be--
(A) consistent with the Uniform Appraisal Standards
for Federal Land Acquisitions or the Uniform Standards
of Professional Appraisal Practice; and
(B) subject to the approval of the Secretary.
(e) Consideration.--
(1) Cash.--Consideration for a sale of land or equalization
of an exchange shall be paid in cash.
(2) Exchange.--Notwithstanding section 206(b) of the
Federal Land Policy and Management Act of 1976 (43 U.S.C.
1716(b)), the Secretary may accept a cash equalization payment
in excess of 25 percent of the value of any land exchanged.
(f) Method of Sale.--
(1) Options.--The Secretary may sell land under subsection
(a) at public or private sale, including competitive sale by
auction, bid, or otherwise, in accordance with such terms,
conditions, and procedures as the Secretary determines are in
the best interest of the United States.
(2) Solicitations.--The Secretary may--
(A) make public or private solicitations for the
sale or exchange of land authorized by this Act; and
(B) reject any offer that the Secretary determines
is not adequate or not in the public interest.
(g) Brokers.--The Secretary may--
(1) use brokers or other third parties in the disposition
of the land authorized by this Act; and
(2) from the proceeds of a sale, pay reasonable commissions
or fees.
SEC. 4. TREATMENT OF PROCEEDS.
(a) Deposit.--The Secretary shall deposit the proceeds of a sale
authorized by this Act in the fund established under Public Law 90-171
(commonly known as the ``Sisk Act'') (16 U.S.C. 484a).
(b) Availability.--Subject to subsection (c), amounts deposited
under subsection (a) shall be available to the Secretary until
expended, without further appropriation, for the acquisition of land
for National Forest purposes in the State of Georgia.
(c) Private Property Protection.--Nothing in this Act authorizes
the use of funds deposited under subsection (a) to be used to acquire
land without the written consent of the owner of the land.[/INST]. Chattahoochee-Oconee National Forest Land Adjustment Act of 2015 (Sec. 3) This bill authorizes the Department of Agriculture (USDA) to may sell or exchange any or all interest of the United States in 30 tracts of National Forest System land in Georgia totaling approximately 3,841 acres. USDA may modify the boundaries of such lands based on land management considerations. USDA shall convey by quitclaim deed land sold or exchanged under this bill. USDA may reserve any rights-of-way or other rights or interests in land sold or exchanged under this bill that are considered necessary for management purposes or to protect the public interest. USDA may not sell or exchange land under this bill for less than market value, as determined by an appraisal or through a competitive bid. Any such appraisal shall be: consistent with the Uniform Appraisal Standards for Federal Land Acquisitions or the Uniform Standards of Professional Appraisal Practice, and subject to USDA's approval. The consideration for sales of lands or equalization of exchanges under this bill shall be paid in cash. USDA may accept a cash equalization payment that exceeds 25% of the value of any of the land to be exchanged under this bill. USDA may sell lands under this bill at public or private sale, including competitive sale by auction, bid, or otherwise, according to such terms, conditions, and procedures that are in the best interest of the United States. USDA may: make public or private solicitations for the sale or exchange of land authorized by this bill, and reject any offer that is determined as not being adequate or not in the public interest. USDA may: use brokers or other third parties in disposing of the lands authorized by this bill; and from the proceeds of such a sale, pay reasonable commissions or fees. (Sec. 4) USDA shall deposit the proceeds of a sale authorized by this bill in the fund established under the Sisk Act. Amounts deposited into such fund shall be made available to USDA for the acquisition of land for national forest purposes in Georgia. Nothing in this bill authorizes the use of the amounts deposited into such fund for the acquisition of land without the written consent of the owner of that land.</s> |
It's all good. In the sense the search is over. There is safety & even some comfort now. I left a couple statements because I know my twitter has few followers and feel its the right thing to let people that have worried and speculated and even set out on foot in search know that it's ok now. There are questions and details that I didn't ask and don't need to know. I dont have details. Once the missing persons report was released it was overwhelming to have such private information out there. And it wasn't mostly my private information. I spoke to media at times on behalf of my husband. Mostly when I was at a loss or even panicking. Or feeling defensive. Not a always a great recipe. Today is a new day. I'm more than relieved. Healing! Love for all. I am in recovery. But in no way do I or even should I represent recovery. I'm far to fallible. But again, I do hope that there is a silver lining to this event and I have been truly inspired to keep on keepin on. I have no more comments.
Much love to all,
Rose Stahl
http://tl.gd/hgc6m9 Β· Reply
Report post (?) ||||| The case of's disappearance has come to a close.
On Sunday, the Terminator 3 actor checked himself into a Los Angeles rehabilitation center after sending an email to friends and family assuring his safety. The 32-year-old star was working hard at sobriety at the time of his disappearance.
Stahl's estranged wife, Rose Murphy, confirmed that the actor is indeed seeking treatment in rehab, telling E! Online, "He wants to be well. He's a good man and we want him home so we can help him."
Nick and Rose separated January 2012 after three years of marriage. Soon after, Stahl began to have issues over custody of his daughter, Marlo, when Murphy filed court papers requesting sole legal and physical custody.
Following Nick's admittance into rehab, Rose told TMZ that a divorce is currently not in the works and is glad to be able to tell her daughter about her father's whereabouts after his weeklong disappearance.
Celebuzz Single Player No Autoplay (CORE) No changes are to be made to this player ||||| Jesse Grant/WireImage
Nick Stahl has made good on his word.
Just a day after telling friends via e-mail he planned to get help and seek treatment, Stahl's wife Rose confirmed to E! News exclusively that the missing Terminator star checked into rehab Saturday night.
Now that the search is finally over, Rose Murphy Stahl has opened up about the painful experience, taking to Twitter to let concerned fans know she's doing OK:
MORE: Nick Stahl's Wife "Extremely Worried" About Missing Actor
"It's all good. In the sense the search is over. There is safety and even some comfort now. I left a couple statements because I know my Twitter has few followers and feel its the right thing to let people that have worried and speculated and even set out on foot in search know that it's ok now," Rose tweeted. "There are questions and details that I didn't ask and don't need to know. I dont have details. Once the missing persons report was released it was overwhelming to have such private information out there. And it wasn't mostly my private information. I spoke to media at times on behalf of my husband. Mostly when I was at a loss or even panicking. Or feeling defensive. Not a always a great recipe.
"Today is a new day. I'm more than relieved. Healing! Love for all. I am in recovery. But in no way do I or even should I represent recovery. I'm far to fallible. But again, I do hope that there is a silver lining to this event and I have been truly inspired to keep on keepin on. I have no more comments. Much love to all, Rose Stahl"
READ: Source: Nick Stahl Has "Gone Missing Before," but Never for This Long
The 32-year-old thesp, who went missing more than a week ago, was "really working hard" at sobriety at the time of his disappearance, according to his wife.
"He wants to be well," Rose told E! News last Friday. "He's a good man and we want him home so we can help him."
Story developingβ¦
(Originally published at 10:27 a.m. PT on May 20, 2012.)
PHOTOS: Nick Stahl: 10 Big Roles | β After going missing for a week, Nick Stahl has surfaced, having checked himself into a rehab clinic on Saturday night, reports E! Online. The Terminator 3 star has had drug abuse problems in the past, and estranged wife Rose says she is happy Stahl is getting help. "It's all good. In the sense the search is over. There is safety and even some comfort now," she tweeted. Rose told TMZ that she talked to him briefly on Saturday, and yesterday confirmed with the rehab center that he is indeed there. Is she contemplating divorce? Celebuzz has more. | <s>[INST]It's all good. In the sense the search is over. There is safety & even some comfort now. I left a couple statements because I know my twitter has few followers and feel its the right thing to let people that have worried and speculated and even set out on foot in search know that it's ok now. There are questions and details that I didn't ask and don't need to know. I dont have details. Once the missing persons report was released it was overwhelming to have such private information out there. And it wasn't mostly my private information. I spoke to media at times on behalf of my husband. Mostly when I was at a loss or even panicking. Or feeling defensive. Not a always a great recipe. Today is a new day. I'm more than relieved. Healing! Love for all. I am in recovery. But in no way do I or even should I represent recovery. I'm far to fallible. But again, I do hope that there is a silver lining to this event and I have been truly inspired to keep on keepin on. I have no more comments.
Much love to all,
Rose Stahl
http://tl.gd/hgc6m9 Β· Reply
Report post (?) ||||| The case of's disappearance has come to a close.
On Sunday, the Terminator 3 actor checked himself into a Los Angeles rehabilitation center after sending an email to friends and family assuring his safety. The 32-year-old star was working hard at sobriety at the time of his disappearance.
Stahl's estranged wife, Rose Murphy, confirmed that the actor is indeed seeking treatment in rehab, telling E! Online, "He wants to be well. He's a good man and we want him home so we can help him."
Nick and Rose separated January 2012 after three years of marriage. Soon after, Stahl began to have issues over custody of his daughter, Marlo, when Murphy filed court papers requesting sole legal and physical custody.
Following Nick's admittance into rehab, Rose told TMZ that a divorce is currently not in the works and is glad to be able to tell her daughter about her father's whereabouts after his weeklong disappearance.
Celebuzz Single Player No Autoplay (CORE) No changes are to be made to this player ||||| Jesse Grant/WireImage
Nick Stahl has made good on his word.
Just a day after telling friends via e-mail he planned to get help and seek treatment, Stahl's wife Rose confirmed to E! News exclusively that the missing Terminator star checked into rehab Saturday night.
Now that the search is finally over, Rose Murphy Stahl has opened up about the painful experience, taking to Twitter to let concerned fans know she's doing OK:
MORE: Nick Stahl's Wife "Extremely Worried" About Missing Actor
"It's all good. In the sense the search is over. There is safety and even some comfort now. I left a couple statements because I know my Twitter has few followers and feel its the right thing to let people that have worried and speculated and even set out on foot in search know that it's ok now," Rose tweeted. "There are questions and details that I didn't ask and don't need to know. I dont have details. Once the missing persons report was released it was overwhelming to have such private information out there. And it wasn't mostly my private information. I spoke to media at times on behalf of my husband. Mostly when I was at a loss or even panicking. Or feeling defensive. Not a always a great recipe.
"Today is a new day. I'm more than relieved. Healing! Love for all. I am in recovery. But in no way do I or even should I represent recovery. I'm far to fallible. But again, I do hope that there is a silver lining to this event and I have been truly inspired to keep on keepin on. I have no more comments. Much love to all, Rose Stahl"
READ: Source: Nick Stahl Has "Gone Missing Before," but Never for This Long
The 32-year-old thesp, who went missing more than a week ago, was "really working hard" at sobriety at the time of his disappearance, according to his wife.
"He wants to be well," Rose told E! News last Friday. "He's a good man and we want him home so we can help him."
Story developingβ¦
(Originally published at 10:27 a.m. PT on May 20, 2012.)
PHOTOS: Nick Stahl: 10 Big Roles[/INST]β After going missing for a week, Nick Stahl has surfaced, having checked himself into a rehab clinic on Saturday night, reports E! Online. The Terminator 3 star has had drug abuse problems in the past, and estranged wife Rose says she is happy Stahl is getting help. "It's all good. In the sense the search is over. There is safety and even some comfort now," she tweeted. Rose told TMZ that she talked to him briefly on Saturday, and yesterday confirmed with the rehab center that he is indeed there. Is she contemplating divorce? Celebuzz has more.</s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Community Savings and Investment Act
of 1998''.
SEC. 2. INCOME TAX ON QUALIFIED COMMUNITY LENDERS.
(a) In General.--Section 11 of the Internal Revenue Code of 1986
(relating to tax imposed on corporations) is amended by redesignating
subsection (d) as subsection (e) and by inserting after subsection (c)
the following new subsection:
``(d) Qualified Community Lenders.--
``(1) In general.--In the case of a qualified community
lender, in lieu of the amount of tax under subsection (b) the
amount of tax imposed by subsection (a) for a taxable year
shall be the sum of--
``(A) 15 percent of so much of the taxable income
as exceeds $250,000 but does not exceed $1,000,000, and
``(B) the highest rate of tax imposed by subsection
(b) multiplied by so much of the taxable income as
exceeds $1,000,000.
``(2) Qualified community lender.--For purposes of
paragraph (1), the term `qualified community lender' means a
bank--
``(A) which achieved a rating of `satisfactory
record of meeting community credit needs', or better,
at the most recent examination of such bank under the
Community Reinvestment Act of 1977,
``(B) whose outstanding local community loans at
all times during the taxable year comprised not less
than 60 percent of the total outstanding loans,
``(C) meets the ownership requirements of paragraph
(3), and
``(D) at all times during the taxable year has
total assets of not more than $1,000,000,000.''.
``(3) Ownership requirements.--
``(A) In general.--The ownership requirements of
this paragraph are met with respect to any bank if--
``(i) no shares of, or other ownership
interests in, the bank are publicly traded, or
``(ii) in the case of a bank the shares of
which or ownership interests in which are
publicly traded, the last known address of the
holders of at least \2/3\ of all such shares or
interests, including persons for whose benefit
such shares or interests are held by another,
is in the home State of the bank or a State
contiguous to such home State.
``(B) Home state defined.--For purposes of
subparagraph (A), the term `home State' means--
``(i) with respect to a national bank or
Federal savings association, the State in which
the main office of the bank or savings
association is located, and
``(ii) with respect to a State bank or
State savings association, the State by which
the bank or savings association is chartered.
``(4) Other definitions.--For purposes of this subsection--
``(A) Bank.--The term `bank'--
``(i) has the meaning given to such term in
section 581, and
``(ii) includes any bank--
``(I) in which at least 80 percent
of the shares of, or other ownership
interests in the bank are owned by
other qualified community lenders, and
``(II) the sole purpose of which is
to serve the banking needs of such
lenders.
``(B) Local community loan.--The term `local
community loan' means--
``(i) any loan originated by a bank to any
person, other than a related person with
respect to the bank, who is a resident of a
community in which the bank is chartered or in
which it operates an office at which deposits
are accepted, and
``(ii) any loan originated by a bank to any
person, other than a related person with
respect to the bank, who is engaged in a trade
or business in any such community, to the
extent that all or substantially all of the
proceeds of such loan are expended in
connection with the trade or business of such
person in any such community.
``(C) Related person.--The term `related person'
means, with respect to any bank, any affiliate of the
bank, any person who is a director, officer, or
principal shareholder of the bank, and any member of
the immediate family of any such person.''.
(b) S Corporation Income.--
(1) In general.--Section 1 of such Code (relating to tax
imposed) is amended by adding at the end the following new
subsection:
``(i) Community Lender Income From S Corporation.--
``(1) In general.--If a taxpayer has community lender
income from a S corporation for any taxable year, the tax
imposed by this section for such taxable year shall be the sum
of--
``(A) the tax computed at the rates and in the same
manner as if this subsection had not been enacted on
the greater of--
``(i) taxable income reduced by community
lender income, or
``(ii) the lesser of--
``(I) the amount of taxable income
taxed at a rate below 28 percent, or
``(II) taxable income reduced by
community lender income, and
``(B) a tax on community lender income computed
at--
``(i) a rate of zero on zero-rate community
lender income,
``(ii) a rate of 15 percent on 15 percent
community lender income, and
``(iii) the highest rate in effect under
this section with respect to the taxpayer on
the excess of community lender income on which
a tax is determined under clause (i) or (ii).
``(2) Community lender income.--For purposes of paragraph
(1)--
``(A) In general.--The term `qualified community
lender income' means taxable income (if any) of a
qualified community lender (as defined in section
11(d)(2)) that is an S corporation, determined at the
entity level.
``(B) Zero-rate community lender income.--The term
`zero-rate community lender income' means the
taxpayer's pro rata share of so much of community
lender income as does not exceed $250,000.
``(C) 15 percent community lender income.--The term
`15 percent community lender income' means the
taxpayer's pro rata share of so much of community
lender income as exceeds $250,000 but does not exceed
$1,000,000.
``(D) Special rules.--
``(i) For purposes of this paragraph, the
taxpayer's pro rata share of community lender
income shall be determined under part II of
subchapter S.
``(ii) This subsection shall be applied
after the application of subsection (h).''.
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after December 31, 1998.
SEC. 3. EXCLUSION FROM INCOME TAXATION FOR INCOME DERIVED FROM BANKING
SERVICES WITHIN DISTRESSED COMMUNITIES.
(a) Federal Taxation.--Part III of subchapter B of chapter 1 of the
Internal Revenue Code of 1986 (relating to items specifically excluded
from gross income) is amended by redesignating section 139 as section
140 and by inserting after section 138 the following new section:
``SEC. 139. BANKING SERVICES WITHIN DISTRESSED COMMUNITIES.
``(a) In General.--At the election of the taxpayer, gross income
shall not include distressed community banking income.
``(b) Distressed Community Banking Income.--For purposes of
subsection (a), the term `distressed community banking income' means
net income of a qualified depository institution which is derived from
the active conduct of a banking business in a distressed community.
``(c) Qualified Depository Institution.--An institution is a
qualified depository institution if--
``(1) such institution is an insured depository institution
(as defined in section 3 of the Federal Deposit Insurance Act
(12 U.S.C. 1813)),
``(2) such institution is located in, or has a branch
located in, a qualified distressed community, and
``(3) as of the last day of the taxable year, at least 85
percent of its loans from its location within the qualified
distressed community are local community loans (as defined in
section 11(d)(4)(B)).
``(d) Distressed Community.--The term `distressed community' has
the meaning given the term `qualified distressed community' by section
233 of the Bank Enterprise Act of 1991 (12 U.S.C. 1834a(b)).''.
(b) Clerical Amendment.--The table of sections for part III of
subchapter B of chapter 1 of such Code is amended by striking the item
relating to section 139 and inserting after the item relating to
section 138 the following new items:
``Sec. 139. Banking services within
distressed communities.
``Sec. 140. Cross references to other
Acts.''.
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after the date of the enactment of
this Act. | Community Savings and Investment Act of 1998 - Amends the Internal Revenue Code to: (1) establish a separate tax rate for a qualified community lender; and (2) permit the exclusion from gross income of distressed community banking income. Defines terms. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Community Savings and Investment Act
of 1998''.
SEC. 2. INCOME TAX ON QUALIFIED COMMUNITY LENDERS.
(a) In General.--Section 11 of the Internal Revenue Code of 1986
(relating to tax imposed on corporations) is amended by redesignating
subsection (d) as subsection (e) and by inserting after subsection (c)
the following new subsection:
``(d) Qualified Community Lenders.--
``(1) In general.--In the case of a qualified community
lender, in lieu of the amount of tax under subsection (b) the
amount of tax imposed by subsection (a) for a taxable year
shall be the sum of--
``(A) 15 percent of so much of the taxable income
as exceeds $250,000 but does not exceed $1,000,000, and
``(B) the highest rate of tax imposed by subsection
(b) multiplied by so much of the taxable income as
exceeds $1,000,000.
``(2) Qualified community lender.--For purposes of
paragraph (1), the term `qualified community lender' means a
bank--
``(A) which achieved a rating of `satisfactory
record of meeting community credit needs', or better,
at the most recent examination of such bank under the
Community Reinvestment Act of 1977,
``(B) whose outstanding local community loans at
all times during the taxable year comprised not less
than 60 percent of the total outstanding loans,
``(C) meets the ownership requirements of paragraph
(3), and
``(D) at all times during the taxable year has
total assets of not more than $1,000,000,000.''.
``(3) Ownership requirements.--
``(A) In general.--The ownership requirements of
this paragraph are met with respect to any bank if--
``(i) no shares of, or other ownership
interests in, the bank are publicly traded, or
``(ii) in the case of a bank the shares of
which or ownership interests in which are
publicly traded, the last known address of the
holders of at least \2/3\ of all such shares or
interests, including persons for whose benefit
such shares or interests are held by another,
is in the home State of the bank or a State
contiguous to such home State.
``(B) Home state defined.--For purposes of
subparagraph (A), the term `home State' means--
``(i) with respect to a national bank or
Federal savings association, the State in which
the main office of the bank or savings
association is located, and
``(ii) with respect to a State bank or
State savings association, the State by which
the bank or savings association is chartered.
``(4) Other definitions.--For purposes of this subsection--
``(A) Bank.--The term `bank'--
``(i) has the meaning given to such term in
section 581, and
``(ii) includes any bank--
``(I) in which at least 80 percent
of the shares of, or other ownership
interests in the bank are owned by
other qualified community lenders, and
``(II) the sole purpose of which is
to serve the banking needs of such
lenders.
``(B) Local community loan.--The term `local
community loan' means--
``(i) any loan originated by a bank to any
person, other than a related person with
respect to the bank, who is a resident of a
community in which the bank is chartered or in
which it operates an office at which deposits
are accepted, and
``(ii) any loan originated by a bank to any
person, other than a related person with
respect to the bank, who is engaged in a trade
or business in any such community, to the
extent that all or substantially all of the
proceeds of such loan are expended in
connection with the trade or business of such
person in any such community.
``(C) Related person.--The term `related person'
means, with respect to any bank, any affiliate of the
bank, any person who is a director, officer, or
principal shareholder of the bank, and any member of
the immediate family of any such person.''.
(b) S Corporation Income.--
(1) In general.--Section 1 of such Code (relating to tax
imposed) is amended by adding at the end the following new
subsection:
``(i) Community Lender Income From S Corporation.--
``(1) In general.--If a taxpayer has community lender
income from a S corporation for any taxable year, the tax
imposed by this section for such taxable year shall be the sum
of--
``(A) the tax computed at the rates and in the same
manner as if this subsection had not been enacted on
the greater of--
``(i) taxable income reduced by community
lender income, or
``(ii) the lesser of--
``(I) the amount of taxable income
taxed at a rate below 28 percent, or
``(II) taxable income reduced by
community lender income, and
``(B) a tax on community lender income computed
at--
``(i) a rate of zero on zero-rate community
lender income,
``(ii) a rate of 15 percent on 15 percent
community lender income, and
``(iii) the highest rate in effect under
this section with respect to the taxpayer on
the excess of community lender income on which
a tax is determined under clause (i) or (ii).
``(2) Community lender income.--For purposes of paragraph
(1)--
``(A) In general.--The term `qualified community
lender income' means taxable income (if any) of a
qualified community lender (as defined in section
11(d)(2)) that is an S corporation, determined at the
entity level.
``(B) Zero-rate community lender income.--The term
`zero-rate community lender income' means the
taxpayer's pro rata share of so much of community
lender income as does not exceed $250,000.
``(C) 15 percent community lender income.--The term
`15 percent community lender income' means the
taxpayer's pro rata share of so much of community
lender income as exceeds $250,000 but does not exceed
$1,000,000.
``(D) Special rules.--
``(i) For purposes of this paragraph, the
taxpayer's pro rata share of community lender
income shall be determined under part II of
subchapter S.
``(ii) This subsection shall be applied
after the application of subsection (h).''.
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after December 31, 1998.
SEC. 3. EXCLUSION FROM INCOME TAXATION FOR INCOME DERIVED FROM BANKING
SERVICES WITHIN DISTRESSED COMMUNITIES.
(a) Federal Taxation.--Part III of subchapter B of chapter 1 of the
Internal Revenue Code of 1986 (relating to items specifically excluded
from gross income) is amended by redesignating section 139 as section
140 and by inserting after section 138 the following new section:
``SEC. 139. BANKING SERVICES WITHIN DISTRESSED COMMUNITIES.
``(a) In General.--At the election of the taxpayer, gross income
shall not include distressed community banking income.
``(b) Distressed Community Banking Income.--For purposes of
subsection (a), the term `distressed community banking income' means
net income of a qualified depository institution which is derived from
the active conduct of a banking business in a distressed community.
``(c) Qualified Depository Institution.--An institution is a
qualified depository institution if--
``(1) such institution is an insured depository institution
(as defined in section 3 of the Federal Deposit Insurance Act
(12 U.S.C. 1813)),
``(2) such institution is located in, or has a branch
located in, a qualified distressed community, and
``(3) as of the last day of the taxable year, at least 85
percent of its loans from its location within the qualified
distressed community are local community loans (as defined in
section 11(d)(4)(B)).
``(d) Distressed Community.--The term `distressed community' has
the meaning given the term `qualified distressed community' by section
233 of the Bank Enterprise Act of 1991 (12 U.S.C. 1834a(b)).''.
(b) Clerical Amendment.--The table of sections for part III of
subchapter B of chapter 1 of such Code is amended by striking the item
relating to section 139 and inserting after the item relating to
section 138 the following new items:
``Sec. 139. Banking services within
distressed communities.
``Sec. 140. Cross references to other
Acts.''.
(c) Effective Date.--The amendments made by this section shall
apply to taxable years beginning after the date of the enactment of
this Act.[/INST]Community Savings and Investment Act of 1998 - Amends the Internal Revenue Code to: (1) establish a separate tax rate for a qualified community lender; and (2) permit the exclusion from gross income of distressed community banking income. Defines terms.</s> |
influenza causes seasonal infections worldwide that can lead to complications and deaths in every age group .
according to information from the who , between 330 million and 1.575 billion individuals suffer from influenza and influenza - like virus every year throughout the world , with deaths of between 0.5 and 1 million individuals . in many countries , including poland , for each age group , the rate of vaccination against influenza is still at a very low level , which generates high social costs , not infrequently family tragedies in the case of irreversible complications of influenza , or death of a loved one . the most effective and cheapest way to combat influenza is through vaccination [ 13 ] .
three pandemics caused by 3 different subtypes of the influenza virus occurred in the twentieth century .
the pandemic of 19181919 , referred to as the spanish flu , was caused by the a / h1n1/ virus ; the pandemic 19571958 , known as asian flu , was caused by the a / h2n2/ ( 14 million of deaths ) ; and the pandemic known as hong kong flu was caused by the a / h3n2/ ( 14 million of deaths ) . according to the present data , the 19181919 pandemic resulted in 50100 million deaths .
people who had lived during the pandemic and who had survived , and remembered the spectre of death caused by influenza , did not challenge the validity of vaccination when the 19571958 asian flu pandemic occurred and were eager to undergo vaccination , notwithstanding the lesser quality of vaccines at that time compared with the present . during the spanish pandemic ,
the highest incidence was recorded in individuals aged 514 years , while the highest mortality rate was recorded in the population aged from 2440 years .
therefore , in order to avoid complications from influenza , and to ensure the appropriate development of children and young people , preventive measures , including regular vaccination against influenza , should be in place .
the high variability of the influenza virus is a characteristic feature that has been known for many years . in each successive seasonal epidemic
these strains are genetically and antigenically different from those which caused illness in the past or even in a number of recent epidemics , not only because of mutations , but also due to changes of reassortment resulting from the segmented genome .
this may in turn , have health and economic impacts associated with the occurrence of epidemic and pandemic influenza . therefore , regular vaccination is one of the few steps that may be taken to protect people , especially in high - risk groups , from the potential , serious complications of influenza .
regular vaccination should be part of good medical practice , as well as people s engagement in their own health and in that of their family . based on numerous studies
, it is estimated that the effectiveness of current inactivated influenza vaccine in reducing morbidity and mortality in high - risk groups ranges from 5070% [ 812 ] .
we should realize that the flu is a disease in which the continuous evolution of the virus is essential for the occurrence of seasonal epidemics in the human population and , from time to time , as pandemic influenza .
it is known that since 9 may 1997 the a / h5n1/hpai influenza virus subtype is circulating within the population , creating more and more new mutants , which has resulted in the registration of an approximate mortality of 56.7% among infected individuals .
the reassortment of the 2 strains of viruses a / h5n1/ ( hpai ) , which is very infectious , but does not have the ability of human to human transmission ; and a(h1n1)pdm09 , a pandemic virus which does have this ability must be feared .
reassortment could result in the creation of a virus with all of the characteristics of the pandemic virus .
for example , during the 2010/2011 epidemic season more people died than during the previous year s influenza pandemic , even though a vaccine was available from 5 different companies , in pharmacies , from the family doctor , or from private medical centres .
according to data from the national institute of public health - national institute of hygiene ( niph - nih ) , the rate of vaccination in children in 2008 was very low . in the group of children aged 6 months to 14 years , only 1.11.6% were vaccinated .
although influenza vaccination for people aged over 65 years was free of charge in many provinces in this group , only 13.4% of this population was immunized , according to the european centre for disease control ( ecdc ) and the venice network new integrated collaboration effort ; while in the case of people with chronic diseases , only 11.1% were immunized ( data venice ecdc and network ) .
the vaccination rate among health care employees is an embarrassing at 6.4% ( data venice ecdc and network ) . according to the latest data from who
, the uptake of vaccine places poland in the penultimate place in europe ( 2010 ) .
the situation is no better in terms of individuals with different types of insurance within private medical centers .
the pandemic announced by who on 11 june 2009 was caused by the influenza virus subtype a / h1n1/v , which proved to be a reassortment . according to data from who and ecdc , the mean number of deaths worldwide was about 18,000 , which is incomparably less than for seasonal influenza .
we must not forget that 1 million people throughout the world die from seasonal influenza and influenza - like viruses .
the global hysteria unleashed because of the purchase of pandemic flu vaccine did not fail to affect poland .
statements were also made by individuals who had no substantive grounds for doing so . with regard to the issue of vaccination against the pandemic influenza virus a(h1n1)pdm09 , the decision taken in poland should be considered as appropriate when taking into account the type of restrictions imposed on poland by pandemic vaccine manufacturers , who placed the entire burden of responsibility for vaccine safety onto the state , which is not the practice for seasonal vaccines .
furthermore , in accordance with manufacturers requirements , the vaccine could not be made available in pharmacies . with regard to the polish position adopted by the minister of health , ewa kopacz , the council of europe voiced its marked appreciation repeatedly . in effect , throughout the world many millions of doses of unused vaccine against pandemic influenza are wasted , representing many millions of euros . moreover , additional costs arise from the disposal of the vaccine purchased surplus to need , and it was a shame that these sizeable funds could not be devoted to other public health purposes instead . as we have stated and written many times , and
what both then and now continues to give us cause for real concern , is the fact that confidence in the who has been undermined , the take - up of all vaccines has decreased , and that there will be a further reduction in the already low take - up of the influenza vaccine , particularly in poland .
therefore , we deplore the fact that all those individuals who expressed themselves so actively in the press , radio and tv did not take action to increase the rate of vaccination against influenza , particularly since the ternary composition of the vaccine for the 2010/2011 season included the a / h1n1/pdm09 pandemic strain .
it is worth emphasizing that those individuals who died in the 2010/2011 epidemic season were in high risk groups , were not vaccinated against influenza , and had infection caused by the virus a(h1n1)pdm09 confirmed by use of molecular biology techniques , which was already a component of the vaccine for this season .
for many years , since the year 2000 , the advisory committee on immunization ( acip ) in the u.s .
has recommended the routine vaccination against influenza of all individuals above the age of 6 months until late old age .
therefore , in the epidemic season , vaccination is recommended for nursing mothers unless they were already vaccinated , and vaccination of household members , caregivers of young children and of individuals who are in close contact with children under the age of 6 months .
the recommendations of the advisory committee on immunization ( acip ) are shown in table 1 . in the 2010/2011 epidemic season , only 5.0% of the population was vaccinated despite the inclusion of the a / h1n1/pdm09 strain in the ternary composition of the vaccine against influenza . in poland in 2009 , split inactivated or subunit vaccines were registered as shown in table 2 .
vaccines against influenza available in poland are inactivated ( containing fragments of killed influenza virus ) , therefore they are not able to multiply in the body and cause disease , but produce a specific immunity directed against the influenza virus .
it is worth noting that irrespective of the recommendations of the advisory committee on immunization ( acip ) , 14 scientific societies also recommend vaccination against influenza ( table 3 ) .
increasingly , the problem of vaccination against influenza is considered in terms of its health and economic aspects , of which we often remain unaware . according to data from the u.s . , depending on the influenza epidemic season , the cost impact of influenza infection is between 76167 billion dollars . the humoral immune response to influenza vaccination in high - risk groups evaluated in studies undertaken by the influenza virus research department of the national centre for influenza niph - nih in collaboration with clinicians
we are convinced that the presentation of specific examples will be helpful in promoting prevention , and will encourage health professionals to protect not only their patients , but also their relatives .
table 5 includes what in our opinion are the main causes of the low prevalence of influenza vaccination .
diagnostic methods have been available in poland for decades , beginning with the gold standard for identification of the pathogen in the chicken embryo or tissue culture , by elisa , immunofluorescence ( if ) , serological methods , and ending with studies using different combinations of molecular biology methods .
currently , in poland and only in the influenza virus research department of the national influenza centre at the niph - nih in warsaw , 12 respiratory viruses influenza type a and b , virus rs type a and b , parainfluenza types 1 , 2 and 3 , human metapneumovirus ( hmpv ) , adenovirus , rhinovirus , coronavirus , 229e / nl63 , and oc43/hku1 can be detected from a single sample from the patient , applying the methods of molecular biology .
however , in the 12 provincial sanitary - epidemiological stations ( pses ) it is possible to diagnose influenza infections using methods of molecular biology , while the remaining 4 pses perform diagnostics using the immunofluorescence method ( if ) .
the importance of virological diagnosis of respiratory infections , particularly influenza , is high , not only in medical , but also in economic terms .
it serves to avoid antibiotics therapy in the absence of indications and also to ensure that appropriate treatment is administered when necessary . the appropriate use of currently available new influenza virus neuraminidase inhibitors , such as zanamivir ( relenza ) and oseltamivir ( tamiflu ) , and consequently , the simultaneous prevention of appearance of strains resistant to these drugs , reduce the length of hospital stay [ 1,2024 ] .
the taking of appropriate measures to prevent the spread of infection refutes those myths associated with vaccination that lead to its avoidance .
one should be aware that , particularly in individuals in high - risk groups ( including healthy young children ) , the effects of influenza in those who are not vaccinated can result in complications , and even death .
therefore , the rapid identification of influenza virus is a priority when considering the possibility of treatment with effective medication .
currently , 2 influenza antiviral agents have been present on the market for many years oseltamivir ( tamiflu ) and zanamivir ( relenza ) active in the case of infection both with influenza a and b [ 13,2024 ] . the effectiveness of these drugs is dependent on several factors . in the case of seasonal influenza infection ,
the medication should be given after laboratory confirmation , preferably up to 36 hours from the onset of symptoms [ 1,2024 ] .
however , in the event of pandemic influenza , it should be administered on the basis of clinical symptoms , without waiting for the laboratory confirmation of infection .
the use of these medicines is indicated not solely for treatment of established infection , but also in prevention , including for post - exposure prophylaxis [ 1,2024 ] .
it should be noted that the use of oseltamivir during an epidemic of influenza was recommended from the age of 1 year .
however , in the situation of a pandemic , both the manufacturer and the european medicines agency ( emea ) recommend the use of this medication for those aged less than 1 year , depending on the child s body weight .
oseltamivir ( tamiflu ) is available in capsular form , which allows for its use not only in the case of small children , but also in patients who are unable to swallow capsules [ 1,2024 ] .
zanamivir ( relenza ) is formulated for inhalation and can be used from the age of 5 years .
these drugs are effective for both seasonal influenza infections as well as for subtypes of other influenza type a and b viruses . according to who and polish data , the new generation of drugs the neuraminidase inhibitors have proved effective in infections with the hpai virus : subtype a / h5n1/ , a / h7n7/ , pandemic influenza virus subtype a(h1n1)pdm09 , as well as in the case of seasonal influenza infection . currently , clinical trials of a new antiviral agent , peramivir , are in progress | summaryinfluenza causes seasonal infections worldwide that can lead to complications and deaths in every age group .
the most effective and cheapest way to combat influenza is through vaccination . in many countries , including poland , for each age group , the rate of vaccination against influenza is still at a very low level , which generates high social costs , not infrequently family tragedies in the case of irreversible complications of influenza , or death of a loved one .
regular vaccination should be part of good medical practice , as well as an individual s engagement in their own health and in that of their family . based on numerous studies
, it is estimated that the effectiveness of current inactivated influenza vaccine in reducing morbidity and mortality in high - risk groups ranges from 5070% . according to data from the national institute of public health - national institute of hygiene , the rate of vaccination in children in 2008 in poland was very low . in the group of children
aged from 6 months to 14 years , only 1.11.6% were vaccinated .
although influenza vaccination for people aged over 65 years was free of charge in many provinces in this group , only 13.4% of this population was immunized , while in the case of people with chronic diseases , only 11.1% were immunized .
the vaccination rate among health care employees is an embarrassing 6.4% .
more educational activities addressed to both medical professionals and patients are required in order to increase influenza vaccine coverage in poland . | <s>[INST]influenza causes seasonal infections worldwide that can lead to complications and deaths in every age group .
according to information from the who , between 330 million and 1.575 billion individuals suffer from influenza and influenza - like virus every year throughout the world , with deaths of between 0.5 and 1 million individuals . in many countries , including poland , for each age group , the rate of vaccination against influenza is still at a very low level , which generates high social costs , not infrequently family tragedies in the case of irreversible complications of influenza , or death of a loved one . the most effective and cheapest way to combat influenza is through vaccination [ 13 ] .
three pandemics caused by 3 different subtypes of the influenza virus occurred in the twentieth century .
the pandemic of 19181919 , referred to as the spanish flu , was caused by the a / h1n1/ virus ; the pandemic 19571958 , known as asian flu , was caused by the a / h2n2/ ( 14 million of deaths ) ; and the pandemic known as hong kong flu was caused by the a / h3n2/ ( 14 million of deaths ) . according to the present data , the 19181919 pandemic resulted in 50100 million deaths .
people who had lived during the pandemic and who had survived , and remembered the spectre of death caused by influenza , did not challenge the validity of vaccination when the 19571958 asian flu pandemic occurred and were eager to undergo vaccination , notwithstanding the lesser quality of vaccines at that time compared with the present . during the spanish pandemic ,
the highest incidence was recorded in individuals aged 514 years , while the highest mortality rate was recorded in the population aged from 2440 years .
therefore , in order to avoid complications from influenza , and to ensure the appropriate development of children and young people , preventive measures , including regular vaccination against influenza , should be in place .
the high variability of the influenza virus is a characteristic feature that has been known for many years . in each successive seasonal epidemic
these strains are genetically and antigenically different from those which caused illness in the past or even in a number of recent epidemics , not only because of mutations , but also due to changes of reassortment resulting from the segmented genome .
this may in turn , have health and economic impacts associated with the occurrence of epidemic and pandemic influenza . therefore , regular vaccination is one of the few steps that may be taken to protect people , especially in high - risk groups , from the potential , serious complications of influenza .
regular vaccination should be part of good medical practice , as well as people s engagement in their own health and in that of their family . based on numerous studies
, it is estimated that the effectiveness of current inactivated influenza vaccine in reducing morbidity and mortality in high - risk groups ranges from 5070% [ 812 ] .
we should realize that the flu is a disease in which the continuous evolution of the virus is essential for the occurrence of seasonal epidemics in the human population and , from time to time , as pandemic influenza .
it is known that since 9 may 1997 the a / h5n1/hpai influenza virus subtype is circulating within the population , creating more and more new mutants , which has resulted in the registration of an approximate mortality of 56.7% among infected individuals .
the reassortment of the 2 strains of viruses a / h5n1/ ( hpai ) , which is very infectious , but does not have the ability of human to human transmission ; and a(h1n1)pdm09 , a pandemic virus which does have this ability must be feared .
reassortment could result in the creation of a virus with all of the characteristics of the pandemic virus .
for example , during the 2010/2011 epidemic season more people died than during the previous year s influenza pandemic , even though a vaccine was available from 5 different companies , in pharmacies , from the family doctor , or from private medical centres .
according to data from the national institute of public health - national institute of hygiene ( niph - nih ) , the rate of vaccination in children in 2008 was very low . in the group of children aged 6 months to 14 years , only 1.11.6% were vaccinated .
although influenza vaccination for people aged over 65 years was free of charge in many provinces in this group , only 13.4% of this population was immunized , according to the european centre for disease control ( ecdc ) and the venice network new integrated collaboration effort ; while in the case of people with chronic diseases , only 11.1% were immunized ( data venice ecdc and network ) .
the vaccination rate among health care employees is an embarrassing at 6.4% ( data venice ecdc and network ) . according to the latest data from who
, the uptake of vaccine places poland in the penultimate place in europe ( 2010 ) .
the situation is no better in terms of individuals with different types of insurance within private medical centers .
the pandemic announced by who on 11 june 2009 was caused by the influenza virus subtype a / h1n1/v , which proved to be a reassortment . according to data from who and ecdc , the mean number of deaths worldwide was about 18,000 , which is incomparably less than for seasonal influenza .
we must not forget that 1 million people throughout the world die from seasonal influenza and influenza - like viruses .
the global hysteria unleashed because of the purchase of pandemic flu vaccine did not fail to affect poland .
statements were also made by individuals who had no substantive grounds for doing so . with regard to the issue of vaccination against the pandemic influenza virus a(h1n1)pdm09 , the decision taken in poland should be considered as appropriate when taking into account the type of restrictions imposed on poland by pandemic vaccine manufacturers , who placed the entire burden of responsibility for vaccine safety onto the state , which is not the practice for seasonal vaccines .
furthermore , in accordance with manufacturers requirements , the vaccine could not be made available in pharmacies . with regard to the polish position adopted by the minister of health , ewa kopacz , the council of europe voiced its marked appreciation repeatedly . in effect , throughout the world many millions of doses of unused vaccine against pandemic influenza are wasted , representing many millions of euros . moreover , additional costs arise from the disposal of the vaccine purchased surplus to need , and it was a shame that these sizeable funds could not be devoted to other public health purposes instead . as we have stated and written many times , and
what both then and now continues to give us cause for real concern , is the fact that confidence in the who has been undermined , the take - up of all vaccines has decreased , and that there will be a further reduction in the already low take - up of the influenza vaccine , particularly in poland .
therefore , we deplore the fact that all those individuals who expressed themselves so actively in the press , radio and tv did not take action to increase the rate of vaccination against influenza , particularly since the ternary composition of the vaccine for the 2010/2011 season included the a / h1n1/pdm09 pandemic strain .
it is worth emphasizing that those individuals who died in the 2010/2011 epidemic season were in high risk groups , were not vaccinated against influenza , and had infection caused by the virus a(h1n1)pdm09 confirmed by use of molecular biology techniques , which was already a component of the vaccine for this season .
for many years , since the year 2000 , the advisory committee on immunization ( acip ) in the u.s .
has recommended the routine vaccination against influenza of all individuals above the age of 6 months until late old age .
therefore , in the epidemic season , vaccination is recommended for nursing mothers unless they were already vaccinated , and vaccination of household members , caregivers of young children and of individuals who are in close contact with children under the age of 6 months .
the recommendations of the advisory committee on immunization ( acip ) are shown in table 1 . in the 2010/2011 epidemic season , only 5.0% of the population was vaccinated despite the inclusion of the a / h1n1/pdm09 strain in the ternary composition of the vaccine against influenza . in poland in 2009 , split inactivated or subunit vaccines were registered as shown in table 2 .
vaccines against influenza available in poland are inactivated ( containing fragments of killed influenza virus ) , therefore they are not able to multiply in the body and cause disease , but produce a specific immunity directed against the influenza virus .
it is worth noting that irrespective of the recommendations of the advisory committee on immunization ( acip ) , 14 scientific societies also recommend vaccination against influenza ( table 3 ) .
increasingly , the problem of vaccination against influenza is considered in terms of its health and economic aspects , of which we often remain unaware . according to data from the u.s . , depending on the influenza epidemic season , the cost impact of influenza infection is between 76167 billion dollars . the humoral immune response to influenza vaccination in high - risk groups evaluated in studies undertaken by the influenza virus research department of the national centre for influenza niph - nih in collaboration with clinicians
we are convinced that the presentation of specific examples will be helpful in promoting prevention , and will encourage health professionals to protect not only their patients , but also their relatives .
table 5 includes what in our opinion are the main causes of the low prevalence of influenza vaccination .
diagnostic methods have been available in poland for decades , beginning with the gold standard for identification of the pathogen in the chicken embryo or tissue culture , by elisa , immunofluorescence ( if ) , serological methods , and ending with studies using different combinations of molecular biology methods .
currently , in poland and only in the influenza virus research department of the national influenza centre at the niph - nih in warsaw , 12 respiratory viruses influenza type a and b , virus rs type a and b , parainfluenza types 1 , 2 and 3 , human metapneumovirus ( hmpv ) , adenovirus , rhinovirus , coronavirus , 229e / nl63 , and oc43/hku1 can be detected from a single sample from the patient , applying the methods of molecular biology .
however , in the 12 provincial sanitary - epidemiological stations ( pses ) it is possible to diagnose influenza infections using methods of molecular biology , while the remaining 4 pses perform diagnostics using the immunofluorescence method ( if ) .
the importance of virological diagnosis of respiratory infections , particularly influenza , is high , not only in medical , but also in economic terms .
it serves to avoid antibiotics therapy in the absence of indications and also to ensure that appropriate treatment is administered when necessary . the appropriate use of currently available new influenza virus neuraminidase inhibitors , such as zanamivir ( relenza ) and oseltamivir ( tamiflu ) , and consequently , the simultaneous prevention of appearance of strains resistant to these drugs , reduce the length of hospital stay [ 1,2024 ] .
the taking of appropriate measures to prevent the spread of infection refutes those myths associated with vaccination that lead to its avoidance .
one should be aware that , particularly in individuals in high - risk groups ( including healthy young children ) , the effects of influenza in those who are not vaccinated can result in complications , and even death .
therefore , the rapid identification of influenza virus is a priority when considering the possibility of treatment with effective medication .
currently , 2 influenza antiviral agents have been present on the market for many years oseltamivir ( tamiflu ) and zanamivir ( relenza ) active in the case of infection both with influenza a and b [ 13,2024 ] . the effectiveness of these drugs is dependent on several factors . in the case of seasonal influenza infection ,
the medication should be given after laboratory confirmation , preferably up to 36 hours from the onset of symptoms [ 1,2024 ] .
however , in the event of pandemic influenza , it should be administered on the basis of clinical symptoms , without waiting for the laboratory confirmation of infection .
the use of these medicines is indicated not solely for treatment of established infection , but also in prevention , including for post - exposure prophylaxis [ 1,2024 ] .
it should be noted that the use of oseltamivir during an epidemic of influenza was recommended from the age of 1 year .
however , in the situation of a pandemic , both the manufacturer and the european medicines agency ( emea ) recommend the use of this medication for those aged less than 1 year , depending on the child s body weight .
oseltamivir ( tamiflu ) is available in capsular form , which allows for its use not only in the case of small children , but also in patients who are unable to swallow capsules [ 1,2024 ] .
zanamivir ( relenza ) is formulated for inhalation and can be used from the age of 5 years .
these drugs are effective for both seasonal influenza infections as well as for subtypes of other influenza type a and b viruses . according to who and polish data , the new generation of drugs the neuraminidase inhibitors have proved effective in infections with the hpai virus : subtype a / h5n1/ , a / h7n7/ , pandemic influenza virus subtype a(h1n1)pdm09 , as well as in the case of seasonal influenza infection . currently , clinical trials of a new antiviral agent , peramivir , are in progress[/INST]summaryinfluenza causes seasonal infections worldwide that can lead to complications and deaths in every age group .
the most effective and cheapest way to combat influenza is through vaccination . in many countries , including poland , for each age group , the rate of vaccination against influenza is still at a very low level , which generates high social costs , not infrequently family tragedies in the case of irreversible complications of influenza , or death of a loved one .
regular vaccination should be part of good medical practice , as well as an individual s engagement in their own health and in that of their family . based on numerous studies
, it is estimated that the effectiveness of current inactivated influenza vaccine in reducing morbidity and mortality in high - risk groups ranges from 5070% . according to data from the national institute of public health - national institute of hygiene , the rate of vaccination in children in 2008 in poland was very low . in the group of children
aged from 6 months to 14 years , only 1.11.6% were vaccinated .
although influenza vaccination for people aged over 65 years was free of charge in many provinces in this group , only 13.4% of this population was immunized , while in the case of people with chronic diseases , only 11.1% were immunized .
the vaccination rate among health care employees is an embarrassing 6.4% .
more educational activities addressed to both medical professionals and patients are required in order to increase influenza vaccine coverage in poland .</s> |
osteoarthritis ( oa ) , also known as degenerative arthritis , is most common in the knee joint
and steadily advances the degradation of the joint cartilage .
it is a chronic illness common
to the joints of the low back , hip , and knee that mostly affects middle - aged people and the
elderly1 . for patients with knee
osteoarthritis
, exercise is the most common and effective therapy for enhancing knee
function and reducing pain ; it is also more cost - effective than other types of medical
interventions .
a proprioceptive exercise
is based on the notion that when a patient performs balance - keeping exercises on unstable
surfaces , proprioception responses occur first among those generated by the somatic senses .
these responses allow compensatory adjustments in the lengths of various muscles , their
tension levels , and the position of the joints to facilitate joint movements6 .
proprioceptive training improves knee
functions in osteoarthritis patients , and quadriceps muscle strengthening is known to
mitigate the symptoms of knee osteoarthritis and improve knee function7 .
proprioceptive neuromuscular facilitation of the afflicted
area is closely related to deteriorated mobility and pain , and restoring proprioceptive
neuromuscular function is essential during the final stage of a rehabilitation program8 .
the advantages of a circuit exercise are reduced
muscle fatigue , which is generally observed during resistance exercise , and improved
exercise efficiency by minimization of the recovery time between exercise sets9 . against this background ,
this study
designed and applied a proprioceptive circuit exercise to patients with knee osteoarthritis
to analyze the impact of the exercise program on knee muscle function and the associated
pain .
this study included 14 female patients , 60 years old , who demonstrated both clinical and
radiological evidence of knee osteoarthritis , as described by the american rheumatism
association10 .
the patients in the
proprioceptive circuit exercise group ( pceg ) were 65.7 3.5 years old and had an average
height of 152.4 5.1 cm and an average weight of 64.7 2.3 kg .
in the control group ( cong :
not the intervention group ) , the average age was 65.1 2.9 years , with an average height
and weight of 153.1 4.5 cm and 60.6 7.69 kg , respectively .
there was no statistically
significant difference in physical characteristics between the two groups ( p<0.05 ) .
the
proprioceptive circuit exercise program ( 20 min / session ) lasted for eight weeks .
the
subjects participated in the exercise program three times a week . three sets ( 10 times / set )
of the proprioceptive circuit exercise per session were performed .
the detailed exercise
program consisted of repetition of walking in place and four different types of
proprioceptive circuit exercise , including half squat , straight lunge , side lunge , and
one - legged balance exercise , on a jumper ( togu , germany ) and aero - step ( togu , germany ) .
for
those participants who were unable to perform exercise properly due to loss of balance on
the equipment , an exercise instructor held the participants hands until the end of each
exercise .
isemed 2000 ( d&r ferstl gmbh , hemau , germany ) was used to measure knee joint
isokinetic strength . a visual analog scale ( vas )
the
data was analyzed by using ibm spss statistics for windows , version 20.0 ( ibm spss . ,
armonk ,
ny , usa ) , and the results from both groups were compared before and after the program .
all the subjects understood the
purpose of this study and provided their written informed consent prior to participation in
the study in accordance with the ethical standards of the declaration of helsinki .
in the pceg , knee joint muscle function showed significant improvement in all examined
areas ( p<0.05 ) , whereas in the cong , no significant improvement was observed ( table 1table 1.comparison of knee joint peak torque in each groupgroupmuscle strengthbefore ( mean sd ) nmafter ( mean sd ) nmpcegrkf*24.3 8.637.7 13.2rke*57.1 23.668.3 26.0lkf*21.9 9.730.3 8.8lke*63.3 19.571.0 24.0cgrkf28.0 8.037.6 12.4rke51.1 10.440.9 18.4lkf23.7 7.629.4 10.7lke44.7 11.044.4 17.0*p < 0.05 .
pceg : proprioceptive circuit exercise group ; cg : control group ; rkf :
right knee flexion ; rke : right knee extension ; lkf : left knee flexion ; lke : left knee
extension ) . as for changes in the level of pain ,
significant improvements were observed
in the pceg ( p < 0.05 ) but not in the cong ( table
2table 2.visual analog scale pain measurement in each groupgroupbefore ( mean sd)after ( mean sd)pceg*6.6 1.63.1 1.1cong6.9 1.67.1 1.4p < 0 .05 .
pceg : proprioceptive circuit exercise group ; cg : control group ; rkf :
right knee flexion ; rke : right knee extension ; lkf : left knee flexion ; lke : left knee
extension p < 0 .05 .
patients with degenerative knee osteoarthritis show reduced quadriceps strength and a
decline in proprioception and balance2 , 3 . reduced proprioception in patients with
osteoarthritis weakens their thigh muscle strength and could limit their walking ability and
dynamic balance11 .
also , joint pain may
have harmful effects on muscle function ( muscle strength and activation ) and senses
( proprioception and balance)5 .
therefore ,
an exercise program was designed to strengthen the thigh muscles , enhance proprioception ,
and reduce pain in patients with degenerative osteoarthritis .
this study showed increased
knee joint muscle function and decreased pain in the group that underwent proprioceptive
circuit exercise training ( p<0.05 ) .
a combined application of proprioceptive circuit
muscle strengthening exercise and proprioceptive exercise is more effective than a single
muscle strengthening training program in terms of improving joint stability11 .
the 8-week proprioceptive circuit
exercise improved postural sway and isokinetic strength , leading to improved ankle joint
stability12 .
also , combining resistance
and proprioceptive training resulted in greater muscle hypertrophy , supporting an improved
knee joint muscle function outcome13 .
diminished knee joint proprioception is highly correlated with the level of pain14 , and the interaction between
proprioception and muscle strength is closely related to functional body movements15 .
also , exercise on an unstable surface
might be helpful for improving the muscle strength and alignment of lower extremities as
well as for improving physical function related to the knee joint16 .
this indicates that application of proprioceptive circuit
exercise improves proprioception and knee joint muscle function , thereby reducing patient
pain .
additionally , pain causes reflex arthrogenous muscle inhibition , reduces activation of
the thigh quadriceps , and weakens the quadriceps5 .
this study showed that proprioceptive circuit exercise in patients with
degenerative knee osteoarthritis can be an effective way of strengthening knee joint muscle
function and reducing pain .
the results are expected to provide a useful basis for future
efforts to enhance knee joint functions and improve pain control in patients with knee
osteoarthritis . | [ purpose ] this study applied proprioceptive circuit exercise to patients with
degenerative knee osteoarthritis and examined its effects on knee joint muscle function
and the level of pain . [ subjects ] in this study , 14 patients with knee osteoarthritis in
two groups , a proprioceptive circuit exercise group ( n = 7 ) and control group ( n = 7 ) ,
were examined .
[ methods ] isomed 2000 ( d&r ferstl gmbh , hemau , germany ) was used to
assess knee joint muscle function , and a visual analog scale was used to measure pain
level .
[ results ] in the proprioceptive circuit exercise group , knee joint muscle function
and pain levels improved significantly , whereas in the control group , no significant
improvement was observed .
[ conclusion ] a proprioceptive circuit exercise may be an
effective way to strengthen knee joint muscle function and reduce pain in patients with
knee osteoarthritis . | <s>[INST]osteoarthritis ( oa ) , also known as degenerative arthritis , is most common in the knee joint
and steadily advances the degradation of the joint cartilage .
it is a chronic illness common
to the joints of the low back , hip , and knee that mostly affects middle - aged people and the
elderly1 . for patients with knee
osteoarthritis
, exercise is the most common and effective therapy for enhancing knee
function and reducing pain ; it is also more cost - effective than other types of medical
interventions .
a proprioceptive exercise
is based on the notion that when a patient performs balance - keeping exercises on unstable
surfaces , proprioception responses occur first among those generated by the somatic senses .
these responses allow compensatory adjustments in the lengths of various muscles , their
tension levels , and the position of the joints to facilitate joint movements6 .
proprioceptive training improves knee
functions in osteoarthritis patients , and quadriceps muscle strengthening is known to
mitigate the symptoms of knee osteoarthritis and improve knee function7 .
proprioceptive neuromuscular facilitation of the afflicted
area is closely related to deteriorated mobility and pain , and restoring proprioceptive
neuromuscular function is essential during the final stage of a rehabilitation program8 .
the advantages of a circuit exercise are reduced
muscle fatigue , which is generally observed during resistance exercise , and improved
exercise efficiency by minimization of the recovery time between exercise sets9 . against this background ,
this study
designed and applied a proprioceptive circuit exercise to patients with knee osteoarthritis
to analyze the impact of the exercise program on knee muscle function and the associated
pain .
this study included 14 female patients , 60 years old , who demonstrated both clinical and
radiological evidence of knee osteoarthritis , as described by the american rheumatism
association10 .
the patients in the
proprioceptive circuit exercise group ( pceg ) were 65.7 3.5 years old and had an average
height of 152.4 5.1 cm and an average weight of 64.7 2.3 kg .
in the control group ( cong :
not the intervention group ) , the average age was 65.1 2.9 years , with an average height
and weight of 153.1 4.5 cm and 60.6 7.69 kg , respectively .
there was no statistically
significant difference in physical characteristics between the two groups ( p<0.05 ) .
the
proprioceptive circuit exercise program ( 20 min / session ) lasted for eight weeks .
the
subjects participated in the exercise program three times a week . three sets ( 10 times / set )
of the proprioceptive circuit exercise per session were performed .
the detailed exercise
program consisted of repetition of walking in place and four different types of
proprioceptive circuit exercise , including half squat , straight lunge , side lunge , and
one - legged balance exercise , on a jumper ( togu , germany ) and aero - step ( togu , germany ) .
for
those participants who were unable to perform exercise properly due to loss of balance on
the equipment , an exercise instructor held the participants hands until the end of each
exercise .
isemed 2000 ( d&r ferstl gmbh , hemau , germany ) was used to measure knee joint
isokinetic strength . a visual analog scale ( vas )
the
data was analyzed by using ibm spss statistics for windows , version 20.0 ( ibm spss . ,
armonk ,
ny , usa ) , and the results from both groups were compared before and after the program .
all the subjects understood the
purpose of this study and provided their written informed consent prior to participation in
the study in accordance with the ethical standards of the declaration of helsinki .
in the pceg , knee joint muscle function showed significant improvement in all examined
areas ( p<0.05 ) , whereas in the cong , no significant improvement was observed ( table 1table 1.comparison of knee joint peak torque in each groupgroupmuscle strengthbefore ( mean sd ) nmafter ( mean sd ) nmpcegrkf*24.3 8.637.7 13.2rke*57.1 23.668.3 26.0lkf*21.9 9.730.3 8.8lke*63.3 19.571.0 24.0cgrkf28.0 8.037.6 12.4rke51.1 10.440.9 18.4lkf23.7 7.629.4 10.7lke44.7 11.044.4 17.0*p < 0.05 .
pceg : proprioceptive circuit exercise group ; cg : control group ; rkf :
right knee flexion ; rke : right knee extension ; lkf : left knee flexion ; lke : left knee
extension ) . as for changes in the level of pain ,
significant improvements were observed
in the pceg ( p < 0.05 ) but not in the cong ( table
2table 2.visual analog scale pain measurement in each groupgroupbefore ( mean sd)after ( mean sd)pceg*6.6 1.63.1 1.1cong6.9 1.67.1 1.4p < 0 .05 .
pceg : proprioceptive circuit exercise group ; cg : control group ; rkf :
right knee flexion ; rke : right knee extension ; lkf : left knee flexion ; lke : left knee
extension p < 0 .05 .
patients with degenerative knee osteoarthritis show reduced quadriceps strength and a
decline in proprioception and balance2 , 3 . reduced proprioception in patients with
osteoarthritis weakens their thigh muscle strength and could limit their walking ability and
dynamic balance11 .
also , joint pain may
have harmful effects on muscle function ( muscle strength and activation ) and senses
( proprioception and balance)5 .
therefore ,
an exercise program was designed to strengthen the thigh muscles , enhance proprioception ,
and reduce pain in patients with degenerative osteoarthritis .
this study showed increased
knee joint muscle function and decreased pain in the group that underwent proprioceptive
circuit exercise training ( p<0.05 ) .
a combined application of proprioceptive circuit
muscle strengthening exercise and proprioceptive exercise is more effective than a single
muscle strengthening training program in terms of improving joint stability11 .
the 8-week proprioceptive circuit
exercise improved postural sway and isokinetic strength , leading to improved ankle joint
stability12 .
also , combining resistance
and proprioceptive training resulted in greater muscle hypertrophy , supporting an improved
knee joint muscle function outcome13 .
diminished knee joint proprioception is highly correlated with the level of pain14 , and the interaction between
proprioception and muscle strength is closely related to functional body movements15 .
also , exercise on an unstable surface
might be helpful for improving the muscle strength and alignment of lower extremities as
well as for improving physical function related to the knee joint16 .
this indicates that application of proprioceptive circuit
exercise improves proprioception and knee joint muscle function , thereby reducing patient
pain .
additionally , pain causes reflex arthrogenous muscle inhibition , reduces activation of
the thigh quadriceps , and weakens the quadriceps5 .
this study showed that proprioceptive circuit exercise in patients with
degenerative knee osteoarthritis can be an effective way of strengthening knee joint muscle
function and reducing pain .
the results are expected to provide a useful basis for future
efforts to enhance knee joint functions and improve pain control in patients with knee
osteoarthritis .[/INST][ purpose ] this study applied proprioceptive circuit exercise to patients with
degenerative knee osteoarthritis and examined its effects on knee joint muscle function
and the level of pain . [ subjects ] in this study , 14 patients with knee osteoarthritis in
two groups , a proprioceptive circuit exercise group ( n = 7 ) and control group ( n = 7 ) ,
were examined .
[ methods ] isomed 2000 ( d&r ferstl gmbh , hemau , germany ) was used to
assess knee joint muscle function , and a visual analog scale was used to measure pain
level .
[ results ] in the proprioceptive circuit exercise group , knee joint muscle function
and pain levels improved significantly , whereas in the control group , no significant
improvement was observed .
[ conclusion ] a proprioceptive circuit exercise may be an
effective way to strengthen knee joint muscle function and reduce pain in patients with
knee osteoarthritis .</s> |
Twitter Inc. (TWTR) jumped 73 percent in its trading debut, as investors paid a premium for its promises of fast growth.
The stock rose to $44.90 at the close in New York from the initial public offering price of $26, delivering the biggest one-day pop for an IPO that raised more than $1 billion since Alibaba.com Ltd. debuted in 2007, according to data compiled by Bloomberg. Twitter sold 70 million shares, raising $1.82 billion.
The microblogging website picked a price that valued it higher than Facebook Inc. (FB) and still drew more interest than anticipated. The San Francisco-based company, which is unprofitable and has one-fifth as many users as Facebook, is benefiting from investorsβ thirst for companies that will grow quickly in expanding markets like mobile advertising.
βThe company did everything to secure the most cash for itself while leaving some money for the IPO buyers,β said Josef Schuster, the founder of IPOX Schuster LLC, a Chicago-based manager of about $1.9 billion. βYou need a pop at the opening to leave a good taste with everyone. They did a pretty good job managing the whole situation.β
At the current price, Twitter is valued at $24.9 billion, or 22 times estimated 2014 sales of $1.14 billion, according to analyst projections compiled by Bloomberg. That compares with 11.2 times that Facebook traded at today, and price-to-sales ratio of 11.7 for LinkedIn Corp. (LNKD)
The New York Stock Exchange trading floor is crowded with traders and journalists on the morning of TwitterΓ’ΒΒs public stock debut, on Nov. 7, 2013. Photograph: New York Stock Exchange via AP Images Close The New York Stock Exchange trading floor is crowded with traders and journalists on... Read More Close Open The New York Stock Exchange trading floor is crowded with traders and journalists on the morning of TwitterΓ’ΒΒs public stock debut, on Nov. 7, 2013. Photograph: New York Stock Exchange via AP Images
Facebook declined 3.2 percent, and LinkedIn fell 4.2 percent today. At its market debut in 2012, Facebookβs stock was flat, propped up by bankers, while LinkedInβs more than doubled on the day it went public in 2011.
Price βHypeβ
The pricing puts the onus on Twitter to deliver on its promises of fast growth after earlier pitching shares as low as $17. Chief Executive Officer Dick Costolo has rallied investor interest in Twitterβs rapid sales curve -- with revenue more than doubling annually -- even with no clear path to making a profit.
The company received orders for about 30 times as many shares as it offered at the $26 IPO price, a person with knowledge of the matter said. About 8 million of the shares, or 11 percent of the total in the IPO, were allocated to retail investors, the person said, asking not to be identified because the information is private. A typical retail allocation is 10 percent to 15 percent.
Still, any price over $40 reflects βhypeβ and makes Twitter too risky of an investment, said Jeffrey Sica, president and chief investment officer of Sica Wealth Management LLC in Morristown, New Jersey.
βAbsolute Frothβ
βI anticipated a very strong open, but when you start to approach these levels this is absolute froth,β he said. βThere is nothing supporting this range. I think this is just way, way above what realistically we should be considering a stable open.β
Brian Wieser, an analyst at Pivotal Research Group in New York, downgraded Twitter to a sell rating with a $30 price target.
βIf youβve got it, sell it,β Wieser said in an interview. βIf there are willing buyers who have a view of the business today that gets them comfortable with this valuation then those people should hold it, but I canβt get there, and Iβm not recommending my clients to hold it.β
CEO Costolo was at the New York Stock Exchange for the stockβs debut under the TWTR symbol, along with CFO Mike Gupta and co-founders Evan Williams, Biz Stone and Jack Dorsey.
Executive Tweets
After the celebration at the exchange, executives dispersed. Costolo went to the New York Twitter office to talk to employees, then flew to Twitterβs San Francisco office to do the same. Twitterβs website and applications let people post 140-character messages to friends and online followers. Dorsey sent a tweet to congratulate the companyβs executive team, receiving more than 200 retweets.
More Twitter News:
βMy first of four client presos today starts in 10 mins. Back at it,β Adam Bain, Twitterβs president of global revenue, said in a tweet.
Twitterβs $1.82 billion IPO is almost as much as the $1.9 billion that Google Inc. raised in its 2004 IPO and makes it the largest IPO by a U.S. technology company since Facebookβs debut in May 2012. Goldman Sachs Group Inc. (GS) led the sale, working with Morgan Stanley and JPMorgan Chase & Co. (JPM)
Anti-Facebook IPO
The price rise underscores how Twitter has so far sidestepped some of the pitfalls that befell Facebookβs IPO last year. Facebookβs offering was marred by a trading snag on the Nasdaq Stock Market and investor backlash over its valuation. The company at the time was priced at 107 times trailing 12-month earnings on a fully diluted basis, making it more expensive than 99 percent of all companies in the Standard & Poorβs 500 Index. Facebook saw its stock quickly sink below its $38 debut price, a level it didnβt cross back above until this August.
By contrast, Twitter decided to list on the New York Stock Exchange and chose Goldman Sachs to lead its offering, while Morgan Stanley (MS) led Facebookβs IPO. The company also sought to avoid hype by filing for an IPO secretly with the Securities and Exchange Commission and earlier setting a price range for its shares at a discount to competitors.
Twitterβs stock gain may erase some of the aftertaste of the Facebook, Zynga Inc. (ZNGA) and Groupon Inc. (GRPN) IPOs, each of which lost half their value within six months of their debuts, sending a chill over consumer-technology IPOs and some Silicon Valley startup valuations.
Twitterβs Journey
Demand for Twitterβs stock exceeded the supply even before bankers started formally asking for orders, people familiar with the matter have said. On Monday, Twitter raised the proposed price range for the 70 million shares sold in the IPO to $23 to $25 each, up from the earlier range of $17 to $20.
βPeople are really looking all the way out to their 2015 and 2016 revenue estimates to price this,β said Larry Levine, a partner in financial-advisory firm McGladrey LLP in Chicago. βThe risk to buying Twitter is if Twitter does not achieve its very lofty growth estimates.β
Twitter will have 544.7 million shares of common stock outstanding after the IPO, its filings show. Including restricted stock and options, Twitter will have about 694.8 million shares outstanding. The sale didnβt include an extra 10.5 million shares that underwriters have an option to buy, according to the companyβs prospectus.
Right Time
The offering caps a journey for Twitter from a niche short-messaging service to a global social-media platform for celebrities, politicians and others. Started in 2006 as a project at failed startup Odeo, the website now logs more than 500 million tweets each day, the company has said. Thatβs up from 2 million a day in January 2009.
βI have e-mails going back to 2009 asking me about when Twitter is going public,β said Bijan Sabet, a general partner at Spark Capital, which owns about 6 percent of Twitterβs shares, worth $1.46 billion. βAnd before that, e-mails asking when Twitter is going to generate revenue. This company has always had a lot of pressure. They took their time in figuring out the best way to go public and the right time to go public.β
Twitter still needs to deliver on its business model. Twitterβs loss widened to $64.6 million in the September quarter from $21.6 million a year earlier, and it is unlikely to be profitable until 2015, according to the average estimate of analysts surveyed by Bloomberg. LinkedIn and Facebook were both profitable at the time of their IPOs.
Mobile Users
While Twitterβs revenue has surged, reaching $534.5 million in the 12 months that ended Sept. 30, user growth is slowing, filings show. The service had 231.7 million monthly users in the quarter that ended in September, up 39 percent from a year earlier. That compares with 65 percent growth in the prior year.
Twitter has been touting its engagement with mobile users, where other Web companies have struggled. About three-fourths of Twitterβs active users accessed the service from mobile devices in the three months ended in September, compared with 69 percent in the year-earlier period, according to the filing. More than 70 percent of advertising revenue comes from those devices, a higher proportion than Facebook.
The money from the public offering will help Twitter build its business outside the U.S., where it got 77 percent of users yet only 26 percent of revenue in the third quarter. The company will also expand its infrastructure and work on products that will help it attract more users and advertisers.
βAll that points to a lot of upside,β said Paul Zwillenberg, a London-based partner and managing director at the Boston Consulting Group.
To contact the reporters on this story: Sarah Frier in New York at [email protected]; Lee Spears in New York at [email protected]
To contact the editors responsible for this story: Pui-Wing Tam at [email protected]; Jeffrey McCracken at [email protected] ||||| Twitter had a strong public stock debut Thursday in the most highly anticipated initial public offering since Facebook's last year.
A banner adorns the facade of the New York Stock Exchange in advance of Twitter's initial public offering Thursday, Nov. 7, 2013, in New York. Twitter shares, valued at $26 per share, are set to begin... (Associated Press)
A technician checks the bell podium of the New York Stock Exchange, Thursday, Nov. 7, 2013. Twitter set a price of $26 per share for its initial public offering on Wednesday evening and will begin trading... (Associated Press)
Twitter CEO Dick Costolo, Chairman and co-founder Jack Dorsey, and co-founders Evan Williams and Biz Stone, front row left to right, applaud as they watch the the New York Stock Exchange opening bell... (Associated Press)
Specialist Glenn Carell, who will handle the Twitter IPO, works at his post on the floor of the New York Stock Exchange, Thursday, Nov. 7, 2013. Twitter set a price of $26 per share for its initial public... (Associated Press)
A man walks his dogs past the New York Stock Exchange prior to the Twitter IPO, Thursday, Nov. 7, 2013 in New York. Twitter set a price of $26 per share for its initial public offering on Wednesday evening... (Associated Press)
Twitter CEO Dick Costolo, center, and Mike Gupta, chief financial officer of Twitter, wait for shares to begin trading during the IPO, on the floor of the New York Stock Exchange, Thursday, Nov. 7, 2013.... (Associated Press)
Twitter Chairman and co-founder Jack Dorsey, co-founders Biz Stone and Evan Williams and, Twitter CEO Dick Costolo pose for a group photo after their company's IPO began trading, on the floor of the New... (Associated Press)
Twitter signage is draped on the facade of the New York Stock Exchange, Thursday, Nov. 7, 2013 in New York. Twitter set a price of $26 per share for its initial public offering on Wednesday evening and... (Associated Press)
Twitter's stock opened at $45.10, or 73 percent above its $26 IPO price, and kept most of that gain by the time it closed. The opening price values Twitter at more than $31 billion based on its outstanding stock, options and restricted stock that'll be available after the IPO. It traded as high as $50.09 in the morning.
The high price comes despite the fact that Twitter has never turned a profit in seven years of existence. Revenue has been growing, but the company is also investing heavily in more data centers and hiring more employees.
Twitter is trading under the ticker symbol "TWTR."
Here's a running account of Twitter's first day of trading, presented in reverse chronological order. All times are EST.
___
_ 4:15 p.m.: AP's (at)liedtkesfc posts photo from Twitter co-founder (at)noah Glass' home: pic.twitter.com/2DduLFRbNZ
___
_ 4:10 p.m.: $TWTR's closing price of $44.90 gives Twitter a value of more than $31 billion.
It's actually 20 cents lower than the opening price, but still 73 percent higher than the $26 IPO price.
RT (at)KenSweet: One way to read this: If you bought Twitter at its first trade of $45.10, you lost (a little) money today. $TWTR
___
_ 4 p.m.: First day of trading is done. Twitter soars about 73 percent from IPO price, keeping most of gain from opening.
___
_ 3:55 p.m.: As Twitter's first trading day nears an end, keep in mind at least one analyst believes $twtr is now a "Sell."
Pivotal Research Group analyst Brian Wieser slashed his rating on Twitter Inc. from "Buy" on Thursday after the stock opened at $45.10, about 50 percent above his price target of $30.
His price target valued the company at 21 times its free cash flow in 2018, a multiple that exceeded even Facebook at 17 times and Google at 16 times. With a stock price of $45, Twitter would be worth 32 times its 2018 free cash flow, which he wrote in a research note was "overly optimistic."
Wieser told AP's (at)BarbaraOrtutay that he still has a very positive view of the business, but believes the company isn't worth as much as it has been trading at.
"The market can beg to differ," he said.
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 3:35 p.m.: Twitter has no shortage of co-founders. AP's (at)liedtkesfc tries to track down the one who wasn't (at)NYSE for opening
Here's his account:
While Twitter founders Jack Dorsey, Evan Williams and Biz Stone were in New York celebrating the company's stock debut Thursday, a former partner involved in Twitter's creation was in the midst of a home improvement project on the other side of the country.
At least that's how it looked when I swung by the home of Noah Glass, (at)noah, in San Francisco's Mission District neighborhood.
Glass, 43, says he and Dorsey conceived Twitter during a brainstorming session after a night of drinking in San Francisco nearly eight years ago. Dorsey has a different account, maintaining he came up with the idea himself on a San Francisco playground. Tweets and blog posts from 2006 make it clear Glass was deeply involved. He even came up with the service's name, originally shortening it to "twittr."
For reasons that aren't entirely clear, Glass was ousted from Twitter before it turned into a cultural phenomenon and didn't even get much company stock, according to a new book about Twitter's history.
I was curious to see how Glass was handling this momentous day for Twitter. So I hopped on a train near Twitter's San Francisco headquarters and rode the subway to the next stop. Glass lives with his 7-month-old daughter and the baby's French-speaking mother at the end of a dirt lot in a small home that was set up after a 1906 earthquake destroyed much of the city. These homes are still known as "earthquake shacks."
The front gate was open, as was the front door. As I walked up to the threshold, I could hear the pounding of a hammer in the back and a baby blissfully playing in a stroller. The French-accented woman nearby cheerfully greeted me, but when I told her that I was a reporter wondering if Noah wanted to talk to me about Twitter, she informed me that he wasn't interested. She was very nice about it, and we wished me a very nice day.
It seemed like a happy home, even if it isn't as grandiose as the mansions that many Twitter employees can now afford to buy. (hash)ForgottenFounder
More on the founders: http://bigstory.ap.org/article/flock-feathered-twitters-nest
_ Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 3:25 p.m.: (at)Twitter CEO (at)DickC says growth is just a question of connecting with potential new users
Twitter CEO Dick Costolo appeared on CNBC ahead of his company's trading debut at the NYSE to talk about his company and its potential for growth.
CNBC's David Faber said that joining Twitter made sense for Faber and a lot of other people early on. But he asked how the company planned to keep growing and attract users outside of its traditional base.
Costolo said that it's all about making connections with people and helping them see how Twitter fits into their lives.
"It's all about, for us, helping people bridge that gap between `I've heard about Twitter,' to getting exactly where you and so many other people here today are."
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 3:05 p.m.: AP's (at)liedtkesfc explores the neighborhood outside (at)Twitter HQ and sees contrasts.
The San Francisco neighborhood outside Twitter's headquarters provides a forlorn contrast to the suddenly rich people working inside the building.
These are among the meaner streets in downtown San Francisco, long populated with the destitute who have no place to live and the miscreants who resort to crime to make ends meet. In hopes of cleaning the area up, the city of San Francisco gave Twitter local tax breaks on employee stock options to help persuade the company to move into the neighborhood two years ago.
But times are still tough here. Scruffy-looking people gathered against the wall of a post office across the street from Twitter's headquarters. Four of them had just spent the night in a homeless shelter. All of them said that they wished that they owned Twitter stock, yet they maintained that they didn't really envy Twitter employees becoming wealthier as the stock soared Thursday.
There was a clump of litter just a few feet away. Amid the empty coffee cups, cigarette butts and empty liquor bottles, there were two scratch-off games for the California lottery that had been discarded because they didn't pay off. (hash)LandofBrokenDreams
_ Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 2:50 p.m.: In Asia, (at)Twitter has competition from local companies, reports AP's (at)YKLeeAP
Led by Japan, Indonesia, South Korea and India, Asia was the fastest growing region for Twitter in summer 2010, according to Semiocast, a Paris-based social media research company. But growth has slowed in South Korea and Japan, a red flag for Twitter as both countries are wealthy and have high rates of mobile device usage _ now the predominant way Twitter is accessed.
New mobile applications from companies such as South Korea's Kakao Corp. and Japan's Line Corp., have experienced explosive growth, making them potent competitors for eyeballs and advertising.
Why are people leaving Twitter or spending less time on it?
Too open. Too crowded. Too difficult.
"In South Korea and Japan, open type social networking services like Twitter and Facebook are losing steam," said Justin Lee, an analyst of mobile messengers and games at BNP Paribas. "Closed social networking services where messages are shared among a small group of people will become more popular."
Twitter remains blocked from China's vast market but another giant, India, is open to Twitter. It has amassed 27 million users there, according to Semiocast. Yet Twitter acknowledged in IPO filings that low use of smartphones in emerging markets such as India could hamper the ability of advertisers to deliver compelling advertisements and hurt its earnings potential.
International users accounted for about three quarters of Twitter's members but only a quarter of revenue in the first nine months of this year. About 25 percent of Twitter's 232 million active users are in Asia.
_ Youkyung Lee, Seoul, South Korea, (at)YKLeeAP
___
_ 2:30 p.m.: (at)Twitter now among the most valuable media companies, notes AP's (at)rnakashi
Like Twitter, the other large media companies in the country rely to some extent on advertising revenue. As of mid-afternoon, Twitter's value is nearly $33 billion, after including options and restricted stock that'll be available after the IPO.
The market value of other media companies: CBS Corp., $34.7 billion; Discovery Communications Inc., $30 billion; Viacom Inc., $38.8 billion; The Walt Disney Co., $120 billion; Time Warner Inc. $60.3 billion.
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 2:10 p.m.: (at)NYSEEuronext has congratulated (at)Twitter "on a successful (hash)NYSEIPO! We're excited to be your partner."
___
_ 1:55 p.m.: Looking back at Twitter's IPO price, here are some quick facts from (at)Dealogic
Twitter priced its IPO at $26, raising $1.82 billion. If the offering's underwriters fully exercise their option to buy more shares, the IPO's value will rise to $2.09 billion. That would make it the second-largest Internet IPO by an American company on record, following Facebook Inc.'s $16 billion, but beating Google Inc.'s $1.92 billion.
The research firm Dealogic says Twitter's IPO is set to be the third-largest U.S.-listed IPO so far this year, behind Plains GP Holdings at $2.9 billion and Zoetis' $2.6 billion.
Including Twitter, U.S.-listed tech industry IPOs have raised $7.8 billion through 41 deals so far this year. That's down from $20.5 billion generated by 35 deals during the same period of 2012, though Facebook accounted for $16 billion of the 2012 total.
Tech companies tend to post bigger first-day jumps than the overall market. The average one-day jump for tech industry IPOs this year is 35 percent, compared with an average gain of 17 percent for 2013 IPOs overall. Twitter's stock opened at 73 percent above the IPO price.
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 1:40 p.m.: (at)Twitter soars while drop in overall market pulls down rest of Internet cos.
Twitter shares are flying high, but other Internet companies are having a tough time getting off the ground.
While Twitter's debut likely helped send shares of Facebook Inc. down, the overall tech industry also took a hit as the markets pulled back from record levels on worries that the Federal Reserve could soon start curtailing its economic stimulus program.
Facebook shares fell $1.07, or 2.2 percent, to $48.05 after dropping as low as $47.41 earlier in the day. Other Internet companies such as LinkedIn Corp., AOL Inc., Google Inc., Pandora Media Inc. and Zillow Inc. all posted small to moderate losses.
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 1:20 p.m.: Will Twitter's stock keep going up? There is risk of Twitter burnout. (hash)TwitterHaters
There's plenty of evidence online about the celebrities who tire of Twitter. The long list of Twitter quitters includes everyone from Alec Baldwin to Miley Cyrus to "Lost" co-creator Damon Lindelof, though some eventually return.
Some get overwhelmed by followers spewing hatred. Others get addicted to interacting with huge fan bases and need to pull away. Even non-celebrity users complain of the amount of time spent posting and replying and vow to close accounts to get on with their lives.
With its public stock debut, the company has been selling potential investors on the idea that its user base of 232 million will continue to grow along with the 500 million tweets that are sent each day. The company's revenue depends on ads it inserts into the stream of messages.
But Wall Street could lose its big bet on social media if prolific tweeters lose their voice.
Read more: http://bigstory.ap.org/article/user-burnout-could-threaten-twitters-prosperity
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 1:05 p.m.: Twitter chairman (at)jack makes reference to first tweet in Vine video post
About two hours ago, Twitter chairman and co-founder Jack Dorsey tweeted this: "just setting up our $twtr _https://vine.co/v/hI1nP3vQOBI" The link is to video on Twitter's Vine app, showing traders shouting on NYSE trading floor.
The tweet, of course, is a reference to the world's first tweet, which was sent by Dorsey on March 21, 2006, and read "just setting up my twttr." Dorsey uses "$twtr" in Thursday's post in a reference to the stock's ticker symbol. Putting a dollar sign before it is a common way to refer to stocks on Twitter.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 12:50 p.m.: (at)Twitter is trading very heavily in its first day on (at)NYSE.
About 82 million shares of Twitter have exchanged hands already. To put that in perspective, Twitter only sold 70 million shares in its IPO. One way to think about it, every share issued in Twitter's IPO has been traded more than once, and the session isn't half over yet.
Of course, not every investor who got shares of Twitter at the $26 IPO price is selling Thursday. Many large institutional investors are buy-and-hold firms. If every investor had sold at the debut, the stock would not have opened at 73 percent above the IPO price.
_ Ken Sweet, New York, (at)KenSweet
___
_ 12:35 p.m.: (at)TDAmeritrade official says stock debut is flawless
"It's gone on pretty flawlessly," says JJ Kinahan, chief strategist at online brokerage TD Ameritrade.
For one, he says, the broader market's downturn isn't affecting Twitter much. Trading is also tight, rather than volatile, which indicates that people feel like it was "pretty fairly priced," he says.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 12:15 p.m.: Learn more about (at)vivienneharr, (at)sirpatstew and (at)bostonpolice official who rang (at)NYSEEuronext opening bell
Crediting its success to its users, Twitter gave the honor of ringing Thursday's opening bell at the New York Stock Exchange to three high-profile tweeters: a child activist, a legendary British actor and a Boston Police official.
Nine-year-old Vivienne Harr used a lemonade stand to raise more than $100,000 to support efforts to eliminate child slavery around the world. Her pink lemonade, along with a ginger-infused version, is now being bottled and sold online. A portion of the profits is donated to groups that work toward ending child slavery. More than 22,000 people follow (at)vivienneharr on Twitter.
Patrick Stewart is known both for his Twitter presence and his stage and screen careers. His highest profile roles have included Captain Jean-Luc Picard in "Star Trek: The Next Generation" and Professor Charles Xavier in the "X-Men" movies. About 722,000 people follow (at)sirpatstew. Stewart tweeted a picture of himself on Halloween dressed as a lobster in a bathtub. It was retweeted nearly 39,000 times.
Cheryl Fiandaca has been chief of public information for the Boston Police Department since July 2012. Fiandaca spearheaded the department's social media efforts, and her department used Twitter to get information to the public in the aftermath of the Boston Marathon bombings. More than 266,000 people follow (at)bostonpolice.
Bree Fowler, New York, (at)APBreeFowler
___
_ 11:55 a.m.: (at)Wedbush analyst (at)MichaelPachter says high debut price suggests (hash)TwitterIPO was managed well.
Wedbush analyst Michael Pachter says the surge "clearly shows that demand exceeds supply of shares."
"It's impossible to know what the real value is," he says.
Still, he acknowledges that the price is "pretty high" and not something he was expecting.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 11:45 a.m.: It's (hash)BusinessAsUsual at (at)Twitter headquarters, though employees seem happy.
Although Twitter's fortunes are already soaring on Wall Street, there haven't been any audible whoops of joy emanating from the company's San Francisco headquarters yet. But almost every employee walking in and out of the building is grinning.
Twitter seems to know that it needs to accelerate its revenue growth to support its lofty stock price. A few employees just came out to usher in a group of advertising agency representatives. (hash)TheNewReality
--Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 11:30 a.m.: (at)Barclays official in charge of stock debut speaks with AP's (at)KenSweet, admits being "a little nervous."
It was the biggest IPO of the year for Glenn Carell, the Barclays Capital official in charge of Twitter's stock debut. He has been doing it for 21 years and says, "I was a little nervous, but it went well."
Twitter hired Barclays to be its "designated market maker," which supervises the trading of a company's stock on the New York Stock Exchange. The IPO process itself was managed by three other investment banks.
_ Ken Sweet, New York, (at)KenSweet
___
_ 11:05 a.m.: RT (at)KenSweet: Twitter took a long time to open due to the deal size. Goldman also likes to take its time.
Goldman Sachs, Morgan Stanley and JPMorgan Chase are the three investment banks in charge of Twitter's IPO.
After debuting at $45.10, the stock is now trading at $47.85, or 84 percent above the IPO price.
___
_ 10:55 a.m.: AP's (at)BarbaraOrtutay notes that the $31 billion value puts Twitter in the ballpark of Yum Brands and Deere & Co.
It's also slightly below State Street Corp.
___
_ 10:53 a.m.: The opening price values Twitter at $31.3 billion.
To calculate its value, the AP is using 694.8 million shares that Twitter is expected to have outstanding after the IPO, counting restricted shares and stock options it plans to issue to employees. At the $26 IPO price, the value was more than $18 billion.
___
_ 10:51 a.m.: Twitter stock opens at $45.10, 73 percent above IPO price
___
_ 10:50 a.m.: Range is now $45 to $45.25, or up to 74 percent above IPO price. Very close to debut.
RT (at)KenSweet: They're closing the book.
___
_ 10:45 a.m. AP's (at)KenSweet says current bid is $45.25. The debut is near in (hash)TwitterIPO.
___
_ 10:40 a.m.: Patrick Stewart tweets on (hash)Ring of opening bell as Twitter trade debut imminent.
RT (at)SirPatStew: Honored to join (at)ev (at)jack (at)biz (at)dickc & the (at)Twitter team at their historic IPO this morning. (hash)Ring! pic.twitter.com/XaJpYW2kIh
___
_ 10:35 a.m.: It's getting close to Twitter's stock debut. First indication for opening price is even narrower: $45.50-$46.50.
The high end would be 79 percent above its IPO price.
___
_ 10:30 a.m.: AP's (at)KenSweet now says opening price narrowed: $45-$47.
He reports: "This is a good sign. Could mean we're finding the right price. Progress."
___
_ 10:20 a.m.: AP's (at)KenSweet says opening price is expected even higher: $43-$47.
The range for first indication means Twitter could start trading at up to 81 percent above its IPO price.
___
_ 10:15 a.m.: RT (at)KenSweet: I've heard some traders mention that this may not open until 1030, maybe 11. But things are changing rapidly.
___
_ 10:10 a.m.: AP market reporter (at)KenSweet explains the role (at)Barclays has in (hash)TwitterIPO.
Trading for Twitter's stock is under the supervision of Barclays Capital. Twitter hired the bank to be its "designated market maker." A DMM supervises the trading of a company's stock. He or she is an experienced trader in charge of ensuring that buying and selling go smoothly. If trading becomes volatile, the DMM can step in and buy shares using his or her firm's own money.
DMMs are especially important the day a company goes public, because the DMM coordinates between Twitter, the company's investment banks and NYSE's floor traders to get a stock trading. If technical problems arise, the NYSE uses DMMs to bypass electronic trading systems, allowing humans to trade a company's stock. That is not possible on all-electronic stock exchanges such as the Nasdaq, which had technical problems during Facebook's IPO last year.
Barclays' role as Twitter's DMM does not mean it is in charge of the entire IPO process. That role falls to Twitter's investment banks: Goldman Sachs, Morgan Stanley and JPMorgan Chase.
Read more: http://bigstory.ap.org/article/twitter-picks-barclays-coordinate-ipo-trading
_ Ken Sweet, New York, (at)KenSweet
___
_ 10 a.m.: (hash)TwitterIPO first indication for opening price: $42-46.
That means Twitter could start trading at up to 77 percent above its IPO price. Trading is to begin soon as representatives from Barclays continue negotiations to find the right price.
_ Ken Sweet, New York, (at)KenSweet
___
_ 9:50 a.m.: With the (hash)Ring of the (hash)NYSEBell past, what will happen? (at)KenSweet reports.
Traders gather around Twitter's booth on the floor of the New York Stock Exchange. At Twitter's post, the company's "designated market maker" starts taking orders from the traders, who are representing dozens of firms and hundreds of investors.
The goal of the DMM, who used to be known as the NYSE's specialists, is to figure out what is the best price to start trading Twitter's shares.
Due to massive investor and media interest in Twitter, the actual negotiation over what are the right price for Twitter's now-public shares will take some time. It could take as little as 20 minutes, or it could take an hour. The NYSE wants to avoid the trading debacle that Nasdaq faced with last year's Facebook's IPO, so it's going to be careful.
Read more: http://bigstory.ap.org/article/going-public-how-twitters-ipo-will-work
_ Ken Sweet, New York, (at)KenSweet
___
_ 9:40 a.m.: The market is open at (at)nyse, though Twitter's stock won't trade right away.
RT (at)NYSEEuronext: (hash)RING! Markets OPEN. (hash)NYSEBell has rung, now begins (hash)TwitterIPO price discovery. Wait for it . pic.twitter.com/gPxGgB6QWa
The opening bid is $35, reports AP's (at)KenSweet. It's the first indication of where the stock will open later in the morning.
As the NYSE's opening bell was rung, the graphic below displayed the hashtag (hash)Ring!
Who rang the bell?
RT (at)NYSEEuronext: (at)Twitter owes success to its users, so gives (hash)NYSEBell to (at)SirPatrickStew, (at)VivienneHarr & (at)Bostonpolice (hash)TwitterIPO pic.twitter.com/fAprlGV8Vs
_ Bree Fowler, New York, (at)APBreeFowler
__
_ 9:25 a.m.: What's being said on Twitter? IPO is the 10th most popular trending topic in the U.S.
IPO is behind Thanksgiving, Texas, NFL and (hash)throwbackthursday.
Worldwide, it doesn't make into the Top 10. Nobel Prize-winning author Albert Camus does. It's his birthday, after all.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 9:05 a.m.: RT (at)KenSweet: Floor trader Kenneth Polcari thinks twitter's $26 share price is pretty fair. Doesn't expect it to double on the open.
___
_ 8:50 a.m.: Busy morning at (at)nyse trading floor, reports AP's (at)KenSweet
RT (at)KenSweet: Orders for Twitter have been coming in since 8 am, floor trader Jonathan Corpina tells me. Very busy.
RT (at)KenSweet: Corpina expects a smooth opening. The NYSE does IPOs all the time, he says. The difference here is volume and media attention.
RT (at)KenSweet: Traders use these handheld wireless computers to send orders. Paper orders ended a long time ago: pic.twitter.com/bwz8UK4xcB
___
_ 8:40 a.m.: Why Twitter went to (at)nyse. Pressure is on with opening bell less than an hour away. (hash)lessonsfromFB
Twitter chose to go public on the NYSE over the all-electronic Nasdaq. One of the reasons why Twitter likely chose the NYSE over the Nasdaq has to do with problems Facebook faced with its Nasdaq-listed IPO last year. A glitch in Nasdaq's trading software led to trading delays and order failures on Facebook's first day of trading.
The NYSE isn't taking any chances with Twitter. The exchange tested its trading software on Oct. 26 to prepare for Twitter's debut. If the NYSE faces technical problems with its ordering software, the exchange can switch over the traditional human-based stock trading that dominated Wall Street for decades.
RT (at)KenSweet: NYSE traders and execs are really playing up the human element to this IPO. It's a shot across the bow at the Nasdaq.
Read more: http://bigstory.ap.org/article/twitter-list-new-york-stock-exchange
_ Ken Sweet, New York, (at)KenSweet
___
_ 8:20 a.m.: AP markets reporter (at)KenSweet says media outnumber traders 5:1 (at)nyse trading floor
It's a media madhouse. But it's still more than an hour before the opening bell, so more traders should be coming. Expect a big crowd.
RT (at)KenSweet: The NYSE is decorated head to toe. with twitter logos. They went big here to promote: pic.twitter.com/pnwRQ9e6QG
___
_ 8 a.m.: After (hash)TwitterIPO pricing, market debut comes Thursday.
It should come as no surprise that Twitter used Twitter to announce its public stock debut.
It began with a tweet on Sept. 12: The 7-year-old company posted on its official Twitter account that it has "confidentially submitted an S-1 to the SEC for a planned IPO." Details about offering emerged after the IPO documents were released publicly later.
On Oct. 24, Twitter set its IPO price target at $17 to $20 per share. It raised that to $23 and $25 per share, signaling an enthusiastic response from prospective investors. The actual price on Wednesday night was even higher, at $26. That bodes well for the company's stock when trading begins.
Twitter also took to Twitter to announce that price: https://twitter.com/twitter/status/398235511254298624/photo/1
The company is offering 70 million shares in the IPO, plus an option to buy another 10.5 million. If all shares are sold, the IPO will raise $2.09 billion, making it the biggest IPO for an Internet company since Facebook raised $16 billion last year.
Of course, Facebook made its debut with high hopes, only to see its stock fall below the IPO price by the second day of trading. Twitter has valued itself at just a fraction of Facebook and sought to cool expectations in the months and weeks leading up to the offering.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay | β Twitter, aka TWTR, wrapped up a strong debut on the New York Stock Exchange today by closing at $44.90 per share, up 73% from the IPO price of $26, reports the Wall Street Journal. The stock opened strong at $45.10 and pretty much stayed that way through the trading day, drawing the inevitable comparisons to Facebook's lousy debut 18 months ago. The closing price puts the value of the company (which has yet to turn a profit in seven years) at $31 billion, reports AP. As Bloomberg puts it, "investors paid a premium for its promises of fast growth." | <s>[INST]Twitter Inc. (TWTR) jumped 73 percent in its trading debut, as investors paid a premium for its promises of fast growth.
The stock rose to $44.90 at the close in New York from the initial public offering price of $26, delivering the biggest one-day pop for an IPO that raised more than $1 billion since Alibaba.com Ltd. debuted in 2007, according to data compiled by Bloomberg. Twitter sold 70 million shares, raising $1.82 billion.
The microblogging website picked a price that valued it higher than Facebook Inc. (FB) and still drew more interest than anticipated. The San Francisco-based company, which is unprofitable and has one-fifth as many users as Facebook, is benefiting from investorsβ thirst for companies that will grow quickly in expanding markets like mobile advertising.
βThe company did everything to secure the most cash for itself while leaving some money for the IPO buyers,β said Josef Schuster, the founder of IPOX Schuster LLC, a Chicago-based manager of about $1.9 billion. βYou need a pop at the opening to leave a good taste with everyone. They did a pretty good job managing the whole situation.β
At the current price, Twitter is valued at $24.9 billion, or 22 times estimated 2014 sales of $1.14 billion, according to analyst projections compiled by Bloomberg. That compares with 11.2 times that Facebook traded at today, and price-to-sales ratio of 11.7 for LinkedIn Corp. (LNKD)
The New York Stock Exchange trading floor is crowded with traders and journalists on the morning of TwitterΓ’ΒΒs public stock debut, on Nov. 7, 2013. Photograph: New York Stock Exchange via AP Images Close The New York Stock Exchange trading floor is crowded with traders and journalists on... Read More Close Open The New York Stock Exchange trading floor is crowded with traders and journalists on the morning of TwitterΓ’ΒΒs public stock debut, on Nov. 7, 2013. Photograph: New York Stock Exchange via AP Images
Facebook declined 3.2 percent, and LinkedIn fell 4.2 percent today. At its market debut in 2012, Facebookβs stock was flat, propped up by bankers, while LinkedInβs more than doubled on the day it went public in 2011.
Price βHypeβ
The pricing puts the onus on Twitter to deliver on its promises of fast growth after earlier pitching shares as low as $17. Chief Executive Officer Dick Costolo has rallied investor interest in Twitterβs rapid sales curve -- with revenue more than doubling annually -- even with no clear path to making a profit.
The company received orders for about 30 times as many shares as it offered at the $26 IPO price, a person with knowledge of the matter said. About 8 million of the shares, or 11 percent of the total in the IPO, were allocated to retail investors, the person said, asking not to be identified because the information is private. A typical retail allocation is 10 percent to 15 percent.
Still, any price over $40 reflects βhypeβ and makes Twitter too risky of an investment, said Jeffrey Sica, president and chief investment officer of Sica Wealth Management LLC in Morristown, New Jersey.
βAbsolute Frothβ
βI anticipated a very strong open, but when you start to approach these levels this is absolute froth,β he said. βThere is nothing supporting this range. I think this is just way, way above what realistically we should be considering a stable open.β
Brian Wieser, an analyst at Pivotal Research Group in New York, downgraded Twitter to a sell rating with a $30 price target.
βIf youβve got it, sell it,β Wieser said in an interview. βIf there are willing buyers who have a view of the business today that gets them comfortable with this valuation then those people should hold it, but I canβt get there, and Iβm not recommending my clients to hold it.β
CEO Costolo was at the New York Stock Exchange for the stockβs debut under the TWTR symbol, along with CFO Mike Gupta and co-founders Evan Williams, Biz Stone and Jack Dorsey.
Executive Tweets
After the celebration at the exchange, executives dispersed. Costolo went to the New York Twitter office to talk to employees, then flew to Twitterβs San Francisco office to do the same. Twitterβs website and applications let people post 140-character messages to friends and online followers. Dorsey sent a tweet to congratulate the companyβs executive team, receiving more than 200 retweets.
More Twitter News:
βMy first of four client presos today starts in 10 mins. Back at it,β Adam Bain, Twitterβs president of global revenue, said in a tweet.
Twitterβs $1.82 billion IPO is almost as much as the $1.9 billion that Google Inc. raised in its 2004 IPO and makes it the largest IPO by a U.S. technology company since Facebookβs debut in May 2012. Goldman Sachs Group Inc. (GS) led the sale, working with Morgan Stanley and JPMorgan Chase & Co. (JPM)
Anti-Facebook IPO
The price rise underscores how Twitter has so far sidestepped some of the pitfalls that befell Facebookβs IPO last year. Facebookβs offering was marred by a trading snag on the Nasdaq Stock Market and investor backlash over its valuation. The company at the time was priced at 107 times trailing 12-month earnings on a fully diluted basis, making it more expensive than 99 percent of all companies in the Standard & Poorβs 500 Index. Facebook saw its stock quickly sink below its $38 debut price, a level it didnβt cross back above until this August.
By contrast, Twitter decided to list on the New York Stock Exchange and chose Goldman Sachs to lead its offering, while Morgan Stanley (MS) led Facebookβs IPO. The company also sought to avoid hype by filing for an IPO secretly with the Securities and Exchange Commission and earlier setting a price range for its shares at a discount to competitors.
Twitterβs stock gain may erase some of the aftertaste of the Facebook, Zynga Inc. (ZNGA) and Groupon Inc. (GRPN) IPOs, each of which lost half their value within six months of their debuts, sending a chill over consumer-technology IPOs and some Silicon Valley startup valuations.
Twitterβs Journey
Demand for Twitterβs stock exceeded the supply even before bankers started formally asking for orders, people familiar with the matter have said. On Monday, Twitter raised the proposed price range for the 70 million shares sold in the IPO to $23 to $25 each, up from the earlier range of $17 to $20.
βPeople are really looking all the way out to their 2015 and 2016 revenue estimates to price this,β said Larry Levine, a partner in financial-advisory firm McGladrey LLP in Chicago. βThe risk to buying Twitter is if Twitter does not achieve its very lofty growth estimates.β
Twitter will have 544.7 million shares of common stock outstanding after the IPO, its filings show. Including restricted stock and options, Twitter will have about 694.8 million shares outstanding. The sale didnβt include an extra 10.5 million shares that underwriters have an option to buy, according to the companyβs prospectus.
Right Time
The offering caps a journey for Twitter from a niche short-messaging service to a global social-media platform for celebrities, politicians and others. Started in 2006 as a project at failed startup Odeo, the website now logs more than 500 million tweets each day, the company has said. Thatβs up from 2 million a day in January 2009.
βI have e-mails going back to 2009 asking me about when Twitter is going public,β said Bijan Sabet, a general partner at Spark Capital, which owns about 6 percent of Twitterβs shares, worth $1.46 billion. βAnd before that, e-mails asking when Twitter is going to generate revenue. This company has always had a lot of pressure. They took their time in figuring out the best way to go public and the right time to go public.β
Twitter still needs to deliver on its business model. Twitterβs loss widened to $64.6 million in the September quarter from $21.6 million a year earlier, and it is unlikely to be profitable until 2015, according to the average estimate of analysts surveyed by Bloomberg. LinkedIn and Facebook were both profitable at the time of their IPOs.
Mobile Users
While Twitterβs revenue has surged, reaching $534.5 million in the 12 months that ended Sept. 30, user growth is slowing, filings show. The service had 231.7 million monthly users in the quarter that ended in September, up 39 percent from a year earlier. That compares with 65 percent growth in the prior year.
Twitter has been touting its engagement with mobile users, where other Web companies have struggled. About three-fourths of Twitterβs active users accessed the service from mobile devices in the three months ended in September, compared with 69 percent in the year-earlier period, according to the filing. More than 70 percent of advertising revenue comes from those devices, a higher proportion than Facebook.
The money from the public offering will help Twitter build its business outside the U.S., where it got 77 percent of users yet only 26 percent of revenue in the third quarter. The company will also expand its infrastructure and work on products that will help it attract more users and advertisers.
βAll that points to a lot of upside,β said Paul Zwillenberg, a London-based partner and managing director at the Boston Consulting Group.
To contact the reporters on this story: Sarah Frier in New York at [email protected]; Lee Spears in New York at [email protected]
To contact the editors responsible for this story: Pui-Wing Tam at [email protected]; Jeffrey McCracken at [email protected] ||||| Twitter had a strong public stock debut Thursday in the most highly anticipated initial public offering since Facebook's last year.
A banner adorns the facade of the New York Stock Exchange in advance of Twitter's initial public offering Thursday, Nov. 7, 2013, in New York. Twitter shares, valued at $26 per share, are set to begin... (Associated Press)
A technician checks the bell podium of the New York Stock Exchange, Thursday, Nov. 7, 2013. Twitter set a price of $26 per share for its initial public offering on Wednesday evening and will begin trading... (Associated Press)
Twitter CEO Dick Costolo, Chairman and co-founder Jack Dorsey, and co-founders Evan Williams and Biz Stone, front row left to right, applaud as they watch the the New York Stock Exchange opening bell... (Associated Press)
Specialist Glenn Carell, who will handle the Twitter IPO, works at his post on the floor of the New York Stock Exchange, Thursday, Nov. 7, 2013. Twitter set a price of $26 per share for its initial public... (Associated Press)
A man walks his dogs past the New York Stock Exchange prior to the Twitter IPO, Thursday, Nov. 7, 2013 in New York. Twitter set a price of $26 per share for its initial public offering on Wednesday evening... (Associated Press)
Twitter CEO Dick Costolo, center, and Mike Gupta, chief financial officer of Twitter, wait for shares to begin trading during the IPO, on the floor of the New York Stock Exchange, Thursday, Nov. 7, 2013.... (Associated Press)
Twitter Chairman and co-founder Jack Dorsey, co-founders Biz Stone and Evan Williams and, Twitter CEO Dick Costolo pose for a group photo after their company's IPO began trading, on the floor of the New... (Associated Press)
Twitter signage is draped on the facade of the New York Stock Exchange, Thursday, Nov. 7, 2013 in New York. Twitter set a price of $26 per share for its initial public offering on Wednesday evening and... (Associated Press)
Twitter's stock opened at $45.10, or 73 percent above its $26 IPO price, and kept most of that gain by the time it closed. The opening price values Twitter at more than $31 billion based on its outstanding stock, options and restricted stock that'll be available after the IPO. It traded as high as $50.09 in the morning.
The high price comes despite the fact that Twitter has never turned a profit in seven years of existence. Revenue has been growing, but the company is also investing heavily in more data centers and hiring more employees.
Twitter is trading under the ticker symbol "TWTR."
Here's a running account of Twitter's first day of trading, presented in reverse chronological order. All times are EST.
___
_ 4:15 p.m.: AP's (at)liedtkesfc posts photo from Twitter co-founder (at)noah Glass' home: pic.twitter.com/2DduLFRbNZ
___
_ 4:10 p.m.: $TWTR's closing price of $44.90 gives Twitter a value of more than $31 billion.
It's actually 20 cents lower than the opening price, but still 73 percent higher than the $26 IPO price.
RT (at)KenSweet: One way to read this: If you bought Twitter at its first trade of $45.10, you lost (a little) money today. $TWTR
___
_ 4 p.m.: First day of trading is done. Twitter soars about 73 percent from IPO price, keeping most of gain from opening.
___
_ 3:55 p.m.: As Twitter's first trading day nears an end, keep in mind at least one analyst believes $twtr is now a "Sell."
Pivotal Research Group analyst Brian Wieser slashed his rating on Twitter Inc. from "Buy" on Thursday after the stock opened at $45.10, about 50 percent above his price target of $30.
His price target valued the company at 21 times its free cash flow in 2018, a multiple that exceeded even Facebook at 17 times and Google at 16 times. With a stock price of $45, Twitter would be worth 32 times its 2018 free cash flow, which he wrote in a research note was "overly optimistic."
Wieser told AP's (at)BarbaraOrtutay that he still has a very positive view of the business, but believes the company isn't worth as much as it has been trading at.
"The market can beg to differ," he said.
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 3:35 p.m.: Twitter has no shortage of co-founders. AP's (at)liedtkesfc tries to track down the one who wasn't (at)NYSE for opening
Here's his account:
While Twitter founders Jack Dorsey, Evan Williams and Biz Stone were in New York celebrating the company's stock debut Thursday, a former partner involved in Twitter's creation was in the midst of a home improvement project on the other side of the country.
At least that's how it looked when I swung by the home of Noah Glass, (at)noah, in San Francisco's Mission District neighborhood.
Glass, 43, says he and Dorsey conceived Twitter during a brainstorming session after a night of drinking in San Francisco nearly eight years ago. Dorsey has a different account, maintaining he came up with the idea himself on a San Francisco playground. Tweets and blog posts from 2006 make it clear Glass was deeply involved. He even came up with the service's name, originally shortening it to "twittr."
For reasons that aren't entirely clear, Glass was ousted from Twitter before it turned into a cultural phenomenon and didn't even get much company stock, according to a new book about Twitter's history.
I was curious to see how Glass was handling this momentous day for Twitter. So I hopped on a train near Twitter's San Francisco headquarters and rode the subway to the next stop. Glass lives with his 7-month-old daughter and the baby's French-speaking mother at the end of a dirt lot in a small home that was set up after a 1906 earthquake destroyed much of the city. These homes are still known as "earthquake shacks."
The front gate was open, as was the front door. As I walked up to the threshold, I could hear the pounding of a hammer in the back and a baby blissfully playing in a stroller. The French-accented woman nearby cheerfully greeted me, but when I told her that I was a reporter wondering if Noah wanted to talk to me about Twitter, she informed me that he wasn't interested. She was very nice about it, and we wished me a very nice day.
It seemed like a happy home, even if it isn't as grandiose as the mansions that many Twitter employees can now afford to buy. (hash)ForgottenFounder
More on the founders: http://bigstory.ap.org/article/flock-feathered-twitters-nest
_ Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 3:25 p.m.: (at)Twitter CEO (at)DickC says growth is just a question of connecting with potential new users
Twitter CEO Dick Costolo appeared on CNBC ahead of his company's trading debut at the NYSE to talk about his company and its potential for growth.
CNBC's David Faber said that joining Twitter made sense for Faber and a lot of other people early on. But he asked how the company planned to keep growing and attract users outside of its traditional base.
Costolo said that it's all about making connections with people and helping them see how Twitter fits into their lives.
"It's all about, for us, helping people bridge that gap between `I've heard about Twitter,' to getting exactly where you and so many other people here today are."
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 3:05 p.m.: AP's (at)liedtkesfc explores the neighborhood outside (at)Twitter HQ and sees contrasts.
The San Francisco neighborhood outside Twitter's headquarters provides a forlorn contrast to the suddenly rich people working inside the building.
These are among the meaner streets in downtown San Francisco, long populated with the destitute who have no place to live and the miscreants who resort to crime to make ends meet. In hopes of cleaning the area up, the city of San Francisco gave Twitter local tax breaks on employee stock options to help persuade the company to move into the neighborhood two years ago.
But times are still tough here. Scruffy-looking people gathered against the wall of a post office across the street from Twitter's headquarters. Four of them had just spent the night in a homeless shelter. All of them said that they wished that they owned Twitter stock, yet they maintained that they didn't really envy Twitter employees becoming wealthier as the stock soared Thursday.
There was a clump of litter just a few feet away. Amid the empty coffee cups, cigarette butts and empty liquor bottles, there were two scratch-off games for the California lottery that had been discarded because they didn't pay off. (hash)LandofBrokenDreams
_ Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 2:50 p.m.: In Asia, (at)Twitter has competition from local companies, reports AP's (at)YKLeeAP
Led by Japan, Indonesia, South Korea and India, Asia was the fastest growing region for Twitter in summer 2010, according to Semiocast, a Paris-based social media research company. But growth has slowed in South Korea and Japan, a red flag for Twitter as both countries are wealthy and have high rates of mobile device usage _ now the predominant way Twitter is accessed.
New mobile applications from companies such as South Korea's Kakao Corp. and Japan's Line Corp., have experienced explosive growth, making them potent competitors for eyeballs and advertising.
Why are people leaving Twitter or spending less time on it?
Too open. Too crowded. Too difficult.
"In South Korea and Japan, open type social networking services like Twitter and Facebook are losing steam," said Justin Lee, an analyst of mobile messengers and games at BNP Paribas. "Closed social networking services where messages are shared among a small group of people will become more popular."
Twitter remains blocked from China's vast market but another giant, India, is open to Twitter. It has amassed 27 million users there, according to Semiocast. Yet Twitter acknowledged in IPO filings that low use of smartphones in emerging markets such as India could hamper the ability of advertisers to deliver compelling advertisements and hurt its earnings potential.
International users accounted for about three quarters of Twitter's members but only a quarter of revenue in the first nine months of this year. About 25 percent of Twitter's 232 million active users are in Asia.
_ Youkyung Lee, Seoul, South Korea, (at)YKLeeAP
___
_ 2:30 p.m.: (at)Twitter now among the most valuable media companies, notes AP's (at)rnakashi
Like Twitter, the other large media companies in the country rely to some extent on advertising revenue. As of mid-afternoon, Twitter's value is nearly $33 billion, after including options and restricted stock that'll be available after the IPO.
The market value of other media companies: CBS Corp., $34.7 billion; Discovery Communications Inc., $30 billion; Viacom Inc., $38.8 billion; The Walt Disney Co., $120 billion; Time Warner Inc. $60.3 billion.
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 2:10 p.m.: (at)NYSEEuronext has congratulated (at)Twitter "on a successful (hash)NYSEIPO! We're excited to be your partner."
___
_ 1:55 p.m.: Looking back at Twitter's IPO price, here are some quick facts from (at)Dealogic
Twitter priced its IPO at $26, raising $1.82 billion. If the offering's underwriters fully exercise their option to buy more shares, the IPO's value will rise to $2.09 billion. That would make it the second-largest Internet IPO by an American company on record, following Facebook Inc.'s $16 billion, but beating Google Inc.'s $1.92 billion.
The research firm Dealogic says Twitter's IPO is set to be the third-largest U.S.-listed IPO so far this year, behind Plains GP Holdings at $2.9 billion and Zoetis' $2.6 billion.
Including Twitter, U.S.-listed tech industry IPOs have raised $7.8 billion through 41 deals so far this year. That's down from $20.5 billion generated by 35 deals during the same period of 2012, though Facebook accounted for $16 billion of the 2012 total.
Tech companies tend to post bigger first-day jumps than the overall market. The average one-day jump for tech industry IPOs this year is 35 percent, compared with an average gain of 17 percent for 2013 IPOs overall. Twitter's stock opened at 73 percent above the IPO price.
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 1:40 p.m.: (at)Twitter soars while drop in overall market pulls down rest of Internet cos.
Twitter shares are flying high, but other Internet companies are having a tough time getting off the ground.
While Twitter's debut likely helped send shares of Facebook Inc. down, the overall tech industry also took a hit as the markets pulled back from record levels on worries that the Federal Reserve could soon start curtailing its economic stimulus program.
Facebook shares fell $1.07, or 2.2 percent, to $48.05 after dropping as low as $47.41 earlier in the day. Other Internet companies such as LinkedIn Corp., AOL Inc., Google Inc., Pandora Media Inc. and Zillow Inc. all posted small to moderate losses.
_ Bree Fowler, New York, (at)APBreeFowler
___
_ 1:20 p.m.: Will Twitter's stock keep going up? There is risk of Twitter burnout. (hash)TwitterHaters
There's plenty of evidence online about the celebrities who tire of Twitter. The long list of Twitter quitters includes everyone from Alec Baldwin to Miley Cyrus to "Lost" co-creator Damon Lindelof, though some eventually return.
Some get overwhelmed by followers spewing hatred. Others get addicted to interacting with huge fan bases and need to pull away. Even non-celebrity users complain of the amount of time spent posting and replying and vow to close accounts to get on with their lives.
With its public stock debut, the company has been selling potential investors on the idea that its user base of 232 million will continue to grow along with the 500 million tweets that are sent each day. The company's revenue depends on ads it inserts into the stream of messages.
But Wall Street could lose its big bet on social media if prolific tweeters lose their voice.
Read more: http://bigstory.ap.org/article/user-burnout-could-threaten-twitters-prosperity
_ Ryan Nakashima, Los Angeles, (at)rnakashi
___
_ 1:05 p.m.: Twitter chairman (at)jack makes reference to first tweet in Vine video post
About two hours ago, Twitter chairman and co-founder Jack Dorsey tweeted this: "just setting up our $twtr _https://vine.co/v/hI1nP3vQOBI" The link is to video on Twitter's Vine app, showing traders shouting on NYSE trading floor.
The tweet, of course, is a reference to the world's first tweet, which was sent by Dorsey on March 21, 2006, and read "just setting up my twttr." Dorsey uses "$twtr" in Thursday's post in a reference to the stock's ticker symbol. Putting a dollar sign before it is a common way to refer to stocks on Twitter.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 12:50 p.m.: (at)Twitter is trading very heavily in its first day on (at)NYSE.
About 82 million shares of Twitter have exchanged hands already. To put that in perspective, Twitter only sold 70 million shares in its IPO. One way to think about it, every share issued in Twitter's IPO has been traded more than once, and the session isn't half over yet.
Of course, not every investor who got shares of Twitter at the $26 IPO price is selling Thursday. Many large institutional investors are buy-and-hold firms. If every investor had sold at the debut, the stock would not have opened at 73 percent above the IPO price.
_ Ken Sweet, New York, (at)KenSweet
___
_ 12:35 p.m.: (at)TDAmeritrade official says stock debut is flawless
"It's gone on pretty flawlessly," says JJ Kinahan, chief strategist at online brokerage TD Ameritrade.
For one, he says, the broader market's downturn isn't affecting Twitter much. Trading is also tight, rather than volatile, which indicates that people feel like it was "pretty fairly priced," he says.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 12:15 p.m.: Learn more about (at)vivienneharr, (at)sirpatstew and (at)bostonpolice official who rang (at)NYSEEuronext opening bell
Crediting its success to its users, Twitter gave the honor of ringing Thursday's opening bell at the New York Stock Exchange to three high-profile tweeters: a child activist, a legendary British actor and a Boston Police official.
Nine-year-old Vivienne Harr used a lemonade stand to raise more than $100,000 to support efforts to eliminate child slavery around the world. Her pink lemonade, along with a ginger-infused version, is now being bottled and sold online. A portion of the profits is donated to groups that work toward ending child slavery. More than 22,000 people follow (at)vivienneharr on Twitter.
Patrick Stewart is known both for his Twitter presence and his stage and screen careers. His highest profile roles have included Captain Jean-Luc Picard in "Star Trek: The Next Generation" and Professor Charles Xavier in the "X-Men" movies. About 722,000 people follow (at)sirpatstew. Stewart tweeted a picture of himself on Halloween dressed as a lobster in a bathtub. It was retweeted nearly 39,000 times.
Cheryl Fiandaca has been chief of public information for the Boston Police Department since July 2012. Fiandaca spearheaded the department's social media efforts, and her department used Twitter to get information to the public in the aftermath of the Boston Marathon bombings. More than 266,000 people follow (at)bostonpolice.
Bree Fowler, New York, (at)APBreeFowler
___
_ 11:55 a.m.: (at)Wedbush analyst (at)MichaelPachter says high debut price suggests (hash)TwitterIPO was managed well.
Wedbush analyst Michael Pachter says the surge "clearly shows that demand exceeds supply of shares."
"It's impossible to know what the real value is," he says.
Still, he acknowledges that the price is "pretty high" and not something he was expecting.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 11:45 a.m.: It's (hash)BusinessAsUsual at (at)Twitter headquarters, though employees seem happy.
Although Twitter's fortunes are already soaring on Wall Street, there haven't been any audible whoops of joy emanating from the company's San Francisco headquarters yet. But almost every employee walking in and out of the building is grinning.
Twitter seems to know that it needs to accelerate its revenue growth to support its lofty stock price. A few employees just came out to usher in a group of advertising agency representatives. (hash)TheNewReality
--Michael Liedtke, San Francisco, (at)liedtkesfc
___
_ 11:30 a.m.: (at)Barclays official in charge of stock debut speaks with AP's (at)KenSweet, admits being "a little nervous."
It was the biggest IPO of the year for Glenn Carell, the Barclays Capital official in charge of Twitter's stock debut. He has been doing it for 21 years and says, "I was a little nervous, but it went well."
Twitter hired Barclays to be its "designated market maker," which supervises the trading of a company's stock on the New York Stock Exchange. The IPO process itself was managed by three other investment banks.
_ Ken Sweet, New York, (at)KenSweet
___
_ 11:05 a.m.: RT (at)KenSweet: Twitter took a long time to open due to the deal size. Goldman also likes to take its time.
Goldman Sachs, Morgan Stanley and JPMorgan Chase are the three investment banks in charge of Twitter's IPO.
After debuting at $45.10, the stock is now trading at $47.85, or 84 percent above the IPO price.
___
_ 10:55 a.m.: AP's (at)BarbaraOrtutay notes that the $31 billion value puts Twitter in the ballpark of Yum Brands and Deere & Co.
It's also slightly below State Street Corp.
___
_ 10:53 a.m.: The opening price values Twitter at $31.3 billion.
To calculate its value, the AP is using 694.8 million shares that Twitter is expected to have outstanding after the IPO, counting restricted shares and stock options it plans to issue to employees. At the $26 IPO price, the value was more than $18 billion.
___
_ 10:51 a.m.: Twitter stock opens at $45.10, 73 percent above IPO price
___
_ 10:50 a.m.: Range is now $45 to $45.25, or up to 74 percent above IPO price. Very close to debut.
RT (at)KenSweet: They're closing the book.
___
_ 10:45 a.m. AP's (at)KenSweet says current bid is $45.25. The debut is near in (hash)TwitterIPO.
___
_ 10:40 a.m.: Patrick Stewart tweets on (hash)Ring of opening bell as Twitter trade debut imminent.
RT (at)SirPatStew: Honored to join (at)ev (at)jack (at)biz (at)dickc & the (at)Twitter team at their historic IPO this morning. (hash)Ring! pic.twitter.com/XaJpYW2kIh
___
_ 10:35 a.m.: It's getting close to Twitter's stock debut. First indication for opening price is even narrower: $45.50-$46.50.
The high end would be 79 percent above its IPO price.
___
_ 10:30 a.m.: AP's (at)KenSweet now says opening price narrowed: $45-$47.
He reports: "This is a good sign. Could mean we're finding the right price. Progress."
___
_ 10:20 a.m.: AP's (at)KenSweet says opening price is expected even higher: $43-$47.
The range for first indication means Twitter could start trading at up to 81 percent above its IPO price.
___
_ 10:15 a.m.: RT (at)KenSweet: I've heard some traders mention that this may not open until 1030, maybe 11. But things are changing rapidly.
___
_ 10:10 a.m.: AP market reporter (at)KenSweet explains the role (at)Barclays has in (hash)TwitterIPO.
Trading for Twitter's stock is under the supervision of Barclays Capital. Twitter hired the bank to be its "designated market maker." A DMM supervises the trading of a company's stock. He or she is an experienced trader in charge of ensuring that buying and selling go smoothly. If trading becomes volatile, the DMM can step in and buy shares using his or her firm's own money.
DMMs are especially important the day a company goes public, because the DMM coordinates between Twitter, the company's investment banks and NYSE's floor traders to get a stock trading. If technical problems arise, the NYSE uses DMMs to bypass electronic trading systems, allowing humans to trade a company's stock. That is not possible on all-electronic stock exchanges such as the Nasdaq, which had technical problems during Facebook's IPO last year.
Barclays' role as Twitter's DMM does not mean it is in charge of the entire IPO process. That role falls to Twitter's investment banks: Goldman Sachs, Morgan Stanley and JPMorgan Chase.
Read more: http://bigstory.ap.org/article/twitter-picks-barclays-coordinate-ipo-trading
_ Ken Sweet, New York, (at)KenSweet
___
_ 10 a.m.: (hash)TwitterIPO first indication for opening price: $42-46.
That means Twitter could start trading at up to 77 percent above its IPO price. Trading is to begin soon as representatives from Barclays continue negotiations to find the right price.
_ Ken Sweet, New York, (at)KenSweet
___
_ 9:50 a.m.: With the (hash)Ring of the (hash)NYSEBell past, what will happen? (at)KenSweet reports.
Traders gather around Twitter's booth on the floor of the New York Stock Exchange. At Twitter's post, the company's "designated market maker" starts taking orders from the traders, who are representing dozens of firms and hundreds of investors.
The goal of the DMM, who used to be known as the NYSE's specialists, is to figure out what is the best price to start trading Twitter's shares.
Due to massive investor and media interest in Twitter, the actual negotiation over what are the right price for Twitter's now-public shares will take some time. It could take as little as 20 minutes, or it could take an hour. The NYSE wants to avoid the trading debacle that Nasdaq faced with last year's Facebook's IPO, so it's going to be careful.
Read more: http://bigstory.ap.org/article/going-public-how-twitters-ipo-will-work
_ Ken Sweet, New York, (at)KenSweet
___
_ 9:40 a.m.: The market is open at (at)nyse, though Twitter's stock won't trade right away.
RT (at)NYSEEuronext: (hash)RING! Markets OPEN. (hash)NYSEBell has rung, now begins (hash)TwitterIPO price discovery. Wait for it . pic.twitter.com/gPxGgB6QWa
The opening bid is $35, reports AP's (at)KenSweet. It's the first indication of where the stock will open later in the morning.
As the NYSE's opening bell was rung, the graphic below displayed the hashtag (hash)Ring!
Who rang the bell?
RT (at)NYSEEuronext: (at)Twitter owes success to its users, so gives (hash)NYSEBell to (at)SirPatrickStew, (at)VivienneHarr & (at)Bostonpolice (hash)TwitterIPO pic.twitter.com/fAprlGV8Vs
_ Bree Fowler, New York, (at)APBreeFowler
__
_ 9:25 a.m.: What's being said on Twitter? IPO is the 10th most popular trending topic in the U.S.
IPO is behind Thanksgiving, Texas, NFL and (hash)throwbackthursday.
Worldwide, it doesn't make into the Top 10. Nobel Prize-winning author Albert Camus does. It's his birthday, after all.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay
___
_ 9:05 a.m.: RT (at)KenSweet: Floor trader Kenneth Polcari thinks twitter's $26 share price is pretty fair. Doesn't expect it to double on the open.
___
_ 8:50 a.m.: Busy morning at (at)nyse trading floor, reports AP's (at)KenSweet
RT (at)KenSweet: Orders for Twitter have been coming in since 8 am, floor trader Jonathan Corpina tells me. Very busy.
RT (at)KenSweet: Corpina expects a smooth opening. The NYSE does IPOs all the time, he says. The difference here is volume and media attention.
RT (at)KenSweet: Traders use these handheld wireless computers to send orders. Paper orders ended a long time ago: pic.twitter.com/bwz8UK4xcB
___
_ 8:40 a.m.: Why Twitter went to (at)nyse. Pressure is on with opening bell less than an hour away. (hash)lessonsfromFB
Twitter chose to go public on the NYSE over the all-electronic Nasdaq. One of the reasons why Twitter likely chose the NYSE over the Nasdaq has to do with problems Facebook faced with its Nasdaq-listed IPO last year. A glitch in Nasdaq's trading software led to trading delays and order failures on Facebook's first day of trading.
The NYSE isn't taking any chances with Twitter. The exchange tested its trading software on Oct. 26 to prepare for Twitter's debut. If the NYSE faces technical problems with its ordering software, the exchange can switch over the traditional human-based stock trading that dominated Wall Street for decades.
RT (at)KenSweet: NYSE traders and execs are really playing up the human element to this IPO. It's a shot across the bow at the Nasdaq.
Read more: http://bigstory.ap.org/article/twitter-list-new-york-stock-exchange
_ Ken Sweet, New York, (at)KenSweet
___
_ 8:20 a.m.: AP markets reporter (at)KenSweet says media outnumber traders 5:1 (at)nyse trading floor
It's a media madhouse. But it's still more than an hour before the opening bell, so more traders should be coming. Expect a big crowd.
RT (at)KenSweet: The NYSE is decorated head to toe. with twitter logos. They went big here to promote: pic.twitter.com/pnwRQ9e6QG
___
_ 8 a.m.: After (hash)TwitterIPO pricing, market debut comes Thursday.
It should come as no surprise that Twitter used Twitter to announce its public stock debut.
It began with a tweet on Sept. 12: The 7-year-old company posted on its official Twitter account that it has "confidentially submitted an S-1 to the SEC for a planned IPO." Details about offering emerged after the IPO documents were released publicly later.
On Oct. 24, Twitter set its IPO price target at $17 to $20 per share. It raised that to $23 and $25 per share, signaling an enthusiastic response from prospective investors. The actual price on Wednesday night was even higher, at $26. That bodes well for the company's stock when trading begins.
Twitter also took to Twitter to announce that price: https://twitter.com/twitter/status/398235511254298624/photo/1
The company is offering 70 million shares in the IPO, plus an option to buy another 10.5 million. If all shares are sold, the IPO will raise $2.09 billion, making it the biggest IPO for an Internet company since Facebook raised $16 billion last year.
Of course, Facebook made its debut with high hopes, only to see its stock fall below the IPO price by the second day of trading. Twitter has valued itself at just a fraction of Facebook and sought to cool expectations in the months and weeks leading up to the offering.
_ Barbara Ortutay, New York, (at)BarbaraOrtutay[/INST]β Twitter, aka TWTR, wrapped up a strong debut on the New York Stock Exchange today by closing at $44.90 per share, up 73% from the IPO price of $26, reports the Wall Street Journal. The stock opened strong at $45.10 and pretty much stayed that way through the trading day, drawing the inevitable comparisons to Facebook's lousy debut 18 months ago. The closing price puts the value of the company (which has yet to turn a profit in seven years) at $31 billion, reports AP. As Bloomberg puts it, "investors paid a premium for its promises of fast growth."</s> |
.
The War Powers Resolution (50 U.S.C. 1541 et seq.; Public Law 93-
148), relating to the exercise of war powers by the President under the
Constitution, is hereby repealed.
TITLE II--EXPEDITED PROCEDURES
SEC. 201. CONGRESSIONAL PRIORITY PROCEDURES.
(a) Definitions.--For purposes of this section--
(1) the term ``resolution'' means any resolution described
in subsection (a) or (b) of section 105; and
(2) the term ``session days'' means days on which the
respective House of Congress is in session.
(b) Referral of Resolutions.--A resolution introduced in the House
of Representatives shall be referred to the Committee on International
Relations of the House of Representatives. A resolution introduced in
the Senate shall be referred to the Committee on Foreign Relations of
the Senate.
(c) Discharge of Committee.--(1) If the committee to which is
referred a resolution has not reported such a resolution (or an
identical resolution) at the end of 7 calendar days after its
introduction, such committee shall be discharged from further
consideration of such resolution, and such resolution shall be placed
on the appropriate calendar of the House of Congress involved.
(2) After a committee reports or is discharged from a resolution,
no other resolution with respect to the same use of force may be
reported by or be discharged from such committee while the first
resolution is before the respective House of Congress (including
remaining on the calendar), a committee of conference, or the
President. This paragraph may not be construed to prohibit concurrent
consideration of a joint resolution described in section 105(a) and a
concurrent resolution described in section 105(b).
(d) Consideration of Resolutions.--(1)(A) Whenever the committee to
which a resolution is referred has reported, or has been discharged
under subsection (c) from further consideration of such resolution,
notwithstanding any rule or precedent of the Senate, including Rule 22,
it is at any time thereafter in order (even though a previous motion to
the same effect has been disagreed to) for any Member of the respective
House of Congress to move to proceed to the consideration of the
resolution and, except as provided in subparagraph (B) of this
paragraph or paragraph (2) of this subsection (insofar as it relates to
germaneness and relevancy of amendments), all points of order against
the resolution and consideration of the resolution are waived. The
motion is highly privileged in the House of Representatives and is
privileged in the Senate and is not debatable. The motion is not
subject to a motion to postpone. A motion to reconsider the vote by
which the motion is agreed to or disagreed to shall be in order, except
that such motion may not be entered for future disposition. If a motion
to proceed to the consideration of the resolution is agreed to, the
resolution shall remain the unfinished business of the respective House
of Congress, to the exclusion of all other business, until disposed of,
except as otherwise provided in subsection (e)(1).
(B) Whenever a point of order is raised in the Senate against the
privileged status of a resolution that has been laid before the Senate
and been initially identified as privileged for consideration under
this section upon its introduction pursuant to section 105, such point
of order shall be submitted directly to the Senate. The point of
order, ``The resolution is not privileged under the Use of Force Act'',
shall be decided by the yeas and the nays after four hours of debate,
equally divided between, and controlled by, the Member raising the
point of order and the manager of the resolution, except that in the
event the manager is in favor of such point of order, the time in
opposition thereto shall be controlled by the Minority Leader or his
designee. Such point of order shall not be considered to establish
precedent for determination of future cases.
(2)(A)(i) Consideration in a House of Congress of the resolution,
and all amendments and debatable motions in connection therewith, shall
be limited to not more than 12 hours, which, except as otherwise
provided in this section, shall be equally divided between, and
controlled by, the Majority Leader and the Minority Leader, or by their
designees.
(ii) The Majority Leader or the Minority Leader or their designees
may, from the time under their control on the resolution, allot
additional time to any Senator during the consideration of any
amendment, debatable motion, or appeal.
(B) Only amendments which are germane and relevant to the
resolution are in order. Debate on any amendment to the resolution
shall be limited to 2 hours, except that debate on any amendment to an
amendment shall be limited to 1 hour. The time of debate for each
amendment shall be equally divided between, and controlled by, the
mover of the amendment and the manager of the resolution, except that
in the event the manager is in favor of any such amendment, the time in
opposition thereto shall be controlled by the Minority Leader or his
designee.
(C) One amendment by the Minority Leader is in order to be offered
under a one-hour time limitation immediately following the expiration
of the 12-hour time limitation if the Minority Leader has had no
opportunity to offer an amendment to the resolution thereto. One
amendment may be offered to the amendment by the Minority Leader under
the preceding sentence, and debate shall be limited on such amendment
to one-half hour which shall be equally divided between, and controlled
by, the mover of the amendment and the manager of the resolution,
except that in the event the manager is in favor of any such amendment,
the time in opposition thereto shall be controlled by the Minority
Leader or his designee.
(D) A motion to postpone or a motion to recommit the resolution is
not in order. A motion to reconsider the vote by which the resolution
is agreed to or disagreed to is in order, except that such motion may
not be entered for future disposition, and debate on such motion shall
be limited to 1 hour.
(3) Whenever all the time for debate on a resolution has been used
or yielded back, no further amendments may be proposed, except as
provided in paragraph (2)(C), and the vote on the adoption of the
resolution shall occur without any intervening motion or amendment,
except that a single quorum call at the conclusion of the debate if
requested in accordance with the rules of the appropriate House of
Congress may occur immediately before such vote.
(4) Appeals from the decisions of the Chair relating to the
application of the Rules of the Senate or the House of Representatives,
as the case may be, to the procedure relating to a resolution shall be
limited to one-half hour of debate, equally divided between, and
controlled by, the Member making the appeal and the manager of the
resolution, except that in the event the manager is in favor of any
such appeal, the time in opposition thereto shall be controlled by the
Minority Leader or his designee.
(e) Treatment of Other House's Resolution.--(1) Except as provided
in paragraph (2), if, before the passage by one House of a resolution
of that House, that House receives from the other House a resolution,
then the following procedures shall apply:
(A) The resolution of the sending House shall not be
referred to a committee in the receiving House.
(B) With respect to a resolution of the House receiving the
resolution, the procedure in that House shall be the same as if
no resolution had been received from the sending House, except
that the resolution of the sending House shall be considered to
have been read for the third time.
(C) If the resolutions of the sending and receiving Houses
are identical, the vote on final passage shall be on the
resolution of the sending House.
(D) If such resolutions are not identical--
(i) the vote on final passage shall be on the
resolution of the sending House, with the text of the
resolution of the receiving House inserted in lieu of
the text of the resolution of the sending House;
(ii) such vote on final passage shall occur without
debate or any intervening action; and
(iii) the resolution shall be returned to the
sending House for proceedings under subsection (g).
(E) Upon disposition of the resolution received from the
other House, it shall no longer be in order to consider the
resolution originated in the receiving House.
(2) If one House receives from the other House a resolution before
any such resolution is introduced in the first House, then the
resolution received shall be referred, in the case of the House of
Representatives, to the Committee on International Relations and, in
the case of the Senate, to the Committee on Foreign Relations, and the
procedures in that House with respect to that resolution shall be the
same under this section as if the resolution received had been
introduced in that House.
(f) Treatment of Identical Resolutions.--If one House receives from
the other House a resolution after the first House has disposed of an
identical resolution, it shall be in order to proceed by nondebatable
motion to consideration of the resolution received by the first House,
and that received resolution shall be disposed of without debate and
without amendment.
(g) Procedures Applicable to Amendments Between the Houses of
Congress.--The following procedures shall apply to dispose of
amendments between the Houses of Congress:
(1) Upon receipt by a House of Congress of a message from
the other House with respect to a resolution, it is in order
for any Member of the House receiving the message to move to
proceed to the consideration of the respective resolution. Such
motion shall be disposed of in the same manner as a motion
under subsection (d)(1)(A). Such a motion is not in order after
conferees have been appointed.
(2)(A) The time for debate in a House of Congress on any
motion required for the disposition of an amendment by the
other House to the resolution shall not exceed 2 hours, equally
divided between, and controlled by, the mover of the motion and
manager of the resolution at each stage of the proceedings
between the two Houses, except that in the event the manager is
in favor of any such motion, the time in opposition thereto
shall be controlled by the Minority Leader or his designee.
(B) The time for debate for each amendment to a motion
shall be limited to one-half hour.
(C) Only motions proposing amendments which are germane and
relevant are in order.
(h) Procedures Applicable to Conference Reports and Presidential
Action.--(1) Either House of Congress may disagree to an amendment or
amendments made by the other House to a resolution or may insist upon
its amendment or amendments to a resolution, and request a conference
with the other House at anytime. In the case of any disagreement
between the two Houses of Congress with respect to an amendment or
amendments to a resolution which is not resolved within 2 session days
after a House of Congress first amends the resolution originated by the
other House, each House shall be deemed to have requested and accepted
a conference with the other House. Upon the request or acceptance of a
conference, in the case of the Senate, the President pro tempore shall
appoint conferees and, in the case of the House of Representatives, the
Speaker of the House shall appoint conferees.
(2) In the event the conferees are unable to agree within 72 hours
after the second House is notified that the first House has agreed to
conference, or after each House is deemed to have agreed to conference,
they shall report back to their respective House in disagreement.
(3) Notwithstanding any rule in either House of Congress concerning
the printing of conference reports in the Congressional Record or
concerning any delay in the consideration of such reports, such report,
including a report filed or returned in disagreement, shall be acted on
in the House of Representatives or the Senate not later than 2 session
days after the first House files the report or, in the case of the
Senate acting first, the report is first made available on the desks of
the Senators.
(4) Debate in a House of Congress on a conference report or a
report filed or returned in disagreement in any such resolution shall
be limited to 3 hours, equally divided between the Majority Leader and
the Minority Leader, and their designees.
(5) In the case of a conference report returned to a House of
Congress in disagreement, an amendment to the amendment in disagreement
is only in order if it is germane and relevant. The time for debate for
such an amendment shall be limited to one-half hour, to be equally
divided between, and controlled by, the mover of the amendment and the
manager of the resolution, except that in the event the manager is in
favor of any such amendment, the time in opposition thereto shall be
controlled by the Minority Leader or his designee.
(6) If a resolution is vetoed by the President, the time for debate
in consideration of the veto message on such measure shall be limited
to 20 hours in each House of Congress, equally divided between, and
controlled by, the Majority Leader and the Minority Leader, and their
designees.
(i) Rules of the Senate and the House.--This section is enacted by
the Congress--
(1) as an exercise of the rulemaking power of the Senate
and House of Representatives, respectively, and as such it is
deemed a part of the rules of each House, respectively, but
applicable only with respect to the procedure to be followed in
that House in the case of a resolution, and it supersedes other
rules only to the extent that it is inconsistent with such
rules; and
(2) with full recognition of the constitutional right of
either House to change rules (so far as relating to the
procedure of that House) at any time, in the same manner, and
to the same extent as in the case of any other rule of that
House.
SEC. 202. REPEAL OF OBSOLETE EXPEDITED PROCEDURES.
Section 1013 of the Department of State Authorization Act, Fiscal
Years 1984 and 1985 (50 U.S.C. 1546a), relating to expedited procedures
for certain joint resolutions and bills, is repealed.
S 564 IS----2
S 564 IS----3 | TABLE OF CONTENTS:
Title I: General Provisions
Title II: Expedited Procedures
Use of Force Act -
Title I: General Provisions
- Authorizes the President, in the absence of a declaration of war or statutory authorization for a specific use of force, to use force abroad to: (1) repel an armed attack upon the United States or its armed forces; (2) respond to a foreign military threat that jeopardizes U.S. national interests under emergency conditions that do not permit sufficient time for the Congress to consider such authorization or a declaration of war; (3) extricate U.S. citizens and nationals located abroad from a direct and imminent threat to their lives; (4) forestall an imminent act of international terrorism directed at U.S. citizens or nationals or to retaliate against the perpetrators of such an act; and (5) protect internationally recognized rights of innocent and free passage in the air and on the seas in circumstances where the threat of violation of such rights poses a danger to the safety of American citizens or U.S. national security.
Requires the President to adhere to principles of necessity and proportionality such that: (1) force may not be used for purposes of aggression; (2) the President shall have determined, before the use of force, that the objective could not have been achieved satisfactorily by means other than the use of force; (3) the use of force shall be exercised with levels of force, in a manner, and for a duration essential to and directly connected with the achievement of the objective; and (4) the diplomatic, military, economic, and humanitarian consequences of the action shall be in reasonable proportion to the benefits of the objective.
(Sec. 102) Directs the President, except where an emergency exists that does not permit sufficient time, to seek the advice of the Congress before any use of force abroad.
Establishes the Congressional Leadership Group on the Use of Force Abroad to facilitate regular consultation between the President and the Congress on foreign and national security policy.
(Sec. 103) Requires the President, within 48 hours of commencing a use of force abroad, to submit a Use of Force report to the Speaker of the House of Representatives and the president pro tempore of the Senate. Provides for periodic reporting on the status, scope, and expected duration of the use of force.
(Sec. 104) Authorizes the President to continue a use of force abroad for longer than 60 days after the date by which the Use of Force report is required only if: (1) the Congress has declared war or provided specific statutory authorization for the extended period; (2) the President has requested the Congress to enact a joint resolution constituting such a declaration or authorization but the resolution has not been subject to a vote in each House; or (3) the President has certified to the Speaker of the House and the president pro tempore of the Senate that an emergency exists that threatens the U.S. national interests and requires the period of limitation to be exceeded.
(Sec. 105) Sets forth conditions under which joint or concurrent resolutions involving declarations of war and the use of force abroad shall receive expedited consideration in the Congress.
(Sec. 106) Prohibits funding for any use of force abroad that is inconsistent with this Act.
(Sec. 107) Authorizes Members of Congress to bring actions alleging violations of this Act. Sets forth provisions regarding judicial review and remedies.
(Sec. 110) Repeals the War Powers Resolution.
Title II: Expedited Procedures
- Sets forth congressional procedures for the consideration of resolutions regarding the use of force abroad. | <s>[INST].
The War Powers Resolution (50 U.S.C. 1541 et seq.; Public Law 93-
148), relating to the exercise of war powers by the President under the
Constitution, is hereby repealed.
TITLE II--EXPEDITED PROCEDURES
SEC. 201. CONGRESSIONAL PRIORITY PROCEDURES.
(a) Definitions.--For purposes of this section--
(1) the term ``resolution'' means any resolution described
in subsection (a) or (b) of section 105; and
(2) the term ``session days'' means days on which the
respective House of Congress is in session.
(b) Referral of Resolutions.--A resolution introduced in the House
of Representatives shall be referred to the Committee on International
Relations of the House of Representatives. A resolution introduced in
the Senate shall be referred to the Committee on Foreign Relations of
the Senate.
(c) Discharge of Committee.--(1) If the committee to which is
referred a resolution has not reported such a resolution (or an
identical resolution) at the end of 7 calendar days after its
introduction, such committee shall be discharged from further
consideration of such resolution, and such resolution shall be placed
on the appropriate calendar of the House of Congress involved.
(2) After a committee reports or is discharged from a resolution,
no other resolution with respect to the same use of force may be
reported by or be discharged from such committee while the first
resolution is before the respective House of Congress (including
remaining on the calendar), a committee of conference, or the
President. This paragraph may not be construed to prohibit concurrent
consideration of a joint resolution described in section 105(a) and a
concurrent resolution described in section 105(b).
(d) Consideration of Resolutions.--(1)(A) Whenever the committee to
which a resolution is referred has reported, or has been discharged
under subsection (c) from further consideration of such resolution,
notwithstanding any rule or precedent of the Senate, including Rule 22,
it is at any time thereafter in order (even though a previous motion to
the same effect has been disagreed to) for any Member of the respective
House of Congress to move to proceed to the consideration of the
resolution and, except as provided in subparagraph (B) of this
paragraph or paragraph (2) of this subsection (insofar as it relates to
germaneness and relevancy of amendments), all points of order against
the resolution and consideration of the resolution are waived. The
motion is highly privileged in the House of Representatives and is
privileged in the Senate and is not debatable. The motion is not
subject to a motion to postpone. A motion to reconsider the vote by
which the motion is agreed to or disagreed to shall be in order, except
that such motion may not be entered for future disposition. If a motion
to proceed to the consideration of the resolution is agreed to, the
resolution shall remain the unfinished business of the respective House
of Congress, to the exclusion of all other business, until disposed of,
except as otherwise provided in subsection (e)(1).
(B) Whenever a point of order is raised in the Senate against the
privileged status of a resolution that has been laid before the Senate
and been initially identified as privileged for consideration under
this section upon its introduction pursuant to section 105, such point
of order shall be submitted directly to the Senate. The point of
order, ``The resolution is not privileged under the Use of Force Act'',
shall be decided by the yeas and the nays after four hours of debate,
equally divided between, and controlled by, the Member raising the
point of order and the manager of the resolution, except that in the
event the manager is in favor of such point of order, the time in
opposition thereto shall be controlled by the Minority Leader or his
designee. Such point of order shall not be considered to establish
precedent for determination of future cases.
(2)(A)(i) Consideration in a House of Congress of the resolution,
and all amendments and debatable motions in connection therewith, shall
be limited to not more than 12 hours, which, except as otherwise
provided in this section, shall be equally divided between, and
controlled by, the Majority Leader and the Minority Leader, or by their
designees.
(ii) The Majority Leader or the Minority Leader or their designees
may, from the time under their control on the resolution, allot
additional time to any Senator during the consideration of any
amendment, debatable motion, or appeal.
(B) Only amendments which are germane and relevant to the
resolution are in order. Debate on any amendment to the resolution
shall be limited to 2 hours, except that debate on any amendment to an
amendment shall be limited to 1 hour. The time of debate for each
amendment shall be equally divided between, and controlled by, the
mover of the amendment and the manager of the resolution, except that
in the event the manager is in favor of any such amendment, the time in
opposition thereto shall be controlled by the Minority Leader or his
designee.
(C) One amendment by the Minority Leader is in order to be offered
under a one-hour time limitation immediately following the expiration
of the 12-hour time limitation if the Minority Leader has had no
opportunity to offer an amendment to the resolution thereto. One
amendment may be offered to the amendment by the Minority Leader under
the preceding sentence, and debate shall be limited on such amendment
to one-half hour which shall be equally divided between, and controlled
by, the mover of the amendment and the manager of the resolution,
except that in the event the manager is in favor of any such amendment,
the time in opposition thereto shall be controlled by the Minority
Leader or his designee.
(D) A motion to postpone or a motion to recommit the resolution is
not in order. A motion to reconsider the vote by which the resolution
is agreed to or disagreed to is in order, except that such motion may
not be entered for future disposition, and debate on such motion shall
be limited to 1 hour.
(3) Whenever all the time for debate on a resolution has been used
or yielded back, no further amendments may be proposed, except as
provided in paragraph (2)(C), and the vote on the adoption of the
resolution shall occur without any intervening motion or amendment,
except that a single quorum call at the conclusion of the debate if
requested in accordance with the rules of the appropriate House of
Congress may occur immediately before such vote.
(4) Appeals from the decisions of the Chair relating to the
application of the Rules of the Senate or the House of Representatives,
as the case may be, to the procedure relating to a resolution shall be
limited to one-half hour of debate, equally divided between, and
controlled by, the Member making the appeal and the manager of the
resolution, except that in the event the manager is in favor of any
such appeal, the time in opposition thereto shall be controlled by the
Minority Leader or his designee.
(e) Treatment of Other House's Resolution.--(1) Except as provided
in paragraph (2), if, before the passage by one House of a resolution
of that House, that House receives from the other House a resolution,
then the following procedures shall apply:
(A) The resolution of the sending House shall not be
referred to a committee in the receiving House.
(B) With respect to a resolution of the House receiving the
resolution, the procedure in that House shall be the same as if
no resolution had been received from the sending House, except
that the resolution of the sending House shall be considered to
have been read for the third time.
(C) If the resolutions of the sending and receiving Houses
are identical, the vote on final passage shall be on the
resolution of the sending House.
(D) If such resolutions are not identical--
(i) the vote on final passage shall be on the
resolution of the sending House, with the text of the
resolution of the receiving House inserted in lieu of
the text of the resolution of the sending House;
(ii) such vote on final passage shall occur without
debate or any intervening action; and
(iii) the resolution shall be returned to the
sending House for proceedings under subsection (g).
(E) Upon disposition of the resolution received from the
other House, it shall no longer be in order to consider the
resolution originated in the receiving House.
(2) If one House receives from the other House a resolution before
any such resolution is introduced in the first House, then the
resolution received shall be referred, in the case of the House of
Representatives, to the Committee on International Relations and, in
the case of the Senate, to the Committee on Foreign Relations, and the
procedures in that House with respect to that resolution shall be the
same under this section as if the resolution received had been
introduced in that House.
(f) Treatment of Identical Resolutions.--If one House receives from
the other House a resolution after the first House has disposed of an
identical resolution, it shall be in order to proceed by nondebatable
motion to consideration of the resolution received by the first House,
and that received resolution shall be disposed of without debate and
without amendment.
(g) Procedures Applicable to Amendments Between the Houses of
Congress.--The following procedures shall apply to dispose of
amendments between the Houses of Congress:
(1) Upon receipt by a House of Congress of a message from
the other House with respect to a resolution, it is in order
for any Member of the House receiving the message to move to
proceed to the consideration of the respective resolution. Such
motion shall be disposed of in the same manner as a motion
under subsection (d)(1)(A). Such a motion is not in order after
conferees have been appointed.
(2)(A) The time for debate in a House of Congress on any
motion required for the disposition of an amendment by the
other House to the resolution shall not exceed 2 hours, equally
divided between, and controlled by, the mover of the motion and
manager of the resolution at each stage of the proceedings
between the two Houses, except that in the event the manager is
in favor of any such motion, the time in opposition thereto
shall be controlled by the Minority Leader or his designee.
(B) The time for debate for each amendment to a motion
shall be limited to one-half hour.
(C) Only motions proposing amendments which are germane and
relevant are in order.
(h) Procedures Applicable to Conference Reports and Presidential
Action.--(1) Either House of Congress may disagree to an amendment or
amendments made by the other House to a resolution or may insist upon
its amendment or amendments to a resolution, and request a conference
with the other House at anytime. In the case of any disagreement
between the two Houses of Congress with respect to an amendment or
amendments to a resolution which is not resolved within 2 session days
after a House of Congress first amends the resolution originated by the
other House, each House shall be deemed to have requested and accepted
a conference with the other House. Upon the request or acceptance of a
conference, in the case of the Senate, the President pro tempore shall
appoint conferees and, in the case of the House of Representatives, the
Speaker of the House shall appoint conferees.
(2) In the event the conferees are unable to agree within 72 hours
after the second House is notified that the first House has agreed to
conference, or after each House is deemed to have agreed to conference,
they shall report back to their respective House in disagreement.
(3) Notwithstanding any rule in either House of Congress concerning
the printing of conference reports in the Congressional Record or
concerning any delay in the consideration of such reports, such report,
including a report filed or returned in disagreement, shall be acted on
in the House of Representatives or the Senate not later than 2 session
days after the first House files the report or, in the case of the
Senate acting first, the report is first made available on the desks of
the Senators.
(4) Debate in a House of Congress on a conference report or a
report filed or returned in disagreement in any such resolution shall
be limited to 3 hours, equally divided between the Majority Leader and
the Minority Leader, and their designees.
(5) In the case of a conference report returned to a House of
Congress in disagreement, an amendment to the amendment in disagreement
is only in order if it is germane and relevant. The time for debate for
such an amendment shall be limited to one-half hour, to be equally
divided between, and controlled by, the mover of the amendment and the
manager of the resolution, except that in the event the manager is in
favor of any such amendment, the time in opposition thereto shall be
controlled by the Minority Leader or his designee.
(6) If a resolution is vetoed by the President, the time for debate
in consideration of the veto message on such measure shall be limited
to 20 hours in each House of Congress, equally divided between, and
controlled by, the Majority Leader and the Minority Leader, and their
designees.
(i) Rules of the Senate and the House.--This section is enacted by
the Congress--
(1) as an exercise of the rulemaking power of the Senate
and House of Representatives, respectively, and as such it is
deemed a part of the rules of each House, respectively, but
applicable only with respect to the procedure to be followed in
that House in the case of a resolution, and it supersedes other
rules only to the extent that it is inconsistent with such
rules; and
(2) with full recognition of the constitutional right of
either House to change rules (so far as relating to the
procedure of that House) at any time, in the same manner, and
to the same extent as in the case of any other rule of that
House.
SEC. 202. REPEAL OF OBSOLETE EXPEDITED PROCEDURES.
Section 1013 of the Department of State Authorization Act, Fiscal
Years 1984 and 1985 (50 U.S.C. 1546a), relating to expedited procedures
for certain joint resolutions and bills, is repealed.
S 564 IS----2
S 564 IS----3[/INST]TABLE OF CONTENTS:
Title I: General Provisions
Title II: Expedited Procedures
Use of Force Act -
Title I: General Provisions
- Authorizes the President, in the absence of a declaration of war or statutory authorization for a specific use of force, to use force abroad to: (1) repel an armed attack upon the United States or its armed forces; (2) respond to a foreign military threat that jeopardizes U.S. national interests under emergency conditions that do not permit sufficient time for the Congress to consider such authorization or a declaration of war; (3) extricate U.S. citizens and nationals located abroad from a direct and imminent threat to their lives; (4) forestall an imminent act of international terrorism directed at U.S. citizens or nationals or to retaliate against the perpetrators of such an act; and (5) protect internationally recognized rights of innocent and free passage in the air and on the seas in circumstances where the threat of violation of such rights poses a danger to the safety of American citizens or U.S. national security.
Requires the President to adhere to principles of necessity and proportionality such that: (1) force may not be used for purposes of aggression; (2) the President shall have determined, before the use of force, that the objective could not have been achieved satisfactorily by means other than the use of force; (3) the use of force shall be exercised with levels of force, in a manner, and for a duration essential to and directly connected with the achievement of the objective; and (4) the diplomatic, military, economic, and humanitarian consequences of the action shall be in reasonable proportion to the benefits of the objective.
(Sec. 102) Directs the President, except where an emergency exists that does not permit sufficient time, to seek the advice of the Congress before any use of force abroad.
Establishes the Congressional Leadership Group on the Use of Force Abroad to facilitate regular consultation between the President and the Congress on foreign and national security policy.
(Sec. 103) Requires the President, within 48 hours of commencing a use of force abroad, to submit a Use of Force report to the Speaker of the House of Representatives and the president pro tempore of the Senate. Provides for periodic reporting on the status, scope, and expected duration of the use of force.
(Sec. 104) Authorizes the President to continue a use of force abroad for longer than 60 days after the date by which the Use of Force report is required only if: (1) the Congress has declared war or provided specific statutory authorization for the extended period; (2) the President has requested the Congress to enact a joint resolution constituting such a declaration or authorization but the resolution has not been subject to a vote in each House; or (3) the President has certified to the Speaker of the House and the president pro tempore of the Senate that an emergency exists that threatens the U.S. national interests and requires the period of limitation to be exceeded.
(Sec. 105) Sets forth conditions under which joint or concurrent resolutions involving declarations of war and the use of force abroad shall receive expedited consideration in the Congress.
(Sec. 106) Prohibits funding for any use of force abroad that is inconsistent with this Act.
(Sec. 107) Authorizes Members of Congress to bring actions alleging violations of this Act. Sets forth provisions regarding judicial review and remedies.
(Sec. 110) Repeals the War Powers Resolution.
Title II: Expedited Procedures
- Sets forth congressional procedures for the consideration of resolutions regarding the use of force abroad.</s> |
null | successful single - cell isolation is a primary step for subsequent
chemical and biological analyses of single cells .
conventional single - cell
isolation methods often encounter operational complexity , limited
efficiency , deterioration of cell viability , incompetence in the isolation
of a single - cell into nanoliter liquid , and/or inability to select
single adherent cells with specific phenotypes . here
, we develop a
hand - held single - cell pipet ( hscp ) that is rapid , operationally simple ,
highly efficient , and inexpensive for unbiased isolation of single
viable suspended cells directly from submicroliter cell suspensions
into nanoliter droplets without the assistance of any additional equipment .
an integrated scp ( iscp ) has also been developed for selective isolation
of single suspended and adherent cells according to the fluorescence
imaging and morphological features .
the isolated single cells can
be conveniently transferred into standard 96-/384-well plates , petri
dishes , or vials for cloning , pcr , and other single - cell biochemical
assays . | <s>[INST]None[/INST]successful single - cell isolation is a primary step for subsequent
chemical and biological analyses of single cells .
conventional single - cell
isolation methods often encounter operational complexity , limited
efficiency , deterioration of cell viability , incompetence in the isolation
of a single - cell into nanoliter liquid , and/or inability to select
single adherent cells with specific phenotypes . here
, we develop a
hand - held single - cell pipet ( hscp ) that is rapid , operationally simple ,
highly efficient , and inexpensive for unbiased isolation of single
viable suspended cells directly from submicroliter cell suspensions
into nanoliter droplets without the assistance of any additional equipment .
an integrated scp ( iscp ) has also been developed for selective isolation
of single suspended and adherent cells according to the fluorescence
imaging and morphological features .
the isolated single cells can
be conveniently transferred into standard 96-/384-well plates , petri
dishes , or vials for cloning , pcr , and other single - cell biochemical
assays .</s> |
triatominae ( hemiptera , reduviidae ) is a subfamily of hematophagous insects known as kissing bugs whose members are principally distributed throughout the neotropical region [ 13 ] .
certain triatomine species are responsible for the transmission of trypanosoma cruzi chagas , 1909 ( kinetoplastida , trypanosomatidae)the etiological agent of chagas disease , which is one of the most dreaded parasitic diseases of latin america .
attempts to control t. cruzi transmission began soon after carlos chagas ' work in the 1900s .
the advent of synthetic insecticides in the 1940s was the first major breakthrough in identifying effective techniques for kissing bug control ; the introduction of pyrethroids , a more cost - effective synthetic type of insecticide , was another important advance that occurred in the 1980s . despite these efforts ,
high levels of vector - borne transmission still occur in many areas , and several endemic countries had to develop large - scale surveillance and intervention programs .
since the chagas disease discovery , the biological control of its vectors has been considered [ 710 ] .
however , its application to effective triatomine control in the field is still incipient ; little success has been achieved by the use of parasitoid wasps , although recent studies with entomopathogenic fungi are promising .
several species clustered in different taxonomic groups might function as triatomine pathogens , predators , or parasitoids [ 12 , 13 ] .
for example , the best - known kissing bug parasitoid telenomus fariai lima , 1927 ( hymenoptera , scelionidae ) , is able to parasitize the eggs of species in three triatomine genera , panstrongylus , rhodnius , and triatoma [ 12 , 14 , 15 ] .
parasitoid wasps are distributed throughout the world in a variety of environments and usually parasitize the eggs of a wide range of insects , many triatominae species among them .
they are considered to have biological , ecological , and economic importance , and some species are employed as pest biological control agents [ 17 , 18 ] . in this communication , we report for the first time the experimental parasitism of eggs of the triatomine species triatoma infestans ( klug , 1834 ) and triatoma vitticeps ( stl , 1859 ) by aprostocetus asthenogmus ( waterston , 1915 ) ( hymenoptera , eulophidae ) .
this species is an endophagous egg parasite that has only been reported to parasitize the ootheca of the cockroaches periplaneta americana ( linnaeus , 1758 ) , periplaneta australasiae ( fabricius , 1775 ) , and periplaneta brunnea burmeister , 1838 ( blattodea , blattidae ) [ 19 , 20 ] .
we also report the first record of a. asthenogmus in south america , which has previously been recorded in the caribbean , india , north africa , the palearctic , china , seychelles , and sri lanka [ 19 , 2124 ] .
in january 2005 , we observed a. asthenogmus adult wasps flying near t. infestans and t. vitticeps colonies established in 2004 at the unidade de medicina tropical of universidade federal do esprito santo , municipality of vitria , state of esprito santo , brazil ( 201753s , 401858w ) .
however , the triatomines and their eggs were maintained in mesh - covered pots , preventing any spontaneous wasp - triatomine egg contact .
we carried out an investigation to determine if a. asthenogmus was able to parasitize triatomine eggs .
the adult wasps were captured using a castro suction device and placed into two pots with recently laid eggs : 11 wasps with 51 eggs of t. infestans and 10 wasps with 79 eggs of t. vitticeps .
the pots were maintained at an environmental temperature ( ~28c ) and observed daily for wasp emergence .
after 24 days , we observed wasps emerging from triatomine eggs . among t. infestans eggs , 29 ( 56.8% ) became parasitized and produced 29 adult wasps , whereas 36 ( 45.5% ) t. vitticeps eggs were parasitized and produced 36 adult wasps ( figure 1 ) .
microhymenoptera of the aphelinidae , eupelmidae , encyrtidae , pteromalidae , and scelionidae families were previously reported to parasitize triatominae eggs naturally and experimentally [ 7 , 12 ] .
however , this is the first report that eulophidae are able to parasitize triatomine eggs [ 19 , 20 ] . in cockroaches ,
a. asthenogmus exhibits gregarious habits with a mean of 69.5 parasitoids emerging per ootheca ( approximately 9 6 mm ) , which can contain up to 16 eggs , and a mean development time of 43 days [ 19 , 25 , 26 ] . in the two species of triatomine we used ,
however , a. asthenogmus showed a solitary habit , with only one adult emerging from each egg and a shorter development time .
these differences could be partially explained by the size variation between triatomine eggs and cockroach oothecas and less resource competition .
t. vitticeps has been reported to be parasitized only by t. fariai , but t. infestans is reportedly parasitized by other microhymenopteran species in addition to t. fariai [ 12 , 14 , 15 ] .
t. vitticeps is a wild and endemic species of the atlantic forest that is responsible for sporadic cases of human chagas disease in that region [ 2730 ] , and t. infestans is considered the most important domiciliated t. cruzi vector that was previously widely distributed in south america [ 31 , 32 ] .
although it could be considered that the particular laboratory conditions ( e.g. , scarcity of natural hosts and the confinement imposed ) could have stimulated a. asthenogmus to use nonnatural hosts , our confirmation of parasitism of triatomine eggs suggests the possibility of this parasitoid acting as a natural enemy of these two species of t. cruzi vectors .
several characteristics of this species suggest that it could be a potential biological control agent of triatomine eggs : a. asthenogmus was apparently attracted by the triatomine colony , it shows a wide geographical distribution , it is a natural parasitoid of several worldwide cockroach pest species , and it requires no preovipositional period ( at least in cockroaches ) and accepts 1- to 30-day - old oothecae .
it is also promising that the adult wasp developmental time in triatomine eggs was shorter than in cockroach oothecae ; moreover , only one adult wasp emerged per triatomine egg , allowing a unique female to parasitize a potentially greater number of triatomine eggs .
a. asthenogmus , first recorded in south america , can parasitize eggs of triatomines , suggesting that it could be a potential biological control agent of these chagas disease vectors .
on the basis of these findings , we suggest that new studies should be carried out to evaluate the host preference plasticity of a. asthenogmus in new environments and its potential as a biological control agent of domiciliary and peridomiciliary triatomine species .
experiments evaluating sex ratios , parasitism capacity , dispersal ability , and possible female wasp competition for egg parasitization ( including possible egg - marking behavior ) should be included in future work . | we report for the first time the parasitism of eggs of two triatomine chagas disease vectors , triatoma infestans and t. vitticeps , by the microhymenopterous parasitoid aprostocetus asthenogmus .
we also describe the first identification of this parasitoid in south america .
a. asthenogmus were captured near unparasitized triatomine colonies in the municipality of vitria , state of esprito santo , brazil , and placed into pots with recently laid triatomine eggs .
after 24 days , we observed wasps emerging from t. infestans and t. vitticeps eggs .
several characteristics of this parasitoid species suggest that it could be a potential biological control agent of triatomine species . | <s>[INST]triatominae ( hemiptera , reduviidae ) is a subfamily of hematophagous insects known as kissing bugs whose members are principally distributed throughout the neotropical region [ 13 ] .
certain triatomine species are responsible for the transmission of trypanosoma cruzi chagas , 1909 ( kinetoplastida , trypanosomatidae)the etiological agent of chagas disease , which is one of the most dreaded parasitic diseases of latin america .
attempts to control t. cruzi transmission began soon after carlos chagas ' work in the 1900s .
the advent of synthetic insecticides in the 1940s was the first major breakthrough in identifying effective techniques for kissing bug control ; the introduction of pyrethroids , a more cost - effective synthetic type of insecticide , was another important advance that occurred in the 1980s . despite these efforts ,
high levels of vector - borne transmission still occur in many areas , and several endemic countries had to develop large - scale surveillance and intervention programs .
since the chagas disease discovery , the biological control of its vectors has been considered [ 710 ] .
however , its application to effective triatomine control in the field is still incipient ; little success has been achieved by the use of parasitoid wasps , although recent studies with entomopathogenic fungi are promising .
several species clustered in different taxonomic groups might function as triatomine pathogens , predators , or parasitoids [ 12 , 13 ] .
for example , the best - known kissing bug parasitoid telenomus fariai lima , 1927 ( hymenoptera , scelionidae ) , is able to parasitize the eggs of species in three triatomine genera , panstrongylus , rhodnius , and triatoma [ 12 , 14 , 15 ] .
parasitoid wasps are distributed throughout the world in a variety of environments and usually parasitize the eggs of a wide range of insects , many triatominae species among them .
they are considered to have biological , ecological , and economic importance , and some species are employed as pest biological control agents [ 17 , 18 ] . in this communication , we report for the first time the experimental parasitism of eggs of the triatomine species triatoma infestans ( klug , 1834 ) and triatoma vitticeps ( stl , 1859 ) by aprostocetus asthenogmus ( waterston , 1915 ) ( hymenoptera , eulophidae ) .
this species is an endophagous egg parasite that has only been reported to parasitize the ootheca of the cockroaches periplaneta americana ( linnaeus , 1758 ) , periplaneta australasiae ( fabricius , 1775 ) , and periplaneta brunnea burmeister , 1838 ( blattodea , blattidae ) [ 19 , 20 ] .
we also report the first record of a. asthenogmus in south america , which has previously been recorded in the caribbean , india , north africa , the palearctic , china , seychelles , and sri lanka [ 19 , 2124 ] .
in january 2005 , we observed a. asthenogmus adult wasps flying near t. infestans and t. vitticeps colonies established in 2004 at the unidade de medicina tropical of universidade federal do esprito santo , municipality of vitria , state of esprito santo , brazil ( 201753s , 401858w ) .
however , the triatomines and their eggs were maintained in mesh - covered pots , preventing any spontaneous wasp - triatomine egg contact .
we carried out an investigation to determine if a. asthenogmus was able to parasitize triatomine eggs .
the adult wasps were captured using a castro suction device and placed into two pots with recently laid eggs : 11 wasps with 51 eggs of t. infestans and 10 wasps with 79 eggs of t. vitticeps .
the pots were maintained at an environmental temperature ( ~28c ) and observed daily for wasp emergence .
after 24 days , we observed wasps emerging from triatomine eggs . among t. infestans eggs , 29 ( 56.8% ) became parasitized and produced 29 adult wasps , whereas 36 ( 45.5% ) t. vitticeps eggs were parasitized and produced 36 adult wasps ( figure 1 ) .
microhymenoptera of the aphelinidae , eupelmidae , encyrtidae , pteromalidae , and scelionidae families were previously reported to parasitize triatominae eggs naturally and experimentally [ 7 , 12 ] .
however , this is the first report that eulophidae are able to parasitize triatomine eggs [ 19 , 20 ] . in cockroaches ,
a. asthenogmus exhibits gregarious habits with a mean of 69.5 parasitoids emerging per ootheca ( approximately 9 6 mm ) , which can contain up to 16 eggs , and a mean development time of 43 days [ 19 , 25 , 26 ] . in the two species of triatomine we used ,
however , a. asthenogmus showed a solitary habit , with only one adult emerging from each egg and a shorter development time .
these differences could be partially explained by the size variation between triatomine eggs and cockroach oothecas and less resource competition .
t. vitticeps has been reported to be parasitized only by t. fariai , but t. infestans is reportedly parasitized by other microhymenopteran species in addition to t. fariai [ 12 , 14 , 15 ] .
t. vitticeps is a wild and endemic species of the atlantic forest that is responsible for sporadic cases of human chagas disease in that region [ 2730 ] , and t. infestans is considered the most important domiciliated t. cruzi vector that was previously widely distributed in south america [ 31 , 32 ] .
although it could be considered that the particular laboratory conditions ( e.g. , scarcity of natural hosts and the confinement imposed ) could have stimulated a. asthenogmus to use nonnatural hosts , our confirmation of parasitism of triatomine eggs suggests the possibility of this parasitoid acting as a natural enemy of these two species of t. cruzi vectors .
several characteristics of this species suggest that it could be a potential biological control agent of triatomine eggs : a. asthenogmus was apparently attracted by the triatomine colony , it shows a wide geographical distribution , it is a natural parasitoid of several worldwide cockroach pest species , and it requires no preovipositional period ( at least in cockroaches ) and accepts 1- to 30-day - old oothecae .
it is also promising that the adult wasp developmental time in triatomine eggs was shorter than in cockroach oothecae ; moreover , only one adult wasp emerged per triatomine egg , allowing a unique female to parasitize a potentially greater number of triatomine eggs .
a. asthenogmus , first recorded in south america , can parasitize eggs of triatomines , suggesting that it could be a potential biological control agent of these chagas disease vectors .
on the basis of these findings , we suggest that new studies should be carried out to evaluate the host preference plasticity of a. asthenogmus in new environments and its potential as a biological control agent of domiciliary and peridomiciliary triatomine species .
experiments evaluating sex ratios , parasitism capacity , dispersal ability , and possible female wasp competition for egg parasitization ( including possible egg - marking behavior ) should be included in future work .[/INST]we report for the first time the parasitism of eggs of two triatomine chagas disease vectors , triatoma infestans and t. vitticeps , by the microhymenopterous parasitoid aprostocetus asthenogmus .
we also describe the first identification of this parasitoid in south america .
a. asthenogmus were captured near unparasitized triatomine colonies in the municipality of vitria , state of esprito santo , brazil , and placed into pots with recently laid triatomine eggs .
after 24 days , we observed wasps emerging from t. infestans and t. vitticeps eggs .
several characteristics of this parasitoid species suggest that it could be a potential biological control agent of triatomine species .</s> |
βββIt was not a typical two-anthem night at Consol Energy Center Wednesday.
But it hadnβt been a normal day in Canada, either, and the Penguins, who were preparing for a game against Philadelphia, felt a gesture of support was in order.
That is why, in the wake of Canadian Forces reservist Nathan Cirillo being shot and killed near the National War Memorial in Ottawa, team officials decided to have anthem singer Jeff Jimerson perform βO Canadaβ before the game, something that usually happens only when a team from Canada is in town. As the words were displayed on arena light boards, fans stood and sang with Mr. Jimerson as players bowed their heads.
And plentyβ ofβ people, especially those in Canada, noticed.
That includes Prime Minister Stephen Harper, who described it as "a wonderful gesture" in a speech to Parliament Thursday.
After thanking fellow Canadians and leaders of other nations, Mr. Harper mentioned that anthem.
β... I wanted to convey all the good wishes that I heard personally not just from Canadians but from our friends outside the country. I heard from President Obama, from Prime Minister Abbott, from Prime Minister Netanyahu, through a statement from Prime Minister Cameron. Weβve heard these expressions across the world.
βI think we were all as Canadians touched by the wonderful gesture shown last night at the Pittsburgh Penguins hockey game. So thank you to our friends in the United States and around the world.β
The reaction has been βoverwhelming,β said Tom McMillan, the teamβs vice president of communications.
In addition to messages sent directly to the team β in both of Canadaβs official languages β the Penguins have heard the anthem has been discussed at length on Canadian talk radio, he said. They even have been fielding interview requests for Mr. Jimerson.
Mr. McMillan noted that the Penguinsβ minor league team in Wilkes-Barre also had received several expressions of gratitude for performing βO Canada,β even though the Baby Penguins had no connection to what happened at Consol Energy Center.
βItβs been constant,β Mr. McMillan said. βNon-stop.β
The messages have come in all forms β from texts to tweets to phone calls β with a few directed to a portion of the Penguinsβ website that deals with anthem singers.
One of those calls, he said, came Thursday afternoon from Donna Speer, widow of former Penguins forward Billy Speer, a native of Ontario who played for the team in the late 1960s.
βWeβre all stunned, in many ways,β Mr. McMillan said. βYouβre trying to do the right thing. We werenβt thinking about what response we would get.β
He said itβs impossible to single out one person who came up with the idea. It evolved after a number of people started to kick around possibilities, and final approval was given by team president David Morehouse.
The Pittsburgh Post-Gazette also was receiving emails from Canadians who wanted to thank the Penguins.
βThanks to the people of Pittsburgh for noticing Canada had a bad day. I was touched, my family across Canada was touched, as were other Canadians,β wrote Bern McNicholl of Vancouver, British Columbia.
βIt was, and remains, a beautiful gesture of friendship and support β and one which will not be soon forgotten,β said Eric Hindson of Calgary, Alberta.
Countless photos and videos of the gesture went viral on social media. A picture of the anthemβs performance from a Post-Gazette reporterβs Twitter account was retweeted or marked as a favorite over 1,200 times. Canadian athletes including PGA golfer Brad Fritsch and Calgary Flames right winger Brian McGrattan offered thanks or praise via Twitter. Overnight, βPensβ and βPittsburghβ trended on Twitter in Ottawa.
Seth Rorabaugh of the Post-Gazette contributed to this report. ||||| A singer at a U.S.-based NHL game between the Pittsburgh Penguins and Philadelphia Flyers performed "O Canada" Wednesday evening in sympathy and support for America's neighbor to the north following the fatal shooting near Canada's parliament in Ottawa.
Interested in ? Add as an interest to stay up to date on the latest news, video, and analysis from ABC News. Add Interest
Jeff Jimerson sang βO Canada,β with fans at Pittsburghβs Consol Energy Center joining him. The Canadian national anthem isnβt normally performed in games between two United States teams.
The shooting -- which left a Canadian soldier dead -- led to the cancellation of Wednesdayβs game between the Toronto Maple Leafs and Ottawa Senators in Ottawa.
The song struck a chord for Penguins and Flyers players and coaches, many of whom grew up in Canada.
βI thought it was a special tribute tonight," said Penguins coach Mike Johnston, who was born in Nova Scotia and has coached throughout Canada. "Certainly, when those events happen, they strike everybody."
The Associated Press contributed to this report. | β The Pittsburgh Penguins and their fans offered a nice show of support to Canada last night before a game against Philadelphia. Hours after a gunman attacked the Parliament in Ottawa, fans joined along in the singing of O Canada as the Canadian flag was projected on the ice, reports ABC News. The Canadian anthem typically isn't sung when a game features two US teams, but the Penguins decided to make an exception. It caught the attention of Canadian Prime Minister Stephen Harper, notes the Pittsburgh Post-Gazette. "I think we were all as Canadians touched by the wonderful gesture shown last night at the Pittsburgh Penguins hockey game," he said. "So thank you to our friends in the United States and around the world." | <s>[INST]βββIt was not a typical two-anthem night at Consol Energy Center Wednesday.
But it hadnβt been a normal day in Canada, either, and the Penguins, who were preparing for a game against Philadelphia, felt a gesture of support was in order.
That is why, in the wake of Canadian Forces reservist Nathan Cirillo being shot and killed near the National War Memorial in Ottawa, team officials decided to have anthem singer Jeff Jimerson perform βO Canadaβ before the game, something that usually happens only when a team from Canada is in town. As the words were displayed on arena light boards, fans stood and sang with Mr. Jimerson as players bowed their heads.
And plentyβ ofβ people, especially those in Canada, noticed.
That includes Prime Minister Stephen Harper, who described it as "a wonderful gesture" in a speech to Parliament Thursday.
After thanking fellow Canadians and leaders of other nations, Mr. Harper mentioned that anthem.
β... I wanted to convey all the good wishes that I heard personally not just from Canadians but from our friends outside the country. I heard from President Obama, from Prime Minister Abbott, from Prime Minister Netanyahu, through a statement from Prime Minister Cameron. Weβve heard these expressions across the world.
βI think we were all as Canadians touched by the wonderful gesture shown last night at the Pittsburgh Penguins hockey game. So thank you to our friends in the United States and around the world.β
The reaction has been βoverwhelming,β said Tom McMillan, the teamβs vice president of communications.
In addition to messages sent directly to the team β in both of Canadaβs official languages β the Penguins have heard the anthem has been discussed at length on Canadian talk radio, he said. They even have been fielding interview requests for Mr. Jimerson.
Mr. McMillan noted that the Penguinsβ minor league team in Wilkes-Barre also had received several expressions of gratitude for performing βO Canada,β even though the Baby Penguins had no connection to what happened at Consol Energy Center.
βItβs been constant,β Mr. McMillan said. βNon-stop.β
The messages have come in all forms β from texts to tweets to phone calls β with a few directed to a portion of the Penguinsβ website that deals with anthem singers.
One of those calls, he said, came Thursday afternoon from Donna Speer, widow of former Penguins forward Billy Speer, a native of Ontario who played for the team in the late 1960s.
βWeβre all stunned, in many ways,β Mr. McMillan said. βYouβre trying to do the right thing. We werenβt thinking about what response we would get.β
He said itβs impossible to single out one person who came up with the idea. It evolved after a number of people started to kick around possibilities, and final approval was given by team president David Morehouse.
The Pittsburgh Post-Gazette also was receiving emails from Canadians who wanted to thank the Penguins.
βThanks to the people of Pittsburgh for noticing Canada had a bad day. I was touched, my family across Canada was touched, as were other Canadians,β wrote Bern McNicholl of Vancouver, British Columbia.
βIt was, and remains, a beautiful gesture of friendship and support β and one which will not be soon forgotten,β said Eric Hindson of Calgary, Alberta.
Countless photos and videos of the gesture went viral on social media. A picture of the anthemβs performance from a Post-Gazette reporterβs Twitter account was retweeted or marked as a favorite over 1,200 times. Canadian athletes including PGA golfer Brad Fritsch and Calgary Flames right winger Brian McGrattan offered thanks or praise via Twitter. Overnight, βPensβ and βPittsburghβ trended on Twitter in Ottawa.
Seth Rorabaugh of the Post-Gazette contributed to this report. ||||| A singer at a U.S.-based NHL game between the Pittsburgh Penguins and Philadelphia Flyers performed "O Canada" Wednesday evening in sympathy and support for America's neighbor to the north following the fatal shooting near Canada's parliament in Ottawa.
Interested in ? Add as an interest to stay up to date on the latest news, video, and analysis from ABC News. Add Interest
Jeff Jimerson sang βO Canada,β with fans at Pittsburghβs Consol Energy Center joining him. The Canadian national anthem isnβt normally performed in games between two United States teams.
The shooting -- which left a Canadian soldier dead -- led to the cancellation of Wednesdayβs game between the Toronto Maple Leafs and Ottawa Senators in Ottawa.
The song struck a chord for Penguins and Flyers players and coaches, many of whom grew up in Canada.
βI thought it was a special tribute tonight," said Penguins coach Mike Johnston, who was born in Nova Scotia and has coached throughout Canada. "Certainly, when those events happen, they strike everybody."
The Associated Press contributed to this report.[/INST]β The Pittsburgh Penguins and their fans offered a nice show of support to Canada last night before a game against Philadelphia. Hours after a gunman attacked the Parliament in Ottawa, fans joined along in the singing of O Canada as the Canadian flag was projected on the ice, reports ABC News. The Canadian anthem typically isn't sung when a game features two US teams, but the Penguins decided to make an exception. It caught the attention of Canadian Prime Minister Stephen Harper, notes the Pittsburgh Post-Gazette. "I think we were all as Canadians touched by the wonderful gesture shown last night at the Pittsburgh Penguins hockey game," he said. "So thank you to our friends in the United States and around the world."</s> |
a triangulation of a manifold can be given a geometric structure by assigning compatible geometric structures to its component simplices .
one of the easiest ways of doing this is to assign constant curvature geometries to the simplices , as these simplices are uniquely determined by their edge lengths .
such a structure gives a finitely parametrized set of geometric structures on a closed manifold . in thurston s formulation of the discrete riemann mapping problem ( see @xcite ) as well as in applied methods such as discrete exterior calculus ( see , e.g. , @xcite , @xcite ) , it is important to not only have a piecewise constant curvature metric assigned to simplices , but also to give a structure to the poincar dual of the triangulation .
such structures arise naturally as incircle duals in thurston s formulation of circle packings and as circumcentric duals in discrete exterior calculus . for piecewise euclidean surfaces and 3-manifolds , in @xcite and @xcite
the first author gives an axiomatic treatment of geometric duality structures that have orthogonal intersections with the primal simplices , and also relates these to discrete conformal variations .
the goal of the present work is to make precise the parametrization of duality structures by partial edge lengths ( giving a discrete analogue of a riemannian metric ) , define the general form of discrete conformal structures based on an axiomatic development related to conformal variation of angle , and derive a local classification of such structures .
the relationship between duality structures and discrete metrics requires some understanding of possible geometric centers for triangles , leading to the definition of the span of a triangle as the space of possible geometric centers
. the axiomatic development of conformal structure follows that in @xcite for piecewise euclidean surfaces , while the construction in piecewise hyperbolic and spherical surfaces is new .
the general formulas for angle and curvature variation of piecewise hyperbolic and spherical surfaces is new ( however , see the parallel work in @xcite ) , generalizing circle packings and other discrete conformal structures previously studied by many authors ( see section [ sec : previous formulations ] for details ) .
the local classification of discrete conformal structures , giving explicit formulas for the structures , is new for each geometry including euclidean .
we will begin by making these geometric structures precise , and then give precise statements of the main results . in this section ,
we make precise some geometric structures .
a triangulated manifold @xmath0 is a topological manifold @xmath1 together with a triangulation @xmath2 of @xmath1 .
a ( triangulated ) _ piecewise constant curvature manifold _ @xmath3 _ with background geometry @xmath4 _ is a triangulated manifold @xmath0 together with a function @xmath5 on the edges of the triangulation such that each simplex can be embedded in @xmath4 , a space of constant curvature , as a ( nondegenerate ) simplex with edge lengths determined by @xmath5 . when the background geometry is euclidean ( @xmath6 ) , hyperbolic ( @xmath7 ) , or spherical ( @xmath8 ) , we call such a manifold _ piecewise flat _ , _ piecewise hyperbolic _ , or _ piecewise spherical _ , respectively .
when the background geometry is clear from context , we may omit it . note
that part of the definition is that the simplices are nondegenerate ; this places inequality restrictions on the possible edge lengths .
for instance , in euclidean background the restrictions can be derived from cayley - menger determinants .
we will use @xmath9 to denote the vertices in triangulation @xmath2 and label them with numbers or letter such as @xmath10 .
we will use @xmath11 to denote edges and label them as a set of vertices @xmath12 , although most of this work could allow multiple edges between the same vertices or edges between the same vertex .
we will use @xmath13 to denote oriented edges and label them with ordered pairs @xmath14 .
triangles will be denoted as a set of vertices , such as @xmath15 . in a piecewise constant curvature manifold , the angle at vertex @xmath16 in a triangle @xmath15
will be denoted @xmath17 .
the set of real valued functions on @xmath18 or @xmath19 will be denoted by @xmath20 and @xmath21 , respectively .
we will use @xmath22 to mean that @xmath23 is a subsimplex of @xmath24 .
the idea of a duality structure is that , in addition to the metric structure of a piecewise constant curvature manifold , we can put a geometric structure on the poincar dual cell complex by introducing geometric centers for pieces of the dual complex .
motivated by the euclidean background case , we see that these geometric centers do not have to be constrained to the simplex , but its affine span . in the more general constant curvature case
, we will need an analogue of the affine span that defines the space of possible simplex centers .
since a piecewise constant curvature manifold is subdivided by simplices that can be embedded into the space @xmath4 , each simplex @xmath25 has a span defined as follows .
first we need to define the underlying space of the span in each geometry . given a constant curvature geometry @xmath4 , we define @xmath26 as follows : * if @xmath27 then we take @xmath26 to be the underlying space @xmath28 . *
if @xmath29 then we take @xmath26 to be the entire space of the klein model , also described as the extended hyperbolic plane in @xcite .
note that in this case , @xmath30 .
* if @xmath31 then we take @xmath26 to be the quotient @xmath32 of the sphere .
we note the following easy facts about @xmath26 . * in each case , the isometry group of @xmath4 acts on @xmath26 .
* in each case , there is a notion of orthogonality between two vectors , induced from the euclidean dot product in the cases of euclidean space and the sphere , and the lorentzian bilinear product using the hyperboloid model of hyperbolic space and projecting to the klein model space . * in each case , any two points in @xmath26 can be connected by a line . in
what follows , we will assume that any simplex modeled on geometry @xmath4 can be isometrically embedded into @xmath26 , and that embedding is unique up to isometry of @xmath4 .
note that , in the case of spherical geometry , the fact that a simplex embeds is a restriction on how big it can be .
we are now ready to define the span . given a simplex @xmath25 and an isometric embedding @xmath33 , the _ span of @xmath25 under @xmath34 _ , denoted @xmath35 , is the set @xmath36 where @xmath37 is the line through the points @xmath38 and @xmath39 .
the _ span of @xmath25 _ , denoted @xmath40 , is the quotient space obtained from the disjoint union @xmath41 by identifying each pair of summands @xmath35 and @xmath42 by an isometry of @xmath4 that agrees with @xmath43 .
we remark that our definition is analogous to the definition of affine span in polytope theory ( c.f . , @xcite ) .
in both definitions , the span is viewed as a ( geodesic ) hyperplane tangent to the simplex / polytope - face as it sits in the ambient geometry .
the span has the property that for any points @xmath44 and @xmath45 , there is a unique line between @xmath46 and @xmath47 in @xmath48 .
the span also has the property that if @xmath49 then there is a natural way in which @xmath50 .
suppose @xmath3 is a piecewise constant curvature manifold with background geometry @xmath4 .
a _ duality structure _ for @xmath0 is a choice of one point @xmath51
\in s\sigma$ ] from each simplex @xmath25 of @xmath2 , subject to : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ if @xmath52 then for any simplex @xmath53 , c[\sigma^{\ell+1 } ] , \ldots , c[\sigma^k]\}$ ] , we have that @xmath54 is orthogonal to @xmath55 intersecting only at @xmath56 $ ] .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we say a duality structure is _ proper _ if it has euclidean or spherical background or has hyperbolic background and the center of each edge is in @xmath57
. notice that in the case of spherical background , the centers lie in @xmath32 and so correspond to two points in @xmath58 .
we will often consider the span as @xmath58 with pairs of points instead of @xmath32 .
proper duality structures are ones such that edge centers are determined by signed distances from the vertices , as determined by the partial edge lengths in the next section . in general
, we will denote the center of edge @xmath59 by @xmath60 and the center of triangle @xmath15 by @xmath61 .
these centers determine edge heights . given a proper duality structure on a triangle @xmath15 , each edge @xmath59 has a corresponding edge height @xmath62 determined by one of the following : * if the center @xmath61 is in the same half plane determined by the span @xmath63 as the simplex @xmath15 is , @xmath62 is the distance between @xmath60 and @xmath61 . * if the center @xmath61 is not in the same half plane determined by the span @xmath63 as the simplex @xmath15 is , @xmath62 is the negative of the distance between @xmath60 and @xmath61 . *
if the center @xmath61 is in @xmath64 but not in @xmath57 , then the height is the distance from @xmath60 to @xmath65 ( see section [ section : hyperbolic basics ] ) with the same sign convention . the definition of duality structure requires choosing centers . for a more explicit parametrization , we will try to adjust the metric structure @xmath5 in some way to ensure a duality structure .
this is the role of metrics and pre - metrics .
the notion of a pre - metric is to reassign parts of the length function to the vertices .
this is motivated partly by the definition of riemannian metrics as tensor valued functions of the points of a manifold .
[ def : pre - metric ] let @xmath66 be a triangulated manifold .
pre - metric _ is an element @xmath67 such that @xmath68 is a piecewise constant curvature manifold with background geometry @xmath4 for the assignment @xmath69 for every edge @xmath70 the @xmath71 are sometimes called partial edge lengths , since one considers the edge @xmath59 divided into two partial edges of length @xmath71 and @xmath72 .
if the partial edge lengths are nonnegative , there is a point on the edge that is distance @xmath71 from vertex @xmath16 and distance @xmath72 from vertex @xmath73 , and this point is called the edge center .
note that if one of the partial edge lengths is negative , there is an interpretation in terms of signed distance , and there is still a center , this time on the span of the edge .
we would like to restrict pre - metrics to those that generate geometries on the poincar dual structure such that dual and primal cells intersect orthogonally .
if one considers the point @xmath60 on the span of an edge @xmath59 that is distance @xmath71 from vertex @xmath16 and @xmath72 from vertex @xmath73 ( distance can be considered with sign so one partial edge length can be negative ) , a center is determined .
one can consider the plane orthogonal to the span s@xmath59 through @xmath60 , and use the intersections of these planes to construct more centers ( e.g. , if the planes of the three edges of a triangle intersect at a point then we use that point as the center of the triangle ) .
this construction is explained in detail for euclidean background in @xcite .
we wish to characterize which conditions on the pre - metrics guarantee that these centers exist and give a duality structure .
we call these metrics , and the actual motivations for the following definitions are characterization theorems given later . the main advantage of metrics over duality structures is that the metrics entirely parametrize the geometry , and so the space of metrics is relatively easy to describe .
[ def : metric ] a _ discrete metric _ , or _
, on @xmath74 with background geometry @xmath4 is a pre - metric @xmath75 such that for every triangle @xmath76 in @xmath2 , @xmath77 a _ piecewise constant curvature , metrized manifold _
@xmath78 with background geometry @xmath4 is a triangulated manifold @xmath74 together with a metric @xmath75 .
we denote the space of all metrics with background geometry @xmath4 on a given triangulated manifold @xmath66 by @xmath79 .
note that the space of metrics @xmath79 on a finite triangulation is determined as a subset of @xmath80 by a number of equalities of the form above ( one for each triangle ) and a number of inequalities ( to ensure the simplices are nondegenerate ) .
a discrete conformal structure is a particular way of determining the metric from information assigned to points ( vertices ) .
it is partly motivated by this characterization of conformal change of a riemannian metric , and also by thurston s formulation of conformal circle packing structure .
a general formulation for euclidean background is described in @xcite , and there are a number of formulations of specific cases of analogous structures in hyperbolic and spherical backgrounds ( see section [ sec : previous formulations ] ) . based on propositions [ prop : euclidean compatibility ] ,
[ prop : hyperbolic compatibility ] , and [ prop : spherical compatibility ] , if we suppose that the pre - metric is determined by weights on the vertex endpoints , there is a restriction that ensures that the resulting pre - metric is actually a discrete metric , i.e. , it determines a duality structure .
in addition , we want conformal structures to have nice formulas for angle variations .
this motivates the following definition .
[ def : conformal structure ] a _ discrete conformal structure _ @xmath81 on a triangulated manifold @xmath74 with background geometry @xmath4 on an open set @xmath82 is a smooth map@xmath83 such that if @xmath84 $ ] then for each @xmath85 and @xmath86 , @xmath87 and @xmath88 if @xmath89 and @xmath90 .
a _ conformal variation _ of a metric @xmath91 $ ] is the change of the metric in the conformal class as @xmath92 changes , and is determined by derivatives such as @xmath93 .
we have chosen the parameter @xmath92 so that the variation formulas above are as simple as possible .
however , we will sometimes choose to parametrize the structures differently ( see theorem [ thm : functional ] ) . also note that with conformal variations , the choice of the set @xmath94 is not particularly important ; we only need the existence of a neighborhood around any point in @xmath94 . in this paper
, we study the relationships between duality structures , discrete metrics , and conformal variations .
the main new contributions are the following : ( 1 ) a characterization of duality structures in hyperbolic and spherical backgrounds , generalizing the notion of length structures arising from circles with given radii and inversive distances , ( 2 ) calculation of the conformal variation of angles in a triangle for hyperbolic and spherical backgrounds together with determining a functional making the curvature variational , and ( 3 ) a classification theorem for discrete conformal variations of euclidean , hyperbolic , and spherical triangles , including the formulation of the notion of discrete conformal variations from basic principles .
the following theorem characterizes duality structures on surfaces in each of the constant curvature backgrounds .
[ thm : duality equals metric ] let @xmath3 be a piecewise constant curvature 2-manifold .
there is a one - to - one correspondence between proper duality structures on @xmath3 and discrete metric structures on @xmath3 .
this theorem follows from propositions [ prop : euclidean compatibility ] , [ prop : hyperbolic compatibility ] , and [ prop : spherical compatibility ] .
the following theorem gives the variation of angle formulas .
the euclidean result is in @xcite , and the hyperbolic and spherical results are new ( compare @xcite ) .
[ thm : angle variation ] for any conformal variation of a metric @xmath91 $ ] with background geometry @xmath4 of a surface @xmath95 , we have for any edge @xmath59 the following formulas .
* in euclidean background , @xmath96 * in hyperbolic background , @xmath97 where @xmath98 is 1 if @xmath61 is timelike and -1 if @xmath61 is spacelike . *
in spherical background , @xmath99 this theorem follows from theorems [ thm : euclidean variation angle ] , [ thm : hyperbolic angle variation ] , and [ thm : spherical angle variation ] together with propositions [ prop : hyperbolic area deriv ] and [ prop : sphere area var ] .
it turns out that although the variables @xmath92 for the conformal variations are quite natural , a change of variables gives that the curvatures are the gradient of a functional , where the curvatures are defined as @xmath100 for each vertex @xmath16 , where the sum is over all triangles containing @xmath16 .
[ thm : functional ] consider a piecewise constant curvature , metrized 2-manifold @xmath101 , where @xmath102 is determined by a conformal structure .
there is a change of variables @xmath103 such that @xmath104 and hence if we fix a @xmath105 there is a functional @xmath106 with the property that @xmath107 furthermore , if all @xmath108 and @xmath109 and then this function is strictly convex if @xmath7 and weakly convex ( strictly convex except for scaling ) if @xmath6 .
this theorem follows from theorems [ thm : euclidean functional ] , [ thm : hyp functional ] , and [ thm : sphere functional ] .
the following theorems classify discrete conformal variations in each of the constant curvature backgrounds .
the results are new for all background geometries .
[ thm : conformal classification ] let @xmath110 be a discrete conformal class with background geometry @xmath4 on a surface @xmath1 .
then there exist @xmath111 and @xmath112 such that the conformal structure can be written as @xmath113 with @xmath114 if @xmath6 , @xmath115 with @xmath116 if @xmath7 , or @xmath117 with @xmath118 if @xmath8 .
this theorem is proven in each case in sections [ section : eucl conf classify ] , [ section : hyp conf classify ] , and [ sec : sphere ] . in light of theorem
[ thm : conformal classification ] , one can also calculate angle variations from theorem [ thm : angle variation ] based on the conformal structures determined by @xmath119 and @xmath120 .
these conformal structures are sometimes referred to as @xmath121 ( see , e.g. , @xcite ) . in this section
we briefly compare our parametrizations with other parametrizations of certain discrete conformal structures .
the formulation in this paper unifies the previous work into a single formula for each background geometry and generalizes some of these .
independently , @xcite derived a formula for the variation of angle that is essentially the same as ours , though we express it and prove it in a different way .
we note that the euclidean background case was treated in @xcite , which also describes the relationship of the general case to previous formulations .
the first formulation of the circle packing conformal structure ( corresponding , in our notation , to @xmath122 and @xmath123 for all vertices and edges ) is in thurston s work @xcite .
many of the relevant calculations are followed through in @xcite , and the first variational formulation is due to colin de verdire in @xcite . in each of these cases ,
the euclidean and hyperbolic cases were treated , and the conformal structures were either circles with given intersection angles between @xmath124 and @xmath125 ( corresponding , in our notation , to @xmath122 and @xmath126 for all vertices and edges ) .
additional work was done by chow - luo in @xcite .
the case of circles with fixed inversive distances ( corresponding , in our notation , to @xmath122 and @xmath127 for all vertices and edges ) was introduced by bowers and stephenson @xcite and the variational perspective was pursued by guo in @xcite ( this was anticipated by springborn s work on volumes of hyperideal simplices in @xcite ) .
the multiplicative conformal structure ( corresponding , in our notation , to @xmath128 for all vertices ) was apparently first suggested in @xcite , but most of the mathematical ideas arose in work of luo @xcite and springborn - schrader - pinkall @xcite in the euclidean case .
generalizing to the hyperbolic case was not obvious , but work in this direction first appeared in work by bobenko - pinkall - springborn @xcite .
it is notable that the proper parametrization variable is not clear in this case , and this issue is discussed in section [ subsect : variational hyp ] .
the unified case for euclidean background is given in @xcite and the hyperbolic case was first described in this paper and independently in @xcite . for more on some of these discrete conformal structures , see the books @xcite , @xcite , and @xcite .
explicit calculation of the variation of angle coefficients in the euclidean circle packing case is due to z. he @xcite , and followed by the first author in @xcite .
the coefficients are closely related to the discrete laplacians found in @xcite , @xcite , @xcite , @xcite , @xcite @xcite , @xcite , @xcite , @xcite , @xcite , and many other places .
there are close connections between these variational viewpoints and hyperbolic volumes , as evidenced by work of brgger @xcite , rivin @xcite , garret @xcite , leibon @xcite , bobenko - springborn @xcite , springborn @xcite , springborn - schrder - pinkall @xcite , and bobenko - pinkall - springborn @xcite , fillastre - izmestiev @xcite , and zhang et .
al . @xcite .
some of this work was generalized to discrete conformal structures in three dimensions by cooper - rivin in @xcite and the first author in @xcite and @xcite .
while the functionals whose variations lead to curvatures in two dimensions are possibly related to the log determinant of the laplacian and surface entropy ( see @xcite ) , in three dimensions the functional is related to regge s formulation of the einstein - hilbert ( total scalar curvature ) functional .
see , e.g. , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite .
clearly , the choice of a pre - metric with euclidean background determines the geometry of each triangle @xmath15 and for any isometric embedding , specifies the triangle s sides @xmath129 with lengths @xmath130 . through each finite edge @xmath131 of the triangle we have a unique line @xmath132 , considered in @xmath133 .
suppose we identify @xmath132 with the real number line such that @xmath134 is at the origin and @xmath135 is on the positive @xmath46 axis .
given these coordinates , we specify the edge centers @xmath136 to be the point @xmath71 on the line .
note that @xmath72 denotes the distance between @xmath60 and @xmath135 , considered with a sign determined by which side of @xmath135 in @xmath132 contains @xmath60 . for each edge @xmath59
, there exists a unique line @xmath137 that passes through @xmath60 and is orthogonal to @xmath132 . in @xcite ( proposition 4 ) , the first author presented a necessary and sufficient condition on the partial edges to guarantee the three lines @xmath138 meet at a single point : [ prop : euclidean compatibility ] suppose @xmath139 is a euclidean pre - metric .
then the perpendiculars @xmath138 meet at a single point if and only if @xmath140 this motivates the euclidean case of definition [ def : metric ] and proves the euclidean case of theorem [ thm : duality equals metric ] .
the conformal structure is defined in such a way as to give the following variational formula .
[ thm : euclidean variation angle ] given a conformal structure , we have @xmath141 if @xmath142 and @xmath143
this theorem is proven in @xcite , generalizing the theorems in special cases given in @xcite and @xcite .
it follows easily ( see , e.g. , @xcite ) that the curvature is variational with respect to a convex functional .
[ thm : euclidean functional ] the partial derivatives of the angles in a triangle are symmetric , i.e. , @xmath144 and hence if we fix a @xmath145 there is a functional @xmath146 with the property that @xmath147 furthermore , if all @xmath108 and @xmath109 and then this function is weakly convex ( strictly convex except for scaling ) . in this section
we prove the characterization theorem .
recall that the only assumptions are : * the compatibility condition [ d - euclidean condition ] for the triangle with vertices @xmath134 , @xmath135 , and @xmath148 .
* the assumption that @xmath71 depends only on @xmath149 and @xmath150 .
we first note that @xmath151 and that @xmath152 since for any triangle with vertices @xmath153 we have @xmath154 we can compute that @xmath155 since @xmath156 it follows that @xmath157 and so it follows that @xmath158 and @xmath159 we can solve these equations , getting @xmath160 for constants @xmath161 and @xmath162 hence @xmath163 we can now use ( [ l deriv ] ) to find that for a constant @xmath164 @xmath165 from this , we compute that @xmath166 we note that in a triangle , since @xmath167 and the right side is independent of @xmath168 differentiating with respect to @xmath169 gives @xmath170 and hence @xmath171 and @xmath172 is independent of the edge , only depending on the vertex , hence we rename @xmath173 to see that the @xmath174 and @xmath164 must be consistent across triangles , consider equation [ eqn : l - eucl ] on both triangles and differentiate with respect to @xmath149 and @xmath150 to see that the @xmath164 agree and then @xmath149 to see that the @xmath174 agree .
before we move to the hyperbolic versions of the previous work , we will review some techniques for computing in hyperbolic geometry .
this section summarizes the elementary facts about the hyperbolic plane @xmath57 that we will use in later calculations .
all of the propositions in this section are discussed in chapter 3 of @xcite .
see also @xcite . for the reader
s convenience , we have included some , but not all , proofs .
we use the hyperboloid model of @xmath57 for the majority of our calculations . in this model ,
the vector space @xmath175 is equipped with a lorentzian inner product @xmath176 given by @xmath177 where @xmath178 is the diagonal matrix with entries 1,1,-1 .
we define a `` hyperbolic magnitude '' @xmath179 ; the only possible hyperbolic lengths are nonnegative scalar multiples of 1 and @xmath16 .
@xmath57 corresponds to those vectors @xmath180 satisfying @xmath181 and @xmath182 .
a vector @xmath183 is termed _ spacelike _ if @xmath184 , _ lightlike _ ( or `` on the light cone '' ) if @xmath185 , and _ timelike _ if @xmath186 .
the vector space structure on @xmath187 gives us several ways to describe a geodesic in @xmath57 : * as a nonempty intersection @xmath188 for linearly independent @xmath189 .
* as a nonempty intersection @xmath190 , where @xmath38 is a spacelike vector and @xmath191 .
* as a path , parametrized by arclength , given by @xmath192 . in this form , @xmath193 , @xmath194 with @xmath195
note @xmath38 and @xmath196 encode the position and direction of @xmath197 at @xmath198 .
the second characterization becomes particularly useful when combined with the lorentzian cross product , which is given by @xmath199 . clearly , the lorentzian cross product has two useful properties : * @xmath200 if and only if @xmath38 and @xmath39 are linearly dependent .
* @xmath201 is @xmath176-orthogonal to both @xmath38 and @xmath39 .
a consequence of the second observation is that given distinct points @xmath202 , one simple way to describe the geodesic through @xmath38 and @xmath39 is @xmath203 . in the sequel
, we will use @xmath204 to denote the hyperbolic distance between two timelike points , and @xmath205 to denote the hyperbolic distance between a timelike point and a geodesic in hyperbolic space determined as the orthogonal complement of a spacelike point .
when @xmath206 satisfy @xmath207 , we have the following interpretations of the quantity @xmath208 : * if @xmath209 and @xmath196 are both timelike , then @xmath210 . *
if @xmath209 is timelike and @xmath196 is spacelike , then @xmath211 and the sign depends upon which of the halfspaces bounded by @xmath212 contains @xmath209 . * if @xmath209 and @xmath196 are both spacelike and @xmath213 and @xmath212 intersect in angle @xmath119 within @xmath57 , @xmath214 .
notice that the last item implies that for spacelike @xmath209 and @xmath196 , @xmath213 and @xmath212 meet at a right angle if and only if @xmath215 .
the following identities simplify calculations that involve lorentzian cross products .
suppose @xmath216 : @xmath217 we have already seen that several different kinds of data can be used to specify a geodesic on @xmath57 .
this allows us to extend our understanding of where geodesics intersect .
[ definition intersection ] given a geodesics @xmath197 on @xmath57 , we will identify @xmath197 with the unique 2-dimensional subspace @xmath218 of @xmath175 such that @xmath219 is the image of @xmath197 . given geodesics @xmath220 on @xmath57
, we define their _ intersection _ to be their intersection as subspaces of @xmath175 , namely @xmath221 .
readers familiar with the klein model of @xmath57 ( the central projection of @xmath57 onto the plane @xmath222 ) should note that this definition is simply a linear - algebraic way of formulating the notion of intersecting 1-hyperplanes in the klein model .
introducing a broader notion of intersection allows us to generalize familiar equations ( like the law of cosines ) and express them in terms of linear algebra . understanding how to interpret the lorentzian inner product is key to relating these different formulas .
often , the linear algebraic interpretation allows us to efficiently treat several seemingly different cases at once .
recall the definition of a triangle ( see section 3.5 in @xcite ) , which allows some of the vertices to be timelike , lightlike , or spacelike .
we will concentrate on triangles with at least two timelike vertices .
[ proposition ratcliffe triangles ] suppose @xmath223 and @xmath224 are either timelike or spacelike
. then @xmath225 where @xmath119 is the angle at @xmath46 in the ( clockwise oriented ) triangle @xmath226 .
[ proposition generalized law of cosines ] suppose @xmath227 , with @xmath228 and @xmath229 or @xmath16 , are the vertices of a triangle in @xmath57 , with angle @xmath119 at @xmath46 .
then @xmath230 assume , without loss of generality , that @xmath231 label the vertices of the triangle in clockwise order .
equation [ eqn : det formula ] implies @xmath232 now apply proposition [ proposition ratcliffe triangles ] to obtain the desired equality . by setting @xmath233
, we obtain a generalized version of the pythagorean theorem : suppose @xmath231 are the vertices of a right triangle , with the right angle at @xmath46 .
then : @xmath234 we will require formulas for performing trigonometry in a hyperbolic right triangle where one of the vertices ( not the one adjacent to the right angle ) may be spacelike or timelike .
suppose we have a right triangle labeled like the one in figure [ fig : right triangle ] .
[ prop : trig ] given a triangle labeled as in figure [ fig : right triangle ] , we have : @xmath235 if @xmath236 is timelike and @xmath237 if @xmath236 is spacelike .
deriving these formulas is an easy application of the generalized pythagorean theorem and the generalized law of cosines .
the next corollary generalizes the familiar formula for the cosine of an angle in a hyperbolic right triangle .
[ corollary cosine right triangle ] suppose @xmath231 are the vertices of a right triangle ( with the right angle at @xmath238 ) satisfying the assumptions of proposition [ proposition generalized law of cosines ] .
then @xmath239 the right angle at @xmath238 means that : @xmath240 and so @xmath241 substituting this into the equation we obtain from the law of cosines , we learn : @xmath242 using equation [ eqn : det formula ] , it is easy to check @xmath243 .
hence : @xmath244 because the lorentzian inner product is nondegenerate , we have a well defined notion of @xmath176-orthogonality and may apply the gram - schmidt procedure to obtain a basis of mutually @xmath176-orthogonal vectors .
this procedure can be used to parametrize a geodesic given in the form @xmath188 by arclength .
[ proposition gram - schmidt ] suppose @xmath193 , and @xmath245
. then the geodesic @xmath246 may be parametrized by arclength as : @xmath247 the geodesic in question can be parametrized by arclength as @xmath248 for some spacelike @xmath196 with @xmath249 ; we simply need to use the gram - schmidt procedure to guarantee that @xmath250 and @xmath194 .
so consider the vector @xmath251 .
notice @xmath252 is the @xmath176-projection of @xmath39 onto the subspace spanned by @xmath38 , and @xmath253 to find @xmath196 , we only need to rescale this projection .
since @xmath254 the appropriate @xmath196 is @xmath255
we interpret a piecewise hyperbolic pre - metric as subdividing each edge @xmath59 of length @xmath256 into two portions of length @xmath257 and @xmath258 , that are assigned to the vertices @xmath16 and @xmath73 respectively .
[ def : edge centers ] given a pre - metric @xmath75 and an isometric embedding of a simplex @xmath59 into @xmath57 : * the _ vertices _ @xmath259 of @xmath59 are the images of @xmath16 and @xmath73 under the embedding . *
the _ edge center @xmath60 induced by @xmath75 _ is the unique point along the line @xmath132 through @xmath260 and @xmath261 such that @xmath60 is ( signed ) distance @xmath71 from @xmath260 and @xmath72 from @xmath261 . *
the _ edge perpendicular @xmath137 _ is the line through @xmath60 that is orthogonal to @xmath132 . unlike in the euclidean setting
, it is possible that the geodesics @xmath137 and @xmath262 do not intersect within @xmath57 . however , these two 1-hyperplanes can be understood as intersecting in the more general sense of definition [ definition intersection ] , namely the two - dimensional subspaces of @xmath187 associated to @xmath137 and @xmath262 intersect in a one - dimensional subspace .
one can then ask for necessary and sufficient conditions on the pre - metric that guarantee that for each simplex @xmath15 @xmath263 or , colloquially , the three perpendiculars of @xmath15 intersect in a single point ( this point is in the span of @xmath15 ) .
this condition can also be interpreted in the klein model of hyperbolic space as the condition that the three lines representing the geodesics intersect at the same point in the plane of the klein model . [
prop : hyperbolic compatibility ] suppose @xmath75 is a piecewise hyperbolic pre - metric .
equation [ eqn : duality intersections ] holds if and only if the following _ compatibility equation _
@xmath264 is satisfied for every simplex @xmath15 .
since the vectors @xmath260 and @xmath60 are timelike of length -1 , equation [ eqn : dijhyp - reln ] has the following equivalent formulation : @xmath265 to simplify our notation , we shall consider a single 2-simplex @xmath266 .
the vertices of the embedded 2-simplex are linearly independent vectors @xmath267 .
consider that if @xmath268 is a point on the perpendicular @xmath137 , then @xmath269 .
likewise the span of edge @xmath131 is given by @xmath270 .
since @xmath60 belongs to both @xmath137 and @xmath131 , the fact that @xmath137 and @xmath131 are perpendicular is equivalent to the equation : @xmath271 identities [ eqn : cross product ident1]-[eqn : det formula ] imply this is equivalent to the equation : @xmath272 hence , equation [ eqn : duality intersections ] holds for simplex @xmath266 if and only if there is a nontrivial solution @xmath268 to the system : @xmath273 this system can be reformulated as a matrix equation @xmath274 that has a nontrivial solution if and only if the determinant of the first matrix is zero .
expanding that determinant and canceling the ( nonzero ) factors of @xmath275 that arise yields equation [ eqn : dijhyp - reln ] .
the last statement follows easily .
this proposition motivates the hyperbolic case of definition [ def : metric ] .
one can gain insight into how the euclidean and hyperbolic compatibility conditions are related by comparing equation [ d - euclidean condition ] and equation [ d - hyperbolic condition ] for small @xmath71 in the same way one compares the euclidean pythagorean theorem with the hyperbolic version , @xmath276 .
various formulations of conformal variations of hyperbolic triangulations of surfaces have been studied in @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite .
we present a unified approach from the perspective of the metric triangulations as defined above .
suppose we wanted to generate a metric from weights assigned to vertices , so that @xmath277 for some function @xmath92 on the vertices .
if this our starting point for conformal structure , in order to compute conformal variations , we will consider what happens to the metric on a triangle @xmath266 when the conformal parameter @xmath278 changes but the other two do not , i.e. , @xmath279 .
we will call this a @xmath278-conformal variation in this section .
the next two propositions analyze the configuration shown in figure [ figure conformal variation ] .
we assume throughout that @xmath280 are linearly independent in @xmath175 , with @xmath281 .
[ prop : inner product identities ] under an @xmath278-conformal variation : @xmath282 bilinearity of the lorentzian inner product implies : @xmath283 however , since @xmath284 , we can also write : @xmath285 hence @xmath286 we get the formula for @xmath287 similarly .
finally , since @xmath288 : @xmath289 the following proposition makes precise what we mean by the colloquial statement that conformal variations give good angle variations .
[ prop : conformal line ] let @xmath290 denote the center of the triangle specified by the vertices @xmath134 and the ( compatible ) partial edge lengths @xmath71 .
suppose further that the edge centers on edges @xmath291 and @xmath292 are timelike . then under a @xmath278-conformal variation ,
the points @xmath293 and @xmath290 lie on a line in @xmath57 if and only if @xmath294 , for some function @xmath295 . without loss of generality ,
assume @xmath296 .
consider the geodesic through @xmath297 and @xmath290 .
as a set , this geodesic can be described by @xmath298 , a characterization we will use to parametrize the geodesic by arclength as @xmath299 for some @xmath300 . specifically , proposition [ proposition gram - schmidt ] implies : @xmath301 the points @xmath293 , and @xmath290 lie on a geodesic if and only if @xmath209 and @xmath302 are collinear .
the three numbers @xmath303 completely characterize the vector @xmath304 . hence , @xmath209 and @xmath302 are collinear if and only if there exists @xmath305 such that @xmath306 for @xmath307 .
we already know @xmath308 , so only @xmath309 and @xmath310 require consideration .
consider our equation for @xmath209 .
the scalar in the denominator will appear in both @xmath309 and @xmath310 . to simplify our notation ,
we will write @xmath311 . now @xmath312 and we can apply the generalized law of cosines ( proposition [ proposition generalized law of cosines ] ) to the triangle @xmath313 in order to rewrite this equation as @xmath314 next consider the right triangle with vertices @xmath315 . by corollary [ corollary cosine right triangle ]
, we have @xmath316 a final substitution into our equation for @xmath309 implies @xmath317 a similar argument for @xmath318 yields @xmath319 from proposition [ prop : inner product identities ] , we know that for @xmath320 @xmath321 comparing these two equations , we see that there exists @xmath322 so that @xmath323 if and only if there exists a smooth function @xmath324 for which @xmath325 .
proposition [ prop : conformal line ] motivates the hyperbolic case of definition [ def : conformal structure ] , where we have chosen to simplify to parameters that make @xmath326 equal to the constant function @xmath327 .
we will now study how the angles change under a conformal variation .
first we see the following .
[ thm : hyperbolic angle variation ] given a conformal structure , then for any simplex @xmath15 @xmath328 where @xmath98 is 1 if @xmath61 is timelike and -1 if @xmath61 is spacelike . for simplicity , we shall consider the problem for a single simplex @xmath266 labeled as in figure [ figure conformal variation ] , with @xmath329 , @xmath330 . we will address the case where @xmath290 is timelike ; the case where @xmath290 is spacelike is similar .
once [ eqn : angle variation ij thmcopy ] is proven , [ eqn : angle variation ii thmcopy ] follows immediately because of the area formula for a hyperbolic triangle : @xmath331 because the variation is conformal , @xmath332 . using the formula for a segment of a circle in the hyperbolic plane
, we have @xmath333 . by proposition [ prop : conformal line ] , under a conformal variation @xmath334 and @xmath290 are collinear .
consequently , the angle adjacent to @xmath297 in the triangle with side lengths @xmath335 , @xmath336 and @xmath302 is @xmath337 .
this , together with the formulas in proposition [ prop : trig ] , allows us to write : @xmath338 using the taylor series for @xmath339 and @xmath340 , we have : @xmath341 and hence , @xmath342 we can also compute the variation of area explicitly .
[ prop : hyperbolic area deriv ] given a conformal structure , then for any simplex @xmath15 with area @xmath343 .
@xmath344 in particular , if the derivatives @xmath345 are positive whenever @xmath346 , then the derivative of the area is positive .
this follows from the formula for the area of a sector of circle as a function of the radius for a hyperbolic surface , since in figure [ figure conformal variation ] we find that the area of each of the small triangles is higher order , leaving only the areas of the skinny triangles in the picture .
the proof of the hyperbolic case of theorem [ thm : conformal classification ] is similar to the proof of the euclidean case , though the calculation is a bit harder in hyperbolic background .
we first note the following : @xmath347 a straightforward calculations gives that @xmath348 or if @xmath349 then @xmath350 since @xmath351 it follows that @xmath352 and @xmath353 one can then easily solve this ode to obtain that : @xmath354 for some constant @xmath161 and @xmath355 for some constant @xmath356 .
it follows that @xmath357 we can now use equation [ eq : coshder ] to see that @xmath358 and so we find that @xmath359 and @xmath360 for some constant @xmath164 .
the compatibility condition ( [ d - hyperbolic condition ] ) implies that @xmath361 is independent of @xmath149 and so we can use equation [ eqn : cosh dij by cosh dij ] to see that @xmath171 and so we can define @xmath362 . it follows that @xmath363 finally , we can use equation [ eqn : cosh dij by cosh dij ] again to write @xmath364 in terms of the coefficients determined in the two triangles adjacent to edge @xmath59 and differentiate to see that the @xmath174 derived in each triangle must be equal .
it then follows from equation [ eqn : hyp length ] that the @xmath164 derived in each triangle must be equal as well .
while the formula ( [ eqn : angle variation ij ] ) is not symmetric in @xmath16 and @xmath73 , we can reparametrize to get a symmetric variation formula .
notice that equation [ eqn : cosh dij by cosh dij ] ( recall that we proved @xmath359 ) implies that @xmath365 if we take new coordinates @xmath366 such that @xmath367 then we have the symmetry @xmath368 the function @xmath369 can be computed explicitly .
it is not hard to see that if @xmath128 then @xmath370 and if not then @xmath371 if @xmath372 then this is @xmath373 and if @xmath374 then this is @xmath375 compare to the formulations in @xcite , @xcite , and @xcite .
it then follows that for a triangle @xmath376 the following form is closed : @xmath377 we can now integrate to get a function on the whole triangulation , where we fix some @xmath105 : @xmath378 [ thm : hyp functional ] the function @xmath326 has the property that @xmath107 furthermore ,
if all @xmath108 and @xmath109 then this function is strictly convex .
the first statement follows from the definition .
the second follows from the facts that in a triangle @xmath266 , @xmath379 for @xmath380 since @xmath381 by proposition [ prop : hyperbolic area deriv ] .
it follows that the matrix of partial derivatives is diagonally dominant .
the arguments presented in the case of hyperbolic background geometry can be adjusted for the case of spherical background geometry .
essentially , this occurs because in the hyperbolic case we are studying properties of the lorentzian inner product @xmath176 , while in spherical geometry we study analogous properties of the euclidean inner product .
because the definitions and arguments in the spherical case are so similar to those of previous sections , we will only state the main results in the spherical case .
to work in the spherical case , we work with the usual dot product @xmath382 on @xmath175 .
geodesics on the sphere correspond to planes in @xmath175 and so given a triangle @xmath15 in the sphere and a pre - metric , a given embedding induces planes @xmath137 , etc . through edge centers and
the condition for inducing a duality structure is @xmath383 [ prop : spherical compatibility ] suppose @xmath75 is a piecewise spherical pre - metric . equation [ eqn : spherical duality intersections ] holds if and only if the following _ compatibility equation _ @xmath384 is satisfied for every simplex @xmath15
. equation [ eqn : dij - reln spherical ] has the following equivalent formulation : @xmath385 note that although the heights @xmath62 require choosing one of the two possible centers , the term @xmath387 does not depend on this choice , since choosing the other center leads to heights @xmath388 and so @xmath389 using this theorem and the definition of a spherical conformal structure , one can derive the spherical case of theorem [ thm : conformal classification ] .
as in the hyperbolic case , it is desirable to change from the variables @xmath149 to variables @xmath391 , so that one can recognize that @xmath392 .
the variables @xmath393 are given by @xmath394 j. dai , x. gu , and f. luo .
_ variational principles for discrete surfaces_. advanced lectures in mathematics ( alm ) , 4 . international press , somerville , ma ; higher education press , beijing , 2008 .
iv+146 pp . | a piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry ( euclidean , hyperbolic , or spherical ) , each simplex has an isometric embedding into the background geometry with the chosen edge lengths .
additional structure is defined either by giving a geometric structure to the poincar dual of the triangulation or by assigning a discrete metric , a way of assigning length to oriented edges .
this notion leads to a notion of discrete conformal structure , generalizing the discrete conformal structures based on circle packings and their generalizations studied by thurston and others .
we define and analyze conformal variations of piecewise constant curvature 2-manifolds , giving particular attention to the variation of angles .
we give formulas for the derivatives of angles in each background geometry , which yield formulas for the derivatives of curvatures .
our formulas allow us to identify particular curvature functionals associated with conformal variations .
finally , we provide a complete classification of discrete conformal structures in each of the background geometries . | <s>[INST]a triangulation of a manifold can be given a geometric structure by assigning compatible geometric structures to its component simplices .
one of the easiest ways of doing this is to assign constant curvature geometries to the simplices , as these simplices are uniquely determined by their edge lengths .
such a structure gives a finitely parametrized set of geometric structures on a closed manifold . in thurston s formulation of the discrete riemann mapping problem ( see @xcite ) as well as in applied methods such as discrete exterior calculus ( see , e.g. , @xcite , @xcite ) , it is important to not only have a piecewise constant curvature metric assigned to simplices , but also to give a structure to the poincar dual of the triangulation .
such structures arise naturally as incircle duals in thurston s formulation of circle packings and as circumcentric duals in discrete exterior calculus . for piecewise euclidean surfaces and 3-manifolds , in @xcite and @xcite
the first author gives an axiomatic treatment of geometric duality structures that have orthogonal intersections with the primal simplices , and also relates these to discrete conformal variations .
the goal of the present work is to make precise the parametrization of duality structures by partial edge lengths ( giving a discrete analogue of a riemannian metric ) , define the general form of discrete conformal structures based on an axiomatic development related to conformal variation of angle , and derive a local classification of such structures .
the relationship between duality structures and discrete metrics requires some understanding of possible geometric centers for triangles , leading to the definition of the span of a triangle as the space of possible geometric centers
. the axiomatic development of conformal structure follows that in @xcite for piecewise euclidean surfaces , while the construction in piecewise hyperbolic and spherical surfaces is new .
the general formulas for angle and curvature variation of piecewise hyperbolic and spherical surfaces is new ( however , see the parallel work in @xcite ) , generalizing circle packings and other discrete conformal structures previously studied by many authors ( see section [ sec : previous formulations ] for details ) .
the local classification of discrete conformal structures , giving explicit formulas for the structures , is new for each geometry including euclidean .
we will begin by making these geometric structures precise , and then give precise statements of the main results . in this section ,
we make precise some geometric structures .
a triangulated manifold @xmath0 is a topological manifold @xmath1 together with a triangulation @xmath2 of @xmath1 .
a ( triangulated ) _ piecewise constant curvature manifold _ @xmath3 _ with background geometry @xmath4 _ is a triangulated manifold @xmath0 together with a function @xmath5 on the edges of the triangulation such that each simplex can be embedded in @xmath4 , a space of constant curvature , as a ( nondegenerate ) simplex with edge lengths determined by @xmath5 . when the background geometry is euclidean ( @xmath6 ) , hyperbolic ( @xmath7 ) , or spherical ( @xmath8 ) , we call such a manifold _ piecewise flat _ , _ piecewise hyperbolic _ , or _ piecewise spherical _ , respectively .
when the background geometry is clear from context , we may omit it . note
that part of the definition is that the simplices are nondegenerate ; this places inequality restrictions on the possible edge lengths .
for instance , in euclidean background the restrictions can be derived from cayley - menger determinants .
we will use @xmath9 to denote the vertices in triangulation @xmath2 and label them with numbers or letter such as @xmath10 .
we will use @xmath11 to denote edges and label them as a set of vertices @xmath12 , although most of this work could allow multiple edges between the same vertices or edges between the same vertex .
we will use @xmath13 to denote oriented edges and label them with ordered pairs @xmath14 .
triangles will be denoted as a set of vertices , such as @xmath15 . in a piecewise constant curvature manifold , the angle at vertex @xmath16 in a triangle @xmath15
will be denoted @xmath17 .
the set of real valued functions on @xmath18 or @xmath19 will be denoted by @xmath20 and @xmath21 , respectively .
we will use @xmath22 to mean that @xmath23 is a subsimplex of @xmath24 .
the idea of a duality structure is that , in addition to the metric structure of a piecewise constant curvature manifold , we can put a geometric structure on the poincar dual cell complex by introducing geometric centers for pieces of the dual complex .
motivated by the euclidean background case , we see that these geometric centers do not have to be constrained to the simplex , but its affine span . in the more general constant curvature case
, we will need an analogue of the affine span that defines the space of possible simplex centers .
since a piecewise constant curvature manifold is subdivided by simplices that can be embedded into the space @xmath4 , each simplex @xmath25 has a span defined as follows .
first we need to define the underlying space of the span in each geometry . given a constant curvature geometry @xmath4 , we define @xmath26 as follows : * if @xmath27 then we take @xmath26 to be the underlying space @xmath28 . *
if @xmath29 then we take @xmath26 to be the entire space of the klein model , also described as the extended hyperbolic plane in @xcite .
note that in this case , @xmath30 .
* if @xmath31 then we take @xmath26 to be the quotient @xmath32 of the sphere .
we note the following easy facts about @xmath26 . * in each case , the isometry group of @xmath4 acts on @xmath26 .
* in each case , there is a notion of orthogonality between two vectors , induced from the euclidean dot product in the cases of euclidean space and the sphere , and the lorentzian bilinear product using the hyperboloid model of hyperbolic space and projecting to the klein model space . * in each case , any two points in @xmath26 can be connected by a line . in
what follows , we will assume that any simplex modeled on geometry @xmath4 can be isometrically embedded into @xmath26 , and that embedding is unique up to isometry of @xmath4 .
note that , in the case of spherical geometry , the fact that a simplex embeds is a restriction on how big it can be .
we are now ready to define the span . given a simplex @xmath25 and an isometric embedding @xmath33 , the _ span of @xmath25 under @xmath34 _ , denoted @xmath35 , is the set @xmath36 where @xmath37 is the line through the points @xmath38 and @xmath39 .
the _ span of @xmath25 _ , denoted @xmath40 , is the quotient space obtained from the disjoint union @xmath41 by identifying each pair of summands @xmath35 and @xmath42 by an isometry of @xmath4 that agrees with @xmath43 .
we remark that our definition is analogous to the definition of affine span in polytope theory ( c.f . , @xcite ) .
in both definitions , the span is viewed as a ( geodesic ) hyperplane tangent to the simplex / polytope - face as it sits in the ambient geometry .
the span has the property that for any points @xmath44 and @xmath45 , there is a unique line between @xmath46 and @xmath47 in @xmath48 .
the span also has the property that if @xmath49 then there is a natural way in which @xmath50 .
suppose @xmath3 is a piecewise constant curvature manifold with background geometry @xmath4 .
a _ duality structure _ for @xmath0 is a choice of one point @xmath51
\in s\sigma$ ] from each simplex @xmath25 of @xmath2 , subject to : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ if @xmath52 then for any simplex @xmath53 , c[\sigma^{\ell+1 } ] , \ldots , c[\sigma^k]\}$ ] , we have that @xmath54 is orthogonal to @xmath55 intersecting only at @xmath56 $ ] .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we say a duality structure is _ proper _ if it has euclidean or spherical background or has hyperbolic background and the center of each edge is in @xmath57
. notice that in the case of spherical background , the centers lie in @xmath32 and so correspond to two points in @xmath58 .
we will often consider the span as @xmath58 with pairs of points instead of @xmath32 .
proper duality structures are ones such that edge centers are determined by signed distances from the vertices , as determined by the partial edge lengths in the next section . in general
, we will denote the center of edge @xmath59 by @xmath60 and the center of triangle @xmath15 by @xmath61 .
these centers determine edge heights . given a proper duality structure on a triangle @xmath15 , each edge @xmath59 has a corresponding edge height @xmath62 determined by one of the following : * if the center @xmath61 is in the same half plane determined by the span @xmath63 as the simplex @xmath15 is , @xmath62 is the distance between @xmath60 and @xmath61 . * if the center @xmath61 is not in the same half plane determined by the span @xmath63 as the simplex @xmath15 is , @xmath62 is the negative of the distance between @xmath60 and @xmath61 . *
if the center @xmath61 is in @xmath64 but not in @xmath57 , then the height is the distance from @xmath60 to @xmath65 ( see section [ section : hyperbolic basics ] ) with the same sign convention . the definition of duality structure requires choosing centers . for a more explicit parametrization , we will try to adjust the metric structure @xmath5 in some way to ensure a duality structure .
this is the role of metrics and pre - metrics .
the notion of a pre - metric is to reassign parts of the length function to the vertices .
this is motivated partly by the definition of riemannian metrics as tensor valued functions of the points of a manifold .
[ def : pre - metric ] let @xmath66 be a triangulated manifold .
pre - metric _ is an element @xmath67 such that @xmath68 is a piecewise constant curvature manifold with background geometry @xmath4 for the assignment @xmath69 for every edge @xmath70 the @xmath71 are sometimes called partial edge lengths , since one considers the edge @xmath59 divided into two partial edges of length @xmath71 and @xmath72 .
if the partial edge lengths are nonnegative , there is a point on the edge that is distance @xmath71 from vertex @xmath16 and distance @xmath72 from vertex @xmath73 , and this point is called the edge center .
note that if one of the partial edge lengths is negative , there is an interpretation in terms of signed distance , and there is still a center , this time on the span of the edge .
we would like to restrict pre - metrics to those that generate geometries on the poincar dual structure such that dual and primal cells intersect orthogonally .
if one considers the point @xmath60 on the span of an edge @xmath59 that is distance @xmath71 from vertex @xmath16 and @xmath72 from vertex @xmath73 ( distance can be considered with sign so one partial edge length can be negative ) , a center is determined .
one can consider the plane orthogonal to the span s@xmath59 through @xmath60 , and use the intersections of these planes to construct more centers ( e.g. , if the planes of the three edges of a triangle intersect at a point then we use that point as the center of the triangle ) .
this construction is explained in detail for euclidean background in @xcite .
we wish to characterize which conditions on the pre - metrics guarantee that these centers exist and give a duality structure .
we call these metrics , and the actual motivations for the following definitions are characterization theorems given later . the main advantage of metrics over duality structures is that the metrics entirely parametrize the geometry , and so the space of metrics is relatively easy to describe .
[ def : metric ] a _ discrete metric _ , or _
, on @xmath74 with background geometry @xmath4 is a pre - metric @xmath75 such that for every triangle @xmath76 in @xmath2 , @xmath77 a _ piecewise constant curvature , metrized manifold _
@xmath78 with background geometry @xmath4 is a triangulated manifold @xmath74 together with a metric @xmath75 .
we denote the space of all metrics with background geometry @xmath4 on a given triangulated manifold @xmath66 by @xmath79 .
note that the space of metrics @xmath79 on a finite triangulation is determined as a subset of @xmath80 by a number of equalities of the form above ( one for each triangle ) and a number of inequalities ( to ensure the simplices are nondegenerate ) .
a discrete conformal structure is a particular way of determining the metric from information assigned to points ( vertices ) .
it is partly motivated by this characterization of conformal change of a riemannian metric , and also by thurston s formulation of conformal circle packing structure .
a general formulation for euclidean background is described in @xcite , and there are a number of formulations of specific cases of analogous structures in hyperbolic and spherical backgrounds ( see section [ sec : previous formulations ] ) . based on propositions [ prop : euclidean compatibility ] ,
[ prop : hyperbolic compatibility ] , and [ prop : spherical compatibility ] , if we suppose that the pre - metric is determined by weights on the vertex endpoints , there is a restriction that ensures that the resulting pre - metric is actually a discrete metric , i.e. , it determines a duality structure .
in addition , we want conformal structures to have nice formulas for angle variations .
this motivates the following definition .
[ def : conformal structure ] a _ discrete conformal structure _ @xmath81 on a triangulated manifold @xmath74 with background geometry @xmath4 on an open set @xmath82 is a smooth map@xmath83 such that if @xmath84 $ ] then for each @xmath85 and @xmath86 , @xmath87 and @xmath88 if @xmath89 and @xmath90 .
a _ conformal variation _ of a metric @xmath91 $ ] is the change of the metric in the conformal class as @xmath92 changes , and is determined by derivatives such as @xmath93 .
we have chosen the parameter @xmath92 so that the variation formulas above are as simple as possible .
however , we will sometimes choose to parametrize the structures differently ( see theorem [ thm : functional ] ) . also note that with conformal variations , the choice of the set @xmath94 is not particularly important ; we only need the existence of a neighborhood around any point in @xmath94 . in this paper
, we study the relationships between duality structures , discrete metrics , and conformal variations .
the main new contributions are the following : ( 1 ) a characterization of duality structures in hyperbolic and spherical backgrounds , generalizing the notion of length structures arising from circles with given radii and inversive distances , ( 2 ) calculation of the conformal variation of angles in a triangle for hyperbolic and spherical backgrounds together with determining a functional making the curvature variational , and ( 3 ) a classification theorem for discrete conformal variations of euclidean , hyperbolic , and spherical triangles , including the formulation of the notion of discrete conformal variations from basic principles .
the following theorem characterizes duality structures on surfaces in each of the constant curvature backgrounds .
[ thm : duality equals metric ] let @xmath3 be a piecewise constant curvature 2-manifold .
there is a one - to - one correspondence between proper duality structures on @xmath3 and discrete metric structures on @xmath3 .
this theorem follows from propositions [ prop : euclidean compatibility ] , [ prop : hyperbolic compatibility ] , and [ prop : spherical compatibility ] .
the following theorem gives the variation of angle formulas .
the euclidean result is in @xcite , and the hyperbolic and spherical results are new ( compare @xcite ) .
[ thm : angle variation ] for any conformal variation of a metric @xmath91 $ ] with background geometry @xmath4 of a surface @xmath95 , we have for any edge @xmath59 the following formulas .
* in euclidean background , @xmath96 * in hyperbolic background , @xmath97 where @xmath98 is 1 if @xmath61 is timelike and -1 if @xmath61 is spacelike . *
in spherical background , @xmath99 this theorem follows from theorems [ thm : euclidean variation angle ] , [ thm : hyperbolic angle variation ] , and [ thm : spherical angle variation ] together with propositions [ prop : hyperbolic area deriv ] and [ prop : sphere area var ] .
it turns out that although the variables @xmath92 for the conformal variations are quite natural , a change of variables gives that the curvatures are the gradient of a functional , where the curvatures are defined as @xmath100 for each vertex @xmath16 , where the sum is over all triangles containing @xmath16 .
[ thm : functional ] consider a piecewise constant curvature , metrized 2-manifold @xmath101 , where @xmath102 is determined by a conformal structure .
there is a change of variables @xmath103 such that @xmath104 and hence if we fix a @xmath105 there is a functional @xmath106 with the property that @xmath107 furthermore , if all @xmath108 and @xmath109 and then this function is strictly convex if @xmath7 and weakly convex ( strictly convex except for scaling ) if @xmath6 .
this theorem follows from theorems [ thm : euclidean functional ] , [ thm : hyp functional ] , and [ thm : sphere functional ] .
the following theorems classify discrete conformal variations in each of the constant curvature backgrounds .
the results are new for all background geometries .
[ thm : conformal classification ] let @xmath110 be a discrete conformal class with background geometry @xmath4 on a surface @xmath1 .
then there exist @xmath111 and @xmath112 such that the conformal structure can be written as @xmath113 with @xmath114 if @xmath6 , @xmath115 with @xmath116 if @xmath7 , or @xmath117 with @xmath118 if @xmath8 .
this theorem is proven in each case in sections [ section : eucl conf classify ] , [ section : hyp conf classify ] , and [ sec : sphere ] . in light of theorem
[ thm : conformal classification ] , one can also calculate angle variations from theorem [ thm : angle variation ] based on the conformal structures determined by @xmath119 and @xmath120 .
these conformal structures are sometimes referred to as @xmath121 ( see , e.g. , @xcite ) . in this section
we briefly compare our parametrizations with other parametrizations of certain discrete conformal structures .
the formulation in this paper unifies the previous work into a single formula for each background geometry and generalizes some of these .
independently , @xcite derived a formula for the variation of angle that is essentially the same as ours , though we express it and prove it in a different way .
we note that the euclidean background case was treated in @xcite , which also describes the relationship of the general case to previous formulations .
the first formulation of the circle packing conformal structure ( corresponding , in our notation , to @xmath122 and @xmath123 for all vertices and edges ) is in thurston s work @xcite .
many of the relevant calculations are followed through in @xcite , and the first variational formulation is due to colin de verdire in @xcite . in each of these cases ,
the euclidean and hyperbolic cases were treated , and the conformal structures were either circles with given intersection angles between @xmath124 and @xmath125 ( corresponding , in our notation , to @xmath122 and @xmath126 for all vertices and edges ) .
additional work was done by chow - luo in @xcite .
the case of circles with fixed inversive distances ( corresponding , in our notation , to @xmath122 and @xmath127 for all vertices and edges ) was introduced by bowers and stephenson @xcite and the variational perspective was pursued by guo in @xcite ( this was anticipated by springborn s work on volumes of hyperideal simplices in @xcite ) .
the multiplicative conformal structure ( corresponding , in our notation , to @xmath128 for all vertices ) was apparently first suggested in @xcite , but most of the mathematical ideas arose in work of luo @xcite and springborn - schrader - pinkall @xcite in the euclidean case .
generalizing to the hyperbolic case was not obvious , but work in this direction first appeared in work by bobenko - pinkall - springborn @xcite .
it is notable that the proper parametrization variable is not clear in this case , and this issue is discussed in section [ subsect : variational hyp ] .
the unified case for euclidean background is given in @xcite and the hyperbolic case was first described in this paper and independently in @xcite . for more on some of these discrete conformal structures , see the books @xcite , @xcite , and @xcite .
explicit calculation of the variation of angle coefficients in the euclidean circle packing case is due to z. he @xcite , and followed by the first author in @xcite .
the coefficients are closely related to the discrete laplacians found in @xcite , @xcite , @xcite , @xcite , @xcite @xcite , @xcite , @xcite , @xcite , @xcite , and many other places .
there are close connections between these variational viewpoints and hyperbolic volumes , as evidenced by work of brgger @xcite , rivin @xcite , garret @xcite , leibon @xcite , bobenko - springborn @xcite , springborn @xcite , springborn - schrder - pinkall @xcite , and bobenko - pinkall - springborn @xcite , fillastre - izmestiev @xcite , and zhang et .
al . @xcite .
some of this work was generalized to discrete conformal structures in three dimensions by cooper - rivin in @xcite and the first author in @xcite and @xcite .
while the functionals whose variations lead to curvatures in two dimensions are possibly related to the log determinant of the laplacian and surface entropy ( see @xcite ) , in three dimensions the functional is related to regge s formulation of the einstein - hilbert ( total scalar curvature ) functional .
see , e.g. , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite .
clearly , the choice of a pre - metric with euclidean background determines the geometry of each triangle @xmath15 and for any isometric embedding , specifies the triangle s sides @xmath129 with lengths @xmath130 . through each finite edge @xmath131 of the triangle we have a unique line @xmath132 , considered in @xmath133 .
suppose we identify @xmath132 with the real number line such that @xmath134 is at the origin and @xmath135 is on the positive @xmath46 axis .
given these coordinates , we specify the edge centers @xmath136 to be the point @xmath71 on the line .
note that @xmath72 denotes the distance between @xmath60 and @xmath135 , considered with a sign determined by which side of @xmath135 in @xmath132 contains @xmath60 . for each edge @xmath59
, there exists a unique line @xmath137 that passes through @xmath60 and is orthogonal to @xmath132 . in @xcite ( proposition 4 ) , the first author presented a necessary and sufficient condition on the partial edges to guarantee the three lines @xmath138 meet at a single point : [ prop : euclidean compatibility ] suppose @xmath139 is a euclidean pre - metric .
then the perpendiculars @xmath138 meet at a single point if and only if @xmath140 this motivates the euclidean case of definition [ def : metric ] and proves the euclidean case of theorem [ thm : duality equals metric ] .
the conformal structure is defined in such a way as to give the following variational formula .
[ thm : euclidean variation angle ] given a conformal structure , we have @xmath141 if @xmath142 and @xmath143
this theorem is proven in @xcite , generalizing the theorems in special cases given in @xcite and @xcite .
it follows easily ( see , e.g. , @xcite ) that the curvature is variational with respect to a convex functional .
[ thm : euclidean functional ] the partial derivatives of the angles in a triangle are symmetric , i.e. , @xmath144 and hence if we fix a @xmath145 there is a functional @xmath146 with the property that @xmath147 furthermore , if all @xmath108 and @xmath109 and then this function is weakly convex ( strictly convex except for scaling ) . in this section
we prove the characterization theorem .
recall that the only assumptions are : * the compatibility condition [ d - euclidean condition ] for the triangle with vertices @xmath134 , @xmath135 , and @xmath148 .
* the assumption that @xmath71 depends only on @xmath149 and @xmath150 .
we first note that @xmath151 and that @xmath152 since for any triangle with vertices @xmath153 we have @xmath154 we can compute that @xmath155 since @xmath156 it follows that @xmath157 and so it follows that @xmath158 and @xmath159 we can solve these equations , getting @xmath160 for constants @xmath161 and @xmath162 hence @xmath163 we can now use ( [ l deriv ] ) to find that for a constant @xmath164 @xmath165 from this , we compute that @xmath166 we note that in a triangle , since @xmath167 and the right side is independent of @xmath168 differentiating with respect to @xmath169 gives @xmath170 and hence @xmath171 and @xmath172 is independent of the edge , only depending on the vertex , hence we rename @xmath173 to see that the @xmath174 and @xmath164 must be consistent across triangles , consider equation [ eqn : l - eucl ] on both triangles and differentiate with respect to @xmath149 and @xmath150 to see that the @xmath164 agree and then @xmath149 to see that the @xmath174 agree .
before we move to the hyperbolic versions of the previous work , we will review some techniques for computing in hyperbolic geometry .
this section summarizes the elementary facts about the hyperbolic plane @xmath57 that we will use in later calculations .
all of the propositions in this section are discussed in chapter 3 of @xcite .
see also @xcite . for the reader
s convenience , we have included some , but not all , proofs .
we use the hyperboloid model of @xmath57 for the majority of our calculations . in this model ,
the vector space @xmath175 is equipped with a lorentzian inner product @xmath176 given by @xmath177 where @xmath178 is the diagonal matrix with entries 1,1,-1 .
we define a `` hyperbolic magnitude '' @xmath179 ; the only possible hyperbolic lengths are nonnegative scalar multiples of 1 and @xmath16 .
@xmath57 corresponds to those vectors @xmath180 satisfying @xmath181 and @xmath182 .
a vector @xmath183 is termed _ spacelike _ if @xmath184 , _ lightlike _ ( or `` on the light cone '' ) if @xmath185 , and _ timelike _ if @xmath186 .
the vector space structure on @xmath187 gives us several ways to describe a geodesic in @xmath57 : * as a nonempty intersection @xmath188 for linearly independent @xmath189 .
* as a nonempty intersection @xmath190 , where @xmath38 is a spacelike vector and @xmath191 .
* as a path , parametrized by arclength , given by @xmath192 . in this form , @xmath193 , @xmath194 with @xmath195
note @xmath38 and @xmath196 encode the position and direction of @xmath197 at @xmath198 .
the second characterization becomes particularly useful when combined with the lorentzian cross product , which is given by @xmath199 . clearly , the lorentzian cross product has two useful properties : * @xmath200 if and only if @xmath38 and @xmath39 are linearly dependent .
* @xmath201 is @xmath176-orthogonal to both @xmath38 and @xmath39 .
a consequence of the second observation is that given distinct points @xmath202 , one simple way to describe the geodesic through @xmath38 and @xmath39 is @xmath203 . in the sequel
, we will use @xmath204 to denote the hyperbolic distance between two timelike points , and @xmath205 to denote the hyperbolic distance between a timelike point and a geodesic in hyperbolic space determined as the orthogonal complement of a spacelike point .
when @xmath206 satisfy @xmath207 , we have the following interpretations of the quantity @xmath208 : * if @xmath209 and @xmath196 are both timelike , then @xmath210 . *
if @xmath209 is timelike and @xmath196 is spacelike , then @xmath211 and the sign depends upon which of the halfspaces bounded by @xmath212 contains @xmath209 . * if @xmath209 and @xmath196 are both spacelike and @xmath213 and @xmath212 intersect in angle @xmath119 within @xmath57 , @xmath214 .
notice that the last item implies that for spacelike @xmath209 and @xmath196 , @xmath213 and @xmath212 meet at a right angle if and only if @xmath215 .
the following identities simplify calculations that involve lorentzian cross products .
suppose @xmath216 : @xmath217 we have already seen that several different kinds of data can be used to specify a geodesic on @xmath57 .
this allows us to extend our understanding of where geodesics intersect .
[ definition intersection ] given a geodesics @xmath197 on @xmath57 , we will identify @xmath197 with the unique 2-dimensional subspace @xmath218 of @xmath175 such that @xmath219 is the image of @xmath197 . given geodesics @xmath220 on @xmath57
, we define their _ intersection _ to be their intersection as subspaces of @xmath175 , namely @xmath221 .
readers familiar with the klein model of @xmath57 ( the central projection of @xmath57 onto the plane @xmath222 ) should note that this definition is simply a linear - algebraic way of formulating the notion of intersecting 1-hyperplanes in the klein model .
introducing a broader notion of intersection allows us to generalize familiar equations ( like the law of cosines ) and express them in terms of linear algebra . understanding how to interpret the lorentzian inner product is key to relating these different formulas .
often , the linear algebraic interpretation allows us to efficiently treat several seemingly different cases at once .
recall the definition of a triangle ( see section 3.5 in @xcite ) , which allows some of the vertices to be timelike , lightlike , or spacelike .
we will concentrate on triangles with at least two timelike vertices .
[ proposition ratcliffe triangles ] suppose @xmath223 and @xmath224 are either timelike or spacelike
. then @xmath225 where @xmath119 is the angle at @xmath46 in the ( clockwise oriented ) triangle @xmath226 .
[ proposition generalized law of cosines ] suppose @xmath227 , with @xmath228 and @xmath229 or @xmath16 , are the vertices of a triangle in @xmath57 , with angle @xmath119 at @xmath46 .
then @xmath230 assume , without loss of generality , that @xmath231 label the vertices of the triangle in clockwise order .
equation [ eqn : det formula ] implies @xmath232 now apply proposition [ proposition ratcliffe triangles ] to obtain the desired equality . by setting @xmath233
, we obtain a generalized version of the pythagorean theorem : suppose @xmath231 are the vertices of a right triangle , with the right angle at @xmath46 .
then : @xmath234 we will require formulas for performing trigonometry in a hyperbolic right triangle where one of the vertices ( not the one adjacent to the right angle ) may be spacelike or timelike .
suppose we have a right triangle labeled like the one in figure [ fig : right triangle ] .
[ prop : trig ] given a triangle labeled as in figure [ fig : right triangle ] , we have : @xmath235 if @xmath236 is timelike and @xmath237 if @xmath236 is spacelike .
deriving these formulas is an easy application of the generalized pythagorean theorem and the generalized law of cosines .
the next corollary generalizes the familiar formula for the cosine of an angle in a hyperbolic right triangle .
[ corollary cosine right triangle ] suppose @xmath231 are the vertices of a right triangle ( with the right angle at @xmath238 ) satisfying the assumptions of proposition [ proposition generalized law of cosines ] .
then @xmath239 the right angle at @xmath238 means that : @xmath240 and so @xmath241 substituting this into the equation we obtain from the law of cosines , we learn : @xmath242 using equation [ eqn : det formula ] , it is easy to check @xmath243 .
hence : @xmath244 because the lorentzian inner product is nondegenerate , we have a well defined notion of @xmath176-orthogonality and may apply the gram - schmidt procedure to obtain a basis of mutually @xmath176-orthogonal vectors .
this procedure can be used to parametrize a geodesic given in the form @xmath188 by arclength .
[ proposition gram - schmidt ] suppose @xmath193 , and @xmath245
. then the geodesic @xmath246 may be parametrized by arclength as : @xmath247 the geodesic in question can be parametrized by arclength as @xmath248 for some spacelike @xmath196 with @xmath249 ; we simply need to use the gram - schmidt procedure to guarantee that @xmath250 and @xmath194 .
so consider the vector @xmath251 .
notice @xmath252 is the @xmath176-projection of @xmath39 onto the subspace spanned by @xmath38 , and @xmath253 to find @xmath196 , we only need to rescale this projection .
since @xmath254 the appropriate @xmath196 is @xmath255
we interpret a piecewise hyperbolic pre - metric as subdividing each edge @xmath59 of length @xmath256 into two portions of length @xmath257 and @xmath258 , that are assigned to the vertices @xmath16 and @xmath73 respectively .
[ def : edge centers ] given a pre - metric @xmath75 and an isometric embedding of a simplex @xmath59 into @xmath57 : * the _ vertices _ @xmath259 of @xmath59 are the images of @xmath16 and @xmath73 under the embedding . *
the _ edge center @xmath60 induced by @xmath75 _ is the unique point along the line @xmath132 through @xmath260 and @xmath261 such that @xmath60 is ( signed ) distance @xmath71 from @xmath260 and @xmath72 from @xmath261 . *
the _ edge perpendicular @xmath137 _ is the line through @xmath60 that is orthogonal to @xmath132 . unlike in the euclidean setting
, it is possible that the geodesics @xmath137 and @xmath262 do not intersect within @xmath57 . however , these two 1-hyperplanes can be understood as intersecting in the more general sense of definition [ definition intersection ] , namely the two - dimensional subspaces of @xmath187 associated to @xmath137 and @xmath262 intersect in a one - dimensional subspace .
one can then ask for necessary and sufficient conditions on the pre - metric that guarantee that for each simplex @xmath15 @xmath263 or , colloquially , the three perpendiculars of @xmath15 intersect in a single point ( this point is in the span of @xmath15 ) .
this condition can also be interpreted in the klein model of hyperbolic space as the condition that the three lines representing the geodesics intersect at the same point in the plane of the klein model . [
prop : hyperbolic compatibility ] suppose @xmath75 is a piecewise hyperbolic pre - metric .
equation [ eqn : duality intersections ] holds if and only if the following _ compatibility equation _
@xmath264 is satisfied for every simplex @xmath15 .
since the vectors @xmath260 and @xmath60 are timelike of length -1 , equation [ eqn : dijhyp - reln ] has the following equivalent formulation : @xmath265 to simplify our notation , we shall consider a single 2-simplex @xmath266 .
the vertices of the embedded 2-simplex are linearly independent vectors @xmath267 .
consider that if @xmath268 is a point on the perpendicular @xmath137 , then @xmath269 .
likewise the span of edge @xmath131 is given by @xmath270 .
since @xmath60 belongs to both @xmath137 and @xmath131 , the fact that @xmath137 and @xmath131 are perpendicular is equivalent to the equation : @xmath271 identities [ eqn : cross product ident1]-[eqn : det formula ] imply this is equivalent to the equation : @xmath272 hence , equation [ eqn : duality intersections ] holds for simplex @xmath266 if and only if there is a nontrivial solution @xmath268 to the system : @xmath273 this system can be reformulated as a matrix equation @xmath274 that has a nontrivial solution if and only if the determinant of the first matrix is zero .
expanding that determinant and canceling the ( nonzero ) factors of @xmath275 that arise yields equation [ eqn : dijhyp - reln ] .
the last statement follows easily .
this proposition motivates the hyperbolic case of definition [ def : metric ] .
one can gain insight into how the euclidean and hyperbolic compatibility conditions are related by comparing equation [ d - euclidean condition ] and equation [ d - hyperbolic condition ] for small @xmath71 in the same way one compares the euclidean pythagorean theorem with the hyperbolic version , @xmath276 .
various formulations of conformal variations of hyperbolic triangulations of surfaces have been studied in @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite .
we present a unified approach from the perspective of the metric triangulations as defined above .
suppose we wanted to generate a metric from weights assigned to vertices , so that @xmath277 for some function @xmath92 on the vertices .
if this our starting point for conformal structure , in order to compute conformal variations , we will consider what happens to the metric on a triangle @xmath266 when the conformal parameter @xmath278 changes but the other two do not , i.e. , @xmath279 .
we will call this a @xmath278-conformal variation in this section .
the next two propositions analyze the configuration shown in figure [ figure conformal variation ] .
we assume throughout that @xmath280 are linearly independent in @xmath175 , with @xmath281 .
[ prop : inner product identities ] under an @xmath278-conformal variation : @xmath282 bilinearity of the lorentzian inner product implies : @xmath283 however , since @xmath284 , we can also write : @xmath285 hence @xmath286 we get the formula for @xmath287 similarly .
finally , since @xmath288 : @xmath289 the following proposition makes precise what we mean by the colloquial statement that conformal variations give good angle variations .
[ prop : conformal line ] let @xmath290 denote the center of the triangle specified by the vertices @xmath134 and the ( compatible ) partial edge lengths @xmath71 .
suppose further that the edge centers on edges @xmath291 and @xmath292 are timelike . then under a @xmath278-conformal variation ,
the points @xmath293 and @xmath290 lie on a line in @xmath57 if and only if @xmath294 , for some function @xmath295 . without loss of generality ,
assume @xmath296 .
consider the geodesic through @xmath297 and @xmath290 .
as a set , this geodesic can be described by @xmath298 , a characterization we will use to parametrize the geodesic by arclength as @xmath299 for some @xmath300 . specifically , proposition [ proposition gram - schmidt ] implies : @xmath301 the points @xmath293 , and @xmath290 lie on a geodesic if and only if @xmath209 and @xmath302 are collinear .
the three numbers @xmath303 completely characterize the vector @xmath304 . hence , @xmath209 and @xmath302 are collinear if and only if there exists @xmath305 such that @xmath306 for @xmath307 .
we already know @xmath308 , so only @xmath309 and @xmath310 require consideration .
consider our equation for @xmath209 .
the scalar in the denominator will appear in both @xmath309 and @xmath310 . to simplify our notation ,
we will write @xmath311 . now @xmath312 and we can apply the generalized law of cosines ( proposition [ proposition generalized law of cosines ] ) to the triangle @xmath313 in order to rewrite this equation as @xmath314 next consider the right triangle with vertices @xmath315 . by corollary [ corollary cosine right triangle ]
, we have @xmath316 a final substitution into our equation for @xmath309 implies @xmath317 a similar argument for @xmath318 yields @xmath319 from proposition [ prop : inner product identities ] , we know that for @xmath320 @xmath321 comparing these two equations , we see that there exists @xmath322 so that @xmath323 if and only if there exists a smooth function @xmath324 for which @xmath325 .
proposition [ prop : conformal line ] motivates the hyperbolic case of definition [ def : conformal structure ] , where we have chosen to simplify to parameters that make @xmath326 equal to the constant function @xmath327 .
we will now study how the angles change under a conformal variation .
first we see the following .
[ thm : hyperbolic angle variation ] given a conformal structure , then for any simplex @xmath15 @xmath328 where @xmath98 is 1 if @xmath61 is timelike and -1 if @xmath61 is spacelike . for simplicity , we shall consider the problem for a single simplex @xmath266 labeled as in figure [ figure conformal variation ] , with @xmath329 , @xmath330 . we will address the case where @xmath290 is timelike ; the case where @xmath290 is spacelike is similar .
once [ eqn : angle variation ij thmcopy ] is proven , [ eqn : angle variation ii thmcopy ] follows immediately because of the area formula for a hyperbolic triangle : @xmath331 because the variation is conformal , @xmath332 . using the formula for a segment of a circle in the hyperbolic plane
, we have @xmath333 . by proposition [ prop : conformal line ] , under a conformal variation @xmath334 and @xmath290 are collinear .
consequently , the angle adjacent to @xmath297 in the triangle with side lengths @xmath335 , @xmath336 and @xmath302 is @xmath337 .
this , together with the formulas in proposition [ prop : trig ] , allows us to write : @xmath338 using the taylor series for @xmath339 and @xmath340 , we have : @xmath341 and hence , @xmath342 we can also compute the variation of area explicitly .
[ prop : hyperbolic area deriv ] given a conformal structure , then for any simplex @xmath15 with area @xmath343 .
@xmath344 in particular , if the derivatives @xmath345 are positive whenever @xmath346 , then the derivative of the area is positive .
this follows from the formula for the area of a sector of circle as a function of the radius for a hyperbolic surface , since in figure [ figure conformal variation ] we find that the area of each of the small triangles is higher order , leaving only the areas of the skinny triangles in the picture .
the proof of the hyperbolic case of theorem [ thm : conformal classification ] is similar to the proof of the euclidean case , though the calculation is a bit harder in hyperbolic background .
we first note the following : @xmath347 a straightforward calculations gives that @xmath348 or if @xmath349 then @xmath350 since @xmath351 it follows that @xmath352 and @xmath353 one can then easily solve this ode to obtain that : @xmath354 for some constant @xmath161 and @xmath355 for some constant @xmath356 .
it follows that @xmath357 we can now use equation [ eq : coshder ] to see that @xmath358 and so we find that @xmath359 and @xmath360 for some constant @xmath164 .
the compatibility condition ( [ d - hyperbolic condition ] ) implies that @xmath361 is independent of @xmath149 and so we can use equation [ eqn : cosh dij by cosh dij ] to see that @xmath171 and so we can define @xmath362 . it follows that @xmath363 finally , we can use equation [ eqn : cosh dij by cosh dij ] again to write @xmath364 in terms of the coefficients determined in the two triangles adjacent to edge @xmath59 and differentiate to see that the @xmath174 derived in each triangle must be equal .
it then follows from equation [ eqn : hyp length ] that the @xmath164 derived in each triangle must be equal as well .
while the formula ( [ eqn : angle variation ij ] ) is not symmetric in @xmath16 and @xmath73 , we can reparametrize to get a symmetric variation formula .
notice that equation [ eqn : cosh dij by cosh dij ] ( recall that we proved @xmath359 ) implies that @xmath365 if we take new coordinates @xmath366 such that @xmath367 then we have the symmetry @xmath368 the function @xmath369 can be computed explicitly .
it is not hard to see that if @xmath128 then @xmath370 and if not then @xmath371 if @xmath372 then this is @xmath373 and if @xmath374 then this is @xmath375 compare to the formulations in @xcite , @xcite , and @xcite .
it then follows that for a triangle @xmath376 the following form is closed : @xmath377 we can now integrate to get a function on the whole triangulation , where we fix some @xmath105 : @xmath378 [ thm : hyp functional ] the function @xmath326 has the property that @xmath107 furthermore ,
if all @xmath108 and @xmath109 then this function is strictly convex .
the first statement follows from the definition .
the second follows from the facts that in a triangle @xmath266 , @xmath379 for @xmath380 since @xmath381 by proposition [ prop : hyperbolic area deriv ] .
it follows that the matrix of partial derivatives is diagonally dominant .
the arguments presented in the case of hyperbolic background geometry can be adjusted for the case of spherical background geometry .
essentially , this occurs because in the hyperbolic case we are studying properties of the lorentzian inner product @xmath176 , while in spherical geometry we study analogous properties of the euclidean inner product .
because the definitions and arguments in the spherical case are so similar to those of previous sections , we will only state the main results in the spherical case .
to work in the spherical case , we work with the usual dot product @xmath382 on @xmath175 .
geodesics on the sphere correspond to planes in @xmath175 and so given a triangle @xmath15 in the sphere and a pre - metric , a given embedding induces planes @xmath137 , etc . through edge centers and
the condition for inducing a duality structure is @xmath383 [ prop : spherical compatibility ] suppose @xmath75 is a piecewise spherical pre - metric . equation [ eqn : spherical duality intersections ] holds if and only if the following _ compatibility equation _ @xmath384 is satisfied for every simplex @xmath15
. equation [ eqn : dij - reln spherical ] has the following equivalent formulation : @xmath385 note that although the heights @xmath62 require choosing one of the two possible centers , the term @xmath387 does not depend on this choice , since choosing the other center leads to heights @xmath388 and so @xmath389 using this theorem and the definition of a spherical conformal structure , one can derive the spherical case of theorem [ thm : conformal classification ] .
as in the hyperbolic case , it is desirable to change from the variables @xmath149 to variables @xmath391 , so that one can recognize that @xmath392 .
the variables @xmath393 are given by @xmath394 j. dai , x. gu , and f. luo .
_ variational principles for discrete surfaces_. advanced lectures in mathematics ( alm ) , 4 . international press , somerville , ma ; higher education press , beijing , 2008 .
iv+146 pp .[/INST] a piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry ( euclidean , hyperbolic , or spherical ) , each simplex has an isometric embedding into the background geometry with the chosen edge lengths .
additional structure is defined either by giving a geometric structure to the poincar dual of the triangulation or by assigning a discrete metric , a way of assigning length to oriented edges .
this notion leads to a notion of discrete conformal structure , generalizing the discrete conformal structures based on circle packings and their generalizations studied by thurston and others .
we define and analyze conformal variations of piecewise constant curvature 2-manifolds , giving particular attention to the variation of angles .
we give formulas for the derivatives of angles in each background geometry , which yield formulas for the derivatives of curvatures .
our formulas allow us to identify particular curvature functionals associated with conformal variations .
finally , we provide a complete classification of discrete conformal structures in each of the background geometries . </s> |
entanglement in quantum multipartite systems is a unique property in quantum world .
it plays an important role in quantum information processing @xcite .
therefore , the study of its essential features and dynamical behavior under the ubiquitous decoherence of relevant quantum system has attracted much attention in recent years @xcite .
for example , it was found that the entanglement of qubits under the markovian decoherence can be terminated in a finite time despite the coherence of single qubit losing in an asymptotical manner @xcite . the phenomenon called as entanglement sudden death ( esd
) @xcite has been observed experimentally @xcite .
this is detrimental to the practical realization of quantum information processing using entanglement .
surprisingly , some further studies indicated that esd is not always the eventual fate of the qubit entanglement .
it was found that the entanglement can revive again after some time of esd @xcite , which has been observed in optical system @xcite .
it has been proven that this revived entanglement plays a constructive role in quantum information protocols @xcite . even in some occasions
, esd does not happen at all , instead finite residual entanglement can be preserved in the long time limit @xcite .
this can be due to the structured environment and physically it results from the formation of a bound state between the qubit and its amplitude damping reservoir @xcite .
these results show rich dynamical behaviors of the entanglement and its characters actually have not been clearly identified .
recently , lpez _ et al .
_ asked a question about where the lost entanglement of the qubits goes @xcite .
interestingly , they found that the lost entanglement of the qubits is exclusively transferred to the reservoirs under the markovian amplitude - damping decoherence dynamics and esd of the qubits is always accompanied with the entanglement sudden birth ( esb ) of the reservoirs .
a similar situation happens for the spin entanglement when the spin degree of freedom for one of the two particles interacts with its momentum degree of freedom @xcite .
all these results mean that the entanglement does not go away , it is still there but just changes the location .
this is reminiscent of the work of yonac _ et al . _
@xcite , in which the entanglement dynamics has been studied in a double jaynes - cummings ( j - c ) model .
they found that the entanglement is transferred periodically among all the bipartite partitions of the whole system but an identity ( see below ) has been satisfied at any time .
this may be not surprising since the double j - c model has no decoherence and any initial information can be preserved in the time evolution .
however , it would be surprising if the identity is still valid in the presence of the decoherence , in which a non - equilibrium relaxation process is involved . in this paper
, we show that it is indeed true for such a system consisted of two qubits locally interacting with two amplitude - damping reservoirs .
it is noted that although the infinite degrees of freedom of the reserviors introduce the irreversibility to the subsystems , this result is still reasonable based on the fact that the global system evolves in a unitary way .
furthermore , we find that the distribution of the entanglement among the bipartite subsystems is dependent of the explicit property of the reservoir and its coupling to the qubit .
the rich dynamical behaviors obtained previously in the literature can be regarded as the special cases of our present result or markovian approximation .
particularly , we find that , instead of entirely transferred to the reservoirs , the entanglement can be stably distributed among all the bipartite subsystems if the qubit and its reservoir can form a bound state and the non - markovian effect is important , and the esd of the qubits is not always accompanied with the occurrence of esb of reservoirs .
irrespective of how the entanglement distributes , it is found that the identity about the entanglement in the whole system can be satisfied at any time , which reveals the profound physics of the entanglement dynamics under decoherence .
this paper is organized as follows . in sec .
[ model ] , the model of two independent qubits in two local reservoirs is given . and
the dynamical entanglement invariance is obtained based on the exact solution of the non - markovian decoherence dynamics of the qubit system . in sec .
[ edd ] , the entanglement distribution over the subsystems when the reservoirs are pbg mediums is studied explicitly .
a stable entanglement - distribution configuration is found in the non - markovian dynamics .
finally , a brief discussion and summary are given in sec .
we consider two qubits interacting with two uncorrelated vacuum reservoirs . due to the dynamical independence between the two local subsystems
, we can firstly solve the single subsystem , then apply the result obtained to the double - qubit case .
the hamiltonian of each local subsystem is @xcite @xmath0 where @xmath1 and @xmath2 are the inversion operators and transition frequency of the qubit , @xmath3 and @xmath4 are the creation and annihilation operators of the @xmath5-th mode with frequency @xmath6 of the radiation field .
the coupling strength between the qubit and the reservoir is denoted by @xmath7 , where @xmath8 and @xmath9 are the unit polarization vector and the normalization volume of the radiation field , @xmath10 is the dipole moment of the qubit , and @xmath11 is the free space permittivity .
for such a system , if the qubit is in its ground state @xmath12 and the reservoir is in vacuum state at the initial time , then the system does not evolve to other states .
when the qubit is in its excited state @xmath13 , the system evolves as @xmath14 here @xmath15 denotes that the qubit jumps to its ground state and one photon is excited in the @xmath5-th mode of the reservoir .
@xmath16 satisfies an integro - differential equation @xmath17 where the kernel function @xmath18 is dependent of the spectral density @xmath19 . introducing the normalized collective state of the reservoir with one excitation as @xmath20 and with zero excitation as @xmath21 @xcite , eq .
( [ t9 ] ) can be written as @xmath22 , where @xmath23 .
it should be emphasized that the introducing of normalized collective state is not a reduction of present model to the j - c model @xcite , as noted in @xcite .
the dynamics is given by eq .
( [ t7 ] ) , which is difficult to obtain analytically since its non - markovian nature . in general the numerical integration should be used .
it is emphasized that our treatment to the dynamics of the system is exact without resorting to the widely used born - markovian approximation . to compare with the conventional approximate result
, we may derive straightforwardly the master equation from eq .
( [ t9 ] ) after tracing over the degree of freedom of the reservoir @xcite , @xmath24+\gamma ( t)[2\sigma _ { -}\rho ( t)\sigma _ { + } \nonumber \\ & & -\sigma _ { + } \sigma _ { -}\rho ( t)-\rho ( t)\sigma _ { + } \sigma _ { - } ] , \label{mstt}\end{aligned}\]]where the time - dependent parameters are given by @xmath25,~\gamma ( t)=-\text{re}[\frac{% \dot{b}(t)}{b(t)}]$ ] .
the time - dependent parameters @xmath26 and @xmath27 play the roles of lamb shifted frequency and decay rate of the qubit , respectively .
the integro - differential equation ( [ t7 ] ) contains the memory effect of the reservoir registered in the time - nonlocal kernel function and thus the dynamics of qubit displays non - markovian effect .
if the time - nonlocal kernel function is replaced by a time - local one , then eq . ( [ mstt ] ) recovers the conventional master equation under born - markovian approximation @xcite . according to the above results ,
the time evolution of a system consisted of two such subsystems with the initial state @xmath28 is given by @xmath29 where @xmath30 and @xmath31 are the coefficients to determine the initial entanglement in the system .
from @xmath32 , one can obtain the time - dependent reduced density matrix of the bipartite subsystem qubit1-qubit2 ( @xmath33 ) by tracing over the reservoir variables .
it reads @xmath34 where @xmath35 and @xmath36 .
similarly , one can obtain the corresponding reduced density matrices for other subsystems like reservoir1-reservoir2 ( @xmath37 ) and qubit - reservoir ( @xmath38 , @xmath39 , @xmath40 , @xmath41 ) . using the concurrence @xcite to quantify entanglement
, we can calculate the entanglement of each subsystem as @xmath42 with @xmath43 for different bipartite partitions labeled by @xmath44 as @xmath45 one can verify that @xmath46 in eqs .
( [ qq])-([qr2 ] ) satisfy an identity @xmath47 where @xmath48 is just the initial entanglement present in @xmath33 .
( [ t15 ] ) recovers the explicit form derived in a double j - c model @xcite when each of the reservoirs contains only one mode , i.e. @xmath49 , where the decoherence is absent and the dynamics is reversible .
it is interesting that this identity is still valid in the present model because the reservoirs containing infinite degrees of freedom here lead to a completely out - of - phase interaction with qubit and an irreversibility .
furthermore , one notes that the identity is not dependent of any detail about @xmath16 , which only determines the detailed dynamical behavior of each components in eq .
( [ t15 ] ) .
this result manifests certain kind of invariant nature of the entanglement .
( [ t15 ] ) can be intuitively understood by the global multipartite entanglement of the whole system .
the global entanglement carried by the subsystem @xmath50 can be straightforwardly calculated from eq .
( [ phit ] ) by generalized concurrence @xcite as @xmath48 , which , coinciding with the bipartite entanglement initially present in @xmath33 , just is the right hand side of eq .
( [ t15 ] ) .
since there is no direct interaction between @xmath51 and @xmath52 , this global entanglement is conserved during the time evolution . from this point ,
our result is consistent with the one in refs . @xcite and @xcite .
another observation of eq .
( [ t15 ] ) is that the different coefficients in the left hand side are essentially determined by the energy / information transfer among the local subsystems .
explicitly , in our model the total excitation number is conserved , so the energy degradation in @xmath53 with factor @xmath16 is compensated by the energy enhancement in @xmath54 with factor @xmath55 .
this causes that @xmath56 , @xmath57 , and @xmath58 , in all of which the double excitation is involved , have similar form except for the different combinations of @xmath16 and @xmath55 in eqs .
( [ qq ] ) , ( [ rr ] ) , and ( [ qr2 ] ) .
the dynamical consequence of the competition of the two terms in these equations causes the sudden death / birth of entanglement characterized by the presence of negative @xmath59 .
a different case happens for @xmath60 , where only single excitation is involved and no sudden death is present . with these observation , one can roughly understand why such combination in left hand side of eq .
( [ t15 ] ) gives the global entanglement . the significance of eq .
( [ t15 ] ) is that it gives us a guideline to judge how the entanglement spreads out over all the bipartite partitions .
it implies that entanglement is not destroyed but re - distributed among all the bipartite subsystems and this re - distribution behavior is not irregular but in certain kind of invariant manner .
the similar invariant property of entanglement evolution has also been studied in ref .
@xcite . in the following
we explicitly discuss the entanglement distribution , especially in the steady state , by taking the reservoir as a photonic band gap ( pbg ) medium @xcite and compare it with the previous results .
we will pay our attention mainly on the consequence of the non - markovian effect on the entanglement distribution and its differences to the results in refs . @xcite and @xcite .
for the pbg medium , the dispersion relation near the upper band - edge is given by @xcite @xmath61 where @xmath62 , @xmath63 is the upper band - edge frequency and @xmath64 is the corresponding characteristic wave vector . in this case
, the kernel function has the form @xmath65 where @xmath66 is a dimensionless constant . in solving eq .
( [ t7 ] ) for @xmath16 , eq .
( [ kn ] ) is evaluated numerically .
here we do not assume that @xmath5 is replaced by @xmath64 outside of the exponential @xcite .
so our result is numerically exact . in the following
we take @xmath67 as the unit of frequency . [
cols="^,^ " , ] in figs .
[ bst ] and [ nbst ] , we show the entanglement evolutions of each subsystem for two typical cases of @xmath68 and @xmath69 , which correspond to the atomic frequency being located at the band gap and at the upper band of the pbg medium , respectively . in the both cases the initial entanglement in @xmath33 begins to transfer to other bipartite partitions with time but their explicit evolutions , in particular the long time behaviors ,
are quite different . in the former case
, the entanglement could be distributed stably among all possible bipartite partitions .
[ bst](a ) shows that after some oscillations , a sizeable entanglement of @xmath33 is preserved for the parameter regime of @xmath70 .
remarkably , the entanglement in @xmath71 forms quickly in the full range of @xmath30 [ fig . [ bst](c ) ] and dominates the distribution . on the contrary , only slight entanglement of @xmath37 is formed in a very narrow parameter regime @xmath72 , as shown in fig .
[ bst](b ) .
however , when @xmath73 is located at the upper band of the pbg medium , the initial entanglement in @xmath33 is transferred completely to the @xmath37 in the long - time limit , as shown in fig .
[ nbst ] . at the initial stage , @xmath74 and @xmath75
are entangled transiently , but there is no stable entanglement distribution .
this result is consistent with that in refs .
it is noted that the entanglement in @xmath76 comes from two parts : one is transferred from @xmath33 , the other is created by the direct interaction between @xmath53 and @xmath54 . this can be seen clearly from fig .
[ bst](c ) when @xmath30 is very small , the initial entanglement of @xmath33 is very small , while that of @xmath76 is rather large , which just results from the interaction between @xmath53 and @xmath54 .
another interesting point is a stable entanglement can even be formed for the non - interacting bipartite system @xmath39 [ see [ bst](d ) when @xmath77 .
this entanglement transfer also results from the local interaction between @xmath53 and @xmath54 @xcite .
it is not difficult to understand these rich behaviors of entanglement distribution according to eqs .
( [ qq])-([qr2 ] ) and its invariance ( [ t15 ] ) . from these equations
, one can clearly see that the entanglement dynamics and its distributions in the bipartite partitions are completely determined by the time - dependent factor @xmath78 of single - qubit excited - state population .
[ tong0 ] shows its time evolutions for the corresponding parameter regimes presented above .
we notice that @xmath79 when @xmath73 is located at the band gap , which means that there is some excited - state population in the long - time limit .
this phenomenon known as population trapping @xcite is responsible for the suppression of the spontaneous emission of two - level system in pbg reservoir and has been experimentally observed @xcite .
such population trapping just manifests the formation of bound states between @xmath53 and @xmath54 @xcite , which has been experimentally verified in @xcite .
consequently , @xmath53 and @xmath54 are so correlated in the bound states that the initial entanglement in @xmath33 can not be fully transferred to @xmath37 .
the oscillation during the evolution is just the manifestation of the strong non - markovian effect induced by the reservoirs .
on the contrary , if @xmath73 is located in the upper band , then @xmath80 and the qubits decay completely to their ground states . in this case
the bound states between @xmath53 and @xmath54 are absent and , according to eq .
( [ t15 ] ) , the initial entanglement in @xmath33 is completely transferred to @xmath37 , as clearly shown in eq .
( [ rr ] ) .
in addition , in refs . @xcite it was emphasized that esd of @xmath33 is always accompanied with esb of @xmath37 .
however , this is not always true .
to clarify this , we examine the condition to obtain esd of the qubits and the companying esb of the reservoirs . from eqs .
( [ qq ] ) and ( [ rr ] ) it is obvious that the condition is @xmath81 and @xmath82 at any @xmath83 and @xmath84 , which means @xmath85 when the bound states is absent , @xmath86 , the condition ( [ dd ] ) can be satisfied when @xmath87 .
so one can always expect esd of the qubits and the companying esb of the reservoirs in the region @xmath88 , as shown in fig .
[ nbst ] and refs .
however , when the bound states are available , the situation changes .
in particular , when @xmath89 in the full range of time evolution , no region of @xmath90 can make the condition ( [ dd ] ) to be satisfied anymore .
for clarification , we present three typical behaviors of the entanglement distribution in fig .
[ td ] . in all these cases
the bound states are available .
[ td](a ) shows the situation where the entanglement is stably distributed among all of the bipartite subsystems .
[ td](b ) indicates that the entanglement of @xmath91 shows esb and revival , while the entanglement of @xmath33 does not exhibit esd .
[ td](c ) shows another example that while the entanglement of @xmath33 has esd and revival @xcite , the entanglement of @xmath37 does not show esb but remains to be zero .
[ td](b , c ) reveal that esd in @xmath33 has no direct relationship with esb in @xmath37 .
the above discussion is not dependent of the explicit spectral density of the individual reservoir . to confirm this
, we consider the reservoir in free space .
the spectral density has the ohmic form @xmath92 , which can be obtained from the free - space dispersion relation @xmath93 .
one can verify that the condition for the formation of bound states is : @xmath94 @xcite . in fig .
[ osd ] , we plot the results in this situation .
the previous results can be recovered when the bound states are absent @xcite . on the contrary , when the bound states are available , a stable entanglement is established among all the bipartite partitions .
therefore , we argue that the stable entanglement distribution resulted from the bound states is a general phenomenon in open quantum system when the non - markovian effect is taken into account . in summary , we have studied the entanglement distribution among all the bipartite subsystems of two qubits embedded into two independent amplitude damping reservoirs .
it is found that the entanglement can be stably distributed in all the bipartite subsystems , which is much different no matter to the markovian approximate result @xcite or to the decoherenceless double j - c model result @xcite , and an identity about the entanglement in all subsystems is always satisfied .
this identity is shown to be independent of any detail of the reservoirs and their coupling to the qubit , which affect only the explicit time evolution behavior and the final distribution .
the result is significant to the study of the physical nature of entanglement under decoherence .
it implies an active way to protect entanglement from decoherence by modifying the properties of the reservoir via the potential usage of the newly emerged technique , i.e. quantum reservoir engineering @xcite .
this work is supported by the fundamental research funds for the central universities under grant no .
lzujbky-2010 - 72 , gansu provincial nsf under grant no .
0803rjza095 , the national nsf of china , the program for ncet , and the cqt wbs grant no . r-710 - 000 - 008 - 271 . | we study the entanglement dynamics of two qubits , each of which is embedded into its local amplitude - damping reservoir , and the entanglement distribution among all the bipartite subsystems including qubit - qubit , qubit - reservoir , and reservoir - reservoir .
it is found that the entanglement can be stably distributed among all components , which is much different to the result obtained under the born - markovian approximation by c. e. lpez _
et al . _
[ phys .
rev .
lett .
* 101 * , 080503 ( 2008 ) ] , and particularly it also satisfies an identity .
our unified treatment includes the previous results as special cases .
the result may give help to understand the physical nature of entanglement under decoherence . | <s>[INST]entanglement in quantum multipartite systems is a unique property in quantum world .
it plays an important role in quantum information processing @xcite .
therefore , the study of its essential features and dynamical behavior under the ubiquitous decoherence of relevant quantum system has attracted much attention in recent years @xcite .
for example , it was found that the entanglement of qubits under the markovian decoherence can be terminated in a finite time despite the coherence of single qubit losing in an asymptotical manner @xcite . the phenomenon called as entanglement sudden death ( esd
) @xcite has been observed experimentally @xcite .
this is detrimental to the practical realization of quantum information processing using entanglement .
surprisingly , some further studies indicated that esd is not always the eventual fate of the qubit entanglement .
it was found that the entanglement can revive again after some time of esd @xcite , which has been observed in optical system @xcite .
it has been proven that this revived entanglement plays a constructive role in quantum information protocols @xcite . even in some occasions
, esd does not happen at all , instead finite residual entanglement can be preserved in the long time limit @xcite .
this can be due to the structured environment and physically it results from the formation of a bound state between the qubit and its amplitude damping reservoir @xcite .
these results show rich dynamical behaviors of the entanglement and its characters actually have not been clearly identified .
recently , lpez _ et al .
_ asked a question about where the lost entanglement of the qubits goes @xcite .
interestingly , they found that the lost entanglement of the qubits is exclusively transferred to the reservoirs under the markovian amplitude - damping decoherence dynamics and esd of the qubits is always accompanied with the entanglement sudden birth ( esb ) of the reservoirs .
a similar situation happens for the spin entanglement when the spin degree of freedom for one of the two particles interacts with its momentum degree of freedom @xcite .
all these results mean that the entanglement does not go away , it is still there but just changes the location .
this is reminiscent of the work of yonac _ et al . _
@xcite , in which the entanglement dynamics has been studied in a double jaynes - cummings ( j - c ) model .
they found that the entanglement is transferred periodically among all the bipartite partitions of the whole system but an identity ( see below ) has been satisfied at any time .
this may be not surprising since the double j - c model has no decoherence and any initial information can be preserved in the time evolution .
however , it would be surprising if the identity is still valid in the presence of the decoherence , in which a non - equilibrium relaxation process is involved . in this paper
, we show that it is indeed true for such a system consisted of two qubits locally interacting with two amplitude - damping reservoirs .
it is noted that although the infinite degrees of freedom of the reserviors introduce the irreversibility to the subsystems , this result is still reasonable based on the fact that the global system evolves in a unitary way .
furthermore , we find that the distribution of the entanglement among the bipartite subsystems is dependent of the explicit property of the reservoir and its coupling to the qubit .
the rich dynamical behaviors obtained previously in the literature can be regarded as the special cases of our present result or markovian approximation .
particularly , we find that , instead of entirely transferred to the reservoirs , the entanglement can be stably distributed among all the bipartite subsystems if the qubit and its reservoir can form a bound state and the non - markovian effect is important , and the esd of the qubits is not always accompanied with the occurrence of esb of reservoirs .
irrespective of how the entanglement distributes , it is found that the identity about the entanglement in the whole system can be satisfied at any time , which reveals the profound physics of the entanglement dynamics under decoherence .
this paper is organized as follows . in sec .
[ model ] , the model of two independent qubits in two local reservoirs is given . and
the dynamical entanglement invariance is obtained based on the exact solution of the non - markovian decoherence dynamics of the qubit system . in sec .
[ edd ] , the entanglement distribution over the subsystems when the reservoirs are pbg mediums is studied explicitly .
a stable entanglement - distribution configuration is found in the non - markovian dynamics .
finally , a brief discussion and summary are given in sec .
we consider two qubits interacting with two uncorrelated vacuum reservoirs . due to the dynamical independence between the two local subsystems
, we can firstly solve the single subsystem , then apply the result obtained to the double - qubit case .
the hamiltonian of each local subsystem is @xcite @xmath0 where @xmath1 and @xmath2 are the inversion operators and transition frequency of the qubit , @xmath3 and @xmath4 are the creation and annihilation operators of the @xmath5-th mode with frequency @xmath6 of the radiation field .
the coupling strength between the qubit and the reservoir is denoted by @xmath7 , where @xmath8 and @xmath9 are the unit polarization vector and the normalization volume of the radiation field , @xmath10 is the dipole moment of the qubit , and @xmath11 is the free space permittivity .
for such a system , if the qubit is in its ground state @xmath12 and the reservoir is in vacuum state at the initial time , then the system does not evolve to other states .
when the qubit is in its excited state @xmath13 , the system evolves as @xmath14 here @xmath15 denotes that the qubit jumps to its ground state and one photon is excited in the @xmath5-th mode of the reservoir .
@xmath16 satisfies an integro - differential equation @xmath17 where the kernel function @xmath18 is dependent of the spectral density @xmath19 . introducing the normalized collective state of the reservoir with one excitation as @xmath20 and with zero excitation as @xmath21 @xcite , eq .
( [ t9 ] ) can be written as @xmath22 , where @xmath23 .
it should be emphasized that the introducing of normalized collective state is not a reduction of present model to the j - c model @xcite , as noted in @xcite .
the dynamics is given by eq .
( [ t7 ] ) , which is difficult to obtain analytically since its non - markovian nature . in general the numerical integration should be used .
it is emphasized that our treatment to the dynamics of the system is exact without resorting to the widely used born - markovian approximation . to compare with the conventional approximate result
, we may derive straightforwardly the master equation from eq .
( [ t9 ] ) after tracing over the degree of freedom of the reservoir @xcite , @xmath24+\gamma ( t)[2\sigma _ { -}\rho ( t)\sigma _ { + } \nonumber \\ & & -\sigma _ { + } \sigma _ { -}\rho ( t)-\rho ( t)\sigma _ { + } \sigma _ { - } ] , \label{mstt}\end{aligned}\]]where the time - dependent parameters are given by @xmath25,~\gamma ( t)=-\text{re}[\frac{% \dot{b}(t)}{b(t)}]$ ] .
the time - dependent parameters @xmath26 and @xmath27 play the roles of lamb shifted frequency and decay rate of the qubit , respectively .
the integro - differential equation ( [ t7 ] ) contains the memory effect of the reservoir registered in the time - nonlocal kernel function and thus the dynamics of qubit displays non - markovian effect .
if the time - nonlocal kernel function is replaced by a time - local one , then eq . ( [ mstt ] ) recovers the conventional master equation under born - markovian approximation @xcite . according to the above results ,
the time evolution of a system consisted of two such subsystems with the initial state @xmath28 is given by @xmath29 where @xmath30 and @xmath31 are the coefficients to determine the initial entanglement in the system .
from @xmath32 , one can obtain the time - dependent reduced density matrix of the bipartite subsystem qubit1-qubit2 ( @xmath33 ) by tracing over the reservoir variables .
it reads @xmath34 where @xmath35 and @xmath36 .
similarly , one can obtain the corresponding reduced density matrices for other subsystems like reservoir1-reservoir2 ( @xmath37 ) and qubit - reservoir ( @xmath38 , @xmath39 , @xmath40 , @xmath41 ) . using the concurrence @xcite to quantify entanglement
, we can calculate the entanglement of each subsystem as @xmath42 with @xmath43 for different bipartite partitions labeled by @xmath44 as @xmath45 one can verify that @xmath46 in eqs .
( [ qq])-([qr2 ] ) satisfy an identity @xmath47 where @xmath48 is just the initial entanglement present in @xmath33 .
( [ t15 ] ) recovers the explicit form derived in a double j - c model @xcite when each of the reservoirs contains only one mode , i.e. @xmath49 , where the decoherence is absent and the dynamics is reversible .
it is interesting that this identity is still valid in the present model because the reservoirs containing infinite degrees of freedom here lead to a completely out - of - phase interaction with qubit and an irreversibility .
furthermore , one notes that the identity is not dependent of any detail about @xmath16 , which only determines the detailed dynamical behavior of each components in eq .
( [ t15 ] ) .
this result manifests certain kind of invariant nature of the entanglement .
( [ t15 ] ) can be intuitively understood by the global multipartite entanglement of the whole system .
the global entanglement carried by the subsystem @xmath50 can be straightforwardly calculated from eq .
( [ phit ] ) by generalized concurrence @xcite as @xmath48 , which , coinciding with the bipartite entanglement initially present in @xmath33 , just is the right hand side of eq .
( [ t15 ] ) .
since there is no direct interaction between @xmath51 and @xmath52 , this global entanglement is conserved during the time evolution . from this point ,
our result is consistent with the one in refs . @xcite and @xcite .
another observation of eq .
( [ t15 ] ) is that the different coefficients in the left hand side are essentially determined by the energy / information transfer among the local subsystems .
explicitly , in our model the total excitation number is conserved , so the energy degradation in @xmath53 with factor @xmath16 is compensated by the energy enhancement in @xmath54 with factor @xmath55 .
this causes that @xmath56 , @xmath57 , and @xmath58 , in all of which the double excitation is involved , have similar form except for the different combinations of @xmath16 and @xmath55 in eqs .
( [ qq ] ) , ( [ rr ] ) , and ( [ qr2 ] ) .
the dynamical consequence of the competition of the two terms in these equations causes the sudden death / birth of entanglement characterized by the presence of negative @xmath59 .
a different case happens for @xmath60 , where only single excitation is involved and no sudden death is present . with these observation , one can roughly understand why such combination in left hand side of eq .
( [ t15 ] ) gives the global entanglement . the significance of eq .
( [ t15 ] ) is that it gives us a guideline to judge how the entanglement spreads out over all the bipartite partitions .
it implies that entanglement is not destroyed but re - distributed among all the bipartite subsystems and this re - distribution behavior is not irregular but in certain kind of invariant manner .
the similar invariant property of entanglement evolution has also been studied in ref .
@xcite . in the following
we explicitly discuss the entanglement distribution , especially in the steady state , by taking the reservoir as a photonic band gap ( pbg ) medium @xcite and compare it with the previous results .
we will pay our attention mainly on the consequence of the non - markovian effect on the entanglement distribution and its differences to the results in refs . @xcite and @xcite .
for the pbg medium , the dispersion relation near the upper band - edge is given by @xcite @xmath61 where @xmath62 , @xmath63 is the upper band - edge frequency and @xmath64 is the corresponding characteristic wave vector . in this case
, the kernel function has the form @xmath65 where @xmath66 is a dimensionless constant . in solving eq .
( [ t7 ] ) for @xmath16 , eq .
( [ kn ] ) is evaluated numerically .
here we do not assume that @xmath5 is replaced by @xmath64 outside of the exponential @xcite .
so our result is numerically exact . in the following
we take @xmath67 as the unit of frequency . [
cols="^,^ " , ] in figs .
[ bst ] and [ nbst ] , we show the entanglement evolutions of each subsystem for two typical cases of @xmath68 and @xmath69 , which correspond to the atomic frequency being located at the band gap and at the upper band of the pbg medium , respectively . in the both cases the initial entanglement in @xmath33 begins to transfer to other bipartite partitions with time but their explicit evolutions , in particular the long time behaviors ,
are quite different . in the former case
, the entanglement could be distributed stably among all possible bipartite partitions .
[ bst](a ) shows that after some oscillations , a sizeable entanglement of @xmath33 is preserved for the parameter regime of @xmath70 .
remarkably , the entanglement in @xmath71 forms quickly in the full range of @xmath30 [ fig . [ bst](c ) ] and dominates the distribution . on the contrary , only slight entanglement of @xmath37 is formed in a very narrow parameter regime @xmath72 , as shown in fig .
[ bst](b ) .
however , when @xmath73 is located at the upper band of the pbg medium , the initial entanglement in @xmath33 is transferred completely to the @xmath37 in the long - time limit , as shown in fig .
[ nbst ] . at the initial stage , @xmath74 and @xmath75
are entangled transiently , but there is no stable entanglement distribution .
this result is consistent with that in refs .
it is noted that the entanglement in @xmath76 comes from two parts : one is transferred from @xmath33 , the other is created by the direct interaction between @xmath53 and @xmath54 . this can be seen clearly from fig .
[ bst](c ) when @xmath30 is very small , the initial entanglement of @xmath33 is very small , while that of @xmath76 is rather large , which just results from the interaction between @xmath53 and @xmath54 .
another interesting point is a stable entanglement can even be formed for the non - interacting bipartite system @xmath39 [ see [ bst](d ) when @xmath77 .
this entanglement transfer also results from the local interaction between @xmath53 and @xmath54 @xcite .
it is not difficult to understand these rich behaviors of entanglement distribution according to eqs .
( [ qq])-([qr2 ] ) and its invariance ( [ t15 ] ) . from these equations
, one can clearly see that the entanglement dynamics and its distributions in the bipartite partitions are completely determined by the time - dependent factor @xmath78 of single - qubit excited - state population .
[ tong0 ] shows its time evolutions for the corresponding parameter regimes presented above .
we notice that @xmath79 when @xmath73 is located at the band gap , which means that there is some excited - state population in the long - time limit .
this phenomenon known as population trapping @xcite is responsible for the suppression of the spontaneous emission of two - level system in pbg reservoir and has been experimentally observed @xcite .
such population trapping just manifests the formation of bound states between @xmath53 and @xmath54 @xcite , which has been experimentally verified in @xcite .
consequently , @xmath53 and @xmath54 are so correlated in the bound states that the initial entanglement in @xmath33 can not be fully transferred to @xmath37 .
the oscillation during the evolution is just the manifestation of the strong non - markovian effect induced by the reservoirs .
on the contrary , if @xmath73 is located in the upper band , then @xmath80 and the qubits decay completely to their ground states . in this case
the bound states between @xmath53 and @xmath54 are absent and , according to eq .
( [ t15 ] ) , the initial entanglement in @xmath33 is completely transferred to @xmath37 , as clearly shown in eq .
( [ rr ] ) .
in addition , in refs . @xcite it was emphasized that esd of @xmath33 is always accompanied with esb of @xmath37 .
however , this is not always true .
to clarify this , we examine the condition to obtain esd of the qubits and the companying esb of the reservoirs . from eqs .
( [ qq ] ) and ( [ rr ] ) it is obvious that the condition is @xmath81 and @xmath82 at any @xmath83 and @xmath84 , which means @xmath85 when the bound states is absent , @xmath86 , the condition ( [ dd ] ) can be satisfied when @xmath87 .
so one can always expect esd of the qubits and the companying esb of the reservoirs in the region @xmath88 , as shown in fig .
[ nbst ] and refs .
however , when the bound states are available , the situation changes .
in particular , when @xmath89 in the full range of time evolution , no region of @xmath90 can make the condition ( [ dd ] ) to be satisfied anymore .
for clarification , we present three typical behaviors of the entanglement distribution in fig .
[ td ] . in all these cases
the bound states are available .
[ td](a ) shows the situation where the entanglement is stably distributed among all of the bipartite subsystems .
[ td](b ) indicates that the entanglement of @xmath91 shows esb and revival , while the entanglement of @xmath33 does not exhibit esd .
[ td](c ) shows another example that while the entanglement of @xmath33 has esd and revival @xcite , the entanglement of @xmath37 does not show esb but remains to be zero .
[ td](b , c ) reveal that esd in @xmath33 has no direct relationship with esb in @xmath37 .
the above discussion is not dependent of the explicit spectral density of the individual reservoir . to confirm this
, we consider the reservoir in free space .
the spectral density has the ohmic form @xmath92 , which can be obtained from the free - space dispersion relation @xmath93 .
one can verify that the condition for the formation of bound states is : @xmath94 @xcite . in fig .
[ osd ] , we plot the results in this situation .
the previous results can be recovered when the bound states are absent @xcite . on the contrary , when the bound states are available , a stable entanglement is established among all the bipartite partitions .
therefore , we argue that the stable entanglement distribution resulted from the bound states is a general phenomenon in open quantum system when the non - markovian effect is taken into account . in summary , we have studied the entanglement distribution among all the bipartite subsystems of two qubits embedded into two independent amplitude damping reservoirs .
it is found that the entanglement can be stably distributed in all the bipartite subsystems , which is much different no matter to the markovian approximate result @xcite or to the decoherenceless double j - c model result @xcite , and an identity about the entanglement in all subsystems is always satisfied .
this identity is shown to be independent of any detail of the reservoirs and their coupling to the qubit , which affect only the explicit time evolution behavior and the final distribution .
the result is significant to the study of the physical nature of entanglement under decoherence .
it implies an active way to protect entanglement from decoherence by modifying the properties of the reservoir via the potential usage of the newly emerged technique , i.e. quantum reservoir engineering @xcite .
this work is supported by the fundamental research funds for the central universities under grant no .
lzujbky-2010 - 72 , gansu provincial nsf under grant no .
0803rjza095 , the national nsf of china , the program for ncet , and the cqt wbs grant no . r-710 - 000 - 008 - 271 .[/INST] we study the entanglement dynamics of two qubits , each of which is embedded into its local amplitude - damping reservoir , and the entanglement distribution among all the bipartite subsystems including qubit - qubit , qubit - reservoir , and reservoir - reservoir .
it is found that the entanglement can be stably distributed among all components , which is much different to the result obtained under the born - markovian approximation by c. e. lpez _
et al . _
[ phys .
rev .
lett .
* 101 * , 080503 ( 2008 ) ] , and particularly it also satisfies an identity .
our unified treatment includes the previous results as special cases .
the result may give help to understand the physical nature of entanglement under decoherence . </s> |
malaria is still one of the main sources of consideration for public health in many countries including iran , particularly in south and southeast regions of the country .
deliberate implementation of control measures has resulted in a substantial reduction of malaria incidence in iran in recent years ( 1 ) , therefore malaria cases were reduced from 11,460 cases in 2008 to 3,239 in 2011(iranian center for disease management and control , cdmc , unpublished data ) . in iran , p. vivax is responsible for the majority of malaria cases while plasmodium falciparum accounts for 1015% of the cases ( cdmc , unpublished ) .
iran entered the malaria pre - elimination program since 2009 and interventions such as preventing strategies , active case detection and timely appropriate treatment of patients have been performed in all endemic areas of the country . in order to achieve malaria elimination , which is a global concept to reduce the incidence of locally acquired infection into zero , early recognition of all parasite carriers bearing various disease symptoms and parasite rates is crucial . in this situation
, active surveillance by precise laboratory methods in endemic areas provides an appropriate tool for detection of all kinds of infections particularly asymptomatic ones containing low parasite densities ( 2 ) .
formerly asymptomatic malaria infections were described in hyper - endemic regions following frequent infective bites and repetitive immune system response toward the parasite attenuating parasitemia to undetectable levels in blood smear ( 3 , 4 ) .
the prevalence of this kind of malaria infection was determined by means of different laboratory techniques in various endemic countries previously ( 59 ) , in parallel with other counties there are a few studies in iran which assessed asymptomatic malaria prevalence in different low endemic areas of the country ( 1012 ) . based on the controversial results of previous studies which show the fluctuation of asymptomatic infection among the plenty of endemic regions , the importance of regional acquiring of symptomless infection
another highly important issue that has to be taking account in asymptomatic malaria investigation is using accurate detection methods to find all carriers , principally who does not have clinical malaria symptoms .
this highlights the vitality of evaluating diagnostic method s delicacy for further decisions on malaria elimination interventions . to date
, light microscopy of giemsa - stained thick and thin blood smears has been remained as the standard laboratory method of malaria diagnosis due to specificity and ability to quantify the level of parasitemia ( 13 ) .
however , the reliance to the results of light microscopy is restricted due to the limitations associated with this method ( 14 ) .
although microscopy is the most commonly used method of malaria diagnosis as the gold standard in iran , chromatographic rapid diagnostic tests ( rdts ) are introduced in remote settings , where microscopic diagnosis is either impractical or unfeasible and as a complementary method for confirming the parasite - infected cases . besides the mentioned methods , the usefulness of molecular methods such as nested - polymerase chain reaction ( pcr ) has been emphasized as highly sensitive means of malaria detection , particularly in sub - clinical parasitemia levels ( 1517 ) .
the aim of this study was to detect low parasite and asymptomatic malaria infections by means of three malaria diagnostic tests ( microscopy , rdt and nested - pcr ) , in a low transmission region of bagh - e - malek in minab district , hormozgan province , southern iran . the results of this investigation would help further case surveillance strategies in the region and additionally all endemic settings of iran , as an essential approach toward achieving malaria elimination all over the country .
the present study was performed as a cross - sectional survey in bagh - e - malek region , which is located in minab district , southeast of hormozgan province .
hormozgan is one of the endemic areas in southern iran , containing about 10.8% of all iranian malaria patients in 2011 ( 349 cases reported based on the iranian cdmc unpublished report ) ( fig .
the higher rate of transmission has been reported from bagh - e malek area , therefore this region was selected for this project .
bagh - e - malek is a lowland area surrounded by mountains , which isolate it from the neighboring regions in minab , which has a population of 1,451 people .
the annual average temperature of minab is 28 c ; pluviometer index of 249 mm and an annual relative humidity of 55.5% .
iran s map , depicting the study area the total malaria cases in this area were 15 in 2011 ( iranian cdmc ) , while plasmodium vivax is the predominant species in bagh - e malek and whole province , also the chief anopheles vectors in minab are anopheles stephensi , an .
. mainly two annual peaks of malaria are seen in this area ; which occurs in may and october .
a total of 200 healthy volunteers were participated in this study from bagh - e malek area ( 62 males and 138 females ) .
briefly 3 ml fresh blood sample were collected during july 2011 from the participants after getting informed consent , for further microscopic , rdt and molecular analysis .
the study was approved by the ethics committee of hormozgan university of medical sciences ( approval no .
inclusion criteria such as lack of having any malaria symptom or receiving anti - malarial drug in three weeks prior to the study and having no travel history to other malaria endemic areas in the past three months were considered in sample collection .
thin films fixed using methanol then every slide stained with 10% giemsa and examined at 1000 with oil immersion to inspect malaria parasites by a skilled microscopist .
further thick and thin blood smear preparation were carried out from all participants , 30 days following the sampling date as well as 60 days afterwards , in order to follow up the samples .
all specimens were tested with the first response malaria pldh / hrp2 combo assay ( premier medical corporation ltd .
the kit contains a two line strip pre - coated with two monoclonal antibodies , one against the pan - specific lactate dehydrogenase , pldh , of the plasmodium species ( p. falciparum , vivax , malariae , ovale ) and the other antibody was against p. falciparum species histidine - rich protein 2 ( hrp2 ) .
briefly , 5 l of whole blood was dispensed onto sample well followed by two drops of assay buffer ( 60 l ) into developer well .
the test control line was observed as an indicator , in order to validate the performance of the test .
finally , differential diagnosis between p. falciparum and non - falciparum species were interpreted as described previously ( 19 ) .
the molecular detection of plasmodium species was performed using nested - pcr amplification of 18 ssrrna of the parasite . to achieve this purpose ,
dna was extracted from whole blood samples using promega kit ( promega , madison , wi , usa ) and stored at 20c until further analysis with primers and cycling conditions that described previously ( 11,20 ) . in brief , 5 l of extracted dna was used in the first nest , by use of primers targeting an external region specific to the plasmodium genus followed by second nest using 2 l of the first nested - pcr product as template to amplify specific p. vivax and p. falciparum fragments using internal primers .
amplification was performed in a total volume of 25 l including , 25 l of templates , 250 nm of primers , 10 mm tris
hcl ( ph 8.3 ) , 50 mm kcl , 2 mm mgcl2 , 125 m of each of the four deoxynucleotide triphosphates and 0.4 u of taq polymerase ( invitrogen , carlsbad , ca ) . first and second nests repeated for 25 and 30 cycles , respectively while the annealing temperature was 72 c for both reactions .
amplicons from the second nest of pcr were electrophoresed on 2% agarose gel and visualized under uv light after staining with ethidium bromide .
a sample was considered positive for p. vivax and p. falciparum if a 120 and 419 base - pair fragment was detected , respectively .
the present study was performed as a cross - sectional survey in bagh - e - malek region , which is located in minab district , southeast of hormozgan province .
hormozgan is one of the endemic areas in southern iran , containing about 10.8% of all iranian malaria patients in 2011 ( 349 cases reported based on the iranian cdmc unpublished report ) ( fig .
the higher rate of transmission has been reported from bagh - e malek area , therefore this region was selected for this project .
bagh - e - malek is a lowland area surrounded by mountains , which isolate it from the neighboring regions in minab , which has a population of 1,451 people .
the annual average temperature of minab is 28 c ; pluviometer index of 249 mm and an annual relative humidity of 55.5% .
iran s map , depicting the study area the total malaria cases in this area were 15 in 2011 ( iranian cdmc ) , while plasmodium vivax is the predominant species in bagh - e malek and whole province , also the chief anopheles vectors in minab are anopheles stephensi , an .
. mainly two annual peaks of malaria are seen in this area ; which occurs in may and october .
a total of 200 healthy volunteers were participated in this study from bagh - e malek area ( 62 males and 138 females ) .
briefly 3 ml fresh blood sample were collected during july 2011 from the participants after getting informed consent , for further microscopic , rdt and molecular analysis .
the study was approved by the ethics committee of hormozgan university of medical sciences ( approval no .
inclusion criteria such as lack of having any malaria symptom or receiving anti - malarial drug in three weeks prior to the study and having no travel history to other malaria endemic areas in the past three months were considered in sample collection .
thin films fixed using methanol then every slide stained with 10% giemsa and examined at 1000 with oil immersion to inspect malaria parasites by a skilled microscopist .
further thick and thin blood smear preparation were carried out from all participants , 30 days following the sampling date as well as 60 days afterwards , in order to follow up the samples .
all specimens were tested with the first response malaria pldh / hrp2 combo assay ( premier medical corporation ltd . ,
the kit contains a two line strip pre - coated with two monoclonal antibodies , one against the pan - specific lactate dehydrogenase , pldh , of the plasmodium species ( p. falciparum , vivax , malariae , ovale ) and the other antibody was against p. falciparum species histidine - rich protein 2 ( hrp2 ) .
briefly , 5 l of whole blood was dispensed onto sample well followed by two drops of assay buffer ( 60 l ) into developer well .
the test control line was observed as an indicator , in order to validate the performance of the test .
finally , differential diagnosis between p. falciparum and non - falciparum species were interpreted as described previously ( 19 ) .
the molecular detection of plasmodium species was performed using nested - pcr amplification of 18 ssrrna of the parasite . to achieve this purpose ,
dna was extracted from whole blood samples using promega kit ( promega , madison , wi , usa ) and stored at 20c until further analysis with primers and cycling conditions that described previously ( 11,20 ) . in brief , 5 l of extracted dna was used in the first nest , by use of primers targeting an external region specific to the plasmodium genus followed by second nest using 2 l of the first nested - pcr product as template to amplify specific p. vivax and p. falciparum fragments using internal primers .
amplification was performed in a total volume of 25 l including , 25 l of templates , 250 nm of primers , 10 mm tris
hcl ( ph 8.3 ) , 50 mm kcl , 2 mm mgcl2 , 125 m of each of the four deoxynucleotide triphosphates and 0.4 u of taq polymerase ( invitrogen , carlsbad , ca ) . first and second nests repeated for 25 and 30 cycles , respectively while the annealing temperature was 72 c for both reactions .
amplicons from the second nest of pcr were electrophoresed on 2% agarose gel and visualized under uv light after staining with ethidium bromide .
a sample was considered positive for p. vivax and p. falciparum if a 120 and 419 base - pair fragment was detected , respectively .
this investigation was carried out in order to assay the concordance between the outcomes of routine malaria diagnostic techniques with nested - pcr detecting method in finding asymptomatic cases in elimination phase of malaria control .
hence , blood samples and smears were collected from 200 individuals residing in the endemic region of bagh - e - malek located in minab district , hormozgan province of iran .
all of specimens were evaluated using microscopic , rdt and nested - pcr analysis in hormozgan provincial health center laboratory .
all of participants were healthy individuals and age range was from 3 to 60 years old ( mean age 27.2 ) ( table 1 ) .
details of demographic data and the frequency of asymptomatic infection detected by use of nested - pcr the entire 200 thick and thin giemsa - stained blood smears were inspected to detect plasmodium parasite by well - trained microscopist in hormozgan provincial health center laboratory and no plasmodium parasite were detected in any examined sample . additionally none of samples was diagnosed to have any malaria parasite during the 60-days follow up protocol , while all of samples remained symptomless .
rdts were tested as a complementary analysis for all of 200 samples using monoclonal antibody coated sticks .
no positive result was discovered for either p. falciparum and/or non - falciparum species in the performed tests . in this cross sectional study ,
nested - pcr amplification was performed as a sensitive and specific method to find parasite genome in extracted dna from asymptomatic samples .
interestingly 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr using specific primers , although they were considered uninfected using microscopic and rdt tests ( table 1 ) .
these cases were considered as asymptomatic malaria patients since they remained symptomless in follow up evaluations ( i.e. thick blood smear and rdt ) prior to treatment .
all positive cases were female and only one of them had a malaria history 20 years prior to the time of this investigation .
moreover , no plasmodium falciparum infection was detected by this technique for all examined samples .
all infected subjects were treated after diagnosis by standard anti - malarial drugs according cdmc of iran protocol and reevaluated after treatment by means of molecular method .
the entire 200 thick and thin giemsa - stained blood smears were inspected to detect plasmodium parasite by well - trained microscopist in hormozgan provincial health center laboratory and no plasmodium parasite were detected in any examined sample . additionally none of samples was diagnosed to have any malaria parasite during the 60-days follow up protocol , while all of samples remained symptomless .
rdts were tested as a complementary analysis for all of 200 samples using monoclonal antibody coated sticks .
no positive result was discovered for either p. falciparum and/or non - falciparum species in the performed tests .
in this cross sectional study , nested - pcr amplification was performed as a sensitive and specific method to find parasite genome in extracted dna from asymptomatic samples . interestingly 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr using specific primers , although they were considered uninfected using microscopic and rdt tests ( table 1 ) .
these cases were considered as asymptomatic malaria patients since they remained symptomless in follow up evaluations ( i.e. thick blood smear and rdt ) prior to treatment .
all positive cases were female and only one of them had a malaria history 20 years prior to the time of this investigation .
moreover , no plasmodium falciparum infection was detected by this technique for all examined samples .
all infected subjects were treated after diagnosis by standard anti - malarial drugs according cdmc of iran protocol and reevaluated after treatment by means of molecular method .
in the elimination phase of malaria control , monitoring all cases particularly hidden parasites is of major importance .
this highlights choosing of an acceptable detecting method , which should be , applied in all incoming asymptomatic investigation afterwards in order to detect every single carrier which continue disease transmission in the population ( 21 ) . currently in malaria endemic areas of iran ,
microscopic and rdt assays are used for active case surveillance , although these methods could detect nearly all of symptomatic infections , in case of asymptomatic and mixed infections a more reliable technique would be helpful especially in elimination program as a public health concern in the country .
although , microscopy is still the diagnosis gold standard , limitations such as requiring well skilled microscopists , technical equipment maintenance , discrepancy in microscopist training and insufficient quality control are associated with this method ( 22 ) .
although expert microscopy could theoretically detect 10 p/l parasitemia , average microscopy has proven to be unable in detecting lower than 100 p/l parasitemia ( 23 ) .
however , it should be mentioned that microscopy is the primary and easiest to establish method in the field situation .
alternatively , despite the simplicity and being easy to use without particular training which highlight the role of rdts in malaria detection , they may have some disadvantages ; for instance , the intensity of test band is subject to amount of antigen particularly low parasite densities , and this may lead to reader variation in test results .
furthermore , the short shelf life of rdts emphasizes requiring of proficient transportation , storage and distribution systems , additionally , diagnose of asymptomatic malaria infection realized to be unreliable using rdts ( 2325 ) .
in addition to the importance of microscopy and rdt , mainly in field settings , in a number of recent investigations molecular methods were nominated as valuable and robust approaches particularly in detecting sub - clinical parasitaemia i.e. asymptomatic carriers , mixed infections and confirmation of plasmodium species in low - transmission areas ( 2629 ) .
however , regarding pcr expenses and equipment requirements in contrast to usual diagnosis methods , the performance of nested - pcr in identifying asymptomatic carriers was compared to conventional microscopic and rdts in symptomless population of bagh - e - malek , a malaria endemic region , in southern iran .
interestingly nested - pcr found three p. vivax carriers while microscopy and rdt missed the cases , one of the patients was a 12-year - old symptomless girl , who experienced a period of fever in the year prior to the study , and her disease has not been diagnosed since her thick and thin blood smears analyzed negative by light microscopy .
the blood films of this patient remained negative even in re - sampling after identifying a positive pcr result .
the current results emphasize the importance of using molecular methods in order to interrupt malaria transmission in iran besides microscopy and rdts as routine methods . it should be noted that toward eliminating malaria from the country and prevention of re - introduction , all the three types of malaria detection tools ( microscopy , rdt and molecular methods such as nested - pcr ) should be used to improve sensitivity , specificity and reliability for active case surveillance in endemic settings . | background : the aim of this study was to detect low parasite and asymptomatic malaria infections by means of three malaria diagnostic tests , in a low transmission region of minab district , hormozgan province , southern iran.methods:blood samples of 200 healthy volunteers from bagh - e - malek area were evaluated using microscopic , rapid diagnostic tests ( rdt ) and nested - pcr to inspect malaria parasite.results:the results showed no plasmodium parasite in subjects by means of microscopy and rdt .
however , 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr while microscopy and rdt missed the cases.conclusion:microscopy as the gold standard method and rdt correctly identified 98.5% of cases , and molecular analysis is sensitive and reliable , especially in the detection of asymptomatic infections for active case surveillance . regarding the existence of asymptomatic malaria in endemic area of hormozgan , iran ,
nested - pcr could be considered as a sensitive tool to interrupt malaria transmission in the country , beside the microscopic and rdt methods . | <s>[INST]malaria is still one of the main sources of consideration for public health in many countries including iran , particularly in south and southeast regions of the country .
deliberate implementation of control measures has resulted in a substantial reduction of malaria incidence in iran in recent years ( 1 ) , therefore malaria cases were reduced from 11,460 cases in 2008 to 3,239 in 2011(iranian center for disease management and control , cdmc , unpublished data ) . in iran , p. vivax is responsible for the majority of malaria cases while plasmodium falciparum accounts for 1015% of the cases ( cdmc , unpublished ) .
iran entered the malaria pre - elimination program since 2009 and interventions such as preventing strategies , active case detection and timely appropriate treatment of patients have been performed in all endemic areas of the country . in order to achieve malaria elimination , which is a global concept to reduce the incidence of locally acquired infection into zero , early recognition of all parasite carriers bearing various disease symptoms and parasite rates is crucial . in this situation
, active surveillance by precise laboratory methods in endemic areas provides an appropriate tool for detection of all kinds of infections particularly asymptomatic ones containing low parasite densities ( 2 ) .
formerly asymptomatic malaria infections were described in hyper - endemic regions following frequent infective bites and repetitive immune system response toward the parasite attenuating parasitemia to undetectable levels in blood smear ( 3 , 4 ) .
the prevalence of this kind of malaria infection was determined by means of different laboratory techniques in various endemic countries previously ( 59 ) , in parallel with other counties there are a few studies in iran which assessed asymptomatic malaria prevalence in different low endemic areas of the country ( 1012 ) . based on the controversial results of previous studies which show the fluctuation of asymptomatic infection among the plenty of endemic regions , the importance of regional acquiring of symptomless infection
another highly important issue that has to be taking account in asymptomatic malaria investigation is using accurate detection methods to find all carriers , principally who does not have clinical malaria symptoms .
this highlights the vitality of evaluating diagnostic method s delicacy for further decisions on malaria elimination interventions . to date
, light microscopy of giemsa - stained thick and thin blood smears has been remained as the standard laboratory method of malaria diagnosis due to specificity and ability to quantify the level of parasitemia ( 13 ) .
however , the reliance to the results of light microscopy is restricted due to the limitations associated with this method ( 14 ) .
although microscopy is the most commonly used method of malaria diagnosis as the gold standard in iran , chromatographic rapid diagnostic tests ( rdts ) are introduced in remote settings , where microscopic diagnosis is either impractical or unfeasible and as a complementary method for confirming the parasite - infected cases . besides the mentioned methods , the usefulness of molecular methods such as nested - polymerase chain reaction ( pcr ) has been emphasized as highly sensitive means of malaria detection , particularly in sub - clinical parasitemia levels ( 1517 ) .
the aim of this study was to detect low parasite and asymptomatic malaria infections by means of three malaria diagnostic tests ( microscopy , rdt and nested - pcr ) , in a low transmission region of bagh - e - malek in minab district , hormozgan province , southern iran . the results of this investigation would help further case surveillance strategies in the region and additionally all endemic settings of iran , as an essential approach toward achieving malaria elimination all over the country .
the present study was performed as a cross - sectional survey in bagh - e - malek region , which is located in minab district , southeast of hormozgan province .
hormozgan is one of the endemic areas in southern iran , containing about 10.8% of all iranian malaria patients in 2011 ( 349 cases reported based on the iranian cdmc unpublished report ) ( fig .
the higher rate of transmission has been reported from bagh - e malek area , therefore this region was selected for this project .
bagh - e - malek is a lowland area surrounded by mountains , which isolate it from the neighboring regions in minab , which has a population of 1,451 people .
the annual average temperature of minab is 28 c ; pluviometer index of 249 mm and an annual relative humidity of 55.5% .
iran s map , depicting the study area the total malaria cases in this area were 15 in 2011 ( iranian cdmc ) , while plasmodium vivax is the predominant species in bagh - e malek and whole province , also the chief anopheles vectors in minab are anopheles stephensi , an .
. mainly two annual peaks of malaria are seen in this area ; which occurs in may and october .
a total of 200 healthy volunteers were participated in this study from bagh - e malek area ( 62 males and 138 females ) .
briefly 3 ml fresh blood sample were collected during july 2011 from the participants after getting informed consent , for further microscopic , rdt and molecular analysis .
the study was approved by the ethics committee of hormozgan university of medical sciences ( approval no .
inclusion criteria such as lack of having any malaria symptom or receiving anti - malarial drug in three weeks prior to the study and having no travel history to other malaria endemic areas in the past three months were considered in sample collection .
thin films fixed using methanol then every slide stained with 10% giemsa and examined at 1000 with oil immersion to inspect malaria parasites by a skilled microscopist .
further thick and thin blood smear preparation were carried out from all participants , 30 days following the sampling date as well as 60 days afterwards , in order to follow up the samples .
all specimens were tested with the first response malaria pldh / hrp2 combo assay ( premier medical corporation ltd .
the kit contains a two line strip pre - coated with two monoclonal antibodies , one against the pan - specific lactate dehydrogenase , pldh , of the plasmodium species ( p. falciparum , vivax , malariae , ovale ) and the other antibody was against p. falciparum species histidine - rich protein 2 ( hrp2 ) .
briefly , 5 l of whole blood was dispensed onto sample well followed by two drops of assay buffer ( 60 l ) into developer well .
the test control line was observed as an indicator , in order to validate the performance of the test .
finally , differential diagnosis between p. falciparum and non - falciparum species were interpreted as described previously ( 19 ) .
the molecular detection of plasmodium species was performed using nested - pcr amplification of 18 ssrrna of the parasite . to achieve this purpose ,
dna was extracted from whole blood samples using promega kit ( promega , madison , wi , usa ) and stored at 20c until further analysis with primers and cycling conditions that described previously ( 11,20 ) . in brief , 5 l of extracted dna was used in the first nest , by use of primers targeting an external region specific to the plasmodium genus followed by second nest using 2 l of the first nested - pcr product as template to amplify specific p. vivax and p. falciparum fragments using internal primers .
amplification was performed in a total volume of 25 l including , 25 l of templates , 250 nm of primers , 10 mm tris
hcl ( ph 8.3 ) , 50 mm kcl , 2 mm mgcl2 , 125 m of each of the four deoxynucleotide triphosphates and 0.4 u of taq polymerase ( invitrogen , carlsbad , ca ) . first and second nests repeated for 25 and 30 cycles , respectively while the annealing temperature was 72 c for both reactions .
amplicons from the second nest of pcr were electrophoresed on 2% agarose gel and visualized under uv light after staining with ethidium bromide .
a sample was considered positive for p. vivax and p. falciparum if a 120 and 419 base - pair fragment was detected , respectively .
the present study was performed as a cross - sectional survey in bagh - e - malek region , which is located in minab district , southeast of hormozgan province .
hormozgan is one of the endemic areas in southern iran , containing about 10.8% of all iranian malaria patients in 2011 ( 349 cases reported based on the iranian cdmc unpublished report ) ( fig .
the higher rate of transmission has been reported from bagh - e malek area , therefore this region was selected for this project .
bagh - e - malek is a lowland area surrounded by mountains , which isolate it from the neighboring regions in minab , which has a population of 1,451 people .
the annual average temperature of minab is 28 c ; pluviometer index of 249 mm and an annual relative humidity of 55.5% .
iran s map , depicting the study area the total malaria cases in this area were 15 in 2011 ( iranian cdmc ) , while plasmodium vivax is the predominant species in bagh - e malek and whole province , also the chief anopheles vectors in minab are anopheles stephensi , an .
. mainly two annual peaks of malaria are seen in this area ; which occurs in may and october .
a total of 200 healthy volunteers were participated in this study from bagh - e malek area ( 62 males and 138 females ) .
briefly 3 ml fresh blood sample were collected during july 2011 from the participants after getting informed consent , for further microscopic , rdt and molecular analysis .
the study was approved by the ethics committee of hormozgan university of medical sciences ( approval no .
inclusion criteria such as lack of having any malaria symptom or receiving anti - malarial drug in three weeks prior to the study and having no travel history to other malaria endemic areas in the past three months were considered in sample collection .
thin films fixed using methanol then every slide stained with 10% giemsa and examined at 1000 with oil immersion to inspect malaria parasites by a skilled microscopist .
further thick and thin blood smear preparation were carried out from all participants , 30 days following the sampling date as well as 60 days afterwards , in order to follow up the samples .
all specimens were tested with the first response malaria pldh / hrp2 combo assay ( premier medical corporation ltd . ,
the kit contains a two line strip pre - coated with two monoclonal antibodies , one against the pan - specific lactate dehydrogenase , pldh , of the plasmodium species ( p. falciparum , vivax , malariae , ovale ) and the other antibody was against p. falciparum species histidine - rich protein 2 ( hrp2 ) .
briefly , 5 l of whole blood was dispensed onto sample well followed by two drops of assay buffer ( 60 l ) into developer well .
the test control line was observed as an indicator , in order to validate the performance of the test .
finally , differential diagnosis between p. falciparum and non - falciparum species were interpreted as described previously ( 19 ) .
the molecular detection of plasmodium species was performed using nested - pcr amplification of 18 ssrrna of the parasite . to achieve this purpose ,
dna was extracted from whole blood samples using promega kit ( promega , madison , wi , usa ) and stored at 20c until further analysis with primers and cycling conditions that described previously ( 11,20 ) . in brief , 5 l of extracted dna was used in the first nest , by use of primers targeting an external region specific to the plasmodium genus followed by second nest using 2 l of the first nested - pcr product as template to amplify specific p. vivax and p. falciparum fragments using internal primers .
amplification was performed in a total volume of 25 l including , 25 l of templates , 250 nm of primers , 10 mm tris
hcl ( ph 8.3 ) , 50 mm kcl , 2 mm mgcl2 , 125 m of each of the four deoxynucleotide triphosphates and 0.4 u of taq polymerase ( invitrogen , carlsbad , ca ) . first and second nests repeated for 25 and 30 cycles , respectively while the annealing temperature was 72 c for both reactions .
amplicons from the second nest of pcr were electrophoresed on 2% agarose gel and visualized under uv light after staining with ethidium bromide .
a sample was considered positive for p. vivax and p. falciparum if a 120 and 419 base - pair fragment was detected , respectively .
this investigation was carried out in order to assay the concordance between the outcomes of routine malaria diagnostic techniques with nested - pcr detecting method in finding asymptomatic cases in elimination phase of malaria control .
hence , blood samples and smears were collected from 200 individuals residing in the endemic region of bagh - e - malek located in minab district , hormozgan province of iran .
all of specimens were evaluated using microscopic , rdt and nested - pcr analysis in hormozgan provincial health center laboratory .
all of participants were healthy individuals and age range was from 3 to 60 years old ( mean age 27.2 ) ( table 1 ) .
details of demographic data and the frequency of asymptomatic infection detected by use of nested - pcr the entire 200 thick and thin giemsa - stained blood smears were inspected to detect plasmodium parasite by well - trained microscopist in hormozgan provincial health center laboratory and no plasmodium parasite were detected in any examined sample . additionally none of samples was diagnosed to have any malaria parasite during the 60-days follow up protocol , while all of samples remained symptomless .
rdts were tested as a complementary analysis for all of 200 samples using monoclonal antibody coated sticks .
no positive result was discovered for either p. falciparum and/or non - falciparum species in the performed tests . in this cross sectional study ,
nested - pcr amplification was performed as a sensitive and specific method to find parasite genome in extracted dna from asymptomatic samples .
interestingly 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr using specific primers , although they were considered uninfected using microscopic and rdt tests ( table 1 ) .
these cases were considered as asymptomatic malaria patients since they remained symptomless in follow up evaluations ( i.e. thick blood smear and rdt ) prior to treatment .
all positive cases were female and only one of them had a malaria history 20 years prior to the time of this investigation .
moreover , no plasmodium falciparum infection was detected by this technique for all examined samples .
all infected subjects were treated after diagnosis by standard anti - malarial drugs according cdmc of iran protocol and reevaluated after treatment by means of molecular method .
the entire 200 thick and thin giemsa - stained blood smears were inspected to detect plasmodium parasite by well - trained microscopist in hormozgan provincial health center laboratory and no plasmodium parasite were detected in any examined sample . additionally none of samples was diagnosed to have any malaria parasite during the 60-days follow up protocol , while all of samples remained symptomless .
rdts were tested as a complementary analysis for all of 200 samples using monoclonal antibody coated sticks .
no positive result was discovered for either p. falciparum and/or non - falciparum species in the performed tests .
in this cross sectional study , nested - pcr amplification was performed as a sensitive and specific method to find parasite genome in extracted dna from asymptomatic samples . interestingly 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr using specific primers , although they were considered uninfected using microscopic and rdt tests ( table 1 ) .
these cases were considered as asymptomatic malaria patients since they remained symptomless in follow up evaluations ( i.e. thick blood smear and rdt ) prior to treatment .
all positive cases were female and only one of them had a malaria history 20 years prior to the time of this investigation .
moreover , no plasmodium falciparum infection was detected by this technique for all examined samples .
all infected subjects were treated after diagnosis by standard anti - malarial drugs according cdmc of iran protocol and reevaluated after treatment by means of molecular method .
in the elimination phase of malaria control , monitoring all cases particularly hidden parasites is of major importance .
this highlights choosing of an acceptable detecting method , which should be , applied in all incoming asymptomatic investigation afterwards in order to detect every single carrier which continue disease transmission in the population ( 21 ) . currently in malaria endemic areas of iran ,
microscopic and rdt assays are used for active case surveillance , although these methods could detect nearly all of symptomatic infections , in case of asymptomatic and mixed infections a more reliable technique would be helpful especially in elimination program as a public health concern in the country .
although , microscopy is still the diagnosis gold standard , limitations such as requiring well skilled microscopists , technical equipment maintenance , discrepancy in microscopist training and insufficient quality control are associated with this method ( 22 ) .
although expert microscopy could theoretically detect 10 p/l parasitemia , average microscopy has proven to be unable in detecting lower than 100 p/l parasitemia ( 23 ) .
however , it should be mentioned that microscopy is the primary and easiest to establish method in the field situation .
alternatively , despite the simplicity and being easy to use without particular training which highlight the role of rdts in malaria detection , they may have some disadvantages ; for instance , the intensity of test band is subject to amount of antigen particularly low parasite densities , and this may lead to reader variation in test results .
furthermore , the short shelf life of rdts emphasizes requiring of proficient transportation , storage and distribution systems , additionally , diagnose of asymptomatic malaria infection realized to be unreliable using rdts ( 2325 ) .
in addition to the importance of microscopy and rdt , mainly in field settings , in a number of recent investigations molecular methods were nominated as valuable and robust approaches particularly in detecting sub - clinical parasitaemia i.e. asymptomatic carriers , mixed infections and confirmation of plasmodium species in low - transmission areas ( 2629 ) .
however , regarding pcr expenses and equipment requirements in contrast to usual diagnosis methods , the performance of nested - pcr in identifying asymptomatic carriers was compared to conventional microscopic and rdts in symptomless population of bagh - e - malek , a malaria endemic region , in southern iran .
interestingly nested - pcr found three p. vivax carriers while microscopy and rdt missed the cases , one of the patients was a 12-year - old symptomless girl , who experienced a period of fever in the year prior to the study , and her disease has not been diagnosed since her thick and thin blood smears analyzed negative by light microscopy .
the blood films of this patient remained negative even in re - sampling after identifying a positive pcr result .
the current results emphasize the importance of using molecular methods in order to interrupt malaria transmission in iran besides microscopy and rdts as routine methods . it should be noted that toward eliminating malaria from the country and prevention of re - introduction , all the three types of malaria detection tools ( microscopy , rdt and molecular methods such as nested - pcr ) should be used to improve sensitivity , specificity and reliability for active case surveillance in endemic settings .[/INST]background : the aim of this study was to detect low parasite and asymptomatic malaria infections by means of three malaria diagnostic tests , in a low transmission region of minab district , hormozgan province , southern iran.methods:blood samples of 200 healthy volunteers from bagh - e - malek area were evaluated using microscopic , rapid diagnostic tests ( rdt ) and nested - pcr to inspect malaria parasite.results:the results showed no plasmodium parasite in subjects by means of microscopy and rdt .
however , 3 p. vivax positive samples ( 1.5% ) were discovered by nested - pcr while microscopy and rdt missed the cases.conclusion:microscopy as the gold standard method and rdt correctly identified 98.5% of cases , and molecular analysis is sensitive and reliable , especially in the detection of asymptomatic infections for active case surveillance . regarding the existence of asymptomatic malaria in endemic area of hormozgan , iran ,
nested - pcr could be considered as a sensitive tool to interrupt malaria transmission in the country , beside the microscopic and rdt methods .</s> |
histopathology is the microscopic examination of tissue sections , which are colored with different stains to display different functional or physical properties .
three dimensional ( 3d ) tissue reconstruction from the digital images of serial sections has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells , enhance the study of biomechanical behavior of the tissue structures towards better treatments ( e.g. tissue - engineering applications ) .
this can be obtained by successively applying two dimensional ( 2d ) image - to - image registrations and then concatenating the set of aligned images to form a 3d volumetric dataset .
various methods based on this idea have been presented for 3d reconstruction from a set of images of same - stain serial sections.[14 ] recently , there is increasing research interest in registering 2d histology images of consecutive sections with different stains,[58 ] , since automatic co - registration of these images allows the spatial alignment of structural and functional elements in different modalities for quantitative study of many physiological and pathological phenomena .
however , there is no work known to the authors addressing the problem of 3d reconstruction from images of sections with different stains . in this paper
, we discuss three strategies for combining the solutions of automatic 2d multi - stain registration and 3d volumetric reconstruction from same - stain sections .
as the 2d multi - stain registration and same - stain volumetric reconstruction are the key steps of all 3d reconstruction strategies , for the completeness , we provide the necessary details about our implementations of 2d registrations in section methods .
two human liver surgical specimens ( a , b ) are used to examine three 3d reconstruction strategies .
local nhs research ethical approval was obtained for use of the human tissue . on specimen
a , four artificial vertical holes were made for the quantitative evaluation of the accuracy of the 3d reconstruction .
specimen b was chosen because there are relatively consistent anatomic features present in the stack of sections . using standard histological techniques , the specimens were formalin fixed
, paraffin embedded , and cut into ~5m sections using a microtome .
for specimen
a , every 4 section was selected and stained with h and e ; every 5 section was stained with sirius red .
twenty five sections of each stain were prepared , with 50 sections in total.for specimen b , every 2 , 3 , 4 section was stained with h and e while every 6 , 7 , 8 sections were stained with ck7 .
fifteen sections of each stain were prepared , with 30 sections in total .
for specimen
a , every 4 section was selected and stained with h and e ; every 5 section was stained with sirius red .
twenty five sections of each stain were prepared , with 50 sections in total . for specimen b ,
every 2 , 3 , 4 section was stained with h and e while every 6 , 7 , 8 sections were stained with ck7 .
sections were scanned at 20 magnification with average image size ~1.4 g ( specimen a ) and 40 with average image size ~18.5 g ( specimen b ) using an aperio xt scanner . to verify the influence of misaligned 2d images on the various 3d reconstruction strategies , images of sections with the following problems
are included :
luminance gradient : sections mounted close to the edge of the glass slide produce images with significant luminance gradients [ figure 1-a1 , 1-a2].non - tissue noise : dust and air bubbles in the slide [ figure 1-a1 , 1-a2].damaged and missing sections : during sectioning and mounting , sections are occasionally torn , folded [ figure 1-b1].staining variations : differences in section thickness , staining duration , and stain concentration result in colour variations [ figure 1-b2 ] .
luminance gradient : sections mounted close to the edge of the glass slide produce images with significant luminance gradients [ figure 1-a1 , 1-a2 ] .
non - tissue noise : dust and air bubbles in the slide [ figure 1-a1 , 1-a2 ] . damaged and missing sections : during sectioning and mounting , sections are occasionally torn , folded [ figure 1-b1 ] .
staining variations : differences in section thickness , staining duration , and stain concentration result in colour variations [ figure 1-b2 ] .
there are several potential approaches for 3d reconstruction from images of differently stained sections which we have implemented and evaluated . an intuitive option is to apply 2d registration sequentially for each stain separately ( i.e. same - stain registration ) after the reference image ( i.e. the first section ) for each stack has been aligned by applying 2d multi - stain registration figure 2 , strategy 1 ) . the second solution is to apply same - stain registration on the stack of images with one stain ( e.g. t1 ) sequentially and then aligning every image in the stack of the other stain ( e.g. t2 ) to its adjacent image in the stack of stain t1 using multi - stain registration [ figure 2 , strategy 2 ] .
the third approach is interlacing images of stain t1 and t2 in the same sequence as sectioning and applying multi - stain registration for all neighboring images [ figure 2 , strategy 3 ] . in
the 3d registration approaches discussed in this paper are the extension of : 1 ) our previous works on 3d volume reconstruction from 2d registration of images of same - stain serial sections and 2 ) our unsupervised content classification based on 2d multi - stain registration method ( manuscript under preparation ) . to make this paper independently readable
strategies of 3d registration of multi - stain pathological images registration consists in two main steps : 1 ) initial rigid alignment of an red , green , blue ( rgb ) image pair at low resolution x0 using a phase correlation based method ( a combination of and to recover scale and rotation ) applied to grayscale image ; 2 ) non - rigid alignment is done by dividing each image into small patches ( from our cross - validation study , the best results are given at 256 256 pixels per patch ) and computing the rigid transformation of these patches separately by applying the phase correlation based method .
the deformation field is then represented by five vectors for each patch , i.e. one at each corner and one at the centre .
a cubic b - spline transform is estimated to approximate the deformation field using regularized least squares error minimization .
the non - rigid transform in step 2 is refined by a multi - resolution ( from coarse x1 to fine xn ) approach .
the patch matching approach is the key to tackle large image size ( gigabytes at high resolution ) .
a challenge when registering histology images with different stains is that different stains highlight different substances in tissues , resulting in dissimilar structural appearances on adjacent tissue sections .
we address this challenge by proposing an unsupervised content classification method , which automatically identifies common content classes from differently stained histology image pair .
this method creates two multi- channel probability images [ figure 3c ] for the non - rigid alignment , as in step 2 where the grayscale images are used for the same - stain registration .
the workflow of multi - stain registration is illustrated in figure 3 , and the results at resolution xi ( 1 i n ) of each step are exemplified on the right hand side . the content classification algorithm is summarized in table 1 , where we assume the input image pair at resolution xi has been pre - registered by the transformation estimated at resolution xi-1 ( within a multi - resolution framework ) .
( a ) original tissue sections stained with h and e and sirius red stains .
each channel is corresponding to a content class automatically identified from the image pair in ( a ) .
( d ) non - rigid registration result content classification algorithm spatial location features are introduced as complementary to the appearance features .
this overcomes the problem where the appearance features alone ( for some stains ) are not sufficient to separate certain image regions , which have similar appearance , but belong to different content classes . as that the content classes are emergent from co - occurrence statistics between the image pairs
registration consists in two main steps : 1 ) initial rigid alignment of an red , green , blue ( rgb ) image pair at low resolution x0 using a phase correlation based method ( a combination of and to recover scale and rotation ) applied to grayscale image ; 2 ) non - rigid alignment is done by dividing each image into small patches ( from our cross - validation study , the best results are given at 256 256 pixels per patch ) and computing the rigid transformation of these patches separately by applying the phase correlation based method .
the deformation field is then represented by five vectors for each patch , i.e. one at each corner and one at the centre .
a cubic b - spline transform is estimated to approximate the deformation field using regularized least squares error minimization .
the non - rigid transform in step 2 is refined by a multi - resolution ( from coarse x1 to fine xn ) approach .
the patch matching approach is the key to tackle large image size ( gigabytes at high resolution ) .
a challenge when registering histology images with different stains is that different stains highlight different substances in tissues , resulting in dissimilar structural appearances on adjacent tissue sections .
we address this challenge by proposing an unsupervised content classification method , which automatically identifies common content classes from differently stained histology image pair .
this method creates two multi- channel probability images [ figure 3c ] for the non - rigid alignment , as in step 2 where the grayscale images are used for the same - stain registration .
the workflow of multi - stain registration is illustrated in figure 3 , and the results at resolution xi ( 1 i n ) of each step are exemplified on the right hand side . the content classification algorithm is summarized in table 1 , where we assume the input image pair at resolution xi has been pre - registered by the transformation estimated at resolution xi-1 ( within a multi - resolution framework ) .
( a ) original tissue sections stained with h and e and sirius red stains .
each channel is corresponding to a content class automatically identified from the image pair in ( a ) .
( d ) non - rigid registration result content classification algorithm spatial location features are introduced as complementary to the appearance features .
this overcomes the problem where the appearance features alone ( for some stains ) are not sufficient to separate certain image regions , which have similar appearance , but belong to different content classes . as that the content classes are emergent from co - occurrence statistics between the image pairs
the 2d unsupervised content classification - based registration method plays a key role in our 3d reconstruction study .
thus , we evaluate the 2d multi - stain registration method using three histological image pairs with six different stains from a liver specimen , a intervertebral disc specimen , and a colon specimen .
we manually annotate 20~30 regions ( the number of pixels per annotation ranges 2000~5600 ) on each image pair .
the alignment accuracy for each image pair is evaluated by measuring hausdorff distance ( m ) of corresponding annotations at full - resolution level ( at which the image was originally scanned ) .
( c ) liver specimen ( reticulin , masson trichrome ) figure 5 illustrates the influence of different 3d reconstruction strategies ( described in materials and methods section ) on the reconstructed specimens by stacking all the registered images of stain a serially as when they were cut .
for example , for the reconstructed specimen a , the odd number images are those stained with h and e and the even number images are stained with sirius red . the hausdorff distances ( m ) are measured at 20 magnification for specimen a. the graphs at the position n depict the distance between the n+1 images and the 1 image ( i.e. accumulated error ) .
each line plotted in the graph corresponds to one manual annotation , as shown in figure 1 .
( a - c ) accumulated hausdorff distances of reconstructed specimen a by applying strategy 1 , 2 , 3 , respectively .
( d ) boxplot of the hausdorff distances between successive images in each stack figure 5d ( strategy 1 ) shows large misalignments exist between successive images of different stains , due to the fact that strategy1 is based on two sets of independent same - stain registrations .
this results in a large accumulated error with respect to the first image [ figure 5a ] .
strategy 2 shows better registration accuracy between stains [ figure 5d ] resulted from applying same - stain registration on odd number images ( h and e stain ) followed by multi - stain registration to align every even number images ( sirius red stain ) to its neighboring h and e image .
there is also less accumulation of errors with respect to the first image [ figure 5b ] .
figure 5d illustrates the strategy 3 also has good registration accuracy between successive images of different stains ; however , accumulated error is larger than strategy 2 [ figure 5c ] . unlike specimen
a , there are no artificial markers on the specimen b. as the influence of anatomic changes overrides the registration errors , for specimen b , we do not provide hausdorff evaluation based on annotations of real anatomic structures .
instead , the smoothness of the reconstructed specimens in coronal views offers a more intuitive qualitative way of comparing the three strategies , as in figure 6 .
view plane locates at annotations b2 figure 6 shows a coronal view of the reconstructed specimens . for specimen a ( top ) , strategy 2 gives the smoothest 3d reconstruction , however , several outliers exist .
strategy 1 has a smooth reconstruction before the first big misalignment presents , which leads to the poor reconstruction of the rest part of the specimen .
although strategy 3 has the smallest hausdorff distance between successive images , as illustrated in figure 5d , the reconstructed volume is not as smooth as strategy 2 , reflecting the fact that strategy 3 has random accumulated registration errors . for specimen b ( bottom )
strategy 1 has larger registration error at the end of the reconstructed stack than other two strategies .
strategy 2 and 3 give much smoother blood vessel walls and specimen boundary , and their difference is minor in this case .
in addition to the registration accuracy , computational efficiency is also an important factor to be considered .
table 2 exemplifies the execution times of same - stain and multi - stain 2d registrations at different resolutions .
all computations were carried out on a desktop computer with the following specifications : intel i7 dual core 3.07 ghz , 8 gb ram , windows 7 .
the 2d unsupervised content classification - based registration method plays a key role in our 3d reconstruction study .
thus , we evaluate the 2d multi - stain registration method using three histological image pairs with six different stains from a liver specimen , a intervertebral disc specimen , and a colon specimen .
we manually annotate 20~30 regions ( the number of pixels per annotation ranges 2000~5600 ) on each image pair .
the alignment accuracy for each image pair is evaluated by measuring hausdorff distance ( m ) of corresponding annotations at full - resolution level ( at which the image was originally scanned ) .
figure 5 illustrates the influence of different 3d reconstruction strategies ( described in materials and methods section ) on the reconstructed specimens by stacking all the registered images of stain a serially as when they were cut .
for example , for the reconstructed specimen a , the odd number images are those stained with h and e and the even number images are stained with sirius red .
the hausdorff distances ( m ) are measured at 20 magnification for specimen a. the graphs at the position n depict the distance between the n+1 images and the 1 image ( i.e. accumulated error ) .
each line plotted in the graph corresponds to one manual annotation , as shown in figure 1 .
( a - c ) accumulated hausdorff distances of reconstructed specimen a by applying strategy 1 , 2 , 3 , respectively .
( d ) boxplot of the hausdorff distances between successive images in each stack figure 5d ( strategy 1 ) shows large misalignments exist between successive images of different stains , due to the fact that strategy1 is based on two sets of independent same - stain registrations .
this results in a large accumulated error with respect to the first image [ figure 5a ] .
strategy 2 shows better registration accuracy between stains [ figure 5d ] resulted from applying same - stain registration on odd number images ( h and e stain ) followed by multi - stain registration to align every even number images ( sirius red stain ) to its neighboring h and e image .
there is also less accumulation of errors with respect to the first image [ figure 5b ] .
figure 5d illustrates the strategy 3 also has good registration accuracy between successive images of different stains ; however , accumulated error is larger than strategy 2 [ figure 5c ] . unlike specimen
a , there are no artificial markers on the specimen b. as the influence of anatomic changes overrides the registration errors , for specimen b , we do not provide hausdorff evaluation based on annotations of real anatomic structures .
instead , the smoothness of the reconstructed specimens in coronal views offers a more intuitive qualitative way of comparing the three strategies , as in figure 6 .
view plane locates at annotations b2 figure 6 shows a coronal view of the reconstructed specimens . for specimen a ( top ) , strategy 2 gives the smoothest 3d reconstruction , however , several outliers exist .
strategy 1 has a smooth reconstruction before the first big misalignment presents , which leads to the poor reconstruction of the rest part of the specimen .
although strategy 3 has the smallest hausdorff distance between successive images , as illustrated in figure 5d , the reconstructed volume is not as smooth as strategy 2 , reflecting the fact that strategy 3 has random accumulated registration errors . for specimen b ( bottom )
strategy 1 has larger registration error at the end of the reconstructed stack than other two strategies .
strategy 2 and 3 give much smoother blood vessel walls and specimen boundary , and their difference is minor in this case .
in addition to the registration accuracy , computational efficiency is also an important factor to be considered .
table 2 exemplifies the execution times of same - stain and multi - stain 2d registrations at different resolutions .
all computations were carried out on a desktop computer with the following specifications : intel i7 dual core 3.07 ghz , 8 gb ram , windows 7 .
in our experiments , we also notice that the multi - stain 2d registration method is less sensitive to problematic sections and performs accurately on serial sections of continuous cut .
however , when the gap between the two sections increases ( i.e. more sections are left out of the reconstruction ) , the registration accuracy correspondingly decreases since larger variations in tissue structures are present between the two sections , and thus affects the result of co - occurrence statistics , and , thus , unsupervised classification performance . in summary ,
strategy 3 ( only involving multi - stain 2d registration ) has an advantage in dealing with some problematic sections and provides good 3d reconstruction results ( when only few sections in the cut are left out of 3d reconstruction ) , however , it requires 2n-1 multi - stain registrations ( n the number of images in each stain ) .
strategy 2 results in the lowest accumulated errors if those problematic sections can be discarded before the registration , but is more sensitive to these problematic sections .
moreover , it only requires n-1 same - stain 2d registrations plus n multi - stain 2d registrations , which is much more computationally efficient than strategy 3 . both strategy 2 and strategy 3 are practically usable . | context : three dimensional ( 3d ) tissue reconstructions from the histology images with different stains allows the spatial alignment of structural and functional elements highlighted by different stains for quantitative study of many physiological and pathological phenomena .
this has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells , and enhance the study of biomechanical behavior of the tissue structures towards better treatments ( e.g. tissue - engineering applications).methods : this paper evaluates three strategies for 3d reconstruction from sets of two dimensional ( 2d ) histological sections with different stains , by combining methods of 2d multi - stain registration and 3d volumetric reconstruction from same stain sections.setting and design : the different strategies have been evaluated on two liver specimens ( 80 sections in total ) stained with hematoxylin and eosin ( h and e ) , sirius red , and cytokeratin ( ck ) 7.results and conclusion : a strategy of using multi - stain registration to align images of a second stain to a volume reconstructed by same - stain registration results in the lowest overall error , although an interlaced image registration approach may be more robust to poor section quality . | <s>[INST]histopathology is the microscopic examination of tissue sections , which are colored with different stains to display different functional or physical properties .
three dimensional ( 3d ) tissue reconstruction from the digital images of serial sections has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells , enhance the study of biomechanical behavior of the tissue structures towards better treatments ( e.g. tissue - engineering applications ) .
this can be obtained by successively applying two dimensional ( 2d ) image - to - image registrations and then concatenating the set of aligned images to form a 3d volumetric dataset .
various methods based on this idea have been presented for 3d reconstruction from a set of images of same - stain serial sections.[14 ] recently , there is increasing research interest in registering 2d histology images of consecutive sections with different stains,[58 ] , since automatic co - registration of these images allows the spatial alignment of structural and functional elements in different modalities for quantitative study of many physiological and pathological phenomena .
however , there is no work known to the authors addressing the problem of 3d reconstruction from images of sections with different stains . in this paper
, we discuss three strategies for combining the solutions of automatic 2d multi - stain registration and 3d volumetric reconstruction from same - stain sections .
as the 2d multi - stain registration and same - stain volumetric reconstruction are the key steps of all 3d reconstruction strategies , for the completeness , we provide the necessary details about our implementations of 2d registrations in section methods .
two human liver surgical specimens ( a , b ) are used to examine three 3d reconstruction strategies .
local nhs research ethical approval was obtained for use of the human tissue . on specimen
a , four artificial vertical holes were made for the quantitative evaluation of the accuracy of the 3d reconstruction .
specimen b was chosen because there are relatively consistent anatomic features present in the stack of sections . using standard histological techniques , the specimens were formalin fixed
, paraffin embedded , and cut into ~5m sections using a microtome .
for specimen
a , every 4 section was selected and stained with h and e ; every 5 section was stained with sirius red .
twenty five sections of each stain were prepared , with 50 sections in total.for specimen b , every 2 , 3 , 4 section was stained with h and e while every 6 , 7 , 8 sections were stained with ck7 .
fifteen sections of each stain were prepared , with 30 sections in total .
for specimen
a , every 4 section was selected and stained with h and e ; every 5 section was stained with sirius red .
twenty five sections of each stain were prepared , with 50 sections in total . for specimen b ,
every 2 , 3 , 4 section was stained with h and e while every 6 , 7 , 8 sections were stained with ck7 .
sections were scanned at 20 magnification with average image size ~1.4 g ( specimen a ) and 40 with average image size ~18.5 g ( specimen b ) using an aperio xt scanner . to verify the influence of misaligned 2d images on the various 3d reconstruction strategies , images of sections with the following problems
are included :
luminance gradient : sections mounted close to the edge of the glass slide produce images with significant luminance gradients [ figure 1-a1 , 1-a2].non - tissue noise : dust and air bubbles in the slide [ figure 1-a1 , 1-a2].damaged and missing sections : during sectioning and mounting , sections are occasionally torn , folded [ figure 1-b1].staining variations : differences in section thickness , staining duration , and stain concentration result in colour variations [ figure 1-b2 ] .
luminance gradient : sections mounted close to the edge of the glass slide produce images with significant luminance gradients [ figure 1-a1 , 1-a2 ] .
non - tissue noise : dust and air bubbles in the slide [ figure 1-a1 , 1-a2 ] . damaged and missing sections : during sectioning and mounting , sections are occasionally torn , folded [ figure 1-b1 ] .
staining variations : differences in section thickness , staining duration , and stain concentration result in colour variations [ figure 1-b2 ] .
there are several potential approaches for 3d reconstruction from images of differently stained sections which we have implemented and evaluated . an intuitive option is to apply 2d registration sequentially for each stain separately ( i.e. same - stain registration ) after the reference image ( i.e. the first section ) for each stack has been aligned by applying 2d multi - stain registration figure 2 , strategy 1 ) . the second solution is to apply same - stain registration on the stack of images with one stain ( e.g. t1 ) sequentially and then aligning every image in the stack of the other stain ( e.g. t2 ) to its adjacent image in the stack of stain t1 using multi - stain registration [ figure 2 , strategy 2 ] .
the third approach is interlacing images of stain t1 and t2 in the same sequence as sectioning and applying multi - stain registration for all neighboring images [ figure 2 , strategy 3 ] . in
the 3d registration approaches discussed in this paper are the extension of : 1 ) our previous works on 3d volume reconstruction from 2d registration of images of same - stain serial sections and 2 ) our unsupervised content classification based on 2d multi - stain registration method ( manuscript under preparation ) . to make this paper independently readable
strategies of 3d registration of multi - stain pathological images registration consists in two main steps : 1 ) initial rigid alignment of an red , green , blue ( rgb ) image pair at low resolution x0 using a phase correlation based method ( a combination of and to recover scale and rotation ) applied to grayscale image ; 2 ) non - rigid alignment is done by dividing each image into small patches ( from our cross - validation study , the best results are given at 256 256 pixels per patch ) and computing the rigid transformation of these patches separately by applying the phase correlation based method .
the deformation field is then represented by five vectors for each patch , i.e. one at each corner and one at the centre .
a cubic b - spline transform is estimated to approximate the deformation field using regularized least squares error minimization .
the non - rigid transform in step 2 is refined by a multi - resolution ( from coarse x1 to fine xn ) approach .
the patch matching approach is the key to tackle large image size ( gigabytes at high resolution ) .
a challenge when registering histology images with different stains is that different stains highlight different substances in tissues , resulting in dissimilar structural appearances on adjacent tissue sections .
we address this challenge by proposing an unsupervised content classification method , which automatically identifies common content classes from differently stained histology image pair .
this method creates two multi- channel probability images [ figure 3c ] for the non - rigid alignment , as in step 2 where the grayscale images are used for the same - stain registration .
the workflow of multi - stain registration is illustrated in figure 3 , and the results at resolution xi ( 1 i n ) of each step are exemplified on the right hand side . the content classification algorithm is summarized in table 1 , where we assume the input image pair at resolution xi has been pre - registered by the transformation estimated at resolution xi-1 ( within a multi - resolution framework ) .
( a ) original tissue sections stained with h and e and sirius red stains .
each channel is corresponding to a content class automatically identified from the image pair in ( a ) .
( d ) non - rigid registration result content classification algorithm spatial location features are introduced as complementary to the appearance features .
this overcomes the problem where the appearance features alone ( for some stains ) are not sufficient to separate certain image regions , which have similar appearance , but belong to different content classes . as that the content classes are emergent from co - occurrence statistics between the image pairs
registration consists in two main steps : 1 ) initial rigid alignment of an red , green , blue ( rgb ) image pair at low resolution x0 using a phase correlation based method ( a combination of and to recover scale and rotation ) applied to grayscale image ; 2 ) non - rigid alignment is done by dividing each image into small patches ( from our cross - validation study , the best results are given at 256 256 pixels per patch ) and computing the rigid transformation of these patches separately by applying the phase correlation based method .
the deformation field is then represented by five vectors for each patch , i.e. one at each corner and one at the centre .
a cubic b - spline transform is estimated to approximate the deformation field using regularized least squares error minimization .
the non - rigid transform in step 2 is refined by a multi - resolution ( from coarse x1 to fine xn ) approach .
the patch matching approach is the key to tackle large image size ( gigabytes at high resolution ) .
a challenge when registering histology images with different stains is that different stains highlight different substances in tissues , resulting in dissimilar structural appearances on adjacent tissue sections .
we address this challenge by proposing an unsupervised content classification method , which automatically identifies common content classes from differently stained histology image pair .
this method creates two multi- channel probability images [ figure 3c ] for the non - rigid alignment , as in step 2 where the grayscale images are used for the same - stain registration .
the workflow of multi - stain registration is illustrated in figure 3 , and the results at resolution xi ( 1 i n ) of each step are exemplified on the right hand side . the content classification algorithm is summarized in table 1 , where we assume the input image pair at resolution xi has been pre - registered by the transformation estimated at resolution xi-1 ( within a multi - resolution framework ) .
( a ) original tissue sections stained with h and e and sirius red stains .
each channel is corresponding to a content class automatically identified from the image pair in ( a ) .
( d ) non - rigid registration result content classification algorithm spatial location features are introduced as complementary to the appearance features .
this overcomes the problem where the appearance features alone ( for some stains ) are not sufficient to separate certain image regions , which have similar appearance , but belong to different content classes . as that the content classes are emergent from co - occurrence statistics between the image pairs
the 2d unsupervised content classification - based registration method plays a key role in our 3d reconstruction study .
thus , we evaluate the 2d multi - stain registration method using three histological image pairs with six different stains from a liver specimen , a intervertebral disc specimen , and a colon specimen .
we manually annotate 20~30 regions ( the number of pixels per annotation ranges 2000~5600 ) on each image pair .
the alignment accuracy for each image pair is evaluated by measuring hausdorff distance ( m ) of corresponding annotations at full - resolution level ( at which the image was originally scanned ) .
( c ) liver specimen ( reticulin , masson trichrome ) figure 5 illustrates the influence of different 3d reconstruction strategies ( described in materials and methods section ) on the reconstructed specimens by stacking all the registered images of stain a serially as when they were cut .
for example , for the reconstructed specimen a , the odd number images are those stained with h and e and the even number images are stained with sirius red . the hausdorff distances ( m ) are measured at 20 magnification for specimen a. the graphs at the position n depict the distance between the n+1 images and the 1 image ( i.e. accumulated error ) .
each line plotted in the graph corresponds to one manual annotation , as shown in figure 1 .
( a - c ) accumulated hausdorff distances of reconstructed specimen a by applying strategy 1 , 2 , 3 , respectively .
( d ) boxplot of the hausdorff distances between successive images in each stack figure 5d ( strategy 1 ) shows large misalignments exist between successive images of different stains , due to the fact that strategy1 is based on two sets of independent same - stain registrations .
this results in a large accumulated error with respect to the first image [ figure 5a ] .
strategy 2 shows better registration accuracy between stains [ figure 5d ] resulted from applying same - stain registration on odd number images ( h and e stain ) followed by multi - stain registration to align every even number images ( sirius red stain ) to its neighboring h and e image .
there is also less accumulation of errors with respect to the first image [ figure 5b ] .
figure 5d illustrates the strategy 3 also has good registration accuracy between successive images of different stains ; however , accumulated error is larger than strategy 2 [ figure 5c ] . unlike specimen
a , there are no artificial markers on the specimen b. as the influence of anatomic changes overrides the registration errors , for specimen b , we do not provide hausdorff evaluation based on annotations of real anatomic structures .
instead , the smoothness of the reconstructed specimens in coronal views offers a more intuitive qualitative way of comparing the three strategies , as in figure 6 .
view plane locates at annotations b2 figure 6 shows a coronal view of the reconstructed specimens . for specimen a ( top ) , strategy 2 gives the smoothest 3d reconstruction , however , several outliers exist .
strategy 1 has a smooth reconstruction before the first big misalignment presents , which leads to the poor reconstruction of the rest part of the specimen .
although strategy 3 has the smallest hausdorff distance between successive images , as illustrated in figure 5d , the reconstructed volume is not as smooth as strategy 2 , reflecting the fact that strategy 3 has random accumulated registration errors . for specimen b ( bottom )
strategy 1 has larger registration error at the end of the reconstructed stack than other two strategies .
strategy 2 and 3 give much smoother blood vessel walls and specimen boundary , and their difference is minor in this case .
in addition to the registration accuracy , computational efficiency is also an important factor to be considered .
table 2 exemplifies the execution times of same - stain and multi - stain 2d registrations at different resolutions .
all computations were carried out on a desktop computer with the following specifications : intel i7 dual core 3.07 ghz , 8 gb ram , windows 7 .
the 2d unsupervised content classification - based registration method plays a key role in our 3d reconstruction study .
thus , we evaluate the 2d multi - stain registration method using three histological image pairs with six different stains from a liver specimen , a intervertebral disc specimen , and a colon specimen .
we manually annotate 20~30 regions ( the number of pixels per annotation ranges 2000~5600 ) on each image pair .
the alignment accuracy for each image pair is evaluated by measuring hausdorff distance ( m ) of corresponding annotations at full - resolution level ( at which the image was originally scanned ) .
figure 5 illustrates the influence of different 3d reconstruction strategies ( described in materials and methods section ) on the reconstructed specimens by stacking all the registered images of stain a serially as when they were cut .
for example , for the reconstructed specimen a , the odd number images are those stained with h and e and the even number images are stained with sirius red .
the hausdorff distances ( m ) are measured at 20 magnification for specimen a. the graphs at the position n depict the distance between the n+1 images and the 1 image ( i.e. accumulated error ) .
each line plotted in the graph corresponds to one manual annotation , as shown in figure 1 .
( a - c ) accumulated hausdorff distances of reconstructed specimen a by applying strategy 1 , 2 , 3 , respectively .
( d ) boxplot of the hausdorff distances between successive images in each stack figure 5d ( strategy 1 ) shows large misalignments exist between successive images of different stains , due to the fact that strategy1 is based on two sets of independent same - stain registrations .
this results in a large accumulated error with respect to the first image [ figure 5a ] .
strategy 2 shows better registration accuracy between stains [ figure 5d ] resulted from applying same - stain registration on odd number images ( h and e stain ) followed by multi - stain registration to align every even number images ( sirius red stain ) to its neighboring h and e image .
there is also less accumulation of errors with respect to the first image [ figure 5b ] .
figure 5d illustrates the strategy 3 also has good registration accuracy between successive images of different stains ; however , accumulated error is larger than strategy 2 [ figure 5c ] . unlike specimen
a , there are no artificial markers on the specimen b. as the influence of anatomic changes overrides the registration errors , for specimen b , we do not provide hausdorff evaluation based on annotations of real anatomic structures .
instead , the smoothness of the reconstructed specimens in coronal views offers a more intuitive qualitative way of comparing the three strategies , as in figure 6 .
view plane locates at annotations b2 figure 6 shows a coronal view of the reconstructed specimens . for specimen a ( top ) , strategy 2 gives the smoothest 3d reconstruction , however , several outliers exist .
strategy 1 has a smooth reconstruction before the first big misalignment presents , which leads to the poor reconstruction of the rest part of the specimen .
although strategy 3 has the smallest hausdorff distance between successive images , as illustrated in figure 5d , the reconstructed volume is not as smooth as strategy 2 , reflecting the fact that strategy 3 has random accumulated registration errors . for specimen b ( bottom )
strategy 1 has larger registration error at the end of the reconstructed stack than other two strategies .
strategy 2 and 3 give much smoother blood vessel walls and specimen boundary , and their difference is minor in this case .
in addition to the registration accuracy , computational efficiency is also an important factor to be considered .
table 2 exemplifies the execution times of same - stain and multi - stain 2d registrations at different resolutions .
all computations were carried out on a desktop computer with the following specifications : intel i7 dual core 3.07 ghz , 8 gb ram , windows 7 .
in our experiments , we also notice that the multi - stain 2d registration method is less sensitive to problematic sections and performs accurately on serial sections of continuous cut .
however , when the gap between the two sections increases ( i.e. more sections are left out of the reconstruction ) , the registration accuracy correspondingly decreases since larger variations in tissue structures are present between the two sections , and thus affects the result of co - occurrence statistics , and , thus , unsupervised classification performance . in summary ,
strategy 3 ( only involving multi - stain 2d registration ) has an advantage in dealing with some problematic sections and provides good 3d reconstruction results ( when only few sections in the cut are left out of 3d reconstruction ) , however , it requires 2n-1 multi - stain registrations ( n the number of images in each stain ) .
strategy 2 results in the lowest accumulated errors if those problematic sections can be discarded before the registration , but is more sensitive to these problematic sections .
moreover , it only requires n-1 same - stain 2d registrations plus n multi - stain 2d registrations , which is much more computationally efficient than strategy 3 . both strategy 2 and strategy 3 are practically usable .[/INST]context : three dimensional ( 3d ) tissue reconstructions from the histology images with different stains allows the spatial alignment of structural and functional elements highlighted by different stains for quantitative study of many physiological and pathological phenomena .
this has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells , and enhance the study of biomechanical behavior of the tissue structures towards better treatments ( e.g. tissue - engineering applications).methods : this paper evaluates three strategies for 3d reconstruction from sets of two dimensional ( 2d ) histological sections with different stains , by combining methods of 2d multi - stain registration and 3d volumetric reconstruction from same stain sections.setting and design : the different strategies have been evaluated on two liver specimens ( 80 sections in total ) stained with hematoxylin and eosin ( h and e ) , sirius red , and cytokeratin ( ck ) 7.results and conclusion : a strategy of using multi - stain registration to align images of a second stain to a volume reconstructed by same - stain registration results in the lowest overall error , although an interlaced image registration approach may be more robust to poor section quality .</s> |
The letter ''B'' of the signage on the Barclays headquarters in Canary Wharf is hoisted up the side of the building in London July 20, 2012.
U.S. prosecutors and European regulators are close to arresting individual traders and charging them with colluding to manipulate global benchmark interest rates, according to people familiar with a sweeping investigation into the rigging scandal.
Federal prosecutors in Washington, D.C., have recently contacted lawyers representing some of the suspects to notify them that criminal charges and arrests could be imminent, said two of those sources, who asked not to be identified because the investigation is ongoing.
Defense lawyers, some of whom represent suspects, said prosecutors have indicated they plan to begin making arrests and filing criminal charges in the next few weeks. In long-running financial investigations it is not uncommon for prosecutors to contact defense lawyers before filing charges to offer suspects a chance to cooperate or take a plea, these lawyers said.
The prospect of charges and arrests means prosecutors are getting a fuller picture of how traders at major banks allegedly sought to influence the London Interbank Offered Rate, or Libor, and other global rates that underpin hundreds of trillions of dollars in assets. The criminal charges would come alongside efforts by regulators to fine major banks, and could show that the alleged activity was not rampant at the lenders.
"The individual criminal charges have no impact on the regulatory moves against the banks," said a European source familiar with the matter. "But banks are hoping that at least regulators will see that the scandal was mainly due to individual misbehavior of a gang of traders."
In Europe, financial regulators are focusing on a ring of traders from several European banks who allegedly sought to rig benchmark interest rates such as Libor, said the European source familiar with the investigation in Europe.
The source, who did not want to be identified because the investigation is ongoing, said regulators are checking emails among a group of traders and believe they are close to piecing together a picture of how the suspects allegedly conspired to make money by manipulating rates. The rates are set daily based on an average of estimates supplied by a panel of banks.
"More than a handful of traders at different banks are involved," said the source familiar with the investigation by European regulators.
There are also probes in Europe concerning Euribor, the Euro Interbank Offered Rate.
It is not clear on which individuals and banks federal prosecutors are most focused. A top U.S. Department of Justice lawyer overseeing the investigation did not respond to a request for comment.
Reuters previously reported that more than a dozen current and former employees of several large banks are under investigation, including Barclays Plc, UBS and Citigroup, and have hired defense lawyers over the past year as a federal grand jury in Washington, D.C., continues to gather evidence.
Activity in the Libor investigation, which has been going on for three years, has quickened since Barclays agreed last month to pay $453 million in fines and penalties to settle allegations with regulators and prosecutors that some of its employees tried to manipulate key interest rates from 2005 through 2009.
Barclays, which signed a non-prosecution agreement with U.S. prosecutors, is the first major bank to reach a settlement in the investigation, which also is looking at the activities of employees at HSBC, Deutsche Bank and other major lenders.
HSBC declined to comment. Officials at Citigroup and UBS were not available for comment.
The Barclays settlement sparked outrage and a series of public hearings in Britain, after which Barclays Chief Executive Bob Diamond announced his resignation from the UK bank.
The revelations have raised questions about the integrity of Libor, which is used as a benchmark in setting prices for loans, mortgages and derivative contracts.
Adding to concerns are documents released by the New York Federal Reserve Bank this month that show regulators in the United States and England had some knowledge that bankers were submitting misleading Libor bids during the 2008 financial crisis to make their financial institutions appear stronger than they really were.
Among other details, the Fed documents included the transcript of an April 2008 telephone call between a Barclays trader in New York and Fed official Fabiola Ravazzolo, in which the unidentified trader said: "So, we know that we're not posting um, an honest Libor."
The source familiar with the investigation in Europe said two traders suspended from Deutsche Bank were among those being investigated. A Deutsche Bank spokesman declined to comment.
The Financial Times said on Wednesday that regulators were looking at suspected communication among four traders who had worked at Barclays, Credit Agricole, HSBC and Deutsche Bank.
Credit Agricole said it had not been accused of any wrongdoing related to the attempted manipulation of Libor by Barclays, but had responded to requests for information from various authorities related to the matter.
Beyond regulatory penalties and criminal charges, banks face a growing number of civil lawsuits from cities, companies and financial institutions claiming they were harmed by rate manipulation. Morgan Stanley recently estimated that the 11 global banks linked to the Libor scandal may face $14 billion in regulatory and legal settlement costs through 2014.
In the United States, the regulatory investigation is being led by the Commodity Futures Trading Commission, which has made the Libor probe one of its top priorities.
(Reporting by Matthew Goldstein and Jennifer Ablan in New York and Philipp Halstrick in Frankfurt, with additional reporting by Emily Flitter in New York and Aruna Viswanatha in Washington, D.C.; Editing by Alwyn Scott, Maureen Bavdek and Dale Hudson) ||||| Article Excerpt
Several groups of traders are under investigation by regulators around the world for allegedly banding together to rig interest rates, people close to the probe said.
The continuing criminal and civil scrutiny includes more than a dozen traders from at least nine banks, often allegedly working together in small groups to target different interest rates on separate continents, the people said.
The emerging details about traders suggest to investigators a widespread conspiracy that continued for several years and cascaded around the world. As a result, the banks where the traders worked are under growing pressure to explain what they knew ... ||||| Regulators from Stockholm to Seoul are re-examining how benchmark borrowing costs are set amid concern they are just as vulnerable to manipulation as the London interbank offered rate.
Stibor, Swedenβs main interbank rate, Sibor, the leading rate in Singapore, and Tibor in Japan are among rates facing fresh scrutiny because, like Libor, they are based on banksβ estimated borrowing costs rather than real trades. In some cases they may be easier to rig than Libor as fewer banks contribute to their calculation, according to academics and analysts.
βMany of the ingredients which would make it easy to manipulate Libor and collude are common in other benchmarks,β said Rosa Abrantes-Metz, an economist with consulting firm Global Economics Group and an associate professor at New York Universityβs Stern School of Business. βRegulatory agencies are starting to take a look at those and there is a growing sense they need to change.β
Barclays Plc, the U.K.βs second-largest bank, was fined a record 290 million pounds ($450 million) last month for attempting to rig Libor and Euribor, its equivalent in euros, to appear more healthy during the financial crisis and boost earnings before it. At least 12 banks including Royal Bank of Scotland Group Plc (RBS) and Deutsche Bank AG are being investigated for manipulating Libor.
Beyond Libor
Regulators and industry groups are now turning their attention to whether other benchmark rates were manipulated in the same way. Swedenβs central bank, the Japanese Bankers Association, the Monetary Authority of Singapore and South Koreaβs Fair Trade Commission have all announced probes into how their domestic rates are set.
Libor is determined by a daily poll carried out on behalf of the British Bankersβ Association that asks banks to estimate how much it would cost to borrow from each other for different periods and in different currencies. Three-month dollar Libor was 0.453 percent on July 19.
Derivatives traders at Barclays asked colleagues who inputted the rate each day to amend their submissions to benefit their trading positions. They also contacted traders at other banks to ask them to do the same. Traders at Deutsche Bank, HSBC Holdings Plc (HSBA), Societe Generale SA and Credit Agricole SA are under investigation for interest-rate manipulation, a person with knowledge of the matter said.
With 18 banks on the panel for U.S. dollar Libor and 43 banks for Euribor, only small moves can be achieved by making deliberately high or low submissions. Manipulation becomes easier when fewer banks are contributing, according to Abrantes- Metz at Global Economics.
Collusion Ability
βCollusion typically occurs in markets with just a few players,β Abrantes-Metz said. βAll else being equal, the smaller the group, the easier it is to collude.β
Stibor, the Stockholm interbank offered rate, is set by five banks after RBS pulled itself off the panel on April 30. It is calculated by Nasdaq OMX Stockholm every day for eight maturities.
Riksbank, the Swedish central bank, said in its biannual Financial Stability Report published June 1 that market participants were concerned about Stibor, the basis for 40 billion Swedish krona ($5.8 billion) of loans and financial contracts.
Stibor Questions
βMany market participants state in the Riksbankβs latest risk survey that there are problems with the Stibor,β the report stated. βThis refers to incentives for the banks to set the Stibor at fair levels, the opinion that too few banks determine the Stibor and the insufficient transparency of the Stibor and its framework.β
The central bank was unavailable for comment because they are on vacation, said spokeswoman Cecilia Roos Isksson.
Nibor, the Norwegian rate, is set by a panel of six banks. Cibor, the Copenhagen rate, is based on a group of eight lenders.
Tibor, the Tokyo interbank offered rate, is set by the Japanese Bankers Association based on submissions from 16 banks for yen and 15 lenders for euroyen, according to the industry groupβs website.
The association yesterday asked the banks to answer questions on how they make their submissions, said spokesman Hisanao Aoki. The reference banks, including lending units of Mitsubishi UFJ Financial Group Inc. (8306), JPMorgan Chase & Co., Deutsche Bank and BNP Paribas SA, must reply by Aug. 10.
Citigroup, UBS
Citigroup Inc. (C) and UBS AG (UBSN) were ordered to suspend some operations in Japan last December after the Financial Services Agency found their employees attempted to influence Tibor to a βfavorable levelβ for derivatives trading. Citigroup was banned from trading tied to Libor and Tibor for two weeks, and UBS received a one-week suspension.
Association officials today met with the ruling Democratic Party of Japanβs finance committee, headed by former Morgan Stanley banker Tsutomu Okubo, to explain how Tibor is set.
βBarclaysβs fine is enormous and far above the rate of such penalties typically imposed on Japanese financial institutions for wrongdoing,β Okubo said at the meeting. βWe must strengthen investorsβ trust in Tokyoβs financial market.β
Association Chairman Yasuhiro Sato, who is also chief executive officer of Mizuho Financial Group Inc. (8411), said today that while the process for setting Tibor is sound, he is open to making changes based on the review.
South Koreaβs antitrust agency this week expanded a probe to see whether a key money-market rate was kept artificially high. The Fair Trade Commission inspected 10 brokerages and nine banks to determine if there was collusion on certificate of deposit rates, the agency said in an e-mailed statement.
Under Pressure
The countryβs 91-day certificate of deposit rate is a benchmark for bank lending and borrowing as well as for interest-rate swaps. Quotes are collected twice a day by the Korea Financial Investment Association from 10 brokerages.
βKorea is a relatively insulated system where the leading banks are influential in the local market and were under pressure to maintain their soundness and their profit margins during the crisis,β said David Marshall, an analyst at research firm CreditSights Inc. in Singapore. Manipulation in Japan, Singapore and Hong Kong is less likely, he said.
The Monetary Authority of Singapore said yesterday it will look into how banks are setting βkey market interest rate benchmarksβ amid similar reviews by regulators in several markets. The Association of Banks in Singapore sets Sibor based on submissions by 12 lenders. RBS said this week it decided to withdraw from the panel following the January announcement of changes to the Edinburgh-based lenderβs strategic priorities. It has also withdrawn from the Tokyo and Hong Kong interbank offered rate-setting panels this year.
Hong Kong
In Hong Kong, the performance of banks in contributing to set the benchmark Hibor rate is βreviewed regularly,β the Hong Kong Association of Banks said in an e-mailed statement today. The Hong Kong Monetary Authority said it hasnβt observed βany anomalyβ over the past 20 years and will monitor the industry groupβs review, according to an e-mailed statement. Hibor is set daily based on quotations provided by 20 lenders, according to the associationβs website.
Barclays Plc (BARC), Britainβs second-biggest lender by assets, said this month it would pull out of the group of 12 banks in the United Arab Emirates whose quotes determine the interbank lending rate in the second biggest Arab economy. Dutch lender Rabobank last month withdrew from the panels that set Libor in Japanese yen, the Canadian dollar, the Swiss franc, the Danish krone and the Swedish krona. It continues to contribute toward Libor in U.S. dollars, euros and pounds.
To contact the reporters on this story: Liam Vaughan in London at [email protected]; Gavin Finch in London at [email protected]
To contact the editors responsible for this story: Edward Evans at [email protected]; Chitra Somayaji at [email protected] | β Looks like Barclays wasn't the only one gaming the Libor system. Investigators are looking into an alleged conspiracy in which traders around the world worked together to rig Libor to boost their personal profits, the Wall Street Journal reports. Several different groups were allegedly working to rig the rate from 2005 to 2011, with the practice spreading as traders switched banks. One cabal alone involved six of the 16 banks that set the daily yen Libor rate. Prosecutors in the US and Europe are close to arresting a number of traders over the scandal, sources tell Reutersβindeed, some of the suspects' lawyers have already been notified of impending arrests. The arrests could take pressure off the banks, making the rate-fixing look more like individual malfeasance than systematic corporate wrongdoing. Meanwhile, Bloomberg reports that regulators from Switzerland to South Korea to Japan are looking into the possibility that their rates might be vulnerable to foul play. | <s>[INST]The letter ''B'' of the signage on the Barclays headquarters in Canary Wharf is hoisted up the side of the building in London July 20, 2012.
U.S. prosecutors and European regulators are close to arresting individual traders and charging them with colluding to manipulate global benchmark interest rates, according to people familiar with a sweeping investigation into the rigging scandal.
Federal prosecutors in Washington, D.C., have recently contacted lawyers representing some of the suspects to notify them that criminal charges and arrests could be imminent, said two of those sources, who asked not to be identified because the investigation is ongoing.
Defense lawyers, some of whom represent suspects, said prosecutors have indicated they plan to begin making arrests and filing criminal charges in the next few weeks. In long-running financial investigations it is not uncommon for prosecutors to contact defense lawyers before filing charges to offer suspects a chance to cooperate or take a plea, these lawyers said.
The prospect of charges and arrests means prosecutors are getting a fuller picture of how traders at major banks allegedly sought to influence the London Interbank Offered Rate, or Libor, and other global rates that underpin hundreds of trillions of dollars in assets. The criminal charges would come alongside efforts by regulators to fine major banks, and could show that the alleged activity was not rampant at the lenders.
"The individual criminal charges have no impact on the regulatory moves against the banks," said a European source familiar with the matter. "But banks are hoping that at least regulators will see that the scandal was mainly due to individual misbehavior of a gang of traders."
In Europe, financial regulators are focusing on a ring of traders from several European banks who allegedly sought to rig benchmark interest rates such as Libor, said the European source familiar with the investigation in Europe.
The source, who did not want to be identified because the investigation is ongoing, said regulators are checking emails among a group of traders and believe they are close to piecing together a picture of how the suspects allegedly conspired to make money by manipulating rates. The rates are set daily based on an average of estimates supplied by a panel of banks.
"More than a handful of traders at different banks are involved," said the source familiar with the investigation by European regulators.
There are also probes in Europe concerning Euribor, the Euro Interbank Offered Rate.
It is not clear on which individuals and banks federal prosecutors are most focused. A top U.S. Department of Justice lawyer overseeing the investigation did not respond to a request for comment.
Reuters previously reported that more than a dozen current and former employees of several large banks are under investigation, including Barclays Plc, UBS and Citigroup, and have hired defense lawyers over the past year as a federal grand jury in Washington, D.C., continues to gather evidence.
Activity in the Libor investigation, which has been going on for three years, has quickened since Barclays agreed last month to pay $453 million in fines and penalties to settle allegations with regulators and prosecutors that some of its employees tried to manipulate key interest rates from 2005 through 2009.
Barclays, which signed a non-prosecution agreement with U.S. prosecutors, is the first major bank to reach a settlement in the investigation, which also is looking at the activities of employees at HSBC, Deutsche Bank and other major lenders.
HSBC declined to comment. Officials at Citigroup and UBS were not available for comment.
The Barclays settlement sparked outrage and a series of public hearings in Britain, after which Barclays Chief Executive Bob Diamond announced his resignation from the UK bank.
The revelations have raised questions about the integrity of Libor, which is used as a benchmark in setting prices for loans, mortgages and derivative contracts.
Adding to concerns are documents released by the New York Federal Reserve Bank this month that show regulators in the United States and England had some knowledge that bankers were submitting misleading Libor bids during the 2008 financial crisis to make their financial institutions appear stronger than they really were.
Among other details, the Fed documents included the transcript of an April 2008 telephone call between a Barclays trader in New York and Fed official Fabiola Ravazzolo, in which the unidentified trader said: "So, we know that we're not posting um, an honest Libor."
The source familiar with the investigation in Europe said two traders suspended from Deutsche Bank were among those being investigated. A Deutsche Bank spokesman declined to comment.
The Financial Times said on Wednesday that regulators were looking at suspected communication among four traders who had worked at Barclays, Credit Agricole, HSBC and Deutsche Bank.
Credit Agricole said it had not been accused of any wrongdoing related to the attempted manipulation of Libor by Barclays, but had responded to requests for information from various authorities related to the matter.
Beyond regulatory penalties and criminal charges, banks face a growing number of civil lawsuits from cities, companies and financial institutions claiming they were harmed by rate manipulation. Morgan Stanley recently estimated that the 11 global banks linked to the Libor scandal may face $14 billion in regulatory and legal settlement costs through 2014.
In the United States, the regulatory investigation is being led by the Commodity Futures Trading Commission, which has made the Libor probe one of its top priorities.
(Reporting by Matthew Goldstein and Jennifer Ablan in New York and Philipp Halstrick in Frankfurt, with additional reporting by Emily Flitter in New York and Aruna Viswanatha in Washington, D.C.; Editing by Alwyn Scott, Maureen Bavdek and Dale Hudson) ||||| Article Excerpt
Several groups of traders are under investigation by regulators around the world for allegedly banding together to rig interest rates, people close to the probe said.
The continuing criminal and civil scrutiny includes more than a dozen traders from at least nine banks, often allegedly working together in small groups to target different interest rates on separate continents, the people said.
The emerging details about traders suggest to investigators a widespread conspiracy that continued for several years and cascaded around the world. As a result, the banks where the traders worked are under growing pressure to explain what they knew ... ||||| Regulators from Stockholm to Seoul are re-examining how benchmark borrowing costs are set amid concern they are just as vulnerable to manipulation as the London interbank offered rate.
Stibor, Swedenβs main interbank rate, Sibor, the leading rate in Singapore, and Tibor in Japan are among rates facing fresh scrutiny because, like Libor, they are based on banksβ estimated borrowing costs rather than real trades. In some cases they may be easier to rig than Libor as fewer banks contribute to their calculation, according to academics and analysts.
βMany of the ingredients which would make it easy to manipulate Libor and collude are common in other benchmarks,β said Rosa Abrantes-Metz, an economist with consulting firm Global Economics Group and an associate professor at New York Universityβs Stern School of Business. βRegulatory agencies are starting to take a look at those and there is a growing sense they need to change.β
Barclays Plc, the U.K.βs second-largest bank, was fined a record 290 million pounds ($450 million) last month for attempting to rig Libor and Euribor, its equivalent in euros, to appear more healthy during the financial crisis and boost earnings before it. At least 12 banks including Royal Bank of Scotland Group Plc (RBS) and Deutsche Bank AG are being investigated for manipulating Libor.
Beyond Libor
Regulators and industry groups are now turning their attention to whether other benchmark rates were manipulated in the same way. Swedenβs central bank, the Japanese Bankers Association, the Monetary Authority of Singapore and South Koreaβs Fair Trade Commission have all announced probes into how their domestic rates are set.
Libor is determined by a daily poll carried out on behalf of the British Bankersβ Association that asks banks to estimate how much it would cost to borrow from each other for different periods and in different currencies. Three-month dollar Libor was 0.453 percent on July 19.
Derivatives traders at Barclays asked colleagues who inputted the rate each day to amend their submissions to benefit their trading positions. They also contacted traders at other banks to ask them to do the same. Traders at Deutsche Bank, HSBC Holdings Plc (HSBA), Societe Generale SA and Credit Agricole SA are under investigation for interest-rate manipulation, a person with knowledge of the matter said.
With 18 banks on the panel for U.S. dollar Libor and 43 banks for Euribor, only small moves can be achieved by making deliberately high or low submissions. Manipulation becomes easier when fewer banks are contributing, according to Abrantes- Metz at Global Economics.
Collusion Ability
βCollusion typically occurs in markets with just a few players,β Abrantes-Metz said. βAll else being equal, the smaller the group, the easier it is to collude.β
Stibor, the Stockholm interbank offered rate, is set by five banks after RBS pulled itself off the panel on April 30. It is calculated by Nasdaq OMX Stockholm every day for eight maturities.
Riksbank, the Swedish central bank, said in its biannual Financial Stability Report published June 1 that market participants were concerned about Stibor, the basis for 40 billion Swedish krona ($5.8 billion) of loans and financial contracts.
Stibor Questions
βMany market participants state in the Riksbankβs latest risk survey that there are problems with the Stibor,β the report stated. βThis refers to incentives for the banks to set the Stibor at fair levels, the opinion that too few banks determine the Stibor and the insufficient transparency of the Stibor and its framework.β
The central bank was unavailable for comment because they are on vacation, said spokeswoman Cecilia Roos Isksson.
Nibor, the Norwegian rate, is set by a panel of six banks. Cibor, the Copenhagen rate, is based on a group of eight lenders.
Tibor, the Tokyo interbank offered rate, is set by the Japanese Bankers Association based on submissions from 16 banks for yen and 15 lenders for euroyen, according to the industry groupβs website.
The association yesterday asked the banks to answer questions on how they make their submissions, said spokesman Hisanao Aoki. The reference banks, including lending units of Mitsubishi UFJ Financial Group Inc. (8306), JPMorgan Chase & Co., Deutsche Bank and BNP Paribas SA, must reply by Aug. 10.
Citigroup, UBS
Citigroup Inc. (C) and UBS AG (UBSN) were ordered to suspend some operations in Japan last December after the Financial Services Agency found their employees attempted to influence Tibor to a βfavorable levelβ for derivatives trading. Citigroup was banned from trading tied to Libor and Tibor for two weeks, and UBS received a one-week suspension.
Association officials today met with the ruling Democratic Party of Japanβs finance committee, headed by former Morgan Stanley banker Tsutomu Okubo, to explain how Tibor is set.
βBarclaysβs fine is enormous and far above the rate of such penalties typically imposed on Japanese financial institutions for wrongdoing,β Okubo said at the meeting. βWe must strengthen investorsβ trust in Tokyoβs financial market.β
Association Chairman Yasuhiro Sato, who is also chief executive officer of Mizuho Financial Group Inc. (8411), said today that while the process for setting Tibor is sound, he is open to making changes based on the review.
South Koreaβs antitrust agency this week expanded a probe to see whether a key money-market rate was kept artificially high. The Fair Trade Commission inspected 10 brokerages and nine banks to determine if there was collusion on certificate of deposit rates, the agency said in an e-mailed statement.
Under Pressure
The countryβs 91-day certificate of deposit rate is a benchmark for bank lending and borrowing as well as for interest-rate swaps. Quotes are collected twice a day by the Korea Financial Investment Association from 10 brokerages.
βKorea is a relatively insulated system where the leading banks are influential in the local market and were under pressure to maintain their soundness and their profit margins during the crisis,β said David Marshall, an analyst at research firm CreditSights Inc. in Singapore. Manipulation in Japan, Singapore and Hong Kong is less likely, he said.
The Monetary Authority of Singapore said yesterday it will look into how banks are setting βkey market interest rate benchmarksβ amid similar reviews by regulators in several markets. The Association of Banks in Singapore sets Sibor based on submissions by 12 lenders. RBS said this week it decided to withdraw from the panel following the January announcement of changes to the Edinburgh-based lenderβs strategic priorities. It has also withdrawn from the Tokyo and Hong Kong interbank offered rate-setting panels this year.
Hong Kong
In Hong Kong, the performance of banks in contributing to set the benchmark Hibor rate is βreviewed regularly,β the Hong Kong Association of Banks said in an e-mailed statement today. The Hong Kong Monetary Authority said it hasnβt observed βany anomalyβ over the past 20 years and will monitor the industry groupβs review, according to an e-mailed statement. Hibor is set daily based on quotations provided by 20 lenders, according to the associationβs website.
Barclays Plc (BARC), Britainβs second-biggest lender by assets, said this month it would pull out of the group of 12 banks in the United Arab Emirates whose quotes determine the interbank lending rate in the second biggest Arab economy. Dutch lender Rabobank last month withdrew from the panels that set Libor in Japanese yen, the Canadian dollar, the Swiss franc, the Danish krone and the Swedish krona. It continues to contribute toward Libor in U.S. dollars, euros and pounds.
To contact the reporters on this story: Liam Vaughan in London at [email protected]; Gavin Finch in London at [email protected]
To contact the editors responsible for this story: Edward Evans at [email protected]; Chitra Somayaji at [email protected][/INST]β Looks like Barclays wasn't the only one gaming the Libor system. Investigators are looking into an alleged conspiracy in which traders around the world worked together to rig Libor to boost their personal profits, the Wall Street Journal reports. Several different groups were allegedly working to rig the rate from 2005 to 2011, with the practice spreading as traders switched banks. One cabal alone involved six of the 16 banks that set the daily yen Libor rate. Prosecutors in the US and Europe are close to arresting a number of traders over the scandal, sources tell Reutersβindeed, some of the suspects' lawyers have already been notified of impending arrests. The arrests could take pressure off the banks, making the rate-fixing look more like individual malfeasance than systematic corporate wrongdoing. Meanwhile, Bloomberg reports that regulators from Switzerland to South Korea to Japan are looking into the possibility that their rates might be vulnerable to foul play.</s> |
it has been realized that the coupled langevin model is a valuable and useful model for a study of various phenomena observed in stochastic ensembles ( for a recent review , see ref .
@xcite ) . independent ( uncorrelated ) additive and/or multiplicative noise has been widely adopted for theoretical analyses because of its mathematical simplicity . in natural phenomena , however , there exist some kinds of correlations in noise , such as spatial and temporal correlations , and a correlation between additive and multiplicative noise . in this paper
we will pay our attention to the spatial correlation in noise .
the langevin model has been usually discussed with the use of the fokker - planck equation ( fpe ) for the probability distribution . in the case of correlated additive noise only ,
the probability distribution is expressed by the multivariate gaussian probability with a covariance matrix .
the effect of correlated additive noise has been extensively studied in neuroscience , where it is an important and essential problem to study the effect of correlations in noise and signals ( for a review , see ref .
it has been shown that the synchrony and variability in neuron ensembles are much influenced by the spatial correlations @xcite-@xcite .
the spatial correlation in additive noise enhances the synchrony of firings in a neuron ensemble , while it works to diminish beneficial roles of independent noise , such as the stochastic and coherent resonances and the population ( pooling ) effect @xcite ; related discussions being given in sec .
the problem becomes much difficult when multiplicative noise exists , for which the probability distribution generally becomes a non - gaussian .
although an analytical expression of the stationary probability distribution for uncorrelated multiplicative noise is available , that for correlated multiplicative noise has not been obtained yet .
indeed , only little theoretical study of the effect of spatially correlated multiplicative noise has been reported for subjects such as the noise - induced phase separation @xcite and the fisher information @xcite-@xcite , as far as the author is concerned . in a recent paper @xcite ,
we have studied stationary and dynamical properties of the coupled langevin model subjected to uncorrelated additive and multiplicative noise .
we employed the augmented moment method ( amm ) which was developed for a study of stochastic systems with finite populations @xcite . in the amm
, we consider global properties of ensembles , taking account of mean and fluctuations ( variances ) of local and global variables .
although a calculation of the probability distribution for the spatially correlated multiplicative noise with the use of the fpe is very difficult as mentioned above , we may easily study its effects by using the amm .
it is the purpose of the present paper to apply the amm to the coupled langevin model including spatially correlated multiplicative noise and to study its effects on the synchrony and variability .
the paper is organized as follows . in sec .
2 , we discuss the amm for the spatially correlated langevin model . with the use of analytical amm and numerical methods ,
the synchrony and variability of the coupled langevin model are investigated . in sec . 3 ,
previous studies on the correlated multiplicative noise using the gaussian approximation @xcite-@xcite are critically discussed .
an application of our study to neuron ensembles is also presented with model calculations . the final sec .
4 is devoted to our conclusion .
we have assumed the @xmath0-unit coupled langevin model subjected to spatially correlated additive and multiplicative noise .
the dynamics of a variable @xmath1 ( @xmath2 to @xmath0 ) is given by @xmath3 with @xmath4 here @xmath5 and @xmath6 are arbitrary functions of @xmath7 , @xmath8 @xmath9 denotes the coordination number , @xmath10 an input signal from external sources , @xmath11 the coupling strength , and @xmath12 the heaviside function : @xmath13 for @xmath14 and @xmath15 otherwise .
we have included additive and multiplicative noise by @xmath16 and @xmath17 , respectively , expressing zero - mean gaussian white noise with correlations given by @xmath18\delta(t - t ' ) , \label{eq : a3 } \\
\left < \xi_{i}(t)\:\xi_{j}(t ' ) \right > & = & \beta^2 [ \delta_{ij}+c_a(1-\delta_{ij})]]\delta(t - t ' ) , \label{eq : a4 } \\ \left < \eta_{i}(t)\:\xi_{j}(t ' ) \right > & = & 0 , \label{eq : a5}\end{aligned}\ ] ] where the bracket @xmath19 denotes the average , @xmath20 ( @xmath21 ) expresses the magnitude of multiplicative ( additive ) noise , and @xmath22 ( @xmath23 ) stands for the degree of the spatial correlation in multiplicative ( additive ) noise .
although our results to be present in the following are valid for any choice of @xmath24 , we have adopted a simple analytic expression given by eq .
( [ eq : a2 ] ) in this study .
we assume that external inputs have a variability defined by @xmath25 with @xmath26 \delta(t - t ' ) , \label{eq : a8}\end{aligned}\ ] ] where @xmath27 and @xmath28 denote the variance and degree of the spatial correlation , respectively , in external signals .
we will investigate the response of the coupled langevin model to correlated external inputs given by eqs .
( [ eq : a6])-([eq : a8 ] ) . in the amm @xcite
, we define the three quantities of @xmath29 , @xmath30 , and @xmath31 expressed by @xmath32 ^ 2 \rangle , \label{eq : b2}\\ \rho(t ) & = & \langle [ x(t)-\mu(t)]^2 \rangle , \label{eq : b3 } \end{aligned}\ ] ] where @xmath33 , @xmath29 expresses the mean , and @xmath30 and @xmath31 denote fluctuations in local ( @xmath1 ) and global variables ( @xmath34 ) , respectively . by using the fokker - planck equation ( fpe ) , we obtain equations of motion for @xmath29 , @xmath30 and @xmath31 which are given by ( argument @xmath35 is suppressed , details being given in the appendix a ) @xmath36 , \label{eq : c1}\\ \frac{d \gamma}{dt } & = & 2f_{1 } \gamma + \frac{2 h_{1 } w}{z } \left(n \rho-\gamma \right ) + 2(g_{1}^2 + 2 g_{0}g_{2})\alpha^2\gamma + \gamma_i+\beta^2 + \alpha^2 g_{0}^2 , \label{eq : c2}\\ \frac{d \rho}{dt } & = & 2 f_{1 } \rho + 2 h_1 w \rho + 2 ( g_{1}^2 + 2 g_{0}g_{2 } ) \alpha^2 \rho \nonumber \\ & + & \frac{1}{n}(\gamma_i+\beta^2+\alpha^2 g_0 ^ 2 ) + \frac{z}{n}(s_i \gamma_i+ c_a \beta^2 + c_m \alpha^2 g_0 ^ 2 ) , \label{eq : c3}\end{aligned}\ ] ] where @xmath37 , @xmath38 , @xmath39 and @xmath40 . original @xmath0-dimensional stochastic differential equations ( des ) given by eqs .
( [ eq : a1])-([eq : a2 ] ) are transformed to the three - dimensional deterministic des given by eqs .
( [ eq : c1])-([eq : c3 ] ) . for @xmath41 ,
equations of motion given by eqs .
( [ eq : c1])-([eq : c3 ] ) reduce to those obtained in our previous study @xcite . when we adopt @xmath5 and @xmath6 given by @xmath42 eqs .
( [ eq : c1])-([eq : c3 ] ) become @xmath43 with @xmath44 where @xmath45 , and @xmath46 and @xmath47 express uncorrelated and correlated contributions , respectively .
we employ eqs .
( [ eq : d3])-([eq : f5 ] ) in the remainder of this paper . in order
to quantitatively discuss the synchronization , we first consider the quantity @xmath48 given by @xmath49 ^ 2 > = 2 [ \gamma(t)-\rho(t ) ] .
\label{eq : e1}\ ] ] when all neurons are in the same state : @xmath50 for all @xmath51 ( the completely synchronous state ) , we obtain @xmath52 in eq .
( [ eq : e1 ] ) . on the contrary , in the asynchronous state
where @xmath53 , it is given by @xmath54 @xcite .
we may define the normalized ratio for the synchrony given by @xcite @xmath55 which is 0 and 1 for completely asynchronous ( @xmath56 ) and synchronous states ( @xmath57 ) , respectively .
the local variability is conventionally given by @xmath58 ^ 2 \rangle}}{\mu(t ) } = \frac{\sqrt{\gamma(t)}}{\mu(t ) } , \label{eq : e3}\end{aligned}\ ] ] where @xmath59 .
similarly , the global variability is defined by @xmath60 ^ 2 \rangle } } { \mu(t ) } = \frac{\sqrt{\rho(t)}}{\mu(t ) } = c_v(t)\;\sqrt{\frac{\rho(t)}{\gamma(t ) } } , \label{eq : e4 } \end{aligned}\ ] ] where @xmath61 .
the stationary solution of eqs .
( [ eq : d3])-([eq : d5 ] ) is given by @xmath62 where @xmath63 in @xmath46 and @xmath47 of eqs .
( [ eq : f4 ] ) and ( [ eq : f5 ] ) is given by eq .
( [ eq : f1 ] ) .
we note in eq .
( [ eq : f1 ] ) that @xmath63 is increased as @xmath64 is increased with an enhancement factor of @xmath65 .
a local fluctuation @xmath66 is increased with increasing input fluctuations ( @xmath27 ) and/or noise ( @xmath20 , @xmath21 ) as eq .
( [ eq : f2 ] ) shows . in the limit of @xmath67 , eqs .
( [ eq : f2 ] ) and ( [ eq : f3 ] ) lead to @xmath68 which expresses the central - limit theorem . from eqs . ( [ eq : e2 ] ) , ( [ eq : f2 ] ) and ( [ eq : f3 ] ) , we obtain @xmath69+h_1 w z r } , \label{eq : f6 } \\ & = & \frac{h_1 w}{z(\lambda-\alpha^2)-h_1 w ( z-1 ) } \hspace{0.5cm}\mbox{for $ s_i = c_a = c_m=0 $ } , \label{eq : f7}\\ & = & \frac{s_i \gamma_i+c_a \beta^2 + c_m \alpha^2 \mu^2 } { \gamma_i+\beta^2+\alpha^2 \mu^2 } \hspace{1cm}\mbox{for $ w=0 $ } , \label{eq : f8}\end{aligned}\ ] ] where @xmath46 and @xmath47 in eq .
( [ eq : f6 ] ) are given by eqs .
( [ eq : f4 ] ) and ( [ eq : f5 ] ) , respectively . equation ( [ eq : f6 ] ) shows that the synchrony @xmath70 is increased with increasing spatial correlations and/or the coupling .
this is more clearly seen in the limit of no spatial correlations [ eq .
( [ eq : f7 ] ) ] or no couplings [ eq . ( [ eq : f8 ] ) ] .
the local and global variabilities , @xmath71 and @xmath72 , defined by eqs .
( [ eq : e3 ] ) and ( [ eq : e4 ] ) , respectively , are generally expressed in terms of @xmath46 and @xmath47 , and they are given for @xmath73 by @xmath74 the local variability @xmath71 only weakly depends on the spatial correlation through the coupling , and it is independent of the correlation for @xmath75 .
in contrast , the global variability @xmath72 is increased ( decreased ) for positive ( negative ) correlations . in the limit of @xmath76 ,
( [ eq : f18 ] ) yields @xmath77 expressing a smaller global variability in a larger-@xmath0 ensemble ( the population or pooling effect ) @xcite .
the stability condition around the stationary state given by eqs .
( [ eq : f1])-([eq : f3 ] ) may be examined from eigenvalues of the jacobian matrix of eqs .
( [ eq : d3])-([eq : d5 ] ) , which are given by @xmath78 the first eigenvalue of @xmath79 arises from an equation of motion for @xmath63 , which is decoupled from the rest of variables .
the stability condition for @xmath63 is given by @xmath80 the stability condition for @xmath66 and @xmath81 is given by @xmath82 then for @xmath83 , @xmath66 and @xmath81 are unstable but @xmath63 remains stable .
it is note that there is a limitation in a parameter value of @xmath84 , as given by @xmath85 which arises from the condition given by @xmath86 [ see eqs .
( [ eq : b3 ] ) and ( [ eq : e1 ] ) ] . when @xmath87 , for example , a physically conceivable value of @xmath22 is given by @xmath88 .
@xmath22 dependence of the synchrony @xmath70 is shown in fig .
[ figa ] where @xmath89 , @xmath90 , @xmath91 , @xmath92 and @xmath93 .
the condition given by eq .
( [ eq : f13 ] ) yields that @xmath94 with @xmath95 for a given set of parameters .
we note that the synchrony is increased with increasing @xmath96 , and that the effect of the correlated variability is more considerable for larger @xmath63 and @xmath11 , as eq .
( [ eq : f6 ] ) shows . in order to study the dynamical properties of our model given by eqs .
( [ eq : a1])-([eq : a2 ] ) , we have performed direct simulations ( dss ) by using the heun method @xcite with a time step of 0.0001 : ds results are averages of 100 trials .
amm calculations have been performed for eqs .
( [ eq : d3])-([eq : d5 ] ) by using the fourth - order runge - kutta method with a time step of 0.01 .
we consider a set of typical parameters of @xmath97 , @xmath89 , @xmath90 , @xmath98 , @xmath92 and @xmath93 .
we apply a pulse input given by @xmath99 with @xmath100 , @xmath101 , where @xmath102 denotes the heaviside function : @xmath103 for @xmath104 and 0 otherwise .
figures [ figb](a)-[figb](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath106 for the correlated multiplicative noise ( @xmath107 and @xmath108 ) . @xmath29 and @xmath105 are increased by an applied input at @xmath109 shown by the chain curve in fig .
[ figb](a ) , by which @xmath30 is slightly increased .
the variability @xmath110 is decreased because of an increased @xmath29 .
the results of the amm shown by the solid curves are in fairly good agreement with those of ds shown by the dashed curves .
in contrast , figs .
[ figc](a)-[figc](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath106 for the correlated additive noise ( @xmath91 and @xmath111 ) . with an applied pulse input ,
@xmath29 is increased and @xmath30 is a little increased , as in the case of figs . [ figb](a ) and [ figb](b ) .
however , the synchrony @xmath105 is decreased in fig .
[ figc](c ) while it is increased in fig .
[ figb](c ) .
this difference arises from the fact that a decrease in @xmath105 in the former case is mainly due to an increase in @xmath46 of the denominator of eq .
( [ eq : f6 ] ) , while in the latter case , its increase arises from an increase in @xmath47 of the numerator of eq .
( [ eq : f6 ] ) .
this point is more easily realized for @xmath75 , for which eq .
( [ eq : f8 ] ) yields @xmath112 the situation is almost the same even for finite @xmath11 , as figs .
[ figb](c ) and [ figc](c ) show .
in both figs . [ figb](d ) and [ figc](d ) , @xmath106 is decreased by an applied input because of an increased @xmath29 .
we have investigated the stationary and dynamical properties of the spatially correlated langevin model given by eqs .
( [ eq : a1])-([eq : a2 ] ) . in ref .
@xcite , we discussed the fisher information in the langevin model subjected to uncorrelated additive and multiplicative noise , which is a typical microscopic model showing the nonextensive behavior @xcite .
it is interesting to calculate the fisher information of the langevin model with correlated multiplicative noise .
such a calculation needs to solve the fpe of the langevin model given by eq .
( [ eq : a9 ] ) because the fisher information is expressed in terms of derivatives of the probability distribution . for additive noise only ( @xmath113 ) , the stationary probability distribution @xmath114 is expressed by the multivariate gaussian distribution given by @xmath115 , \label{eq : l1}\end{aligned}\ ] ] with the covariance matrix , @xmath116 , expressed by @xmath117 , \label{eq : l2}\end{aligned}\ ] ] where @xmath118 and @xmath119 . from eqs .
( [ eq : l1 ] ) and ( [ eq : l2 ] ) , we obtain the fisher information given by @xcite @xmath120}. \label{eq : l3}\end{aligned}\ ] ] when multiplicative noise exists , a calculation of even stationary distribution becomes difficult , and it is generally not given by the gaussian .
the stationary distribution for _ uncorrelated _ additive and multiplicative noise ( @xmath121 , @xmath122 ) is given by @xcite @xmath123 in the limit of @xmath124 and @xmath125 ( _ i.e. _ uncorrelated additive noise only ) , eq .
( [ eq : l4 ] ) becomes the gaussian distribution given by @xmath126 in the opposite limit of @xmath127 , @xmath128 and @xmath129 ( _ i.e. _ uncorrelated multiplicative noise only ) , eq .
( [ eq : l4 ] ) reduces to @xmath130 yielding the fisher information given by @xmath131 where @xmath132 and @xmath133 @xcite .
unfortunately , we have not succeeded in obtaining the analytic expression for the stationary distribution of the langevin model including _ correlated _ multiplicative noise . in some previous studies @xcite-@xcite , the stationary distribution for correlated multiplicative noise only
( @xmath121 , @xmath134 and @xmath135 ) is assumed to be expressed by the gaussian distribution given by eq .
( [ eq : l1 ] ) with the covariance matrix given by @xmath136 , \label{eq : l6}\end{aligned}\ ] ] where @xmath137 ( @xmath138 ) denotes the average of @xmath1 and @xmath139 a variance due to multiplicative noise .
this is equivalent to assume that the multiplicative - noise term in the fpe given by eq .
( [ eq : a9 ] ) is approximated as @xmath140 \frac{\partial}{\partial x_{i } } x_i \frac{\partial}{\partial x_j } x_j \:p(\ { x_{k } \ } ) , \nonumber \\ & \simeq & \frac{\alpha^2}{2 } \sum_{i } \sum_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \langle x_i \rangle \frac{\partial}{\partial x_j } \langle x_j \rangle \:p ( \ { x_k \}),\nonumber \\ & = & \frac{\alpha^2}{2 } \sum_j \sum_{i } \mu_i \mu_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \frac{\partial}{\partial x_j } p(\ { x_{k } \ } ) .
\label{eq : l7 } \end{aligned}\ ] ] if we adopt the gaussian approximation given by eq .
( [ eq : l7 ] ) , with which multiplicative noise may be treated in the same way as additive noise , we obtain the amm equations given by eqs .
( [ eq : d3])-([eq : d5 ] ) but without the third term of @xmath141 in eq .
( [ eq : d3 ] ) . by using the gaussian approximation given by eq .
( [ eq : l6 ] ) , abbott and dayan ( ad ) @xcite obtained the fisher information expressed by [ eq .
( 4.7 ) of ref .
@xcite ] @xmath142 } + 2 n k , \label{eq : h5 } \\ & = & \frac{1 } { \sigma_m^2 \mu^2 c_m}+ \frac{2n}{\mu^2 } \hspace{3.6cm}\mbox{for $ n \rightarrow \infty $ } , \label{eq : h6 } \\ & = & \frac{n}{\sigma_m^2 \mu^2 } + \frac{2n}{\mu^2 } \hspace{2cm}\mbox{for $ c_m=0 $ } , \label{eq : h4}\end{aligned}\ ] ] with @xmath143 ^ 2=1/\mu^2 $ ] . equation ( [ eq : h4 ] ) is not in agreement with the exact expression given by eq .
( [ eq : l9 ] ) for uncorrelated multiplicative noise only . in stead of using the langevin model
, we may alternatively calculate the fisher information of a spatially correlated nonextensive system by using the maximum - entropy method . in our recent paper @xcite
, we have obtained the analytic , stationary probability distribution which maximizes the tsallis entropy @xcite under the constraints for a given set of the variance ( @xmath144 ) and covariance ( @xmath145 ) .
the fisher information is expressed by @xcite @xmath146 } , \label{eq : f12 } \\ & = & \frac{1}{c \:\sigma^2 } \hspace{2cm}\mbox{for $ n \rightarrow \infty $ } , \\ & = & \frac{n}{\sigma^2 } \hspace{2cm}\mbox{for $ c = 0.0$}. \label{eq : f14}\end{aligned}\ ] ] the fisher information given by eq .
( [ eq : f12 ] ) is increased ( decreased ) by a negative ( positive ) correlation .
this implies from the cramr - rao theorem that an unbiased estimate of fluctuations is improved by a negative spatial correlation , by which the synchrony is decreased as shown by eqs .
( [ eq : f6 ] ) and ( [ eq : f8 ] ) . @xmath0 and @xmath84 dependences of the fisher information given by eq .
( [ eq : f12 ] ) are different from those of @xmath147 given by eq .
( [ eq : h5 ] ) , although they are the same as those for additive noise only [ eq . ( [ eq : l3 ] ) ] .
it is noted that the gaussian approximation given by eq .
( [ eq : l6 ] ) or ( [ eq : l7 ] ) assumes the gaussian distribution , although multiplicative noise generally yields the non - gaussian distribution as shown by eqs .
( [ eq : l4 ] ) and ( [ eq : l8 ] ) . the spurious second term ( @xmath148 ) in eq .
( [ eq : h5 ] ) which is independent of @xmath22 and @xmath139 , arises from an inappropriate gaussian approximation . in discussing the fisher information of spatially correlated nonextensive systems
, we must take into account the detailed structure of the non - gaussian distribution . when @xmath27 and @xmath28 in eq .
( [ eq : a8 ] ) are allowed to be time dependent , they may carry input information .
this is easily realized if the amm equations given by eqs .
( [ eq : d3])-([eq : d5 ] ) are explicitly expressed in terms of @xmath63 , @xmath66 , and @xmath70 as @xmath149 + \frac{1}{\gamma } [ \gamma_i(t ) s_i(t)+ c_m \alpha^2 \mu^2+c_a \beta^2 ] \nonumber \\ & + & \left ( \frac{2 h_1 w}{z } \right ) ( 1+zs)(1-s ) , \label{eq : g5}\end{aligned}\ ] ] which are derived with the use of eq .
( [ eq : e2 ] ) . in order to numerically examine the possibility that input information is conveyed by @xmath150 and @xmath151
, we first apply a fluctuation - driven input given by @xmath152 with @xmath153 , @xmath154 , @xmath155 and @xmath156 for @xmath97 , @xmath107 , @xmath108 , @xmath89 , @xmath90 and @xmath93 .
time courses of @xmath29 , @xmath30 , @xmath105 and @xmath110 are shown in figs .
[ figg](a)-[figg](d ) : the chain curves in figs .
[ figg](a ) and [ figg](b ) express @xmath157 and @xmath150 , respectively .
when the magnitude of @xmath150 is increased at @xmath109 , @xmath30 and @xmath106 are much increased , while there is no changes in @xmath29 because it is decoupled from the rest of variables in eq .
( [ eq : d3 ] ) .
@xmath105 is slightly modified only at @xmath158 and @xmath159 where the @xmath150 is on and off .
next we apply a synchrony - driven input @xmath151 given by @xmath160 with @xmath161 , @xmath162 , @xmath163 and @xmath164 .
figures [ figh](a)-[figh](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath110 : the chain curves in figs . [ figh](a ) and [ figh](c ) express @xmath157 and @xmath151 , respectively .
an increase in synchrony - driven input at @xmath109 induces a significant increase in @xmath105 and slight increases in @xmath30 and @xmath106 , but no changes in @xmath29 . when we regard a variable @xmath1 in the langevin model given by eqs .
( [ eq : a1])-([eq : a2 ] ) as the firing rate @xmath165 ( @xmath166 ) of a neuron @xmath51 in a neuron ensemble , our model expresses the neuronal model proposed in refs .
it belongs to the firing - rate ( rate - code ) models such as the wilson - cowan @xcite and hopfield models @xcite , in which a neuron is regarded as a transducer from input rate signals to output rate ones .
alternative neuronal models are spiking - neuron ( temporal - code ) models such as the hodgkin - huxley @xcite , fitzhugh - nagumo @xcite and integrate - and - fire ( if ) models @xcite .
various attempts have been proposed to obtain the firing - rate model , starting from spiking - neuron models @xcite-@xcite .
it is difficult to analytically calculate the firing rate based on spiking - neuron models , except for the if - type model @xcite .
it has been shown with the use of the if model that information transmission is possible by noise - coded signals @xcite , and that the modulation of the synchrony is possible without a change in firing rate @xcite .
model calculations shown in figs .
[ figg ] and [ figh ] have demonstrated the possibility that information may be conveyed by @xmath150 and @xmath151 , which is partly supported by results of the if model @xcite-@xcite .
some relevant results have been reported in neuronal experiments @xcite-@xcite . in motor tasks of monkey , firing rate and synchrony
are considered to encode behavioral events and cognitive events , respectively @xcite . during visual tasks , rate and synchrony
are suggested to encode task - related signals and expectation , respectively @xcite .
a change in synchrony may amplify behaviorally relevant signals in v4 of monkey @xcite .
the synchrony is modified without a change in firing rate in some experiments @xcite .
synchrony - dependent firing - rate signal is shown to propagate in iteratively constructed networks _ in vitro _ @xcite .
with the use of dss and the amm @xcite , the effects of spatially correlated additive and multiplicative noise have been discussed on the synchrony and variability in the coupled langevin model .
our calculations have shown the following : ( i ) the synchrony is increased ( decreased ) by the positive ( negative ) correlation in additive and multiplicative noise [ eq . ( [ eq : f6 ] ) ] , ( ii ) although an applied pulse input works to increase the synchrony for correlated multiplicative noise , it is possible to decrease the synchrony when correlated additive noise coexists with uncorrelated multiplicative one , ( iii ) the local variability @xmath71 is almost independent of spatial correlations , while global variability @xmath72 is increased ( decreased ) with increasing the positive ( negative ) correlation , and ( iv ) information may be carried by variance and synchrony in input signals .
the item ( iv ) is consistent with the results of refs . @xcite-@xcite and elucidates some phenomena observed in neuronal experiments @xcite-@xcite .
although we have applied the amm to the langevin model in this paper , it is possible to apply it to other types of stochastic neuronal models such as the fitzhugh and hodgkin - huxley models subjected to correlated additive and multiplicative noise , which is left as our future study .
this work is partly supported by a grant - in - aid for scientific research from the japanese ministry of education , culture , sports , science and technology . the fokker - planck equation ( fpe ) for the langevin equation given by eqs .
( [ eq : a1])-([eq : a2 ] ) in the stratonovich representation is expressed by @xcite @xmath167 \:p(\ { x_{k } \},t)\ } \nonumber \\ & & + \frac{\gamma_i}{2}\sum_{i}\sum_{j } \frac{\partial^2}{\partial x_{i } \partial x_{j } } \ { [ \delta_{ij}+s_i ( 1-\delta_{ij } ) ] \:p(\ { x_{k } \},t ) \ }
\nonumber \\ & & + \frac{\beta^2}{2}\sum_{i}\sum_{j } \frac{\partial^2}{\partial x_{i } \partial x_{j } } \ { [ \delta_{ij}+c_a ( 1-\delta_{ij } ) ] \:p(\ { x_{k } \},t ) \ }
\nonumber \\ & & + \frac{\alpha^2}{2}\sum_{i } \sum_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \ { g(x_i ) \frac{\partial}{\partial x_j } [ g(x_{j } ) \:p(\ { x_{k } \},t ) ] \ } , \label{eq : a9}\end{aligned}\ ] ] where @xmath168 and @xmath169 is absorbed in a new definition of @xmath27 in its second term
. equations of motion for moments , @xmath170 and @xmath171 , are derived with the use of fpe @xcite : @xmath172
\rangle + \langle x_j\ : [ f(x_i)+ h(u_i ) ] \rangle \nonumber \\ & + & \frac{\alpha^2}{2 } [ \langle x_i g'(x_j ) g(x_j ) \rangle + \langle x_j g'(x_i ) g(x_i)\rangle ] \nonumber \\ & + & \delta_{ij } [ \gamma_i+\beta^2 + \alpha^2\:\langle g(x_i)^2 \rangle ] \nonumber \\ & + & ( 1-\delta_{ij } ) [ s_i\gamma_i+c_a \beta^2 + c_m \alpha^2 \langle g(x_i)g(x_j ) \rangle ] .
\label{eq : a11}\end{aligned}\ ] ] in the amm @xcite , the three quantities of @xmath63 , @xmath66 and @xmath81 are defined by eqs .
( [ eq : b1])-([eq : b3 ] ) .
we use the expansion given by @xmath173 and the relations given by @xmath174 for example , eq .
( [ eq : b5 ] ) for @xmath175 is calculated as follows : @xmath176 equations ( [ eq : b6 ] ) and ( [ eq : b7 ] ) are calculated in a similar way .
then , we have obtained equations of motion for @xmath29 , @xmath30 and @xmath31 given by eqs .
( [ eq : c1])-([eq : c3 ] ) . in the heun method for the ordinary differential equation of @xmath177 , a value of @xmath7 at @xmath178
is evaluated by @xmath179 $ ] with @xmath180 and @xmath181 , while it is given by @xmath182 in the euler method , @xmath183 being the time step .
the heum method for the stochastic ordinary differential equation meets the stratonovich calculus employed in the fpe @xcite .
w. rmelin , siam j. numer . anal . * 19 * ( 1982 ) 604 ; a. greiner , w. strittmatter , and j. honerkamp , j. stat . phys . * 51 * ( 1988 ) 95 ; r. f. fox , i. r. gatland , r. roy , and g. vemuri , phys .
rev . a * 38 * ( 1988 ) 5938 .
h. hasegawa , phys .
e * 77 * , 031133 ( 2008 ) .
y. aviel and w. gerstner , phys .
e * 73 * , 051908 ( 2006 ) .
m. oizumi , y. miyawaki , and m. okada , j. phys .
* 76 * , 044803 ( 2007 ) .
b. lindner and l. schimansky - geier , phys
lett . * 86 * , 2934 ( 2001 ) .
a. renart , r. moreno - bose , x - j .
wang , and n. parga , neural comput . * 19 * , 1 ( 2007 ) .
j. heinzle , p. knig , r. f. salazar , cogn . neurodyn . * 1 * , 225 ( 2007 ) .
a. riehle , s. grn , m. diesmann , and a. aertsen , science * 278 * , 1950 ( 1997 ) .
s. c. de oliveira , a. thiele , and k. p. hoffman , j. neurosci .
* 17 * , 9248 ( 1997 ) .
p. fries , j. h. reynolds , a. e. rorie , and r. desimine , science * 291 * , 1560 ( 2001 ) .
a. d. reyes , nat .
* 6 * , 593 ( 2003 ) .
f. grammont and a. riehle , biol . cybern . * 88 * , 360 ( 2003 )
. p. h. e. tiesinga and t. j. sejnowski , neural comput .
* 16 * , 251 ( 2004 ) .
h. risken , _ the fokker - planck equation : methods of solution and applcation _ , ( springer , berlin 1992 ) . | the synchrony and variability have been discussed of the coupled langevin model subjected to spatially correlated additive and multiplicative noise .
we have employed numerical simulations and the analytical augmented - moment method which is the second - order moment method for local and global variables [ h. hasegawa , phys .
rev .
e * 67 * , 041903 ( 2003 ) ] .
it has been shown that the synchrony of an ensemble is increased ( decreased ) by a positive ( negative ) spatial correlation in both additive and multiplicative noise . although the variability for local fluctuations is almost insensitive to spatial correlations , that for global fluctuations is increased ( decreased ) by positive ( negative ) correlations .
when a pulse input is applied , the synchrony is increased for the correlated multiplicative noise , whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise .
an application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals , which accounts for some neuronal experiments .
* synchrony and variability induced by spatially correlated additive and multiplicative noise + in the coupled langevin model * hideo hasegawa _ department of physics , tokyo gakugei university + koganei , tokyo 184 - 8501 , japan _
( ) _ pacs no . _ : 05.10.gg , 05.40.ca , 84.35.+i | <s>[INST]it has been realized that the coupled langevin model is a valuable and useful model for a study of various phenomena observed in stochastic ensembles ( for a recent review , see ref .
@xcite ) . independent ( uncorrelated ) additive and/or multiplicative noise has been widely adopted for theoretical analyses because of its mathematical simplicity . in natural phenomena , however , there exist some kinds of correlations in noise , such as spatial and temporal correlations , and a correlation between additive and multiplicative noise . in this paper
we will pay our attention to the spatial correlation in noise .
the langevin model has been usually discussed with the use of the fokker - planck equation ( fpe ) for the probability distribution . in the case of correlated additive noise only ,
the probability distribution is expressed by the multivariate gaussian probability with a covariance matrix .
the effect of correlated additive noise has been extensively studied in neuroscience , where it is an important and essential problem to study the effect of correlations in noise and signals ( for a review , see ref .
it has been shown that the synchrony and variability in neuron ensembles are much influenced by the spatial correlations @xcite-@xcite .
the spatial correlation in additive noise enhances the synchrony of firings in a neuron ensemble , while it works to diminish beneficial roles of independent noise , such as the stochastic and coherent resonances and the population ( pooling ) effect @xcite ; related discussions being given in sec .
the problem becomes much difficult when multiplicative noise exists , for which the probability distribution generally becomes a non - gaussian .
although an analytical expression of the stationary probability distribution for uncorrelated multiplicative noise is available , that for correlated multiplicative noise has not been obtained yet .
indeed , only little theoretical study of the effect of spatially correlated multiplicative noise has been reported for subjects such as the noise - induced phase separation @xcite and the fisher information @xcite-@xcite , as far as the author is concerned . in a recent paper @xcite ,
we have studied stationary and dynamical properties of the coupled langevin model subjected to uncorrelated additive and multiplicative noise .
we employed the augmented moment method ( amm ) which was developed for a study of stochastic systems with finite populations @xcite . in the amm
, we consider global properties of ensembles , taking account of mean and fluctuations ( variances ) of local and global variables .
although a calculation of the probability distribution for the spatially correlated multiplicative noise with the use of the fpe is very difficult as mentioned above , we may easily study its effects by using the amm .
it is the purpose of the present paper to apply the amm to the coupled langevin model including spatially correlated multiplicative noise and to study its effects on the synchrony and variability .
the paper is organized as follows . in sec .
2 , we discuss the amm for the spatially correlated langevin model . with the use of analytical amm and numerical methods ,
the synchrony and variability of the coupled langevin model are investigated . in sec . 3 ,
previous studies on the correlated multiplicative noise using the gaussian approximation @xcite-@xcite are critically discussed .
an application of our study to neuron ensembles is also presented with model calculations . the final sec .
4 is devoted to our conclusion .
we have assumed the @xmath0-unit coupled langevin model subjected to spatially correlated additive and multiplicative noise .
the dynamics of a variable @xmath1 ( @xmath2 to @xmath0 ) is given by @xmath3 with @xmath4 here @xmath5 and @xmath6 are arbitrary functions of @xmath7 , @xmath8 @xmath9 denotes the coordination number , @xmath10 an input signal from external sources , @xmath11 the coupling strength , and @xmath12 the heaviside function : @xmath13 for @xmath14 and @xmath15 otherwise .
we have included additive and multiplicative noise by @xmath16 and @xmath17 , respectively , expressing zero - mean gaussian white noise with correlations given by @xmath18\delta(t - t ' ) , \label{eq : a3 } \\
\left < \xi_{i}(t)\:\xi_{j}(t ' ) \right > & = & \beta^2 [ \delta_{ij}+c_a(1-\delta_{ij})]]\delta(t - t ' ) , \label{eq : a4 } \\ \left < \eta_{i}(t)\:\xi_{j}(t ' ) \right > & = & 0 , \label{eq : a5}\end{aligned}\ ] ] where the bracket @xmath19 denotes the average , @xmath20 ( @xmath21 ) expresses the magnitude of multiplicative ( additive ) noise , and @xmath22 ( @xmath23 ) stands for the degree of the spatial correlation in multiplicative ( additive ) noise .
although our results to be present in the following are valid for any choice of @xmath24 , we have adopted a simple analytic expression given by eq .
( [ eq : a2 ] ) in this study .
we assume that external inputs have a variability defined by @xmath25 with @xmath26 \delta(t - t ' ) , \label{eq : a8}\end{aligned}\ ] ] where @xmath27 and @xmath28 denote the variance and degree of the spatial correlation , respectively , in external signals .
we will investigate the response of the coupled langevin model to correlated external inputs given by eqs .
( [ eq : a6])-([eq : a8 ] ) . in the amm @xcite
, we define the three quantities of @xmath29 , @xmath30 , and @xmath31 expressed by @xmath32 ^ 2 \rangle , \label{eq : b2}\\ \rho(t ) & = & \langle [ x(t)-\mu(t)]^2 \rangle , \label{eq : b3 } \end{aligned}\ ] ] where @xmath33 , @xmath29 expresses the mean , and @xmath30 and @xmath31 denote fluctuations in local ( @xmath1 ) and global variables ( @xmath34 ) , respectively . by using the fokker - planck equation ( fpe ) , we obtain equations of motion for @xmath29 , @xmath30 and @xmath31 which are given by ( argument @xmath35 is suppressed , details being given in the appendix a ) @xmath36 , \label{eq : c1}\\ \frac{d \gamma}{dt } & = & 2f_{1 } \gamma + \frac{2 h_{1 } w}{z } \left(n \rho-\gamma \right ) + 2(g_{1}^2 + 2 g_{0}g_{2})\alpha^2\gamma + \gamma_i+\beta^2 + \alpha^2 g_{0}^2 , \label{eq : c2}\\ \frac{d \rho}{dt } & = & 2 f_{1 } \rho + 2 h_1 w \rho + 2 ( g_{1}^2 + 2 g_{0}g_{2 } ) \alpha^2 \rho \nonumber \\ & + & \frac{1}{n}(\gamma_i+\beta^2+\alpha^2 g_0 ^ 2 ) + \frac{z}{n}(s_i \gamma_i+ c_a \beta^2 + c_m \alpha^2 g_0 ^ 2 ) , \label{eq : c3}\end{aligned}\ ] ] where @xmath37 , @xmath38 , @xmath39 and @xmath40 . original @xmath0-dimensional stochastic differential equations ( des ) given by eqs .
( [ eq : a1])-([eq : a2 ] ) are transformed to the three - dimensional deterministic des given by eqs .
( [ eq : c1])-([eq : c3 ] ) . for @xmath41 ,
equations of motion given by eqs .
( [ eq : c1])-([eq : c3 ] ) reduce to those obtained in our previous study @xcite . when we adopt @xmath5 and @xmath6 given by @xmath42 eqs .
( [ eq : c1])-([eq : c3 ] ) become @xmath43 with @xmath44 where @xmath45 , and @xmath46 and @xmath47 express uncorrelated and correlated contributions , respectively .
we employ eqs .
( [ eq : d3])-([eq : f5 ] ) in the remainder of this paper . in order
to quantitatively discuss the synchronization , we first consider the quantity @xmath48 given by @xmath49 ^ 2 > = 2 [ \gamma(t)-\rho(t ) ] .
\label{eq : e1}\ ] ] when all neurons are in the same state : @xmath50 for all @xmath51 ( the completely synchronous state ) , we obtain @xmath52 in eq .
( [ eq : e1 ] ) . on the contrary , in the asynchronous state
where @xmath53 , it is given by @xmath54 @xcite .
we may define the normalized ratio for the synchrony given by @xcite @xmath55 which is 0 and 1 for completely asynchronous ( @xmath56 ) and synchronous states ( @xmath57 ) , respectively .
the local variability is conventionally given by @xmath58 ^ 2 \rangle}}{\mu(t ) } = \frac{\sqrt{\gamma(t)}}{\mu(t ) } , \label{eq : e3}\end{aligned}\ ] ] where @xmath59 .
similarly , the global variability is defined by @xmath60 ^ 2 \rangle } } { \mu(t ) } = \frac{\sqrt{\rho(t)}}{\mu(t ) } = c_v(t)\;\sqrt{\frac{\rho(t)}{\gamma(t ) } } , \label{eq : e4 } \end{aligned}\ ] ] where @xmath61 .
the stationary solution of eqs .
( [ eq : d3])-([eq : d5 ] ) is given by @xmath62 where @xmath63 in @xmath46 and @xmath47 of eqs .
( [ eq : f4 ] ) and ( [ eq : f5 ] ) is given by eq .
( [ eq : f1 ] ) .
we note in eq .
( [ eq : f1 ] ) that @xmath63 is increased as @xmath64 is increased with an enhancement factor of @xmath65 .
a local fluctuation @xmath66 is increased with increasing input fluctuations ( @xmath27 ) and/or noise ( @xmath20 , @xmath21 ) as eq .
( [ eq : f2 ] ) shows . in the limit of @xmath67 , eqs .
( [ eq : f2 ] ) and ( [ eq : f3 ] ) lead to @xmath68 which expresses the central - limit theorem . from eqs . ( [ eq : e2 ] ) , ( [ eq : f2 ] ) and ( [ eq : f3 ] ) , we obtain @xmath69+h_1 w z r } , \label{eq : f6 } \\ & = & \frac{h_1 w}{z(\lambda-\alpha^2)-h_1 w ( z-1 ) } \hspace{0.5cm}\mbox{for $ s_i = c_a = c_m=0 $ } , \label{eq : f7}\\ & = & \frac{s_i \gamma_i+c_a \beta^2 + c_m \alpha^2 \mu^2 } { \gamma_i+\beta^2+\alpha^2 \mu^2 } \hspace{1cm}\mbox{for $ w=0 $ } , \label{eq : f8}\end{aligned}\ ] ] where @xmath46 and @xmath47 in eq .
( [ eq : f6 ] ) are given by eqs .
( [ eq : f4 ] ) and ( [ eq : f5 ] ) , respectively . equation ( [ eq : f6 ] ) shows that the synchrony @xmath70 is increased with increasing spatial correlations and/or the coupling .
this is more clearly seen in the limit of no spatial correlations [ eq .
( [ eq : f7 ] ) ] or no couplings [ eq . ( [ eq : f8 ] ) ] .
the local and global variabilities , @xmath71 and @xmath72 , defined by eqs .
( [ eq : e3 ] ) and ( [ eq : e4 ] ) , respectively , are generally expressed in terms of @xmath46 and @xmath47 , and they are given for @xmath73 by @xmath74 the local variability @xmath71 only weakly depends on the spatial correlation through the coupling , and it is independent of the correlation for @xmath75 .
in contrast , the global variability @xmath72 is increased ( decreased ) for positive ( negative ) correlations . in the limit of @xmath76 ,
( [ eq : f18 ] ) yields @xmath77 expressing a smaller global variability in a larger-@xmath0 ensemble ( the population or pooling effect ) @xcite .
the stability condition around the stationary state given by eqs .
( [ eq : f1])-([eq : f3 ] ) may be examined from eigenvalues of the jacobian matrix of eqs .
( [ eq : d3])-([eq : d5 ] ) , which are given by @xmath78 the first eigenvalue of @xmath79 arises from an equation of motion for @xmath63 , which is decoupled from the rest of variables .
the stability condition for @xmath63 is given by @xmath80 the stability condition for @xmath66 and @xmath81 is given by @xmath82 then for @xmath83 , @xmath66 and @xmath81 are unstable but @xmath63 remains stable .
it is note that there is a limitation in a parameter value of @xmath84 , as given by @xmath85 which arises from the condition given by @xmath86 [ see eqs .
( [ eq : b3 ] ) and ( [ eq : e1 ] ) ] . when @xmath87 , for example , a physically conceivable value of @xmath22 is given by @xmath88 .
@xmath22 dependence of the synchrony @xmath70 is shown in fig .
[ figa ] where @xmath89 , @xmath90 , @xmath91 , @xmath92 and @xmath93 .
the condition given by eq .
( [ eq : f13 ] ) yields that @xmath94 with @xmath95 for a given set of parameters .
we note that the synchrony is increased with increasing @xmath96 , and that the effect of the correlated variability is more considerable for larger @xmath63 and @xmath11 , as eq .
( [ eq : f6 ] ) shows . in order to study the dynamical properties of our model given by eqs .
( [ eq : a1])-([eq : a2 ] ) , we have performed direct simulations ( dss ) by using the heun method @xcite with a time step of 0.0001 : ds results are averages of 100 trials .
amm calculations have been performed for eqs .
( [ eq : d3])-([eq : d5 ] ) by using the fourth - order runge - kutta method with a time step of 0.01 .
we consider a set of typical parameters of @xmath97 , @xmath89 , @xmath90 , @xmath98 , @xmath92 and @xmath93 .
we apply a pulse input given by @xmath99 with @xmath100 , @xmath101 , where @xmath102 denotes the heaviside function : @xmath103 for @xmath104 and 0 otherwise .
figures [ figb](a)-[figb](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath106 for the correlated multiplicative noise ( @xmath107 and @xmath108 ) . @xmath29 and @xmath105 are increased by an applied input at @xmath109 shown by the chain curve in fig .
[ figb](a ) , by which @xmath30 is slightly increased .
the variability @xmath110 is decreased because of an increased @xmath29 .
the results of the amm shown by the solid curves are in fairly good agreement with those of ds shown by the dashed curves .
in contrast , figs .
[ figc](a)-[figc](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath106 for the correlated additive noise ( @xmath91 and @xmath111 ) . with an applied pulse input ,
@xmath29 is increased and @xmath30 is a little increased , as in the case of figs . [ figb](a ) and [ figb](b ) .
however , the synchrony @xmath105 is decreased in fig .
[ figc](c ) while it is increased in fig .
[ figb](c ) .
this difference arises from the fact that a decrease in @xmath105 in the former case is mainly due to an increase in @xmath46 of the denominator of eq .
( [ eq : f6 ] ) , while in the latter case , its increase arises from an increase in @xmath47 of the numerator of eq .
( [ eq : f6 ] ) .
this point is more easily realized for @xmath75 , for which eq .
( [ eq : f8 ] ) yields @xmath112 the situation is almost the same even for finite @xmath11 , as figs .
[ figb](c ) and [ figc](c ) show .
in both figs . [ figb](d ) and [ figc](d ) , @xmath106 is decreased by an applied input because of an increased @xmath29 .
we have investigated the stationary and dynamical properties of the spatially correlated langevin model given by eqs .
( [ eq : a1])-([eq : a2 ] ) . in ref .
@xcite , we discussed the fisher information in the langevin model subjected to uncorrelated additive and multiplicative noise , which is a typical microscopic model showing the nonextensive behavior @xcite .
it is interesting to calculate the fisher information of the langevin model with correlated multiplicative noise .
such a calculation needs to solve the fpe of the langevin model given by eq .
( [ eq : a9 ] ) because the fisher information is expressed in terms of derivatives of the probability distribution . for additive noise only ( @xmath113 ) , the stationary probability distribution @xmath114 is expressed by the multivariate gaussian distribution given by @xmath115 , \label{eq : l1}\end{aligned}\ ] ] with the covariance matrix , @xmath116 , expressed by @xmath117 , \label{eq : l2}\end{aligned}\ ] ] where @xmath118 and @xmath119 . from eqs .
( [ eq : l1 ] ) and ( [ eq : l2 ] ) , we obtain the fisher information given by @xcite @xmath120}. \label{eq : l3}\end{aligned}\ ] ] when multiplicative noise exists , a calculation of even stationary distribution becomes difficult , and it is generally not given by the gaussian .
the stationary distribution for _ uncorrelated _ additive and multiplicative noise ( @xmath121 , @xmath122 ) is given by @xcite @xmath123 in the limit of @xmath124 and @xmath125 ( _ i.e. _ uncorrelated additive noise only ) , eq .
( [ eq : l4 ] ) becomes the gaussian distribution given by @xmath126 in the opposite limit of @xmath127 , @xmath128 and @xmath129 ( _ i.e. _ uncorrelated multiplicative noise only ) , eq .
( [ eq : l4 ] ) reduces to @xmath130 yielding the fisher information given by @xmath131 where @xmath132 and @xmath133 @xcite .
unfortunately , we have not succeeded in obtaining the analytic expression for the stationary distribution of the langevin model including _ correlated _ multiplicative noise . in some previous studies @xcite-@xcite , the stationary distribution for correlated multiplicative noise only
( @xmath121 , @xmath134 and @xmath135 ) is assumed to be expressed by the gaussian distribution given by eq .
( [ eq : l1 ] ) with the covariance matrix given by @xmath136 , \label{eq : l6}\end{aligned}\ ] ] where @xmath137 ( @xmath138 ) denotes the average of @xmath1 and @xmath139 a variance due to multiplicative noise .
this is equivalent to assume that the multiplicative - noise term in the fpe given by eq .
( [ eq : a9 ] ) is approximated as @xmath140 \frac{\partial}{\partial x_{i } } x_i \frac{\partial}{\partial x_j } x_j \:p(\ { x_{k } \ } ) , \nonumber \\ & \simeq & \frac{\alpha^2}{2 } \sum_{i } \sum_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \langle x_i \rangle \frac{\partial}{\partial x_j } \langle x_j \rangle \:p ( \ { x_k \}),\nonumber \\ & = & \frac{\alpha^2}{2 } \sum_j \sum_{i } \mu_i \mu_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \frac{\partial}{\partial x_j } p(\ { x_{k } \ } ) .
\label{eq : l7 } \end{aligned}\ ] ] if we adopt the gaussian approximation given by eq .
( [ eq : l7 ] ) , with which multiplicative noise may be treated in the same way as additive noise , we obtain the amm equations given by eqs .
( [ eq : d3])-([eq : d5 ] ) but without the third term of @xmath141 in eq .
( [ eq : d3 ] ) . by using the gaussian approximation given by eq .
( [ eq : l6 ] ) , abbott and dayan ( ad ) @xcite obtained the fisher information expressed by [ eq .
( 4.7 ) of ref .
@xcite ] @xmath142 } + 2 n k , \label{eq : h5 } \\ & = & \frac{1 } { \sigma_m^2 \mu^2 c_m}+ \frac{2n}{\mu^2 } \hspace{3.6cm}\mbox{for $ n \rightarrow \infty $ } , \label{eq : h6 } \\ & = & \frac{n}{\sigma_m^2 \mu^2 } + \frac{2n}{\mu^2 } \hspace{2cm}\mbox{for $ c_m=0 $ } , \label{eq : h4}\end{aligned}\ ] ] with @xmath143 ^ 2=1/\mu^2 $ ] . equation ( [ eq : h4 ] ) is not in agreement with the exact expression given by eq .
( [ eq : l9 ] ) for uncorrelated multiplicative noise only . in stead of using the langevin model
, we may alternatively calculate the fisher information of a spatially correlated nonextensive system by using the maximum - entropy method . in our recent paper @xcite
, we have obtained the analytic , stationary probability distribution which maximizes the tsallis entropy @xcite under the constraints for a given set of the variance ( @xmath144 ) and covariance ( @xmath145 ) .
the fisher information is expressed by @xcite @xmath146 } , \label{eq : f12 } \\ & = & \frac{1}{c \:\sigma^2 } \hspace{2cm}\mbox{for $ n \rightarrow \infty $ } , \\ & = & \frac{n}{\sigma^2 } \hspace{2cm}\mbox{for $ c = 0.0$}. \label{eq : f14}\end{aligned}\ ] ] the fisher information given by eq .
( [ eq : f12 ] ) is increased ( decreased ) by a negative ( positive ) correlation .
this implies from the cramr - rao theorem that an unbiased estimate of fluctuations is improved by a negative spatial correlation , by which the synchrony is decreased as shown by eqs .
( [ eq : f6 ] ) and ( [ eq : f8 ] ) . @xmath0 and @xmath84 dependences of the fisher information given by eq .
( [ eq : f12 ] ) are different from those of @xmath147 given by eq .
( [ eq : h5 ] ) , although they are the same as those for additive noise only [ eq . ( [ eq : l3 ] ) ] .
it is noted that the gaussian approximation given by eq .
( [ eq : l6 ] ) or ( [ eq : l7 ] ) assumes the gaussian distribution , although multiplicative noise generally yields the non - gaussian distribution as shown by eqs .
( [ eq : l4 ] ) and ( [ eq : l8 ] ) . the spurious second term ( @xmath148 ) in eq .
( [ eq : h5 ] ) which is independent of @xmath22 and @xmath139 , arises from an inappropriate gaussian approximation . in discussing the fisher information of spatially correlated nonextensive systems
, we must take into account the detailed structure of the non - gaussian distribution . when @xmath27 and @xmath28 in eq .
( [ eq : a8 ] ) are allowed to be time dependent , they may carry input information .
this is easily realized if the amm equations given by eqs .
( [ eq : d3])-([eq : d5 ] ) are explicitly expressed in terms of @xmath63 , @xmath66 , and @xmath70 as @xmath149 + \frac{1}{\gamma } [ \gamma_i(t ) s_i(t)+ c_m \alpha^2 \mu^2+c_a \beta^2 ] \nonumber \\ & + & \left ( \frac{2 h_1 w}{z } \right ) ( 1+zs)(1-s ) , \label{eq : g5}\end{aligned}\ ] ] which are derived with the use of eq .
( [ eq : e2 ] ) . in order to numerically examine the possibility that input information is conveyed by @xmath150 and @xmath151
, we first apply a fluctuation - driven input given by @xmath152 with @xmath153 , @xmath154 , @xmath155 and @xmath156 for @xmath97 , @xmath107 , @xmath108 , @xmath89 , @xmath90 and @xmath93 .
time courses of @xmath29 , @xmath30 , @xmath105 and @xmath110 are shown in figs .
[ figg](a)-[figg](d ) : the chain curves in figs .
[ figg](a ) and [ figg](b ) express @xmath157 and @xmath150 , respectively .
when the magnitude of @xmath150 is increased at @xmath109 , @xmath30 and @xmath106 are much increased , while there is no changes in @xmath29 because it is decoupled from the rest of variables in eq .
( [ eq : d3 ] ) .
@xmath105 is slightly modified only at @xmath158 and @xmath159 where the @xmath150 is on and off .
next we apply a synchrony - driven input @xmath151 given by @xmath160 with @xmath161 , @xmath162 , @xmath163 and @xmath164 .
figures [ figh](a)-[figh](d ) show time courses of @xmath29 , @xmath30 , @xmath105 and @xmath110 : the chain curves in figs . [ figh](a ) and [ figh](c ) express @xmath157 and @xmath151 , respectively .
an increase in synchrony - driven input at @xmath109 induces a significant increase in @xmath105 and slight increases in @xmath30 and @xmath106 , but no changes in @xmath29 . when we regard a variable @xmath1 in the langevin model given by eqs .
( [ eq : a1])-([eq : a2 ] ) as the firing rate @xmath165 ( @xmath166 ) of a neuron @xmath51 in a neuron ensemble , our model expresses the neuronal model proposed in refs .
it belongs to the firing - rate ( rate - code ) models such as the wilson - cowan @xcite and hopfield models @xcite , in which a neuron is regarded as a transducer from input rate signals to output rate ones .
alternative neuronal models are spiking - neuron ( temporal - code ) models such as the hodgkin - huxley @xcite , fitzhugh - nagumo @xcite and integrate - and - fire ( if ) models @xcite .
various attempts have been proposed to obtain the firing - rate model , starting from spiking - neuron models @xcite-@xcite .
it is difficult to analytically calculate the firing rate based on spiking - neuron models , except for the if - type model @xcite .
it has been shown with the use of the if model that information transmission is possible by noise - coded signals @xcite , and that the modulation of the synchrony is possible without a change in firing rate @xcite .
model calculations shown in figs .
[ figg ] and [ figh ] have demonstrated the possibility that information may be conveyed by @xmath150 and @xmath151 , which is partly supported by results of the if model @xcite-@xcite .
some relevant results have been reported in neuronal experiments @xcite-@xcite . in motor tasks of monkey , firing rate and synchrony
are considered to encode behavioral events and cognitive events , respectively @xcite . during visual tasks , rate and synchrony
are suggested to encode task - related signals and expectation , respectively @xcite .
a change in synchrony may amplify behaviorally relevant signals in v4 of monkey @xcite .
the synchrony is modified without a change in firing rate in some experiments @xcite .
synchrony - dependent firing - rate signal is shown to propagate in iteratively constructed networks _ in vitro _ @xcite .
with the use of dss and the amm @xcite , the effects of spatially correlated additive and multiplicative noise have been discussed on the synchrony and variability in the coupled langevin model .
our calculations have shown the following : ( i ) the synchrony is increased ( decreased ) by the positive ( negative ) correlation in additive and multiplicative noise [ eq . ( [ eq : f6 ] ) ] , ( ii ) although an applied pulse input works to increase the synchrony for correlated multiplicative noise , it is possible to decrease the synchrony when correlated additive noise coexists with uncorrelated multiplicative one , ( iii ) the local variability @xmath71 is almost independent of spatial correlations , while global variability @xmath72 is increased ( decreased ) with increasing the positive ( negative ) correlation , and ( iv ) information may be carried by variance and synchrony in input signals .
the item ( iv ) is consistent with the results of refs . @xcite-@xcite and elucidates some phenomena observed in neuronal experiments @xcite-@xcite .
although we have applied the amm to the langevin model in this paper , it is possible to apply it to other types of stochastic neuronal models such as the fitzhugh and hodgkin - huxley models subjected to correlated additive and multiplicative noise , which is left as our future study .
this work is partly supported by a grant - in - aid for scientific research from the japanese ministry of education , culture , sports , science and technology . the fokker - planck equation ( fpe ) for the langevin equation given by eqs .
( [ eq : a1])-([eq : a2 ] ) in the stratonovich representation is expressed by @xcite @xmath167 \:p(\ { x_{k } \},t)\ } \nonumber \\ & & + \frac{\gamma_i}{2}\sum_{i}\sum_{j } \frac{\partial^2}{\partial x_{i } \partial x_{j } } \ { [ \delta_{ij}+s_i ( 1-\delta_{ij } ) ] \:p(\ { x_{k } \},t ) \ }
\nonumber \\ & & + \frac{\beta^2}{2}\sum_{i}\sum_{j } \frac{\partial^2}{\partial x_{i } \partial x_{j } } \ { [ \delta_{ij}+c_a ( 1-\delta_{ij } ) ] \:p(\ { x_{k } \},t ) \ }
\nonumber \\ & & + \frac{\alpha^2}{2}\sum_{i } \sum_j [ \delta_{ij}+c_m(1-\delta_{ij } ) ] \frac{\partial}{\partial x_{i } } \ { g(x_i ) \frac{\partial}{\partial x_j } [ g(x_{j } ) \:p(\ { x_{k } \},t ) ] \ } , \label{eq : a9}\end{aligned}\ ] ] where @xmath168 and @xmath169 is absorbed in a new definition of @xmath27 in its second term
. equations of motion for moments , @xmath170 and @xmath171 , are derived with the use of fpe @xcite : @xmath172
\rangle + \langle x_j\ : [ f(x_i)+ h(u_i ) ] \rangle \nonumber \\ & + & \frac{\alpha^2}{2 } [ \langle x_i g'(x_j ) g(x_j ) \rangle + \langle x_j g'(x_i ) g(x_i)\rangle ] \nonumber \\ & + & \delta_{ij } [ \gamma_i+\beta^2 + \alpha^2\:\langle g(x_i)^2 \rangle ] \nonumber \\ & + & ( 1-\delta_{ij } ) [ s_i\gamma_i+c_a \beta^2 + c_m \alpha^2 \langle g(x_i)g(x_j ) \rangle ] .
\label{eq : a11}\end{aligned}\ ] ] in the amm @xcite , the three quantities of @xmath63 , @xmath66 and @xmath81 are defined by eqs .
( [ eq : b1])-([eq : b3 ] ) .
we use the expansion given by @xmath173 and the relations given by @xmath174 for example , eq .
( [ eq : b5 ] ) for @xmath175 is calculated as follows : @xmath176 equations ( [ eq : b6 ] ) and ( [ eq : b7 ] ) are calculated in a similar way .
then , we have obtained equations of motion for @xmath29 , @xmath30 and @xmath31 given by eqs .
( [ eq : c1])-([eq : c3 ] ) . in the heun method for the ordinary differential equation of @xmath177 , a value of @xmath7 at @xmath178
is evaluated by @xmath179 $ ] with @xmath180 and @xmath181 , while it is given by @xmath182 in the euler method , @xmath183 being the time step .
the heum method for the stochastic ordinary differential equation meets the stratonovich calculus employed in the fpe @xcite .
w. rmelin , siam j. numer . anal . * 19 * ( 1982 ) 604 ; a. greiner , w. strittmatter , and j. honerkamp , j. stat . phys . * 51 * ( 1988 ) 95 ; r. f. fox , i. r. gatland , r. roy , and g. vemuri , phys .
rev . a * 38 * ( 1988 ) 5938 .
h. hasegawa , phys .
e * 77 * , 031133 ( 2008 ) .
y. aviel and w. gerstner , phys .
e * 73 * , 051908 ( 2006 ) .
m. oizumi , y. miyawaki , and m. okada , j. phys .
* 76 * , 044803 ( 2007 ) .
b. lindner and l. schimansky - geier , phys
lett . * 86 * , 2934 ( 2001 ) .
a. renart , r. moreno - bose , x - j .
wang , and n. parga , neural comput . * 19 * , 1 ( 2007 ) .
j. heinzle , p. knig , r. f. salazar , cogn . neurodyn . * 1 * , 225 ( 2007 ) .
a. riehle , s. grn , m. diesmann , and a. aertsen , science * 278 * , 1950 ( 1997 ) .
s. c. de oliveira , a. thiele , and k. p. hoffman , j. neurosci .
* 17 * , 9248 ( 1997 ) .
p. fries , j. h. reynolds , a. e. rorie , and r. desimine , science * 291 * , 1560 ( 2001 ) .
a. d. reyes , nat .
* 6 * , 593 ( 2003 ) .
f. grammont and a. riehle , biol . cybern . * 88 * , 360 ( 2003 )
. p. h. e. tiesinga and t. j. sejnowski , neural comput .
* 16 * , 251 ( 2004 ) .
h. risken , _ the fokker - planck equation : methods of solution and applcation _ , ( springer , berlin 1992 ) .[/INST] the synchrony and variability have been discussed of the coupled langevin model subjected to spatially correlated additive and multiplicative noise .
we have employed numerical simulations and the analytical augmented - moment method which is the second - order moment method for local and global variables [ h. hasegawa , phys .
rev .
e * 67 * , 041903 ( 2003 ) ] .
it has been shown that the synchrony of an ensemble is increased ( decreased ) by a positive ( negative ) spatial correlation in both additive and multiplicative noise . although the variability for local fluctuations is almost insensitive to spatial correlations , that for global fluctuations is increased ( decreased ) by positive ( negative ) correlations .
when a pulse input is applied , the synchrony is increased for the correlated multiplicative noise , whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise .
an application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals , which accounts for some neuronal experiments .
* synchrony and variability induced by spatially correlated additive and multiplicative noise + in the coupled langevin model * hideo hasegawa _ department of physics , tokyo gakugei university + koganei , tokyo 184 - 8501 , japan _
( ) _ pacs no . _ : 05.10.gg , 05.40.ca , 84.35.+i </s> |
comminuted tibial plateau fractures were associated with functional disability ; however with the advent of various surgical devices there has been marked improvement in functional outcome .
the goal in these types of fractures is to restore joint congruity , ensure joint stability , alignment , and achieve full range of motion .
the articular incongruity may not be always correlated with poor functional outcome . while treating these fractures not only the bony injury but also the soft tissue damage must be considered .
many authors have encountered poor results in patients treated with open reduction and internal fixation of tibial plateau fractures with poor soft tissue envelope .
the methods of fixation that have been used to address these fractures which include closed reduction and cast bracing [ 4 , 5 ] , open reduction and internal fixation , circular frame application [ 79 ] , percutaneous screw fixation , ligamentosis , wire guided cannulated screw , minimal invasive plating techniques , and various other techniques are used with open approaches in conjugation with the open techniques to treat these fractures .
high energy tibial fractures mostly affect the younger age group in productive life years and have significant socioeconomic impact due to time taken to recover and subsequent requirement of total knee replacement in some cases .
the specialisation in research has led to creation of various outcome measures like patient- , disease- , and domain - specific ones .
the outcome measures have moved towards functional limitations and complete body functions in order to assess an impact of the given condition on the activities in their specific environment .
the aim of current study was to take such an approach to review the functional outcome in cases of schatzker types v and vi tibial plateau fractures treated by open reduction and internal fixation .
the inpatient records of patients with schatzker types v and vi tibial plateau fractures treated with open reduction and internal fixation between february 2009 and march 2013 were searched from medical record section of the institution .
one hundred and thirty - seven consecutive patients of tibial plateau fractures treated with open reduction and internal fixation were identified .
patients excluded from the study were tibial plateau fractures of schatzker types i , ii , iii , and iv , open fractures , associated ipsilateral lower limb fractures , spine or pelvic fractures , and those lost to follow - up and treated by other methods .
seventy - two patients were excluded from the study who did not meet the inclusion criteria .
five patients had died ; sixty - seven patients could not be located or lost to follow - up .
so , sixty - five patients ( 63 males and 2 females ) were included in this study .
they were studied to determine the mode of injury , demographic data , delay in surgery , treatment given , associated ligament injuries detected following fracture fixation , complications of either the fracture or treatment , and revision surgery if any required .
the data regarding comorbid conditions , associated limb injuries , and side of injury was also collected .
the surgery was delayed in cases with soft tissue injury indicated by soft tissue edema or blister formation .
the patient was taken up for surgery once the soft tissue edema and blisters resolved with appearance of skin wrinkles .
preoperative antibiotic ( 1.5 gm cefuroxime intravenous ) was administered in all the cases one hour prior to skin incision as a single dose .
the operative procedures were performed in a standard operating room under regional or general anaesthesia under tourniquet control .
the fracture was approached through anterolateral or posteromedial side or both depending upon the fracture configuration .
the posteromedial exposure was performed with skin incision posterior to the posteromedial edge of the tibia and extension along the course of pes anserinus tendons .
pes tendons were retracted anterior while medial gastrocnemius along with popliteus was retracted posteriorly to approach the posteromedial aspect of tibia .
submeniscal arthrotomy was performed to visualize the articular surface and meniscal repair was done wherever required .
the fixed angle locking plates were used on the medial and lateral sides depending on the fracture configuration ( figures 1(a ) and 1(b ) ) .
medial proximal tibia plates are used to buttress the posteromedial fragment mainly which is often single and noncomminuted .
the lateral proximal tibial plates are used in bridging mode ; hence they are longer than the medial proximal tibial locking plates . cannulated
the radiographs including the immediate postinjury , postoperative , and follow - up radiographs were studied to confirm the correct classification of the fracture , treatment employed , articular reduction achieved , and any loss of articular reduction or malalignment on follow - up radiographs .
the joint reduction was considered to be satisfactory if articular depression was less than or equal to five millimetres and plateau widening was less than or equal to five millimetres compared to the width of the distal femoral condyle .
the patients were advised non - weight - bearing mobilisation and quadriceps exercises on the first postoperative day .
they were reviewed at 3 weeks , 6 weeks , 12 weeks , and at monthly intervals thereafter till radiological union and maximal functional recovery .
union was defined as bone healing by direct means as seen in at least two radiographic planes .
full painless weight bearing over the operated limb was considered as an indirect sign of healing .
all the patients were reviewed in the months of february and march 2014 with oxford knee score ( oks ) questionnaire .
the patients were asked twelve questions about the degree of pain in knee , any difficulty in toilet activities , ability to perform household activities , climbing up or down stairs , ability to knee , night pains , any limp in the operated limb , ability to kneel and stand again , and any discomfort in washing and drying oneself due to knee and various other questions mentioned in oxford knee score .
the patients were graded as poor ( 0 to 19 ) , moderate ( 20 to 29 ) , good ( 30 to 39 ) , and excellent ( 40 to 48 ) .
the patients who had scored more than 40 were considered as cases with satisfactory functional outcome and minimal disability ( figure 2 ) .
data was analyzed by using student 's t - test and correlations were analysed using the pearson correlation coefficient . the statistical significance was determined at p value less than 0.05 .
there were 27 tibial plateau fractures of schatzker type v ( 41.53% ) and 38 were of type vi ( 58.4% ) treated by open reduction and internal fixation .
the mechanism of injury was motor vehicle accident in 53 patients , pedestrian struck by vehicle in eight , falling from height in three , and history of assault in one case ( table 1 ) .
the age of the patients varied from 23 to 72 years ( mean age = 42.98 years ) .
there was involvement of right side in 40 cases while the number was 25 on the left side and none of the cases had bilateral tibial plateau fracture .
the majority of the fractures were treated within 14 days ; however in five cases there was delay of more than two weeks . in two cases
, there were multiple injuries and definitive fixation was staged while in the rest of the three patients surgery was delayed due to poor local skin condition .
there was loss of articular reduction manifested by articular depression ( > 4 mm ) in five patients . among these patients four had good functional recovery while one had fair outcome .
none of the patients had tibial plateau widening greater than 5 mm with respect to femoral condyles .
the mean medial proximal tibial angle was 84.2 ( ranging from 83 to 92 ) and mean posterior proximal tibial angle was 8.1 ( ranging from 3 to 14 ) .
two patients with closed fracture had undergone fasciotomy for the compartment syndrome and required skin grafting for the closure of wound .
five patients had associated other musculoskeletal injuries including contralateral limb fractures and upper limb fractures .
eight patients ( 12.3% ) had associated ipsilateral knee ligament and meniscal injuries detected after fixation of the fractures .
three among them had isolated medial collateral injury and one had associated lateral meniscus injury with medial collateral injury which was managed conservatively .
two patients had anterior cruciate ligament with lateral meniscus injury and one among them had medial collateral injury in addition to it .
ligament reconstruction was not done in these patients as they were not willing for the second operative intervention .
superficial wound infection developed in six ( 9.2% ) patients which was resolved with regular dressings and oral antibiotics .
three ( 4.6% ) patients had developed deep wound infection and one among them had developed osteomyelitis .
all of the three patients who had developed deep wound infection had to undergo secondary procedures . in two cases
the debridement was done twice ; however in one case even after three debridements there was no resolution of infection and decision to remove implant along with ilizarov 's fixation was carried out .
patient had developed nonunion in the follow - up period so secondary bone grafting with ipsilateral iliac crest being done at a later stage .
one patient who had deep wound infection opted for implant removal after one year of surgery though there was no sign of infection at that time .
of the six patients who had developed infection , two had type 2 diabetes mellitus .
primary bone grafting at the time of fracture fixation was carried out in eleven cases while secondary bone grafting was done in a case of nonunion .
of the eleven cases of primary bone grafting , bone graft substitutes in the form of calcium hydroxyapatite ( g - bone , surgiwear pvt . ltd . , shahjahanpur , india ) were used in five cases while in the rest six cases and in case of secondary bone grafting ipsilateral iliac crest bone graft was used . the functional outcome in our case
seven ( 10.7% ) had scored between 30 and 39 , three ( 4.6% ) had scored between 20 and 29 , and one patient ( 1.5% ) had a score of 18 ( table 2 ) .
age at the time of trauma had no correlation with the functional outcome ( r = 0.0864 ; p = 0.4937 ) and moreover type of fracture ( type v or vi ) did not have any significant impact on the results ( coefficient of determination = 0.0358 ; p = 0.777 ) .
the mean oks score in type v was 43.962 and in type vi was 41.657 .
infection had an impact on functional outcome in tibial plateau fractures ( t = 6.36 ; p < 0.00001 ) .
the majority of the studies in orthopaedic literature with respect to operatively treated tibial plateau fractures are physician based assessments like radiographic articular reduction , motion at the knee , and any instability .
the current trend is to use patient - specific tools to measure functional outcomes . in our study
it is a patient - specific tool to assess the patient 's perspective regarding the outcome of the surgery .
it was initially developed to assess the outcome following total knee arthroplasty , but subsequently its purview was extended to other surgical interventions around knee .
we had used one year as the minimum follow - up period because the results of knee are unlikely to change after one year and moreover function at the end of one year is a good prognostic indication for future knee function .
open reduction and internal fixation with plating is considered one of the acceptable methods of treatment in schatzker type v and type vi tibial plateau fractures .
excellent results in 81% of the cases have been reported in one of the series by lachiewicz and funcik .
oh et al . have also reported excellent results in 91% of the cases treated with open reduction and internal fixation of proximal tibial plateau fractures .
touliatos et al . have reported excellent result in 57% of their cases while in our series 83% had excellent and 10.7% had good functional outcome .
the comparison can not be drawn between these studies as they have used different methods for evaluation of results .
use of various methods of indirect reduction like kirschner 's wires and femoral distractor along with image intensifier was able to achieve acceptable articular reduction with minimal soft tissue damage .
the degenerative changes in knee joint are mainly due to inadequate restoration of articular surface , limb malalignment , joint instability , and delayed mobilization of knee joint . however , parkkinen et al . in their study on lateral tibial fractures had reported that postoperative articular congruity and neutral mechanical axis had little effect on the medium term functional outcome in tibial plateau fractures .
marsh et al . in their review of anatomic reduction in articular fractures had found little correlation between functional outcome and anatomical reduction . in our study
also there was loss of articular reduction ( > 4 mm ) in five patients .
but four among these five had good functional recovery while one had fair outcome . moreover , the patients in our study were mainly of middle age group ( mean age42 years ) and did not experience new onset of osteoarthritis .
the reported incidence of soft tissue injuries associated with tibial plateau fractures injuries has been as high as 56% .
stannard et al . had reported association of ligament injuries in 85% of the cases of type vi while the number was 79% in type v tibial plateau fractures .
they had also noticed high incidence of lateral meniscus injury in their study . however , schatzker et al .
had observed the associated ligament injuries in 7.4% of the cases of the tibial plateau .
prasad et al . had noticed anterior cruciate ligament injury in 6.5% of the cases and collateral ligament strain in 21% of the cases . in our study
there is marked variation in the incidence of associated ligament injuries reported in the literature .
the reason for that may be the use of magnetic resonance imaging by some authors ( stannard et al . ) while others ( schatzker et al . and prasad et al .
the soft tissue injuries can have marked effect on the functional outcome in tibial plateau fractures .
tibial plateau fractures are fraught with various complications with respect to fixation methods and soft tissue envelope .
there are numerous methods of management for the high energy proximal tibial fractures but the optimal treatment remains controversial .
the high complication rate associated with open reduction and internal fixation was due to single midline incision that was used to approach both anterolateral and posteromedial fragments .
the dual incision to approach the posteromedial fragment and anterolateral fragment is associated with lower local wound complication .
infection is one of the most dreaded complications encountered in the management of these fractures treated with open reduction and internal fixation .
the timing of the surgery and careful handling of soft tissue along with minimal devascularisation can minimize the chances of infection .
had reported deep wound infections ( 3.6% ) in two patients and superficial infection in three patients ( 5.4% ) .
. reported one case of septic arthritis ( 2% ) and five of superficial wound infections ( 10.6% ) in their case series of 47 operatively treated patients .
had reported infection in five of their 117 cases ( 4.2% ) , which were successfully treated with debridement and intravenous antibiotics . in our study , six patients ( 9.2% ) had superficial infection .
three patients had developed deep wound infection and one among them had osteomyelitis that was treated by removal of hardware , debridement , and application of ilizarov 's external fixator along with autogenous bone grafting at later stage ( figures 3(a ) and 3(b ) ) .
lower oxford knee scores were noted in patients who had infection ( superficial or deep ) as compared to those who did not experience any wound complication .
our results show that infection has an impact on functional outcome in tibial plateau fractures ( t value = 6.36 ; p value is < 0.00001 ) .
the reason for it could be the decrease in compliance with the physiotherapy protocols in the patients who had infective episode .
this may be either due to repeated surgeries or guarded approach in mobilising these patients . finally , we acknowledge that this study has certain limitations including lack of control group , follow - up period of less than five years , being not a single surgeon series , correlation between knee alignment and oxford knee scores being not ascertained , being not able to trace large number of patients , and retrospective nature of the study . despite these limitations we believe this study provides reliable and valid information through the use of oxford knee score and intermediate functional outcome in these types of injuries . in conclusion ,
open reduction and internal fixation is an excellent method of treatment of type v and type vi tibial plateau fractures in judiciously selected cases .
the high oxford knee score in these cases supports the fact that operative intervention can alter the lifestyle of the patients markedly . | objective . to review functional outcome in high energy tibial plateau fractures treated by plating
. design .
retrospective analysis .
material and methods .
sixty - five patients with schatzker type v and type vi tibial plateau fractures treated with open reduction and internal fixation using plates were included in the study .
the functional evaluation of the patients was carried out with oxford knee scoring .
results .
fifty - four cases ( 83% ) had oxford knee score between 40 and 48 .
seven ( 10.7% ) had score between 30 and 39 , three ( 4.6% ) had score between 20 and 29 , and one patient ( 1.5% ) had a score of 18 .
delayed union was seen in two cases and nonunion was seen in one case .
the superficial wound infection was noticed in ( 9.2% ) patients which was resolved with regular dressings and oral antibiotics .
three ( 4.6% ) patients had developed deep wound infection and one among them had developed osteomyelitis .
conclusion .
open reduction and internal fixation in high energy tibial plateau fractures can provide good functional results in appropriately selected cases . | <s>[INST]comminuted tibial plateau fractures were associated with functional disability ; however with the advent of various surgical devices there has been marked improvement in functional outcome .
the goal in these types of fractures is to restore joint congruity , ensure joint stability , alignment , and achieve full range of motion .
the articular incongruity may not be always correlated with poor functional outcome . while treating these fractures not only the bony injury but also the soft tissue damage must be considered .
many authors have encountered poor results in patients treated with open reduction and internal fixation of tibial plateau fractures with poor soft tissue envelope .
the methods of fixation that have been used to address these fractures which include closed reduction and cast bracing [ 4 , 5 ] , open reduction and internal fixation , circular frame application [ 79 ] , percutaneous screw fixation , ligamentosis , wire guided cannulated screw , minimal invasive plating techniques , and various other techniques are used with open approaches in conjugation with the open techniques to treat these fractures .
high energy tibial fractures mostly affect the younger age group in productive life years and have significant socioeconomic impact due to time taken to recover and subsequent requirement of total knee replacement in some cases .
the specialisation in research has led to creation of various outcome measures like patient- , disease- , and domain - specific ones .
the outcome measures have moved towards functional limitations and complete body functions in order to assess an impact of the given condition on the activities in their specific environment .
the aim of current study was to take such an approach to review the functional outcome in cases of schatzker types v and vi tibial plateau fractures treated by open reduction and internal fixation .
the inpatient records of patients with schatzker types v and vi tibial plateau fractures treated with open reduction and internal fixation between february 2009 and march 2013 were searched from medical record section of the institution .
one hundred and thirty - seven consecutive patients of tibial plateau fractures treated with open reduction and internal fixation were identified .
patients excluded from the study were tibial plateau fractures of schatzker types i , ii , iii , and iv , open fractures , associated ipsilateral lower limb fractures , spine or pelvic fractures , and those lost to follow - up and treated by other methods .
seventy - two patients were excluded from the study who did not meet the inclusion criteria .
five patients had died ; sixty - seven patients could not be located or lost to follow - up .
so , sixty - five patients ( 63 males and 2 females ) were included in this study .
they were studied to determine the mode of injury , demographic data , delay in surgery , treatment given , associated ligament injuries detected following fracture fixation , complications of either the fracture or treatment , and revision surgery if any required .
the data regarding comorbid conditions , associated limb injuries , and side of injury was also collected .
the surgery was delayed in cases with soft tissue injury indicated by soft tissue edema or blister formation .
the patient was taken up for surgery once the soft tissue edema and blisters resolved with appearance of skin wrinkles .
preoperative antibiotic ( 1.5 gm cefuroxime intravenous ) was administered in all the cases one hour prior to skin incision as a single dose .
the operative procedures were performed in a standard operating room under regional or general anaesthesia under tourniquet control .
the fracture was approached through anterolateral or posteromedial side or both depending upon the fracture configuration .
the posteromedial exposure was performed with skin incision posterior to the posteromedial edge of the tibia and extension along the course of pes anserinus tendons .
pes tendons were retracted anterior while medial gastrocnemius along with popliteus was retracted posteriorly to approach the posteromedial aspect of tibia .
submeniscal arthrotomy was performed to visualize the articular surface and meniscal repair was done wherever required .
the fixed angle locking plates were used on the medial and lateral sides depending on the fracture configuration ( figures 1(a ) and 1(b ) ) .
medial proximal tibia plates are used to buttress the posteromedial fragment mainly which is often single and noncomminuted .
the lateral proximal tibial plates are used in bridging mode ; hence they are longer than the medial proximal tibial locking plates . cannulated
the radiographs including the immediate postinjury , postoperative , and follow - up radiographs were studied to confirm the correct classification of the fracture , treatment employed , articular reduction achieved , and any loss of articular reduction or malalignment on follow - up radiographs .
the joint reduction was considered to be satisfactory if articular depression was less than or equal to five millimetres and plateau widening was less than or equal to five millimetres compared to the width of the distal femoral condyle .
the patients were advised non - weight - bearing mobilisation and quadriceps exercises on the first postoperative day .
they were reviewed at 3 weeks , 6 weeks , 12 weeks , and at monthly intervals thereafter till radiological union and maximal functional recovery .
union was defined as bone healing by direct means as seen in at least two radiographic planes .
full painless weight bearing over the operated limb was considered as an indirect sign of healing .
all the patients were reviewed in the months of february and march 2014 with oxford knee score ( oks ) questionnaire .
the patients were asked twelve questions about the degree of pain in knee , any difficulty in toilet activities , ability to perform household activities , climbing up or down stairs , ability to knee , night pains , any limp in the operated limb , ability to kneel and stand again , and any discomfort in washing and drying oneself due to knee and various other questions mentioned in oxford knee score .
the patients were graded as poor ( 0 to 19 ) , moderate ( 20 to 29 ) , good ( 30 to 39 ) , and excellent ( 40 to 48 ) .
the patients who had scored more than 40 were considered as cases with satisfactory functional outcome and minimal disability ( figure 2 ) .
data was analyzed by using student 's t - test and correlations were analysed using the pearson correlation coefficient . the statistical significance was determined at p value less than 0.05 .
there were 27 tibial plateau fractures of schatzker type v ( 41.53% ) and 38 were of type vi ( 58.4% ) treated by open reduction and internal fixation .
the mechanism of injury was motor vehicle accident in 53 patients , pedestrian struck by vehicle in eight , falling from height in three , and history of assault in one case ( table 1 ) .
the age of the patients varied from 23 to 72 years ( mean age = 42.98 years ) .
there was involvement of right side in 40 cases while the number was 25 on the left side and none of the cases had bilateral tibial plateau fracture .
the majority of the fractures were treated within 14 days ; however in five cases there was delay of more than two weeks . in two cases
, there were multiple injuries and definitive fixation was staged while in the rest of the three patients surgery was delayed due to poor local skin condition .
there was loss of articular reduction manifested by articular depression ( > 4 mm ) in five patients . among these patients four had good functional recovery while one had fair outcome .
none of the patients had tibial plateau widening greater than 5 mm with respect to femoral condyles .
the mean medial proximal tibial angle was 84.2 ( ranging from 83 to 92 ) and mean posterior proximal tibial angle was 8.1 ( ranging from 3 to 14 ) .
two patients with closed fracture had undergone fasciotomy for the compartment syndrome and required skin grafting for the closure of wound .
five patients had associated other musculoskeletal injuries including contralateral limb fractures and upper limb fractures .
eight patients ( 12.3% ) had associated ipsilateral knee ligament and meniscal injuries detected after fixation of the fractures .
three among them had isolated medial collateral injury and one had associated lateral meniscus injury with medial collateral injury which was managed conservatively .
two patients had anterior cruciate ligament with lateral meniscus injury and one among them had medial collateral injury in addition to it .
ligament reconstruction was not done in these patients as they were not willing for the second operative intervention .
superficial wound infection developed in six ( 9.2% ) patients which was resolved with regular dressings and oral antibiotics .
three ( 4.6% ) patients had developed deep wound infection and one among them had developed osteomyelitis .
all of the three patients who had developed deep wound infection had to undergo secondary procedures . in two cases
the debridement was done twice ; however in one case even after three debridements there was no resolution of infection and decision to remove implant along with ilizarov 's fixation was carried out .
patient had developed nonunion in the follow - up period so secondary bone grafting with ipsilateral iliac crest being done at a later stage .
one patient who had deep wound infection opted for implant removal after one year of surgery though there was no sign of infection at that time .
of the six patients who had developed infection , two had type 2 diabetes mellitus .
primary bone grafting at the time of fracture fixation was carried out in eleven cases while secondary bone grafting was done in a case of nonunion .
of the eleven cases of primary bone grafting , bone graft substitutes in the form of calcium hydroxyapatite ( g - bone , surgiwear pvt . ltd . , shahjahanpur , india ) were used in five cases while in the rest six cases and in case of secondary bone grafting ipsilateral iliac crest bone graft was used . the functional outcome in our case
seven ( 10.7% ) had scored between 30 and 39 , three ( 4.6% ) had scored between 20 and 29 , and one patient ( 1.5% ) had a score of 18 ( table 2 ) .
age at the time of trauma had no correlation with the functional outcome ( r = 0.0864 ; p = 0.4937 ) and moreover type of fracture ( type v or vi ) did not have any significant impact on the results ( coefficient of determination = 0.0358 ; p = 0.777 ) .
the mean oks score in type v was 43.962 and in type vi was 41.657 .
infection had an impact on functional outcome in tibial plateau fractures ( t = 6.36 ; p < 0.00001 ) .
the majority of the studies in orthopaedic literature with respect to operatively treated tibial plateau fractures are physician based assessments like radiographic articular reduction , motion at the knee , and any instability .
the current trend is to use patient - specific tools to measure functional outcomes . in our study
it is a patient - specific tool to assess the patient 's perspective regarding the outcome of the surgery .
it was initially developed to assess the outcome following total knee arthroplasty , but subsequently its purview was extended to other surgical interventions around knee .
we had used one year as the minimum follow - up period because the results of knee are unlikely to change after one year and moreover function at the end of one year is a good prognostic indication for future knee function .
open reduction and internal fixation with plating is considered one of the acceptable methods of treatment in schatzker type v and type vi tibial plateau fractures .
excellent results in 81% of the cases have been reported in one of the series by lachiewicz and funcik .
oh et al . have also reported excellent results in 91% of the cases treated with open reduction and internal fixation of proximal tibial plateau fractures .
touliatos et al . have reported excellent result in 57% of their cases while in our series 83% had excellent and 10.7% had good functional outcome .
the comparison can not be drawn between these studies as they have used different methods for evaluation of results .
use of various methods of indirect reduction like kirschner 's wires and femoral distractor along with image intensifier was able to achieve acceptable articular reduction with minimal soft tissue damage .
the degenerative changes in knee joint are mainly due to inadequate restoration of articular surface , limb malalignment , joint instability , and delayed mobilization of knee joint . however , parkkinen et al . in their study on lateral tibial fractures had reported that postoperative articular congruity and neutral mechanical axis had little effect on the medium term functional outcome in tibial plateau fractures .
marsh et al . in their review of anatomic reduction in articular fractures had found little correlation between functional outcome and anatomical reduction . in our study
also there was loss of articular reduction ( > 4 mm ) in five patients .
but four among these five had good functional recovery while one had fair outcome . moreover , the patients in our study were mainly of middle age group ( mean age42 years ) and did not experience new onset of osteoarthritis .
the reported incidence of soft tissue injuries associated with tibial plateau fractures injuries has been as high as 56% .
stannard et al . had reported association of ligament injuries in 85% of the cases of type vi while the number was 79% in type v tibial plateau fractures .
they had also noticed high incidence of lateral meniscus injury in their study . however , schatzker et al .
had observed the associated ligament injuries in 7.4% of the cases of the tibial plateau .
prasad et al . had noticed anterior cruciate ligament injury in 6.5% of the cases and collateral ligament strain in 21% of the cases . in our study
there is marked variation in the incidence of associated ligament injuries reported in the literature .
the reason for that may be the use of magnetic resonance imaging by some authors ( stannard et al . ) while others ( schatzker et al . and prasad et al .
the soft tissue injuries can have marked effect on the functional outcome in tibial plateau fractures .
tibial plateau fractures are fraught with various complications with respect to fixation methods and soft tissue envelope .
there are numerous methods of management for the high energy proximal tibial fractures but the optimal treatment remains controversial .
the high complication rate associated with open reduction and internal fixation was due to single midline incision that was used to approach both anterolateral and posteromedial fragments .
the dual incision to approach the posteromedial fragment and anterolateral fragment is associated with lower local wound complication .
infection is one of the most dreaded complications encountered in the management of these fractures treated with open reduction and internal fixation .
the timing of the surgery and careful handling of soft tissue along with minimal devascularisation can minimize the chances of infection .
had reported deep wound infections ( 3.6% ) in two patients and superficial infection in three patients ( 5.4% ) .
. reported one case of septic arthritis ( 2% ) and five of superficial wound infections ( 10.6% ) in their case series of 47 operatively treated patients .
had reported infection in five of their 117 cases ( 4.2% ) , which were successfully treated with debridement and intravenous antibiotics . in our study , six patients ( 9.2% ) had superficial infection .
three patients had developed deep wound infection and one among them had osteomyelitis that was treated by removal of hardware , debridement , and application of ilizarov 's external fixator along with autogenous bone grafting at later stage ( figures 3(a ) and 3(b ) ) .
lower oxford knee scores were noted in patients who had infection ( superficial or deep ) as compared to those who did not experience any wound complication .
our results show that infection has an impact on functional outcome in tibial plateau fractures ( t value = 6.36 ; p value is < 0.00001 ) .
the reason for it could be the decrease in compliance with the physiotherapy protocols in the patients who had infective episode .
this may be either due to repeated surgeries or guarded approach in mobilising these patients . finally , we acknowledge that this study has certain limitations including lack of control group , follow - up period of less than five years , being not a single surgeon series , correlation between knee alignment and oxford knee scores being not ascertained , being not able to trace large number of patients , and retrospective nature of the study . despite these limitations we believe this study provides reliable and valid information through the use of oxford knee score and intermediate functional outcome in these types of injuries . in conclusion ,
open reduction and internal fixation is an excellent method of treatment of type v and type vi tibial plateau fractures in judiciously selected cases .
the high oxford knee score in these cases supports the fact that operative intervention can alter the lifestyle of the patients markedly .[/INST]objective . to review functional outcome in high energy tibial plateau fractures treated by plating
. design .
retrospective analysis .
material and methods .
sixty - five patients with schatzker type v and type vi tibial plateau fractures treated with open reduction and internal fixation using plates were included in the study .
the functional evaluation of the patients was carried out with oxford knee scoring .
results .
fifty - four cases ( 83% ) had oxford knee score between 40 and 48 .
seven ( 10.7% ) had score between 30 and 39 , three ( 4.6% ) had score between 20 and 29 , and one patient ( 1.5% ) had a score of 18 .
delayed union was seen in two cases and nonunion was seen in one case .
the superficial wound infection was noticed in ( 9.2% ) patients which was resolved with regular dressings and oral antibiotics .
three ( 4.6% ) patients had developed deep wound infection and one among them had developed osteomyelitis .
conclusion .
open reduction and internal fixation in high energy tibial plateau fractures can provide good functional results in appropriately selected cases .</s> |
the role of coulomb correlations in topological band insulators has recently received wide attention.@xcite as a result of spin - orbit coupling , the band structure of these materials exhibits charge excitation spectra whose physical characteristics can depend strongly on the coulomb interaction .
iridium compounds , such as na@xmath1iro@xmath2 and a@xmath1ir@xmath1o@xmath3 ( a = pr , eu ) have recently been proposed as materials in which the interplay of spin - orbit interaction and electronic correlation effects might be important .
@xcite the phase diagram of a prototype bulk system of this kind was studied by yoshida _
et al._@xcite within an extension of the two - band model proposed by bernevig , hughes , and zhang ( bhz),@xcite where an onsite hubbard term is included to account for correlations .
it was shown that , in the paramagnetic limit , such a system exhibits a first - order quantum phase transition , where the weakly correlated phase corresponds to a topological band insulator and the strongly correlated phase to a mott insulator . at surfaces of topological insulators ,
metallic edge states may exist which are protected against perturbations associated with impurities and other interactions that do not break the time - reversal symmetry of the system.@xcite because of these unique properties , heterostructures involving topological band insulators @xcite are presently of great interest since they might be relevant for future technological applications .
for instance , as shown by ueda _
et al._,@xcite the interface of a topological band insulator and a mott insulator also exhibits an edge state which maintains its helical characteristics within the mott insulator .
moreover , the quasi - particle properties and depth profile of this state within the mott insulator depend strongly on the local coulomb energy . in the present work we study
the role of electronic correlations at the interface between a topological insulator and a mott insulator .
the important difference between our approach and the one by ueda _
et al._@xcite is that we include spin - orbit coupling also within the mott insulator .
thus , with decreasing coulomb energy , the mott insulator does not become a metal but a topological band insulator .
the electronic properties in the vicinity of the interface are treated self - consistently by using the layer dynamical mean field theory ( dmft).@xcite local many - body interactions are evaluated via finite - temperature exact diagonalization ( ed ) .
@xcite separate single - site dmft calculations are performed for the asymptotic semi - infinite bulk regions .
their influence on the interface region is taken into account via complex embedding potentials.@xcite for simplicity , a square lattice geometry is used , as illustrated in fig .
[ fig1].@xcite to incorporate spin - orbit interactions , the generalized two - orbital bhz model is used , which includes the site - dependent coulomb energy as well as the interorbital hybridization .
( color online ) one - dimensional interface between two - dimensional topological band and mott insulators .
the coulomb energies on the left and right side of the interface are defined as @xmath4 and @xmath5 , respectively .
the electronic properties in the embedding region are calculated self - consistently within the layer dmft .
the properties of the asymptotic bulk regions are taken into account via embedding potentials.,width=283,height=207 ] the main result of this study is the displacement of the edge state from the interface toward the interior of the mott insulator when the local coulomb energy on the corresponding side of the heterostructure is near the critical value for the mott transition . the edge state is then buried deeply within the mott insulator so that the boundary between the band and mott insulating phases no longer coincides with the physical interface of the two constituents of the heterostructure .
the origin of this novel proximity effect is the fact that the mott transition is first order . as a consequence , within the coexistence region topological
band and mott insulating phases compete .
their relative stability depends sensitively on temperature and local coulomb energy .
moreover , because of the penetration of the edge state wave function into the mott insulator , near the interface the properties of the nominal mott insulator are also influenced by the presence of the neighboring topological band insulator . as a result
, the mott insulating phase within a certain depth can be converted into the more stable topological band insulating phase .
the edge state is thereby displaced away from the physical interface which becomes the boundary between two weakly and strongly correlated topological band insulators .
as the coulomb energy in the mott insulator increases beyond the coexistence region , the edge state is localized again at the interface .
its depth within the mott insulator diminishes as the mott gap increases . below the coexistence domain ,
the edge disappears since
the heterostrucure then consists of two correlated topological band insulators .
we emphasize that the displacement of the edge state away from the interface of the heterostructure is a consequence of the interorbital hybridization ( spin - orbit coupling ) in the mott insulator . in the absence of spin - orbit coupling ,
the coexistence domain involves trivial metallic and insulating phases so that a topological band insulating solution does not occur .
thus , if an edge state exists , it is localized at the physical interface .
we also demonstrate that the ordinary proximity effect,@xcite i.e. , the appearance of a kondo peak in a mott insulator due to neighboring metallic states , is accompanied by an secondary reverse proximity effect , as a result of which the kondo peak leads to an increase of the density of states ( dos ) in the neighboring metallic layer .
the outline of this paper is as follows .
section ii presents the main aspects of the theoretical approach .
in particular , we introduce the generalized bhz two - band model which provides the basis for the topological band as well as mott insulating phases .
also , the embedding scheme is described in which the effect of the asymptotic bulk materials on either side of the interface are taken into account via complex local potentials .
finally , the inhomogeneous layer dmft is outlined , as well as the finite - temperature exact diagonalization scheme for the treatment of local many - body interactions .
section iii provides the discussion of the results .
we first present the phase diagram of the asymptotic bulk materials and illustrate the edge state at the solid - vacuum interface .
the main part discusses the electronic properties of the interface between topological band and mott insulators , in particular , the location of the edge state as a function of the coulomb energy within the mott insulator .
we consider a one - dimensional interface between a two - dimensional ( 2-d ) topological band insulator ( bi ) and a 2-d mott insulator ( mi ) , which occupy the left and right half - space , respectively .
the @xmath6 direction is parallel to the interface , while the @xmath7 axis , which points from left to right , is chosen as the interface normal . to represent the semi - infinite systems on both sides , we employ the generalized bernevig - hughes - zhang model , @xmath8 the first term in the second line of eq .
( [ eq1 ] ) , @xmath9 represents two tight - binding bands originating from two orbitals , where @xmath10 ( @xmath11 ) creates ( annihilates ) an electron with orbital @xmath12 in spin state @xmath13 on a 2-d square lattice point at @xmath14 , with @xmath6 and @xmath7 giving its @xmath6 and @xmath7 positions , respectively . in eq .
( [ eq2 ] ) , @xmath15 and @xmath16 are the site energy and nearest - neighbor hopping integral for orbital @xmath17 , @xmath18 is the coulomb energy , which will be described below , @xmath19 denotes the orbital occupation , and the summation over @xmath20 and @xmath21 in the second term is taken over nearest - neighbor lattice - point pairs . the second term in the second line of eq .
( [ eq1 ] ) , which arises from spin - orbit coupling and is responsible for the opening of a topological energy band gap , reads @xmath22,\label{eq3}\ ] ] where @xmath23 specifies the hopping direction measured relative to the @xmath6 axis ( @xmath24 and @xmath25 correspond to the hopping to the positive @xmath6 and @xmath7 directions , respectively ) .
the last term in eq .
( [ eq1 ] ) , @xmath26 expresses the onsite coulomb repulsion between electrons with opposite spin in the same orbital @xmath17 .
we assume that the coulomb energy can vary with lattice layers , while it is constant within the same layer .
it should be noted that the term @xmath27 in eq .
( [ eq2 ] ) ensures that the system becomes electron - hole symmetric when chemical potential @xmath28 is chosen as @xmath29 .
et al_.@xcite studied the effect of strong coulomb correlations on a topological band insulator by applying single - site dmft@xcite to periodic 2-d bulk systems described by the same generalized bhz model .
it was shown that the system undergoes a quantum phase transition from a topological band insulator to a mott insulator when one increases the onsite coulomb energy @xmath0 , while keeping the system nonmagnetic . as schematically illustrated in fig .
[ fig2 ] , the phase transition is of first order and exhibits hysteresis behavior , i.e. , both topological band and mott insulating solutions are found if @xmath0 is within the coexistence region @xmath30 $ ] .
the width of this region decreases with increasing temperature @xmath31 and vanishes at a critical value @xmath32 . in the present work , both the topological band insulator on the left half - space and the mott insulator on the right half - space
are represented by the generalized bhz model as described above . as indicated in fig .
[ fig1 ] , the layer dependent coulomb energy , @xmath18 , is set to be @xmath4 and @xmath5 in the left and right half - spaces , respectively , where @xmath33 and @xmath34 ( see fig . 2 below ) .
we note that our model differs from that in the recent work of ueda _
et al_.@xcite , in which the mott insulator was represented by two independent hubbard bands without the spin - orbit coupling term defined in eq .
( [ eq3 ] ) . we calculate the finite - temperature green s function of the interface between two semi - infinite systems by using the layer dmft technique.@xcite a finite number of lattice layers in the interface region
is treated explicitly , whereas the effect of the outer regions is taken into account via the embedding potentials@xcite which include correlation effects in the bulk region.@xcite as we consider nonmagnetic solutions in the present work , the green s function and other quantities are diagonal with respect to spin . in the following ,
we show only the up - spin component of the equations and omit spin indices for simplicity . by introducing the wave number in the @xmath6 direction , @xmath35 , the green s function in the embedded region
is given as @xmath36^{-1 } \mid y'\alpha'\rangle,\label{eq5}\end{aligned}\ ] ] where the embedding hamiltonian in the mixed representation , @xmath37 , is a @xmath38 matrix with @xmath39 being the number of the embedded lattice layers .
it consists of four terms : @xmath40 where @xmath41 denotes the one - electron part of the hamiltonian in eq .
( [ eq1 ] ) .
the superscript @xmath39 emphasizes the fact that @xmath42 is a @xmath43 matrix for an isolated slab . the second term in eq .
( [ eq6 ] ) is the coulomb self - energy . within single - site dmft , it is layer diagonal and @xmath35-independent : @xmath44 the last two terms in eq .
( [ eq6 ] ) are the embedding potentials . since @xmath45 in eq .
( [ eq1 ] ) includes only nearest - neighbor hopping terms , @xmath46 ( @xmath47 ) is non - vanishing only when both layer indices are equal to @xmath48 ( @xmath49 ) , the outermost layer of the embedded slab region on the left ( right ) hand side .
thus , they are written as @xmath50 we now explain how we can derive the embedding potential for the left - hand side .
we assume that the electronic structure in the half - space to the left of the embedded slab region converges to that of the bulk crystal with coulomb repulsion energy @xmath4 .
thus , within the single - site approximation , the coulomb self - energy of all layers is assumed to be identical to that in the interior of the bulk with @xmath4 , @xmath51 .
this quantity is a @xmath52 matrix in orbital space .
now , let us consider the green s function of the semi - infinite solid in which the self - energies of all layers are equal to @xmath51 .
we extract from this green s function a @xmath52 matrix spanned by the two orbital components of the outermost surface layer , which is denoted by @xmath53 .
the embedding potential , i.e. , the @xmath54 matrix appearing on the right hand side of eq .
( [ eq8 ] ) , is then given by@xcite @xmath55 with @xmath56 where @xmath57 ( @xmath58 ) is the transfer matrix for electrons which hop between two nearest - neighbor lattice layers toward the positive ( negative ) @xmath7 direction . in order to obtain @xmath59 in eq .
( [ eq10 ] ) , we use the following trick .
we add one additional lattice layer having the bulk self - energy @xmath60 on top of the semi - infinite substrate expressed by the embedding potential @xmath46 .
then , the @xmath52 surface green s function of the resultant new semi - infinite solid is given by @xmath61^{-1},\label{eq12}\ ] ] where @xmath62 is given by @xmath63 we now make use of the fact that the semi - infinite solid obtained by putting one bulk lattice on top of the semi - infinite bulk system is exactly the same as that without the additional lattice layer .
thus , @xmath59 on the right - hand side of eq .
( [ eq10 ] ) must coincide with @xmath59 calculated by eq .
( [ eq12 ] ) .
thus , by inserting @xmath59 in eq .
( [ eq12 ] ) into the right - hand side of eq .
( [ eq10 ] ) , one obtains a set of equations to determine the three independent elements of the embedding potential , @xmath64 for given @xmath35 and @xmath65 .
in contrast to one - band models , for which one can derive an analytical expression of the embedding potential from a quadratic equation obtained by following the same procedure as described above,@xcite the embedding potential for the present two - band model can be computed only numerically . to determine @xmath46
, one needs the bulk self - energy @xmath66 in eq .
( [ eq12 ] ) , which can be determined from an independent dmft calculation for the 2-d bulk system with coulomb repulsion energy @xmath4 , before evaluating the interface properties .
similarly , the embedding potential for the right - hand side can be derived by combining the two following equations .
@xmath67 @xmath68^{-1},\label{eq15}\ ] ] where @xmath69 denotes the coulomb self - energy of the 2-d bulk system with coulomb interaction @xmath5 .
starting from some initial self - energy matrix , one calculates the local components of the lattice green s function for each layer , @xmath70 , by using eq .
( [ eq5 ] ) .
then , the bath green s function determining the weiss mean - field of layer @xmath7 is obtained by removing the local self - energy : @xmath71^{-1 } , \label{eq16}\ ] ] where @xmath72 is the @xmath52 matrix defined by eq .
( [ eq7 ] ) . in the present work ,
the quantum impurity problem is solved by making use of the exact diagonalization ( ed ) formalism,@xcite in which @xmath73 is approximated by a noninteracting green s function of a finite cluster consisting of two impurity levels with energy @xmath74 coupled to @xmath75 bath orbitals with energy @xmath76 .
thus , @xmath77^{-1},\label{eq17}\ ] ] with @xmath78 where @xmath74 , @xmath76 and @xmath79 are real fitting parameters chosen such that the weighted sum of @xmath80 over a sufficiently large matsubara frequency range is minimized.@xcite then , after adding the onsite coulomb repulsion terms eq .
( [ eq4 ] ) to this @xmath81-level cluster , the interacting green s function of the cluster , @xmath82 , is derived by combining the arnoldi algorithm for computing the lowest eigenstates with the lanczos procedure for calculating the green s function.@xcite finally , the cluster self - energy is obtained from the equation : @xmath83^{-1 } -\left[\hat{g}^{cl } ( y , i\omega_n)\right]^{-1}.\label{eq19}\ ] ] in the ed formalism , the cluster self - energy is assumed to be a physically reasonable representation of the lattice self - energy .
thus , @xmath84 is used as the input self - energy @xmath72 in eq .
( [ eq5 ] ) for the next dmft iteration .
this procedure is iterated until the difference between the input and output self - energy matrices for all the lattice layers in the embedded region becomes sufficiently small . in the calculation presented in the next section ,
we use @xmath85 bath orbitals ( 4 per orbital ) , so that the total number of energy levels per cluster equals 10 .
in the present work , the parameters of the non - interacting part of the hamiltonian are chosen as @xmath86 , @xmath87 , @xmath88 , @xmath89 , and @xmath90 .
the same parameter set was used previously in ref . .
we consider only the electron - hole symmetric case with chemical potential @xmath29 . in the absence of correlations , the bulk bands extend from @xmath91 to @xmath92 and the band gap from @xmath93 to @xmath94 .
the dmft calculations are performed at a relatively small temperature : @xmath95 .
( color online ) schematic bulk phase diagram of correlated topological band insulator , derived within generalized bhz two - orbital model and single - site dmft . in the region limited by the lines
@xmath96 and @xmath97 , band and mott insulating states may coexist .
the true phase boundary defining the relative stability of these phases is indicated by the line @xmath98 .
, width=283,height=188 ] figure [ fig2 ] illustrates schematically the bulk phase diagram of the constituents of the present heterostructure . at small @xmath0 ,
one has a weakly correlated topological band insulator which corresponds to the system on the left - hand side in fig .
[ fig1 ] . at large @xmath0 ,
the system becomes a mott insulator which is taken to be the dominant phase on the right - hand side of the interface .
we note that in the present model the mott insulating phase is nontopological with a vanishing chern number , in contrast to the topological kondo insulator.@xcite the band gap in the band insulator also varies with @xmath0 .
it is largest in the noninteracting limit and gradually decreases with increasing @xmath0 until @xmath0 approaches @xmath97 .
this behavior corresponds to the usual band - narrowing effect , which has been discussed in previous work.@xcite as a result of local coulomb interactions , spectral weight within the region of the bulk bands is transferred to low energies and hubbard bands appear at high energies . for the parameters specified above , we find that the coexistence region is limited by the boundaries @xmath99 and @xmath100 . because of the first - order nature of the mott transition , various quantities , such as the orbital polarization , the double occupancy of the subbands , the spectral weight at the chemical potential , etc .
exhibit the usual hysteresis behavior ( not shown here ) .
an important aspect of the interface properties discussed in subsection [ sec_3d ] is the fact that they may be used to determine the relative stability of the band and mott insulating phases in the coexistence region .
for instance , at @xmath101 we estimate @xmath102 .
as will be shown below , an edge state appears at the interface of a weakly correlated topological band insulator and a strongly correlated mott insulator .
the intriguing question then arises what happens to the edge state when the coulomb energy in the mott insulator lies within the coexistence region .
depending on the precise values of @xmath0 and @xmath31 , the mott insulating phase can become unstable and may therefore be converted into a band insulating phase .
before we discuss this case , we consider in the following two subsections ( i ) the behavior of the edge state at the bare surface of a topological band insulator and ( ii ) the properties of the interface between two topological insulators .
these results serve a useful reference for the subsequent analysis of the interface with a mott insulator ( color online ) variation of edge state at bare surface of correlated topological band insulator as a function layer index @xmath7 for various coulomb energies @xmath0 , as calculated within inhomogeneous dmft .
plotted is the function @xmath103 , defined in eq .
( [ g ] ) , which represents the partially integrated density of states within a few @xmath31 of the chemical potential ( @xmath101 ) .
the embedding region at the surface comprises 12 atomic layers beyond which bulk behavior is assumed .
, width=283,height=188 ] figure [ fig3 ] shows the spectral weight near the chemical potential at the surface of a correlated topological band insulator as a function of distance from the surface for several values of @xmath0 .
plotted is the function @xmath103 which provides a measure of the dos within a few @xmath31 of the chemical potential .
this quantity is defined as @xmath104 where @xmath105 is the interacting dos of subband @xmath17 and the weight function @xmath106 is defined as : @xmath107 $ ] .
( the width of @xmath106 is about @xmath108 ; its integrated weight is unity . ) as a result of particle - hole symmetry , @xmath109 . at the surface of a topological insulator ,
a metallic edge state connecting the bulk valence and conduction bands appears .
as the chemical potential is located at the middle of the energy gap when the system is electron - hole symmetric , the edge state contributes to an increase in dos at @xmath28 for several surface layers , which is clearly seen in fig .
with increasing values of @xmath0 , the gap in the topological band insulator diminishes due to correlation effects , so that the penetration depth of the edge state increases
. the peak of the edge state at larger @xmath0 also shifts to the second layer ( see below ) . at the same time , the high - energy tails of @xmath110 on both sides of @xmath111 start overlapping with the bulk bands due to band - gap narrowing . for @xmath112 ,
this results in a rapid increase in the calculated values of @xmath103 in the interior of the solid .
( color online ) intensity plot of interacting dos of orbital @xmath113 , @xmath114 in surface layer of semi - infinite topological insulator as a function of parallel momentum @xmath35 for several values of @xmath0 .
, scaledwidth=40.0% ] ( color online ) interacting dos , @xmath115 , in first three surface layers of topological insulator at @xmath116 .
solid ( red ) curves : orbital @xmath113 , dashed ( blue ) curves : @xmath117 .
these spectra are derived by extrapolating the lattice green s function from matsubara frequencies to @xmath118 with a small imaginary energy @xmath119 via the routine _ ratint_. the spectral weight near @xmath29 in panel ( a ) is due to the metallic edge state , while the dos in panel ( c ) approaches the one characteristic of the bulk band gap .
, scaledwidth=35.0% ] to illustrate the energy dispersion of the edge state with @xmath35 in the case of a free surface , we show in fig .
[ fig4 ] the @xmath35-resolved dos of the first layer ( @xmath120 ) for various coulomb energies .
these results were derived by extrapolating the self - energy from the matsubara axis to real energies via the routine _ ratint _ ( for details see ref . ) and then evaluating the integrand on the right hand side of eq .
( [ eq5 ] ) .
one can clearly see a metallic edge state crossing the chemical potential @xmath29 at @xmath121 with a positive group velocity .
this indicates that the increase in dos seen in fig .
[ fig3 ] for surface layers arises from the edge state around @xmath121 .
the energy dispersion curve of the edge state for the down - spin ( not shown ) is obtained by reflecting the one for the up - spin shown in fig .
[ fig4 ] with respect to @xmath121 , so that the two dispersion curves with the opposite spins cross at @xmath121 . with increasing @xmath0 ,
the dispersion of the edge state becomes flatter and the bulk band gap is reduced .
also , the width of the bulk bands decreases and hubbard bands appear below and above the band region . since the weight function @xmath110 in eq .
( [ g ] ) acts nearly like a @xmath122-function at low @xmath31 , the correlation induced band narrowing of the edge state gives rise to an increase of @xmath103 . as shown in fig .
[ fig3 ] , this is indeed the case for layers @xmath123 .
remarkably , this increase of density for @xmath123 is compensated by a corresponding decrease for layers @xmath120 and @xmath124 , so that the layer - integrated weight of the edge state close to @xmath28 remains nearly constant . according to the dispersions shown in fig .
[ fig4 ] , the dos of the edge state in the surface layer has the typical shape of a one - dimensional tight - binding system , with a minimum at the center and logarithmic van hove singularities at the band limits .
this is illustrated in fig .
[ fig5](a ) for @xmath116 . panels ( b ) and ( c ) indicate how this one - dimensional metallic spectral distribution converts to the one of the topological band insulator as one moves away from the surface .
we also note that the dos at @xmath125 in fig .
[ fig5 ] decays with increasing @xmath7 more slowly than @xmath103 in fig .
[ fig3 ] owing to a small imaginary energy @xmath119 introduced in extrapolating the lattice green s function .
the peaks at larger energies are sensitive to details of the extrapolation procedure . as will be seen in subsection [ sec_3d ] , the low - energy spectral distribution of the edge state of the bare surface shown in fig .
5 differs qualitatively from the one of edge state at the interface between a topological band insulator and a mott insulator .
the main reason is the appearance of a kondo peak in the mott insulator and a new single - particle feature at @xmath28 at the surface of the topological insulator .
figure [ fig6](a ) shows the partially integrated dos @xmath103 at the interface between a weakly correlated topological band insulator ( @xmath126 ) and more strongly correlated ones ( @xmath127 ) as a function of layer index @xmath7 .
these curves vary monotonously across the interface between two asymptotic values of @xmath103 which are the same as those in the interior of the semi - infinite solid shown in fig .
as mentioned above , the asymptotic values starts growing due to band narrowing only for @xmath112 .
therefore , the curves for @xmath128 and 8 in fig . [ fig6](a ) are practically constant throughout the system , while the curves for @xmath129 and @xmath130 exhibit a smooth variation between the two asymptotic values . evidently , there is no sign of a topological edge state at the interface .
figure [ fig6](b ) shows the occupancy @xmath131 as a function of layer index @xmath7 for the three systems shown in panel ( a ) . as we consider electron - hole symmetric systems , the occupancies of the two orbitals are related by @xmath132 .
it is seen that the orbital polarization , i.e. , @xmath133 , is strongly reduced in the right - hand system with increasing values of coulomb energy @xmath0 .
( at the mott transition , both orbitals become half - filled , i.e. , @xmath134 . )
whereas the variation of @xmath131 occurs very rapidly within one or two layers near the interface , the variation of @xmath135 for @xmath136 is more gradual and comparable to the one at the bare surface shown in fig .
this difference is related to the fact that , because of the finite width of the weight function @xmath110 , @xmath137 is mainly sensitive to the density of states of the low - energy bulk bands , in particular , at larger @xmath0 , when the band gap shrinks .
( color online ) ( a ) partially integrated spectral weight , @xmath103 , and ( b ) occupancy @xmath131 of orbital @xmath113 as functions of layer index near the interface between two correlated topological band insulators .
the systems on the left and right sides have local coulomb energies @xmath126 and @xmath127 , respectively . the location of the interface is indicated by the dashed line .
the embedding region consists of 10 layers on the left and 20 layers on the right side of the interface .
the asymptotic behavior is derived from dmft calculations for the respective bulk materials .
, width=283,height=377 ] we now discuss in more detail the properties of the edge state between a topological band insulator ( @xmath126 ) and a mott insulator whose coulomb energy is close to the coexistence region . to obtain the self - consistent solution of the layer - coupled dmft equation , we adopt the following procedure : on the left ( right ) boundary of the embedded region , we apply the embedding potential for a semi - infinite solid in the topological insulator phase with @xmath126 ( mott insulator phase with varying value of @xmath5 ) , so that the physical states in the asymptotic regions are fixed . within the embedded region , the initial values of the cluster parameters in eq .
( [ eq18 ] ) , which determine the initial weiss mean - field for each layer , are taken to be the parameters representing the bulk topological insulator with @xmath4 ( mott insulator with @xmath5 ) to the left ( right ) of the interface boundary .
thus , roughly speaking , initially the system to the left ( right ) of the boundary surface is in the topological insulator ( mott insulator ) phase .
we then proceed with the standard dmft iteration procedure , in which the self - energy and the cluster parameters of the layers in the embedded region are updated according to the prescription described in sec .
[ sec_2 ] .
the iteration procedure is repeated until the local self - energy and green s function of each layer converge and no longer change with further iterations .
( color online ) ( a ) edge state at interface between topological band insulator ( left ) and mott insulator ( right ) .
shown is the partially integrated density of states @xmath103 of orbital @xmath113 as a function of layer index .
the embedding region consists of 21 layers : 6 layers at @xmath126 and 15 layers in the range @xmath138 .
outside the embedding range , bulk behavior is assumed .
the location of the edge state is seen to be a sensitive function of the coulomb energy in the mott insulator . the maximum value @xmath139 is associated with the kondo peak .
( b ) amplitude of the edge state as a function of layer index at @xmath140 for increasing numbers of iterations in the self - consistency procedure .
the maximum due to the kondo peak is seen to shift toward the right - hand side of the embedding region .
the solid vertical line locates the phase boundary between topological and mott insulating phases , with both having the same coulomb repulsion @xmath141 , at the 160th dmft iteration .
, width=283,height=377 ] figure [ fig7](a ) shows the partially integrated dos @xmath103 at @xmath29 for several values of @xmath5 as a function of layer index @xmath7 .
this quantity exhibits a prominent maximum near the interface which is associated with the edge state appearing at the phase boundary between the topological and mott insulators .
the edge state for @xmath142 is seen to be well localized at the interface .
the mott gap in the right - hand system at this coulomb energy is rather large , so that the edge state decays rapidly into the mott insulator . in the band insulating system on the left side , the gap is also large , so that the shape of the edge state in this region is similar to the one at the insulator - vacuum interface shown in fig .
[ fig3 ] .
( color online ) ( a ) interacting dos , @xmath115 , at interface between topological band insulator ( @xmath126 ) and mott insulator ( @xmath142 ) .
solid ( red ) curves : orbital @xmath113 , dashed ( blue ) curves : orbital @xmath117 . panels ( a ) and ( b ) correspond to two surface layers on the right of the interface ( @xmath143 in fig . [ fig7 ] ) , panels ( c ) to ( f ) to four surface layers on the left of the interface ( @xmath144 ) .
these spectra are obtained by extrapolating the lattice green s function to @xmath118 with a small imaginary energy @xmath119 via the routine _ ratint_. the central spectral feature in panel (
b ) corresponds to the kondo peak induced in the mott insulator via the usual proximity effect due to the metallic edge state , while in panel ( c ) the low - energy feature is induced in the surface layer of the topological insulator via a reverse proximity effect caused by the kondo peak .
, width=332 ] we point out that the amplitude of @xmath103 in the first layer of the mott insulator for @xmath142 is significantly larger than in the surface layer of the topological band insulator .
this enhancement is related to the fact that , as a result of a proximity effect , a kondo resonance appears in the mott insulator due to the screening of the localized spins via the helical edge states.@xcite thus , the interface may be viewed as a kondo - lattice , where the metallicity is associated with the edge state induced by the topological band insulator .
this is illustrated in fig .
8 , which shows the variation of the interacting dos with layer index for @xmath126 , @xmath142 . in the first layer of the mott insulator ( panel ( b ) ) , the dos at low energies has a three - peak structure , consisting of kondo peak and van - hove singularities at the limits of the edge state . the maximum of @xmath145 at @xmath146 ( see fig .
7(a ) ) can therefore serve as a signature of the kondo peak . in the second layer , only a weak remnant of this peak is observed .
in contrast , the first layer of the band insulator is dominated by the van hove features of the one - dimensional metallic edge state . the deeper layers
reveal the appearance of the bulk band gap , in close correspondence to the behavior at the bare surface shown in fig .
5 . as can be seen in fig .
[ fig8](c ) , the dos near @xmath125 in the surface layer of the topological insulator is enhanced due to the presence of the mott insulator .
this is also evident by comparing @xmath147 for @xmath116 at the free surface ( see fig . [ fig3 ] ) with the corresponding value ( @xmath148 ) in the surface layer for @xmath126 ( fig .
[ fig7](a ) ) .
thus , the kondo peak in the mott insulator gives rise , via the single - particle hopping across the interface , to a low - energy spectral feature at the surface of the topological band insulator .
note that this feature is also present for @xmath149 .
it is therefore not induced by the small local self - energy in the band insulator , but by the large self - energy in the neighboring layer exhibiting the kondo peak .
this mechanism may therefore be viewed as a reverse proximity effect , in contrast to the usual one , in which the metal states induce the kondo peak in the mott insulator .
this kind of feedback effect occurs also at interfaces between ordinary metals and mott insulators ( see , for instance , the small peak for @xmath150 in fig . 1 of ref . ) . in the latter case
, however , this effect is very small because of the dominant metallic dos . in the present heterostructure ,
this effect is much more pronounced because of the minimum of the density of states of the edge state in the surface layer of the topological band insulator .
so far we have discussed the formation of the kondo peak for @xmath126 and @xmath142 .
returning to fig .
[ fig7](a ) , we point out that , when the coulomb energy @xmath5 in the right - hand system is lowered , the maximum of the edge state shifts away from the interface toward the interior of the mott insulator . evidently , due the proximity of the topological band insulator , the topological band insulating phase is more stable in the surface region of the mott insulator , so that the effective boundary between the topological and mott phases moves away from the physical interface . from a numerical point of view , one observes that the self - energy and cluster parameters of the boundary layers are converted from those characteristic of the mott insulator phase to those characteristic of the topological insulator phase with increasing iterations , in a layer - by - layer fashion , starting from the first boundary layer , toward the interior of the mott insulator , until no further phase conversion of layers takes place .
note that for the lowest two coulomb energies shown in fig .
[ fig7](a ) ( @xmath151 and @xmath152 ) , the mott insulator is within the bulk coexistence region ( @xmath153 , see fig .
[ fig2 ] ) , so that the actual phase depends sensitively on the properties near the interface . for @xmath152 ,
the bulk mott insulator phase is more stable than the bulk topological insulator phase , so that the dos profile shown in fig .
[ fig7](a ) does not shift any more with further iterations . on the other hand
, @xmath151 seems to be very close to @xmath154 , so that one needs hundreds of iterations to reach the dos profile in fig . [ fig7](a ) .
it is to be noted that to ensure the persistence of the edge state at these coulomb energies , the bulk phase in the asymptotic region on the right - hand side is assumed to be mott insulating . as discussed in the previous subsection , if instead both constituents of the heterostructure are topological band insulators , the edge state disappears . to illustrate this delicate balance between topological and mott insulating solutions in the interface region , we show in fig .
[ fig7](b ) the edge state for @xmath126 and @xmath140 . beyond the 15 surface layers of the right - hand system ,
bulk mott insulating behavior is assumed .
in addition , these 15 layers are initially assumed to be in the mott insulating phase . with increasing number of iterations , the peak of the edge state
is seen to shift toward the right side of the embedded region .
apparently , at @xmath140 , the bulk topological insulator phase is more stable than the bulk mott insulator phase , so that the conversion of layers from the mott phase to topological phase does not stop until all layers in the embedded region are converted .
in other words , for this value of @xmath5 , one can not find a stable mott solution of the dmft equation in contrast to the cases with larger @xmath5 shown in panel ( a ) .
the marked increase of spectral weight between layers 15 and 16 reflects the fact the nominal boundary of the heterostructure now comprises neighboring topological insulating phases for different values of @xmath0 ( see fig . [ fig6 ] ) .
accordingly , the shape of the ` buried ' edge state within the right - hand system approaches that at the interface between systems with identical coulomb energies in the coexistence range , but with topological band insulating and mott insulating phases present on either side .
( color online ) edge state at interface between topological band insulator and mott insulator in the coexistence region with @xmath155 .
the mott gap at this coulomb energy is much larger than the topological band gap .
thus , the asymptotic value of @xmath103 on the right - hand side is much lower than on the left - hand side , and the decay of the edge state within the mott insulator is more rapid .
the vertical bar denotes the kondo peak in the surface layer of the mott insulator at the effective boundary with the topological band insulator .
, width=283,height=188 ] the edge state in such a case is shown in fig .
[ fig9 ] for @xmath155 , where bulk mott insulating ( bulk topological band insulating ) behavior is enforced on the right ( left ) side of the embedding region , respectively .
the asymptotic value of @xmath135 on the right - hand side is very small because of the large size of the mott gap .
for the same reason , the decay of the edge state in the mott insulator is more rapid than within the band insulator .
the spatial distribution of this edge state is very similar to the one in fig .
[ fig7 ] deep within the nominal mott insulator . as stated above , since @xmath155 is very close to @xmath154 at @xmath101 , the bulk topological insulator on the left - hand side and the bulk mott insulator on the right - hand side
have nearly the same stability .
therefore , the dos profile in fig .
[ fig9 ] does not move with additional dmft iterations .
evidently , the phenomenon observed in fig .
[ fig7 ] is a proximity effect , where the band insulating properties on one side of the interface are induced up to a certain depth on the other side , for instance , via the penetration of the edge state wave function across the boundary layer , although asymptotically this side is a mott insulator .
the boundary between band and mott insulating phases then does not coincide with the nominal interface .
the results discussed above suggest that the embedding scheme might be useful for the study of the relative stability of coexisting phases in dmft calculations .
let us assume @xmath156 lies in the coexistence domain , with band insulating ( mott insulating ) properties enforced on the left ( right ) side of the embedded region .
as long as @xmath157 , the topological band insulating solution is more stable , so that the edge state will be located at the right boundary of the embedded region .
conversely , if @xmath158 , the mott phase is more stable , so that the edge state shifts toward the left boundary .
the edge state at the interface between topological band and mott insulators has been investigated within inhomogeneous dmft .
the generalized bernevig - hughes - zhang two - band model is used to describe the interplay between interorbital hybridization and local coulomb energy .
the electronic properties in the vicinity of the interface are treated self - consistently by making use of the embedding scheme , where the effect of the asymptotic semi - infinite bulk materials is described in terms of complex local potentials .
the finite - temperature exact diagonalization method is employed to evaluate the on - site many - body interactions . the main result of this work is the observation that , close to the critical coulomb energy of the correlated topological insulator , the edge state is expelled from the interface toward the interior of the mott insulator .
thus , as a result of the proximity with the topological band insulator , the mott insulating phase within a certain depth is converted to a topological band insulating phase , where the width of the conversion region depends on the local coulomb energy within the mott insulator . with increasing coulomb energy , the mott gap widens and the topological edge state is pushed again toward the interface .
its decay within the mott insulator then becomes more rapid . at coulomb energies below the mott transition ,
the edge state ceases to exist since in this case the interface corresponds to that between two weakly and moderately correlated topological band insulators . the origin of the interface - induced conversion from mott insulating to band insulating behavior is the coexistence region associated with the first - order nature of the mott transition .
depending on the temperature of the sample , either the mott insulating or the band insulating solution is more stable at a given value of the local coulomb energy .
these results suggest that the embedding method might be useful to determine the relative stability of mott and band insulating phases in dmft calculations .
in addition , the conversion between mott and band insulating phases might be observed experimentally in alloy heterostructures in which the existence of these phases can be tuned continuously by varying the material parameters .
we have also shown that the normal proximity effect , where a kondo peak in a mott insulator is induced via neighboring metallic states , gives rise to a reverse proximity effect , where the kondo peak leads to an enhanced density of states at the surface of the neighboring metal .
the work of h. i. was supported by jsps kakenhi ( no . 24540328 ) .
thanks the alexander von humboldt foundation for support .
part of the computations were carried out using the jlich juropa supercomputer .
l. thanks theo costi for useful discussions . | the electronic structure at the interface between a topological band insulator and a mott insulator is studied within layer dynamical mean field theory . to represent the bulk phases of these systems
, we use the generalized bernevig - hughes - zhang model that incorporates the hubbard - like onsite coulomb energy @xmath0 in addition to the spin - orbit coupling term that causes band inversion .
the topological and mott insulating phases are realized by appropriately choosing smaller and larger values of @xmath0 , respectively .
as expected , the interface is found to be metallic because of the localized edge state .
when the coulomb energy in the mott insulator is close to the critical value , however , this edge state exhibits its largest amplitude deep within the mott insulator rather than at the interface .
this finding corresponds to a new type of proximity effect induced by the neighboring topological band insulator and demonstrates that , as a result of spin - orbit coupling within the mott insulator , several layers near the interface convert from the mott insulating phase to a topological insulating phase .
moreover , we argue that the ordinary proximity effect , whereby a kondo peak is induced in a mott insulator by neighboring metallic states , is accompanied by an additional reverse proximity effect , by which the kondo peak gives rise to an enhancement of the density of states in the neighboring metallic layer . | <s>[INST]the role of coulomb correlations in topological band insulators has recently received wide attention.@xcite as a result of spin - orbit coupling , the band structure of these materials exhibits charge excitation spectra whose physical characteristics can depend strongly on the coulomb interaction .
iridium compounds , such as na@xmath1iro@xmath2 and a@xmath1ir@xmath1o@xmath3 ( a = pr , eu ) have recently been proposed as materials in which the interplay of spin - orbit interaction and electronic correlation effects might be important .
@xcite the phase diagram of a prototype bulk system of this kind was studied by yoshida _
et al._@xcite within an extension of the two - band model proposed by bernevig , hughes , and zhang ( bhz),@xcite where an onsite hubbard term is included to account for correlations .
it was shown that , in the paramagnetic limit , such a system exhibits a first - order quantum phase transition , where the weakly correlated phase corresponds to a topological band insulator and the strongly correlated phase to a mott insulator . at surfaces of topological insulators ,
metallic edge states may exist which are protected against perturbations associated with impurities and other interactions that do not break the time - reversal symmetry of the system.@xcite because of these unique properties , heterostructures involving topological band insulators @xcite are presently of great interest since they might be relevant for future technological applications .
for instance , as shown by ueda _
et al._,@xcite the interface of a topological band insulator and a mott insulator also exhibits an edge state which maintains its helical characteristics within the mott insulator .
moreover , the quasi - particle properties and depth profile of this state within the mott insulator depend strongly on the local coulomb energy . in the present work we study
the role of electronic correlations at the interface between a topological insulator and a mott insulator .
the important difference between our approach and the one by ueda _
et al._@xcite is that we include spin - orbit coupling also within the mott insulator .
thus , with decreasing coulomb energy , the mott insulator does not become a metal but a topological band insulator .
the electronic properties in the vicinity of the interface are treated self - consistently by using the layer dynamical mean field theory ( dmft).@xcite local many - body interactions are evaluated via finite - temperature exact diagonalization ( ed ) .
@xcite separate single - site dmft calculations are performed for the asymptotic semi - infinite bulk regions .
their influence on the interface region is taken into account via complex embedding potentials.@xcite for simplicity , a square lattice geometry is used , as illustrated in fig .
[ fig1].@xcite to incorporate spin - orbit interactions , the generalized two - orbital bhz model is used , which includes the site - dependent coulomb energy as well as the interorbital hybridization .
( color online ) one - dimensional interface between two - dimensional topological band and mott insulators .
the coulomb energies on the left and right side of the interface are defined as @xmath4 and @xmath5 , respectively .
the electronic properties in the embedding region are calculated self - consistently within the layer dmft .
the properties of the asymptotic bulk regions are taken into account via embedding potentials.,width=283,height=207 ] the main result of this study is the displacement of the edge state from the interface toward the interior of the mott insulator when the local coulomb energy on the corresponding side of the heterostructure is near the critical value for the mott transition . the edge state is then buried deeply within the mott insulator so that the boundary between the band and mott insulating phases no longer coincides with the physical interface of the two constituents of the heterostructure .
the origin of this novel proximity effect is the fact that the mott transition is first order . as a consequence , within the coexistence region topological
band and mott insulating phases compete .
their relative stability depends sensitively on temperature and local coulomb energy .
moreover , because of the penetration of the edge state wave function into the mott insulator , near the interface the properties of the nominal mott insulator are also influenced by the presence of the neighboring topological band insulator . as a result
, the mott insulating phase within a certain depth can be converted into the more stable topological band insulating phase .
the edge state is thereby displaced away from the physical interface which becomes the boundary between two weakly and strongly correlated topological band insulators .
as the coulomb energy in the mott insulator increases beyond the coexistence region , the edge state is localized again at the interface .
its depth within the mott insulator diminishes as the mott gap increases . below the coexistence domain ,
the edge disappears since
the heterostrucure then consists of two correlated topological band insulators .
we emphasize that the displacement of the edge state away from the interface of the heterostructure is a consequence of the interorbital hybridization ( spin - orbit coupling ) in the mott insulator . in the absence of spin - orbit coupling ,
the coexistence domain involves trivial metallic and insulating phases so that a topological band insulating solution does not occur .
thus , if an edge state exists , it is localized at the physical interface .
we also demonstrate that the ordinary proximity effect,@xcite i.e. , the appearance of a kondo peak in a mott insulator due to neighboring metallic states , is accompanied by an secondary reverse proximity effect , as a result of which the kondo peak leads to an increase of the density of states ( dos ) in the neighboring metallic layer .
the outline of this paper is as follows .
section ii presents the main aspects of the theoretical approach .
in particular , we introduce the generalized bhz two - band model which provides the basis for the topological band as well as mott insulating phases .
also , the embedding scheme is described in which the effect of the asymptotic bulk materials on either side of the interface are taken into account via complex local potentials .
finally , the inhomogeneous layer dmft is outlined , as well as the finite - temperature exact diagonalization scheme for the treatment of local many - body interactions .
section iii provides the discussion of the results .
we first present the phase diagram of the asymptotic bulk materials and illustrate the edge state at the solid - vacuum interface .
the main part discusses the electronic properties of the interface between topological band and mott insulators , in particular , the location of the edge state as a function of the coulomb energy within the mott insulator .
we consider a one - dimensional interface between a two - dimensional ( 2-d ) topological band insulator ( bi ) and a 2-d mott insulator ( mi ) , which occupy the left and right half - space , respectively .
the @xmath6 direction is parallel to the interface , while the @xmath7 axis , which points from left to right , is chosen as the interface normal . to represent the semi - infinite systems on both sides , we employ the generalized bernevig - hughes - zhang model , @xmath8 the first term in the second line of eq .
( [ eq1 ] ) , @xmath9 represents two tight - binding bands originating from two orbitals , where @xmath10 ( @xmath11 ) creates ( annihilates ) an electron with orbital @xmath12 in spin state @xmath13 on a 2-d square lattice point at @xmath14 , with @xmath6 and @xmath7 giving its @xmath6 and @xmath7 positions , respectively . in eq .
( [ eq2 ] ) , @xmath15 and @xmath16 are the site energy and nearest - neighbor hopping integral for orbital @xmath17 , @xmath18 is the coulomb energy , which will be described below , @xmath19 denotes the orbital occupation , and the summation over @xmath20 and @xmath21 in the second term is taken over nearest - neighbor lattice - point pairs . the second term in the second line of eq .
( [ eq1 ] ) , which arises from spin - orbit coupling and is responsible for the opening of a topological energy band gap , reads @xmath22,\label{eq3}\ ] ] where @xmath23 specifies the hopping direction measured relative to the @xmath6 axis ( @xmath24 and @xmath25 correspond to the hopping to the positive @xmath6 and @xmath7 directions , respectively ) .
the last term in eq .
( [ eq1 ] ) , @xmath26 expresses the onsite coulomb repulsion between electrons with opposite spin in the same orbital @xmath17 .
we assume that the coulomb energy can vary with lattice layers , while it is constant within the same layer .
it should be noted that the term @xmath27 in eq .
( [ eq2 ] ) ensures that the system becomes electron - hole symmetric when chemical potential @xmath28 is chosen as @xmath29 .
et al_.@xcite studied the effect of strong coulomb correlations on a topological band insulator by applying single - site dmft@xcite to periodic 2-d bulk systems described by the same generalized bhz model .
it was shown that the system undergoes a quantum phase transition from a topological band insulator to a mott insulator when one increases the onsite coulomb energy @xmath0 , while keeping the system nonmagnetic . as schematically illustrated in fig .
[ fig2 ] , the phase transition is of first order and exhibits hysteresis behavior , i.e. , both topological band and mott insulating solutions are found if @xmath0 is within the coexistence region @xmath30 $ ] .
the width of this region decreases with increasing temperature @xmath31 and vanishes at a critical value @xmath32 . in the present work , both the topological band insulator on the left half - space and the mott insulator on the right half - space
are represented by the generalized bhz model as described above . as indicated in fig .
[ fig1 ] , the layer dependent coulomb energy , @xmath18 , is set to be @xmath4 and @xmath5 in the left and right half - spaces , respectively , where @xmath33 and @xmath34 ( see fig . 2 below ) .
we note that our model differs from that in the recent work of ueda _
et al_.@xcite , in which the mott insulator was represented by two independent hubbard bands without the spin - orbit coupling term defined in eq .
( [ eq3 ] ) . we calculate the finite - temperature green s function of the interface between two semi - infinite systems by using the layer dmft technique.@xcite a finite number of lattice layers in the interface region
is treated explicitly , whereas the effect of the outer regions is taken into account via the embedding potentials@xcite which include correlation effects in the bulk region.@xcite as we consider nonmagnetic solutions in the present work , the green s function and other quantities are diagonal with respect to spin . in the following ,
we show only the up - spin component of the equations and omit spin indices for simplicity . by introducing the wave number in the @xmath6 direction , @xmath35 , the green s function in the embedded region
is given as @xmath36^{-1 } \mid y'\alpha'\rangle,\label{eq5}\end{aligned}\ ] ] where the embedding hamiltonian in the mixed representation , @xmath37 , is a @xmath38 matrix with @xmath39 being the number of the embedded lattice layers .
it consists of four terms : @xmath40 where @xmath41 denotes the one - electron part of the hamiltonian in eq .
( [ eq1 ] ) .
the superscript @xmath39 emphasizes the fact that @xmath42 is a @xmath43 matrix for an isolated slab . the second term in eq .
( [ eq6 ] ) is the coulomb self - energy . within single - site dmft , it is layer diagonal and @xmath35-independent : @xmath44 the last two terms in eq .
( [ eq6 ] ) are the embedding potentials . since @xmath45 in eq .
( [ eq1 ] ) includes only nearest - neighbor hopping terms , @xmath46 ( @xmath47 ) is non - vanishing only when both layer indices are equal to @xmath48 ( @xmath49 ) , the outermost layer of the embedded slab region on the left ( right ) hand side .
thus , they are written as @xmath50 we now explain how we can derive the embedding potential for the left - hand side .
we assume that the electronic structure in the half - space to the left of the embedded slab region converges to that of the bulk crystal with coulomb repulsion energy @xmath4 .
thus , within the single - site approximation , the coulomb self - energy of all layers is assumed to be identical to that in the interior of the bulk with @xmath4 , @xmath51 .
this quantity is a @xmath52 matrix in orbital space .
now , let us consider the green s function of the semi - infinite solid in which the self - energies of all layers are equal to @xmath51 .
we extract from this green s function a @xmath52 matrix spanned by the two orbital components of the outermost surface layer , which is denoted by @xmath53 .
the embedding potential , i.e. , the @xmath54 matrix appearing on the right hand side of eq .
( [ eq8 ] ) , is then given by@xcite @xmath55 with @xmath56 where @xmath57 ( @xmath58 ) is the transfer matrix for electrons which hop between two nearest - neighbor lattice layers toward the positive ( negative ) @xmath7 direction . in order to obtain @xmath59 in eq .
( [ eq10 ] ) , we use the following trick .
we add one additional lattice layer having the bulk self - energy @xmath60 on top of the semi - infinite substrate expressed by the embedding potential @xmath46 .
then , the @xmath52 surface green s function of the resultant new semi - infinite solid is given by @xmath61^{-1},\label{eq12}\ ] ] where @xmath62 is given by @xmath63 we now make use of the fact that the semi - infinite solid obtained by putting one bulk lattice on top of the semi - infinite bulk system is exactly the same as that without the additional lattice layer .
thus , @xmath59 on the right - hand side of eq .
( [ eq10 ] ) must coincide with @xmath59 calculated by eq .
( [ eq12 ] ) .
thus , by inserting @xmath59 in eq .
( [ eq12 ] ) into the right - hand side of eq .
( [ eq10 ] ) , one obtains a set of equations to determine the three independent elements of the embedding potential , @xmath64 for given @xmath35 and @xmath65 .
in contrast to one - band models , for which one can derive an analytical expression of the embedding potential from a quadratic equation obtained by following the same procedure as described above,@xcite the embedding potential for the present two - band model can be computed only numerically . to determine @xmath46
, one needs the bulk self - energy @xmath66 in eq .
( [ eq12 ] ) , which can be determined from an independent dmft calculation for the 2-d bulk system with coulomb repulsion energy @xmath4 , before evaluating the interface properties .
similarly , the embedding potential for the right - hand side can be derived by combining the two following equations .
@xmath67 @xmath68^{-1},\label{eq15}\ ] ] where @xmath69 denotes the coulomb self - energy of the 2-d bulk system with coulomb interaction @xmath5 .
starting from some initial self - energy matrix , one calculates the local components of the lattice green s function for each layer , @xmath70 , by using eq .
( [ eq5 ] ) .
then , the bath green s function determining the weiss mean - field of layer @xmath7 is obtained by removing the local self - energy : @xmath71^{-1 } , \label{eq16}\ ] ] where @xmath72 is the @xmath52 matrix defined by eq .
( [ eq7 ] ) . in the present work ,
the quantum impurity problem is solved by making use of the exact diagonalization ( ed ) formalism,@xcite in which @xmath73 is approximated by a noninteracting green s function of a finite cluster consisting of two impurity levels with energy @xmath74 coupled to @xmath75 bath orbitals with energy @xmath76 .
thus , @xmath77^{-1},\label{eq17}\ ] ] with @xmath78 where @xmath74 , @xmath76 and @xmath79 are real fitting parameters chosen such that the weighted sum of @xmath80 over a sufficiently large matsubara frequency range is minimized.@xcite then , after adding the onsite coulomb repulsion terms eq .
( [ eq4 ] ) to this @xmath81-level cluster , the interacting green s function of the cluster , @xmath82 , is derived by combining the arnoldi algorithm for computing the lowest eigenstates with the lanczos procedure for calculating the green s function.@xcite finally , the cluster self - energy is obtained from the equation : @xmath83^{-1 } -\left[\hat{g}^{cl } ( y , i\omega_n)\right]^{-1}.\label{eq19}\ ] ] in the ed formalism , the cluster self - energy is assumed to be a physically reasonable representation of the lattice self - energy .
thus , @xmath84 is used as the input self - energy @xmath72 in eq .
( [ eq5 ] ) for the next dmft iteration .
this procedure is iterated until the difference between the input and output self - energy matrices for all the lattice layers in the embedded region becomes sufficiently small . in the calculation presented in the next section ,
we use @xmath85 bath orbitals ( 4 per orbital ) , so that the total number of energy levels per cluster equals 10 .
in the present work , the parameters of the non - interacting part of the hamiltonian are chosen as @xmath86 , @xmath87 , @xmath88 , @xmath89 , and @xmath90 .
the same parameter set was used previously in ref . .
we consider only the electron - hole symmetric case with chemical potential @xmath29 . in the absence of correlations , the bulk bands extend from @xmath91 to @xmath92 and the band gap from @xmath93 to @xmath94 .
the dmft calculations are performed at a relatively small temperature : @xmath95 .
( color online ) schematic bulk phase diagram of correlated topological band insulator , derived within generalized bhz two - orbital model and single - site dmft . in the region limited by the lines
@xmath96 and @xmath97 , band and mott insulating states may coexist .
the true phase boundary defining the relative stability of these phases is indicated by the line @xmath98 .
, width=283,height=188 ] figure [ fig2 ] illustrates schematically the bulk phase diagram of the constituents of the present heterostructure . at small @xmath0 ,
one has a weakly correlated topological band insulator which corresponds to the system on the left - hand side in fig .
[ fig1 ] . at large @xmath0 ,
the system becomes a mott insulator which is taken to be the dominant phase on the right - hand side of the interface .
we note that in the present model the mott insulating phase is nontopological with a vanishing chern number , in contrast to the topological kondo insulator.@xcite the band gap in the band insulator also varies with @xmath0 .
it is largest in the noninteracting limit and gradually decreases with increasing @xmath0 until @xmath0 approaches @xmath97 .
this behavior corresponds to the usual band - narrowing effect , which has been discussed in previous work.@xcite as a result of local coulomb interactions , spectral weight within the region of the bulk bands is transferred to low energies and hubbard bands appear at high energies . for the parameters specified above , we find that the coexistence region is limited by the boundaries @xmath99 and @xmath100 . because of the first - order nature of the mott transition , various quantities , such as the orbital polarization , the double occupancy of the subbands , the spectral weight at the chemical potential , etc .
exhibit the usual hysteresis behavior ( not shown here ) .
an important aspect of the interface properties discussed in subsection [ sec_3d ] is the fact that they may be used to determine the relative stability of the band and mott insulating phases in the coexistence region .
for instance , at @xmath101 we estimate @xmath102 .
as will be shown below , an edge state appears at the interface of a weakly correlated topological band insulator and a strongly correlated mott insulator .
the intriguing question then arises what happens to the edge state when the coulomb energy in the mott insulator lies within the coexistence region .
depending on the precise values of @xmath0 and @xmath31 , the mott insulating phase can become unstable and may therefore be converted into a band insulating phase .
before we discuss this case , we consider in the following two subsections ( i ) the behavior of the edge state at the bare surface of a topological band insulator and ( ii ) the properties of the interface between two topological insulators .
these results serve a useful reference for the subsequent analysis of the interface with a mott insulator ( color online ) variation of edge state at bare surface of correlated topological band insulator as a function layer index @xmath7 for various coulomb energies @xmath0 , as calculated within inhomogeneous dmft .
plotted is the function @xmath103 , defined in eq .
( [ g ] ) , which represents the partially integrated density of states within a few @xmath31 of the chemical potential ( @xmath101 ) .
the embedding region at the surface comprises 12 atomic layers beyond which bulk behavior is assumed .
, width=283,height=188 ] figure [ fig3 ] shows the spectral weight near the chemical potential at the surface of a correlated topological band insulator as a function of distance from the surface for several values of @xmath0 .
plotted is the function @xmath103 which provides a measure of the dos within a few @xmath31 of the chemical potential .
this quantity is defined as @xmath104 where @xmath105 is the interacting dos of subband @xmath17 and the weight function @xmath106 is defined as : @xmath107 $ ] .
( the width of @xmath106 is about @xmath108 ; its integrated weight is unity . ) as a result of particle - hole symmetry , @xmath109 . at the surface of a topological insulator ,
a metallic edge state connecting the bulk valence and conduction bands appears .
as the chemical potential is located at the middle of the energy gap when the system is electron - hole symmetric , the edge state contributes to an increase in dos at @xmath28 for several surface layers , which is clearly seen in fig .
with increasing values of @xmath0 , the gap in the topological band insulator diminishes due to correlation effects , so that the penetration depth of the edge state increases
. the peak of the edge state at larger @xmath0 also shifts to the second layer ( see below ) . at the same time , the high - energy tails of @xmath110 on both sides of @xmath111 start overlapping with the bulk bands due to band - gap narrowing . for @xmath112 ,
this results in a rapid increase in the calculated values of @xmath103 in the interior of the solid .
( color online ) intensity plot of interacting dos of orbital @xmath113 , @xmath114 in surface layer of semi - infinite topological insulator as a function of parallel momentum @xmath35 for several values of @xmath0 .
, scaledwidth=40.0% ] ( color online ) interacting dos , @xmath115 , in first three surface layers of topological insulator at @xmath116 .
solid ( red ) curves : orbital @xmath113 , dashed ( blue ) curves : @xmath117 .
these spectra are derived by extrapolating the lattice green s function from matsubara frequencies to @xmath118 with a small imaginary energy @xmath119 via the routine _ ratint_. the spectral weight near @xmath29 in panel ( a ) is due to the metallic edge state , while the dos in panel ( c ) approaches the one characteristic of the bulk band gap .
, scaledwidth=35.0% ] to illustrate the energy dispersion of the edge state with @xmath35 in the case of a free surface , we show in fig .
[ fig4 ] the @xmath35-resolved dos of the first layer ( @xmath120 ) for various coulomb energies .
these results were derived by extrapolating the self - energy from the matsubara axis to real energies via the routine _ ratint _ ( for details see ref . ) and then evaluating the integrand on the right hand side of eq .
( [ eq5 ] ) .
one can clearly see a metallic edge state crossing the chemical potential @xmath29 at @xmath121 with a positive group velocity .
this indicates that the increase in dos seen in fig .
[ fig3 ] for surface layers arises from the edge state around @xmath121 .
the energy dispersion curve of the edge state for the down - spin ( not shown ) is obtained by reflecting the one for the up - spin shown in fig .
[ fig4 ] with respect to @xmath121 , so that the two dispersion curves with the opposite spins cross at @xmath121 . with increasing @xmath0 ,
the dispersion of the edge state becomes flatter and the bulk band gap is reduced .
also , the width of the bulk bands decreases and hubbard bands appear below and above the band region . since the weight function @xmath110 in eq .
( [ g ] ) acts nearly like a @xmath122-function at low @xmath31 , the correlation induced band narrowing of the edge state gives rise to an increase of @xmath103 . as shown in fig .
[ fig3 ] , this is indeed the case for layers @xmath123 .
remarkably , this increase of density for @xmath123 is compensated by a corresponding decrease for layers @xmath120 and @xmath124 , so that the layer - integrated weight of the edge state close to @xmath28 remains nearly constant . according to the dispersions shown in fig .
[ fig4 ] , the dos of the edge state in the surface layer has the typical shape of a one - dimensional tight - binding system , with a minimum at the center and logarithmic van hove singularities at the band limits .
this is illustrated in fig .
[ fig5](a ) for @xmath116 . panels ( b ) and ( c ) indicate how this one - dimensional metallic spectral distribution converts to the one of the topological band insulator as one moves away from the surface .
we also note that the dos at @xmath125 in fig .
[ fig5 ] decays with increasing @xmath7 more slowly than @xmath103 in fig .
[ fig3 ] owing to a small imaginary energy @xmath119 introduced in extrapolating the lattice green s function .
the peaks at larger energies are sensitive to details of the extrapolation procedure . as will be seen in subsection [ sec_3d ] , the low - energy spectral distribution of the edge state of the bare surface shown in fig .
5 differs qualitatively from the one of edge state at the interface between a topological band insulator and a mott insulator .
the main reason is the appearance of a kondo peak in the mott insulator and a new single - particle feature at @xmath28 at the surface of the topological insulator .
figure [ fig6](a ) shows the partially integrated dos @xmath103 at the interface between a weakly correlated topological band insulator ( @xmath126 ) and more strongly correlated ones ( @xmath127 ) as a function of layer index @xmath7 .
these curves vary monotonously across the interface between two asymptotic values of @xmath103 which are the same as those in the interior of the semi - infinite solid shown in fig .
as mentioned above , the asymptotic values starts growing due to band narrowing only for @xmath112 .
therefore , the curves for @xmath128 and 8 in fig . [ fig6](a ) are practically constant throughout the system , while the curves for @xmath129 and @xmath130 exhibit a smooth variation between the two asymptotic values . evidently , there is no sign of a topological edge state at the interface .
figure [ fig6](b ) shows the occupancy @xmath131 as a function of layer index @xmath7 for the three systems shown in panel ( a ) . as we consider electron - hole symmetric systems , the occupancies of the two orbitals are related by @xmath132 .
it is seen that the orbital polarization , i.e. , @xmath133 , is strongly reduced in the right - hand system with increasing values of coulomb energy @xmath0 .
( at the mott transition , both orbitals become half - filled , i.e. , @xmath134 . )
whereas the variation of @xmath131 occurs very rapidly within one or two layers near the interface , the variation of @xmath135 for @xmath136 is more gradual and comparable to the one at the bare surface shown in fig .
this difference is related to the fact that , because of the finite width of the weight function @xmath110 , @xmath137 is mainly sensitive to the density of states of the low - energy bulk bands , in particular , at larger @xmath0 , when the band gap shrinks .
( color online ) ( a ) partially integrated spectral weight , @xmath103 , and ( b ) occupancy @xmath131 of orbital @xmath113 as functions of layer index near the interface between two correlated topological band insulators .
the systems on the left and right sides have local coulomb energies @xmath126 and @xmath127 , respectively . the location of the interface is indicated by the dashed line .
the embedding region consists of 10 layers on the left and 20 layers on the right side of the interface .
the asymptotic behavior is derived from dmft calculations for the respective bulk materials .
, width=283,height=377 ] we now discuss in more detail the properties of the edge state between a topological band insulator ( @xmath126 ) and a mott insulator whose coulomb energy is close to the coexistence region . to obtain the self - consistent solution of the layer - coupled dmft equation , we adopt the following procedure : on the left ( right ) boundary of the embedded region , we apply the embedding potential for a semi - infinite solid in the topological insulator phase with @xmath126 ( mott insulator phase with varying value of @xmath5 ) , so that the physical states in the asymptotic regions are fixed . within the embedded region , the initial values of the cluster parameters in eq .
( [ eq18 ] ) , which determine the initial weiss mean - field for each layer , are taken to be the parameters representing the bulk topological insulator with @xmath4 ( mott insulator with @xmath5 ) to the left ( right ) of the interface boundary .
thus , roughly speaking , initially the system to the left ( right ) of the boundary surface is in the topological insulator ( mott insulator ) phase .
we then proceed with the standard dmft iteration procedure , in which the self - energy and the cluster parameters of the layers in the embedded region are updated according to the prescription described in sec .
[ sec_2 ] .
the iteration procedure is repeated until the local self - energy and green s function of each layer converge and no longer change with further iterations .
( color online ) ( a ) edge state at interface between topological band insulator ( left ) and mott insulator ( right ) .
shown is the partially integrated density of states @xmath103 of orbital @xmath113 as a function of layer index .
the embedding region consists of 21 layers : 6 layers at @xmath126 and 15 layers in the range @xmath138 .
outside the embedding range , bulk behavior is assumed .
the location of the edge state is seen to be a sensitive function of the coulomb energy in the mott insulator . the maximum value @xmath139 is associated with the kondo peak .
( b ) amplitude of the edge state as a function of layer index at @xmath140 for increasing numbers of iterations in the self - consistency procedure .
the maximum due to the kondo peak is seen to shift toward the right - hand side of the embedding region .
the solid vertical line locates the phase boundary between topological and mott insulating phases , with both having the same coulomb repulsion @xmath141 , at the 160th dmft iteration .
, width=283,height=377 ] figure [ fig7](a ) shows the partially integrated dos @xmath103 at @xmath29 for several values of @xmath5 as a function of layer index @xmath7 .
this quantity exhibits a prominent maximum near the interface which is associated with the edge state appearing at the phase boundary between the topological and mott insulators .
the edge state for @xmath142 is seen to be well localized at the interface .
the mott gap in the right - hand system at this coulomb energy is rather large , so that the edge state decays rapidly into the mott insulator . in the band insulating system on the left side , the gap is also large , so that the shape of the edge state in this region is similar to the one at the insulator - vacuum interface shown in fig .
[ fig3 ] .
( color online ) ( a ) interacting dos , @xmath115 , at interface between topological band insulator ( @xmath126 ) and mott insulator ( @xmath142 ) .
solid ( red ) curves : orbital @xmath113 , dashed ( blue ) curves : orbital @xmath117 . panels ( a ) and ( b ) correspond to two surface layers on the right of the interface ( @xmath143 in fig . [ fig7 ] ) , panels ( c ) to ( f ) to four surface layers on the left of the interface ( @xmath144 ) .
these spectra are obtained by extrapolating the lattice green s function to @xmath118 with a small imaginary energy @xmath119 via the routine _ ratint_. the central spectral feature in panel (
b ) corresponds to the kondo peak induced in the mott insulator via the usual proximity effect due to the metallic edge state , while in panel ( c ) the low - energy feature is induced in the surface layer of the topological insulator via a reverse proximity effect caused by the kondo peak .
, width=332 ] we point out that the amplitude of @xmath103 in the first layer of the mott insulator for @xmath142 is significantly larger than in the surface layer of the topological band insulator .
this enhancement is related to the fact that , as a result of a proximity effect , a kondo resonance appears in the mott insulator due to the screening of the localized spins via the helical edge states.@xcite thus , the interface may be viewed as a kondo - lattice , where the metallicity is associated with the edge state induced by the topological band insulator .
this is illustrated in fig .
8 , which shows the variation of the interacting dos with layer index for @xmath126 , @xmath142 . in the first layer of the mott insulator ( panel ( b ) ) , the dos at low energies has a three - peak structure , consisting of kondo peak and van - hove singularities at the limits of the edge state . the maximum of @xmath145 at @xmath146 ( see fig .
7(a ) ) can therefore serve as a signature of the kondo peak . in the second layer , only a weak remnant of this peak is observed .
in contrast , the first layer of the band insulator is dominated by the van hove features of the one - dimensional metallic edge state . the deeper layers
reveal the appearance of the bulk band gap , in close correspondence to the behavior at the bare surface shown in fig .
5 . as can be seen in fig .
[ fig8](c ) , the dos near @xmath125 in the surface layer of the topological insulator is enhanced due to the presence of the mott insulator .
this is also evident by comparing @xmath147 for @xmath116 at the free surface ( see fig . [ fig3 ] ) with the corresponding value ( @xmath148 ) in the surface layer for @xmath126 ( fig .
[ fig7](a ) ) .
thus , the kondo peak in the mott insulator gives rise , via the single - particle hopping across the interface , to a low - energy spectral feature at the surface of the topological band insulator .
note that this feature is also present for @xmath149 .
it is therefore not induced by the small local self - energy in the band insulator , but by the large self - energy in the neighboring layer exhibiting the kondo peak .
this mechanism may therefore be viewed as a reverse proximity effect , in contrast to the usual one , in which the metal states induce the kondo peak in the mott insulator .
this kind of feedback effect occurs also at interfaces between ordinary metals and mott insulators ( see , for instance , the small peak for @xmath150 in fig . 1 of ref . ) . in the latter case
, however , this effect is very small because of the dominant metallic dos . in the present heterostructure ,
this effect is much more pronounced because of the minimum of the density of states of the edge state in the surface layer of the topological band insulator .
so far we have discussed the formation of the kondo peak for @xmath126 and @xmath142 .
returning to fig .
[ fig7](a ) , we point out that , when the coulomb energy @xmath5 in the right - hand system is lowered , the maximum of the edge state shifts away from the interface toward the interior of the mott insulator . evidently , due the proximity of the topological band insulator , the topological band insulating phase is more stable in the surface region of the mott insulator , so that the effective boundary between the topological and mott phases moves away from the physical interface . from a numerical point of view , one observes that the self - energy and cluster parameters of the boundary layers are converted from those characteristic of the mott insulator phase to those characteristic of the topological insulator phase with increasing iterations , in a layer - by - layer fashion , starting from the first boundary layer , toward the interior of the mott insulator , until no further phase conversion of layers takes place .
note that for the lowest two coulomb energies shown in fig .
[ fig7](a ) ( @xmath151 and @xmath152 ) , the mott insulator is within the bulk coexistence region ( @xmath153 , see fig .
[ fig2 ] ) , so that the actual phase depends sensitively on the properties near the interface . for @xmath152 ,
the bulk mott insulator phase is more stable than the bulk topological insulator phase , so that the dos profile shown in fig .
[ fig7](a ) does not shift any more with further iterations . on the other hand
, @xmath151 seems to be very close to @xmath154 , so that one needs hundreds of iterations to reach the dos profile in fig . [ fig7](a ) .
it is to be noted that to ensure the persistence of the edge state at these coulomb energies , the bulk phase in the asymptotic region on the right - hand side is assumed to be mott insulating . as discussed in the previous subsection , if instead both constituents of the heterostructure are topological band insulators , the edge state disappears . to illustrate this delicate balance between topological and mott insulating solutions in the interface region , we show in fig .
[ fig7](b ) the edge state for @xmath126 and @xmath140 . beyond the 15 surface layers of the right - hand system ,
bulk mott insulating behavior is assumed .
in addition , these 15 layers are initially assumed to be in the mott insulating phase . with increasing number of iterations , the peak of the edge state
is seen to shift toward the right side of the embedded region .
apparently , at @xmath140 , the bulk topological insulator phase is more stable than the bulk mott insulator phase , so that the conversion of layers from the mott phase to topological phase does not stop until all layers in the embedded region are converted .
in other words , for this value of @xmath5 , one can not find a stable mott solution of the dmft equation in contrast to the cases with larger @xmath5 shown in panel ( a ) .
the marked increase of spectral weight between layers 15 and 16 reflects the fact the nominal boundary of the heterostructure now comprises neighboring topological insulating phases for different values of @xmath0 ( see fig . [ fig6 ] ) .
accordingly , the shape of the ` buried ' edge state within the right - hand system approaches that at the interface between systems with identical coulomb energies in the coexistence range , but with topological band insulating and mott insulating phases present on either side .
( color online ) edge state at interface between topological band insulator and mott insulator in the coexistence region with @xmath155 .
the mott gap at this coulomb energy is much larger than the topological band gap .
thus , the asymptotic value of @xmath103 on the right - hand side is much lower than on the left - hand side , and the decay of the edge state within the mott insulator is more rapid .
the vertical bar denotes the kondo peak in the surface layer of the mott insulator at the effective boundary with the topological band insulator .
, width=283,height=188 ] the edge state in such a case is shown in fig .
[ fig9 ] for @xmath155 , where bulk mott insulating ( bulk topological band insulating ) behavior is enforced on the right ( left ) side of the embedding region , respectively .
the asymptotic value of @xmath135 on the right - hand side is very small because of the large size of the mott gap .
for the same reason , the decay of the edge state in the mott insulator is more rapid than within the band insulator .
the spatial distribution of this edge state is very similar to the one in fig .
[ fig7 ] deep within the nominal mott insulator . as stated above , since @xmath155 is very close to @xmath154 at @xmath101 , the bulk topological insulator on the left - hand side and the bulk mott insulator on the right - hand side
have nearly the same stability .
therefore , the dos profile in fig .
[ fig9 ] does not move with additional dmft iterations .
evidently , the phenomenon observed in fig .
[ fig7 ] is a proximity effect , where the band insulating properties on one side of the interface are induced up to a certain depth on the other side , for instance , via the penetration of the edge state wave function across the boundary layer , although asymptotically this side is a mott insulator .
the boundary between band and mott insulating phases then does not coincide with the nominal interface .
the results discussed above suggest that the embedding scheme might be useful for the study of the relative stability of coexisting phases in dmft calculations .
let us assume @xmath156 lies in the coexistence domain , with band insulating ( mott insulating ) properties enforced on the left ( right ) side of the embedded region .
as long as @xmath157 , the topological band insulating solution is more stable , so that the edge state will be located at the right boundary of the embedded region .
conversely , if @xmath158 , the mott phase is more stable , so that the edge state shifts toward the left boundary .
the edge state at the interface between topological band and mott insulators has been investigated within inhomogeneous dmft .
the generalized bernevig - hughes - zhang two - band model is used to describe the interplay between interorbital hybridization and local coulomb energy .
the electronic properties in the vicinity of the interface are treated self - consistently by making use of the embedding scheme , where the effect of the asymptotic semi - infinite bulk materials is described in terms of complex local potentials .
the finite - temperature exact diagonalization method is employed to evaluate the on - site many - body interactions . the main result of this work is the observation that , close to the critical coulomb energy of the correlated topological insulator , the edge state is expelled from the interface toward the interior of the mott insulator .
thus , as a result of the proximity with the topological band insulator , the mott insulating phase within a certain depth is converted to a topological band insulating phase , where the width of the conversion region depends on the local coulomb energy within the mott insulator . with increasing coulomb energy , the mott gap widens and the topological edge state is pushed again toward the interface .
its decay within the mott insulator then becomes more rapid . at coulomb energies below the mott transition ,
the edge state ceases to exist since in this case the interface corresponds to that between two weakly and moderately correlated topological band insulators . the origin of the interface - induced conversion from mott insulating to band insulating behavior is the coexistence region associated with the first - order nature of the mott transition .
depending on the temperature of the sample , either the mott insulating or the band insulating solution is more stable at a given value of the local coulomb energy .
these results suggest that the embedding method might be useful to determine the relative stability of mott and band insulating phases in dmft calculations .
in addition , the conversion between mott and band insulating phases might be observed experimentally in alloy heterostructures in which the existence of these phases can be tuned continuously by varying the material parameters .
we have also shown that the normal proximity effect , where a kondo peak in a mott insulator is induced via neighboring metallic states , gives rise to a reverse proximity effect , where the kondo peak leads to an enhanced density of states at the surface of the neighboring metal .
the work of h. i. was supported by jsps kakenhi ( no . 24540328 ) .
thanks the alexander von humboldt foundation for support .
part of the computations were carried out using the jlich juropa supercomputer .
l. thanks theo costi for useful discussions .[/INST] the electronic structure at the interface between a topological band insulator and a mott insulator is studied within layer dynamical mean field theory . to represent the bulk phases of these systems
, we use the generalized bernevig - hughes - zhang model that incorporates the hubbard - like onsite coulomb energy @xmath0 in addition to the spin - orbit coupling term that causes band inversion .
the topological and mott insulating phases are realized by appropriately choosing smaller and larger values of @xmath0 , respectively .
as expected , the interface is found to be metallic because of the localized edge state .
when the coulomb energy in the mott insulator is close to the critical value , however , this edge state exhibits its largest amplitude deep within the mott insulator rather than at the interface .
this finding corresponds to a new type of proximity effect induced by the neighboring topological band insulator and demonstrates that , as a result of spin - orbit coupling within the mott insulator , several layers near the interface convert from the mott insulating phase to a topological insulating phase .
moreover , we argue that the ordinary proximity effect , whereby a kondo peak is induced in a mott insulator by neighboring metallic states , is accompanied by an additional reverse proximity effect , by which the kondo peak gives rise to an enhancement of the density of states in the neighboring metallic layer . </s> |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Skilled Workforce Enhancement Act of
2001''.
SEC. 2. CREDIT FOR EXPENSES FOR LONG-TERM TRAINING OF EMPLOYEES IN
HIGHLY SKILLED SMALL BUSINESS TRADES.
(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 new section:
``SEC. 45E. EXPENSES FOR LONG-TERM TRAINING OF EMPLOYEES IN HIGHLY
SKILLED SMALL BUSINESS TRADES.
``(a) General Rule.--For purposes of section 38, in the case of a
small business employer, the highly skilled trades training credit
determined under this section for the taxable year is $15,000 for each
employee having a qualified training year ending with or within such
taxable year (whether or not such employee is an employee of the
taxpayer as of the close of such taxable year).
``(b) Definitions.--For purposes of this section--
``(1) Small business employer.--
``(A) In general.--The term `small business
employer' means, with respect to any taxable year, any
employer who employed an average of 250 or fewer
employees on business days during such taxable year.
``(B) Controlled groups.--For purposes of
subparagraph (A), all persons treated as a single
employer under subsection (b), (c), (m), or (o) of
section 414 shall be treated as a single employer.
``(2) Qualified training year.--
``(A) In general.--The term `qualified training
year' means each year during the training period in
which the employee received at least 1,500 hours of
training (including on-the-job training and training at
multi-employer training facilities) from the taxpayer
(or any predecessor) under a qualified training program
as an apprentice in any highly skilled trade.
``(B) Highly skilled trades.--For purposes of
subparagraph (A), the term `highly skilled trades'
means--
``(i) precision machinists,
``(ii) die makers,
``(iii) mold makers,
``(iv) tool and die designers,
``(v) heating, ventilating, air
conditioning, refrigeration, and roofing
contractors,
``(vi) the trade of masonry,
``(vii) plumbers,
``(viii) pipefitters,
``(ix) patternmakers,
``(x) foundry technicians,
``(xi) electricians,
``(xii) recreational marine production and
design workers,
``(xiii) 2-way radio technicians,
``(xiv) welders,
``(xv) shipfitters,
``(xvi) propellor machinists,
``(xvii) electronic instrumentation
specialists, and
``(xviii) other highly skilled trades
specified in regulations prescribed by the
Secretary.
Such term shall not include any trade if the customary
apprenticeship period for such trade is less than 2
years.
``(C) Qualified training program.--
``(i) In general.--The term `qualified
training program' means a written plan of study
and training for individuals in, or entering
into, highly skilled trades.
``(ii) Description of programs.--A plan
under clause (i) must be a program described in
one of the following subclauses:
``(I) An apprenticeship program
registered and certified with the
Secretary of Labor under section 1 of
the National Apprenticeship Act (29
U.S.C. 50).
``(II) A program licensed,
registered, or certified by the
workforce investment board or
apprenticeship agency or council of a
State or administered in compliance
with apprenticeship laws of a State.
``(III) A program conducted by a
vocational or technical education
school, community college, or
industrial or trade training
organization.
``(IV) A program which conforms to
apprentice training programs developed
or administered by an employer trade
group or committee.
``(V) An industry sponsored or
administered program which is clearly
identified and commonly
recognized within an industry and which meets the requirements of
clause (iii).
``(iii) Requirements.--A program meets the
requirements of this clause if such program--
``(I) is accessible to individuals
without discrimination on the basis of
race, sex, color, religion, or national
origin,
``(II) provides an overview of the
trade, including the history and modern
developments in such trade,
``(III) provides related
instruction of the fundamental,
intermediate, and advanced skills,
techniques, and materials of the trade,
``(IV) provides training in math,
measurement, and blueprint reading
skills, if such skills are required in
the trade,
``(V) provides training on trade
specific tools and equipment,
``(VI) provides on-the-job training
which allows performance of work under
close supervision of an instructor or
skilled worker, and
``(VII) provides periodic review
and evaluation of participants to
demonstrate proficiency in skills,
including the use of tests and
assessment of individual and group
projects.
``(3) Training period.--The term `training period' means,
with respect to an employee, the period--
``(A) beginning on the date that the employee
begins employment with the taxpayer as an apprentice in
the highly skilled trade, and
``(B) ending on the earlier of--
``(i) the date that such apprenticeship
with the employer ends, or
``(ii) the date which is 4 years after the
date referred to in subparagraph (A).
``(c) Coordination With Other Credits.--The amount of credit
otherwise allowable under sections 51(a) and 1396(a) with respect to
any employee shall be reduced by the credit allowed by this section
with respect to such employee.''.
(b) Credit Made Part of General Business Credit.--Subsection (b) of
section 38 of such Code is amended by striking ``plus'' at the end of
paragraph (12), by striking the period at the end of paragraph (13) and
inserting ``, plus'', and by adding at the end the following new
paragraph:
``(14) in the case of a small business employer (as defined
in section 45E(b)), the highly skilled trades training credit
determined under section 45E(a).''.
(c) Denial of Double Benefit.--Section 280C of such Code is amended
by adding at the end the following new subsection:
``(d) Credit for Training Expenses for Employees in Highly Skilled
Small Business Trades.--No deduction shall be allowed for that portion
of the expenses otherwise allowable as a deduction for the taxable year
which is equal to the amount of the credit determined for the taxable
year under section 45E(a).''.
(d) Clerical Amendment.--The table of sections for subpart D of
part IV of subchapter A of chapter 1 of such Code is amended by adding
at the end the following new item:
``Sec. 45E. Expenses for long-term
training of employees in highly
skilled small business
trades.''.
(e) Effective Date.--The amendments made by this section shall
apply to expenses paid or incurred in the taxable years ending after
the date of the enactment of this Act. | Skilled Workforce Enhancement Act of 2001 - Amends the Internal Revenue Code to provide small employers with a highly skilled trades training credit. | <s>[INST]SECTION 1. SHORT TITLE.
This Act may be cited as the ``Skilled Workforce Enhancement Act of
2001''.
SEC. 2. CREDIT FOR EXPENSES FOR LONG-TERM TRAINING OF EMPLOYEES IN
HIGHLY SKILLED SMALL BUSINESS TRADES.
(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 new section:
``SEC. 45E. EXPENSES FOR LONG-TERM TRAINING OF EMPLOYEES IN HIGHLY
SKILLED SMALL BUSINESS TRADES.
``(a) General Rule.--For purposes of section 38, in the case of a
small business employer, the highly skilled trades training credit
determined under this section for the taxable year is $15,000 for each
employee having a qualified training year ending with or within such
taxable year (whether or not such employee is an employee of the
taxpayer as of the close of such taxable year).
``(b) Definitions.--For purposes of this section--
``(1) Small business employer.--
``(A) In general.--The term `small business
employer' means, with respect to any taxable year, any
employer who employed an average of 250 or fewer
employees on business days during such taxable year.
``(B) Controlled groups.--For purposes of
subparagraph (A), all persons treated as a single
employer under subsection (b), (c), (m), or (o) of
section 414 shall be treated as a single employer.
``(2) Qualified training year.--
``(A) In general.--The term `qualified training
year' means each year during the training period in
which the employee received at least 1,500 hours of
training (including on-the-job training and training at
multi-employer training facilities) from the taxpayer
(or any predecessor) under a qualified training program
as an apprentice in any highly skilled trade.
``(B) Highly skilled trades.--For purposes of
subparagraph (A), the term `highly skilled trades'
means--
``(i) precision machinists,
``(ii) die makers,
``(iii) mold makers,
``(iv) tool and die designers,
``(v) heating, ventilating, air
conditioning, refrigeration, and roofing
contractors,
``(vi) the trade of masonry,
``(vii) plumbers,
``(viii) pipefitters,
``(ix) patternmakers,
``(x) foundry technicians,
``(xi) electricians,
``(xii) recreational marine production and
design workers,
``(xiii) 2-way radio technicians,
``(xiv) welders,
``(xv) shipfitters,
``(xvi) propellor machinists,
``(xvii) electronic instrumentation
specialists, and
``(xviii) other highly skilled trades
specified in regulations prescribed by the
Secretary.
Such term shall not include any trade if the customary
apprenticeship period for such trade is less than 2
years.
``(C) Qualified training program.--
``(i) In general.--The term `qualified
training program' means a written plan of study
and training for individuals in, or entering
into, highly skilled trades.
``(ii) Description of programs.--A plan
under clause (i) must be a program described in
one of the following subclauses:
``(I) An apprenticeship program
registered and certified with the
Secretary of Labor under section 1 of
the National Apprenticeship Act (29
U.S.C. 50).
``(II) A program licensed,
registered, or certified by the
workforce investment board or
apprenticeship agency or council of a
State or administered in compliance
with apprenticeship laws of a State.
``(III) A program conducted by a
vocational or technical education
school, community college, or
industrial or trade training
organization.
``(IV) A program which conforms to
apprentice training programs developed
or administered by an employer trade
group or committee.
``(V) An industry sponsored or
administered program which is clearly
identified and commonly
recognized within an industry and which meets the requirements of
clause (iii).
``(iii) Requirements.--A program meets the
requirements of this clause if such program--
``(I) is accessible to individuals
without discrimination on the basis of
race, sex, color, religion, or national
origin,
``(II) provides an overview of the
trade, including the history and modern
developments in such trade,
``(III) provides related
instruction of the fundamental,
intermediate, and advanced skills,
techniques, and materials of the trade,
``(IV) provides training in math,
measurement, and blueprint reading
skills, if such skills are required in
the trade,
``(V) provides training on trade
specific tools and equipment,
``(VI) provides on-the-job training
which allows performance of work under
close supervision of an instructor or
skilled worker, and
``(VII) provides periodic review
and evaluation of participants to
demonstrate proficiency in skills,
including the use of tests and
assessment of individual and group
projects.
``(3) Training period.--The term `training period' means,
with respect to an employee, the period--
``(A) beginning on the date that the employee
begins employment with the taxpayer as an apprentice in
the highly skilled trade, and
``(B) ending on the earlier of--
``(i) the date that such apprenticeship
with the employer ends, or
``(ii) the date which is 4 years after the
date referred to in subparagraph (A).
``(c) Coordination With Other Credits.--The amount of credit
otherwise allowable under sections 51(a) and 1396(a) with respect to
any employee shall be reduced by the credit allowed by this section
with respect to such employee.''.
(b) Credit Made Part of General Business Credit.--Subsection (b) of
section 38 of such Code is amended by striking ``plus'' at the end of
paragraph (12), by striking the period at the end of paragraph (13) and
inserting ``, plus'', and by adding at the end the following new
paragraph:
``(14) in the case of a small business employer (as defined
in section 45E(b)), the highly skilled trades training credit
determined under section 45E(a).''.
(c) Denial of Double Benefit.--Section 280C of such Code is amended
by adding at the end the following new subsection:
``(d) Credit for Training Expenses for Employees in Highly Skilled
Small Business Trades.--No deduction shall be allowed for that portion
of the expenses otherwise allowable as a deduction for the taxable year
which is equal to the amount of the credit determined for the taxable
year under section 45E(a).''.
(d) Clerical Amendment.--The table of sections for subpart D of
part IV of subchapter A of chapter 1 of such Code is amended by adding
at the end the following new item:
``Sec. 45E. Expenses for long-term
training of employees in highly
skilled small business
trades.''.
(e) Effective Date.--The amendments made by this section shall
apply to expenses paid or incurred in the taxable years ending after
the date of the enactment of this Act.[/INST]Skilled Workforce Enhancement Act of 2001 - Amends the Internal Revenue Code to provide small employers with a highly skilled trades training credit.</s> |
the question of whether the solar diameter changes on timescales of years to centuries is very controversial . a recent paper ( thuillier et al 2005a ) presents a detailed summary of the issue .
in essence , different measurement and analysis techniques , and sometimes even identical instruments and similar analysis methods , yield incompatible results .
it is not presumptuous to infer that the cause of this controversy is that for the majority of the techniques , the results are at the borderline of the sensitivity of the technique .
the major exception to the above statement is the technique of helioseismology , particularly of the f - modes of oscillation .
schou et al . (
1997 ) and antia ( 1998 ) have demonstrated that the frequencies of f - modes can be used to estimate the solar radius .
since these frequencies have been measured with a precision of one part in @xmath0 , one may expect to determine the solar radius to similar precision .
changes in the f - mode frequencies have been used to determine changes in the solar radius ( see e.g. , dziembowski et al .
1998 , antia et al .
2000 , etc . ) .
the radius changes are estimated assuming that the fractional change in radius is uniform in the range of sensitivity of the method .
the radius change determined by f - modes is the change at the radius where the f - modes are concentrated .
one way of quantifying the depth at which the f - modes are sensitive is to look at the depth at which energy of the f - modes is concentrated .
this is shown in fig . 1 , where we plot the density for f - modes of several degrees .
the range of degrees on the plot reflects the range of available f - mode frequencies .
we see that for the lowest degree mode in the figure ( @xmath1 ) , the peak in the energy is at about 6.3 mm ( where temperature @xmath2 is about 41000k ) , and for the highest degree ( @xmath3 ) it is at 3.3 mm ( @xmath4k ) .
there are of course , other criteria by which one can determine radius ( see e.g. cox 1980 , unno et al .
however , here we show the energy density because that is the criterion used by various authors when discussing their radius - change results . in any event
, the different methods do not significantly alter the conclusions of this paper .
it should be noted that although the f - modes have a precision of one part in @xmath0 or so , the changes in radius can not be determined with this precision since that depends on how large the changes in f - modes are , and these changes happen to be very small . as a result , the radius - change measurements are not always very precise as can be seen from the results shown below .
consequently , even in the case of radius determination using f - mode oscillations , there does not seem to be consensus yet as to the exact amount by which the radius changes .
the results obtained so far ( dziembowski et al .
1998 , 2000 , 2001 ; antia et al .
2000 , 2001 ; antia & basu 2004 ) are not in agreement with each other .
dziembowski et al .
( 1998 ) , using mdi data , found that the solar radius reached a minimum around the minimum activity period in 1996 and was larger , by about 5 km , 6 months before and after the minimum .
however , later results , using longer time intervals , did not find any systematic changes ( dziembowski et al .
2000 ) . on the other hand , antia et al .
( 2000 ) using global oscillation network group ( gong ) data found that the solar radius decreased by about 5 km between 1995 and 1998 , and this variation appeared to be correlated ( but in antiphase ) with the level of solar activity .
subsequently antia et al .
( 2001 ) , using both gong and mdi data , put an upper limit of 1 km / year for the change in solar radius .
meanwhile , on a related paper , dziembowski et al . ( 2001 ) claimed a solar radius decrease as a rate of 1.5 km yr@xmath5 during 1996 - 2000 .
antia et al .
( 2001 ) made some sense of all these discrepant results by showing that the variation in f - mode frequencies could be divided into at least two components : one oscillatory , with a period of 1 yr , and a second , non - oscillatory , and probably correlated with solar activity .
they argued that the oscillatory component is most likely an artifact introduced by the orbital period of the earth .
they also showed that most of the discrepancy between different results could be explained by the use of data sets that cover different time periods and by the failure to remove the oscillatory component . upon performing those corrections ,
all the different investigations appear to indicate that the solar radius decreases with increasing solar activity . in a more recent investigation antia & basu ( 2004 ) examined the changes in f - mode frequencies using eight years of mdi data .
they obtain an upper limit of about 1 km / year for radius changes during the entire solar cycle .
it is to be noted , however , that even this result is not very clear cut , since different degree ranges of f - modes implied different radius changes .
when the available higher degree modes were used ( @xmath6 ) , they got an average change of @xmath7 km yr@xmath5 between 1996 and 2004 .
f - modes in the range @xmath8 show a change of @xmath9 km yr@xmath5 for the same period , but for @xmath10 , no observable change was obtained , ( @xmath11 km per year ) .
antia & basu ( 2004 ) suggested that the difference in the results yielded by the different degree ranges indicated that the evidence for radius change was not conclusive . in this paper
we will present an alternative interpretation of these observations , i.e. , that the sun does not expand or contract homologously with the change in solar activity .
we construct models to calculate the change in solar radius with change in solar activity .
the numerical code that we use to compute the structure and evolution of the solar model is an outgrowth of yrec ( winnick et al 2002 ) into which the effects of magnetic fields and turbulence have been included .
the starting values of the basic solar papameters are : @xmath12 cm and @xmath13 erg / s .
these particular choices have negligible effects on the results .
the version of the code used in these calculations is one - dimensional .
the inclusion of magnetic fields considers their contribution to pressure and internal energy , and their modification of energy transfer , primarily convection .
the dynamical effects modify turbulent pressure and energy transport .
the detailed formulation of the modifications to yrec is based on the approach first presented by lydon & sofia ( 1995 ) , and subsequently expanded by li & sofia ( 2001 ) , and li et al .
( 2002 , 2003 ) .
because the location , magnitude and temporal behavior of the internal field are not known , we made two general assumptions : ( 1 ) the magnitude of the magnetic field would be that required to cause a luminosity change of 0.1 percent over the cycle , and ( 2 ) the temporal behavior assumed is sinusoidal , and it mimics the shape of the activity cycle determined , for example , by the averaged sunspot number .
we computed four cases ( listed in table 1 ) , three with only magnetic fields at different depths , and one with both magnetic fields and turbulence . for the cases with only magnetic fields , the field configuration was gaussian .
guided by the observation of p - mode oscillations , we were led to the inclusion of turbulence ( li et al .
2003 ) . in this case , the properties of the turbulence were derived from numerical simulations of the outer region of the solar convective envelope ( robinson et al .
2003 ) , and the magnetic field distribution was dictated by a feedback process between turbulence and magnetic field . although the specific details of the calculations reported here are contained in li et al .
( 2003 ) we present in this paper the results of the calculations that are relevant to the radius problem , and not contained in that paper .
the lower panel of fig .
2 shows the difference in magnetic energy per unit mass ( @xmath14 ) between the years 2000 and 1996 for all cases where only magnetic fields are taken into account .
the upper panel of the figure shows the ratio between the radius change as a function of radius to the radius change at 5 mm .
3 is similar to fig . 2 , but for the case in which turbulence ( modulated by the magnetic field ) is included .
the lower panel shows the difference in turbulent ( @xmath15 , where @xmath16 is the magnitude of the turbulent velocity ) plus magnetic ( @xmath17 ) energy per unit mass between the years 2000 and 1996 ( @xmath18 ) , and the upper panel the ratio between the radius change as a function of radius to the radius change at 5 mm . from fig . 2 we notice that in all cases the radius increases with increasing solar activity
this is to be expected , since all the contribution of the magnetic field to pressure and internal energy is positive , and consequently , it can only lead to an increase of the radius .
we also notice that the increase of the radius is monotonic towards the surface .
this is because the increase at a given radius is made up of the sum of the increase at all levels below it .
finally , we notice that the expansion , which only increases in the magnetic region , is accelerated towards the shallower layers . this can be understood since , for a given value of the magnetic field , the ratio of magnetic to total pressure increases with increasing radius , and so does the expansion .
3 represents the case that , according to li et al .
( 2003 ) , meets all the observational requirements imposed by helioseismology . in particular , it produces the correct cycle - related variations of the p - mode oscillations , it does not alter the depth of the convection zone , and it produces diameter changes in opposite phase of the activity cycle . in this case
, the magnetic field slows down turbulent flows so that the increase of magnetic pressure when the magnetic field grows is overcompensated by the corresponding decrease in turbulent pressure . in all cases , the radius variation at the solar surface [ which is measured by any limb - observing instrument , such as the solar disk sextant ( sofia et al .
1994 ) , and picard thuillier et al .
( 2005b ) ] , can be hundreds of times larger than the radius variation inferred by f - mode oscillations , which represents changes at several mm . to determine the depth of the level of the `` diameter '' provided by the f - mode oscillations
, we refer to fig .
1 , which represents the kinetic energy of the modes of different @xmath19-values ( abscissa in arbitrary units ) . we can see that for higher @xmath19s , the peak energy occurs at shallower layers than for lower-@xmath19 modes .
it would appear that 5 mm is a good number to represent the depth of the layer given by f - mode oscillations of all degrees observed .
thus , the upper panel of figs .
2 and 3 give the magnification factor between radius changes determined from f - mode oscillations , and the radius changes that can be expected at the photospheric level , and thus to be observed by all limb - observing instruments . because @xmath20 increases in the shallower layers , the high-@xmath19 modes , which peak in shallower layers , should show a larger radius change than the low-@xmath19 modes , which peak at deeper layers .
we believe this is precisely what the results obtained by antia & basu ( 2004 ) imply .
we have shown that the model of variability of the solar interior that obeys all observational constraints ( global parameters and p - mode and f - mode oscillations ) produces variations of the solar radius that increase by a factor of approximately 1000 from a depth of 5 mm to the solar surface .
this model includes the effects of a variable dynamo magnetic field , and of a field - modulated turbulence , and it explains features of the f - mode oscillations in different degree ranges that were previously not understood . on the basis of the above argument , we conclude that results from f - mode oscillations that the solar radius only changes by about 1 km / year does not preclude the less - sensitive efforts to measure variations of the solar radius at the photosphere by limb observations since the latter are likely to be much larger than the former .
limb observations are made by a number of ground - based instruments , and from above the atmosphere by the solar disk sextant ( sds ) balloon - borne experiment ( sofia et al .
1994 ) , and will be made starting in 2008 by the picard microsatellite ( thuillier et al .
2005b ) . in thermal equilibrium
the space - based instruments have a theoretical precision of about 1 milli arc s ( about 1 km ) .
picard should easily reach such a precision .
balloon based observations , however , can not reach this precision because the short duration of the flights prevents the instrument from reaching thermal equilibrium .
the current sds results have reached a precision of the order @xmath21 arc s ( egidi et al 2005 ) .
antia , h.m . ,
basu , s. , 2004 , in proc : soho 14 / gong 2004 workshop ( esa sp-559 ) .
`` helio- and asteroseismology : towards a golden future '' .
12 - 16 july , 2004 .
new haven , connecticut , usa . editor : d. danesy .
, p.301 basu , s. , pinsonneault , m. h. , & bahcall , j. n. 2000 , , 529 , 1084 li , l. h. , basu , s. , sofia , s. , demarque , p. , & guenther , d. b. 2003 , , 591 , 1267 li , l. h. , robinson , f. j. , demarque , p. , sofia , s. & guenther , d. b. 2002 , , 567 , 1192 li , l. h. , & sofia , s. 2001 , , 249 , 1204 | we show in this paper that the changes of the solar diameter in response to variations of large scale magnetic fields and turbulence are not homologous . for the best current model ,
the variation at the photospheric level is over 1000 times larger than the variation at a depth of 5 mm , which is about the level at which f - mode solar oscillations determine diameter variations .
this model is supported by observations that indicate larger diameter changes for high degree f - modes than for low degree f - modes , since energy of the former are concentrated at shallower layers than the latter . | <s>[INST]the question of whether the solar diameter changes on timescales of years to centuries is very controversial . a recent paper ( thuillier et al 2005a ) presents a detailed summary of the issue .
in essence , different measurement and analysis techniques , and sometimes even identical instruments and similar analysis methods , yield incompatible results .
it is not presumptuous to infer that the cause of this controversy is that for the majority of the techniques , the results are at the borderline of the sensitivity of the technique .
the major exception to the above statement is the technique of helioseismology , particularly of the f - modes of oscillation .
schou et al . (
1997 ) and antia ( 1998 ) have demonstrated that the frequencies of f - modes can be used to estimate the solar radius .
since these frequencies have been measured with a precision of one part in @xmath0 , one may expect to determine the solar radius to similar precision .
changes in the f - mode frequencies have been used to determine changes in the solar radius ( see e.g. , dziembowski et al .
1998 , antia et al .
2000 , etc . ) .
the radius changes are estimated assuming that the fractional change in radius is uniform in the range of sensitivity of the method .
the radius change determined by f - modes is the change at the radius where the f - modes are concentrated .
one way of quantifying the depth at which the f - modes are sensitive is to look at the depth at which energy of the f - modes is concentrated .
this is shown in fig . 1 , where we plot the density for f - modes of several degrees .
the range of degrees on the plot reflects the range of available f - mode frequencies .
we see that for the lowest degree mode in the figure ( @xmath1 ) , the peak in the energy is at about 6.3 mm ( where temperature @xmath2 is about 41000k ) , and for the highest degree ( @xmath3 ) it is at 3.3 mm ( @xmath4k ) .
there are of course , other criteria by which one can determine radius ( see e.g. cox 1980 , unno et al .
however , here we show the energy density because that is the criterion used by various authors when discussing their radius - change results . in any event
, the different methods do not significantly alter the conclusions of this paper .
it should be noted that although the f - modes have a precision of one part in @xmath0 or so , the changes in radius can not be determined with this precision since that depends on how large the changes in f - modes are , and these changes happen to be very small . as a result , the radius - change measurements are not always very precise as can be seen from the results shown below .
consequently , even in the case of radius determination using f - mode oscillations , there does not seem to be consensus yet as to the exact amount by which the radius changes .
the results obtained so far ( dziembowski et al .
1998 , 2000 , 2001 ; antia et al .
2000 , 2001 ; antia & basu 2004 ) are not in agreement with each other .
dziembowski et al .
( 1998 ) , using mdi data , found that the solar radius reached a minimum around the minimum activity period in 1996 and was larger , by about 5 km , 6 months before and after the minimum .
however , later results , using longer time intervals , did not find any systematic changes ( dziembowski et al .
2000 ) . on the other hand , antia et al .
( 2000 ) using global oscillation network group ( gong ) data found that the solar radius decreased by about 5 km between 1995 and 1998 , and this variation appeared to be correlated ( but in antiphase ) with the level of solar activity .
subsequently antia et al .
( 2001 ) , using both gong and mdi data , put an upper limit of 1 km / year for the change in solar radius .
meanwhile , on a related paper , dziembowski et al . ( 2001 ) claimed a solar radius decrease as a rate of 1.5 km yr@xmath5 during 1996 - 2000 .
antia et al .
( 2001 ) made some sense of all these discrepant results by showing that the variation in f - mode frequencies could be divided into at least two components : one oscillatory , with a period of 1 yr , and a second , non - oscillatory , and probably correlated with solar activity .
they argued that the oscillatory component is most likely an artifact introduced by the orbital period of the earth .
they also showed that most of the discrepancy between different results could be explained by the use of data sets that cover different time periods and by the failure to remove the oscillatory component . upon performing those corrections ,
all the different investigations appear to indicate that the solar radius decreases with increasing solar activity . in a more recent investigation antia & basu ( 2004 ) examined the changes in f - mode frequencies using eight years of mdi data .
they obtain an upper limit of about 1 km / year for radius changes during the entire solar cycle .
it is to be noted , however , that even this result is not very clear cut , since different degree ranges of f - modes implied different radius changes .
when the available higher degree modes were used ( @xmath6 ) , they got an average change of @xmath7 km yr@xmath5 between 1996 and 2004 .
f - modes in the range @xmath8 show a change of @xmath9 km yr@xmath5 for the same period , but for @xmath10 , no observable change was obtained , ( @xmath11 km per year ) .
antia & basu ( 2004 ) suggested that the difference in the results yielded by the different degree ranges indicated that the evidence for radius change was not conclusive . in this paper
we will present an alternative interpretation of these observations , i.e. , that the sun does not expand or contract homologously with the change in solar activity .
we construct models to calculate the change in solar radius with change in solar activity .
the numerical code that we use to compute the structure and evolution of the solar model is an outgrowth of yrec ( winnick et al 2002 ) into which the effects of magnetic fields and turbulence have been included .
the starting values of the basic solar papameters are : @xmath12 cm and @xmath13 erg / s .
these particular choices have negligible effects on the results .
the version of the code used in these calculations is one - dimensional .
the inclusion of magnetic fields considers their contribution to pressure and internal energy , and their modification of energy transfer , primarily convection .
the dynamical effects modify turbulent pressure and energy transport .
the detailed formulation of the modifications to yrec is based on the approach first presented by lydon & sofia ( 1995 ) , and subsequently expanded by li & sofia ( 2001 ) , and li et al .
( 2002 , 2003 ) .
because the location , magnitude and temporal behavior of the internal field are not known , we made two general assumptions : ( 1 ) the magnitude of the magnetic field would be that required to cause a luminosity change of 0.1 percent over the cycle , and ( 2 ) the temporal behavior assumed is sinusoidal , and it mimics the shape of the activity cycle determined , for example , by the averaged sunspot number .
we computed four cases ( listed in table 1 ) , three with only magnetic fields at different depths , and one with both magnetic fields and turbulence . for the cases with only magnetic fields , the field configuration was gaussian .
guided by the observation of p - mode oscillations , we were led to the inclusion of turbulence ( li et al .
2003 ) . in this case , the properties of the turbulence were derived from numerical simulations of the outer region of the solar convective envelope ( robinson et al .
2003 ) , and the magnetic field distribution was dictated by a feedback process between turbulence and magnetic field . although the specific details of the calculations reported here are contained in li et al .
( 2003 ) we present in this paper the results of the calculations that are relevant to the radius problem , and not contained in that paper .
the lower panel of fig .
2 shows the difference in magnetic energy per unit mass ( @xmath14 ) between the years 2000 and 1996 for all cases where only magnetic fields are taken into account .
the upper panel of the figure shows the ratio between the radius change as a function of radius to the radius change at 5 mm .
3 is similar to fig . 2 , but for the case in which turbulence ( modulated by the magnetic field ) is included .
the lower panel shows the difference in turbulent ( @xmath15 , where @xmath16 is the magnitude of the turbulent velocity ) plus magnetic ( @xmath17 ) energy per unit mass between the years 2000 and 1996 ( @xmath18 ) , and the upper panel the ratio between the radius change as a function of radius to the radius change at 5 mm . from fig . 2 we notice that in all cases the radius increases with increasing solar activity
this is to be expected , since all the contribution of the magnetic field to pressure and internal energy is positive , and consequently , it can only lead to an increase of the radius .
we also notice that the increase of the radius is monotonic towards the surface .
this is because the increase at a given radius is made up of the sum of the increase at all levels below it .
finally , we notice that the expansion , which only increases in the magnetic region , is accelerated towards the shallower layers . this can be understood since , for a given value of the magnetic field , the ratio of magnetic to total pressure increases with increasing radius , and so does the expansion .
3 represents the case that , according to li et al .
( 2003 ) , meets all the observational requirements imposed by helioseismology . in particular , it produces the correct cycle - related variations of the p - mode oscillations , it does not alter the depth of the convection zone , and it produces diameter changes in opposite phase of the activity cycle . in this case
, the magnetic field slows down turbulent flows so that the increase of magnetic pressure when the magnetic field grows is overcompensated by the corresponding decrease in turbulent pressure . in all cases , the radius variation at the solar surface [ which is measured by any limb - observing instrument , such as the solar disk sextant ( sofia et al .
1994 ) , and picard thuillier et al .
( 2005b ) ] , can be hundreds of times larger than the radius variation inferred by f - mode oscillations , which represents changes at several mm . to determine the depth of the level of the `` diameter '' provided by the f - mode oscillations
, we refer to fig .
1 , which represents the kinetic energy of the modes of different @xmath19-values ( abscissa in arbitrary units ) . we can see that for higher @xmath19s , the peak energy occurs at shallower layers than for lower-@xmath19 modes .
it would appear that 5 mm is a good number to represent the depth of the layer given by f - mode oscillations of all degrees observed .
thus , the upper panel of figs .
2 and 3 give the magnification factor between radius changes determined from f - mode oscillations , and the radius changes that can be expected at the photospheric level , and thus to be observed by all limb - observing instruments . because @xmath20 increases in the shallower layers , the high-@xmath19 modes , which peak in shallower layers , should show a larger radius change than the low-@xmath19 modes , which peak at deeper layers .
we believe this is precisely what the results obtained by antia & basu ( 2004 ) imply .
we have shown that the model of variability of the solar interior that obeys all observational constraints ( global parameters and p - mode and f - mode oscillations ) produces variations of the solar radius that increase by a factor of approximately 1000 from a depth of 5 mm to the solar surface .
this model includes the effects of a variable dynamo magnetic field , and of a field - modulated turbulence , and it explains features of the f - mode oscillations in different degree ranges that were previously not understood . on the basis of the above argument , we conclude that results from f - mode oscillations that the solar radius only changes by about 1 km / year does not preclude the less - sensitive efforts to measure variations of the solar radius at the photosphere by limb observations since the latter are likely to be much larger than the former .
limb observations are made by a number of ground - based instruments , and from above the atmosphere by the solar disk sextant ( sds ) balloon - borne experiment ( sofia et al .
1994 ) , and will be made starting in 2008 by the picard microsatellite ( thuillier et al .
2005b ) . in thermal equilibrium
the space - based instruments have a theoretical precision of about 1 milli arc s ( about 1 km ) .
picard should easily reach such a precision .
balloon based observations , however , can not reach this precision because the short duration of the flights prevents the instrument from reaching thermal equilibrium .
the current sds results have reached a precision of the order @xmath21 arc s ( egidi et al 2005 ) .
antia , h.m . ,
basu , s. , 2004 , in proc : soho 14 / gong 2004 workshop ( esa sp-559 ) .
`` helio- and asteroseismology : towards a golden future '' .
12 - 16 july , 2004 .
new haven , connecticut , usa . editor : d. danesy .
, p.301 basu , s. , pinsonneault , m. h. , & bahcall , j. n. 2000 , , 529 , 1084 li , l. h. , basu , s. , sofia , s. , demarque , p. , & guenther , d. b. 2003 , , 591 , 1267 li , l. h. , robinson , f. j. , demarque , p. , sofia , s. & guenther , d. b. 2002 , , 567 , 1192 li , l. h. , & sofia , s. 2001 , , 249 , 1204[/INST] we show in this paper that the changes of the solar diameter in response to variations of large scale magnetic fields and turbulence are not homologous . for the best current model ,
the variation at the photospheric level is over 1000 times larger than the variation at a depth of 5 mm , which is about the level at which f - mode solar oscillations determine diameter variations .
this model is supported by observations that indicate larger diameter changes for high degree f - modes than for low degree f - modes , since energy of the former are concentrated at shallower layers than the latter . </s> |
in the constituent quark model , mesons and baryons are described by quark and anti - quark pair and three quarks respectively .
many hadrons known so far are described by this model very well . on the other hand ,
the existence of exotic baryons such as pentaquark and dibaryon has been suggested theoretically , because qcd requires only that hadrons should be color singlet , but does not restrict the number of quarks @xcite .
although many experimental efforts to search for these exotics were made , there was no clear evidence .
it was about 30 years later from the establishment of qcd that the first report about the exotic pentaquark , which is now called @xmath0 , was made by spring-8/leps collaboration @xcite .
they showed a peak in mass distribution of @xmath15 system via @xmath16 reaction where neutrons in @xmath17c nuclei were used as a target .
this discovery stimulated many physicists , and many works have been done from both theoretical and experimental sides .
diakonov et al . ,
using the framework of chiral soliton model , regarded @xmath0 as a member of anti - decuplet which is the third excited state of soliton field and predicted that its mass was 1530 mev/@xmath4 and the width was 15 mev/@xmath4 by treating the known @xmath18(1710 , 1/2@xmath19 ) resonance as a member of this anti - decuplet @xcite .
jaffe and wilczek proposed diquark - diquark - antiquark nature of @xmath0 in the anti - decuplet plus octet representation of su(3 ) @xcite .
many other theoretical studies such as constituent quark model , qcd sum rules and lattice qcd were devoted to @xmath0 @xcite .
experimentally , the observation at leps was immediately confirmed by several experiments @xcite .
recently , however , null results were reported from several high energy experiments where they searched for @xmath0 with much higher statistics @xcite .
most recently , clas collaboration has reported some results of a series of high statistical search for @xmath0 . in @xcite , @xmath0
was not observed and the upper limit of production cross section via @xmath20 reaction was set to be 0.8 nb .
these negative results make the existence of @xmath0 be in more puzzling situation .
however titov et al . , using quark constituent coupling rules , shows that the production of the @xmath0 is suppressed relative to the @xmath21 resonance by about three orders of magnitude for high energy experiments @xcite .
therefore , in order to confirm the existence of @xmath0 , high statistics experiments at low energy region with hadronic reaction become crucial .
many experimental data of @xmath0 are from photo - production experiments . in general the @xmath0 production cross section via hadronic reaction is expected to be much larger than that via photo - induced reaction .
now , physical properties such as spin , parity and width have not been determined experimentally yet . in order to measure these values ,
we need more statistics . from these viewpoints , the study of @xmath0 production using meson beam such as @xmath2 and @xmath22 is essential .
therefore we carried out an experiment to search for @xmath0 via @xmath23 reaction . in this reaction , the threshold momentum is 1.71 gev/@xmath3 .
we used 1.87 and 1.92 gev/@xmath3 @xmath2 beam .
the @xmath24 reaction near the @xmath0 production threshold was studied in 1960s using a bubble chamber @xcite .
the main backgrounds of the ( @xmath25 ) reaction are @xmath26 production , @xmath21 production and 3-body phase space .
the cross sections of these reactions were measured to be @xmath27 and @xmath28b respectively at beam momentum from 1.8 to 2.2 gev/@xmath3 .
it is remarkable feature that in this momentum range the background is small because other channels do not open . in this past experiment
the invariant mass of @xmath29 and @xmath30 were surveyed . any peak structure was not observed .
however numbers of @xmath29 and @xmath30 events were only 86 and 249 respectively .
the understanding of production mechanism is quite important to understand @xmath0 .
therefore a measurement of the production cross section with a simple reaction is important experimentally .
theoretically calculations with hadronic models using effective interaction lagrangians and form factors were made by several authors @xcite .
they try to understand the @xmath0 production mechanism via @xmath31 and @xmath32 reactions near the production threshold comprehensively .
the theoretical calculations predict that the @xmath0 production cross section of @xmath33 reaction ranges from several @xmath8b to several hundred @xmath8b .
however the parameters such as @xmath34 used in these calculations are not determined experimentally .
therefore these calculation should be compared with experimental data . in this letter
we report the results of an experiment to search for @xmath0 via @xmath33 reaction .
we have performed the e522 experiment at the k2 beam line of the kek 12 gev proton synchrotron in 2004 .
the main objective of this experiment was to search for h - dibaryon resonance with ( @xmath35 ) reaction .
we searched for the enhancement at the threshold region of the double-@xmath36 system , which was first measured at kek - ps e224 experiment @xcite , with much better statistics @xcite .
besides this reaction , we optionally took @xmath37 data , because the @xmath0 search via mesonic reaction became crucial to confirm its existence and the k2 beam line is a unique beam line which can provide up to 2 gev/@xmath3 @xmath38 beam .
we used a @xmath2 beam of 1.87 and 1.92 gev/@xmath3 . as a target
, we used a scintillation fiber ( scifi ) target ( @xmath39 ) and a bulk target of polyethylene ( @xmath40 ) .
the scifi target is 20 cm long , and is the same one used in the hyperon - nucleon scattering experiment ( kek - ps e289 ) @xcite .
it was mainly used to detect decay particles from @xmath41 reaction for the h - dibaryon resonance search . for ( @xmath25 ) data
, we mainly used the 10 cm long polyethylene target to enhance the contribution from free protons .
the scifi target was also used to detect tracks of the charged particles other than @xmath42 produced by reactions . at the beam momentum of 1.87 gev/@xmath3 , 2.9@xmath43 and 3.0@xmath43 @xmath2 beam particles
were irradiated to the scifi and the polyethylene targets respectively . at 1.92 gev/@xmath3 ,
7.4@xmath43 @xmath2 beam particles were irradiated to only the polyethylene target . for the calibration we took the following data . in order to estimate the contribution from carbon in the scifi and polyethylene targets , we took data with a carbon target .
the ( @xmath44 ) data were analyzed to measure the @xmath45 peak position for the calibration of the missing mass spectrum .
the experimental setup consisted of two parts ; one part was a beam line spectrometer to analyze momentum of each incident beam particle and the other part was a forward spectrometer to detect scattered particles .
the set up was almost similar to the one used at kek - ps e373 experiment and detail of the experimental setup is described elsewhere @xcite .
the k2 beam line is designed to transport charged particles up to 2.0 gev/@xmath3 .
[ kuramasp ] ( a ) shows the beam line spectrometer .
the @xmath2 beam was bent by 15 degree at the bending magnet ( d2 ) and focused at the target by two quadrapole magnets ( q6 , q7 ) .
the typical intensity of @xmath2 was 330k counts during 2 sec .
spill with a primary proton beam of @xmath46 .
each beam particle was defined by the hit of t1 and t2 counters placed about 7.2 m apart each other and @xmath2 was selected at a trigger by two aerogel cherenkov counters ( bac1,2 ) , of which threshold velocity was 0.971 , placed just upstream of the t2 counter .
the beam momentum was analyzed with 5 wire chambers placed upstream and downstream of the d2 magnet . the momentum resolution is estimated to be @xmath47 mev/@xmath3 from a simulation . between two quadrapole magnets ( q6 , q7 ) and the target , 3 proportional chambers were placed to measure the beam direction .
the timing for all detectors was determined by the t2 counter .
the scattered particles were detected by the forward spectrometer shown in fig .
[ kuramasp ] ( b ) .
the kurama magnet is 80 cm long and the magnetic field strength is 0.93 t . the momentum of each scattered particle was measured using 3 drift chambers ( dc1,2,3 ) and scintillation hodoscopes ( vh , ch ) placed upstream and downstream of kurama .
the momentum resolution was 1.9 % ( r.m.s . ) for 0.8 gev/@xmath3 @xmath42 .
the time - of - flight of each scattered particle was measured by a tof wall ( ftof ) placed at end of the spectrometer .
a typical time resolution was 132 ps .
two cherenkov counters ( bvac , fac ) were installed between the target and kurama to veto @xmath2 . besides this particle identification with these cherenkov counters at the trigger level , we selected the charge and momentum range of each scattered particle at 1st trigger level using the hit combination of each segments of ch hodoscope and ftof .
momentum of each particle was determined using the hit combination . by combining time - of - flight information of the hit ftof segment with this momentum information
, the mass of each scattered particle was roughly calculated .
we selected @xmath42 with this mass trigger ( mt ) at 2nd trigger level .
this mass trigger rejected mainly @xmath2 which survived due to the inefficiency of the cherenkov counters . in the offline analysis , mass and momentum of each scattered particle are calculated more accurately as shown in fig .
the @xmath42 mesons are clearly identified .
mesons were selected cleanly .
, width=264 ]
+ cc cut & efficiency(% ) + + time - of - flight cut & 93.8 @xmath48 0.1 + beam @xmath49 cut & 84.6 @xmath48 0.1 + beam momentum cut & 94.8 @xmath48 0.1 + + mass - momentum cut & @xmath50 + runge - kutta @xmath49 cut & [email protected] + + vertex cut & 92.8@xmath48 0.5 + closest distance cut & 97.8 @xmath480.1 + total & [email protected] + we describe the analysis procedure to search for @xmath0 from the missing mass spectrum of the @xmath37 reaction . to obtain this spectrum
, we applied the following cuts ; 1 ) selection of @xmath2 in the beam and momentum analysis , 2 ) identification of the scattered @xmath42 and momentum analysis , and 3 ) selection of the reaction vertex point .
the efficiencies of these cuts in the analysis , which are described in detail in the following paragraphs , are summarized in table [ tab : summary_ana_eff ] .
the efficiencies of the track - finding routine are described in the next section and listed in table [ tab : summary_eff ] .
the incident @xmath2 was identified using time - of - flight information between t1 and t2 .
the contamination of @xmath42 was negligible , and we selected @xmath51 region of its time resolution ( 70ps ) as good events .
each incident @xmath2 momentum was calculated by fitting the hit positions at the beam line chambers ( bdc1,2,3 and bpc1,2 ) with second order transfer matrix calculated by transport @xcite .
the @xmath49 distribution of this fitting was consistent with the expectation except a tail towards large @xmath49 .
we selected c.l.=95% region for @xmath49 cut whose efficiency was 84.6 % as the result of rejecting the large @xmath49 events .
the event whose beam momentum was less than 1.8 gev/@xmath3 or larger than 2.0 gev/@xmath3 was rejected considering the momentum acceptance of the beam line .
trajectories of outgoing particles were reconstructed by using the information of hit positions at the drift chambers ( dc1 - 3 ) and the hodoscopes ( vh , ch ) and of the field map in kurama .
at first , the local tracks upstream and downstream of kurama were searched by the straight - line fittings , and the consistency between these local tracks were checked to reject the decay events of @xmath42 .
then we used runge - kutta method for the momentum analysis @xcite .
the scattered @xmath42 s were selected by the momentum dependent mass cut and we selected 3@xmath6 region as shown in fig [ mass ] .
the contamination of @xmath2 after this cut was about 3% . in the ( @xmath25 ) reaction ,
the momenta of scattered @xmath42 ranged from 0.4 to 1.1 gev/@xmath3 .
therefore the effect of multiple scattering made the @xmath49 distribution of runge - kutta tracking broader than the ideal one . to study the cut position of @xmath49 cut , we compared with the distribution obtained by the monte carlo simulation based on geant4 @xcite which included all materials of the spectrometer and the electro - magnetic process , the hadoronic process and the decay process .
the simulated @xmath49 distribution reproduces real data except a long tail towards large @xmath49 , not only for ( @xmath25 ) reaction but also for ( @xmath44 ) and ( @xmath35 ) reactions where the typical momenta of @xmath22 were around 1.6 and 1.2 gev/@xmath3 respectively . from this study , we selected @xmath52 region where the @xmath49 distribution was consistent with the simulation . in the momentum reconstruction ,
energy loss effect in the materials of the spectrometer was not taken into account .
the energy loss in the target was corrected using the reconstructed momenta of the incident and outgoing particles with their directions and the calculated vertex positions .
the vertex point was calculated by the closest distant point between tracks of beam and outgoing particles .
we required the vertex point to be less than 80 mm from the target center .
the beam size ( 1.4 @xmath53 1.3 @xmath54 ) was small enough in comparison with the target size . because the scifi target enabled us to see particle trajectories as image data , we could estimate the efficiency of this vertex cut precisely by comparing the vertex position calculated by the spectrometer with one obtained in the image data .
the efficiency of this cut was estimated to be 92.8 @xmath48 0.5 % .
we also checked the distribution of the closest distance between tracks of beam and outgoing particles at the vertex point .
the events where the closest distance was greater than 7 mm , which corresponded to 3@xmath6 , were rejected considering that beam or outgoing particles reacted more than 2 times in the target .
[ missmass_pi+k ] shows the missing mass spectrum of the ( @xmath44 ) reaction at the beam momentum of 1.92 gev/@xmath3 .
the peak due to @xmath45 is clearly observed .
the beam momentum was normalized so as to make the obtained @xmath45 peak consistent with the pdg value .
we fitted this spectrum with two gaussian peaks assuming that the broad peak was attributed to quasi - free protons in carbon and the narrow one was attributed to free protons .
the obtained width was [email protected] mev/@xmath4 ( fwhm ) which was almost consistent with the expected value of 28.3 mev/@xmath4 from the simulation . to estimate the missing mass resolution in the simulation , the position resolutions of the drift chambers , the momentum resolution of the beam spectrometer and the effects of the energy loss and the multiple scattering in materials for incident and outgoing particles
were taken into account .
using the same program code , the missing mass resolution for @xmath0 was estimated to be 13.4 mev/@xmath4 ( fwhm ) . in @xmath0 production , the momentum of the outgoing particle is much lower than that in the @xmath45 production . therefore the missing mass resolution is better for @xmath0 . )
reaction with a polyethylene target .
the beam momentum was adjusted so as to make the obtained @xmath45 peak consistent with the pdg value .
the hatched spectrum is the expected spectrum from the simulation .
the obtained peak width of 33.3 @xmath48 4.8 mev/@xmath4 ( fwhm ) is almost same with the expected value 28.3 mev/@xmath4 .
, width=264 ]
the missing mass spectra for each beam momentum are shown in fig .
[ missmass_pi - k ] . in order to know the contribution from carbon nuclei in the scifi and polyethylene targets ,
carbon target data are also shown as the hatched spectra , which are normalized by the number of beam particle and the number of carbon nuclei in each target .
the statistics of the carbon target data is about ten times lower than that of ch@xmath55 data .
the net contribution from free protons is compatible with the expectation from the cross sections of background reactions measured in @xcite .
because half of data at beam momentum of 1.87 gev/@xmath3 was taken with the scifi target , the contribution from free protons at 1.87 gev/@xmath3 is smaller than that at 1.92 gev/@xmath3 . )
reaction at 1.92 gev/@xmath3 .
( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this
fitting , the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line .
, title="fig:",width=302 ] ) reaction at 1.92 gev/@xmath3 .
( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this fitting ,
the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line . , title="fig:",width=302 ] ) reaction at 1.92 gev/@xmath3 . ( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this
fitting , the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line .
, width=340 ] fig .
[ missmass_pi - k ] ( a ) shows the missing mass spectrum of the @xmath37 reaction at 1.87 gev/@xmath3 . in this spectrum ,
data for the scifi target and the polyethylene target are combined .
any peak was not observed in this spectrum . fig .
[ missmass_pi - k ] ( b ) shows the missing mass spectrum of @xmath58 reaction at 1.92 gev/@xmath3 .
it seems that there is a bump around 1.53 gev/@xmath57 .
however there is a possibility that the structure is only a statistical fluctuation .
we fitted this histogram with the background of a cubic function and a gaussian peak ( see fig .
[ fit_missmass_pi - k ] ) .
the peak position is 1530.6 @xmath59(stat.)@xmath60(syst . )
mev/@xmath4 , the width is @xmath61=9.8@xmath62 mev/@xmath4 ( fwhm ) and the count of the peak is 139@xmath63(stat.)@xmath4810(syst . ) .
the uncertainty of count resulting from varying the fitting range and binning is considered as the systematic error .
the obtained width is consistent with the expected value of 13.4 mev/@xmath4 within the error .
we also fitted this spectrum with the fixed width of 13.4 mev/@xmath4 .
the count of this bump was obtained to be 183@xmath4871(stat.)@xmath4810(syst . ) .
the statistical significance of this bump was considered by two expressions .
the first expression is the naive estimator @xmath64 where @xmath65 is the peak count within 2@xmath6 region from the center and @xmath66 is the background within the same region , and the significance is 2.7@xmath6 .
the second estimate of significance is given by @xmath67 , where @xmath68 is full area of the bump from the fit and @xmath69 is its fully correlated uncertainty .
the significance of 2.5@xmath6 is obtained by the second expression .
we fitted the histogram with only the background of a cubic function assuming that there is no peak structure .
the fitting result is shown by a dashed line in fig .
[ fit_missmass_pi - k ] .
the statistical significance of the bump from this background is estimated to be 1.9@xmath6 using the first expression , @xmath70 .
the statistical significance obtained in the present experiment is not sufficient to claim this bump as the evidence of @xmath0 .
however it is quite important to estimate the upper limit of the production cross section of @xmath0 via the @xmath71 reaction .
therefore we have obtained the upper limit of the production cross section . to derive the upper limit ,
the peak count obtained from the fitting with the fixed width is used at beam momentum of 1.92 gev/@xmath3 .
we used a single tail approach assuming that the peak count fluctuates based on gaussian statistics .
then the upper limit of the peak count is @xmath72=274 at 90% confidence level , where @xmath68 denotes the peak count obtained from the fitting and @xmath73 , @xmath74 denote the statistical and systematic errors respectively , and we use this count for the following calculations . in the missing mass spectrum at 1.87 gev/@xmath3
, we could not find any obvious peak structure .
we estimated that the signal from @xmath0(@xmath75 ) is less than 1.28@xmath76 at 90 % confidence level , where @xmath77 represents the count in the missing mass spectrum corresponding to @xmath78 region from the peak position ( 1530.6 mev/@xmath4 ) obtained from 1.92 gev/@xmath3 data .
we calculated that @xmath75 were 62 and 52 for the scifi target and the polyethylene target , respectively .
the production cross section of @xmath0 was calculated by the following equation .
@xmath79 here @xmath80 and @xmath81 represent the number of @xmath0 , beam particles and protons in the target .
the solid angle covered by kurama spectrometer at laboratory frame is represented by d@xmath82 .
others represent various efficiencies , and are summarized in table[tab : summary_eff ] .
+ .summary of the various efficiencies for the calculation of the production cross section . [ cols="^,^,^ " , ] the coefficient @xmath83 is the correction factor to obtain the number of real @xmath2 . in this experiment , we could not distinguish @xmath84 and @xmath85 from @xmath2 .
we referred the past experiment where a gas cherenkov counter was used to distinguish @xmath84 and @xmath85 and estimated that this contamination was 12.4% @xcite .
we also calculated the reaction rate of @xmath2 in the target with geant simulation and obtained to be 4% .
adding these value , we estimated that @xmath83 was 83.6% .
the efficiencies of track - finding routines used in the analysis program for beam and scattered particles have to be estimated , because routines have criteria to find tracks such as minimum number of hit chambers and can not find out a part of tracks due to the inefficiency of the drift chambers or multi charged hit events .
the coefficient @xmath86 is the track - finding efficiency for beam particles and obtained to be 72.7% .
the reason for the inefficiency is mainly due to the dead channel of bdc3 .
the coefficient @xmath87 is the track - finding efficiency for scattered particles and obtained to be 84.6% by analyzing the data produced by the monte carlo simulation with the same analysis program .
the validity of this estimation was checked using scattered proton events taken with ( @xmath35 ) trigger data .
the scattered protons could be selected by using information of hit combination of ch and ftof counters and of time - of - flight without tracking .
we estimated the track - finding efficiency by analyzing such pre - selected proton events .
results obtained from the simulated events and pre - selected proton events were consistent within 2.0% which denoted the error of the efficiency .
the coefficient @xmath88 represents the correction factor due to the overkilling rate of the cherenkov counters ( bvac , fac ) which was 9.2% .
therefore @xmath88 was obtained to be 90.8% .
the coefficients , @xmath89 and @xmath90 , represent the correction factors due to the decay rate before arriving ftof wall and the interaction rate of @xmath42 in the materials of the target and the forward spectrometer respectively .
these factors were also calculated with the monte carlo simulation based on geant4 and obtained to be 57.6% and 89.8% respectively .
the coefficients , @xmath91 and @xmath92 , are the efficiencies of the daq system and 2nd level mass trigger , and obtained to be 93.5% and 95.7% respectively .
the coefficient @xmath93 is the analysis cut efficiency and summarized in table[tab : summary_ana_eff ] and estimated to be 49.6% .
finally , the solid angle covered by the spectrometer ( @xmath94 ) is 0.141 @xmath48 0.004 sr for @xmath95 reaction assuming that the mass of @xmath0 is 1530.6 mev/@xmath4 .
scattered angles at the laboratory system range from @xmath96 to @xmath97 and the mean value of scattered angles is 8.2 @xmath98 .
reaction at beam momentum of 1.87 and 1.92gev/@xmath3 .
the theoretical calculations by t. hyodo et al .
@xcite are also shown together .
they calculated the total cross section for @xmath99 and @xmath100 using scalar and vector meson coupling constants , @xmath101 and @xmath102 , respectively .
the dot - dashed and dashed lines are calculations for @xmath103 with ( @xmath104 ) = ( 1.37 , @xmath50.23 ) and ( 1.80 , @xmath50.31 ) respectively .
the dotted and solid lines are calculations for @xmath105 with ( @xmath104 ) = ( 0.104 , @xmath50.209 ) and ( 0.22 , @xmath50.44 ) respectively .
, width=321 ] using these values , we obtained the upper limit of the differential cross section via @xmath95 reaction for 1.92 gev/@xmath3 data to be @xmath106 at 90% confidence level . assuming that @xmath42 is produced isotropically in the center of mass system , 10.4% of @xmath42 is accepted by the spectrometer . therefore ,
if the @xmath42 is produced with s - wave , the upper limit of the total cross section is obtained to be @xmath107 at 90% confidence level .
we obtained the upper limit of the cross section from the 1.87 gev/@xmath3 data as well as 1.92 gev/@xmath3 data .
because we used two different targets , we derived the upper limit for each target . from the scifi target data , the upper limit for @xmath108 and @xmath6
are obtained to be 1.7 @xmath8b / sr and 2.1 @xmath8b respectively . from the polyethylene target data , the upper limit for @xmath108 and @xmath6
are obtained to be 1.6 @xmath8b / sr and 1.8 @xmath8b respectively .
these results from the two targets are consistent each other .
the theoretical calculations for this reaction have been done by w. liu and c. m. ko @xcite and y. oh et al .
these theoretical calculations depend on the values of the form factor and coupling constants . in ref .
@xcite , liu and ko calculated the cross section taking into account only the s - channel diagrams .
they used @xmath109 , which corresponds to 20 mev/@xmath4 width of @xmath0 , and a cutoff value of @xmath110 gev for the form factor .
they predict that the cross section is about 50 @xmath8b .
y. oh et al . calculated the cross section taking into account the s - channel diagrams and t - channel diagrams where the @xmath111 is exchanged .
they used @xmath112=2.2 , which corresponds to 5 mev/@xmath4 width of @xmath0 , and the same cutoff value used by c. m. ko et al .. because there is no information about @xmath113 , they used several values from @xmath52.2 to 2.2 as @xmath113 .
the calculated cross section ranges from about 2 @xmath8b to 190 @xmath8b .
present results are quite smaller than the theoretical calculations and gives strong constraint to these unknown parameters . recently
, a theoretical study of production mechanism via hadronic reactions has been done vigorously by t. hyodo et al .
[ cross_section ] shows the obtained upper limit of the cross section for each @xmath2 beam momentum together with their theoretical calculations .
they took particular note of the importance of two meson coupling , and calculated the total cross sections of the reaction @xmath95 and @xmath114 in case of @xmath99 and @xmath100 .
they obtained the scalar and vector coupling constants of @xmath115 using the su(3 ) symmetry from the decay width of @xmath116 .
the obtained coupling constants have uncertainty due to the experimental uncertainties of the branching ratio .
they restricted the coupling constants to be consistent with our present results for the dotted , dot - dashed and dashed lines in fig .
[ cross_section ] .
the ratio of cross sections of @xmath2 and @xmath22 induced reactions can be calculated more reliably than the absolute value of the cross section . by using the coupling constant which explain the present data , they find that the ratio is very different for two @xmath117 assignments . in the case of @xmath99
the ratio of the cross section , @xmath118 , is @xmath119 50 , while in the case of @xmath120 it is @xmath119 3.3 .
an experiment to search for @xmath0 via @xmath114 has being performed at kek ( kek - ps e559 ) .
this experiment together with the present results provides deeper understanding on the existence of @xmath0 .
we have searched for @xmath0 via @xmath58 reaction with @xmath2 beams of 1.87 and 1.92 gev/@xmath3 . in the missing mass spectrum at the beam momentum of 1.87 gev/@xmath3 , no clear peak was found . at 1.92 gev/@xmath3 ,
a bump has been found at 1530.6 mev/@xmath4 .
the statistical significance of this bump is [email protected]@xmath6 which is not sufficient to claim this bump as the evidence of @xmath0 .
we have obtained the upper limit of @xmath0 production cross section via @xmath7 reaction at 90% confidence level assuming that @xmath0 is produced isotropically in the center of mass system .
the upper limit have been obtained to be 1.8 and 3.9 @xmath8b at beam momenta of 1.87 and 1.92 gev/@xmath3 , respectively .
we would like to express our thanks to staffs of kek ps and beam channel group for their support to provide beam with the excellent condition during the experiment .
we also acknowledge to t. hyodo for the theoretical discussion .
one of the authors ( k. m. ) thanks to the japan society for the promotion of science ( jsps ) for support .
the work of j.k.ahn was supported by a korea research foundation grant ( krf-2003 - 015-c00130 ) .
this work was supported by the grant - in - aid for specially promoted research ( no.15001001 ) from the ministry of education , culture , science and technology , japan
. 0 r.l .
jaffe , proc .
topical conference on baryon resonances , oxford , july 1976 , slac - pub-1774 .
t. nakano et al . , phys .
91 ( 2003 ) 012002 .
d. diakonov , v. petrov , m. polyakov , z. phys . a 359 ( 1997 ) 305 .
r. jaffe , f. wilczek , phys .
91 ( 2003 ) 232003 .
k. goeke , h .- c .
kim , m. praszalowicz and g .- s .
yang , prog .
nucl . part .
55 ( 2005 ) 350 .
diana collaboration , v. v. barmin et al .
, phys . atom .
66 ( 2003 ) 1715 .
clas collabaration , s. stepanyan et al .
lett 91 ( 2003 ) 252001 .
saphir collabaration , j. barth et al .
b 572 ( 2003 ) 127 .
clas collabaration , v. kubarovsky et al .
lett 92 ( 2004 ) 032001 .
a. e. asratyan , a. g. dolgolenko and m. a. kubantsev , phys .
67 ( 2004 ) 682 .
hermes collabaration , a. airapetian et al . ,
b 585 ( 2004 ) 213 .
zeus collabaration , s. chekanov et al .
b 591 ( 2004 ) 7 .
cosy - tof collabaration , m. abdel - bary et al .
b 595 ( 2004 ) 127 .
svd collabaration , a. aleev et al .
, arxiv : hep - ex/0401024 .
aslanyan et al . , arxiv : hep - ex/0403044 .
hyper - cp collabaration , m.j .
longo et al . , phys . rev .
d 70 ( 2004 ) 111101(r ) .
hera - b collabaration , i. abt et al .
lett 93 ( 2004 ) 212003 .
aleph collabaration , s. schael et al .
b 599 ( 2004 ) 1 .
bes collabaration , j. z. bai et al .
, phys . rev .
d 70 ( 2004 ) 012004 .
babar collabaration , b. aubert et al .
, hep - ex/0502004 .
cdf collabaration , d. o. litvintsev et al .
b ( proc . suppl . ) 142 ( 2005 ) 374 .
sphinx collabaration , yu . m. antipov et al .
j. a21 , ( 2004 ) 455 .
phenix collabaration , c. pinkerton et al . , j. phys .
g 30 ( 2004 ) s1201 .
clas collabaration , m. battaglieri et al .
lett 96 ( 2006 ) 042001 .
titov , a. hosaka , s. date , y. ohahi , phys .
c 70 ( 2004 ) 042202 .
o. i. dahl et al . , phys .
163 ( 1967 ) 1377 .
w. liu and c. m. ko , phys .
c 68 ( 2003 ) 045203 .
oh , h. kim , and s. h. lee , phys . rev .
d 69 ( 2004 ) 014009 .
y. oh , h. kim , and s. h. lee , phys . rev .
d 69 ( 2004 ) 074016 .
t. hyodo , a. hosaka , and e. oset , phys .
b 579 ( 2004 ) 290 . j.k .
ahn et al . , phys . lett .
b 444 267 ( 1998 ) .
yoon et al . , proc . of the yitp workshop
`` multi - quark hadrons ; for , five and more ? '' , http://www.slac.stanford.edu/econf/c0402171/files/manuscripts/yoon.pdf .
ahn et al . , nucl .
instr . and meth . a 457 137 ( 2001 ) .
a. ichikawa et al . , phys .
b 500 ( 2001 ) 37 . k.l .
brown et al . , cern 76 - 13 , ( 1976 ) , slac-91 , ( 1974 ) . j. myrheim and l. bugge , nucl .
methods . 160 ( 1979 )
. s. agostinelli et al . , nucl .
. methods . a 506 ( 2003 ) 250 .
a. yamamoto , kek report 81 - 13 , ( 1981 ) .
y. kondo , ph.d .
thesis , kyoto university ( 2000 ) , ( unpublished ) .
t. hyodo , and a. hosaka , phys .
c 72 ( 2005 ) 055202 . | we have searched for @xmath0 via @xmath1 reaction using 1.87 and 1.92 gev / c @xmath2 beam at the k2 beam line of the kek 12 gev proton synchrotron . in the missing mass spectrum at beam momentum of 1.92 gev/@xmath3 ,
a bump has been found at 1530 mev/@xmath4 which is consistent with the mass reported by several experiments .
the statistical significance of this bump , however , is only [email protected]@xmath6 .
therefore we have derived the upper limit of @xmath0 production cross section via @xmath7 reaction which is 3.9@xmath8b at 90% confidence level assuming that @xmath0 is produced isotropically in the center of mass system .
_ @xmath9department of physics , kyoto university , kyoto 606 - 8502 , japan + @xmath10kek , high energy accelerator research organization , tsukuba 305 - 0801 , japan + @xmath11physics department , gifu university , gifu 501 - 1193 , japan + @xmath12department of physics , osaka university , toyonaka 560 - 0043 , japan + @xmath13department of physics , osaka city university , osaka 558 - 8585 , japan + @xmath14department of physics , pusan national university , pusan 609 - 735 , korea + _ _ pacs : _ 12.39.mk ; 13.75.-n , 13.75.gx ; 14.20.-c + _ keywords : _ glueball and nonstandard multi - quark / gluon states , hadron - induced low- and intermediate - energy reaction and scattering , pion - baryon interactions , baryons | <s>[INST]in the constituent quark model , mesons and baryons are described by quark and anti - quark pair and three quarks respectively .
many hadrons known so far are described by this model very well . on the other hand ,
the existence of exotic baryons such as pentaquark and dibaryon has been suggested theoretically , because qcd requires only that hadrons should be color singlet , but does not restrict the number of quarks @xcite .
although many experimental efforts to search for these exotics were made , there was no clear evidence .
it was about 30 years later from the establishment of qcd that the first report about the exotic pentaquark , which is now called @xmath0 , was made by spring-8/leps collaboration @xcite .
they showed a peak in mass distribution of @xmath15 system via @xmath16 reaction where neutrons in @xmath17c nuclei were used as a target .
this discovery stimulated many physicists , and many works have been done from both theoretical and experimental sides .
diakonov et al . ,
using the framework of chiral soliton model , regarded @xmath0 as a member of anti - decuplet which is the third excited state of soliton field and predicted that its mass was 1530 mev/@xmath4 and the width was 15 mev/@xmath4 by treating the known @xmath18(1710 , 1/2@xmath19 ) resonance as a member of this anti - decuplet @xcite .
jaffe and wilczek proposed diquark - diquark - antiquark nature of @xmath0 in the anti - decuplet plus octet representation of su(3 ) @xcite .
many other theoretical studies such as constituent quark model , qcd sum rules and lattice qcd were devoted to @xmath0 @xcite .
experimentally , the observation at leps was immediately confirmed by several experiments @xcite .
recently , however , null results were reported from several high energy experiments where they searched for @xmath0 with much higher statistics @xcite .
most recently , clas collaboration has reported some results of a series of high statistical search for @xmath0 . in @xcite , @xmath0
was not observed and the upper limit of production cross section via @xmath20 reaction was set to be 0.8 nb .
these negative results make the existence of @xmath0 be in more puzzling situation .
however titov et al . , using quark constituent coupling rules , shows that the production of the @xmath0 is suppressed relative to the @xmath21 resonance by about three orders of magnitude for high energy experiments @xcite .
therefore , in order to confirm the existence of @xmath0 , high statistics experiments at low energy region with hadronic reaction become crucial .
many experimental data of @xmath0 are from photo - production experiments . in general the @xmath0 production cross section via hadronic reaction is expected to be much larger than that via photo - induced reaction .
now , physical properties such as spin , parity and width have not been determined experimentally yet . in order to measure these values ,
we need more statistics . from these viewpoints , the study of @xmath0 production using meson beam such as @xmath2 and @xmath22 is essential .
therefore we carried out an experiment to search for @xmath0 via @xmath23 reaction . in this reaction , the threshold momentum is 1.71 gev/@xmath3 .
we used 1.87 and 1.92 gev/@xmath3 @xmath2 beam .
the @xmath24 reaction near the @xmath0 production threshold was studied in 1960s using a bubble chamber @xcite .
the main backgrounds of the ( @xmath25 ) reaction are @xmath26 production , @xmath21 production and 3-body phase space .
the cross sections of these reactions were measured to be @xmath27 and @xmath28b respectively at beam momentum from 1.8 to 2.2 gev/@xmath3 .
it is remarkable feature that in this momentum range the background is small because other channels do not open . in this past experiment
the invariant mass of @xmath29 and @xmath30 were surveyed . any peak structure was not observed .
however numbers of @xmath29 and @xmath30 events were only 86 and 249 respectively .
the understanding of production mechanism is quite important to understand @xmath0 .
therefore a measurement of the production cross section with a simple reaction is important experimentally .
theoretically calculations with hadronic models using effective interaction lagrangians and form factors were made by several authors @xcite .
they try to understand the @xmath0 production mechanism via @xmath31 and @xmath32 reactions near the production threshold comprehensively .
the theoretical calculations predict that the @xmath0 production cross section of @xmath33 reaction ranges from several @xmath8b to several hundred @xmath8b .
however the parameters such as @xmath34 used in these calculations are not determined experimentally .
therefore these calculation should be compared with experimental data . in this letter
we report the results of an experiment to search for @xmath0 via @xmath33 reaction .
we have performed the e522 experiment at the k2 beam line of the kek 12 gev proton synchrotron in 2004 .
the main objective of this experiment was to search for h - dibaryon resonance with ( @xmath35 ) reaction .
we searched for the enhancement at the threshold region of the double-@xmath36 system , which was first measured at kek - ps e224 experiment @xcite , with much better statistics @xcite .
besides this reaction , we optionally took @xmath37 data , because the @xmath0 search via mesonic reaction became crucial to confirm its existence and the k2 beam line is a unique beam line which can provide up to 2 gev/@xmath3 @xmath38 beam .
we used a @xmath2 beam of 1.87 and 1.92 gev/@xmath3 . as a target
, we used a scintillation fiber ( scifi ) target ( @xmath39 ) and a bulk target of polyethylene ( @xmath40 ) .
the scifi target is 20 cm long , and is the same one used in the hyperon - nucleon scattering experiment ( kek - ps e289 ) @xcite .
it was mainly used to detect decay particles from @xmath41 reaction for the h - dibaryon resonance search . for ( @xmath25 ) data
, we mainly used the 10 cm long polyethylene target to enhance the contribution from free protons .
the scifi target was also used to detect tracks of the charged particles other than @xmath42 produced by reactions . at the beam momentum of 1.87 gev/@xmath3 , 2.9@xmath43 and 3.0@xmath43 @xmath2 beam particles
were irradiated to the scifi and the polyethylene targets respectively . at 1.92 gev/@xmath3 ,
7.4@xmath43 @xmath2 beam particles were irradiated to only the polyethylene target . for the calibration we took the following data . in order to estimate the contribution from carbon in the scifi and polyethylene targets , we took data with a carbon target .
the ( @xmath44 ) data were analyzed to measure the @xmath45 peak position for the calibration of the missing mass spectrum .
the experimental setup consisted of two parts ; one part was a beam line spectrometer to analyze momentum of each incident beam particle and the other part was a forward spectrometer to detect scattered particles .
the set up was almost similar to the one used at kek - ps e373 experiment and detail of the experimental setup is described elsewhere @xcite .
the k2 beam line is designed to transport charged particles up to 2.0 gev/@xmath3 .
[ kuramasp ] ( a ) shows the beam line spectrometer .
the @xmath2 beam was bent by 15 degree at the bending magnet ( d2 ) and focused at the target by two quadrapole magnets ( q6 , q7 ) .
the typical intensity of @xmath2 was 330k counts during 2 sec .
spill with a primary proton beam of @xmath46 .
each beam particle was defined by the hit of t1 and t2 counters placed about 7.2 m apart each other and @xmath2 was selected at a trigger by two aerogel cherenkov counters ( bac1,2 ) , of which threshold velocity was 0.971 , placed just upstream of the t2 counter .
the beam momentum was analyzed with 5 wire chambers placed upstream and downstream of the d2 magnet . the momentum resolution is estimated to be @xmath47 mev/@xmath3 from a simulation . between two quadrapole magnets ( q6 , q7 ) and the target , 3 proportional chambers were placed to measure the beam direction .
the timing for all detectors was determined by the t2 counter .
the scattered particles were detected by the forward spectrometer shown in fig .
[ kuramasp ] ( b ) .
the kurama magnet is 80 cm long and the magnetic field strength is 0.93 t . the momentum of each scattered particle was measured using 3 drift chambers ( dc1,2,3 ) and scintillation hodoscopes ( vh , ch ) placed upstream and downstream of kurama .
the momentum resolution was 1.9 % ( r.m.s . ) for 0.8 gev/@xmath3 @xmath42 .
the time - of - flight of each scattered particle was measured by a tof wall ( ftof ) placed at end of the spectrometer .
a typical time resolution was 132 ps .
two cherenkov counters ( bvac , fac ) were installed between the target and kurama to veto @xmath2 . besides this particle identification with these cherenkov counters at the trigger level , we selected the charge and momentum range of each scattered particle at 1st trigger level using the hit combination of each segments of ch hodoscope and ftof .
momentum of each particle was determined using the hit combination . by combining time - of - flight information of the hit ftof segment with this momentum information
, the mass of each scattered particle was roughly calculated .
we selected @xmath42 with this mass trigger ( mt ) at 2nd trigger level .
this mass trigger rejected mainly @xmath2 which survived due to the inefficiency of the cherenkov counters . in the offline analysis , mass and momentum of each scattered particle are calculated more accurately as shown in fig .
the @xmath42 mesons are clearly identified .
mesons were selected cleanly .
, width=264 ]
+ cc cut & efficiency(% ) + + time - of - flight cut & 93.8 @xmath48 0.1 + beam @xmath49 cut & 84.6 @xmath48 0.1 + beam momentum cut & 94.8 @xmath48 0.1 + + mass - momentum cut & @xmath50 + runge - kutta @xmath49 cut & [email protected] + + vertex cut & 92.8@xmath48 0.5 + closest distance cut & 97.8 @xmath480.1 + total & [email protected] + we describe the analysis procedure to search for @xmath0 from the missing mass spectrum of the @xmath37 reaction . to obtain this spectrum
, we applied the following cuts ; 1 ) selection of @xmath2 in the beam and momentum analysis , 2 ) identification of the scattered @xmath42 and momentum analysis , and 3 ) selection of the reaction vertex point .
the efficiencies of these cuts in the analysis , which are described in detail in the following paragraphs , are summarized in table [ tab : summary_ana_eff ] .
the efficiencies of the track - finding routine are described in the next section and listed in table [ tab : summary_eff ] .
the incident @xmath2 was identified using time - of - flight information between t1 and t2 .
the contamination of @xmath42 was negligible , and we selected @xmath51 region of its time resolution ( 70ps ) as good events .
each incident @xmath2 momentum was calculated by fitting the hit positions at the beam line chambers ( bdc1,2,3 and bpc1,2 ) with second order transfer matrix calculated by transport @xcite .
the @xmath49 distribution of this fitting was consistent with the expectation except a tail towards large @xmath49 .
we selected c.l.=95% region for @xmath49 cut whose efficiency was 84.6 % as the result of rejecting the large @xmath49 events .
the event whose beam momentum was less than 1.8 gev/@xmath3 or larger than 2.0 gev/@xmath3 was rejected considering the momentum acceptance of the beam line .
trajectories of outgoing particles were reconstructed by using the information of hit positions at the drift chambers ( dc1 - 3 ) and the hodoscopes ( vh , ch ) and of the field map in kurama .
at first , the local tracks upstream and downstream of kurama were searched by the straight - line fittings , and the consistency between these local tracks were checked to reject the decay events of @xmath42 .
then we used runge - kutta method for the momentum analysis @xcite .
the scattered @xmath42 s were selected by the momentum dependent mass cut and we selected 3@xmath6 region as shown in fig [ mass ] .
the contamination of @xmath2 after this cut was about 3% . in the ( @xmath25 ) reaction ,
the momenta of scattered @xmath42 ranged from 0.4 to 1.1 gev/@xmath3 .
therefore the effect of multiple scattering made the @xmath49 distribution of runge - kutta tracking broader than the ideal one . to study the cut position of @xmath49 cut , we compared with the distribution obtained by the monte carlo simulation based on geant4 @xcite which included all materials of the spectrometer and the electro - magnetic process , the hadoronic process and the decay process .
the simulated @xmath49 distribution reproduces real data except a long tail towards large @xmath49 , not only for ( @xmath25 ) reaction but also for ( @xmath44 ) and ( @xmath35 ) reactions where the typical momenta of @xmath22 were around 1.6 and 1.2 gev/@xmath3 respectively . from this study , we selected @xmath52 region where the @xmath49 distribution was consistent with the simulation . in the momentum reconstruction ,
energy loss effect in the materials of the spectrometer was not taken into account .
the energy loss in the target was corrected using the reconstructed momenta of the incident and outgoing particles with their directions and the calculated vertex positions .
the vertex point was calculated by the closest distant point between tracks of beam and outgoing particles .
we required the vertex point to be less than 80 mm from the target center .
the beam size ( 1.4 @xmath53 1.3 @xmath54 ) was small enough in comparison with the target size . because the scifi target enabled us to see particle trajectories as image data , we could estimate the efficiency of this vertex cut precisely by comparing the vertex position calculated by the spectrometer with one obtained in the image data .
the efficiency of this cut was estimated to be 92.8 @xmath48 0.5 % .
we also checked the distribution of the closest distance between tracks of beam and outgoing particles at the vertex point .
the events where the closest distance was greater than 7 mm , which corresponded to 3@xmath6 , were rejected considering that beam or outgoing particles reacted more than 2 times in the target .
[ missmass_pi+k ] shows the missing mass spectrum of the ( @xmath44 ) reaction at the beam momentum of 1.92 gev/@xmath3 .
the peak due to @xmath45 is clearly observed .
the beam momentum was normalized so as to make the obtained @xmath45 peak consistent with the pdg value .
we fitted this spectrum with two gaussian peaks assuming that the broad peak was attributed to quasi - free protons in carbon and the narrow one was attributed to free protons .
the obtained width was [email protected] mev/@xmath4 ( fwhm ) which was almost consistent with the expected value of 28.3 mev/@xmath4 from the simulation . to estimate the missing mass resolution in the simulation , the position resolutions of the drift chambers , the momentum resolution of the beam spectrometer and the effects of the energy loss and the multiple scattering in materials for incident and outgoing particles
were taken into account .
using the same program code , the missing mass resolution for @xmath0 was estimated to be 13.4 mev/@xmath4 ( fwhm ) . in @xmath0 production , the momentum of the outgoing particle is much lower than that in the @xmath45 production . therefore the missing mass resolution is better for @xmath0 . )
reaction with a polyethylene target .
the beam momentum was adjusted so as to make the obtained @xmath45 peak consistent with the pdg value .
the hatched spectrum is the expected spectrum from the simulation .
the obtained peak width of 33.3 @xmath48 4.8 mev/@xmath4 ( fwhm ) is almost same with the expected value 28.3 mev/@xmath4 .
, width=264 ]
the missing mass spectra for each beam momentum are shown in fig .
[ missmass_pi - k ] . in order to know the contribution from carbon nuclei in the scifi and polyethylene targets ,
carbon target data are also shown as the hatched spectra , which are normalized by the number of beam particle and the number of carbon nuclei in each target .
the statistics of the carbon target data is about ten times lower than that of ch@xmath55 data .
the net contribution from free protons is compatible with the expectation from the cross sections of background reactions measured in @xcite .
because half of data at beam momentum of 1.87 gev/@xmath3 was taken with the scifi target , the contribution from free protons at 1.87 gev/@xmath3 is smaller than that at 1.92 gev/@xmath3 . )
reaction at 1.92 gev/@xmath3 .
( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this
fitting , the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line .
, title="fig:",width=302 ] ) reaction at 1.92 gev/@xmath3 .
( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this fitting ,
the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line . , title="fig:",width=302 ] ) reaction at 1.92 gev/@xmath3 . ( a ) we fitted this spectrum with third order polynomial background and a gaussian peak ( solid line ) . in this
fitting , the width was a parameter and obtained to be @xmath56 mev/@xmath4 ( fwhm ) which was consistent with the expected value of 13.4 mev/@xmath57 within the error .
we also executed the fitting with the fixed width of 13.4 mev/@xmath4 ( see text ) .
the dashed line represents the fitting result with only third order polynomial background assuming that there is no peak structure .
( b ) residual plot from the background function obtained from the fitting with third order polynomial background and a gaussian peak .
the difference between backgrounds obtained from two fits , gaussian peak plus background and background only , was represented by the solid line .
, width=340 ] fig .
[ missmass_pi - k ] ( a ) shows the missing mass spectrum of the @xmath37 reaction at 1.87 gev/@xmath3 . in this spectrum ,
data for the scifi target and the polyethylene target are combined .
any peak was not observed in this spectrum . fig .
[ missmass_pi - k ] ( b ) shows the missing mass spectrum of @xmath58 reaction at 1.92 gev/@xmath3 .
it seems that there is a bump around 1.53 gev/@xmath57 .
however there is a possibility that the structure is only a statistical fluctuation .
we fitted this histogram with the background of a cubic function and a gaussian peak ( see fig .
[ fit_missmass_pi - k ] ) .
the peak position is 1530.6 @xmath59(stat.)@xmath60(syst . )
mev/@xmath4 , the width is @xmath61=9.8@xmath62 mev/@xmath4 ( fwhm ) and the count of the peak is 139@xmath63(stat.)@xmath4810(syst . ) .
the uncertainty of count resulting from varying the fitting range and binning is considered as the systematic error .
the obtained width is consistent with the expected value of 13.4 mev/@xmath4 within the error .
we also fitted this spectrum with the fixed width of 13.4 mev/@xmath4 .
the count of this bump was obtained to be 183@xmath4871(stat.)@xmath4810(syst . ) .
the statistical significance of this bump was considered by two expressions .
the first expression is the naive estimator @xmath64 where @xmath65 is the peak count within 2@xmath6 region from the center and @xmath66 is the background within the same region , and the significance is 2.7@xmath6 .
the second estimate of significance is given by @xmath67 , where @xmath68 is full area of the bump from the fit and @xmath69 is its fully correlated uncertainty .
the significance of 2.5@xmath6 is obtained by the second expression .
we fitted the histogram with only the background of a cubic function assuming that there is no peak structure .
the fitting result is shown by a dashed line in fig .
[ fit_missmass_pi - k ] .
the statistical significance of the bump from this background is estimated to be 1.9@xmath6 using the first expression , @xmath70 .
the statistical significance obtained in the present experiment is not sufficient to claim this bump as the evidence of @xmath0 .
however it is quite important to estimate the upper limit of the production cross section of @xmath0 via the @xmath71 reaction .
therefore we have obtained the upper limit of the production cross section . to derive the upper limit ,
the peak count obtained from the fitting with the fixed width is used at beam momentum of 1.92 gev/@xmath3 .
we used a single tail approach assuming that the peak count fluctuates based on gaussian statistics .
then the upper limit of the peak count is @xmath72=274 at 90% confidence level , where @xmath68 denotes the peak count obtained from the fitting and @xmath73 , @xmath74 denote the statistical and systematic errors respectively , and we use this count for the following calculations . in the missing mass spectrum at 1.87 gev/@xmath3
, we could not find any obvious peak structure .
we estimated that the signal from @xmath0(@xmath75 ) is less than 1.28@xmath76 at 90 % confidence level , where @xmath77 represents the count in the missing mass spectrum corresponding to @xmath78 region from the peak position ( 1530.6 mev/@xmath4 ) obtained from 1.92 gev/@xmath3 data .
we calculated that @xmath75 were 62 and 52 for the scifi target and the polyethylene target , respectively .
the production cross section of @xmath0 was calculated by the following equation .
@xmath79 here @xmath80 and @xmath81 represent the number of @xmath0 , beam particles and protons in the target .
the solid angle covered by kurama spectrometer at laboratory frame is represented by d@xmath82 .
others represent various efficiencies , and are summarized in table[tab : summary_eff ] .
+ .summary of the various efficiencies for the calculation of the production cross section . [ cols="^,^,^ " , ] the coefficient @xmath83 is the correction factor to obtain the number of real @xmath2 . in this experiment , we could not distinguish @xmath84 and @xmath85 from @xmath2 .
we referred the past experiment where a gas cherenkov counter was used to distinguish @xmath84 and @xmath85 and estimated that this contamination was 12.4% @xcite .
we also calculated the reaction rate of @xmath2 in the target with geant simulation and obtained to be 4% .
adding these value , we estimated that @xmath83 was 83.6% .
the efficiencies of track - finding routines used in the analysis program for beam and scattered particles have to be estimated , because routines have criteria to find tracks such as minimum number of hit chambers and can not find out a part of tracks due to the inefficiency of the drift chambers or multi charged hit events .
the coefficient @xmath86 is the track - finding efficiency for beam particles and obtained to be 72.7% .
the reason for the inefficiency is mainly due to the dead channel of bdc3 .
the coefficient @xmath87 is the track - finding efficiency for scattered particles and obtained to be 84.6% by analyzing the data produced by the monte carlo simulation with the same analysis program .
the validity of this estimation was checked using scattered proton events taken with ( @xmath35 ) trigger data .
the scattered protons could be selected by using information of hit combination of ch and ftof counters and of time - of - flight without tracking .
we estimated the track - finding efficiency by analyzing such pre - selected proton events .
results obtained from the simulated events and pre - selected proton events were consistent within 2.0% which denoted the error of the efficiency .
the coefficient @xmath88 represents the correction factor due to the overkilling rate of the cherenkov counters ( bvac , fac ) which was 9.2% .
therefore @xmath88 was obtained to be 90.8% .
the coefficients , @xmath89 and @xmath90 , represent the correction factors due to the decay rate before arriving ftof wall and the interaction rate of @xmath42 in the materials of the target and the forward spectrometer respectively .
these factors were also calculated with the monte carlo simulation based on geant4 and obtained to be 57.6% and 89.8% respectively .
the coefficients , @xmath91 and @xmath92 , are the efficiencies of the daq system and 2nd level mass trigger , and obtained to be 93.5% and 95.7% respectively .
the coefficient @xmath93 is the analysis cut efficiency and summarized in table[tab : summary_ana_eff ] and estimated to be 49.6% .
finally , the solid angle covered by the spectrometer ( @xmath94 ) is 0.141 @xmath48 0.004 sr for @xmath95 reaction assuming that the mass of @xmath0 is 1530.6 mev/@xmath4 .
scattered angles at the laboratory system range from @xmath96 to @xmath97 and the mean value of scattered angles is 8.2 @xmath98 .
reaction at beam momentum of 1.87 and 1.92gev/@xmath3 .
the theoretical calculations by t. hyodo et al .
@xcite are also shown together .
they calculated the total cross section for @xmath99 and @xmath100 using scalar and vector meson coupling constants , @xmath101 and @xmath102 , respectively .
the dot - dashed and dashed lines are calculations for @xmath103 with ( @xmath104 ) = ( 1.37 , @xmath50.23 ) and ( 1.80 , @xmath50.31 ) respectively .
the dotted and solid lines are calculations for @xmath105 with ( @xmath104 ) = ( 0.104 , @xmath50.209 ) and ( 0.22 , @xmath50.44 ) respectively .
, width=321 ] using these values , we obtained the upper limit of the differential cross section via @xmath95 reaction for 1.92 gev/@xmath3 data to be @xmath106 at 90% confidence level . assuming that @xmath42 is produced isotropically in the center of mass system , 10.4% of @xmath42 is accepted by the spectrometer . therefore ,
if the @xmath42 is produced with s - wave , the upper limit of the total cross section is obtained to be @xmath107 at 90% confidence level .
we obtained the upper limit of the cross section from the 1.87 gev/@xmath3 data as well as 1.92 gev/@xmath3 data .
because we used two different targets , we derived the upper limit for each target . from the scifi target data , the upper limit for @xmath108 and @xmath6
are obtained to be 1.7 @xmath8b / sr and 2.1 @xmath8b respectively . from the polyethylene target data , the upper limit for @xmath108 and @xmath6
are obtained to be 1.6 @xmath8b / sr and 1.8 @xmath8b respectively .
these results from the two targets are consistent each other .
the theoretical calculations for this reaction have been done by w. liu and c. m. ko @xcite and y. oh et al .
these theoretical calculations depend on the values of the form factor and coupling constants . in ref .
@xcite , liu and ko calculated the cross section taking into account only the s - channel diagrams .
they used @xmath109 , which corresponds to 20 mev/@xmath4 width of @xmath0 , and a cutoff value of @xmath110 gev for the form factor .
they predict that the cross section is about 50 @xmath8b .
y. oh et al . calculated the cross section taking into account the s - channel diagrams and t - channel diagrams where the @xmath111 is exchanged .
they used @xmath112=2.2 , which corresponds to 5 mev/@xmath4 width of @xmath0 , and the same cutoff value used by c. m. ko et al .. because there is no information about @xmath113 , they used several values from @xmath52.2 to 2.2 as @xmath113 .
the calculated cross section ranges from about 2 @xmath8b to 190 @xmath8b .
present results are quite smaller than the theoretical calculations and gives strong constraint to these unknown parameters . recently
, a theoretical study of production mechanism via hadronic reactions has been done vigorously by t. hyodo et al .
[ cross_section ] shows the obtained upper limit of the cross section for each @xmath2 beam momentum together with their theoretical calculations .
they took particular note of the importance of two meson coupling , and calculated the total cross sections of the reaction @xmath95 and @xmath114 in case of @xmath99 and @xmath100 .
they obtained the scalar and vector coupling constants of @xmath115 using the su(3 ) symmetry from the decay width of @xmath116 .
the obtained coupling constants have uncertainty due to the experimental uncertainties of the branching ratio .
they restricted the coupling constants to be consistent with our present results for the dotted , dot - dashed and dashed lines in fig .
[ cross_section ] .
the ratio of cross sections of @xmath2 and @xmath22 induced reactions can be calculated more reliably than the absolute value of the cross section . by using the coupling constant which explain the present data , they find that the ratio is very different for two @xmath117 assignments . in the case of @xmath99
the ratio of the cross section , @xmath118 , is @xmath119 50 , while in the case of @xmath120 it is @xmath119 3.3 .
an experiment to search for @xmath0 via @xmath114 has being performed at kek ( kek - ps e559 ) .
this experiment together with the present results provides deeper understanding on the existence of @xmath0 .
we have searched for @xmath0 via @xmath58 reaction with @xmath2 beams of 1.87 and 1.92 gev/@xmath3 . in the missing mass spectrum at the beam momentum of 1.87 gev/@xmath3 , no clear peak was found . at 1.92 gev/@xmath3 ,
a bump has been found at 1530.6 mev/@xmath4 .
the statistical significance of this bump is [email protected]@xmath6 which is not sufficient to claim this bump as the evidence of @xmath0 .
we have obtained the upper limit of @xmath0 production cross section via @xmath7 reaction at 90% confidence level assuming that @xmath0 is produced isotropically in the center of mass system .
the upper limit have been obtained to be 1.8 and 3.9 @xmath8b at beam momenta of 1.87 and 1.92 gev/@xmath3 , respectively .
we would like to express our thanks to staffs of kek ps and beam channel group for their support to provide beam with the excellent condition during the experiment .
we also acknowledge to t. hyodo for the theoretical discussion .
one of the authors ( k. m. ) thanks to the japan society for the promotion of science ( jsps ) for support .
the work of j.k.ahn was supported by a korea research foundation grant ( krf-2003 - 015-c00130 ) .
this work was supported by the grant - in - aid for specially promoted research ( no.15001001 ) from the ministry of education , culture , science and technology , japan
. 0 r.l .
jaffe , proc .
topical conference on baryon resonances , oxford , july 1976 , slac - pub-1774 .
t. nakano et al . , phys .
91 ( 2003 ) 012002 .
d. diakonov , v. petrov , m. polyakov , z. phys . a 359 ( 1997 ) 305 .
r. jaffe , f. wilczek , phys .
91 ( 2003 ) 232003 .
k. goeke , h .- c .
kim , m. praszalowicz and g .- s .
yang , prog .
nucl . part .
55 ( 2005 ) 350 .
diana collaboration , v. v. barmin et al .
, phys . atom .
66 ( 2003 ) 1715 .
clas collabaration , s. stepanyan et al .
lett 91 ( 2003 ) 252001 .
saphir collabaration , j. barth et al .
b 572 ( 2003 ) 127 .
clas collabaration , v. kubarovsky et al .
lett 92 ( 2004 ) 032001 .
a. e. asratyan , a. g. dolgolenko and m. a. kubantsev , phys .
67 ( 2004 ) 682 .
hermes collabaration , a. airapetian et al . ,
b 585 ( 2004 ) 213 .
zeus collabaration , s. chekanov et al .
b 591 ( 2004 ) 7 .
cosy - tof collabaration , m. abdel - bary et al .
b 595 ( 2004 ) 127 .
svd collabaration , a. aleev et al .
, arxiv : hep - ex/0401024 .
aslanyan et al . , arxiv : hep - ex/0403044 .
hyper - cp collabaration , m.j .
longo et al . , phys . rev .
d 70 ( 2004 ) 111101(r ) .
hera - b collabaration , i. abt et al .
lett 93 ( 2004 ) 212003 .
aleph collabaration , s. schael et al .
b 599 ( 2004 ) 1 .
bes collabaration , j. z. bai et al .
, phys . rev .
d 70 ( 2004 ) 012004 .
babar collabaration , b. aubert et al .
, hep - ex/0502004 .
cdf collabaration , d. o. litvintsev et al .
b ( proc . suppl . ) 142 ( 2005 ) 374 .
sphinx collabaration , yu . m. antipov et al .
j. a21 , ( 2004 ) 455 .
phenix collabaration , c. pinkerton et al . , j. phys .
g 30 ( 2004 ) s1201 .
clas collabaration , m. battaglieri et al .
lett 96 ( 2006 ) 042001 .
titov , a. hosaka , s. date , y. ohahi , phys .
c 70 ( 2004 ) 042202 .
o. i. dahl et al . , phys .
163 ( 1967 ) 1377 .
w. liu and c. m. ko , phys .
c 68 ( 2003 ) 045203 .
oh , h. kim , and s. h. lee , phys . rev .
d 69 ( 2004 ) 014009 .
y. oh , h. kim , and s. h. lee , phys . rev .
d 69 ( 2004 ) 074016 .
t. hyodo , a. hosaka , and e. oset , phys .
b 579 ( 2004 ) 290 . j.k .
ahn et al . , phys . lett .
b 444 267 ( 1998 ) .
yoon et al . , proc . of the yitp workshop
`` multi - quark hadrons ; for , five and more ? '' , http://www.slac.stanford.edu/econf/c0402171/files/manuscripts/yoon.pdf .
ahn et al . , nucl .
instr . and meth . a 457 137 ( 2001 ) .
a. ichikawa et al . , phys .
b 500 ( 2001 ) 37 . k.l .
brown et al . , cern 76 - 13 , ( 1976 ) , slac-91 , ( 1974 ) . j. myrheim and l. bugge , nucl .
methods . 160 ( 1979 )
. s. agostinelli et al . , nucl .
. methods . a 506 ( 2003 ) 250 .
a. yamamoto , kek report 81 - 13 , ( 1981 ) .
y. kondo , ph.d .
thesis , kyoto university ( 2000 ) , ( unpublished ) .
t. hyodo , and a. hosaka , phys .
c 72 ( 2005 ) 055202 .[/INST] we have searched for @xmath0 via @xmath1 reaction using 1.87 and 1.92 gev / c @xmath2 beam at the k2 beam line of the kek 12 gev proton synchrotron . in the missing mass spectrum at beam momentum of 1.92 gev/@xmath3 ,
a bump has been found at 1530 mev/@xmath4 which is consistent with the mass reported by several experiments .
the statistical significance of this bump , however , is only [email protected]@xmath6 .
therefore we have derived the upper limit of @xmath0 production cross section via @xmath7 reaction which is 3.9@xmath8b at 90% confidence level assuming that @xmath0 is produced isotropically in the center of mass system .
_ @xmath9department of physics , kyoto university , kyoto 606 - 8502 , japan + @xmath10kek , high energy accelerator research organization , tsukuba 305 - 0801 , japan + @xmath11physics department , gifu university , gifu 501 - 1193 , japan + @xmath12department of physics , osaka university , toyonaka 560 - 0043 , japan + @xmath13department of physics , osaka city university , osaka 558 - 8585 , japan + @xmath14department of physics , pusan national university , pusan 609 - 735 , korea + _ _ pacs : _ 12.39.mk ; 13.75.-n , 13.75.gx ; 14.20.-c + _ keywords : _ glueball and nonstandard multi - quark / gluon states , hadron - induced low- and intermediate - energy reaction and scattering , pion - baryon interactions , baryons </s> |
tuberculosis ( tb ) has been declared a global health emergency by the world health organization ( who ) .
it is estimated that about one third of the worlds population is currently infected with the responsible actinobacteria mycobacterium tuberculosis ( mtb).1 resistance of mtb to available antibiotics has increased drastically , and multidrug - resistant ( mdr ) strains of mtb as well as extensively drug - resistant ( xdr ) strains are becoming a major health problem worldwide.1 furthermore , cases have recently been reported where no available first- and second - line drugs are effective , and this has led to the term totally drug - resistant ( tdr ) tb.2 resistant strains of mtb require longer treatment , which may lead to interruption of therapy and , in turn , lead to further drug resistance . the usual drug regimen for tb at present consists of antibiotics discovered more than 60 years ago , and includes isoniazid , rifampicin , pyrazinamide , and ethambutol.3 these antibiotics act by disruption of cell wall synthesis4 and inhibition of rna synthesis.4c-5 it was quickly discovered that monotherapy led to resistance in the bacteria , and therefore the recommended tb treatment today utilizes a combination of the four first - line drugs for two months , and thereafter a pharmacotherapy with rifampicin and isoniazid for an additional four months.3 considering the long treatment time , the adverse effects associated with the drugs , and the problems with resistant strains , it is clear that there is a great need for novel antibiotics that possess new antitubercular modes of action and that can be used in combination with existing drugs .
proteasomes are responsible for degrading proteins , and so help maintain intracellular protein homeostasis.6 the human proteasome consists of a cylindrical 26s particle composed of a 20s core catalytic component capped at one or both ends with a 19s regulatory subunit , which recognizes and binds the substrate protein . in eukaryotic proteasomes , the 20s core particle is composed of four heptameric rings , of which the two inner rings are made up of seven different -subunits , with only three of them responsible for the proteolytic activity ( 1 , 2 , 5 , with peptidyl - glutamyl - peptide - hydrolyzing , trypsin - like and chymotrypsin - like activities , respectively).7 the mtb proteasome displays the same overall structure as the proteasomes of eukaryotic systems.8 however , prokaryotic 20s proteasomes , including those from mtb , have been shown to have open cylindrical ends , in contrast to the tighter ends of eukaryotic proteasomes , and possess only one type of -subunit , usually resembling the eukaryotic 5 chymotrypsin - like structure.8,9 proteolytic activity involves the -hydroxyl group of the n - terminal threonine , which is present in the active site of proteasome subunits.7a7d in many diseases , such as cancer , auto - immune diseases , and neurodegenerative diseases , cells accumulate various proteins , and the human proteasome has thus emerged as a promising therapeutic target.6a,7a the first human proteasome inhibitor , bortezomib ( velcade ) , was approved for clinical use in the usa in 2003 and in europe in 2004 for the treatment of multiple myeloma ( figure 1 ) .
the x - ray structure of the yeast proteasome in complex with the compound was reported in 2006 , giving valuable insights into its binding interactions.10 serious toxicity associated with peptidyl boronates , such as bortezomib , is mainly due to the inhibition of the 5 subunit of the human proteasome,11 precluding the use for treatment of , for example , infectious diseases .
therefore , the search for alternative classes of inhibitors with greater selectivity towards prokaryotic proteasomes is ongoing .
proteasomes have been shown to be of great importance to mtb ; they help the bacteria survive the nitrosative stress caused by the hosts immune response12 and increase their ability to persist in infected mice.13 furthermore , the actinobacteria are unusual among prokaryotes in that they express proteasomes , meaning that selective action against bacteria of this phylum should be possible.6b,14 it is particularly interesting that proteasome inhibitors have been shown to be active on nonreplicating mtb .
this is important since nonreplicating mtb ( which to a large extent underlie the need for long treatment times ) , display reduced protein synthesis , and are left unaffected by most antitranscription or antitranslation agents currently used for treatment.15 only a few classes of compounds have proven to be active on nonreplicating mtb , for example , oxathiazol-2-ones , quinolones , and allylic thiocyanates.7c,16 mtb proteasome inhibitors displaying species selectivity , thus low associated toxicity , are promising candidates for the development of new antitubercular drugs .
have previously reported that the 1,3,4-oxathiazol-2-one compounds ht1171 and gl5 ( figure 1 ) act as suicide - substrate inhibitors of the mtb proteasome displaying high selectivity over the human proteasome and other proteases , including trypsin , cathepsin b , and matrix metalloproteases.7c they demonstrated that the oxathiazol-2-one moiety acts as an electrophilic warhead , such that the active - site nucleophile , the n - terminal threonine residue , is effectively cyclocarbonylated by an irreversible covalent attack on the heterocycle.7c,8b moreover , oxathiazolones have been reported to have antimycobacterial activity when they were exploited as carboxylic acid bioisosteres in substituted pyridines and pyrazines.17 in an attempt to identify a new generation of species - selective proteasome inhibitors , gryder et al . investigated the effect of replacing the boronate group on the dipeptide backbone of bortezomib with an oxathiazol-2-one moiety .
unfortunately , the resulting compound was not active on the mtb proteasome and only slightly active on the human 20s proteasome.18 more recently , yang et al
. assessed the antitubercular activity of a series of gl5-type oxathiazol-2-ones , together with their dithiazol-3-one analogues , on the virulent mtb h37rv strain , achieving a lowest minimum inhibitory concentration ( mic ) value of 4 g ml ( 15 m ) for ht1171.16 g these compounds also possessed mycobacterial cell wall permeation properties , and were active against nonreplicating mtb .
they have therefore been proposed as highly interesting antitubercular agents for the synergistic combination treatment of tb.7c in the present study , we further investigate the structure activity relationships of 1,3,4-oxathiazol-2-one derivatives with respect to both their potency as mtb proteasome inhibitors and their selectivity over the chymotrypsin - like catalytic activity of the human proteasome as an early assessment of potential toxicity .
furthermore , the compounds were optimized with regard to solubility and stability . finally , activity against replicating and nonreplicating mtb and cytotoxicity to mammalian cells
in a first effort to investigate the chemical space , a wide variety of oxathiazol-2-ones were prepared from the corresponding commercially available amides by treatment with chlorocarbonyl sulfenyl chloride at 100 c for 15 min with microwave ( mw ) heating ( method a ) or at room temperature overnight ( method b ) .
isolated products were thereafter evaluated for proteasome inhibition based on the assay procedures described by lin et al.7c ( table 1 , entries 123 ) .
compounds were tested for chymotrypsin - like peptidase activity against both the mtb 20s open - gate proteasome ( in which the alpha subunit has an 8-residue deletion at the n - terminus , as described by lin et al.8a ) and the human 20s proteasome , tracked by cleavage of the fluorogenic substrate suc - llvy-7-amino-4-methylcoumarin .
method a reagents and conditions : amide ( 1.0 equiv ) , chlorocarbonyl sulfenyl chloride ( 1.5 equiv ) , 1,4-dioxane ( 4.0 ml mmol ) , 100 c mw , 15 min .
method b : amide ( 1.0 equiv ) , chlorocarbonyl sulfenyl chloride ( 2.0 equiv ) , thf ( 4.0 ml mmol ) , rt , o / n . [ a ] chemical stability in pbs ph 7.4 at 25 c as % remaining after 24 h. [ b ] the amide was prepared , and
[ c ] reagents and conditions : 14 ( 1.0 mmol ) , dess
martin periodinane ( 1.1 mmol ) , ch2cl2 ( 5 ml ) , 0 c , 2 h. [ d ] general method for the synthesis of 3-substituted dioxazolones .
reagents and conditions : starting hydroxamic acid ( 1.0 equiv ) , 1,1-carbonyldiimidazole ( 1.1 equiv ) , ch3cn ( 4.0 ml mmol ) , 0 c , 1 h. [ e ] the hydroxamic acid was prepared and used as starting material for the dioxazolone synthesis without further purification .
the 5-aryl - substituted 1,3,4-oxathiazol-2-ones in entries 14 ( table 1 , 14 ) have previously been reported as inhibitors of the mtb proteasome.19 to further develop the core structure , we decided to find out if elongated compounds with different spacers could have a positive impact on the activity . for this purpose ,
various tethers between the aryl and the heterocyclic warhead were introduced in the 5-position , for example , alkene , alkyne , and methylene linkers .
we found that an sp - hybridized carbon directly coupled to the oxathiazol-2-one ring in the 5-postion was crucial for the compounds activity .
additionally , the introduction of the ( e)-alkene linker ( entries 1718 ) gave inhibitors equally or more potent ( 17 and 18 ; ic50=420 and 640 nm , respectively ) toward the mtb proteasome compared to when the aryl was substituted directly onto the oxathiazol-2-one ( 14 ) .
more importantly , this type of compound was not active on the human proteasome ( ic50>100 000 nm ) . for compounds with an alkyne- or carbonyl - containing spacer ( 19 and 20 ) ,
the activities on the mtb proteasome were slightly lower compared to olefinic inhibitors 17 and 18 .
moreover , these linkers provided less selective inhibitors . when an sp - hybridized carbon was used as a linker atom , no activity
was obtained against the mtb proteasome , and little or no inhibition was seen towards the human proteasome ( entries 916 ) .
interestingly , when an ethyl bridge was introduced instead of the double bond between the phenyl and oxathiazol-2-one ( compare moieties 15 and 17 ) , no inhibition was observed for the mtb proteasome , but the saturated compound instead gained some activity toward the human proteasome .
this suggests that the ( e)-double bond is important both for the mycobacterial inhibition and the selectivity over the human proteasome .
however , the allowed substitution pattern of the ( e)-alkene linker seems to be slightly constrained ; when an additional phenyl group was introduced onto the ethylene linker , no activity was detected against the mtb proteasome ( entry 23 ) . instead , compound 23 became a more potent inhibitor of the human proteasome .
the aryl group of the styryl moiety also seems to be important for the interaction with the mtb protein . when a vinyl group was substituted onto the oxathiazol-2-one , the activity decreased from 420 nm for 17 to 27 000 nm for 21 .
the effect is probably due to the lack of an aryl group as well as the effect of the hybridization of the carbon directly attached to the oxathiazol-2-one . to summarize the results depicted in table 1
, it appears that an aryl group conjugated with the oxathiazolone scaffold is highly beneficial for the inhibition of the mtb proteasome ( see products 14 and 1722 ) , and in particular high selectivity over the human proteasome is caused by the presence of the ( e)-alkene linker ( 17 and 18 ) .
this may also be coupled to the loss of activity for the unconjugated 15 . to increase the scope of the investigation
, we wished to evaluate other heterocyclic warheads such as the dioxazolones ( table 1 , entries 2425 ) , but these compounds suffered from poor stability due to rapid hydrolysis .
the oxathiazol-2-one was also replaced with a boronic acid functionality ( table 1 , entries 2627 ) in an attempt to mimic the reversible covalently - bonded warhead used in bortezomib . however , the simple boronic acid analogues were completely inactive on both the mtb and human proteasomes , suggesting that the oxathiazol-2-one moiety is a more useful electrophile for the inactivation of the target .
a series of 5-styryl - oxathiazol-2-ones was synthesized to further investigate the effect of the phenyl substitution on the structure activity relationship of proteasome inhibitors . for this , we developed a synthetic route where aryl iodides or bromides were used as starting material in a microwave - assisted mizoroki heck cross - coupling reaction with acrylamide to yield the corresponding 3-substituted acrylamides.20 , 21 the final 5-substituted - oxathiazolones were obtained by treating the corresponding amides with chlorocarbonyl sulfenyl chloride ( scheme 1 ) .
a diverse set of para - substituted 5-styryl - oxathiazolones were chosen to explore the structural requirements of the active site ( table 2 , entries 112 ) .
the majority of the compounds displayed the same range of inhibiting activity against the mtb proteasome as 17 and 18 ( ic50 values between 4151700 nm ) .
the results showed no clear trend in activity for electron - rich and electron - poor aryl substituents , although electron - poor phenyl groups gave slightly better inhibition of the mtb proteasome compared to electron - rich phenyls .
the inhibition of the human proteasome was unfortunately also affected , giving a poorer selectivity profile . however , based on the relative activities for nonstyryl containing 21 and 22 ( table 1 , entries 2122 ) , it is evident that the phenyl group is important for inhibition of the mtb proteasome .
structure activity relationship of 5-styryl - oxathiazolone inhibitors with the mtb and human proteasome .
method c reagents and conditions : starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , pd(oac)2 ( 0.05 equiv ) , tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min . method d reagents and conditions : .
starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) and pd(oac)2 ( 0.05 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min .
method e reagents and conditions : starting aryl bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) and trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , naoac ( 3.0 equiv ) , dmf ( 4.0 ml mmol ) , 140 c mw , 15 min .
[ a ] chemical stability in pbs ph 7.4 at 25 c ; as % remaining after 24 h. [ b ] isolated yield over two steps .
four of the compounds with the best inhibition and selectivity profiles ( table 2 , 3033 ) were chosen for further investigation .
for these compounds , the corresponding ortho- and meta - analogues were synthesized and evaluated in the enzyme activity assay ( table 2 , entries 1421 ) .
the para - substituted analogues ( table 2 , entries 36 ) were more active than ortho- and meta - substituted analogues on the mtb proteasome , with ic50 values in the range of 4751080 nm .
furthermore , no inhibition of the human proteasome was detected for these compounds . when substituents were introduced in the meta - position ( table 2 , entries 1417 ) , inhibitory activity of the mtb proteasome decreased ( ic50 14509900 nm ) and poorer selectivity was observed .
the ortho - substituted analogues ( entries 1821 ) , despite the same mesomeric contribution as the para - analogues on the styryl moiety , showed almost no inhibition of the mtb proteasome ( ic50 22 000 > 100 000 nm ) .
the same trend was observed for chloro - functionalized 39 and disubstituted 40 ( table 2 , entries 1213 ) ; the para - substituted compound was more active on the mtb proteasome and had superior selectivity with regard to the human proteasome .
overall , the styryl - analogues 2848 in table 2 displayed good stability but poor solubility ( 0.17.1 m ) . to hopefully improve the solubility of the compounds , a small series of nitrogen- , oxygen- and sulfur - containing heterocyclic derivatives were prepared ( table 3 ) .
the introduction of five - membered , six - membered , and bicyclic heterocycles into the scaffold generally improved the solubility with retained chemical stability .
furthermore , the heterocyclic analogues were active on the mtb proteasome , although slightly higher ic50 values were obtained compared to the compounds in table 2 .
however , for the five - membered heterocycle - substituted oxathiazolones , the compounds were not as selective with regard to the human proteasome ( table 3 , entries 35 and 9 ) .
method c reagents and conditions : starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , pd(oac)2 ( 0.05 equiv ) , tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min . method d reagents and conditions : .
starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) and pd(oac)2 ( 0.05 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min .
method e reagents and conditions : starting aryl bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) and trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , naoac ( 3.0 equiv ) , dmf ( 4.0 ml mmol ) , 140 c mw , 15 min .
[ a ] chemical stability in pbs ph 7.4 at 25 c ; as % remaining after 24 h. [ b ] isolated yield over two steps .
[ c ] the compound interferes with the assay at 10 m , therefore it was not possible to measure human proteasome inhibition .
[ d ] reagents and conditions : 1 ) ( 2e)-3-(1h - indolyl-3-yl)acrylic acid ( 2.0 mmol ) , 1,1-carbonyldiimidazole ( 2.0 mmol ) , dmf ( 10 ml ) , rt , 30 min , 2 ) nh4hco3 ( 4.0 mmol ) , rt , o / n . based on these promising results for both inhibition and selectivity of the 5-styryl - oxathiazol-2-ones ,
active mtb proteasome inhibitors displaying full to moderate selectivity were tested against a virulent strain of mtb ( h37rv ) .
four 5-aryl - oxathiazol-2-ones ( table 4 , entries 14 ) were also tested for comparison , as well as three known antitubercular agents as a reference ( entries 30 - 32 ) .
cytotoxicity for mammalian cells was investigated using the vero cell line ( african green monkey kidney cells ) ; the results are reported in table 4 .
the minimum inhibitory concentration ( mic ) was determined against aerobically - grown mtb h37rv using a 10-point serial dilution by optical density ( od ) and relative fluorescence units ( rfu ) measurement .
the highest concentration of compound tested was 20 m . the % growth was plotted , and a curve was fitted using the gompertz fit .
the mic was defined as the minimum concentration at which growth was completely inhibited and was calculated from the inflection point of the fitted curve to the lower asymptote ( zero growth ) .
cytotoxicity was measured against the vero cell line ; the tc50 is the concentration required to inhibit growth by 50 % over 48 h. n.d.=not determined . [
a ] known antitubercular agents were used as reference compounds.3 the oxathiazolones had little or no activity against replicating bacteria when compared to the known antitubercular agents used as reference ( entries 30 - 32 in table 4 ) .
a few compounds showed > 20 % inhibition of growth at the maximum concentration tested ( 20 m ) , but none had an mic20 m . there was no clear difference between the 5-styryl - oxathiazol-2-ones ( entries 529 ) and the previously reported 5-aryl - analogues ( entries 14 ) or with respect to the electronic nature and/or position of the ring substitution .
this finding is consistent with the mic values ( 15299 m ) for a series of 5-aryl - oxathiazol-2-ones recently tested on the same mtb strain.16 g compounds demonstrated some cytotoxicity against the vero cell line , with tc50 values ( concentration required to inhibit growth by 50 % over 48 h ) in the range of 1141 m ( when tested ) .
however , these results indicate that our new inhibitors are generally 1000/4000-fold less toxic than the approved human proteasome inhibitor bortezomib ( tc50 less than 10 nm).7c the observed cytotoxicity might be related to the inhibition of the trypsin - like and caspase - like activity of the mammalian proteasome.22 alternatively , it might be due to the non - proteasome - related activity of the styryl oxathiazolone compounds towards other cellular enzymes that catalyze bond cleavage via the same mechanism as the mtb - proteasome ( i.e. nucleophilic attack ) .
on the other hand , a previous report from lin et al . demonstrated generally reduced inhibition potency for the parent aryl - oxathiazolone inhibitors ( e.g. compounds 14 included in our study ) toward 1 and 2 non - chymotrypsin - like active sites of the proteasome.7c additionally high selectivity towards other human proteases , including trypsin , cathepsin b , and matrix metalloproteases was reported for the same proteasome inhibitors.7c however , recent research by bassett et al . has revealed cytotoxicity towards vero cells for a number of proteasome inhibitors reported as antitubercular agents.23 previous work suggested that the proteasome plays a key role during oxidative and nitrosative stress,12 and that proteasome inhibitors are bactericidal against nonreplicating mtb subjected to nitrosative stress.7c we therefore determined whether the 5-styryl - oxathiazolone class of compounds had activity against mtb under nonreplicating conditions . for this we used a starvation model , in which bacteria are nutrientdeprived for 14 days,24 to induce the nonreplicating state , after which they are exposed to compounds over 21 days in this state ( figure 2 ) .
mtb was grown aerobically , washed , and resuspended in pbs - tyloxapol for 14 d. compounds were added with the indicated concentrations .
all four 5-styryl - oxathiazol-2-ones tested ( 17 , 33 , 37 , and 39 ) were bactericidal against nonreplicating mtb , displaying a very rapid kill ( > 4 logs in 714 days ) .
all compounds gave complete sterilization of cultures within 14 days at the lowest concentration tested ( 20 m ) .
the 5-(4-chloro)styryl - oxathiazol-2-one inhibitor ( 39 ) was most effective , reducing the colony - forming units ( cfu)/ml below the detection limit in only seven days at all concentrations .
our results demonstrate that 5-styryl - oxathiazol-2-ones provide a promising scaffold for mtb proteasome inhibitors . in the current study
we found that conjugated 5-styryl - oxathiazolones are equally or more potent inhibitors of the mtb proteasome compared to the previously reported 5-aryl - oxathiazolones .
as part of this investigation we prepared a series of novel 5-styryl - oxathiazolones from the corresponding aryl iodides or bromides by a microwave - assisted mizoroki heck coupling with acrylamide .
our enzyme activity results showed that para - substituted 5-styryl - oxathiazol-2-ones were superior to ortho- and meta - substitution with regard to mtb proteasome ic50 values , as well as their relative lack of effects against the chymotrypsin - like peptidase activity of human proteasomes .
we also produced a small series of oxathiazolones in which solubility - enhancing heterocyclic groups were introduced .
however , we gained solubility at the expense of selectivity regarding the human proteasome . finally , a selection of the synthesized inhibitors showed rapid bactericidal activity against nonreplicating mtb , although they were not very active against actively replicating cells .
the present results suggest that this new class of mtb proteasome inhibitors can be used as the basis for development of novel antitubercular drugs that are effective when protein synthesis of the mycobacteria is drastically reduced , such as in the nonreplicative state or during antibiotic treatment .
further development will include the improvement of the safety profile of this class of mtb proteasome inhibitors.30
general chemistry . analytical thin - layer chromatography ( tlc ) was performed on silica gel 60 f-254 plates ( merck ) and visualized with uv light .
flash column chromatography was performed on columns prepacked with pharma - sil ( 5 g/10 g , hydrophilic high surface activity silica , uct , inc . ,
h and c nmr spectra were recorded on varian mercury plus instruments ( palo alto , usa ) ; h nmr spectra at 399.9 mhz and c nmr spectra at 100.5 mhz .
the chemical shifts for h nmr and c nmr were referenced to tetramethylsilane ( tms ) via residual solvent signals ( h , cdcl3 at 7.26 ppm and [ d6]-dimethylsulfoxide ( dmso ) at 2.50 ppm ; c , cdcl3 at 77.0 ppm and [ d6]dmso at 39.5 ppm ) , while chemical shifts for f nmr were referenced to cfcl3 used as internal standard ( 0.0 ppm ) .
the microwave reactions were performed in a biotage initiator ( uppsala , sweden ) producing controlled irradiation at 2450 mhz with a power of 0300 w. the reaction temperature was determined using the built - in on - line infrared ( ir ) sensor .
all reactions were performed in sealed microwave - transparent process vials designed for 0.52 , 25 , or 1020 ml reaction volumes .
gas chromatography / electron ionization mass spectrometry ( gc / ei - ms ) was performed on a varian saturn 3900/2100 system equipped with a cp - sil 8 cb capillary column ( 30 m0.25 mm , 0.25 m ) operating at an ei potential of 70 ev .
analytical high - performance liquid chromatography / electrospray ionization mass spectrometry ( hplc / esi - ms ) was performed on a gilson hplc system ( middleton , usa ) with a finnigan aqa esi quadropole mass spectrometer with electrospray ionization ( thermo fisher scientific , waltham , usa ) and using an onyx monolithic c18 column 4.650 mm ( phenomenex , torrance , usa ) with ch3cn / h2o in 0.05 % hcooh as mobile phase at a flow rate of 4 ml min or on a dionex ultimate 3000 hplc system ( sunnyvale , usa ) with a bruker amazon sl ion trap mass spectrometer ( billerica , usa ) , using a phenomenex kinetex c18 column ( 503.0 mm , 2.6 m particle size , 100 pore size ) with ch3cn / h2o in 0.05 % hcooh as mobile phase at a flow rate of 1.5 ml min .
detection was by uv ( diode array detector ) and ms ( esi+ mode ) .
preparative hplc purification was performed by uv - triggered ( 254 nm ) fraction collection with a dionex ultimate 3000 hplc system , using an agilent prepht zorbax sb - c8 column ( 21.2150 mm , 5 m particle size ) ( santa clara , usa ) with ch3cn / h2o in 0.05 % trifluoroacetic acid ( tfa ) as mobile phase .
high - resolution mass spectrometry ( hrms ) was performed on a micromass q - tof2 mass spectrometer ( waters , milford , usa ) equipped with an electrospray ion source .
hrms data are provided for all novel compounds , unless low ionization level , intrinsic to the physicochemical properties of the specific molecules , did not permit the measurement of the corresponding molecular mass data . however , in some cases , it was possible to determine the low resolution molecular mass by the varian saturn 3900/2100 gc / ms system and/or by the bruker amazon sl ion trap mass spectrometer during the lc / ms analysis .
general method for the synthesis of 5-substituted oxathiazol-2-one. method a : a mixture of starting amide ( 1.0 equiv ) and chlorocarbonyl sulfenyl chloride ( 1.5 equiv ) in 1,4-dioxane ( 4.0 ml mmol ) was irradiated with microwaves at 100 c for 15 min .
the mixture was allowed to cool down to rt , and the solvent evaporated at reduced pressure .
the crude material was purified by silica gel column chromatography and/or preparative hplc to give the final compound with purity>95 % by hplc analysis ( =254 nm ) .
method b : a mixture of starting amide ( 1.0 equiv ) and chlorocarbonyl sulfenyl chloride ( 2.0 equiv ) in freshly distilled thf ( 4.0 ml mmol ) was stirred o / n at rt .
the solvent was evaporated at reduced pressure , and the crude material was purified by silica gel column chromatography and/or preparative hplc to give the final compound with purity>95 % by hplc analysis ( =254 nm ) .
5-phenyl-1,3,4-oxathiazol-2-one ( 1).7c according to method a , benzamide ( 121 mg , 1.0 mmol ) was used to give , after preparative hplc purification , 77 mg ( 43 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.53 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.997.96 ( m , 2 h ) , 7.607.55 ( m , 1 h ) , 7.527.47 ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.8 , 157.4 , 132.6 , 129.0 , 127.4 , 125.8 ; hrms m / z for c8h5no2s as [ m+h ] adduct not found due to low ionization level .
5-(pyrazin-2-yl)-1,3,4-oxathiazol-2-one ( 2).17 according to method b , pyrazinamide ( 123 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after preparative hplc purification , 42 mg ( 23 % isolated yield ) of the title compound as white crystals .
tlc : rf=0.29 ( pentane / etoac 1:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =9.29 ( s , 1 h ) , 8.79 ( s , 1 h ) , 8.75 ppm ( s , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =172.2 , 154.6 , 147.2 , 144.7 , 144.3 , 140.2 ppm ; esi - ms m / z : 182 [ m+h ] ; hrms m / z calcd for c6h3n3o2s [ m+h ] 182.0024 , found 182.0031 .
5-(3-methoxyphenyl)-1,3,4-oxathiazol-2-one ( 3).7c according to method b , 3-methoxybenzamide ( 151 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 80 mg ( 38 % isolated yield ) of the title compound as a white powder .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.537.49 ( m , 2 h ) , 7.417.39 ( m , 1 h ) , 7.277.20 ( m , 1 h ) , 3.84 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 159.5 , 156.6 , 130.6 , 126.8 , 119.5 , 118.9 , 111.7 , 55.5 ppm ; esi - ms m / z : 210 [ m+h ] ; hrms m / z for c9h7no3s as [ m+h ] adduct not found due to low ionization level .
3-fluorobenzamide ( 139 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 163 mg ( 83 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.79 ( pentane/ etoac 100:3 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.78 ( dt , j=7.6 , 1.2 hz , 1 h ) , 7.70 ( ddd , j=9.2 , 2.8 , 1.6 hz , 1 h ) , 7.65 ( td , j=8.0 , 5.9 hz , 1 h ) , 7.53 ppm ( tdd , j=8.8 , 2.8 , 0.8 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 162.1 ( d , j=244.0 hz ) , 155.6 ( d , j=3.1 hz ) , 131.7 ( d , j=8.4 hz ) , 127.6 ( d , j=9.2 hz ) , 123.4 ( d , j=3.0 hz ) , 119.7 ( d , j=21.4 hz ) , 113.8 ppm ( d , j=23.7 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =111.4 ppm ( td , j=9.3 , 5.3 hz ) ; ei - ms m / z : 197 [ m ] ; hrms m / z for c8h4fno2s as [ m+h ] adduct not found due to low ionization level .
according to method a , 3-chloropropionamide ( 81 mg , 0.75 mmol ) was used to give , after silica column purification ( pentane / etoac 100:2 ) , 75 mg ( 60 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.31 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm):99 % ; h nmr ( 400 mhz , cdcl3 ) : =3.84 ( t , j=6.4 hz , 2 h ) , 3.11 ppm ( t , j=6.4 hz , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.9 , 38.4 , 33.7 ppm ; ei - ms m / z : 166/168 [ m+1 ] ; esi - ms m / z : 166/168 [ m+h ] ; hrms m / z for c4h4clno2s as [ m+h ] adduct not found due to low ionization level
according to method a , cyclopropanecarboxamide ( 85 mg , 1.0 mmol ) was reacted to give , after silica column purification ( pentane / etoac 100:1 ) , 38 mg ( 27 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.51 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) 99 % ; h nmr ( 400 mhz , cdcl3 ) : =1.981.90 ( m , 1 h ) , 1.181.12 ( m , 2 h ) , 1.111.04 ppm ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.2 , 162.7 , 11.2 , 8.4 ppm ; ei - ms m / z : 143 [ m ] ; hrms m / z for c5h5no2s as [ m+h ] adduct not found due to low ionization level . 5-pentyl-1,3,4-oxathiazol-2-one ( 7 ) . according to method a , hexanamide ( 86 mg , 0.75 mmol ) was used to give , after silica column purification ( pentane / etoac 100:1 ) , 73 mg ( 56 % isolated yield ) of the title compound as colorless oil .
tlc : rf=0.65 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =2.61 ( t , j=7.0 hz , 2 h ) , 1.73 ( quin , j=7.0 hz , 2 h ) , 1.401.30 ( m , 4 h ) , 0.91 ppm ( t , j=7.0 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.4 , 162.0 , 30.9 , 30.4 , 25.0 , 22.1 , 13.8 ppm ; ei - ms m / z : 174 [ m+1 ] ; esi - ms m / z : 174 [ m+h ] ; hrms m / z for c7h11no2s as [ m+h ] adduct not found due to low ionization level .
according to method b , fluoroacetamide ( 154 mg , 2.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:2 ) , 64 mg ( 24 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.55 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm)=96 % ; h nmr ( 400 mhz , [ d6]dmso ) : =5.39 ppm ( d , j=45.6 hz , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 155.7 ( d , j=21.5 hz ) , 76.9 ppm ( d , j=171.0 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =0.96 ppm ( t , j=45.5 hz ) ; ei - ms m / z : 135 [ m ] , 196 ; hrms m / z for c3h2fno2s as [ m+h ] adduct not found due to low ionization level . 5-benzyl-1,3,4-oxathiazol-2-one ( 9).25 according to method a , 2-phenylacetamide ( 135 mg , 1.0 mmol ) was reacted to yield , after preparative hplc purification , the title compound as a white powder ( 83 mg , 43 % ) .
tlc : rf=0.39 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , cdcl3 ) : =7.407.28 ( m , 5 h ) , 3.93 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.0 , 160.0 , 132.3 , 129,1 , 129.0 , 127.9 , 37.0 ppm ; hrms m / z for c9h7no2s as [ m+h ] adduct not found due to low ionization level .
according to method a , 4-methoxyphenylacetamide ( 83 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 30 mg ( 27 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.35 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , cdcl3 ) : =7.28 ( t , j=7.8 hz , 1 h ) , 6.906.82 ( m , 3 h ) , 3.90 ( s , 2 h ) , 3.81 ppm ( s , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.0 , 160.0 , 133.7 , 130.0 , 121.3 , 114.9 , 113.2 , 55.3 , 37.0 ppm ; ei - ms m / z : 184 , 147 ; esi - ms m / z : 224 [ m+h ] ; hrms m / z calcd for c10h9no3s [ m+h ] 224.0381 , found 224.0380 .
according to method a , 2-(4-formylphenoxy)acetamide ( 90 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 47 mg ( 39 % isolated yield ) of the title compound as white powder .
tlc : rf=0.10 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =9.92 ( s , 1 h ) , 7.89 ( d , j=8.8 hz , 2 h ) , 7.09 ( d , j=8.8 hz , 2 h ) , 5.05 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =190.5 , 172.6 , 161.9 , 155.8 , 132.1 , 131.3 , 115.0 , 63.2 ppm ; ei - ms m / z : 238 [ m+1 ] ; esi - ms m / z : 238 [ m+h ] ; hrms m / z calcd for c10h7no4s [ m+h ] 238.0174 , found 238.0175 .
according to method a , 1-naphthylacetamide ( 93 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 62 mg ( 51 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.48 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =8.03 ( d , j=7.8 hz , 1 h ) , 7.927.83 ( m , 2 h ) ,
7.617.51 ( m , 2 h ) , 7.507.45 ( m , 2 h ) , 4.38 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.9 , 159.9 , 133.9 , 131.6 , 129.0 , 128.5 , 128.3 , 126.9 , 126.1 , 125.5 , 123.2 , 34.6 ppm ; ei - ms m / z : 228 , 167 ; esi - ms m / z : 244 [ m+h ] ; hrms m / z calcd for c13h9no2s [ m+h ] 244.0432 , found 244.0427 .
according to method b , 2-(trifluoromethyl)phenylacetamide ( 152 mg , 0.75 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after two silica column purification ( 1 : pentane / etoac 100:0 10:1 , 2 : pentane / etoac 100:0 100:2 ) , 110 mg ( 56 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.53 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.72 ( d , j=7.8 hz , 1 h ) , 7.58 ( t , j=7.8 hz , 1 h ) , 7.497.41 ppm ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.7 , 158.9 , 132.3 , 132.0 , 130.5 ( q , j=1.5 hz ) , 129.1 ( q , j=30.7 hz ) , 128.3 , 126.6 ( q , j=5.4 hz ) , 124.0 ( q , j=273.7 hz ) , 33.8 ppm ( q , j=2.3 hz ) ; f nmr ( 376 mhz , cdcl3 ) : 59.8 ppm ; esi - ms m / z : 262 [ m+h ] ; hrms m / z calcd for c10h6f3no2s [ m+h ] 262.0150 , found 262.0154 .
according to method b , 2-hydroxy-2-phenylacetamide ( 151 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column ( pentane / etoac 100:0 1:1 ) and preparative hplc purification , 84 mg ( 40 % isolated yield ) of the title compound as a pale yellow oil .
tlc : rf=0.17 ( pentane / etoac 5:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.487.32 ( m , 5 h ) , 6.73 ( d , j=5.5 hz , 1 h ) , 5.65 ppm ( d , j=5.5 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.0 , 161.9 , 138.3 , 128.5 , 128.4 , 126.7 , 69.9 ppm ; esi - ms m / z : 232 [ m+na ] ; hrms m / z for c9h7no3s as [ m+h ] adduct not found due to low ionization level .
3-phenylpropionic acid ( 150 mg , 1.0 mmol ) and 1,1-carbonyldiimidazole ( 357 mg , 2.2 mmol ) were dissolved in dmf ( 5 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 316 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 220 ml ) and brine ( 20 ml ) .
evaporation of solvent gave 171 mg of the crude corresponding amide , purified by precipitation from etoac / pentane to afford 92 mg ( 62 % isolated yield ) of 3-phenylpropionamide as a white solid .
tlc : rf=0.28 ( pentane / etoac 1:1 ) ; gc / ms purity : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.356.98 ( m , 6 h ) , 6.76 ( bs , 1 h ) , 2.81 ( t , j=8.0 hz , 2 h ) , 2.36 ppm ( t , j=8.0 hz , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 141.5 , 128.2 , 128.1 , 125.8 , 36.7 , 30.9 ppm ; ei - ms m / z : 149 [ m ] . according to method b , 3-phenylpropionamide ( 150 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 147 mg ( 71 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.79 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.357.20 ( m , 5 h ) , 2.98 ppm ( s , 4 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.3 , 161.2 , 139.6 , 128.4 , 128.3 , 126.4 , 31.2 , 30.4 ppm ; esi - ms m / z : 208 [ m+h ] ; hrms m / z for c10h9no2s as [ m+h ] adduct not found due to low ionization level .
( r)-()-2-methoxyphenylacetic acid ( 332 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 649 mg , 4.0 mmol ) were dissolved in dmf ( 10 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 632 mg , 8.0 mmol ) was added and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 230 ml ) and brine ( 30 ml ) .
evaporation of solvent gave 180 mg ( 55 % yield ) of the crude ( r)-2-methoxy-2-phenylacetamide as a white powder , used for the next step without further purification .
gc / ms purity : 99 % ; ei - ms m / z : 166 [ m+1 ] .
according to method b , ( r)-2-methoxy-2-phenylacetamide ( 180 mg , 1.1 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 140 mg ( 58 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.64 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.487.38 ( m , 5 h ) , 5.44 ( s , 1 h ) , 3.43 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 159.4 , 135.4 , 129.0 , 128.7 , 127.2 , 78.8 , 57.3 ppm ; esi - ms m / z : 164 ; hrms m / z calcd for c10h9no3s [ m+h ] 224.0381 , found 224.0379 .
( e)-5-styryl-1,3,4-oxathiazol-2-one ( 17).26 according to method b , trans - cinnamamide ( 147 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 10:1 ) and trituration in pentane / etoac / meoh 10:1:1 drop , 82 mg ( 40 % isolated yield ) of the title compound as a pale yellow powder .
tlc : rf=0.76 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.567.49 ( m , 2 h ) , 7.50 ( d , j=16.4 hz , 1 h ) , 7.447.39 ( m , 3 h ) , 6.64 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.6 , 142.0 , 134.1 , 130.6 , 129.1 , 127.8 , 112.8 ppm ; ei - ms m / z : 191 , 161 , 129 ; esi - ms m / z : 206 [ m+h ] ; hrms m / z calcd for c10h7no2s [ m+h ] 262.0276 , found 262.0273 .
b , 4-(trifluoromethyl)cinnamamide ( 183 mg , 0.85 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 97 mg ( 42 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.57 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.01 ( d , j=8.2 hz , 2 h ) , 7.79 ( d , j=8.2 hz , 2 h ) , 7.63 ( d , j=16.4 hz , 1 h ) , 7.17 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 157.0 , 139.5 , 138.2 ppm ( q , j=1.5 hz ) , 129.9 ( q , j=32.2 hz ) , 128.8 , 125.7 ( q , j=3.8 hz ) , 124.0 ( q , j=272.2 hz ) , 116.0 ; f nmr ( 376 mhz , [ d6]dmso ) : =61.3 ppm ; esi - ms m / z : 274 [ m+h ] ; hrms m / z for c11h6f3no2s as [ m+h ] adduct not found due to low ionization level .
martin periodinane ( 467 mg , 1.1 mmol ) was added to a precooled solution ( t=0 c ) of 5-(hydroxy(phenyl)methyl)-1,3,4-oxathiazol-2-one ( 14 ) ( 209 mg , 1.0 mmol ) in anhydrous ch2cl2 ( 5 ml ) .
the resulting reaction mixture was stirred 2 h at 0 c and then filtered to remove the formed solid .
the mother liquor was washed with h2o ( 10 ml ) and dried on anhydrous na2so4 .
evaporation of the solvent under reduced pressure gave 347 mg of the crude material that was triturated with etoac for 30 min at rt .
filtration of the formed solid and evaporation of the solvent gave 117 mg of a colorless oil that was purified by silica column purification ( pentane / etoac 100:0 10:1 ) to give 118 mg ( 57 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.48 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.188.13 ( m , 2 h ) , 7.787.72 ( m , 1 h ) , 7.637.57 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =177.4 , 172.3 , 153.3 , 134.5 , 133.5 , 130.6 , 128.6 ppm ; ei - ms m / z : 208 [ m+1 ] ; esi - ms m / z : 208 [ m+h ] ; hrms m / z calcd for c9h5no3s [ m+h ] 208.0068 , found 208.0070 .
5-(phenylethynyl)-1,3,4-oxathiazol-2-one ( 20 ) . in a round - bottom flask , socl2 ( 714 mg , 6.0 mmol )
was added to a solution of phenylpropiolic acid ( 730 mg , 5.0 mmol ) in chcl3 ( 10 ml ) at rt after addition of dmf ( 1 drop ) , the reaction mixture was stirred 1 h at rt to the resulting solution was then added 25 % aq nh4oh ( 2.5 ml ) at 10 c .
the reaction mixture was allowed to return to rt and stirred 30 min at this temperature .
chcl3 ( 10 ml ) and h2o ( 10 ml ) where added , the aqueous layer was extracted with chcl3 ( 220 ml ) and the combined organic phases were dried over na2so4 .
evaporation of the solvent under reduced pressure gave 377 mg ( 52 % isolated yield ) of the crude 3-phenylpropiolamide as a white solid , which was used for the next step without further purification .
tlc : rf=0.72 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.14 ( bs , 1 h ) , 7.66 ( bs , 1 h ) , 7.617.52 ( m , 2 h ) , 7.517.42 ppm ( m , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =153.9 , 132.0 , 130.2 , 128.9 , 119.9 , 84.2 , 82.9 ppm ; esi - ms m / z : 146 [ m+h ] , 291 [ 2 m+h ] . according to method b , 3-phenylpropiolamide ( 150 mg , 1.03 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by silica column ( pentane / etoac 100:1 10:1 ) followed by preparative hplc purification , 51 mg ( 24 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.80 ( pentane / etoac 9 : 1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.757.71 ( m , 2 h ) , 7.647.58 ( m , 1 h ) , 7.567.50 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =172.3 , 141.5 , 132.6 , 131.6 , 129.2 , 118.1 , 92.3 , 75.7 ppm ; esi - ms m / z : 204 [ m+h ] ; hrms m / z for c10h5no2s as [ m+h ] adduct not found due to low ionization level .
5-vinyl-1,3,4-oxathiazol-2-one ( 21).27 according to method b , acrylamide ( 107 mg , 1.5 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after two silica column purification ( 1 : pentane / etoac 100:0 10:1 , 2 : pentane / etoac 100:0 100:2 ) , 15 mg ( 8 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.73 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , cdcl3 ) : =6.32 ( dd , j=17.6 , 10.9 hz , 1 h ) , 6.23 ( d , j=17.6 hz , 1 h ) , 5.92 ppm ( d , j=10.5 hz , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.1 , 157.0 , 127.9 , 122.9 ppm ; ei - ms m / z : 129 [ m ] ; hrms m / z for c4h3no2s as [ m+h ] adduct not found due to low ionization level .
according to method b , 4,4,4-trifluorocrotonamide ( 306 mg , 2.2 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:2 ) , 350 mg ( 81 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.69 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.127.01 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =172.7 , 154.2 , 127.1 ( q , j=34.3 hz ) , 124.0 ( q , j=6.9 hz ) , 122.5 ppm ( q , j=268.4 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =63.5 ppm ( d , j=5.6 hz ) ; hrms m / z for c5h2f3no2s as [ m+h ] adduct not found due to low ionization level .
2-phenyl - trans - cinnamic acid ( 224 mg , 1.0 mmol ) and 1,1-carbonyldiimidazole ( 357 mg , 2.2 mmol ) were dissolved in dmf ( 5 ml ) and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 316 mg , 4.0 mmol ) was added and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 220 ml ) and brine ( 20 ml ) .
evaporation of solvent gave 212 mg of the crude corresponding amide , purified by silica column chromatography ( pentane / etoac 1:1 3:1 ) to afford 150 mg ( 67 % isolated yield ) of 2-phenyl - trans - cinnamamide as white crystals .
tlc : rf=0.63 ( pentane / etoac=1:1 ) ; gc / ms purity : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.467.35 ( m , 4 h ) , 7.30 ( bs , 1 h ) , 7.247.15 ( m , 5 h ) , 7.036.97 ( m , 2 h ) , 6.90 ppm ( bs , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =170.0 , 136.7 , 136.6 , 135.0 , 133.9 , 129.7 , 129.3 , 128.8 , 128.2 , 128.1 , 127.8 ppm ; ei - ms m / z : 223 [ m ] .
according to method b , 2-phenyl - trans - cinnamamide ( 256 mg , 1.1 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 290 mg ( 90 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.77 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.65 ( s , 1 h ) , 7.507.43 ( m , 3 h ) ,
7.357.29 ( m , 2 h ) , 7.287.20 ( m , 3 h ) , 7.137.08 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 158.5 , 137.6 , 134.1 , 134.0 , 130.3 , 129.9 , 129.4 , 128.9 , 128.6 , 128.4 , 127.8 ppm ; esi - ms m / z : 282 [ m+h ] ; hrms m / z calcd for c16h11no2s [ m+h ] 282.0589 , found 282.0587 .
benzhydroxamic acid ( 137 mg , 1.0 mmol ) was reacted with 1,1-carbonyldiimidazole to give , after silica column purification ( pentane / etoac 100:0 100:5 ) , 86 mg of the crude dioxazolone which was purified by precipitation from etoac / pentane to give 80 mg ( 49 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.87 ( pentane / etoac=9:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.877.83 ( m , 2 h ) , 7.767.71 ( m , 1 h ) , 7.677.61 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =163.0 , 153.9 , 133.7 , 129.6 , 126.4 , 120.3 ppm ; hrms m / z for c8h5no3 as [ m+h ] adduct not found due to low ionization level .
( e)-3-styryl-1,4,2-dioxazol-5-one ( 25). trans - cinnamic acid ( 296 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 486 mg , 3.0 mmol ) were dissolved in thf ( 8 ml ) , and the mixture was stirred at rt .
after 1 h , hydroxylamine hydrochloride ( 278 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt for 2 d. 5 % aq khso4 ( 30 ml ) was added , and the mixture was extracted with etoac ( 230 ml ) . the collected organic phases were washed with brine ( 30 ml ) and dried over na2so4 .
evaporation of solvent gave 280 mg ( 86 % isolated yield ) of the corresponding n - hydroxycinnamamide as a pale pink solid , used in the next step without further purification .
lc purity ( 254 nm)=95 % ; esi - ms : m / z 164 [ m+h ] .
the obtained n - hydroxycinnamamide ( 140 mg , 0.86 mmol ) was reacted with 1,1-carbonyldiimidazole to give , after silica column purification ( ch3cn ) and evaporation of the solvent by freeze - drying , 123 mg of the crude dioxazolone which was purified by preparative hplc to give 83 mg ( 51 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.64 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.847.78 ( m , 2 h ) , 7.56 ( d , j=16.4 hz , 1 h ) , 7.497.43 ( m , 3 h ) , 7.15 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =163.2 , 153.6 , 142.2 , 133.8 , 130.8 , 129.0 , 128.4 , 106.9 ppm ; esi - ms m / z : 190 [ m+h ] ; hrms m / z for c10h7no3 as [ m+h ] adduct not found due to low ionization level .
general method for the synthesis of 2-substituted acrylamide. method c ( mizoroki heck reaction , electron - rich iodide ) a suitable microwave vial was loaded with solid reactants and reagents : starting iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , palladium(ii ) acetate ( 0.05 equiv ) , and tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) .
ch3cn ( 4.0 ml mmol ) was added , followed by liquid reactants : starting iodide ( 1.0 equiv , in case ) .
oxygen was removed by bubbling gaseous nitrogen into the resulting mixture for 15 min , then triethylamine ( 3.0 equiv ) was added , the vial was capped , and the reaction mixture was irradiated with microwaves at 120 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
method d ( mizoroki heck reaction , electron - poor iodide ) a suitable microwave vial was loaded with solid reactants and reagents : starting iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , and palladium(ii ) acetate ( 0.05 equiv ) .
ch3cn ( 4.0 ml mmol ) was added , followed by liquid reactants : starting iodide ( 1.0 equiv , in case ) .
oxygen was removed by bubbling gaseous nitrogen into the resulting mixture for 15 min , then triethylamine ( 3.0 equiv ) was added , the vial was capped , and the reaction mixture was irradiated with microwaves at 120 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
method e ( mizoroki heck reaction , electron - poor bromide ) a suitable microwave vial was loaded with solid reactants and reagents : starting bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) , trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , and naoac ( 3.0 equiv ) .
dry dmf ( 4.0 ml mmol ) was added , followed by liquid reactants : starting bromide ( 1.0 equiv , in case ) .
the vial was capped , and the reaction mixture was irradiated with microwaves at 140 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
4-iodoanisole ( 234 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 139 mg of the crude corresponding acrylate , that was purified by silica column chromatography ( etoac / meoh 100:5 100:10 ) to afford 133 mg ( 75 % isolated yield ) of ( e)-3-(4-methoxyphenyl)acrylamide as a white powder .
tlc : rf=0.34 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.52 ( dm , j=8.6 hz , 2 h ) , 7.45 ( bs , 1 h ) , 7.38 ( d , j=16.0 hz , 1 h ) , 7.036.97 ( m , 3 h ) , 6.47 ( d , j=15.6 hz , 1 h ) , 3.80 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.9 , 160.3 , 138.8 , 129.1 , 127.4 , 119.8 , 114.4 , 55.2 ppm ; esi - ms m / z : 178 [ m+h ] .
according to method b , ( e)-3-(4-methoxyphenyl)acrylamide ( 256 mg , 1.4 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 240 mg ( 71 % isolated yield ) of the title compound as a pale yellow powder . lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.73 ( dm , j=8.6 hz , 2 h ) , 7.49 ( d , j=16.0 hz , 1 h ) , 6.99 ( dm , j=8.6 hz , 2 h ) , 6.83 ( d , j=16.4 hz , 1 h ) , 3.81 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 161.1 , 157.7 , 141.2 , 130.0 , 126.8 , 114.4 , 110.6 , 55.4 ppm ; esi - ms m / z : 236 [ m+h ] ; hrms m / z calcd for c11h9no3s [ m+h ] 236.0381 , found 236.0383 .
1-iodo-4-isopropylbenzene ( 246 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 150 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 118 mg ( 62 % isolated yield ) of ( e)-3-(4-isopropylphenyl)acrylamide as an off - white powder .
tlc : rf=0.42 ( etoac ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.49 ( bs , 1 h ) , 7.47 ( d , j=8.0 hz , 2 h ) , 7.37 ( d , j=16.0 hz , 1 h ) , 7.28 ( d , j=8.0 hz , 2 h ) , 7.05 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.90 ( sep , j=7.0 hz , 1 h ) , 1.20 ppm ( d , j=7.0 hz , 6 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 150.0 , 139.1 , 132.5 , 127.6 , 126.9 , 121.3 , 33.3 , 23.7 ppm ; esi - ms m / z : 190 [ m+h ] , 231 [ m+ch3cn+h ] , 379 [ 2 m+h ] . according to method b , ( e)-3-(4-isopropylphenyl)acrylamide ( 118 mg , 0.62 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by silica column chromatography ( pentane / etoac 100:0 100:2 ) and preparative hplc purification , 102 mg ( 66 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.60 ( pentane / etoac 10 : 1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.69 ( d , j=8.1 hz , 2 h ) , 7.50 ( d , j=16.3 hz , 1 h ) , 7.31 ( d , j=8.1 hz , 2 h ) , 6.93 ( d , j=16.3 hz , 1 h ) , 2.92 ( sep , j=6.8 hz , 1 h ) , 1.21 ppm ( d , j=6.8 hz , 6 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 151.2 , 141.4 , 131.9 , 128.3 , 126.9 , 112.2 , 33.4 , 23.6 ppm ; esi - ms m / z : 248 [ m+h ] , 289 [ m+ch3cn+h ] ; hrms m / z for c13h13no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-4-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 126 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 95 mg ( 59 % isolated yield ) of ( e)-3-(p - tolyl)acrylamide as a white powder .
tlc : rf=0.36 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.48 ( bs , 1 h ) , 7.44 ( d , j=8.0 hz , 2 h ) , 7.37 ( d , j=16.0 hz , 1 h ) , 7.22 ( d , j=8.0 hz , 2 h ) , 7.04 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.32 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 150.8 , 139.1 , 132.1 , 129.5 , 127.5 , 121.3 , 20.9 ppm ; esi - ms m / z : 162 [ m+h ] , 203 [ m+ch3cn+h ] , 323 [ 2 m+h ] . according to method b , ( e)-3-(p - tolyl)acrylamide ( 95 mg , 0.59 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 41 mg ( 32 % isolated yield ) of the title compound as white crystals .
lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.66 ( d , j=8.1 hz , 2 h ) , 7.49 ( d , j=16.4 hz , 1 h ) , 7.25 ( d , j=8.1 hz , 2 h ) , 6.92 ( d , j=16.4 hz , 1 h ) , 2.34 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 141.4 , 140.5 , 131.4 , 129.6 , 128.2 , 112.2 , 21.0 ppm ; esi - ms m / z : 220 [ m+h ] , 261 [ m+ch3cn+h ] ; hrms m / z for c11h9no2s as [ m+h ] adduct not found due to low ionization level .
( e)-5-(4-ethylstyryl)-1,3,4-oxathiazol-2-one ( 31 ) . according to method c , 1-ethyl-4-iodobenzene ( 232 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 170 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 88 mg ( 50 % isolated yield ) of ( e)-3-(4-ethylphenyl)acrylamide as a white powder .
tlc : rf=0.40 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.49 ( bs , 1 h ) , 7.47 ( d , j=8.0 hz , 2 h ) , 7.38 ( d , j=16.0 hz , 1 h ) , 7.25 ( d , j=8.0 hz , 2 h ) , 7.04 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.62 ( q , j=7.6 hz , 2 h ) , 1.18 ppm ( t , j=7.6 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 145.4 , 139.1 , 132.4 , 128.3 , 127.6 , 121.3 , 28.1 , 15.4 ppm ; esi - ms m / z : 176 [ m+h ] , 217 [ m+ch3cn+h ] , 351 [ 2 m+h ] . according to method b , ( e)-3-(4-ethylphenyl)acrylamide ( 88 mg , 0.50 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 50 mg ( 43 % isolated yield ) of the title compound as yellow crystals . lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.68 ( d , j=8.1 hz , 2 h ) , 7.50 ( d , j=16.4 hz , 1 h ) , 7.28 ( d , j=8.1 hz , 2 h ) , 6.93 ( d , j=16.4 hz , 1 h ) , 2.63 ( q , j=7.7 hz , 2 h ) , 1.18 ppm ( t , j=7.7 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 146.7 , 141.4 , 131.7 , 128.4 , 128.3 , 112.2 , 28.1 , 15.3 ppm ; esi - ms m / z : 234 [ m+h ] , 275 [ m+ch3cn+h ] ; hrms m / z for c12h11no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-4-trifluoromethoxy - benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac ; 2 pentane / etoac 1:1 0:1 ) to afford 221 mg of a 1:1 mixture of ( e)-3-(4-(trifluoromethoxy)phenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.48 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 232 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 221 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.25 ml ) to give , after purification by silica column chromatography ( pentane / etoac 100:0 100:2 ) , 185 mg ( 64 % isolated yield after two steps ) of the title compound as a white powder .
tlc : rf=0.55 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 94 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.93 ( dm , j=9.0 hz , 2 h ) , 7.58 ( d , j=16.4 hz , 1 h ) , 7.43 ( dm , j=8.0 hz , 2 h ) , 7.05 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.2 , 149.4 , 139.7 , 133.5 , 130.2 , 121.3 , 120.0 ( q , j=256.9 hz ) , 114.4 ppm ; esi - ms m / z : 290 [ m+h ] ; hrms m / z for c11h6f3no3s as [ m+h ] adduct not found due to low ionization level .
d , ethyl 4-iodobenzoate ( 276 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 147 mg ( 67 % isolated yield ) of ( e)-ethyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate as an off - white powder .
tlc : rf=0.53 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( dm , j=8.3 hz , 2 h ) , 7.69 ( dm , j=8.3 hz , 2 h ) , 7.61 ( bs , 1 h ) , 7.46 ( d , j=16.0 hz , 1 h ) , 7.20 ( bs , 1 h ) , 6.73 ( d , j=16.0 hz , 1 h ) , 4.31 ( q , j=6.9 hz , 2 h ) , 1.33 ppm ( t , j=6.9 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.2 , 165.3 , 139.4 , 137.8 , 130.2 , 129.7 , 127.7 , 124.9 , 60.8 , 14.1 ppm ; esi - ms m / z : 220 [ m+h ] , 439 [ 2 m+h ] . according to method b , ( e)-ethyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate ( 147 mg , 0.67 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 129 mg ( 69 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.39 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.6 hz , 2 h ) , 7.92 ( bd , j=8.6 hz , 2 h ) , 7.59 ( d , j=16.4 hz , 1 h ) , 7.13 ( d , j=16.4 hz , 1 h ) , 4.33 ( q , j=7.1 hz , 2 h ) , 1.33 ppm ( t , j=7.1 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 165.2 , 157.0 , 139.9 , 138.6 , 130.9 , 129.5 , 128.4 , 115.7 , 60.9 , 14.1 ppm ; esi - ms m / z : 278 [ m+h ] ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0482 .
4-iodobenzophenone ( 308 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 158 mg ( 63 % isolated yield ) of ( e)-3-(4-benzoylphenyl)acrylamide as an off - white powder .
tlc : rf=0.47 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.807.66 ( m , 7 h ) , 7.63 ( bs , 1 h ) , 7.617.55 ( m , 2 h ) , 7.50 ( d , j=15.8 hz , 1 h ) , 7.21 ( bs , 1 h ) , 6.75 ppm ( d , j=15.8 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =156.0 , 127.1 , 99.8 , 98.8 , 98.1 , 97.8 , 93.6 , 91.1 , 90.4 , 89.5 , 88.5 , 85.8 ppm ; esi - ms m / z : 252 [ m+h ] , 503 [ 2 m+h ] . according to method b , ( e)-3-(4-benzoylphenyl)acrylamide ( 158 mg , 0.63 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 157 mg ( 80 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.26 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.96 ( dm , j=8.8 hz , 2 h ) , 7.807.74 ( m , 4 h ) , 7.737.67 ( m , 1 h ) , 7.64 ( d , j=16.4 hz , 1 h ) , 7.617.55 ( m , 2 h ) , 7.16 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =195.1 , 173.4 , 157.1 , 140.0 , 138.1 , 138.0 , 136.8 , 132.9 , 130.1 , 129.6 , 128.6 , 128.2 , 115.6 ppm ; esi - ms m / z : 310 [ m+h ] ; hrms m / z calcd for c17h11no3s [ m+h ] 310.0538 , found 310.0535 .
d , methyl 4-iodobenzoate ( 262 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 124 mg ( 60 % isolated yield ) of ( e)-methyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate as an off - white powder .
tlc : rf=0.47 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.3 hz , 2 h ) , 7.70 ( bd , j=8.3 hz , 2 h ) , 7.61 ( bs , 1 h ) , 7.46 ( d , j=15.9 hz , 1 h ) , 7.20 ( bs , 1 h ) , 6.73 ( d , j=15.9 hz , 1 h ) , 3.86 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.2 , 165.8 , 139.5 , 137.8 , 129.9 , 129.7 , 127.8 , 125.0 , 52.2 ppm ; esi - ms m / z : 206 [ m+h ] , 411 [ 2 m+h ] . according to method b , ( e)-methyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate ( 124 mg , 0.60 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 108 mg ( 68 % isolated yield ) of the title compound as white powder .
tlc : rf=0.32 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.6 hz , 2 h ) , 7.92 ( bd , j=8.6 hz , 2 h ) , 7.60 ( d , j=16.4 hz , 1 h ) , 7.13 ( d , j=16.4 hz , 1 h ) , 3.87 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 165.7 , 157.0 , 139.8 , 138.7 , 130.6 , 129.6 , 128.4 , 115.7 , 52.3 ppm ; esi - ms m / z : 264 [ m+h ] ; hrms m / z calcd for c12h9no4s [ m+h ] 264.0331 , found 264.0336 .
1-iodo-4-nitrobenzene ( 249 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 95 mg ( 49 % isolated yield ) of ( e)-3-(4-nitrophenyl)acrylamide as a yellow powder .
tlc : rf=0.53 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.26 ( bd , j=9.0 hz , 2 h ) , 7.83 ( bd , j=9.0 hz , 2 h ) , 7.66 ( bs , 1 h ) , 7.52 ( d , j=15.9 hz , 1 h ) , 7.27 ( bs , 1 h ) , 6.80 ppm ( d , j=15.9 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.9 , 147.5 , 141.5 , 136.8 , 128.6 , 126.7 , 124.1 ppm ; esi - ms m / z : 193 [ m+h ] .
according to method b , ( e)-3-(4-nitrophenyl)acrylamide ( 95 mg , 0.49 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 99 mg ( 80 % isolated yield ) of the title compound as a pale yellow powder .
tlc : rf=0.24 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.26 ( bd , j=8.9 hz , 2 h ) , 8.07 ( bd , j=8.9 hz , 2 h ) , 7.67 ( d , j=16.4 hz , 1 h ) , 7.24 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.8 , 147.9 , 140.7 , 138.7 , 129.2 , 124.0 , 117.3 ppm ; esi - ms m / z : 251 [ m+h ] ; hrms m / z for c10h6n2o4s as [ m+h ] adduct not found due to low ionization level .
4-iodobenzonitrile ( 229 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac , 2 pentane / etoac 1:1 0:1 ) to afford 123 mg of a 1:2 mixture of ( e)-3-(4-cyanophenyl)acrylamide and starting acrylamide as white a powder .
tlc : mizoroki heck product rf=0.37 , acrylamide rf=0.31 ( etoac ) ; esi - ms : m / z 173 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 123 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.21 ml ) to give , after purification by precipitation from etoac / pentane , 47 mg ( 20 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.21 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.4 hz , 2 h ) , 7.90 ( bd , j=8.4 hz , 2 h ) , 7.61 ( d , j=16.4 hz , 1 h ) , 7.20 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.9 , 139.3 , 138.8 , 132.8 , 128.8 , 118.6 , 116.6 , 112.2 ppm ; esi - ms m / z : 231 [ m+h ] ; hrms m / z calcd for c11h6n2o2s [ m+h ] 231.0228 , found 231.0226 .
( e)-4-(2-(2-oxo-1,3,4-oxathiazol-5-yl)vinyl)benzaldehyde ( 38 ) . according to method d , 4-iodobenzaldehyde ( 232 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction . after microwave irradiation ,
the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac , 2 pentane / etoac 1:1 0:1 ) to afford 100 mg of a 2:3 mixture of ( e)-3-(4-formylphenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.37 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 176 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 100 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.10 ml ) to give , after purification by precipitation from etoac / pentane , 36 mg ( 15 % isolated yield after two steps ) of the title compound as a pale yellow powder .
tlc : rf=0.18 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =10.03 ( s , 1 h ) , 8.01 ( bd , j=8.4 hz , 2 h ) , 7.95 ( bd , j=8.4 hz , 2 h ) , 7.62 ( d , j=16.4 hz , 1 h ) , 7.19 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =192.6 , 173.3 , 157.0 , 139.9 , 139.8 , 136.8 , 129.9 , 128.8 , 116.2 ppm ; esi - ms m / z : 234 [ m+h ] ; hrms m / z for c11h7no3s as [ m+h ] adduct not found due to low ionization level .
1-chloro-4-iodobenzene ( 238 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 123 mg ( 68 % isolated yield ) of ( e)-3-(4-chlorophenyl)acrylamide as a yellow powder .
tlc : rf=0.60 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.58 ( dm , j=8.4 hz , 2 h ) , 7.54 ( bs , 1 h ) , 7.47 ( dm , j=8.4 hz , 2 h ) , 7.40 ( d , j=15.9 hz , 1 h ) , 7.13 ( bs , 1 h ) , 6.61 ppm ( d , j=15.9 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.4 , 137.8 , 133.9 , 133.8 , 129.2 , 128.9 , 123.2 ppm ; esi - ms m / z : 182/184 [ m+h ] , 363/365 [ 2 m+h ] . according to method b , ( e)-3-(4-chlorophenyl)acrylamide ( 123 mg , 0.68 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 118 mg ( 73 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.68 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.81 ( dm , j=8.4 hz , 2 h ) , 7.54 ( d , j=16.3 hz , 1 h ) , 7.50 ( dm , j=8.4 hz , 2 h ) , 7.03 ppm ( d , j=16.3 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.2 , 140.0 , 134.9 , 133.2 , 129.9 , 129.0 , 114.0 ppm ; esi - ms m / z : 240/242 [ m+h ] ; hrms m / z for c10h6clno2s as [ m+h ] adduct not found due to low ionization level .
1,4-dichloro-2-iodobenzene ( 273 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac ; 2 pentane / etoac 1:1 0:1 ) to afford 184 mg of a 1:1 mixture of ( e)-3-(2,5-dichlorophenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.69 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 216/217 [ m+h ] . according to method b ,
the obtained mizoroki heck reaction mixture ( 184 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.24 ml ) to give , after purification by precipitation from etoac / pentane , 31 mg ( 11 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.79 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.18 ( d , j=2.5 hz , 1 h ) , 7.63 ( d , j=16.2 hz , 1 h ) , 7.61 ( d , j=8.7 hz , 1 h ) , 7.53 ( dd , j=8.7 , 2.5 hz , 1 h ) , 7.25 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.2 , 156.6 , 134.4 , 133.5 , 132.7 , 132.1 , 131.6 , 131.4 , 127.5 , 117.6 ppm ; esi - ms m / z : 274/276 [ m+h ] ; hrms m / z for c10h5cl2no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-3-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude to ( e)-3-(m - tolyl)acrylamide , esi - ms m / z : 162 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after silica column chromatography ( ch2cl2/isohexane 1:9 ) and recrystallization in ch3cn , 76 mg ( 35 % isolated yield after step two ) as a white solid .
esi - ms m / z : 220 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.47 ( d , j=16.2 hz , 1 h ) , 7.347.20 ( m , 4 h ) , 6.63 ( d , j=16.2 hz , 1 h ) , 2.39 ppm ( m , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.7 , 142.1 , 138.8 , 134.0 , 131.4 , 129.0 , 128.5 , 125.0 , 112.6 , 21.3 ppm ; hrms m / z calcd for c11h9no2s [ m+h ] 220.0432 , found 220.0437 .
( e)-5-(3-ethylstyryl)-1,3,4-oxathiazol-2-one ( 42 ) . according to method e , 1-bromo-3-ethylbenzene ( 370 mg , 2.0 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , filtered through a plug of cotton , and concentrated under reduced pressure .
the residue was dissolved in etoac ( 25 ml ) and washed with h2o ( 25 ml ) , and the organic phase was dried over mgso4 and evaporated to yield the crude ( e)-3-(3-ethylphenyl)acrylamide as a pale yellow solid .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.67 ml ) to give , after silica column chromatography ( etoac / isohexane 2:100 5:100 ) and recrystallization in ch3cn , 77 mg ( 17 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 234 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.48 ( d , j=16.2 hz , 1 h ) , 7.367.23 ( m , 4 h ) , 6.63 ( d , j=16.2 hz , 1 h ) , 2.68 ( q , j=7.6 hz , 2 h ) , 1.27 ppm ( t , j=7.6 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.8 , 145.1 , 142.2 , 134.1 , 130.3 , 129.1 , 127.4 , 125.3 , 112.6 , 28.7 , 15.5 ppm ; hrms m / z calcd for c12h11no2s [ m+h ] 234.0589 , found 234.0591 .
1-iodo-3-(trifluoromethoxy)benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(3-(trifluoromethoxy)phenyl)acrylamide as a pale yellow solid .
tlc : rf=0.47 ( etoac : iso - hexane , 75:25 ) ; esi - ms m / z : 232 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.22 ml ) to give , after silica column chromatography ( etylacetate / isohexane 1:100 ) , 176 mg ( 61 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 299 [ m+h ] ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.81 ( m , 1 h ) , 7.78 , ( dm , j=8.0 hz , 1 h ) , 7.55 ( d , j=16.4 hz , 1 h ) , 7.54 ( m , 1 h ) , 7.38 ( m , 1 h ) , 7.01 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.8 , 157.5 , 149.3 , 140.0 , 137.1 , 131.3 , 127.7 , 122.9 , 121.0 , 120.5 ( q , j=257 hz ) , 115.6 ppm ; hrms m / z calcd for c11h6f3no3s [ m+h ] 299.0099 , found 299.0103 .
( e)-ethyl 3-(2-(2-oxo-1,3,4-oxathiazol-5-yl)vinyl)benzoate ( 44 ) . according to method d , ethyl-3-iodobenzoate ( 276 mg , 1.0 mmol )
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to afford 206 mg of ( e)-3-(3- ethoxycarbonyl)acrylamide as pale yellow solid .
tlc : rf=0.58 , ( etoac ) ; esi - ms m / z : 220 [ m+h ] .
according to method a , the crude 3-substituted acrylamide ( 206 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.17 ml ) to give , after recrystallization in ethylacetate / isohexane , 118 mg ( 43 % isolated yield after two steps ) as a white solid , 43 % yield .
esi - ms m / z : 278 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.24 ( m , 1 h ) , 8.05 , ( dm , j=7.7 hz , 1 h ) , 7.97 ( dm , j=7.8 hz , 1 h ) , 7.60 ( d , j=16.4 hz , 1 h ) , 7.58 ( dd , j=7.7 , 7.8 hz , 1 h ) , 7.05 ( d , j=16.4 hz , 1 h ) , 4.32 ppm ( q , j=7.2 hz , 2 h ) , 1.32 ( t ,
j=7.2 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.9 , 165.8 , 157.6 , 140.7 , 135.2 , 132.6 , 131.2 , 131.1 , 129.9 , 129.4 , 114.9 , 61.5 , 14.6 ppm ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0486 .
1-iodo-2-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(o - tolyl)acrylamide as a pale yellow solid , 149 mg .
tlc : rf=0.48 ( etoac ) ; esi - ms m / z : 162 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.26 ml ) to give , after silica column chromatography ( etoac / isohexane 1:100 ) , 70 mg ( 32 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 220 [ m+h ] ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.69 ( d , j=16.2 hz , 1 h ) , 7.48 ( dm , j=7.8 hz , 1 h ) , 7.257.13 ( m , 3 h ) , 6.49 ( d , j=16.2 hz , 1 h ) , 2.37 ppm ( m , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.8 , 139.5 , 137.6 , 133.0 , 131.0 , 130.3 , 126.5 , 125.9 , 113.8 , 19.8 ppm ; hrms m / z calcd for c11h9no2s [ m+h ] 220.0432 , found 220.0436 .
1-bromo-2-ethylbenzene ( 218 mg , 1.0 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and filtered through a plug of cotton .
the reaction mixture was then extracted between etoac ( 25 ml ) and h2o ( 25 ml ) , and the organic phase was dried over mgso4 and evaporated to yield the crude ( e)-3-(2-ethylphenyl)acrylamide as a pale yellow solid , 117 mg .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.23 ml ) to give , after silica column chromatography ( etoac / isohexane 2:100 ) , 90 mg ( 19 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 234 [ m+h ] ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , cdcl3 ) : =7.80 ( d , j=16.2 hz , 1 h ) , 7.57 ( m , 1 h ) , 7.35 ( m , 1 h ) , 7.287.22 ( m , 2 h ) , 6.58 ( d , j=16.2 hz , 1 h ) , 2.79 ( q , j=7.5 hz , 2 h ) , 1.24 ppm ( t , j=7.5 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.8 , 143.8 , 139.3 , 132.3 , 130.6 , 129.4 , 126.5 , 126.1 , 113.9 , 26.4 , 15.9 ppm ; hrms m / z calcd for c12h11no2s [ m+h ] 234.0589 , found 234.0584 .
1-iodo-2-(trifluoromethoxy)benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(2-(trifluoromethoxy)phenyl)acrylamide as a pale yellow solid , 229 mg .
tlc : rf=0.49 ( etoac / iso - hexane 75:25 ) ; esi - ms m / z : 232 [ m+h ] . according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.20 ml ) to give , after precipitation from etoac / isohexane , 110 mg ( 38 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 299 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.04 ( d , j=7.8 hz , 1 h ) , 7.54 ( m , 1 h ) , 7.47 ( d , j=16.4 hz , 1 h ) , 7.457.38 ( m , 2 h ) , 7.08 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 157.1 , 146.7 , 132.9 , 132.6 , 128.7 , 128.6 , 127.5 , 122.1 , 120.6 ( q , j=258 hz ) , 110.0 ppm ; hrms m / z calcd for c11h6f3no3s [ m+h ] 299.0099 , found 299.0096 .
ethyl 2-bromobenzoate ( 506 mg , 2.2 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the product was filtered and washed with etoac ( 20 ml ) give ( e)-ethyl 2-(3-amino-3-oxoprop-1-en-1-yl)benzoate as a pale white solid , 391 mg . according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.60 ml ) to give , after filtration and washing with etoac ( 10 ml ) , 198 mg ( 32 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 278 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.18 ( d , j=16.2 hz , 1 h ) , 7.95 ( dm , j=8.0 hz , 1 h ) , 7.90 ( dd , j=7.8 , 1.6 hz , 1 h ) , 7.65 ( ddd , j=8.0 , 7.6 , 1.6 hz , 1 h ) , 7.54 ( ddm , j=7.8 , 7.6 hz , 1 h ) , 6.92 ( d , j=16.2 hz , 1 h ) , 4.33 ( q , j=7.2 hz , 2 h ) , 1.33 ppm ( t , j=7.2 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.8 , 166.7 , 157.6 , 139.7 , 125.1 , 133.0 , 130.9 , 130.5 , 130.3 , 128.1 , 116.0 , 61.7 , 14.5 ppm ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0485 .
4-iodopyridine ( 205 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cn ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( pentane / etoac 1:1 0:1 , then etoac / meoh 9:1 ) to afford 120 mg of a 1:1 mixture of ( e)-3-(pyridin-4-yl)acrylamide and starting acrylamide as a pale yellow solid .
tlc : mizoroki heck product rf=0.25 , acrylamide rf=0.72 ( etoac / meoh 9:1 ) ; esi - ms m / z : 149 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 120 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after purification by preparative hplc , 15 mg ( 7 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.32 ( pentane / etoac=1:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.668.63 ( m , 2 h ) , 7.757.72 ( m , 2 h ) , 7.53 ( d , j=16.3 hz , 1 h ) , 7.27 ppm ( d , j=16.3 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.2 , 156.8 , 150.4 , 141.3 , 138.7 , 121.9 , 117.6 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0255 .
3-iodo-2-methoxy - pyridine ( 235 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cn ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( pentane / etoac 1:1 0:1 , then etoac / meoh 9:1 ) to afford 184 mg of a 1:1 mixture of ( e)-3-(2-methoxypyridin-3-yl)acrylamide and starting acrylamide as a pale yellow oil .
tlc : mizoroki heck product rf=0.68 , acrylamide rf=0.60 ( etoac / meoh 9:1 ) ; esi - ms m / z : 179 [ m+h ] .
according to method a , the obtained mizoroki heck reaction mixture ( 184 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after purification by trituration with et2o followed by precipitation from ch3cn / h2o , 91 mg ( 39 % isolated yield after two steps ) of the title compound as a pale yellow solid .
tlc : rf=0.80 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.23 ( dd , j=4.9 , 1.8 hz , 1 h ) , 8.17 ( dd , j=7.4 , 1.8 hz , 1 h ) , 7.56 ( d , j=16.5 hz , 1 h ) , 7.09 ( dd , j=7.4 , 4.9 hz , 1 h ) , 7.06 ( d , j=16.5 hz , 1 h ) , 3.98 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 161.1 , 157.4 , 148.7 , 138.2 , 135.1 , 117.8 , 117.1 , 115.4 , 53.9 ppm ; esi - ms m / z : 237 [ m+h ] ; hrms m / z calcd for c10h8n2o3s [ m+h ] 237.0334 , found 237.0338 .
2-iodothiophene ( 210 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by precipitation from ch3oh / h2o to afford 70 mg ( 46 % isolated yield ) of ( e)-3-(thiophen-2-yl)acrylamide as an off - white solid .
tlc : rf=0.52 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.71 ( d , j=15.3 hz , 1 h ) , 7.28 ( bd , j=5.1 hz , 1 h ) , 7.17 ( bd , j=3.5 hz , 1 h ) , 6.98 ( dd , j=5.1 , 3.5 hz , 1 h ) , 6.19 ( d , j=15.3 hz , 1 h ) , 5.36 ppm ( bs , 2 h ) ; esi - ms m / z : 154 [ m+h ] . according to method b , ( e)-3-(thiophen-2-yl)acrylamide ( 70 mg , 0,46 mmol ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 46 mg ( 45 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.63 ( pentane / etoac 20:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.76 ( bd , j=5.1 hz , 1 h ) , 7.72 ( d , j=16.1 hz , 1 h ) , 7.59 ( bd , j=3.7 hz , 1 h ) , 7.17 ( dd , j=5.1 , 3.7 hz , 1 h ) , 6.61 ppm ( d , j=16.1 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.0 , 138.9 , 134.3 , 131.8 , 130.2 , 128.7 , 111.3 ppm ; esi - ms m / z : 212 [ m+h ] ; hrms m / z calcd for c8h5no2s2 [ m+h ] 211.9840 , found 211.9837 .
3-iodothiophene ( 210 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave the crude corresponding acrylate , that was purified by precipitation from etoac / pentane followed by silica column purification ( pentane / etoac 1:1 0:1 ) to afford 115 mg ( 75 % isolated yield ) of ( e)-3-(thiophen-3-yl)acrylamide as a white solid .
tlc : rf=0.46 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.64 ( d , j=15.4 hz , 1 h ) , 7.47 ( bd , j=2.9 hz , 1 h ) , 7.33 ( dd , j=5.1 , 2.9 hz , 1 h ) , 7.28 ( bd , j=5.1 hz , 1 h ) , 6.30 ppm ( d , j=15.4 hz , 1 h ) , 5.53 ( bs , 2 h ) ; esi - ms m / z : 154 [ m+h ] .
according to method b , ( e)-3-(thiophen-3-yl)acrylamide ( 115 mg , 0,75 mmol ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 84 mg ( 53 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.55 ( pentane / etoac=20:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.028.00 ( m , 1 h ) , 7.667.61 ( m , 2 h ) , 7.55 ( d , j=16.2 hz , 1 h ) , 6.82 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.6 , 137.5 , 135.4 , 129.6 , 127.9 , 125.7 , 112.6 ppm ; esi - ms : m / z 212 [ m+h ] ; hrms m / z calcd for c8h5no2s2 [ m+h ] 211.9840 , found 211.9841 .
5-iodo-2-furaldehyde ( 222 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave a crude mixture that was taken in ch3oh / h2o and then filtered to remove the precipitated homocoupling byproduct .
evaporation of the solvent gave 262 mg of a crude mixture , which was purified by flash silica column ( pentane / etoac 1:1 0:1 ) to give 88 mg of a mixture containing the desired ( e)-3-(5-formylfuran-2-yl)acrylamide as a yellow solid .
tlc : mizoroki heck compound rf=0.44 ( etoac ) ; lc purity ( 254 nm ) : 30 % ; esi - ms m / z : 166 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 88 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 10 mg ( 5 % isolated yield after two steps ) of the title compound as a white powder .
tlc : rf=0.70 ( pentane / etoac=20 : 1 ) ; lc purity ( 254 nm ) : 90 % ; h nmr ( 400 mhz , [ d6]dmso ) : =9.66 ( s , 1 h ) , 7.63 ( d , j=3.7 hz , 1 h ) , 7.47 ( d , j=16.2 hz , 1 h ) , 7.24 ( d , j=3.7 hz , 1 h ) , 6.83 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =178.7 , 173.1 , 156.4 , 154.5 , 152.8 , 127.1 , 124.3 , 116.8 , 115.0 ppm ; esi - ms m / z : 224 [ m+h ] ; hrms m / z calcd for c9h5no4s [ m+h ] 224.0018 , found 224.0015 .
( e)-5-(2-(pyridin-2-yl)vinyl)-1,3,4-oxathiazol-2-one ( 54 ) . according to method e , 2-bromopyridine ( 237 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was irradiated for additional 60 min at 160 c to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 126 mg of a mixture containing the desired ( e)-3-(pyridin-2-yl)acrylamide as a yellow oil .
tlc : mizoroki heck compound rf=0.07 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm)=70 % ; esi - ms m / z : 149 [ m+h ] .
according to method a , the obtained mizoroki heck reaction mixture ( 126 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) to give , after purification by preparative hplc , 8 mg ( 3 % isolated yield after two steps ) of the title compound as a brown powder .
lc purity ( 254 nm ) : 92 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.698.65 ( m , 1 h ) , 7.89 ( td , j=7.8 , 2.0 hz , 1 h ) , 7.78 ( dm , j=8.0 hz , 1 h ) , 7.58 ( d , j=16.0 hz , 1 h ) , 7.43 ( ddd , j=7.8 , 4.7 , 1.2 hz , 1 h ) , 7.20 ppm ( d , j=16.0 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.9 , 152.0 , 150.1 , 140.3 , 137.4 , 125.0 , 124.8 , 116.0 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0234 .
( e)-5-(2-(pyridin-3-yl)vinyl)-1,3,4-oxathiazol-2-one ( 55 ) . according to method e , 3-bromopyridine ( 237 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 102 mg of a mixture containing the desired ( e)-3-(pyridin-3-yl)acrylamide as a white solid .
tlc : mizoroki heck compound rf=0.26 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm ) : 90 % ; esi - ms m / z : 149 [ m+h ] . according to method a , the obtained mizoroki heck reaction mixture ( 102 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) by microwave irradiation , followed by thermal heating at 70 c for 2 d to give , after purification by preparative hplc , 45 mg ( 15 % isolated yield after two steps ) of the title compound as a white powder .
lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.92 ( bd , j=2.1 hz , 1 h ) , 8.59 ( dd , j=4.9 , 1.8 hz , 1 h ) , 8.24 ( dm , j=8.0 hz , 1 h ) , 7.58 ( d , j=16.4 hz , 1 h ) , 7.47 ( bdd , j=7.5 , 4.3 hz , 1 h ) , 7.16 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.0 , 150.9 , 149.8 , 138.1 , 134.4 , 130.1 , 123.9 , 115.1 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0229 .
( e)-5-(2-(2-oxo-2 h - thiadiazolo[2,3-a]pyridin-8-yl)vinyl)-1,3,4-oxathiazol-2-one ( 56 ) . according to method e , 2-amino-3-bromopyridine ( 260 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was irradiated for additional 15 min at 160 c to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 94 mg of a mixture containing the desired ( e)-3-(2-aminopyridin-3-yl)acrylamide as a yellow solid .
tlc : mizoroki heck compound rf=0.22 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm)=90 % ; esi - ms m / z : 164 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 94 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) , to give , after purification by trituration in ch3cn / h2o , 16 mg ( 4 % isolated yield after two steps ) of the title compound as a pale yellow solid .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.02 ( dd , j=7.0 , 1.3 hz , 1 h ) , 7.95 ( dm , j=7.0 hz , 1 h ) , 7.72 ( d , j=16.0 hz , 1 h ) , 7.62 ( dd , j=16.2 , 0.6 hz , 1 h ) , 6.89 ppm ( t , j=7.0 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.3 , 173.3 , 157.1 , 148.0 , 137.1 , 134.8 , 126.1 , 125.0 , 117.4 , 111.6 ppm ; esi - ms m / z : 280 [ m+h ] ; hrms m / z calcd for c10h5n3o3s2 [ m+h ] 279.9851 , found 279.9843 .
ghsqc and ghmqc experiments showed no correlations between proton he and carbon c , suggesting the following structure ( figure 3 ) as the most probable one .
( 2e)-3-(1h - indol-3-yl)acrylic acid ( 378 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 656 mg , 2.0 mmol ) were dissolved in anhydrous dmf ( 10 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 639 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt o / n .
etoac ( 100 ml ) was added , and the organic phase was washed with h2o ( 250 ml ) and brine ( 50 ml ) .
evaporation of solvent gave 397 mg of the crude corresponding amide , purified by silica column chromatography ( pentane / etoac 1:1 0:1 ) to afford 116 mg ( 31 % isolated yield ) of ( e)-3-(1h - indol-3-yl)acrylamide as a yellow sticky oil .
tlc : rf=0.24 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; esi - ms m / z : 187 [ m+h ] .
according to method b , ( e)-3-(1h - indol-3-yl)acrylamide ( 58 mg , 0.31 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after preparative hplc purification , 9 mg ( 12 % isolated yield ) of the title compound as a pale yellow powder .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =11.84 ( bs , 1 h ) , 8.00 ( s , 1 h ) , 7.94 ( dm , j=7.2 hz , 1 h ) , 7.75 ( d , j=16.2 hz , 1 h ) , 7.48 ( dm , j=8.1 hz , 1 h ) , 7.267.15 ( m , 2 h ) , 6.66 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.7 , 159.3 , 138.1 , 136.7 , 132.4 , 125.4 , 123.4 , 121.8 , 120.5 , 113.1 , 112.5 , 107.0 ppm ; esi - ms m / z : 245 [ m+h ] ; hrms m / z calcd for c12h8n2o2s [ m+h ] 245.0385 , found 245.0384 .
the sequences for the open - gate alpha8a ( rv2109c residues 9240 ) and a slightly truncated beta ( rv2110c ) ( residues 1285 ) subunits of the m. tuberculosis proteasome were amplified by pcr from total dna of mtb strain h37rv28 using the polymerase pfu ultra ( agilent technologies , la jolla , usa ) .
the c - terminus of the beta subunit was modified to incorporate a 6-histidine tag after the terminal glycine residue.8a the genes were inserted into the vector prsf duet-1 , which is a vector for coexpressing two proteins , both controlled by t7 promoters , from novagen ( merckmillipore , darmstadt , germany ) , and cloned in e. coli top10 cells ( invitrogen , carlsbad , usa ) . expression and purification
were performed as previously described.8a briefly , 6 l cultures of e. coli bl21(de3 ) cells in luria bertani broth with 30 g / ml kanamycin were grown for 2022 h at 37 c after induction with 0.4 mm isopropyl beta - d1 thiogalactopyranoside .
the cells were harvested by centrifugation , resuspended in lysis buffer ( 50 mm na3po4 , ph 8 , 300 mm nacl , 10 mm imidazole with 0.25 mg ml lysozyme , 0.02 mg ml rnase , and 0.01 mg ml dnase ) , incubated 30 min at rt and lysed by passage through a constant cell disruption system ( constant systems ltd , daventry , uk ) at 2 kbar .
full proteasome molecules were isolated from the cleared lysate with 1 ml ni - sepharose ( ge - healthcare , uppsala , sweden ) , and eluted with 250 mm imidazole .
the buffer was exchanged on an econo - pac 10dg desalting column ( bio - rad , hercules , usa ) to 10 mm tris ph 7.5 , 100 mm nacl before a final purification step by size - exclusion chromatography on a hiload 16/60 superdex 200 column ( ge healthcare , little chalfront , uk ) equilibrated with the same buffer .
the fractions containing the proteasome as analyzed by sds - page were pooled and concentrated to 1 mg ml ( measured by a280 , extinction coefficient 33 810 m cm ) in a vivaspin 20 , molecular weight cut - off 100 kda ( sartorius stedin biotech , goettingen , germany ) .
the protein production and assay were based on that of lin et al.8b both mtb and human proteasomes were assayed in 20 mm hepes , 0.5 mm edta ph 7.5 , with 25 m suc - llvy - amc ( bachem ag , switzerland ) as substrate , in a final volume of 100 l on a white 96-well assay plate ( cliniplate , thermo fisher scientific oy , finland ) . the increase in fluorescence caused by cleavage of amc ( 7-amino-4-methylcoumarin ) was measured using a fluoroskan ascent fluorescent plate reader ( thermo fisher scientific oy , finland ) equipped with a 390 nm filter for excitation and 460 nm filter for emission .
human 20s proteasome ( boston biochemicals , usa ) was assayed at 1 nm concentration in the presence of a tenfold excess of human pa28 activator ( boston biochemicals ) , as recommended by the manufacturer .
threefold dilutions of inhibitor ( 10 mm stock solution in dmso ) from an initial concentration of 100 m were performed on the assay plate in buffer containing the above concentrations of enzyme ; the final volume in the well after dilution was 96 l .
the plate was sealed and preincubated at rt for 3 h for mtb proteasome or 1 h for human proteasome .
next , substrate ( 5 l of 500 m in a buffer made from a 10 mm stock solution in dmso ) was added , and the fluorescence read in the plate reader immediately ( t=0 ) , then after 3 h for the mtb proteasome and after 1 h for the human proteasome .
the t=0 value was subtracted from the final value , and plotted against the logarithm of the inhibitor concentration ; the data were fitted to the standard ic50 equation using graphpad prism 5 ( graphpad software inc .
the mic were determined as previously described29 in middlebrook 7h9 medium containing 10 % v / v oadc ( oleic acid , bovine serum albumin , d - glucose , catalase ; becton dickinson , usa ) and 0.05 % w / v tween 80 .
briefly , compounds were tested in 10-point , two - fold serial dilutions with the highest concentration of 20 m against mtb h37rv expressing a fluorescent protein ( dsred ) .
growth was measured using od590 and rfu after 5 d. curves were fitted using the gompertz function , with mic defined as the minimum concentration required to inhibit growth .
data are reported for optical density at 590 nm ( od590 ) and relative fluorescence units ( rfu ) .
mtb was grown aerobically in middlebrook 7h9 medium containing 10 % v / v oadc and 0.05 % w / v tween 80 , washed , and resuspended in pbs with 0.05 % w / v tyloxapol for 14 d. compounds were added , and viability was determined by plating serial dilutions to determine colony forming units ( cfu ) on middlebrook 7h10 agar plus 10 % v / v oadc .
cytotoxicity was monitored against vero african green monkey kidney epithelial cells ( atcc ccl-81 ) grown in dmem , high glucose , glutamax ( invitrogen ) , supplemented with 10 % fbs , and penicillin streptomycin solution ( gibco ) .
cell viability was measured after 48 h using cell titer glo ( promega ) , and growth inhibition curves were fitted using the levenberg marquardt algorithm .
the tc50 was defined as the compound concentration that gave 50 % inhibition of growth .
hplc analyses were performed using a shimadzu 10 a system with a scl-10avp controller , 2 lc-10ad pumps with a 0.5 ml gradient mixer at the high pressure side , a sil-10 a ( rebuilt to also run 96-well plates ) , a cma 260 degasser , and a waters pda 996 photodiode array detector . a zorbax eclipse xdb - c8 , 5 m ,
2.150 mm column was utilized from dalco chromtech ab ( sollentuna , sweden ) with ch3cn / h2o in 0.05 % tfa as mobile phase and 1 ml min .
the chromatograms were registered at the wavelengths 230 , 254 , and 280 nm . all solutions containing the sample compound were prepared from 10 mm dmso stock solutions stored in glass vials at ambient temperature .
high standards ( hs ) were made by diluting the dmso stock solution 200 times with ch3cn+pbs ph 7.4 ( 1 + 1 ) , obtaining a 50 m solution .
low standards ( ls ) were prepared by diluting hs 20 times with ch3cn+pbs ph 7.4 ( 1 + 1 ) , obtaining a 2.5 m solution .
the hs solution was chromatographed a second time after 24 h to determine the chemical stability .
it was very important to exchange the septa after the first injection to avoid evaporation of the ch3cn .
the solubility solutions were prepared by diluting the dmso stock solution 100 times with pbs ph 7.4 , obtaining a nominal concentration of 100 m .
the solutions were left for 18 h at ambient temperature before filtration . when filtering the sample solution , the first 0.1 ml was discarded , and the rest was collected .
the solubility was determined using a two - point calibration curve forced through the origin . to evaluate the quality of the standard curve
the optimal quotient should equal the value of the concentration ratio , that is , 20.0 . when evaluating the solubility ,
the wavelength used was that which gives the area quotient closest to 20 . the stability ( given in percent remaining )
was obtained by multiplying the area after the 24 h run by 100 and dividing it by the area of the first hs injection .
mw , microwaves ; mtb , mycobacterium tuberculosis ; mdr , multidrug resistant ; xdr , extensively drug resistant ; tdr , totally drug resistant ; mic , minimum inhibitory concentration ; cfu , colony forming units notes . | this is the first report of 5-styryl - oxathiazol-2-ones as inhibitors of the mycobacterium tuberculosis ( mtb ) proteasome . as part of the study , the structure activity relationship of oxathiazolones as mtb proteasome inhibitors has been investigated .
furthermore , the prepared compounds displayed a good selectivity profile for mtb compared to the human proteasome .
the 5-styryl - oxathiazol-2-one inhibitors identified showed little activity against replicating mtb , but were rapidly bactericidal against nonreplicating bacteria .
( e)-5-(4-chlorostyryl)-1,3,4-oxathiazol-2-one ) was most effective , reducing the colony - forming units ( cfu)/ml below the detection limit in only seven days at all concentrations tested .
the results suggest that this new class of mtb proteasome inhibitors has the potential to be further developed into novel antitubercular agents for synergistic combination therapies with existing drugs . | <s>[INST]tuberculosis ( tb ) has been declared a global health emergency by the world health organization ( who ) .
it is estimated that about one third of the worlds population is currently infected with the responsible actinobacteria mycobacterium tuberculosis ( mtb).1 resistance of mtb to available antibiotics has increased drastically , and multidrug - resistant ( mdr ) strains of mtb as well as extensively drug - resistant ( xdr ) strains are becoming a major health problem worldwide.1 furthermore , cases have recently been reported where no available first- and second - line drugs are effective , and this has led to the term totally drug - resistant ( tdr ) tb.2 resistant strains of mtb require longer treatment , which may lead to interruption of therapy and , in turn , lead to further drug resistance . the usual drug regimen for tb at present consists of antibiotics discovered more than 60 years ago , and includes isoniazid , rifampicin , pyrazinamide , and ethambutol.3 these antibiotics act by disruption of cell wall synthesis4 and inhibition of rna synthesis.4c-5 it was quickly discovered that monotherapy led to resistance in the bacteria , and therefore the recommended tb treatment today utilizes a combination of the four first - line drugs for two months , and thereafter a pharmacotherapy with rifampicin and isoniazid for an additional four months.3 considering the long treatment time , the adverse effects associated with the drugs , and the problems with resistant strains , it is clear that there is a great need for novel antibiotics that possess new antitubercular modes of action and that can be used in combination with existing drugs .
proteasomes are responsible for degrading proteins , and so help maintain intracellular protein homeostasis.6 the human proteasome consists of a cylindrical 26s particle composed of a 20s core catalytic component capped at one or both ends with a 19s regulatory subunit , which recognizes and binds the substrate protein . in eukaryotic proteasomes , the 20s core particle is composed of four heptameric rings , of which the two inner rings are made up of seven different -subunits , with only three of them responsible for the proteolytic activity ( 1 , 2 , 5 , with peptidyl - glutamyl - peptide - hydrolyzing , trypsin - like and chymotrypsin - like activities , respectively).7 the mtb proteasome displays the same overall structure as the proteasomes of eukaryotic systems.8 however , prokaryotic 20s proteasomes , including those from mtb , have been shown to have open cylindrical ends , in contrast to the tighter ends of eukaryotic proteasomes , and possess only one type of -subunit , usually resembling the eukaryotic 5 chymotrypsin - like structure.8,9 proteolytic activity involves the -hydroxyl group of the n - terminal threonine , which is present in the active site of proteasome subunits.7a7d in many diseases , such as cancer , auto - immune diseases , and neurodegenerative diseases , cells accumulate various proteins , and the human proteasome has thus emerged as a promising therapeutic target.6a,7a the first human proteasome inhibitor , bortezomib ( velcade ) , was approved for clinical use in the usa in 2003 and in europe in 2004 for the treatment of multiple myeloma ( figure 1 ) .
the x - ray structure of the yeast proteasome in complex with the compound was reported in 2006 , giving valuable insights into its binding interactions.10 serious toxicity associated with peptidyl boronates , such as bortezomib , is mainly due to the inhibition of the 5 subunit of the human proteasome,11 precluding the use for treatment of , for example , infectious diseases .
therefore , the search for alternative classes of inhibitors with greater selectivity towards prokaryotic proteasomes is ongoing .
proteasomes have been shown to be of great importance to mtb ; they help the bacteria survive the nitrosative stress caused by the hosts immune response12 and increase their ability to persist in infected mice.13 furthermore , the actinobacteria are unusual among prokaryotes in that they express proteasomes , meaning that selective action against bacteria of this phylum should be possible.6b,14 it is particularly interesting that proteasome inhibitors have been shown to be active on nonreplicating mtb .
this is important since nonreplicating mtb ( which to a large extent underlie the need for long treatment times ) , display reduced protein synthesis , and are left unaffected by most antitranscription or antitranslation agents currently used for treatment.15 only a few classes of compounds have proven to be active on nonreplicating mtb , for example , oxathiazol-2-ones , quinolones , and allylic thiocyanates.7c,16 mtb proteasome inhibitors displaying species selectivity , thus low associated toxicity , are promising candidates for the development of new antitubercular drugs .
have previously reported that the 1,3,4-oxathiazol-2-one compounds ht1171 and gl5 ( figure 1 ) act as suicide - substrate inhibitors of the mtb proteasome displaying high selectivity over the human proteasome and other proteases , including trypsin , cathepsin b , and matrix metalloproteases.7c they demonstrated that the oxathiazol-2-one moiety acts as an electrophilic warhead , such that the active - site nucleophile , the n - terminal threonine residue , is effectively cyclocarbonylated by an irreversible covalent attack on the heterocycle.7c,8b moreover , oxathiazolones have been reported to have antimycobacterial activity when they were exploited as carboxylic acid bioisosteres in substituted pyridines and pyrazines.17 in an attempt to identify a new generation of species - selective proteasome inhibitors , gryder et al . investigated the effect of replacing the boronate group on the dipeptide backbone of bortezomib with an oxathiazol-2-one moiety .
unfortunately , the resulting compound was not active on the mtb proteasome and only slightly active on the human 20s proteasome.18 more recently , yang et al
. assessed the antitubercular activity of a series of gl5-type oxathiazol-2-ones , together with their dithiazol-3-one analogues , on the virulent mtb h37rv strain , achieving a lowest minimum inhibitory concentration ( mic ) value of 4 g ml ( 15 m ) for ht1171.16 g these compounds also possessed mycobacterial cell wall permeation properties , and were active against nonreplicating mtb .
they have therefore been proposed as highly interesting antitubercular agents for the synergistic combination treatment of tb.7c in the present study , we further investigate the structure activity relationships of 1,3,4-oxathiazol-2-one derivatives with respect to both their potency as mtb proteasome inhibitors and their selectivity over the chymotrypsin - like catalytic activity of the human proteasome as an early assessment of potential toxicity .
furthermore , the compounds were optimized with regard to solubility and stability . finally , activity against replicating and nonreplicating mtb and cytotoxicity to mammalian cells
in a first effort to investigate the chemical space , a wide variety of oxathiazol-2-ones were prepared from the corresponding commercially available amides by treatment with chlorocarbonyl sulfenyl chloride at 100 c for 15 min with microwave ( mw ) heating ( method a ) or at room temperature overnight ( method b ) .
isolated products were thereafter evaluated for proteasome inhibition based on the assay procedures described by lin et al.7c ( table 1 , entries 123 ) .
compounds were tested for chymotrypsin - like peptidase activity against both the mtb 20s open - gate proteasome ( in which the alpha subunit has an 8-residue deletion at the n - terminus , as described by lin et al.8a ) and the human 20s proteasome , tracked by cleavage of the fluorogenic substrate suc - llvy-7-amino-4-methylcoumarin .
method a reagents and conditions : amide ( 1.0 equiv ) , chlorocarbonyl sulfenyl chloride ( 1.5 equiv ) , 1,4-dioxane ( 4.0 ml mmol ) , 100 c mw , 15 min .
method b : amide ( 1.0 equiv ) , chlorocarbonyl sulfenyl chloride ( 2.0 equiv ) , thf ( 4.0 ml mmol ) , rt , o / n . [ a ] chemical stability in pbs ph 7.4 at 25 c as % remaining after 24 h. [ b ] the amide was prepared , and
[ c ] reagents and conditions : 14 ( 1.0 mmol ) , dess
martin periodinane ( 1.1 mmol ) , ch2cl2 ( 5 ml ) , 0 c , 2 h. [ d ] general method for the synthesis of 3-substituted dioxazolones .
reagents and conditions : starting hydroxamic acid ( 1.0 equiv ) , 1,1-carbonyldiimidazole ( 1.1 equiv ) , ch3cn ( 4.0 ml mmol ) , 0 c , 1 h. [ e ] the hydroxamic acid was prepared and used as starting material for the dioxazolone synthesis without further purification .
the 5-aryl - substituted 1,3,4-oxathiazol-2-ones in entries 14 ( table 1 , 14 ) have previously been reported as inhibitors of the mtb proteasome.19 to further develop the core structure , we decided to find out if elongated compounds with different spacers could have a positive impact on the activity . for this purpose ,
various tethers between the aryl and the heterocyclic warhead were introduced in the 5-position , for example , alkene , alkyne , and methylene linkers .
we found that an sp - hybridized carbon directly coupled to the oxathiazol-2-one ring in the 5-postion was crucial for the compounds activity .
additionally , the introduction of the ( e)-alkene linker ( entries 1718 ) gave inhibitors equally or more potent ( 17 and 18 ; ic50=420 and 640 nm , respectively ) toward the mtb proteasome compared to when the aryl was substituted directly onto the oxathiazol-2-one ( 14 ) .
more importantly , this type of compound was not active on the human proteasome ( ic50>100 000 nm ) . for compounds with an alkyne- or carbonyl - containing spacer ( 19 and 20 ) ,
the activities on the mtb proteasome were slightly lower compared to olefinic inhibitors 17 and 18 .
moreover , these linkers provided less selective inhibitors . when an sp - hybridized carbon was used as a linker atom , no activity
was obtained against the mtb proteasome , and little or no inhibition was seen towards the human proteasome ( entries 916 ) .
interestingly , when an ethyl bridge was introduced instead of the double bond between the phenyl and oxathiazol-2-one ( compare moieties 15 and 17 ) , no inhibition was observed for the mtb proteasome , but the saturated compound instead gained some activity toward the human proteasome .
this suggests that the ( e)-double bond is important both for the mycobacterial inhibition and the selectivity over the human proteasome .
however , the allowed substitution pattern of the ( e)-alkene linker seems to be slightly constrained ; when an additional phenyl group was introduced onto the ethylene linker , no activity was detected against the mtb proteasome ( entry 23 ) . instead , compound 23 became a more potent inhibitor of the human proteasome .
the aryl group of the styryl moiety also seems to be important for the interaction with the mtb protein . when a vinyl group was substituted onto the oxathiazol-2-one , the activity decreased from 420 nm for 17 to 27 000 nm for 21 .
the effect is probably due to the lack of an aryl group as well as the effect of the hybridization of the carbon directly attached to the oxathiazol-2-one . to summarize the results depicted in table 1
, it appears that an aryl group conjugated with the oxathiazolone scaffold is highly beneficial for the inhibition of the mtb proteasome ( see products 14 and 1722 ) , and in particular high selectivity over the human proteasome is caused by the presence of the ( e)-alkene linker ( 17 and 18 ) .
this may also be coupled to the loss of activity for the unconjugated 15 . to increase the scope of the investigation
, we wished to evaluate other heterocyclic warheads such as the dioxazolones ( table 1 , entries 2425 ) , but these compounds suffered from poor stability due to rapid hydrolysis .
the oxathiazol-2-one was also replaced with a boronic acid functionality ( table 1 , entries 2627 ) in an attempt to mimic the reversible covalently - bonded warhead used in bortezomib . however , the simple boronic acid analogues were completely inactive on both the mtb and human proteasomes , suggesting that the oxathiazol-2-one moiety is a more useful electrophile for the inactivation of the target .
a series of 5-styryl - oxathiazol-2-ones was synthesized to further investigate the effect of the phenyl substitution on the structure activity relationship of proteasome inhibitors . for this , we developed a synthetic route where aryl iodides or bromides were used as starting material in a microwave - assisted mizoroki heck cross - coupling reaction with acrylamide to yield the corresponding 3-substituted acrylamides.20 , 21 the final 5-substituted - oxathiazolones were obtained by treating the corresponding amides with chlorocarbonyl sulfenyl chloride ( scheme 1 ) .
a diverse set of para - substituted 5-styryl - oxathiazolones were chosen to explore the structural requirements of the active site ( table 2 , entries 112 ) .
the majority of the compounds displayed the same range of inhibiting activity against the mtb proteasome as 17 and 18 ( ic50 values between 4151700 nm ) .
the results showed no clear trend in activity for electron - rich and electron - poor aryl substituents , although electron - poor phenyl groups gave slightly better inhibition of the mtb proteasome compared to electron - rich phenyls .
the inhibition of the human proteasome was unfortunately also affected , giving a poorer selectivity profile . however , based on the relative activities for nonstyryl containing 21 and 22 ( table 1 , entries 2122 ) , it is evident that the phenyl group is important for inhibition of the mtb proteasome .
structure activity relationship of 5-styryl - oxathiazolone inhibitors with the mtb and human proteasome .
method c reagents and conditions : starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , pd(oac)2 ( 0.05 equiv ) , tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min . method d reagents and conditions : .
starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) and pd(oac)2 ( 0.05 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min .
method e reagents and conditions : starting aryl bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) and trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , naoac ( 3.0 equiv ) , dmf ( 4.0 ml mmol ) , 140 c mw , 15 min .
[ a ] chemical stability in pbs ph 7.4 at 25 c ; as % remaining after 24 h. [ b ] isolated yield over two steps .
four of the compounds with the best inhibition and selectivity profiles ( table 2 , 3033 ) were chosen for further investigation .
for these compounds , the corresponding ortho- and meta - analogues were synthesized and evaluated in the enzyme activity assay ( table 2 , entries 1421 ) .
the para - substituted analogues ( table 2 , entries 36 ) were more active than ortho- and meta - substituted analogues on the mtb proteasome , with ic50 values in the range of 4751080 nm .
furthermore , no inhibition of the human proteasome was detected for these compounds . when substituents were introduced in the meta - position ( table 2 , entries 1417 ) , inhibitory activity of the mtb proteasome decreased ( ic50 14509900 nm ) and poorer selectivity was observed .
the ortho - substituted analogues ( entries 1821 ) , despite the same mesomeric contribution as the para - analogues on the styryl moiety , showed almost no inhibition of the mtb proteasome ( ic50 22 000 > 100 000 nm ) .
the same trend was observed for chloro - functionalized 39 and disubstituted 40 ( table 2 , entries 1213 ) ; the para - substituted compound was more active on the mtb proteasome and had superior selectivity with regard to the human proteasome .
overall , the styryl - analogues 2848 in table 2 displayed good stability but poor solubility ( 0.17.1 m ) . to hopefully improve the solubility of the compounds , a small series of nitrogen- , oxygen- and sulfur - containing heterocyclic derivatives were prepared ( table 3 ) .
the introduction of five - membered , six - membered , and bicyclic heterocycles into the scaffold generally improved the solubility with retained chemical stability .
furthermore , the heterocyclic analogues were active on the mtb proteasome , although slightly higher ic50 values were obtained compared to the compounds in table 2 .
however , for the five - membered heterocycle - substituted oxathiazolones , the compounds were not as selective with regard to the human proteasome ( table 3 , entries 35 and 9 ) .
method c reagents and conditions : starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , pd(oac)2 ( 0.05 equiv ) , tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min . method d reagents and conditions : .
starting aryl iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) and pd(oac)2 ( 0.05 equiv ) , et3n ( 3.0 equiv ) , ch3cn ( 4.0 ml mmol ) , 120 c mw , 15 min .
method e reagents and conditions : starting aryl bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) and trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , naoac ( 3.0 equiv ) , dmf ( 4.0 ml mmol ) , 140 c mw , 15 min .
[ a ] chemical stability in pbs ph 7.4 at 25 c ; as % remaining after 24 h. [ b ] isolated yield over two steps .
[ c ] the compound interferes with the assay at 10 m , therefore it was not possible to measure human proteasome inhibition .
[ d ] reagents and conditions : 1 ) ( 2e)-3-(1h - indolyl-3-yl)acrylic acid ( 2.0 mmol ) , 1,1-carbonyldiimidazole ( 2.0 mmol ) , dmf ( 10 ml ) , rt , 30 min , 2 ) nh4hco3 ( 4.0 mmol ) , rt , o / n . based on these promising results for both inhibition and selectivity of the 5-styryl - oxathiazol-2-ones ,
active mtb proteasome inhibitors displaying full to moderate selectivity were tested against a virulent strain of mtb ( h37rv ) .
four 5-aryl - oxathiazol-2-ones ( table 4 , entries 14 ) were also tested for comparison , as well as three known antitubercular agents as a reference ( entries 30 - 32 ) .
cytotoxicity for mammalian cells was investigated using the vero cell line ( african green monkey kidney cells ) ; the results are reported in table 4 .
the minimum inhibitory concentration ( mic ) was determined against aerobically - grown mtb h37rv using a 10-point serial dilution by optical density ( od ) and relative fluorescence units ( rfu ) measurement .
the highest concentration of compound tested was 20 m . the % growth was plotted , and a curve was fitted using the gompertz fit .
the mic was defined as the minimum concentration at which growth was completely inhibited and was calculated from the inflection point of the fitted curve to the lower asymptote ( zero growth ) .
cytotoxicity was measured against the vero cell line ; the tc50 is the concentration required to inhibit growth by 50 % over 48 h. n.d.=not determined . [
a ] known antitubercular agents were used as reference compounds.3 the oxathiazolones had little or no activity against replicating bacteria when compared to the known antitubercular agents used as reference ( entries 30 - 32 in table 4 ) .
a few compounds showed > 20 % inhibition of growth at the maximum concentration tested ( 20 m ) , but none had an mic20 m . there was no clear difference between the 5-styryl - oxathiazol-2-ones ( entries 529 ) and the previously reported 5-aryl - analogues ( entries 14 ) or with respect to the electronic nature and/or position of the ring substitution .
this finding is consistent with the mic values ( 15299 m ) for a series of 5-aryl - oxathiazol-2-ones recently tested on the same mtb strain.16 g compounds demonstrated some cytotoxicity against the vero cell line , with tc50 values ( concentration required to inhibit growth by 50 % over 48 h ) in the range of 1141 m ( when tested ) .
however , these results indicate that our new inhibitors are generally 1000/4000-fold less toxic than the approved human proteasome inhibitor bortezomib ( tc50 less than 10 nm).7c the observed cytotoxicity might be related to the inhibition of the trypsin - like and caspase - like activity of the mammalian proteasome.22 alternatively , it might be due to the non - proteasome - related activity of the styryl oxathiazolone compounds towards other cellular enzymes that catalyze bond cleavage via the same mechanism as the mtb - proteasome ( i.e. nucleophilic attack ) .
on the other hand , a previous report from lin et al . demonstrated generally reduced inhibition potency for the parent aryl - oxathiazolone inhibitors ( e.g. compounds 14 included in our study ) toward 1 and 2 non - chymotrypsin - like active sites of the proteasome.7c additionally high selectivity towards other human proteases , including trypsin , cathepsin b , and matrix metalloproteases was reported for the same proteasome inhibitors.7c however , recent research by bassett et al . has revealed cytotoxicity towards vero cells for a number of proteasome inhibitors reported as antitubercular agents.23 previous work suggested that the proteasome plays a key role during oxidative and nitrosative stress,12 and that proteasome inhibitors are bactericidal against nonreplicating mtb subjected to nitrosative stress.7c we therefore determined whether the 5-styryl - oxathiazolone class of compounds had activity against mtb under nonreplicating conditions . for this we used a starvation model , in which bacteria are nutrientdeprived for 14 days,24 to induce the nonreplicating state , after which they are exposed to compounds over 21 days in this state ( figure 2 ) .
mtb was grown aerobically , washed , and resuspended in pbs - tyloxapol for 14 d. compounds were added with the indicated concentrations .
all four 5-styryl - oxathiazol-2-ones tested ( 17 , 33 , 37 , and 39 ) were bactericidal against nonreplicating mtb , displaying a very rapid kill ( > 4 logs in 714 days ) .
all compounds gave complete sterilization of cultures within 14 days at the lowest concentration tested ( 20 m ) .
the 5-(4-chloro)styryl - oxathiazol-2-one inhibitor ( 39 ) was most effective , reducing the colony - forming units ( cfu)/ml below the detection limit in only seven days at all concentrations .
our results demonstrate that 5-styryl - oxathiazol-2-ones provide a promising scaffold for mtb proteasome inhibitors . in the current study
we found that conjugated 5-styryl - oxathiazolones are equally or more potent inhibitors of the mtb proteasome compared to the previously reported 5-aryl - oxathiazolones .
as part of this investigation we prepared a series of novel 5-styryl - oxathiazolones from the corresponding aryl iodides or bromides by a microwave - assisted mizoroki heck coupling with acrylamide .
our enzyme activity results showed that para - substituted 5-styryl - oxathiazol-2-ones were superior to ortho- and meta - substitution with regard to mtb proteasome ic50 values , as well as their relative lack of effects against the chymotrypsin - like peptidase activity of human proteasomes .
we also produced a small series of oxathiazolones in which solubility - enhancing heterocyclic groups were introduced .
however , we gained solubility at the expense of selectivity regarding the human proteasome . finally , a selection of the synthesized inhibitors showed rapid bactericidal activity against nonreplicating mtb , although they were not very active against actively replicating cells .
the present results suggest that this new class of mtb proteasome inhibitors can be used as the basis for development of novel antitubercular drugs that are effective when protein synthesis of the mycobacteria is drastically reduced , such as in the nonreplicative state or during antibiotic treatment .
further development will include the improvement of the safety profile of this class of mtb proteasome inhibitors.30
general chemistry . analytical thin - layer chromatography ( tlc ) was performed on silica gel 60 f-254 plates ( merck ) and visualized with uv light .
flash column chromatography was performed on columns prepacked with pharma - sil ( 5 g/10 g , hydrophilic high surface activity silica , uct , inc . ,
h and c nmr spectra were recorded on varian mercury plus instruments ( palo alto , usa ) ; h nmr spectra at 399.9 mhz and c nmr spectra at 100.5 mhz .
the chemical shifts for h nmr and c nmr were referenced to tetramethylsilane ( tms ) via residual solvent signals ( h , cdcl3 at 7.26 ppm and [ d6]-dimethylsulfoxide ( dmso ) at 2.50 ppm ; c , cdcl3 at 77.0 ppm and [ d6]dmso at 39.5 ppm ) , while chemical shifts for f nmr were referenced to cfcl3 used as internal standard ( 0.0 ppm ) .
the microwave reactions were performed in a biotage initiator ( uppsala , sweden ) producing controlled irradiation at 2450 mhz with a power of 0300 w. the reaction temperature was determined using the built - in on - line infrared ( ir ) sensor .
all reactions were performed in sealed microwave - transparent process vials designed for 0.52 , 25 , or 1020 ml reaction volumes .
gas chromatography / electron ionization mass spectrometry ( gc / ei - ms ) was performed on a varian saturn 3900/2100 system equipped with a cp - sil 8 cb capillary column ( 30 m0.25 mm , 0.25 m ) operating at an ei potential of 70 ev .
analytical high - performance liquid chromatography / electrospray ionization mass spectrometry ( hplc / esi - ms ) was performed on a gilson hplc system ( middleton , usa ) with a finnigan aqa esi quadropole mass spectrometer with electrospray ionization ( thermo fisher scientific , waltham , usa ) and using an onyx monolithic c18 column 4.650 mm ( phenomenex , torrance , usa ) with ch3cn / h2o in 0.05 % hcooh as mobile phase at a flow rate of 4 ml min or on a dionex ultimate 3000 hplc system ( sunnyvale , usa ) with a bruker amazon sl ion trap mass spectrometer ( billerica , usa ) , using a phenomenex kinetex c18 column ( 503.0 mm , 2.6 m particle size , 100 pore size ) with ch3cn / h2o in 0.05 % hcooh as mobile phase at a flow rate of 1.5 ml min .
detection was by uv ( diode array detector ) and ms ( esi+ mode ) .
preparative hplc purification was performed by uv - triggered ( 254 nm ) fraction collection with a dionex ultimate 3000 hplc system , using an agilent prepht zorbax sb - c8 column ( 21.2150 mm , 5 m particle size ) ( santa clara , usa ) with ch3cn / h2o in 0.05 % trifluoroacetic acid ( tfa ) as mobile phase .
high - resolution mass spectrometry ( hrms ) was performed on a micromass q - tof2 mass spectrometer ( waters , milford , usa ) equipped with an electrospray ion source .
hrms data are provided for all novel compounds , unless low ionization level , intrinsic to the physicochemical properties of the specific molecules , did not permit the measurement of the corresponding molecular mass data . however , in some cases , it was possible to determine the low resolution molecular mass by the varian saturn 3900/2100 gc / ms system and/or by the bruker amazon sl ion trap mass spectrometer during the lc / ms analysis .
general method for the synthesis of 5-substituted oxathiazol-2-one. method a : a mixture of starting amide ( 1.0 equiv ) and chlorocarbonyl sulfenyl chloride ( 1.5 equiv ) in 1,4-dioxane ( 4.0 ml mmol ) was irradiated with microwaves at 100 c for 15 min .
the mixture was allowed to cool down to rt , and the solvent evaporated at reduced pressure .
the crude material was purified by silica gel column chromatography and/or preparative hplc to give the final compound with purity>95 % by hplc analysis ( =254 nm ) .
method b : a mixture of starting amide ( 1.0 equiv ) and chlorocarbonyl sulfenyl chloride ( 2.0 equiv ) in freshly distilled thf ( 4.0 ml mmol ) was stirred o / n at rt .
the solvent was evaporated at reduced pressure , and the crude material was purified by silica gel column chromatography and/or preparative hplc to give the final compound with purity>95 % by hplc analysis ( =254 nm ) .
5-phenyl-1,3,4-oxathiazol-2-one ( 1).7c according to method a , benzamide ( 121 mg , 1.0 mmol ) was used to give , after preparative hplc purification , 77 mg ( 43 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.53 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.997.96 ( m , 2 h ) , 7.607.55 ( m , 1 h ) , 7.527.47 ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.8 , 157.4 , 132.6 , 129.0 , 127.4 , 125.8 ; hrms m / z for c8h5no2s as [ m+h ] adduct not found due to low ionization level .
5-(pyrazin-2-yl)-1,3,4-oxathiazol-2-one ( 2).17 according to method b , pyrazinamide ( 123 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after preparative hplc purification , 42 mg ( 23 % isolated yield ) of the title compound as white crystals .
tlc : rf=0.29 ( pentane / etoac 1:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =9.29 ( s , 1 h ) , 8.79 ( s , 1 h ) , 8.75 ppm ( s , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =172.2 , 154.6 , 147.2 , 144.7 , 144.3 , 140.2 ppm ; esi - ms m / z : 182 [ m+h ] ; hrms m / z calcd for c6h3n3o2s [ m+h ] 182.0024 , found 182.0031 .
5-(3-methoxyphenyl)-1,3,4-oxathiazol-2-one ( 3).7c according to method b , 3-methoxybenzamide ( 151 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 80 mg ( 38 % isolated yield ) of the title compound as a white powder .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.537.49 ( m , 2 h ) , 7.417.39 ( m , 1 h ) , 7.277.20 ( m , 1 h ) , 3.84 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 159.5 , 156.6 , 130.6 , 126.8 , 119.5 , 118.9 , 111.7 , 55.5 ppm ; esi - ms m / z : 210 [ m+h ] ; hrms m / z for c9h7no3s as [ m+h ] adduct not found due to low ionization level .
3-fluorobenzamide ( 139 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 163 mg ( 83 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.79 ( pentane/ etoac 100:3 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.78 ( dt , j=7.6 , 1.2 hz , 1 h ) , 7.70 ( ddd , j=9.2 , 2.8 , 1.6 hz , 1 h ) , 7.65 ( td , j=8.0 , 5.9 hz , 1 h ) , 7.53 ppm ( tdd , j=8.8 , 2.8 , 0.8 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 162.1 ( d , j=244.0 hz ) , 155.6 ( d , j=3.1 hz ) , 131.7 ( d , j=8.4 hz ) , 127.6 ( d , j=9.2 hz ) , 123.4 ( d , j=3.0 hz ) , 119.7 ( d , j=21.4 hz ) , 113.8 ppm ( d , j=23.7 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =111.4 ppm ( td , j=9.3 , 5.3 hz ) ; ei - ms m / z : 197 [ m ] ; hrms m / z for c8h4fno2s as [ m+h ] adduct not found due to low ionization level .
according to method a , 3-chloropropionamide ( 81 mg , 0.75 mmol ) was used to give , after silica column purification ( pentane / etoac 100:2 ) , 75 mg ( 60 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.31 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm):99 % ; h nmr ( 400 mhz , cdcl3 ) : =3.84 ( t , j=6.4 hz , 2 h ) , 3.11 ppm ( t , j=6.4 hz , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.9 , 38.4 , 33.7 ppm ; ei - ms m / z : 166/168 [ m+1 ] ; esi - ms m / z : 166/168 [ m+h ] ; hrms m / z for c4h4clno2s as [ m+h ] adduct not found due to low ionization level
according to method a , cyclopropanecarboxamide ( 85 mg , 1.0 mmol ) was reacted to give , after silica column purification ( pentane / etoac 100:1 ) , 38 mg ( 27 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.51 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) 99 % ; h nmr ( 400 mhz , cdcl3 ) : =1.981.90 ( m , 1 h ) , 1.181.12 ( m , 2 h ) , 1.111.04 ppm ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.2 , 162.7 , 11.2 , 8.4 ppm ; ei - ms m / z : 143 [ m ] ; hrms m / z for c5h5no2s as [ m+h ] adduct not found due to low ionization level . 5-pentyl-1,3,4-oxathiazol-2-one ( 7 ) . according to method a , hexanamide ( 86 mg , 0.75 mmol ) was used to give , after silica column purification ( pentane / etoac 100:1 ) , 73 mg ( 56 % isolated yield ) of the title compound as colorless oil .
tlc : rf=0.65 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =2.61 ( t , j=7.0 hz , 2 h ) , 1.73 ( quin , j=7.0 hz , 2 h ) , 1.401.30 ( m , 4 h ) , 0.91 ppm ( t , j=7.0 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.4 , 162.0 , 30.9 , 30.4 , 25.0 , 22.1 , 13.8 ppm ; ei - ms m / z : 174 [ m+1 ] ; esi - ms m / z : 174 [ m+h ] ; hrms m / z for c7h11no2s as [ m+h ] adduct not found due to low ionization level .
according to method b , fluoroacetamide ( 154 mg , 2.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:2 ) , 64 mg ( 24 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.55 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm)=96 % ; h nmr ( 400 mhz , [ d6]dmso ) : =5.39 ppm ( d , j=45.6 hz , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 155.7 ( d , j=21.5 hz ) , 76.9 ppm ( d , j=171.0 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =0.96 ppm ( t , j=45.5 hz ) ; ei - ms m / z : 135 [ m ] , 196 ; hrms m / z for c3h2fno2s as [ m+h ] adduct not found due to low ionization level . 5-benzyl-1,3,4-oxathiazol-2-one ( 9).25 according to method a , 2-phenylacetamide ( 135 mg , 1.0 mmol ) was reacted to yield , after preparative hplc purification , the title compound as a white powder ( 83 mg , 43 % ) .
tlc : rf=0.39 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , cdcl3 ) : =7.407.28 ( m , 5 h ) , 3.93 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.0 , 160.0 , 132.3 , 129,1 , 129.0 , 127.9 , 37.0 ppm ; hrms m / z for c9h7no2s as [ m+h ] adduct not found due to low ionization level .
according to method a , 4-methoxyphenylacetamide ( 83 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 30 mg ( 27 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.35 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , cdcl3 ) : =7.28 ( t , j=7.8 hz , 1 h ) , 6.906.82 ( m , 3 h ) , 3.90 ( s , 2 h ) , 3.81 ppm ( s , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =174.0 , 160.0 , 133.7 , 130.0 , 121.3 , 114.9 , 113.2 , 55.3 , 37.0 ppm ; ei - ms m / z : 184 , 147 ; esi - ms m / z : 224 [ m+h ] ; hrms m / z calcd for c10h9no3s [ m+h ] 224.0381 , found 224.0380 .
according to method a , 2-(4-formylphenoxy)acetamide ( 90 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 47 mg ( 39 % isolated yield ) of the title compound as white powder .
tlc : rf=0.10 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =9.92 ( s , 1 h ) , 7.89 ( d , j=8.8 hz , 2 h ) , 7.09 ( d , j=8.8 hz , 2 h ) , 5.05 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =190.5 , 172.6 , 161.9 , 155.8 , 132.1 , 131.3 , 115.0 , 63.2 ppm ; ei - ms m / z : 238 [ m+1 ] ; esi - ms m / z : 238 [ m+h ] ; hrms m / z calcd for c10h7no4s [ m+h ] 238.0174 , found 238.0175 .
according to method a , 1-naphthylacetamide ( 93 mg , 0.50 mmol ) was used to yield , after preparative hplc purification , 62 mg ( 51 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.48 ( isohexane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =8.03 ( d , j=7.8 hz , 1 h ) , 7.927.83 ( m , 2 h ) ,
7.617.51 ( m , 2 h ) , 7.507.45 ( m , 2 h ) , 4.38 ppm ( s , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.9 , 159.9 , 133.9 , 131.6 , 129.0 , 128.5 , 128.3 , 126.9 , 126.1 , 125.5 , 123.2 , 34.6 ppm ; ei - ms m / z : 228 , 167 ; esi - ms m / z : 244 [ m+h ] ; hrms m / z calcd for c13h9no2s [ m+h ] 244.0432 , found 244.0427 .
according to method b , 2-(trifluoromethyl)phenylacetamide ( 152 mg , 0.75 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after two silica column purification ( 1 : pentane / etoac 100:0 10:1 , 2 : pentane / etoac 100:0 100:2 ) , 110 mg ( 56 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.53 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.72 ( d , j=7.8 hz , 1 h ) , 7.58 ( t , j=7.8 hz , 1 h ) , 7.497.41 ppm ( m , 2 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.7 , 158.9 , 132.3 , 132.0 , 130.5 ( q , j=1.5 hz ) , 129.1 ( q , j=30.7 hz ) , 128.3 , 126.6 ( q , j=5.4 hz ) , 124.0 ( q , j=273.7 hz ) , 33.8 ppm ( q , j=2.3 hz ) ; f nmr ( 376 mhz , cdcl3 ) : 59.8 ppm ; esi - ms m / z : 262 [ m+h ] ; hrms m / z calcd for c10h6f3no2s [ m+h ] 262.0150 , found 262.0154 .
according to method b , 2-hydroxy-2-phenylacetamide ( 151 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column ( pentane / etoac 100:0 1:1 ) and preparative hplc purification , 84 mg ( 40 % isolated yield ) of the title compound as a pale yellow oil .
tlc : rf=0.17 ( pentane / etoac 5:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.487.32 ( m , 5 h ) , 6.73 ( d , j=5.5 hz , 1 h ) , 5.65 ppm ( d , j=5.5 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.0 , 161.9 , 138.3 , 128.5 , 128.4 , 126.7 , 69.9 ppm ; esi - ms m / z : 232 [ m+na ] ; hrms m / z for c9h7no3s as [ m+h ] adduct not found due to low ionization level .
3-phenylpropionic acid ( 150 mg , 1.0 mmol ) and 1,1-carbonyldiimidazole ( 357 mg , 2.2 mmol ) were dissolved in dmf ( 5 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 316 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 220 ml ) and brine ( 20 ml ) .
evaporation of solvent gave 171 mg of the crude corresponding amide , purified by precipitation from etoac / pentane to afford 92 mg ( 62 % isolated yield ) of 3-phenylpropionamide as a white solid .
tlc : rf=0.28 ( pentane / etoac 1:1 ) ; gc / ms purity : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.356.98 ( m , 6 h ) , 6.76 ( bs , 1 h ) , 2.81 ( t , j=8.0 hz , 2 h ) , 2.36 ppm ( t , j=8.0 hz , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 141.5 , 128.2 , 128.1 , 125.8 , 36.7 , 30.9 ppm ; ei - ms m / z : 149 [ m ] . according to method b , 3-phenylpropionamide ( 150 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 147 mg ( 71 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.79 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.357.20 ( m , 5 h ) , 2.98 ppm ( s , 4 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.3 , 161.2 , 139.6 , 128.4 , 128.3 , 126.4 , 31.2 , 30.4 ppm ; esi - ms m / z : 208 [ m+h ] ; hrms m / z for c10h9no2s as [ m+h ] adduct not found due to low ionization level .
( r)-()-2-methoxyphenylacetic acid ( 332 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 649 mg , 4.0 mmol ) were dissolved in dmf ( 10 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 632 mg , 8.0 mmol ) was added and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 230 ml ) and brine ( 30 ml ) .
evaporation of solvent gave 180 mg ( 55 % yield ) of the crude ( r)-2-methoxy-2-phenylacetamide as a white powder , used for the next step without further purification .
gc / ms purity : 99 % ; ei - ms m / z : 166 [ m+1 ] .
according to method b , ( r)-2-methoxy-2-phenylacetamide ( 180 mg , 1.1 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 140 mg ( 58 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.64 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.487.38 ( m , 5 h ) , 5.44 ( s , 1 h ) , 3.43 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 159.4 , 135.4 , 129.0 , 128.7 , 127.2 , 78.8 , 57.3 ppm ; esi - ms m / z : 164 ; hrms m / z calcd for c10h9no3s [ m+h ] 224.0381 , found 224.0379 .
( e)-5-styryl-1,3,4-oxathiazol-2-one ( 17).26 according to method b , trans - cinnamamide ( 147 mg , 1.0 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 10:1 ) and trituration in pentane / etoac / meoh 10:1:1 drop , 82 mg ( 40 % isolated yield ) of the title compound as a pale yellow powder .
tlc : rf=0.76 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.567.49 ( m , 2 h ) , 7.50 ( d , j=16.4 hz , 1 h ) , 7.447.39 ( m , 3 h ) , 6.64 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.6 , 142.0 , 134.1 , 130.6 , 129.1 , 127.8 , 112.8 ppm ; ei - ms m / z : 191 , 161 , 129 ; esi - ms m / z : 206 [ m+h ] ; hrms m / z calcd for c10h7no2s [ m+h ] 262.0276 , found 262.0273 .
b , 4-(trifluoromethyl)cinnamamide ( 183 mg , 0.85 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 97 mg ( 42 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.57 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.01 ( d , j=8.2 hz , 2 h ) , 7.79 ( d , j=8.2 hz , 2 h ) , 7.63 ( d , j=16.4 hz , 1 h ) , 7.17 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 157.0 , 139.5 , 138.2 ppm ( q , j=1.5 hz ) , 129.9 ( q , j=32.2 hz ) , 128.8 , 125.7 ( q , j=3.8 hz ) , 124.0 ( q , j=272.2 hz ) , 116.0 ; f nmr ( 376 mhz , [ d6]dmso ) : =61.3 ppm ; esi - ms m / z : 274 [ m+h ] ; hrms m / z for c11h6f3no2s as [ m+h ] adduct not found due to low ionization level .
martin periodinane ( 467 mg , 1.1 mmol ) was added to a precooled solution ( t=0 c ) of 5-(hydroxy(phenyl)methyl)-1,3,4-oxathiazol-2-one ( 14 ) ( 209 mg , 1.0 mmol ) in anhydrous ch2cl2 ( 5 ml ) .
the resulting reaction mixture was stirred 2 h at 0 c and then filtered to remove the formed solid .
the mother liquor was washed with h2o ( 10 ml ) and dried on anhydrous na2so4 .
evaporation of the solvent under reduced pressure gave 347 mg of the crude material that was triturated with etoac for 30 min at rt .
filtration of the formed solid and evaporation of the solvent gave 117 mg of a colorless oil that was purified by silica column purification ( pentane / etoac 100:0 10:1 ) to give 118 mg ( 57 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.48 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.188.13 ( m , 2 h ) , 7.787.72 ( m , 1 h ) , 7.637.57 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =177.4 , 172.3 , 153.3 , 134.5 , 133.5 , 130.6 , 128.6 ppm ; ei - ms m / z : 208 [ m+1 ] ; esi - ms m / z : 208 [ m+h ] ; hrms m / z calcd for c9h5no3s [ m+h ] 208.0068 , found 208.0070 .
5-(phenylethynyl)-1,3,4-oxathiazol-2-one ( 20 ) . in a round - bottom flask , socl2 ( 714 mg , 6.0 mmol )
was added to a solution of phenylpropiolic acid ( 730 mg , 5.0 mmol ) in chcl3 ( 10 ml ) at rt after addition of dmf ( 1 drop ) , the reaction mixture was stirred 1 h at rt to the resulting solution was then added 25 % aq nh4oh ( 2.5 ml ) at 10 c .
the reaction mixture was allowed to return to rt and stirred 30 min at this temperature .
chcl3 ( 10 ml ) and h2o ( 10 ml ) where added , the aqueous layer was extracted with chcl3 ( 220 ml ) and the combined organic phases were dried over na2so4 .
evaporation of the solvent under reduced pressure gave 377 mg ( 52 % isolated yield ) of the crude 3-phenylpropiolamide as a white solid , which was used for the next step without further purification .
tlc : rf=0.72 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.14 ( bs , 1 h ) , 7.66 ( bs , 1 h ) , 7.617.52 ( m , 2 h ) , 7.517.42 ppm ( m , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =153.9 , 132.0 , 130.2 , 128.9 , 119.9 , 84.2 , 82.9 ppm ; esi - ms m / z : 146 [ m+h ] , 291 [ 2 m+h ] . according to method b , 3-phenylpropiolamide ( 150 mg , 1.03 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by silica column ( pentane / etoac 100:1 10:1 ) followed by preparative hplc purification , 51 mg ( 24 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.80 ( pentane / etoac 9 : 1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.757.71 ( m , 2 h ) , 7.647.58 ( m , 1 h ) , 7.567.50 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =172.3 , 141.5 , 132.6 , 131.6 , 129.2 , 118.1 , 92.3 , 75.7 ppm ; esi - ms m / z : 204 [ m+h ] ; hrms m / z for c10h5no2s as [ m+h ] adduct not found due to low ionization level .
5-vinyl-1,3,4-oxathiazol-2-one ( 21).27 according to method b , acrylamide ( 107 mg , 1.5 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after two silica column purification ( 1 : pentane / etoac 100:0 10:1 , 2 : pentane / etoac 100:0 100:2 ) , 15 mg ( 8 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.73 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , cdcl3 ) : =6.32 ( dd , j=17.6 , 10.9 hz , 1 h ) , 6.23 ( d , j=17.6 hz , 1 h ) , 5.92 ppm ( d , j=10.5 hz , 1 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.1 , 157.0 , 127.9 , 122.9 ppm ; ei - ms m / z : 129 [ m ] ; hrms m / z for c4h3no2s as [ m+h ] adduct not found due to low ionization level .
according to method b , 4,4,4-trifluorocrotonamide ( 306 mg , 2.2 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:2 ) , 350 mg ( 81 % isolated yield ) of the title compound as a colorless oil .
tlc : rf=0.69 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.127.01 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =172.7 , 154.2 , 127.1 ( q , j=34.3 hz ) , 124.0 ( q , j=6.9 hz ) , 122.5 ppm ( q , j=268.4 hz ) ; f nmr ( 376 mhz , [ d6]dmso ) : =63.5 ppm ( d , j=5.6 hz ) ; hrms m / z for c5h2f3no2s as [ m+h ] adduct not found due to low ionization level .
2-phenyl - trans - cinnamic acid ( 224 mg , 1.0 mmol ) and 1,1-carbonyldiimidazole ( 357 mg , 2.2 mmol ) were dissolved in dmf ( 5 ml ) and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 316 mg , 4.0 mmol ) was added and the resulting suspension was stirred at rt for 3 d. etoac ( 50 ml ) was added , and the organic phase was washed with h2o ( 220 ml ) and brine ( 20 ml ) .
evaporation of solvent gave 212 mg of the crude corresponding amide , purified by silica column chromatography ( pentane / etoac 1:1 3:1 ) to afford 150 mg ( 67 % isolated yield ) of 2-phenyl - trans - cinnamamide as white crystals .
tlc : rf=0.63 ( pentane / etoac=1:1 ) ; gc / ms purity : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.467.35 ( m , 4 h ) , 7.30 ( bs , 1 h ) , 7.247.15 ( m , 5 h ) , 7.036.97 ( m , 2 h ) , 6.90 ppm ( bs , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =170.0 , 136.7 , 136.6 , 135.0 , 133.9 , 129.7 , 129.3 , 128.8 , 128.2 , 128.1 , 127.8 ppm ; ei - ms m / z : 223 [ m ] .
according to method b , 2-phenyl - trans - cinnamamide ( 256 mg , 1.1 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after silica column purification ( pentane / etoac 100:0 100:1 ) , 290 mg ( 90 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.77 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.65 ( s , 1 h ) , 7.507.43 ( m , 3 h ) ,
7.357.29 ( m , 2 h ) , 7.287.20 ( m , 3 h ) , 7.137.08 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 158.5 , 137.6 , 134.1 , 134.0 , 130.3 , 129.9 , 129.4 , 128.9 , 128.6 , 128.4 , 127.8 ppm ; esi - ms m / z : 282 [ m+h ] ; hrms m / z calcd for c16h11no2s [ m+h ] 282.0589 , found 282.0587 .
benzhydroxamic acid ( 137 mg , 1.0 mmol ) was reacted with 1,1-carbonyldiimidazole to give , after silica column purification ( pentane / etoac 100:0 100:5 ) , 86 mg of the crude dioxazolone which was purified by precipitation from etoac / pentane to give 80 mg ( 49 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.87 ( pentane / etoac=9:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.877.83 ( m , 2 h ) , 7.767.71 ( m , 1 h ) , 7.677.61 ppm ( m , 2 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =163.0 , 153.9 , 133.7 , 129.6 , 126.4 , 120.3 ppm ; hrms m / z for c8h5no3 as [ m+h ] adduct not found due to low ionization level .
( e)-3-styryl-1,4,2-dioxazol-5-one ( 25). trans - cinnamic acid ( 296 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 486 mg , 3.0 mmol ) were dissolved in thf ( 8 ml ) , and the mixture was stirred at rt .
after 1 h , hydroxylamine hydrochloride ( 278 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt for 2 d. 5 % aq khso4 ( 30 ml ) was added , and the mixture was extracted with etoac ( 230 ml ) . the collected organic phases were washed with brine ( 30 ml ) and dried over na2so4 .
evaporation of solvent gave 280 mg ( 86 % isolated yield ) of the corresponding n - hydroxycinnamamide as a pale pink solid , used in the next step without further purification .
lc purity ( 254 nm)=95 % ; esi - ms : m / z 164 [ m+h ] .
the obtained n - hydroxycinnamamide ( 140 mg , 0.86 mmol ) was reacted with 1,1-carbonyldiimidazole to give , after silica column purification ( ch3cn ) and evaporation of the solvent by freeze - drying , 123 mg of the crude dioxazolone which was purified by preparative hplc to give 83 mg ( 51 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.64 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.847.78 ( m , 2 h ) , 7.56 ( d , j=16.4 hz , 1 h ) , 7.497.43 ( m , 3 h ) , 7.15 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =163.2 , 153.6 , 142.2 , 133.8 , 130.8 , 129.0 , 128.4 , 106.9 ppm ; esi - ms m / z : 190 [ m+h ] ; hrms m / z for c10h7no3 as [ m+h ] adduct not found due to low ionization level .
general method for the synthesis of 2-substituted acrylamide. method c ( mizoroki heck reaction , electron - rich iodide ) a suitable microwave vial was loaded with solid reactants and reagents : starting iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , palladium(ii ) acetate ( 0.05 equiv ) , and tri - tert - butylphosphonium tetrafluoroborate ( 0.10 equiv ) .
ch3cn ( 4.0 ml mmol ) was added , followed by liquid reactants : starting iodide ( 1.0 equiv , in case ) .
oxygen was removed by bubbling gaseous nitrogen into the resulting mixture for 15 min , then triethylamine ( 3.0 equiv ) was added , the vial was capped , and the reaction mixture was irradiated with microwaves at 120 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
method d ( mizoroki heck reaction , electron - poor iodide ) a suitable microwave vial was loaded with solid reactants and reagents : starting iodide ( 1.0 equiv ) , acrylamide ( 2.0 equiv ) , and palladium(ii ) acetate ( 0.05 equiv ) .
ch3cn ( 4.0 ml mmol ) was added , followed by liquid reactants : starting iodide ( 1.0 equiv , in case ) .
oxygen was removed by bubbling gaseous nitrogen into the resulting mixture for 15 min , then triethylamine ( 3.0 equiv ) was added , the vial was capped , and the reaction mixture was irradiated with microwaves at 120 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
method e ( mizoroki heck reaction , electron - poor bromide ) a suitable microwave vial was loaded with solid reactants and reagents : starting bromide ( 1.0 equiv ) , acrylamide ( 1.5 equiv ) , trans - bis(acetato)bis[o-(di - o - tolylphosphino)benzyl]dipalladium(ii ) ( 0.05 equiv ) , and naoac ( 3.0 equiv ) .
dry dmf ( 4.0 ml mmol ) was added , followed by liquid reactants : starting bromide ( 1.0 equiv , in case ) .
the vial was capped , and the reaction mixture was irradiated with microwaves at 140 c for 15 min .
the mixture was allowed to cool down to rt , and the collected crude material was purified by silica gel column chromatography to give the desired 3-substituted acrylamide .
4-iodoanisole ( 234 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 139 mg of the crude corresponding acrylate , that was purified by silica column chromatography ( etoac / meoh 100:5 100:10 ) to afford 133 mg ( 75 % isolated yield ) of ( e)-3-(4-methoxyphenyl)acrylamide as a white powder .
tlc : rf=0.34 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.52 ( dm , j=8.6 hz , 2 h ) , 7.45 ( bs , 1 h ) , 7.38 ( d , j=16.0 hz , 1 h ) , 7.036.97 ( m , 3 h ) , 6.47 ( d , j=15.6 hz , 1 h ) , 3.80 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.9 , 160.3 , 138.8 , 129.1 , 127.4 , 119.8 , 114.4 , 55.2 ppm ; esi - ms m / z : 178 [ m+h ] .
according to method b , ( e)-3-(4-methoxyphenyl)acrylamide ( 256 mg , 1.4 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 240 mg ( 71 % isolated yield ) of the title compound as a pale yellow powder . lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.73 ( dm , j=8.6 hz , 2 h ) , 7.49 ( d , j=16.0 hz , 1 h ) , 6.99 ( dm , j=8.6 hz , 2 h ) , 6.83 ( d , j=16.4 hz , 1 h ) , 3.81 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 161.1 , 157.7 , 141.2 , 130.0 , 126.8 , 114.4 , 110.6 , 55.4 ppm ; esi - ms m / z : 236 [ m+h ] ; hrms m / z calcd for c11h9no3s [ m+h ] 236.0381 , found 236.0383 .
1-iodo-4-isopropylbenzene ( 246 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 150 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 118 mg ( 62 % isolated yield ) of ( e)-3-(4-isopropylphenyl)acrylamide as an off - white powder .
tlc : rf=0.42 ( etoac ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.49 ( bs , 1 h ) , 7.47 ( d , j=8.0 hz , 2 h ) , 7.37 ( d , j=16.0 hz , 1 h ) , 7.28 ( d , j=8.0 hz , 2 h ) , 7.05 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.90 ( sep , j=7.0 hz , 1 h ) , 1.20 ppm ( d , j=7.0 hz , 6 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 150.0 , 139.1 , 132.5 , 127.6 , 126.9 , 121.3 , 33.3 , 23.7 ppm ; esi - ms m / z : 190 [ m+h ] , 231 [ m+ch3cn+h ] , 379 [ 2 m+h ] . according to method b , ( e)-3-(4-isopropylphenyl)acrylamide ( 118 mg , 0.62 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by silica column chromatography ( pentane / etoac 100:0 100:2 ) and preparative hplc purification , 102 mg ( 66 % isolated yield ) of the title compound as a white solid .
tlc : rf=0.60 ( pentane / etoac 10 : 1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.69 ( d , j=8.1 hz , 2 h ) , 7.50 ( d , j=16.3 hz , 1 h ) , 7.31 ( d , j=8.1 hz , 2 h ) , 6.93 ( d , j=16.3 hz , 1 h ) , 2.92 ( sep , j=6.8 hz , 1 h ) , 1.21 ppm ( d , j=6.8 hz , 6 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 151.2 , 141.4 , 131.9 , 128.3 , 126.9 , 112.2 , 33.4 , 23.6 ppm ; esi - ms m / z : 248 [ m+h ] , 289 [ m+ch3cn+h ] ; hrms m / z for c13h13no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-4-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 126 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 95 mg ( 59 % isolated yield ) of ( e)-3-(p - tolyl)acrylamide as a white powder .
tlc : rf=0.36 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.48 ( bs , 1 h ) , 7.44 ( d , j=8.0 hz , 2 h ) , 7.37 ( d , j=16.0 hz , 1 h ) , 7.22 ( d , j=8.0 hz , 2 h ) , 7.04 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.32 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 150.8 , 139.1 , 132.1 , 129.5 , 127.5 , 121.3 , 20.9 ppm ; esi - ms m / z : 162 [ m+h ] , 203 [ m+ch3cn+h ] , 323 [ 2 m+h ] . according to method b , ( e)-3-(p - tolyl)acrylamide ( 95 mg , 0.59 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 41 mg ( 32 % isolated yield ) of the title compound as white crystals .
lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.66 ( d , j=8.1 hz , 2 h ) , 7.49 ( d , j=16.4 hz , 1 h ) , 7.25 ( d , j=8.1 hz , 2 h ) , 6.92 ( d , j=16.4 hz , 1 h ) , 2.34 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 141.4 , 140.5 , 131.4 , 129.6 , 128.2 , 112.2 , 21.0 ppm ; esi - ms m / z : 220 [ m+h ] , 261 [ m+ch3cn+h ] ; hrms m / z for c11h9no2s as [ m+h ] adduct not found due to low ionization level .
( e)-5-(4-ethylstyryl)-1,3,4-oxathiazol-2-one ( 31 ) . according to method c , 1-ethyl-4-iodobenzene ( 232 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum to give 170 mg of the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / meoh 100:0 100:10 ) to afford 88 mg ( 50 % isolated yield ) of ( e)-3-(4-ethylphenyl)acrylamide as a white powder .
tlc : rf=0.40 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.49 ( bs , 1 h ) , 7.47 ( d , j=8.0 hz , 2 h ) , 7.38 ( d , j=16.0 hz , 1 h ) , 7.25 ( d , j=8.0 hz , 2 h ) , 7.04 ( bs , 1 h ) , 6.55 ( d , j=16.0 hz , 1 h ) , 2.62 ( q , j=7.6 hz , 2 h ) , 1.18 ppm ( t , j=7.6 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.8 , 145.4 , 139.1 , 132.4 , 128.3 , 127.6 , 121.3 , 28.1 , 15.4 ppm ; esi - ms m / z : 176 [ m+h ] , 217 [ m+ch3cn+h ] , 351 [ 2 m+h ] . according to method b , ( e)-3-(4-ethylphenyl)acrylamide ( 88 mg , 0.50 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 50 mg ( 43 % isolated yield ) of the title compound as yellow crystals . lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.68 ( d , j=8.1 hz , 2 h ) , 7.50 ( d , j=16.4 hz , 1 h ) , 7.28 ( d , j=8.1 hz , 2 h ) , 6.93 ( d , j=16.4 hz , 1 h ) , 2.63 ( q , j=7.7 hz , 2 h ) , 1.18 ppm ( t , j=7.7 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.5 , 146.7 , 141.4 , 131.7 , 128.4 , 128.3 , 112.2 , 28.1 , 15.3 ppm ; esi - ms m / z : 234 [ m+h ] , 275 [ m+ch3cn+h ] ; hrms m / z for c12h11no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-4-trifluoromethoxy - benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac ; 2 pentane / etoac 1:1 0:1 ) to afford 221 mg of a 1:1 mixture of ( e)-3-(4-(trifluoromethoxy)phenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.48 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 232 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 221 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.25 ml ) to give , after purification by silica column chromatography ( pentane / etoac 100:0 100:2 ) , 185 mg ( 64 % isolated yield after two steps ) of the title compound as a white powder .
tlc : rf=0.55 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 94 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.93 ( dm , j=9.0 hz , 2 h ) , 7.58 ( d , j=16.4 hz , 1 h ) , 7.43 ( dm , j=8.0 hz , 2 h ) , 7.05 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.2 , 149.4 , 139.7 , 133.5 , 130.2 , 121.3 , 120.0 ( q , j=256.9 hz ) , 114.4 ppm ; esi - ms m / z : 290 [ m+h ] ; hrms m / z for c11h6f3no3s as [ m+h ] adduct not found due to low ionization level .
d , ethyl 4-iodobenzoate ( 276 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 147 mg ( 67 % isolated yield ) of ( e)-ethyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate as an off - white powder .
tlc : rf=0.53 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( dm , j=8.3 hz , 2 h ) , 7.69 ( dm , j=8.3 hz , 2 h ) , 7.61 ( bs , 1 h ) , 7.46 ( d , j=16.0 hz , 1 h ) , 7.20 ( bs , 1 h ) , 6.73 ( d , j=16.0 hz , 1 h ) , 4.31 ( q , j=6.9 hz , 2 h ) , 1.33 ppm ( t , j=6.9 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.2 , 165.3 , 139.4 , 137.8 , 130.2 , 129.7 , 127.7 , 124.9 , 60.8 , 14.1 ppm ; esi - ms m / z : 220 [ m+h ] , 439 [ 2 m+h ] . according to method b , ( e)-ethyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate ( 147 mg , 0.67 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 129 mg ( 69 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.39 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.6 hz , 2 h ) , 7.92 ( bd , j=8.6 hz , 2 h ) , 7.59 ( d , j=16.4 hz , 1 h ) , 7.13 ( d , j=16.4 hz , 1 h ) , 4.33 ( q , j=7.1 hz , 2 h ) , 1.33 ppm ( t , j=7.1 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 165.2 , 157.0 , 139.9 , 138.6 , 130.9 , 129.5 , 128.4 , 115.7 , 60.9 , 14.1 ppm ; esi - ms m / z : 278 [ m+h ] ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0482 .
4-iodobenzophenone ( 308 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 158 mg ( 63 % isolated yield ) of ( e)-3-(4-benzoylphenyl)acrylamide as an off - white powder .
tlc : rf=0.47 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.807.66 ( m , 7 h ) , 7.63 ( bs , 1 h ) , 7.617.55 ( m , 2 h ) , 7.50 ( d , j=15.8 hz , 1 h ) , 7.21 ( bs , 1 h ) , 6.75 ppm ( d , j=15.8 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =156.0 , 127.1 , 99.8 , 98.8 , 98.1 , 97.8 , 93.6 , 91.1 , 90.4 , 89.5 , 88.5 , 85.8 ppm ; esi - ms m / z : 252 [ m+h ] , 503 [ 2 m+h ] . according to method b , ( e)-3-(4-benzoylphenyl)acrylamide ( 158 mg , 0.63 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 157 mg ( 80 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.26 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.96 ( dm , j=8.8 hz , 2 h ) , 7.807.74 ( m , 4 h ) , 7.737.67 ( m , 1 h ) , 7.64 ( d , j=16.4 hz , 1 h ) , 7.617.55 ( m , 2 h ) , 7.16 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =195.1 , 173.4 , 157.1 , 140.0 , 138.1 , 138.0 , 136.8 , 132.9 , 130.1 , 129.6 , 128.6 , 128.2 , 115.6 ppm ; esi - ms m / z : 310 [ m+h ] ; hrms m / z calcd for c17h11no3s [ m+h ] 310.0538 , found 310.0535 .
d , methyl 4-iodobenzoate ( 262 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 124 mg ( 60 % isolated yield ) of ( e)-methyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate as an off - white powder .
tlc : rf=0.47 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.3 hz , 2 h ) , 7.70 ( bd , j=8.3 hz , 2 h ) , 7.61 ( bs , 1 h ) , 7.46 ( d , j=15.9 hz , 1 h ) , 7.20 ( bs , 1 h ) , 6.73 ( d , j=15.9 hz , 1 h ) , 3.86 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.2 , 165.8 , 139.5 , 137.8 , 129.9 , 129.7 , 127.8 , 125.0 , 52.2 ppm ; esi - ms m / z : 206 [ m+h ] , 411 [ 2 m+h ] . according to method b , ( e)-methyl 4-(3-amino-3-oxoprop-1-en-1-yl)benzoate ( 124 mg , 0.60 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 108 mg ( 68 % isolated yield ) of the title compound as white powder .
tlc : rf=0.32 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.6 hz , 2 h ) , 7.92 ( bd , j=8.6 hz , 2 h ) , 7.60 ( d , j=16.4 hz , 1 h ) , 7.13 ( d , j=16.4 hz , 1 h ) , 3.87 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 165.7 , 157.0 , 139.8 , 138.7 , 130.6 , 129.6 , 128.4 , 115.7 , 52.3 ppm ; esi - ms m / z : 264 [ m+h ] ; hrms m / z calcd for c12h9no4s [ m+h ] 264.0331 , found 264.0336 .
1-iodo-4-nitrobenzene ( 249 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 95 mg ( 49 % isolated yield ) of ( e)-3-(4-nitrophenyl)acrylamide as a yellow powder .
tlc : rf=0.53 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.26 ( bd , j=9.0 hz , 2 h ) , 7.83 ( bd , j=9.0 hz , 2 h ) , 7.66 ( bs , 1 h ) , 7.52 ( d , j=15.9 hz , 1 h ) , 7.27 ( bs , 1 h ) , 6.80 ppm ( d , j=15.9 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.9 , 147.5 , 141.5 , 136.8 , 128.6 , 126.7 , 124.1 ppm ; esi - ms m / z : 193 [ m+h ] .
according to method b , ( e)-3-(4-nitrophenyl)acrylamide ( 95 mg , 0.49 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 99 mg ( 80 % isolated yield ) of the title compound as a pale yellow powder .
tlc : rf=0.24 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.26 ( bd , j=8.9 hz , 2 h ) , 8.07 ( bd , j=8.9 hz , 2 h ) , 7.67 ( d , j=16.4 hz , 1 h ) , 7.24 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.8 , 147.9 , 140.7 , 138.7 , 129.2 , 124.0 , 117.3 ppm ; esi - ms m / z : 251 [ m+h ] ; hrms m / z for c10h6n2o4s as [ m+h ] adduct not found due to low ionization level .
4-iodobenzonitrile ( 229 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac , 2 pentane / etoac 1:1 0:1 ) to afford 123 mg of a 1:2 mixture of ( e)-3-(4-cyanophenyl)acrylamide and starting acrylamide as white a powder .
tlc : mizoroki heck product rf=0.37 , acrylamide rf=0.31 ( etoac ) ; esi - ms : m / z 173 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 123 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.21 ml ) to give , after purification by precipitation from etoac / pentane , 47 mg ( 20 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.21 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.98 ( bd , j=8.4 hz , 2 h ) , 7.90 ( bd , j=8.4 hz , 2 h ) , 7.61 ( d , j=16.4 hz , 1 h ) , 7.20 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.9 , 139.3 , 138.8 , 132.8 , 128.8 , 118.6 , 116.6 , 112.2 ppm ; esi - ms m / z : 231 [ m+h ] ; hrms m / z calcd for c11h6n2o2s [ m+h ] 231.0228 , found 231.0226 .
( e)-4-(2-(2-oxo-1,3,4-oxathiazol-5-yl)vinyl)benzaldehyde ( 38 ) . according to method d , 4-iodobenzaldehyde ( 232 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction . after microwave irradiation ,
the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac , 2 pentane / etoac 1:1 0:1 ) to afford 100 mg of a 2:3 mixture of ( e)-3-(4-formylphenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.37 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 176 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 100 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.10 ml ) to give , after purification by precipitation from etoac / pentane , 36 mg ( 15 % isolated yield after two steps ) of the title compound as a pale yellow powder .
tlc : rf=0.18 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =10.03 ( s , 1 h ) , 8.01 ( bd , j=8.4 hz , 2 h ) , 7.95 ( bd , j=8.4 hz , 2 h ) , 7.62 ( d , j=16.4 hz , 1 h ) , 7.19 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =192.6 , 173.3 , 157.0 , 139.9 , 139.8 , 136.8 , 129.9 , 128.8 , 116.2 ppm ; esi - ms m / z : 234 [ m+h ] ; hrms m / z for c11h7no3s as [ m+h ] adduct not found due to low ionization level .
1-chloro-4-iodobenzene ( 238 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to 0 c , and the collected precipitate was washed with cold ch3cn ( 3 ml ) and dried by vacuum .
the crude corresponding acrylate was purified by silica column chromatography ( etoac / meoh 1:0 10:1 ) to afford 123 mg ( 68 % isolated yield ) of ( e)-3-(4-chlorophenyl)acrylamide as a yellow powder .
tlc : rf=0.60 ( etoac ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.58 ( dm , j=8.4 hz , 2 h ) , 7.54 ( bs , 1 h ) , 7.47 ( dm , j=8.4 hz , 2 h ) , 7.40 ( d , j=15.9 hz , 1 h ) , 7.13 ( bs , 1 h ) , 6.61 ppm ( d , j=15.9 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =166.4 , 137.8 , 133.9 , 133.8 , 129.2 , 128.9 , 123.2 ppm ; esi - ms m / z : 182/184 [ m+h ] , 363/365 [ 2 m+h ] . according to method b , ( e)-3-(4-chlorophenyl)acrylamide ( 123 mg , 0.68 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after purification by precipitation from etoac / pentane , 118 mg ( 73 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.68 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.81 ( dm , j=8.4 hz , 2 h ) , 7.54 ( d , j=16.3 hz , 1 h ) , 7.50 ( dm , j=8.4 hz , 2 h ) , 7.03 ppm ( d , j=16.3 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.2 , 140.0 , 134.9 , 133.2 , 129.9 , 129.0 , 114.0 ppm ; esi - ms m / z : 240/242 [ m+h ] ; hrms m / z for c10h6clno2s as [ m+h ] adduct not found due to low ionization level .
1,4-dichloro-2-iodobenzene ( 273 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( double purification : 1 etoac ; 2 pentane / etoac 1:1 0:1 ) to afford 184 mg of a 1:1 mixture of ( e)-3-(2,5-dichlorophenyl)acrylamide and starting acrylamide as a white powder .
tlc : mizoroki heck product rf=0.69 , acrylamide rf=0.31 ( etoac ) ; esi - ms m / z : 216/217 [ m+h ] . according to method b ,
the obtained mizoroki heck reaction mixture ( 184 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.24 ml ) to give , after purification by precipitation from etoac / pentane , 31 mg ( 11 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.79 ( pentane / etoac 10:1 ) ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.18 ( d , j=2.5 hz , 1 h ) , 7.63 ( d , j=16.2 hz , 1 h ) , 7.61 ( d , j=8.7 hz , 1 h ) , 7.53 ( dd , j=8.7 , 2.5 hz , 1 h ) , 7.25 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.2 , 156.6 , 134.4 , 133.5 , 132.7 , 132.1 , 131.6 , 131.4 , 127.5 , 117.6 ppm ; esi - ms m / z : 274/276 [ m+h ] ; hrms m / z for c10h5cl2no2s as [ m+h ] adduct not found due to low ionization level .
1-iodo-3-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude to ( e)-3-(m - tolyl)acrylamide , esi - ms m / z : 162 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after silica column chromatography ( ch2cl2/isohexane 1:9 ) and recrystallization in ch3cn , 76 mg ( 35 % isolated yield after step two ) as a white solid .
esi - ms m / z : 220 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.47 ( d , j=16.2 hz , 1 h ) , 7.347.20 ( m , 4 h ) , 6.63 ( d , j=16.2 hz , 1 h ) , 2.39 ppm ( m , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.7 , 142.1 , 138.8 , 134.0 , 131.4 , 129.0 , 128.5 , 125.0 , 112.6 , 21.3 ppm ; hrms m / z calcd for c11h9no2s [ m+h ] 220.0432 , found 220.0437 .
( e)-5-(3-ethylstyryl)-1,3,4-oxathiazol-2-one ( 42 ) . according to method e , 1-bromo-3-ethylbenzene ( 370 mg , 2.0 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , filtered through a plug of cotton , and concentrated under reduced pressure .
the residue was dissolved in etoac ( 25 ml ) and washed with h2o ( 25 ml ) , and the organic phase was dried over mgso4 and evaporated to yield the crude ( e)-3-(3-ethylphenyl)acrylamide as a pale yellow solid .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.67 ml ) to give , after silica column chromatography ( etoac / isohexane 2:100 5:100 ) and recrystallization in ch3cn , 77 mg ( 17 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 234 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , cdcl3 ) : =7.48 ( d , j=16.2 hz , 1 h ) , 7.367.23 ( m , 4 h ) , 6.63 ( d , j=16.2 hz , 1 h ) , 2.68 ( q , j=7.6 hz , 2 h ) , 1.27 ppm ( t , j=7.6 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.4 , 157.8 , 145.1 , 142.2 , 134.1 , 130.3 , 129.1 , 127.4 , 125.3 , 112.6 , 28.7 , 15.5 ppm ; hrms m / z calcd for c12h11no2s [ m+h ] 234.0589 , found 234.0591 .
1-iodo-3-(trifluoromethoxy)benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(3-(trifluoromethoxy)phenyl)acrylamide as a pale yellow solid .
tlc : rf=0.47 ( etoac : iso - hexane , 75:25 ) ; esi - ms m / z : 232 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.22 ml ) to give , after silica column chromatography ( etylacetate / isohexane 1:100 ) , 176 mg ( 61 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 299 [ m+h ] ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.81 ( m , 1 h ) , 7.78 , ( dm , j=8.0 hz , 1 h ) , 7.55 ( d , j=16.4 hz , 1 h ) , 7.54 ( m , 1 h ) , 7.38 ( m , 1 h ) , 7.01 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.8 , 157.5 , 149.3 , 140.0 , 137.1 , 131.3 , 127.7 , 122.9 , 121.0 , 120.5 ( q , j=257 hz ) , 115.6 ppm ; hrms m / z calcd for c11h6f3no3s [ m+h ] 299.0099 , found 299.0103 .
( e)-ethyl 3-(2-(2-oxo-1,3,4-oxathiazol-5-yl)vinyl)benzoate ( 44 ) . according to method d , ethyl-3-iodobenzoate ( 276 mg , 1.0 mmol )
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to afford 206 mg of ( e)-3-(3- ethoxycarbonyl)acrylamide as pale yellow solid .
tlc : rf=0.58 , ( etoac ) ; esi - ms m / z : 220 [ m+h ] .
according to method a , the crude 3-substituted acrylamide ( 206 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.17 ml ) to give , after recrystallization in ethylacetate / isohexane , 118 mg ( 43 % isolated yield after two steps ) as a white solid , 43 % yield .
esi - ms m / z : 278 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.24 ( m , 1 h ) , 8.05 , ( dm , j=7.7 hz , 1 h ) , 7.97 ( dm , j=7.8 hz , 1 h ) , 7.60 ( d , j=16.4 hz , 1 h ) , 7.58 ( dd , j=7.7 , 7.8 hz , 1 h ) , 7.05 ( d , j=16.4 hz , 1 h ) , 4.32 ppm ( q , j=7.2 hz , 2 h ) , 1.32 ( t ,
j=7.2 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.9 , 165.8 , 157.6 , 140.7 , 135.2 , 132.6 , 131.2 , 131.1 , 129.9 , 129.4 , 114.9 , 61.5 , 14.6 ppm ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0486 .
1-iodo-2-methylbenzene ( 218 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(o - tolyl)acrylamide as a pale yellow solid , 149 mg .
tlc : rf=0.48 ( etoac ) ; esi - ms m / z : 162 [ m+h ] .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.26 ml ) to give , after silica column chromatography ( etoac / isohexane 1:100 ) , 70 mg ( 32 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 220 [ m+h ] ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.69 ( d , j=16.2 hz , 1 h ) , 7.48 ( dm , j=7.8 hz , 1 h ) , 7.257.13 ( m , 3 h ) , 6.49 ( d , j=16.2 hz , 1 h ) , 2.37 ppm ( m , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.8 , 139.5 , 137.6 , 133.0 , 131.0 , 130.3 , 126.5 , 125.9 , 113.8 , 19.8 ppm ; hrms m / z calcd for c11h9no2s [ m+h ] 220.0432 , found 220.0436 .
1-bromo-2-ethylbenzene ( 218 mg , 1.0 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and filtered through a plug of cotton .
the reaction mixture was then extracted between etoac ( 25 ml ) and h2o ( 25 ml ) , and the organic phase was dried over mgso4 and evaporated to yield the crude ( e)-3-(2-ethylphenyl)acrylamide as a pale yellow solid , 117 mg .
according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.23 ml ) to give , after silica column chromatography ( etoac / isohexane 2:100 ) , 90 mg ( 19 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 234 [ m+h ] ; lc purity ( 254 nm ) : 98 % ; h nmr ( 400 mhz , cdcl3 ) : =7.80 ( d , j=16.2 hz , 1 h ) , 7.57 ( m , 1 h ) , 7.35 ( m , 1 h ) , 7.287.22 ( m , 2 h ) , 6.58 ( d , j=16.2 hz , 1 h ) , 2.79 ( q , j=7.5 hz , 2 h ) , 1.24 ppm ( t , j=7.5 hz , 3 h ) ; c nmr ( 100 mhz , cdcl3 ) : =173.5 , 157.8 , 143.8 , 139.3 , 132.3 , 130.6 , 129.4 , 126.5 , 126.1 , 113.9 , 26.4 , 15.9 ppm ; hrms m / z calcd for c12h11no2s [ m+h ] 234.0589 , found 234.0584 .
1-iodo-2-(trifluoromethoxy)benzene ( 288 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( etoac / isohexane 50:50 75:25 ) to ( e)-3-(2-(trifluoromethoxy)phenyl)acrylamide as a pale yellow solid , 229 mg .
tlc : rf=0.49 ( etoac / iso - hexane 75:25 ) ; esi - ms m / z : 232 [ m+h ] . according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.20 ml ) to give , after precipitation from etoac / isohexane , 110 mg ( 38 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 299 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.04 ( d , j=7.8 hz , 1 h ) , 7.54 ( m , 1 h ) , 7.47 ( d , j=16.4 hz , 1 h ) , 7.457.38 ( m , 2 h ) , 7.08 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.7 , 157.1 , 146.7 , 132.9 , 132.6 , 128.7 , 128.6 , 127.5 , 122.1 , 120.6 ( q , j=258 hz ) , 110.0 ppm ; hrms m / z calcd for c11h6f3no3s [ m+h ] 299.0099 , found 299.0096 .
ethyl 2-bromobenzoate ( 506 mg , 2.2 mmol ) was used as starting bromide in the mizoroki heck reaction .
after microwave irradiation , the product was filtered and washed with etoac ( 20 ml ) give ( e)-ethyl 2-(3-amino-3-oxoprop-1-en-1-yl)benzoate as a pale white solid , 391 mg . according to method a , the crude 3-substituted acrylamide was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.60 ml ) to give , after filtration and washing with etoac ( 10 ml ) , 198 mg ( 32 % isolated yield after two steps ) as a white solid .
esi - ms m / z : 278 [ m+h ] ; lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.18 ( d , j=16.2 hz , 1 h ) , 7.95 ( dm , j=8.0 hz , 1 h ) , 7.90 ( dd , j=7.8 , 1.6 hz , 1 h ) , 7.65 ( ddd , j=8.0 , 7.6 , 1.6 hz , 1 h ) , 7.54 ( ddm , j=7.8 , 7.6 hz , 1 h ) , 6.92 ( d , j=16.2 hz , 1 h ) , 4.33 ( q , j=7.2 hz , 2 h ) , 1.33 ppm ( t , j=7.2 hz , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.8 , 166.7 , 157.6 , 139.7 , 125.1 , 133.0 , 130.9 , 130.5 , 130.3 , 128.1 , 116.0 , 61.7 , 14.5 ppm ; hrms m / z calcd for c13h11no4s [ m+h ] 278.0487 , found 278.0485 .
4-iodopyridine ( 205 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cn ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( pentane / etoac 1:1 0:1 , then etoac / meoh 9:1 ) to afford 120 mg of a 1:1 mixture of ( e)-3-(pyridin-4-yl)acrylamide and starting acrylamide as a pale yellow solid .
tlc : mizoroki heck product rf=0.25 , acrylamide rf=0.72 ( etoac / meoh 9:1 ) ; esi - ms m / z : 149 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 120 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after purification by preparative hplc , 15 mg ( 7 % isolated yield after two steps ) of the title compound as an off - white powder .
tlc : rf=0.32 ( pentane / etoac=1:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.668.63 ( m , 2 h ) , 7.757.72 ( m , 2 h ) , 7.53 ( d , j=16.3 hz , 1 h ) , 7.27 ppm ( d , j=16.3 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.2 , 156.8 , 150.4 , 141.3 , 138.7 , 121.9 , 117.6 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0255 .
3-iodo-2-methoxy - pyridine ( 235 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after microwave irradiation , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cn ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by silica column chromatography ( pentane / etoac 1:1 0:1 , then etoac / meoh 9:1 ) to afford 184 mg of a 1:1 mixture of ( e)-3-(2-methoxypyridin-3-yl)acrylamide and starting acrylamide as a pale yellow oil .
tlc : mizoroki heck product rf=0.68 , acrylamide rf=0.60 ( etoac / meoh 9:1 ) ; esi - ms m / z : 179 [ m+h ] .
according to method a , the obtained mizoroki heck reaction mixture ( 184 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.34 ml ) to give , after purification by trituration with et2o followed by precipitation from ch3cn / h2o , 91 mg ( 39 % isolated yield after two steps ) of the title compound as a pale yellow solid .
tlc : rf=0.80 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.23 ( dd , j=4.9 , 1.8 hz , 1 h ) , 8.17 ( dd , j=7.4 , 1.8 hz , 1 h ) , 7.56 ( d , j=16.5 hz , 1 h ) , 7.09 ( dd , j=7.4 , 4.9 hz , 1 h ) , 7.06 ( d , j=16.5 hz , 1 h ) , 3.98 ppm ( s , 3 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.6 , 161.1 , 157.4 , 148.7 , 138.2 , 135.1 , 117.8 , 117.1 , 115.4 , 53.9 ppm ; esi - ms m / z : 237 [ m+h ] ; hrms m / z calcd for c10h8n2o3s [ m+h ] 237.0334 , found 237.0338 .
2-iodothiophene ( 210 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave the crude corresponding acrylate , which was purified by precipitation from ch3oh / h2o to afford 70 mg ( 46 % isolated yield ) of ( e)-3-(thiophen-2-yl)acrylamide as an off - white solid .
tlc : rf=0.52 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.71 ( d , j=15.3 hz , 1 h ) , 7.28 ( bd , j=5.1 hz , 1 h ) , 7.17 ( bd , j=3.5 hz , 1 h ) , 6.98 ( dd , j=5.1 , 3.5 hz , 1 h ) , 6.19 ( d , j=15.3 hz , 1 h ) , 5.36 ppm ( bs , 2 h ) ; esi - ms m / z : 154 [ m+h ] . according to method b , ( e)-3-(thiophen-2-yl)acrylamide ( 70 mg , 0,46 mmol ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 46 mg ( 45 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.63 ( pentane / etoac 20:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =7.76 ( bd , j=5.1 hz , 1 h ) , 7.72 ( d , j=16.1 hz , 1 h ) , 7.59 ( bd , j=3.7 hz , 1 h ) , 7.17 ( dd , j=5.1 , 3.7 hz , 1 h ) , 6.61 ppm ( d , j=16.1 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.0 , 138.9 , 134.3 , 131.8 , 130.2 , 128.7 , 111.3 ppm ; esi - ms m / z : 212 [ m+h ] ; hrms m / z calcd for c8h5no2s2 [ m+h ] 211.9840 , found 211.9837 .
3-iodothiophene ( 210 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave the crude corresponding acrylate , that was purified by precipitation from etoac / pentane followed by silica column purification ( pentane / etoac 1:1 0:1 ) to afford 115 mg ( 75 % isolated yield ) of ( e)-3-(thiophen-3-yl)acrylamide as a white solid .
tlc : rf=0.46 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , cdcl3 ) : =7.64 ( d , j=15.4 hz , 1 h ) , 7.47 ( bd , j=2.9 hz , 1 h ) , 7.33 ( dd , j=5.1 , 2.9 hz , 1 h ) , 7.28 ( bd , j=5.1 hz , 1 h ) , 6.30 ppm ( d , j=15.4 hz , 1 h ) , 5.53 ( bs , 2 h ) ; esi - ms m / z : 154 [ m+h ] .
according to method b , ( e)-3-(thiophen-3-yl)acrylamide ( 115 mg , 0,75 mmol ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 84 mg ( 53 % isolated yield ) of the title compound as a white powder .
tlc : rf=0.55 ( pentane / etoac=20:1 ) ; lc purity ( 254 nm ) : 95 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.028.00 ( m , 1 h ) , 7.667.61 ( m , 2 h ) , 7.55 ( d , j=16.2 hz , 1 h ) , 6.82 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.5 , 157.6 , 137.5 , 135.4 , 129.6 , 127.9 , 125.7 , 112.6 ppm ; esi - ms : m / z 212 [ m+h ] ; hrms m / z calcd for c8h5no2s2 [ m+h ] 211.9840 , found 211.9841 .
5-iodo-2-furaldehyde ( 222 mg , 1.0 mmol ) was used as starting iodide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=120 c ) , the reaction mixture was irradiated for additional 30 min at the same temperature to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through silica gel ( ch3cnetoacetoac / meoh 10:1 ) .
evaporation of the solvent gave a crude mixture that was taken in ch3oh / h2o and then filtered to remove the precipitated homocoupling byproduct .
evaporation of the solvent gave 262 mg of a crude mixture , which was purified by flash silica column ( pentane / etoac 1:1 0:1 ) to give 88 mg of a mixture containing the desired ( e)-3-(5-formylfuran-2-yl)acrylamide as a yellow solid .
tlc : mizoroki heck compound rf=0.44 ( etoac ) ; lc purity ( 254 nm ) : 30 % ; esi - ms m / z : 166 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 88 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.40 ml ) to give , after purification by silica column ( pentane / etoac 100:0 1:1 ) followed by preparative hplc purification , 10 mg ( 5 % isolated yield after two steps ) of the title compound as a white powder .
tlc : rf=0.70 ( pentane / etoac=20 : 1 ) ; lc purity ( 254 nm ) : 90 % ; h nmr ( 400 mhz , [ d6]dmso ) : =9.66 ( s , 1 h ) , 7.63 ( d , j=3.7 hz , 1 h ) , 7.47 ( d , j=16.2 hz , 1 h ) , 7.24 ( d , j=3.7 hz , 1 h ) , 6.83 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =178.7 , 173.1 , 156.4 , 154.5 , 152.8 , 127.1 , 124.3 , 116.8 , 115.0 ppm ; esi - ms m / z : 224 [ m+h ] ; hrms m / z calcd for c9h5no4s [ m+h ] 224.0018 , found 224.0015 .
( e)-5-(2-(pyridin-2-yl)vinyl)-1,3,4-oxathiazol-2-one ( 54 ) . according to method e , 2-bromopyridine ( 237 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was irradiated for additional 60 min at 160 c to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 126 mg of a mixture containing the desired ( e)-3-(pyridin-2-yl)acrylamide as a yellow oil .
tlc : mizoroki heck compound rf=0.07 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm)=70 % ; esi - ms m / z : 149 [ m+h ] .
according to method a , the obtained mizoroki heck reaction mixture ( 126 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) to give , after purification by preparative hplc , 8 mg ( 3 % isolated yield after two steps ) of the title compound as a brown powder .
lc purity ( 254 nm ) : 92 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.698.65 ( m , 1 h ) , 7.89 ( td , j=7.8 , 2.0 hz , 1 h ) , 7.78 ( dm , j=8.0 hz , 1 h ) , 7.58 ( d , j=16.0 hz , 1 h ) , 7.43 ( ddd , j=7.8 , 4.7 , 1.2 hz , 1 h ) , 7.20 ppm ( d , j=16.0 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.3 , 156.9 , 152.0 , 150.1 , 140.3 , 137.4 , 125.0 , 124.8 , 116.0 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0234 .
( e)-5-(2-(pyridin-3-yl)vinyl)-1,3,4-oxathiazol-2-one ( 55 ) . according to method e , 3-bromopyridine ( 237 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 102 mg of a mixture containing the desired ( e)-3-(pyridin-3-yl)acrylamide as a white solid .
tlc : mizoroki heck compound rf=0.26 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm ) : 90 % ; esi - ms m / z : 149 [ m+h ] . according to method a , the obtained mizoroki heck reaction mixture ( 102 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) by microwave irradiation , followed by thermal heating at 70 c for 2 d to give , after purification by preparative hplc , 45 mg ( 15 % isolated yield after two steps ) of the title compound as a white powder .
lc purity ( 254 nm ) : 99 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.92 ( bd , j=2.1 hz , 1 h ) , 8.59 ( dd , j=4.9 , 1.8 hz , 1 h ) , 8.24 ( dm , j=8.0 hz , 1 h ) , 7.58 ( d , j=16.4 hz , 1 h ) , 7.47 ( bdd , j=7.5 , 4.3 hz , 1 h ) , 7.16 ppm ( d , j=16.4 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =173.4 , 157.0 , 150.9 , 149.8 , 138.1 , 134.4 , 130.1 , 123.9 , 115.1 ppm ; esi - ms m / z : 207 [ m+h ] ; hrms m / z calcd for c9h6n2o2s [ m+h ] 207.0228 , found 207.0229 .
( e)-5-(2-(2-oxo-2 h - thiadiazolo[2,3-a]pyridin-8-yl)vinyl)-1,3,4-oxathiazol-2-one ( 56 ) . according to method e , 2-amino-3-bromopyridine ( 260 mg , 1.5 mmol ) was used as starting bromide in the mizoroki heck reaction .
after 15 min of microwave irradiation ( t=140 c ) , the reaction mixture was irradiated for additional 15 min at 160 c to afford full conversion .
the resulting reaction mixture was cooled down to rt , and the formed pd black was removed by filtration through celite ( etoac / meoh 1:1 ) .
evaporation of the solvent under reduced pressure gave a crude mixture containing dmf , which was taken in etoac ( 20 ml ) .
the organic phase was washed with h2o ( 240 ml ) , the h2o phases were extracted with etoac ( 2100 ml ) , and the collected organic phases were dried over na2so4 .
evaporation of solvent gave 94 mg of a mixture containing the desired ( e)-3-(2-aminopyridin-3-yl)acrylamide as a yellow solid .
tlc : mizoroki heck compound rf=0.22 ( etoac / meoh 10:1 ) ; lc purity ( 254 nm)=90 % ; esi - ms m / z : 164 [ m+h ] .
according to method b , the obtained mizoroki heck reaction mixture ( 94 mg ) was reacted with an excess of chlorocarbonyl sulfenyl chloride ( 0.50 ml ) , to give , after purification by trituration in ch3cn / h2o , 16 mg ( 4 % isolated yield after two steps ) of the title compound as a pale yellow solid .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =8.02 ( dd , j=7.0 , 1.3 hz , 1 h ) , 7.95 ( dm , j=7.0 hz , 1 h ) , 7.72 ( d , j=16.0 hz , 1 h ) , 7.62 ( dd , j=16.2 , 0.6 hz , 1 h ) , 6.89 ppm ( t , j=7.0 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.3 , 173.3 , 157.1 , 148.0 , 137.1 , 134.8 , 126.1 , 125.0 , 117.4 , 111.6 ppm ; esi - ms m / z : 280 [ m+h ] ; hrms m / z calcd for c10h5n3o3s2 [ m+h ] 279.9851 , found 279.9843 .
ghsqc and ghmqc experiments showed no correlations between proton he and carbon c , suggesting the following structure ( figure 3 ) as the most probable one .
( 2e)-3-(1h - indol-3-yl)acrylic acid ( 378 mg , 2.0 mmol ) and 1,1-carbonyldiimidazole ( 656 mg , 2.0 mmol ) were dissolved in anhydrous dmf ( 10 ml ) , and the mixture was stirred at rt .
after 30 min , nh4hco3 ( 639 mg , 4.0 mmol ) was added , and the resulting suspension was stirred at rt o / n .
etoac ( 100 ml ) was added , and the organic phase was washed with h2o ( 250 ml ) and brine ( 50 ml ) .
evaporation of solvent gave 397 mg of the crude corresponding amide , purified by silica column chromatography ( pentane / etoac 1:1 0:1 ) to afford 116 mg ( 31 % isolated yield ) of ( e)-3-(1h - indol-3-yl)acrylamide as a yellow sticky oil .
tlc : rf=0.24 ( etoac ) ; lc purity ( 254 nm ) : 95 % ; esi - ms m / z : 187 [ m+h ] .
according to method b , ( e)-3-(1h - indol-3-yl)acrylamide ( 58 mg , 0.31 mmol ) was reacted with chlorocarbonyl sulfenyl chloride to give , after preparative hplc purification , 9 mg ( 12 % isolated yield ) of the title compound as a pale yellow powder .
lc purity ( 254 nm ) : 97 % ; h nmr ( 400 mhz , [ d6]dmso ) : =11.84 ( bs , 1 h ) , 8.00 ( s , 1 h ) , 7.94 ( dm , j=7.2 hz , 1 h ) , 7.75 ( d , j=16.2 hz , 1 h ) , 7.48 ( dm , j=8.1 hz , 1 h ) , 7.267.15 ( m , 2 h ) , 6.66 ppm ( d , j=16.2 hz , 1 h ) ; c nmr ( 100 mhz , [ d6]dmso ) : =174.7 , 159.3 , 138.1 , 136.7 , 132.4 , 125.4 , 123.4 , 121.8 , 120.5 , 113.1 , 112.5 , 107.0 ppm ; esi - ms m / z : 245 [ m+h ] ; hrms m / z calcd for c12h8n2o2s [ m+h ] 245.0385 , found 245.0384 .
the sequences for the open - gate alpha8a ( rv2109c residues 9240 ) and a slightly truncated beta ( rv2110c ) ( residues 1285 ) subunits of the m. tuberculosis proteasome were amplified by pcr from total dna of mtb strain h37rv28 using the polymerase pfu ultra ( agilent technologies , la jolla , usa ) .
the c - terminus of the beta subunit was modified to incorporate a 6-histidine tag after the terminal glycine residue.8a the genes were inserted into the vector prsf duet-1 , which is a vector for coexpressing two proteins , both controlled by t7 promoters , from novagen ( merckmillipore , darmstadt , germany ) , and cloned in e. coli top10 cells ( invitrogen , carlsbad , usa ) . expression and purification
were performed as previously described.8a briefly , 6 l cultures of e. coli bl21(de3 ) cells in luria bertani broth with 30 g / ml kanamycin were grown for 2022 h at 37 c after induction with 0.4 mm isopropyl beta - d1 thiogalactopyranoside .
the cells were harvested by centrifugation , resuspended in lysis buffer ( 50 mm na3po4 , ph 8 , 300 mm nacl , 10 mm imidazole with 0.25 mg ml lysozyme , 0.02 mg ml rnase , and 0.01 mg ml dnase ) , incubated 30 min at rt and lysed by passage through a constant cell disruption system ( constant systems ltd , daventry , uk ) at 2 kbar .
full proteasome molecules were isolated from the cleared lysate with 1 ml ni - sepharose ( ge - healthcare , uppsala , sweden ) , and eluted with 250 mm imidazole .
the buffer was exchanged on an econo - pac 10dg desalting column ( bio - rad , hercules , usa ) to 10 mm tris ph 7.5 , 100 mm nacl before a final purification step by size - exclusion chromatography on a hiload 16/60 superdex 200 column ( ge healthcare , little chalfront , uk ) equilibrated with the same buffer .
the fractions containing the proteasome as analyzed by sds - page were pooled and concentrated to 1 mg ml ( measured by a280 , extinction coefficient 33 810 m cm ) in a vivaspin 20 , molecular weight cut - off 100 kda ( sartorius stedin biotech , goettingen , germany ) .
the protein production and assay were based on that of lin et al.8b both mtb and human proteasomes were assayed in 20 mm hepes , 0.5 mm edta ph 7.5 , with 25 m suc - llvy - amc ( bachem ag , switzerland ) as substrate , in a final volume of 100 l on a white 96-well assay plate ( cliniplate , thermo fisher scientific oy , finland ) . the increase in fluorescence caused by cleavage of amc ( 7-amino-4-methylcoumarin ) was measured using a fluoroskan ascent fluorescent plate reader ( thermo fisher scientific oy , finland ) equipped with a 390 nm filter for excitation and 460 nm filter for emission .
human 20s proteasome ( boston biochemicals , usa ) was assayed at 1 nm concentration in the presence of a tenfold excess of human pa28 activator ( boston biochemicals ) , as recommended by the manufacturer .
threefold dilutions of inhibitor ( 10 mm stock solution in dmso ) from an initial concentration of 100 m were performed on the assay plate in buffer containing the above concentrations of enzyme ; the final volume in the well after dilution was 96 l .
the plate was sealed and preincubated at rt for 3 h for mtb proteasome or 1 h for human proteasome .
next , substrate ( 5 l of 500 m in a buffer made from a 10 mm stock solution in dmso ) was added , and the fluorescence read in the plate reader immediately ( t=0 ) , then after 3 h for the mtb proteasome and after 1 h for the human proteasome .
the t=0 value was subtracted from the final value , and plotted against the logarithm of the inhibitor concentration ; the data were fitted to the standard ic50 equation using graphpad prism 5 ( graphpad software inc .
the mic were determined as previously described29 in middlebrook 7h9 medium containing 10 % v / v oadc ( oleic acid , bovine serum albumin , d - glucose , catalase ; becton dickinson , usa ) and 0.05 % w / v tween 80 .
briefly , compounds were tested in 10-point , two - fold serial dilutions with the highest concentration of 20 m against mtb h37rv expressing a fluorescent protein ( dsred ) .
growth was measured using od590 and rfu after 5 d. curves were fitted using the gompertz function , with mic defined as the minimum concentration required to inhibit growth .
data are reported for optical density at 590 nm ( od590 ) and relative fluorescence units ( rfu ) .
mtb was grown aerobically in middlebrook 7h9 medium containing 10 % v / v oadc and 0.05 % w / v tween 80 , washed , and resuspended in pbs with 0.05 % w / v tyloxapol for 14 d. compounds were added , and viability was determined by plating serial dilutions to determine colony forming units ( cfu ) on middlebrook 7h10 agar plus 10 % v / v oadc .
cytotoxicity was monitored against vero african green monkey kidney epithelial cells ( atcc ccl-81 ) grown in dmem , high glucose , glutamax ( invitrogen ) , supplemented with 10 % fbs , and penicillin streptomycin solution ( gibco ) .
cell viability was measured after 48 h using cell titer glo ( promega ) , and growth inhibition curves were fitted using the levenberg marquardt algorithm .
the tc50 was defined as the compound concentration that gave 50 % inhibition of growth .
hplc analyses were performed using a shimadzu 10 a system with a scl-10avp controller , 2 lc-10ad pumps with a 0.5 ml gradient mixer at the high pressure side , a sil-10 a ( rebuilt to also run 96-well plates ) , a cma 260 degasser , and a waters pda 996 photodiode array detector . a zorbax eclipse xdb - c8 , 5 m ,
2.150 mm column was utilized from dalco chromtech ab ( sollentuna , sweden ) with ch3cn / h2o in 0.05 % tfa as mobile phase and 1 ml min .
the chromatograms were registered at the wavelengths 230 , 254 , and 280 nm . all solutions containing the sample compound were prepared from 10 mm dmso stock solutions stored in glass vials at ambient temperature .
high standards ( hs ) were made by diluting the dmso stock solution 200 times with ch3cn+pbs ph 7.4 ( 1 + 1 ) , obtaining a 50 m solution .
low standards ( ls ) were prepared by diluting hs 20 times with ch3cn+pbs ph 7.4 ( 1 + 1 ) , obtaining a 2.5 m solution .
the hs solution was chromatographed a second time after 24 h to determine the chemical stability .
it was very important to exchange the septa after the first injection to avoid evaporation of the ch3cn .
the solubility solutions were prepared by diluting the dmso stock solution 100 times with pbs ph 7.4 , obtaining a nominal concentration of 100 m .
the solutions were left for 18 h at ambient temperature before filtration . when filtering the sample solution , the first 0.1 ml was discarded , and the rest was collected .
the solubility was determined using a two - point calibration curve forced through the origin . to evaluate the quality of the standard curve
the optimal quotient should equal the value of the concentration ratio , that is , 20.0 . when evaluating the solubility ,
the wavelength used was that which gives the area quotient closest to 20 . the stability ( given in percent remaining )
was obtained by multiplying the area after the 24 h run by 100 and dividing it by the area of the first hs injection .
mw , microwaves ; mtb , mycobacterium tuberculosis ; mdr , multidrug resistant ; xdr , extensively drug resistant ; tdr , totally drug resistant ; mic , minimum inhibitory concentration ; cfu , colony forming units notes .[/INST]this is the first report of 5-styryl - oxathiazol-2-ones as inhibitors of the mycobacterium tuberculosis ( mtb ) proteasome . as part of the study , the structure activity relationship of oxathiazolones as mtb proteasome inhibitors has been investigated .
furthermore , the prepared compounds displayed a good selectivity profile for mtb compared to the human proteasome .
the 5-styryl - oxathiazol-2-one inhibitors identified showed little activity against replicating mtb , but were rapidly bactericidal against nonreplicating bacteria .
( e)-5-(4-chlorostyryl)-1,3,4-oxathiazol-2-one ) was most effective , reducing the colony - forming units ( cfu)/ml below the detection limit in only seven days at all concentrations tested .
the results suggest that this new class of mtb proteasome inhibitors has the potential to be further developed into novel antitubercular agents for synergistic combination therapies with existing drugs .</s> |
a few years ago an approach was put forward @xcite in which heavy mass scales in four dimensions could be replaced by lighter mass scales in higher dimensions .
such a class of theories is nowadays conventionally considered in the context of the brane paradigm . in one class of models extra dimensions
are felt only by gravity ( as well as other fields transforming as singlet under the standard - model gauge group ) ; in the other class they are felt also by gauge fields . in the former case ,
the standard - model fields are confined to a ( 3 + 1)-dimensional subspace of a higher - dimensional space some dimensions of which are compactified with a relatively large radius .
the absence of any observed deviation from ordinary newtonian gravity in cavendish - type laboratory experiments implies that the largest compactification radius is smaller than around 0.2 mm @xcite .
the main goal in both classes of models is to provide a unified theory in which the electroweak scale @xmath5 and the high energy scales ( planck @xcite , string @xcite , and gut scales @xcite ) can coexist .
the same scenario has also been successfully applied to neutrino as well as to axion phenomenology .
namely , a higher - dimensional seesaw mechanism may provide light neutrino masses without heavy mass scales @xcite .
similarly , axion invisibility can be achieved in extra dimensions even with a low fundamental peccei - quinn ( pq ) scale @xcite .
the cern axion solar telescope ( cast ) is designed to search for solar axions of a broad energy spectrum which peaks at about 4 kev , through their conversion into real photons inside the transverse magnetic field @xcite .
this telescope may improve the current laboratory bounds on the axion - photon coupling , @xmath6 for @xmath7 ev and @xmath8 for @xmath9 @xcite , by a factor of ten or even more .
it also has the potential to extend for the first time the axion searches beyond the limit @xmath10 arising from astrophysical constraints on anomalous energy loss by stars @xcite .
although the cast telescope could in principle be sensitive to axion masses in the range of a few kev , the coherence - loss constraints @xcite reduce the sensitivity down to around 1 ev .
the first goal of the present note is to interpret prospects of cast in the light of the theory with large extra spatial dimensions .
we focus on the case when the limit on the size of two large extra compact dimensions is set by direct tests of gravity @xcite .
our second goal is to explore the potential of cast for testing the presence of large extra dimensions .
axions are pseudoscalars arising in models which resolve the strong _ cp _ problem in quantum chromodynamics ( qcd ) by the pq mechanism @xcite . owing to their potential abundance in the early universe
, they are also well - motivated candidates for the dark matter of the universe . in both classes of ( conventional ) invisible axion models
referred to as ksvz or hadronic axion models @xcite ( where axions do not couple to electrons at tree level ) and dfsz or grand unified theory ( gut ) models @xcite , the axion - photon coupling strength is given by the relation @xmath11 here @xmath12 is a model - dependent numerical parameter for hadronic axions , while for dfsz axions @xmath13 .
furthermore , the mass of the ( qcd ) axion @xmath4 is related to the pq symmetry breaking scale @xmath14 by @xmath15 in order to avoid ambiguities owing to the model - dependence of the parameter @xmath12 for hadronic axions , it proved more convenient to make constraints on the axion - photon coupling than on the pq energy scale or on the axion mass .
in contrast , cosmological considerations and astrophysical arguments ( i.e. , axion emission due to nucleon - nucleon bremsstrahlung from the supernova sn 1987a ) bound the axion mass into two possible ranges @xcite .
the first window is @xmath16 , in which case the axion could constitute the cold dark matter of the universe . the second one , being around ten to twenty electronvolts , appears to be of interest for hot dark matter .
however , such astrophysical constraints on @xmath4 , although the most stringent , suffer from statistical weakness ( with only 19 neutrinos being observed ) as well as from all uncertainties related to the axion emission from a hot / dense medium .
it is therefore of crucial importance to probe the axion properties in a model - independent way @xcite .
currently , laboratory searches for solar axions @xcite are being extended by the cast experiment at cern .
this telescope uses a decommissioned lhc prototype magnet with a field of 9 t and a length @xmath17 of 10 m. the magnet contains two straight beam pipes with an effective cross sectional area @xmath18 , and is mounted on a moving platform with low - background x - ray detectors on either end allowing it to track the sun about 3 hours per day .
hadronic axions could be produced abundantly in the core of the sun by the primakoff conversion of the blackbody photons in the coulomb fields of nuclei and electrons in the solar plasma .
the outgoing axion flux is robust and does not depend on subtle details of the solar model .
it is approximately given by @xcite @xmath19 here @xmath20 is the axion flux at the earth , differential with respect to axion energy ( @xmath21 ) , and expressed as a function of axion mass ( @xmath22 ) .
the quantities @xmath21 , @xmath23 , and @xmath22 are to be taken in kev .
the probability for an axion - to - photon conversion in the presence of a transverse magnetic field ( @xmath24 ) and a refractive medium ( i ) is given by @xcite @xmath25 , \label{eq4}\end{aligned}\ ] ] where @xmath26 is the momentum difference between photons in the medium and axions , and @xmath27 denotes the inverse absorption length for x - rays .
the effective mass ( plasma frequency ) for an x - ray in he can be described in terms of the operating pressure @xmath28 ( at 300 k ) as @xmath29 .
the coherence condition @xmath30 @xcite requires @xmath31 for a photon energy of 4.2 kev ( the average axion energy ) and a coherence length of 10 m in vacuum . to search for axions more massive
, coherence can be restored by filling the magnetic conversion region with buffer gas .
integrating over all axion energies , the expected number of photons @xmath32 , being detected during the times of solar alignment with the magnet ( @xmath33 ) , is finally @xmath34 assuming 100% detection efficiency for the conversion x - rays . at a fixed pressure @xmath28 ,
the response of cast will be a sharply peaked function of the actual axion mass @xmath22 , with the fractional resolution @xmath35 . a general analysis of the experimental prospects @xcite explores the full two - dimensional ( @xmath36 ) space for qcd axions rather than the narrow band defined by conventional axion models ( although it remains the best - motivated region ) , as it is shown in fig .
the experiment is being operated in a scanning mode in which the gas pressure is varied in appropriate steps ( 1yr with vacuum , an additional 1yr with a he gas pressure increased from 0 - 1atm in 100 increments , and an additional 1yr with 1 - 10atm in 365 increments ) to cover a range of possible axion masses up to 0.82 ev .
large extra dimensions aim to stabilize the mass hierarchy ( i.e. , the hierarchy between the planck scale and the electroweak scale ) by producing the hugeness of the planck mass @xmath37 via the relation @xmath38 where @xmath39 is the full volume of the compactified space , and the fundamental scale is set at @xmath40 .
as already stressed , a singlet higher - dimensional axion field is also free to propagate into the bulk and therefore a similar volume - suppressed formula can be used to lower the fundamental peccei - quinn symmetry - breaking scale @xmath41 @xcite @xmath42 where @xmath43 is the string scale , @xmath44 . since the phenomenologically allowed region for @xmath14 ( also generating the coupling between the axion and matter ) is such that @xmath45 , the axion must be restricted to a subspace of the full higher - dimensional bulk ( @xmath46 ) , if @xmath41 is to reside in the tev - range @xcite .
still , @xmath47 is possible for @xmath48 @xcite . in ref .
@xcite the full generalization of the higher - dimensional pq mechanism was given , including a thorough discussion of how extra space dimensions may contribute to the invisibility of the pq axion .
all new phenomena contributing to the invisibility of the axion and found there rely on a nontrivial axion mass matrix .
such a matrix is induced by a mixing between the four - dimensional axion and the infinite tower of kk excitations .
the most interesting phenomenological consequence implied by such a mixing is a decoupling of the mass eigenstate of the axion from the pq scale ( for @xmath49 ) . since this feature is crucial for our considerations here
, we discuss it in more detail below .
now , we can focus on the higher - dimensional case by considering first the kk decomposition of the axion field . as a major step ,
we need to calculate the estimated number of x - rays at the pressure @xmath50 as a function of the kk axion mass .
the masses of the kk modes are given by @xmath51 where we assume that all @xmath52 extra dimensions are of the same size @xmath1 .
when the mass splitting for the size @xmath1 ( @xmath53 ) is sufficiently small , one is allowed to use integration instead of summation @xcite .
we have already mentioned that because of the nontrivial axion mass matrix , neither the four - dimensional axion nor the kk states represent the mass eigenstates . instead , the eigenvalues are given as solutions to the transcendental equation @xcite @xmath54 hence , in order to estimate the number of modes with the kk index between @xmath52 and @xmath55 , one should parameterize the whole set of eigenvalues of ( [ eq9 ] ) .
this can be done by solving ( [ eq9 ] ) for two limiting cases , @xmath56 and @xmath57 .
we find for the eigenvalues @xmath58 and @xmath59 the results from ref .
@xcite , where only the mass of the axion zero - mode was estimated , can now be easily reproduced from our expressions ( [ eq10 ] ) and ( [ eq11 ] ) . in fig .
[ fig1 ] we show the mass of the first kk state as a function of @xmath60 .
it can be seen how the mass quickly approaches its limiting value ( 3/2)@xmath61 . a similar feature was found in ref .
@xcite for the zero - mode . , where @xmath4 is given by eq .
( [ eq2]).,width=302 ] finally , the total number of x - rays due to all modes of the kk tower reads @xmath62 and @xmath63 where @xmath64 is the surface of a unit radius in @xmath65 dimensions and @xmath66 is defined as @xmath67 with @xmath68 and @xmath69 .
the function @xmath66 arises from the mixing between the kk axion modes entering the kk decomposition of the higher - dimensional axion field and the corresponding normalized mass eigenstates @xcite .
it also implies both production and detection of kk axions to occur on our standard - model brane .
the function @xmath66 also incorporates the effect of rapid decoherency @xcite of the only linear combination of kk states of the bulk axion which couples to standard - model fields .
this means that the production and subsequent detection of this particular linear combination of kk states are strongly suppressed . as a consequence
our results always reflect a volume - suppressed coupling @xmath70 .
if it was not for the decoherency , the linear combination would be coupled to photons with an unsuppressed coupling @xmath71 .
in order to achieve an upper limit on the coupling of the axion to photons from the prospects of cast in the framework of large extra dimensions , we apply the central limit theorem at 3@xmath72 level @xmath73 where @xmath74 is the background of the x - ray detector ( with numerical values taken from ref .
@xcite ) . for the sake of simplicity
, it is assumed that all axions have an average energy of 4.2 kev .
combining eq .
( [ eq14 ] ) with eqs .
( [ eq3])-([eq5 ] ) and ( [ eq12])-([eq13a ] ) for the case of two extra dimensions ( we take the largest compactification radius of 0.150 mm as set by direct tests of newton s law @xcite ) , we have derived limits on the axion - photon coupling @xmath75 as a function of the fundamental pq mass , as shown in fig . [ fig2 ] . as a function of the fundamental pq mass @xmath4 .
the solid line , corresponding to prospects of cast for qcd axions , is obtained using numerical values from ref .
the dashed region marks the theoretically favored relation between @xmath75 and @xmath4 in axion models in four dimensions . the dashed and dot - dashed line correspond to prospects of cast for kk axions in the case of two extra dimensions ( @xmath76 mm ) for @xmath77 and for @xmath78 , respectively.,width=302 ] although the multiplicity of kk states to which cast could be sensitive is large ( @xmath79 for @xmath77 and @xmath80 for @xmath78 ) , one can see from fig .
[ fig2 ] that the upper limit on @xmath75 is only at most an order of magnitude more stringent than that obtained in conventional theories .
this is due to the fact that cast is a tuning experiment , i.e. , the coherence condition at a fixed pressure is fulfilled only within a very narrow window of axion masses around @xmath81 .
the corresponding width ranges ( depending on pressure ) from @xmath82 down to @xmath83 .
another feature visible in fig .
[ fig2 ] is a strong decrease in sensitivity to @xmath75 for @xmath84 if @xmath78 and for somewhat lower values if @xmath77 .
this is due to the fact that in the regime @xmath56 , @xmath66 decreases as fast as @xmath85 .
it is just the regime in which the obtained limits on @xmath75 can not be coupled with the zero - mode axion mass ( @xmath86 ) via relations ( [ eq1 ] ) and ( [ eq2 ] ) because in higher dimensions the mass of the axion is approximatively given as @xmath87 @xcite .
in contrast with the case of ordinary qcd axions , in theories with large extra dimensions zero - mode axions with masses outside the favored band ( as determined by conventional axion models in four dimensions ) arise quite naturally .
now we would like to point to a new phenomenon predicted for cast : sensitivity to particular kk axions . we have already noted that physical kk modes are given by eqs .
( [ eq10 ] ) and ( [ eq11 ] ) .
it is expected that more than one axion signal may be observed at different pressures of the gas .
therefore , the detection of the corresponding x - rays at least at two pressures may be the signal for the presence of large extra dimensions .
as the cast experiment is scanning the range of axion masses up to 0.82 ev , this requirement actually defines a sensitivity of the experiment to test the compactification radius . from eqs .
( [ eq10 ] ) and ( [ eq11 ] ) we obtain @xmath88 if @xmath89 and @xmath90 if @xmath91 , with @xmath92 .
it should be noted here that with the cast sensitivity to @xmath75 the former result holds only for @xmath93 ; for @xmath56 the sensitivity rapidly decreases due to the suppression from the @xmath66 function .
the present modifications of cast may increase its sensitivity to @xmath75 by a factor of 1.5 @xcite , providing the sensitivity as mentioned above is of the order of that derived from the solar age consideration @xcite .
note that in a recent review of the particle data group @xcite the bound on @xmath1 for the case of two extra dimensions , coming from astrophysics , was listed to have a value within the range 90 to 660 nm ( for the most stringent constraints , see the recent work @xcite ) . in conclusion
, we have explored the potential of the cast experiment for observing kk axions coming from the solar interior . because of the restrictive coherence condition , in theories with two extra dimensions ( with @xmath76 mm ) a sensitivity in axion - photon coupling improves at most one order of magnitude in both data taking phases . in this case , the obtained limit on @xmath75 can not be coupled with the mass of the axion , which is essentially given by the ( common ) radius of the extra dimensions . in addition , we have demonstrated that the cast experiment , being a tuning experiment with respect to axion masses , may not be sensitive only to an integrated effect of kk modes up to the kinematical limit but also to particular kk axions . with a requirement to have at least two signals while changing pressure of the gas , we have found that cast is capable of probing ( two ) large extra dimensions with a compactification radius @xmath1 down to around 250 nm if @xmath2 , and down to around 370 nm if @xmath3
. 100 i. antoniadis , phys .
b * 246 * , 377 ( 1990 ) ; n. arkani - hamed , s. dimopoulos , and g. dvali , phys .
b * 429 * , 263 ( 1998 ) ; phys .
d * 59 * 086004 ( 1999 ) ; i. antoniadis , n. arkani - hamed , s. dimopoulos , and g. dvali , nucl .
* b516 * , 70 ( 1998 ) . c. d. hoyle _
et al_. , phys .
86 * , 1418 ( 2001 ) ; e. g. adelberger for the et - wash group , arxiv : hep - ex/0202008 .
e. witten , nucl .
b * 471 * , 135 ( 1996 ) ; j. d. lykken , phys .
d * 54 * , 3693 ( 1996 ) .
k. r. dienes , e. dudas , and t. gherghetta , phys .
b * 436 * , 55 ( 1998 ) ; nucl .
b * 537 * , 47 ( 1999 ) .
k. r. dienes , e. dudas , and t. gherghetta , nucl .
b * 557 * , 25 ( 1999 ) ; n. arkani - hamed , s. dimopoulos , g. dvali , and j. march - russell , phys .
d * 65 * , 024032 ( 2002 ) .
k. r. dienes , e. dudas , and t. gherghetta , phys .
d * 62 * , 105023 ( 2000 ) .
k. zioutas _
et al_. , nucl . instr . and meth . a * 425 * , 480 ( 1999 ) .
c. e. aalseth _
et al_. , ( cast collaboration ) , nucl .
b ( proc . suppl . )
* 110 * , 85 ( 2002 ) ; i. g. irastorza _
et al_. , ( cast collaboration ) , nucl .
b ( proc . suppl . )
* 114 * , 75 ( 2003 ) ; j. i. collar _
et al_. , ( cast collaboration ) , arxiv : hep - ex/0304024 ; c. eleftheriadis _
et al_. , ( cast collaboration ) , arxiv : astro - ph/0305534 . s. moriyama _
et al_. , phys .
b * 434 * , 147 ( 1998 ) ; y. inoue _ et al_. , phys .
b * 536 * , 18 ( 2002 ) .
g. g. raffelt , arxiv : hep - ph/0207144 . k. van bibber , p. m. mcintyre , d. e. morris , and g. g. raffelt , phys .
d * 39 * , 2089 ( 1989 ) .
d. m. lazarus _
et al_. , phys .
lett . * 69 * , 2333 ( 1992 ) .
r. d. peccei and h. r. quinn , phys .
lett . * 38 * , 1440 ( 1977 ) ; phys .
d * 16 * , 1791 ( 1977 ) .
j. e. kim , phys .
* 43 * , 103 ( 1979 ) ; m. a. shifman , a. i. vainshtein , and v. i. zakharov , nucl . phys . * b166 * , 493 ( 1980 ) . m. dine , w. fischler , and m. srednicki , phys .
b * 104 * , 199 ( 1981 ) ; a. r. zhitnitski , yad
. fiz . * 31 * , 497 ( 1980 ) [ sov .
. phys . * 31 * , 260 ( 1980 ) ] .
see , e.g. , g. g. raffelt , _ stars as laboratories for fundamental physics _ ( the university of chicago press , chicago , 1996 ) .
_ et al_. , phys .
b * 442 * , 38 ( 1998 ) .
m. krmar _
et al_. , phys .
d * 64 * , 115016 ( 2001 ) .
f. t. avignone iii _
et al_. , phys .
* 81 * , 5068 ( 1998 ) .
r. bernabei _
et al_. , phys .
b * 515 * , 6 ( 2001 ) . l. di lella , a. pilaftsis , g. raffelt , and k. zioutas , phys . rev .
d * 62 * , 125011 ( 2000 ) .
s. chang , s. tazawa , and m. yamaguchi , phys .
d * 61 * , 084005 ( 2000 ) .
r. horvat , m. krmar , and b. laki , phys .
d * 65 * , 087701 ( 2002 ) . g. f. guidice , r. rattazzi , and j. d. wells , nucl .
b544 * , 3 ( 1999 ) ; t. han , j. d. lykken , and r. j. zhang , phys .
d * 59 * , 105006 ( 1999 ) . by simply scaling the solar age limit of qcd axions ( @xmath94 ) @xcite with @xmath95 due to the multiplicity of kk modes and observing that an allowed maximum mass is @xmath96 before the solar flux gets suppressed by the kinematic threshold , one obtains for two extra dimensions : ( i ) for @xmath97 mm : @xmath98 if @xmath77 and @xmath99 if @xmath78 , and ( ii ) for @xmath100 nm : @xmath101 if @xmath77 and @xmath102 if @xmath78 . k. hagiwara _
et al_. ( particle data group ) , phys . rev .
d * 66 * , 010001 ( 2002 ) .
s. hannestad and g. g. raffelt , phys .
d * 67 * , 125008 ( 2003 ) . | we explore the potential of the cern axion solar telescope ( cast ) for testing the presence of large extra dimensions . the cast experiment has originally been proposed to search for solar axions with a sensitivity supposed to provide a limit on the axion - photon coupling @xmath0 or even lower .
the expected bound on the coupling constant is by a factor of ten more stringent than the current experimental results .
this bound extends for the first time beyond the limit dictated by astrophysical considerations . as a tuning experiment planning to explore the axion mass region up to about 1 ev
, cast would also be sensitive to the existence of kaluza - klein massive states .
therefore , the detection of x - rays at least at two pressures may be the signature of large extra dimensions . from this requirement
we find that cast may test ( two ) large extra dimensions with a ( common ) compactification radius @xmath1 down to around 250 nm if @xmath2 , and down to around 370 nm if @xmath3 , where @xmath4 is the peccei - quinn mass . | <s>[INST]a few years ago an approach was put forward @xcite in which heavy mass scales in four dimensions could be replaced by lighter mass scales in higher dimensions .
such a class of theories is nowadays conventionally considered in the context of the brane paradigm . in one class of models extra dimensions
are felt only by gravity ( as well as other fields transforming as singlet under the standard - model gauge group ) ; in the other class they are felt also by gauge fields . in the former case ,
the standard - model fields are confined to a ( 3 + 1)-dimensional subspace of a higher - dimensional space some dimensions of which are compactified with a relatively large radius .
the absence of any observed deviation from ordinary newtonian gravity in cavendish - type laboratory experiments implies that the largest compactification radius is smaller than around 0.2 mm @xcite .
the main goal in both classes of models is to provide a unified theory in which the electroweak scale @xmath5 and the high energy scales ( planck @xcite , string @xcite , and gut scales @xcite ) can coexist .
the same scenario has also been successfully applied to neutrino as well as to axion phenomenology .
namely , a higher - dimensional seesaw mechanism may provide light neutrino masses without heavy mass scales @xcite .
similarly , axion invisibility can be achieved in extra dimensions even with a low fundamental peccei - quinn ( pq ) scale @xcite .
the cern axion solar telescope ( cast ) is designed to search for solar axions of a broad energy spectrum which peaks at about 4 kev , through their conversion into real photons inside the transverse magnetic field @xcite .
this telescope may improve the current laboratory bounds on the axion - photon coupling , @xmath6 for @xmath7 ev and @xmath8 for @xmath9 @xcite , by a factor of ten or even more .
it also has the potential to extend for the first time the axion searches beyond the limit @xmath10 arising from astrophysical constraints on anomalous energy loss by stars @xcite .
although the cast telescope could in principle be sensitive to axion masses in the range of a few kev , the coherence - loss constraints @xcite reduce the sensitivity down to around 1 ev .
the first goal of the present note is to interpret prospects of cast in the light of the theory with large extra spatial dimensions .
we focus on the case when the limit on the size of two large extra compact dimensions is set by direct tests of gravity @xcite .
our second goal is to explore the potential of cast for testing the presence of large extra dimensions .
axions are pseudoscalars arising in models which resolve the strong _ cp _ problem in quantum chromodynamics ( qcd ) by the pq mechanism @xcite . owing to their potential abundance in the early universe
, they are also well - motivated candidates for the dark matter of the universe . in both classes of ( conventional ) invisible axion models
referred to as ksvz or hadronic axion models @xcite ( where axions do not couple to electrons at tree level ) and dfsz or grand unified theory ( gut ) models @xcite , the axion - photon coupling strength is given by the relation @xmath11 here @xmath12 is a model - dependent numerical parameter for hadronic axions , while for dfsz axions @xmath13 .
furthermore , the mass of the ( qcd ) axion @xmath4 is related to the pq symmetry breaking scale @xmath14 by @xmath15 in order to avoid ambiguities owing to the model - dependence of the parameter @xmath12 for hadronic axions , it proved more convenient to make constraints on the axion - photon coupling than on the pq energy scale or on the axion mass .
in contrast , cosmological considerations and astrophysical arguments ( i.e. , axion emission due to nucleon - nucleon bremsstrahlung from the supernova sn 1987a ) bound the axion mass into two possible ranges @xcite .
the first window is @xmath16 , in which case the axion could constitute the cold dark matter of the universe . the second one , being around ten to twenty electronvolts , appears to be of interest for hot dark matter .
however , such astrophysical constraints on @xmath4 , although the most stringent , suffer from statistical weakness ( with only 19 neutrinos being observed ) as well as from all uncertainties related to the axion emission from a hot / dense medium .
it is therefore of crucial importance to probe the axion properties in a model - independent way @xcite .
currently , laboratory searches for solar axions @xcite are being extended by the cast experiment at cern .
this telescope uses a decommissioned lhc prototype magnet with a field of 9 t and a length @xmath17 of 10 m. the magnet contains two straight beam pipes with an effective cross sectional area @xmath18 , and is mounted on a moving platform with low - background x - ray detectors on either end allowing it to track the sun about 3 hours per day .
hadronic axions could be produced abundantly in the core of the sun by the primakoff conversion of the blackbody photons in the coulomb fields of nuclei and electrons in the solar plasma .
the outgoing axion flux is robust and does not depend on subtle details of the solar model .
it is approximately given by @xcite @xmath19 here @xmath20 is the axion flux at the earth , differential with respect to axion energy ( @xmath21 ) , and expressed as a function of axion mass ( @xmath22 ) .
the quantities @xmath21 , @xmath23 , and @xmath22 are to be taken in kev .
the probability for an axion - to - photon conversion in the presence of a transverse magnetic field ( @xmath24 ) and a refractive medium ( i ) is given by @xcite @xmath25 , \label{eq4}\end{aligned}\ ] ] where @xmath26 is the momentum difference between photons in the medium and axions , and @xmath27 denotes the inverse absorption length for x - rays .
the effective mass ( plasma frequency ) for an x - ray in he can be described in terms of the operating pressure @xmath28 ( at 300 k ) as @xmath29 .
the coherence condition @xmath30 @xcite requires @xmath31 for a photon energy of 4.2 kev ( the average axion energy ) and a coherence length of 10 m in vacuum . to search for axions more massive
, coherence can be restored by filling the magnetic conversion region with buffer gas .
integrating over all axion energies , the expected number of photons @xmath32 , being detected during the times of solar alignment with the magnet ( @xmath33 ) , is finally @xmath34 assuming 100% detection efficiency for the conversion x - rays . at a fixed pressure @xmath28 ,
the response of cast will be a sharply peaked function of the actual axion mass @xmath22 , with the fractional resolution @xmath35 . a general analysis of the experimental prospects @xcite explores the full two - dimensional ( @xmath36 ) space for qcd axions rather than the narrow band defined by conventional axion models ( although it remains the best - motivated region ) , as it is shown in fig .
the experiment is being operated in a scanning mode in which the gas pressure is varied in appropriate steps ( 1yr with vacuum , an additional 1yr with a he gas pressure increased from 0 - 1atm in 100 increments , and an additional 1yr with 1 - 10atm in 365 increments ) to cover a range of possible axion masses up to 0.82 ev .
large extra dimensions aim to stabilize the mass hierarchy ( i.e. , the hierarchy between the planck scale and the electroweak scale ) by producing the hugeness of the planck mass @xmath37 via the relation @xmath38 where @xmath39 is the full volume of the compactified space , and the fundamental scale is set at @xmath40 .
as already stressed , a singlet higher - dimensional axion field is also free to propagate into the bulk and therefore a similar volume - suppressed formula can be used to lower the fundamental peccei - quinn symmetry - breaking scale @xmath41 @xcite @xmath42 where @xmath43 is the string scale , @xmath44 . since the phenomenologically allowed region for @xmath14 ( also generating the coupling between the axion and matter ) is such that @xmath45 , the axion must be restricted to a subspace of the full higher - dimensional bulk ( @xmath46 ) , if @xmath41 is to reside in the tev - range @xcite .
still , @xmath47 is possible for @xmath48 @xcite . in ref .
@xcite the full generalization of the higher - dimensional pq mechanism was given , including a thorough discussion of how extra space dimensions may contribute to the invisibility of the pq axion .
all new phenomena contributing to the invisibility of the axion and found there rely on a nontrivial axion mass matrix .
such a matrix is induced by a mixing between the four - dimensional axion and the infinite tower of kk excitations .
the most interesting phenomenological consequence implied by such a mixing is a decoupling of the mass eigenstate of the axion from the pq scale ( for @xmath49 ) . since this feature is crucial for our considerations here
, we discuss it in more detail below .
now , we can focus on the higher - dimensional case by considering first the kk decomposition of the axion field . as a major step ,
we need to calculate the estimated number of x - rays at the pressure @xmath50 as a function of the kk axion mass .
the masses of the kk modes are given by @xmath51 where we assume that all @xmath52 extra dimensions are of the same size @xmath1 .
when the mass splitting for the size @xmath1 ( @xmath53 ) is sufficiently small , one is allowed to use integration instead of summation @xcite .
we have already mentioned that because of the nontrivial axion mass matrix , neither the four - dimensional axion nor the kk states represent the mass eigenstates . instead , the eigenvalues are given as solutions to the transcendental equation @xcite @xmath54 hence , in order to estimate the number of modes with the kk index between @xmath52 and @xmath55 , one should parameterize the whole set of eigenvalues of ( [ eq9 ] ) .
this can be done by solving ( [ eq9 ] ) for two limiting cases , @xmath56 and @xmath57 .
we find for the eigenvalues @xmath58 and @xmath59 the results from ref .
@xcite , where only the mass of the axion zero - mode was estimated , can now be easily reproduced from our expressions ( [ eq10 ] ) and ( [ eq11 ] ) . in fig .
[ fig1 ] we show the mass of the first kk state as a function of @xmath60 .
it can be seen how the mass quickly approaches its limiting value ( 3/2)@xmath61 . a similar feature was found in ref .
@xcite for the zero - mode . , where @xmath4 is given by eq .
( [ eq2]).,width=302 ] finally , the total number of x - rays due to all modes of the kk tower reads @xmath62 and @xmath63 where @xmath64 is the surface of a unit radius in @xmath65 dimensions and @xmath66 is defined as @xmath67 with @xmath68 and @xmath69 .
the function @xmath66 arises from the mixing between the kk axion modes entering the kk decomposition of the higher - dimensional axion field and the corresponding normalized mass eigenstates @xcite .
it also implies both production and detection of kk axions to occur on our standard - model brane .
the function @xmath66 also incorporates the effect of rapid decoherency @xcite of the only linear combination of kk states of the bulk axion which couples to standard - model fields .
this means that the production and subsequent detection of this particular linear combination of kk states are strongly suppressed . as a consequence
our results always reflect a volume - suppressed coupling @xmath70 .
if it was not for the decoherency , the linear combination would be coupled to photons with an unsuppressed coupling @xmath71 .
in order to achieve an upper limit on the coupling of the axion to photons from the prospects of cast in the framework of large extra dimensions , we apply the central limit theorem at 3@xmath72 level @xmath73 where @xmath74 is the background of the x - ray detector ( with numerical values taken from ref .
@xcite ) . for the sake of simplicity
, it is assumed that all axions have an average energy of 4.2 kev .
combining eq .
( [ eq14 ] ) with eqs .
( [ eq3])-([eq5 ] ) and ( [ eq12])-([eq13a ] ) for the case of two extra dimensions ( we take the largest compactification radius of 0.150 mm as set by direct tests of newton s law @xcite ) , we have derived limits on the axion - photon coupling @xmath75 as a function of the fundamental pq mass , as shown in fig . [ fig2 ] . as a function of the fundamental pq mass @xmath4 .
the solid line , corresponding to prospects of cast for qcd axions , is obtained using numerical values from ref .
the dashed region marks the theoretically favored relation between @xmath75 and @xmath4 in axion models in four dimensions . the dashed and dot - dashed line correspond to prospects of cast for kk axions in the case of two extra dimensions ( @xmath76 mm ) for @xmath77 and for @xmath78 , respectively.,width=302 ] although the multiplicity of kk states to which cast could be sensitive is large ( @xmath79 for @xmath77 and @xmath80 for @xmath78 ) , one can see from fig .
[ fig2 ] that the upper limit on @xmath75 is only at most an order of magnitude more stringent than that obtained in conventional theories .
this is due to the fact that cast is a tuning experiment , i.e. , the coherence condition at a fixed pressure is fulfilled only within a very narrow window of axion masses around @xmath81 .
the corresponding width ranges ( depending on pressure ) from @xmath82 down to @xmath83 .
another feature visible in fig .
[ fig2 ] is a strong decrease in sensitivity to @xmath75 for @xmath84 if @xmath78 and for somewhat lower values if @xmath77 .
this is due to the fact that in the regime @xmath56 , @xmath66 decreases as fast as @xmath85 .
it is just the regime in which the obtained limits on @xmath75 can not be coupled with the zero - mode axion mass ( @xmath86 ) via relations ( [ eq1 ] ) and ( [ eq2 ] ) because in higher dimensions the mass of the axion is approximatively given as @xmath87 @xcite .
in contrast with the case of ordinary qcd axions , in theories with large extra dimensions zero - mode axions with masses outside the favored band ( as determined by conventional axion models in four dimensions ) arise quite naturally .
now we would like to point to a new phenomenon predicted for cast : sensitivity to particular kk axions . we have already noted that physical kk modes are given by eqs .
( [ eq10 ] ) and ( [ eq11 ] ) .
it is expected that more than one axion signal may be observed at different pressures of the gas .
therefore , the detection of the corresponding x - rays at least at two pressures may be the signal for the presence of large extra dimensions .
as the cast experiment is scanning the range of axion masses up to 0.82 ev , this requirement actually defines a sensitivity of the experiment to test the compactification radius . from eqs .
( [ eq10 ] ) and ( [ eq11 ] ) we obtain @xmath88 if @xmath89 and @xmath90 if @xmath91 , with @xmath92 .
it should be noted here that with the cast sensitivity to @xmath75 the former result holds only for @xmath93 ; for @xmath56 the sensitivity rapidly decreases due to the suppression from the @xmath66 function .
the present modifications of cast may increase its sensitivity to @xmath75 by a factor of 1.5 @xcite , providing the sensitivity as mentioned above is of the order of that derived from the solar age consideration @xcite .
note that in a recent review of the particle data group @xcite the bound on @xmath1 for the case of two extra dimensions , coming from astrophysics , was listed to have a value within the range 90 to 660 nm ( for the most stringent constraints , see the recent work @xcite ) . in conclusion
, we have explored the potential of the cast experiment for observing kk axions coming from the solar interior . because of the restrictive coherence condition , in theories with two extra dimensions ( with @xmath76 mm ) a sensitivity in axion - photon coupling improves at most one order of magnitude in both data taking phases . in this case , the obtained limit on @xmath75 can not be coupled with the mass of the axion , which is essentially given by the ( common ) radius of the extra dimensions . in addition , we have demonstrated that the cast experiment , being a tuning experiment with respect to axion masses , may not be sensitive only to an integrated effect of kk modes up to the kinematical limit but also to particular kk axions . with a requirement to have at least two signals while changing pressure of the gas , we have found that cast is capable of probing ( two ) large extra dimensions with a compactification radius @xmath1 down to around 250 nm if @xmath2 , and down to around 370 nm if @xmath3
. 100 i. antoniadis , phys .
b * 246 * , 377 ( 1990 ) ; n. arkani - hamed , s. dimopoulos , and g. dvali , phys .
b * 429 * , 263 ( 1998 ) ; phys .
d * 59 * 086004 ( 1999 ) ; i. antoniadis , n. arkani - hamed , s. dimopoulos , and g. dvali , nucl .
* b516 * , 70 ( 1998 ) . c. d. hoyle _
et al_. , phys .
86 * , 1418 ( 2001 ) ; e. g. adelberger for the et - wash group , arxiv : hep - ex/0202008 .
e. witten , nucl .
b * 471 * , 135 ( 1996 ) ; j. d. lykken , phys .
d * 54 * , 3693 ( 1996 ) .
k. r. dienes , e. dudas , and t. gherghetta , phys .
b * 436 * , 55 ( 1998 ) ; nucl .
b * 537 * , 47 ( 1999 ) .
k. r. dienes , e. dudas , and t. gherghetta , nucl .
b * 557 * , 25 ( 1999 ) ; n. arkani - hamed , s. dimopoulos , g. dvali , and j. march - russell , phys .
d * 65 * , 024032 ( 2002 ) .
k. r. dienes , e. dudas , and t. gherghetta , phys .
d * 62 * , 105023 ( 2000 ) .
k. zioutas _
et al_. , nucl . instr . and meth . a * 425 * , 480 ( 1999 ) .
c. e. aalseth _
et al_. , ( cast collaboration ) , nucl .
b ( proc . suppl . )
* 110 * , 85 ( 2002 ) ; i. g. irastorza _
et al_. , ( cast collaboration ) , nucl .
b ( proc . suppl . )
* 114 * , 75 ( 2003 ) ; j. i. collar _
et al_. , ( cast collaboration ) , arxiv : hep - ex/0304024 ; c. eleftheriadis _
et al_. , ( cast collaboration ) , arxiv : astro - ph/0305534 . s. moriyama _
et al_. , phys .
b * 434 * , 147 ( 1998 ) ; y. inoue _ et al_. , phys .
b * 536 * , 18 ( 2002 ) .
g. g. raffelt , arxiv : hep - ph/0207144 . k. van bibber , p. m. mcintyre , d. e. morris , and g. g. raffelt , phys .
d * 39 * , 2089 ( 1989 ) .
d. m. lazarus _
et al_. , phys .
lett . * 69 * , 2333 ( 1992 ) .
r. d. peccei and h. r. quinn , phys .
lett . * 38 * , 1440 ( 1977 ) ; phys .
d * 16 * , 1791 ( 1977 ) .
j. e. kim , phys .
* 43 * , 103 ( 1979 ) ; m. a. shifman , a. i. vainshtein , and v. i. zakharov , nucl . phys . * b166 * , 493 ( 1980 ) . m. dine , w. fischler , and m. srednicki , phys .
b * 104 * , 199 ( 1981 ) ; a. r. zhitnitski , yad
. fiz . * 31 * , 497 ( 1980 ) [ sov .
. phys . * 31 * , 260 ( 1980 ) ] .
see , e.g. , g. g. raffelt , _ stars as laboratories for fundamental physics _ ( the university of chicago press , chicago , 1996 ) .
_ et al_. , phys .
b * 442 * , 38 ( 1998 ) .
m. krmar _
et al_. , phys .
d * 64 * , 115016 ( 2001 ) .
f. t. avignone iii _
et al_. , phys .
* 81 * , 5068 ( 1998 ) .
r. bernabei _
et al_. , phys .
b * 515 * , 6 ( 2001 ) . l. di lella , a. pilaftsis , g. raffelt , and k. zioutas , phys . rev .
d * 62 * , 125011 ( 2000 ) .
s. chang , s. tazawa , and m. yamaguchi , phys .
d * 61 * , 084005 ( 2000 ) .
r. horvat , m. krmar , and b. laki , phys .
d * 65 * , 087701 ( 2002 ) . g. f. guidice , r. rattazzi , and j. d. wells , nucl .
b544 * , 3 ( 1999 ) ; t. han , j. d. lykken , and r. j. zhang , phys .
d * 59 * , 105006 ( 1999 ) . by simply scaling the solar age limit of qcd axions ( @xmath94 ) @xcite with @xmath95 due to the multiplicity of kk modes and observing that an allowed maximum mass is @xmath96 before the solar flux gets suppressed by the kinematic threshold , one obtains for two extra dimensions : ( i ) for @xmath97 mm : @xmath98 if @xmath77 and @xmath99 if @xmath78 , and ( ii ) for @xmath100 nm : @xmath101 if @xmath77 and @xmath102 if @xmath78 . k. hagiwara _
et al_. ( particle data group ) , phys . rev .
d * 66 * , 010001 ( 2002 ) .
s. hannestad and g. g. raffelt , phys .
d * 67 * , 125008 ( 2003 ) .[/INST] we explore the potential of the cern axion solar telescope ( cast ) for testing the presence of large extra dimensions . the cast experiment has originally been proposed to search for solar axions with a sensitivity supposed to provide a limit on the axion - photon coupling @xmath0 or even lower .
the expected bound on the coupling constant is by a factor of ten more stringent than the current experimental results .
this bound extends for the first time beyond the limit dictated by astrophysical considerations . as a tuning experiment planning to explore the axion mass region up to about 1 ev
, cast would also be sensitive to the existence of kaluza - klein massive states .
therefore , the detection of x - rays at least at two pressures may be the signature of large extra dimensions . from this requirement
we find that cast may test ( two ) large extra dimensions with a ( common ) compactification radius @xmath1 down to around 250 nm if @xmath2 , and down to around 370 nm if @xmath3 , where @xmath4 is the peccei - quinn mass . </s> |
SECTION 1. MEDICARE TREATMENT FOR CERTAIN CANCER HOSPITALS.
(a) In General.--Section 1886(d)(1)(B) of the Social Security Act
(42 U.S.C. 1395ww(d)(1)(B)) is amended--
(1) by striking ``or'' at the end of clause (iv);
(2) by striking the semicolon at the end of clause (v) and
inserting ``, or''; and
(3) by inserting after clause (v) the following new clause:
``(vi) a hospital that--
``(I) is located in a State which ranks (according
to the National Cancer Institute's statistics published
in May 2005 for 2001 and 2002) first among all States
in the incidence of prostate cancer, third in the
incidence rate for non-Hodgkins lymphoma, fourth in the
incidence rates for thyroid cancer and ovarian cancer,
and third in the highest death rates from uterine
cancer and breast cancer;
``(II) is located in a State that, as of December
31, 2005, had only one center under section 414 of the
Public Health Service Act that has been designated by
the National Cancer Institute as a comprehensive center
currently serving all 21 counties in the most densely
populated State in the nation, serving more than 70,000
patient visits annually;
``(III) as of December 31, 2005, served as the
teaching and clinical care, research and training
hospital for the Center described in subclause (II),
providing significant financial and operational support
to such Center;
``(IV) as of December 31, 2005, served as a core
and essential element in such Center which conducts
more than 130 clinical trial activities, national
cooperative group studies, investigator-initiated and
peer review studies and received during 2003 at least
$80,000,000 in research grant awards;
``(V) as of December 31, 2005, can demonstrate that
it has been a unique and an integral component of such
Center since such Center's inception;
``(VI) as of December 31, 2005, includes dedicated
patient care units organized primarily for the
treatment of and research on cancer with approximately
125 beds, 75 percent of which are dedicated to cancer
patients, and contains a radiation oncology department
as well as specialized emergency services for oncology
patients;
``(VII) as of December 31, 2003, is identified as
the focus of the Center's inpatient activities in the
Center's application as an NCI-designated comprehensive
cancer center and shares the NCI comprehensive cancer
designation with the Center; and
``(VIII) as of December 31, 2005, has been
recognized with a certificate of approval by the
American College of Surgeons Commission on Cancer;''.
(b) Conforming Amendment.--Section 1886(d)(3)(E) of such Act (42
U.S.C. 1395ww(d)(3)(E)) is amended by striking ``clause (v)'' and
inserting ``clauses (v) and (vi)''.
(c) Payment.--
(1) Application to cost reporting periods.--Any
classification by reason of section 1886(d)(1)(B)(vi) of the
Social Security Act (42 U.S.C. 1395ww(d)(1)(B)(vi)) (as added
by subsection (a)) shall apply to all cost reporting periods
beginning on or after January 1, 2005.
(2) Base target amount.--Notwithstanding section
1886(b)(3)(E) of the Social Security Act (42 U.S.C.
1395ww(b)(3)(E), in the case of a hospital described in section
1886(d)(1)(B)(vi) of the Social Security Act, as added by
subsection (a), such hospital shall be permitted to resubmit
the 2005 Medicare 2552 cost report incorporating a cancer
hospital sub-provider number, and apply the Medicare ratio-of-
cost-to-charge settlement methodology for outpatient cancer
services. In the case of such hospital the PPS cancer exemption
under section 1886(b)(3)(E)(i) of such Act for the first cost
reporting period beginning on or after January 1, 2005, shall
be the allowable operating costs of inpatient hospital services
(referred to in subclause (I) of such section) for such first
cost reporting period.
(3) Deadline for payments.--Any payments owed to a hospital
as a result of this section for periods occurring before the
date of the enactment of this Act shall be made expeditiously,
but in no event later than 1 year after such date of enactment.
(d) Maintenance of Exemption.--Once admitted as a PPS cancer-exempt
hospital, a hospital described in section 1886(d)(1)(B)(vi) of the
Social Security Act shall retain that status as long as the Center
referred to in such section remains a comprehensive cancer center. | Amends title XVIII (Medicare) of the Social Security Act, with respect to inpatient hospital service payments to certain hospitals (subsection (d) hospitals) on the basis of prospective rates, to exclude certain cancer hospitals from the meaning of subsection (d) hospital. | <s>[INST]SECTION 1. MEDICARE TREATMENT FOR CERTAIN CANCER HOSPITALS.
(a) In General.--Section 1886(d)(1)(B) of the Social Security Act
(42 U.S.C. 1395ww(d)(1)(B)) is amended--
(1) by striking ``or'' at the end of clause (iv);
(2) by striking the semicolon at the end of clause (v) and
inserting ``, or''; and
(3) by inserting after clause (v) the following new clause:
``(vi) a hospital that--
``(I) is located in a State which ranks (according
to the National Cancer Institute's statistics published
in May 2005 for 2001 and 2002) first among all States
in the incidence of prostate cancer, third in the
incidence rate for non-Hodgkins lymphoma, fourth in the
incidence rates for thyroid cancer and ovarian cancer,
and third in the highest death rates from uterine
cancer and breast cancer;
``(II) is located in a State that, as of December
31, 2005, had only one center under section 414 of the
Public Health Service Act that has been designated by
the National Cancer Institute as a comprehensive center
currently serving all 21 counties in the most densely
populated State in the nation, serving more than 70,000
patient visits annually;
``(III) as of December 31, 2005, served as the
teaching and clinical care, research and training
hospital for the Center described in subclause (II),
providing significant financial and operational support
to such Center;
``(IV) as of December 31, 2005, served as a core
and essential element in such Center which conducts
more than 130 clinical trial activities, national
cooperative group studies, investigator-initiated and
peer review studies and received during 2003 at least
$80,000,000 in research grant awards;
``(V) as of December 31, 2005, can demonstrate that
it has been a unique and an integral component of such
Center since such Center's inception;
``(VI) as of December 31, 2005, includes dedicated
patient care units organized primarily for the
treatment of and research on cancer with approximately
125 beds, 75 percent of which are dedicated to cancer
patients, and contains a radiation oncology department
as well as specialized emergency services for oncology
patients;
``(VII) as of December 31, 2003, is identified as
the focus of the Center's inpatient activities in the
Center's application as an NCI-designated comprehensive
cancer center and shares the NCI comprehensive cancer
designation with the Center; and
``(VIII) as of December 31, 2005, has been
recognized with a certificate of approval by the
American College of Surgeons Commission on Cancer;''.
(b) Conforming Amendment.--Section 1886(d)(3)(E) of such Act (42
U.S.C. 1395ww(d)(3)(E)) is amended by striking ``clause (v)'' and
inserting ``clauses (v) and (vi)''.
(c) Payment.--
(1) Application to cost reporting periods.--Any
classification by reason of section 1886(d)(1)(B)(vi) of the
Social Security Act (42 U.S.C. 1395ww(d)(1)(B)(vi)) (as added
by subsection (a)) shall apply to all cost reporting periods
beginning on or after January 1, 2005.
(2) Base target amount.--Notwithstanding section
1886(b)(3)(E) of the Social Security Act (42 U.S.C.
1395ww(b)(3)(E), in the case of a hospital described in section
1886(d)(1)(B)(vi) of the Social Security Act, as added by
subsection (a), such hospital shall be permitted to resubmit
the 2005 Medicare 2552 cost report incorporating a cancer
hospital sub-provider number, and apply the Medicare ratio-of-
cost-to-charge settlement methodology for outpatient cancer
services. In the case of such hospital the PPS cancer exemption
under section 1886(b)(3)(E)(i) of such Act for the first cost
reporting period beginning on or after January 1, 2005, shall
be the allowable operating costs of inpatient hospital services
(referred to in subclause (I) of such section) for such first
cost reporting period.
(3) Deadline for payments.--Any payments owed to a hospital
as a result of this section for periods occurring before the
date of the enactment of this Act shall be made expeditiously,
but in no event later than 1 year after such date of enactment.
(d) Maintenance of Exemption.--Once admitted as a PPS cancer-exempt
hospital, a hospital described in section 1886(d)(1)(B)(vi) of the
Social Security Act shall retain that status as long as the Center
referred to in such section remains a comprehensive cancer center.[/INST]Amends title XVIII (Medicare) of the Social Security Act, with respect to inpatient hospital service payments to certain hospitals (subsection (d) hospitals) on the basis of prospective rates, to exclude certain cancer hospitals from the meaning of subsection (d) hospital.</s> |
Women with insomnia or other sleep problems have an increased risk of giving birth prematurely, a new study suggests.
The observational study, in Obstetrics & Gynecology, included 2,172 women with a sleep disorder who gave birth between 2007 and 2012 to single children after 22 to 44 weeks of gestation. They were matched with the same number of women with the identical ethnic, health and behavioral characteristics, but who did not have a sleep disorder.
Over all, women with sleep disorders had a 14.6 percent prevalence of preterm birth (before 37 weeks of gestation), compared with 10.9 percent in those without a diagnosis. Those with insomnia had a 30 percent increased risk, and those with sleep apnea a 40 percent increased risk, compared with women without a sleep problem.
Women with insomnia were nearly twice as likely to deliver before 34 weeks gestation.
βMore severe sleep disorders are often underdiagnosed, because poor sleep is common during pregnancy,β said the lead author, Jennifer N. Felder, a postdoctoral researcher in psychology at the University of California, San Francisco. βBut for women having sleep problems that are severe, impairing and distressing, itβs important to talk to their health care providers.β ||||| (Reuters Health) - Women who experience sleep disorders like insomnia and apnea during pregnancy may be more likely to deliver premature babies than pregnant women who donβt have trouble sleeping, a U.S. study suggests.
Compared with women who didnβt have sleep problems, women with insomnia were 30 percent more likely to have a preemie and the odds for women with sleep apnea, a breathing disorder, were 50 percent higher, the study found.
βIt is normal to experience sleep changes during pregnancy - often due to discomfort, pain or frequent trips to the bathroom,β said lead study author Jennifer Felder, of the University of California, San Francisco.
βThe current study focused on more impairing sleep problems that were severe enough to result in a sleep disorder diagnosis,β Felder said by email.
Apnea, a potentially serious sleep disorder that involves repeated stops and starts in breathing, has been linked to high blood pressure during pregnancy, which is an independent risk factor for preterm births. Obesity and advanced age can make apnea more likely.
Even though many pregnant women have insomnia at some point, previous studies havenβt offered a clear picture of how this type of sleep deprivation influences the odds of preterm births.
Worldwide, preterm birth is the leading cause of death for children under 5 years old, the researchers note in the journal Obstetrics and Gynecology.
Pregnancy normally lasts about 40 weeks, and babies born after 37 weeks are considered full term. The new study focused on preterm infants, delivered at 34 to 36 weeksβ gestation, and extremely premature babies delivered before 34 weeks.
In the weeks immediately after birth, preemies often have difficulty breathing and digesting food. They can also encounter longer-term challenges such as impaired vision, hearing, and cognitive skills as well as social and behavioral problems.
The study team examined data on more than 3 million births in California from 2007 to 2012. They focused on 2,172 women who had a sleep disorder diagnosis and compared their birth outcomes to a randomly selected group of 2,172 mothers who were similar in many ways but had no sleep issues.
Women with sleep disorders were more likely to be black, age 35 or older, obese, and to have other medical issues like high blood pressure, diabetes and infections as well as higher odds of smoking or using drugs and alcohol while pregnant. They were also more likely to have a history of preterm birth.
Overall, almost 15 percent of women with sleep disorders had a preterm birth, compared with 11 percent of women without sleep issues.
The study wasnβt a controlled experiment designed to prove how or even whether sleep disorders directly cause preterm births.
Even so, the results offer fresh evidence of the link between sleep disorders and early arrivals, said Dr. Ghada Bourjeily, a researcher at Warren Alpert Medical School of Brown University in Providence, Rhode Island, who wasnβt involved in the study.
βSleep appears to get worse in pregnancy in many, even women who do not have a preexisting sleep disorder,β Bourjeily said by email. βUnfortunately, we do not know yet whether improving sleep quality before or during pregnancy would prevent development of negative outcomes such as preterm birth.β
Starting pregnancy at a healthy weight, however, may make sleep disorders less likely, said Dr. Amos Grunebaum, director of obstetrics at NewYork-Presbyterian Hospital/Weill Cornell Medical Center in New York.
βBeing overweight or obese increases your risk of having a sleep disorder,β Grunebaum, who wasnβt involved in the study, said by email. βIt also increases pregnancy complications.β
When sleep disorders do surface during pregnancy, women should discuss symptoms in detail with their doctors, said Dr. Milena Pavlova, a researcher at Brigham and Womenβs Hospital in Boston who wasnβt involved in the study. This includes any issues with breathing, gasping or choking at night or any uncomfortable leg or body sensations that prevent sleep.
Expectant mothers should also make sleep a priority in their schedules, Pavlova, who wasnβt involved in the study, said by email.
βAllow enough time for sleep - the life you save may be your babyβs,β Pavlova said.
SOURCE: bit.ly/2j2fR06 Obstetrics and Gynecology, online August 8, 2017. ||||| Andrew Lichtenstein/Corbis/Getty
Despite strides in maternal medicine, premature birth remains a vexing problem for obstetricians worldwide. But an analysis of medical records from almost 3 million pregnant women in California1 suggests that a surprisingly simple intervention β better sleep β might help to address the issue.
Researchers found that women who had been diagnosed with insomnia or sleep apnoea were about twice as likely as women without sleep disorders to deliver their babies more than six weeks early.
βIt seems obvious, but strangely this study has not been done before,β says Laura Jelliffe-Pawlowski, an epidemiologist at the University of California, San Francisco (UCSF), and an author of the research, which was published on 8 August in the journal Obstetrics and Gynecology1. βSeeing this relationship is important because we are just starved for interventions that can make a difference.β
Public-health experts say that better treatment for pregnant women with serious sleep disorders could save babies' lives, and do so with approaches that avoid the use of medication. Every year, 15 million babies worldwide are born prematurely β more than three weeks before the typical full-term pregnancy of 40 weeks. These children have less time to develop in the womb, and 1.1 million will die from birth-related complications. Many others are left with hearing impairment, learning disabilities, cerebral palsy and other health issues.
The new study is part of the UCSF Preterm Birth Initiative, an ambitious US$100-million effort to study prematurity, focusing on California and East Africa. The researchers working on the effort plan to mine large quantities of historical data, ensuring that any findings are statistically significant. They hope to use these findings to identify medical and social interventions that could reduce preterm births, and test them in trials of pregnant women.The programme is funded by the Bill and Melinda Gates Foundation and philanthropists Lynne and Marc Benioff.
Forty winks for forty weeks
Jennifer Felder, a postdoctoral researcher in clinical psychology at UCSF who led the study, says that she had been troubled by the lack of research on sleep and pregnancy. Because pregnant women often have some difficulty sleeping, she suspects that doctors and researchers had not thought to examine the consequences of sleep disorders more closely.
Felder and her colleagues acquired the records of almost three million births that took place in California between 2007 and 2012, which were scrubbed of identifying information but linked to hospital-discharge papers from the women who had given birth. Each record contained a medical history of the mother and notes taken throughout her pregnancy and baby's delivery. Doctors had diagnosed about 2,300 of the women with a sleep disorder during their pregnancy. Insomnia and sleep apnoea were the main problems, although narcolepsy, excessive sleepiness and restless leg syndrome were also seen.
Insomnia, the researchers found, increased a woman's risk of preterm birth by 30%, while sleep apnoea increased the risk by 40%. Sleep disorders also increased the risk of very premature births: 5.3% of women with sleep issues delivered their babies at less than 34 weeks' pregnancy, compared to 2.9% for women without such a diagnosis.
Felder says that a lack of sleep is unlikely to be a direct cause of early births. But it could trigger other processes, such as inflammation, that eventually result in prematurity. A 2010 review of studies linked premature birth to the presence of the inflammatory proteins C-reactive protein and interleukin-6, in amniotic fluid2. To explore the idea, the UCSF initiative will soon begin to examine immune-system proteins in pregnant women using blood stored in a repository associated with Californiaβs department of public health. The scientists will compare samples with an attention to premature birth and insomnia.
And in the meantime, sleep troubles in expectant mothers can alert doctors to potential danger. βI counsel women on how to have the best pregnancy outcome,β says Louis Muglia, the director of the Center for Prevention of Preterm Birth at Cincinnati Childrenβs Hospital Medical Center in Ohio. βNow I might start asking, 'do you get a good nightβs sleep?'.β | β A new study suggests that one way to cut down on premature births is to make sure pregnant women get good sleep. The observational study, published in the journal Obstetrics & Gynecology, found that women diagnosed with some kind of sleep disorder were more likely to give birth early, reports the New York Times. Overall, 15% of such women had preemies, compared to 11% among women without a sleep disorder. More specifically, a diagnosis of insomnia raised the risk of having a pre-term birth by 30% and sleep apnea by 40%. Similarly, sleep disorders were associated with more births characterized as "very premature," reports Nature. The study found that 5.3% of women with such disorders delivered 34 weeks or earlier, compared with 2.9% for those without a disorder. βIt seems obvious, but strangely this study has not been done before,β says co-author Laura Jelliffe-Pawlowski, an epidemiologist at the University of California, San Francisco. "Seeing this relationship is important because we are just starved for interventions that can make a difference.β The authors make clear they're referring to women with diagnosed problems, not merely to women who occasionally have trouble sleeping while pregnant, which is fairly common. They found that sleep disorders are more common among women who are black, 35 or older, obese, and have other medical issues, reports Reuters. Based on the study, one piece of advice for women planning to have kids is to try to start the pregnancy at a healthy weight. (Some evidence supports therapy over pills to treat insomnia.) | <s>[INST]Women with insomnia or other sleep problems have an increased risk of giving birth prematurely, a new study suggests.
The observational study, in Obstetrics & Gynecology, included 2,172 women with a sleep disorder who gave birth between 2007 and 2012 to single children after 22 to 44 weeks of gestation. They were matched with the same number of women with the identical ethnic, health and behavioral characteristics, but who did not have a sleep disorder.
Over all, women with sleep disorders had a 14.6 percent prevalence of preterm birth (before 37 weeks of gestation), compared with 10.9 percent in those without a diagnosis. Those with insomnia had a 30 percent increased risk, and those with sleep apnea a 40 percent increased risk, compared with women without a sleep problem.
Women with insomnia were nearly twice as likely to deliver before 34 weeks gestation.
βMore severe sleep disorders are often underdiagnosed, because poor sleep is common during pregnancy,β said the lead author, Jennifer N. Felder, a postdoctoral researcher in psychology at the University of California, San Francisco. βBut for women having sleep problems that are severe, impairing and distressing, itβs important to talk to their health care providers.β ||||| (Reuters Health) - Women who experience sleep disorders like insomnia and apnea during pregnancy may be more likely to deliver premature babies than pregnant women who donβt have trouble sleeping, a U.S. study suggests.
Compared with women who didnβt have sleep problems, women with insomnia were 30 percent more likely to have a preemie and the odds for women with sleep apnea, a breathing disorder, were 50 percent higher, the study found.
βIt is normal to experience sleep changes during pregnancy - often due to discomfort, pain or frequent trips to the bathroom,β said lead study author Jennifer Felder, of the University of California, San Francisco.
βThe current study focused on more impairing sleep problems that were severe enough to result in a sleep disorder diagnosis,β Felder said by email.
Apnea, a potentially serious sleep disorder that involves repeated stops and starts in breathing, has been linked to high blood pressure during pregnancy, which is an independent risk factor for preterm births. Obesity and advanced age can make apnea more likely.
Even though many pregnant women have insomnia at some point, previous studies havenβt offered a clear picture of how this type of sleep deprivation influences the odds of preterm births.
Worldwide, preterm birth is the leading cause of death for children under 5 years old, the researchers note in the journal Obstetrics and Gynecology.
Pregnancy normally lasts about 40 weeks, and babies born after 37 weeks are considered full term. The new study focused on preterm infants, delivered at 34 to 36 weeksβ gestation, and extremely premature babies delivered before 34 weeks.
In the weeks immediately after birth, preemies often have difficulty breathing and digesting food. They can also encounter longer-term challenges such as impaired vision, hearing, and cognitive skills as well as social and behavioral problems.
The study team examined data on more than 3 million births in California from 2007 to 2012. They focused on 2,172 women who had a sleep disorder diagnosis and compared their birth outcomes to a randomly selected group of 2,172 mothers who were similar in many ways but had no sleep issues.
Women with sleep disorders were more likely to be black, age 35 or older, obese, and to have other medical issues like high blood pressure, diabetes and infections as well as higher odds of smoking or using drugs and alcohol while pregnant. They were also more likely to have a history of preterm birth.
Overall, almost 15 percent of women with sleep disorders had a preterm birth, compared with 11 percent of women without sleep issues.
The study wasnβt a controlled experiment designed to prove how or even whether sleep disorders directly cause preterm births.
Even so, the results offer fresh evidence of the link between sleep disorders and early arrivals, said Dr. Ghada Bourjeily, a researcher at Warren Alpert Medical School of Brown University in Providence, Rhode Island, who wasnβt involved in the study.
βSleep appears to get worse in pregnancy in many, even women who do not have a preexisting sleep disorder,β Bourjeily said by email. βUnfortunately, we do not know yet whether improving sleep quality before or during pregnancy would prevent development of negative outcomes such as preterm birth.β
Starting pregnancy at a healthy weight, however, may make sleep disorders less likely, said Dr. Amos Grunebaum, director of obstetrics at NewYork-Presbyterian Hospital/Weill Cornell Medical Center in New York.
βBeing overweight or obese increases your risk of having a sleep disorder,β Grunebaum, who wasnβt involved in the study, said by email. βIt also increases pregnancy complications.β
When sleep disorders do surface during pregnancy, women should discuss symptoms in detail with their doctors, said Dr. Milena Pavlova, a researcher at Brigham and Womenβs Hospital in Boston who wasnβt involved in the study. This includes any issues with breathing, gasping or choking at night or any uncomfortable leg or body sensations that prevent sleep.
Expectant mothers should also make sleep a priority in their schedules, Pavlova, who wasnβt involved in the study, said by email.
βAllow enough time for sleep - the life you save may be your babyβs,β Pavlova said.
SOURCE: bit.ly/2j2fR06 Obstetrics and Gynecology, online August 8, 2017. ||||| Andrew Lichtenstein/Corbis/Getty
Despite strides in maternal medicine, premature birth remains a vexing problem for obstetricians worldwide. But an analysis of medical records from almost 3 million pregnant women in California1 suggests that a surprisingly simple intervention β better sleep β might help to address the issue.
Researchers found that women who had been diagnosed with insomnia or sleep apnoea were about twice as likely as women without sleep disorders to deliver their babies more than six weeks early.
βIt seems obvious, but strangely this study has not been done before,β says Laura Jelliffe-Pawlowski, an epidemiologist at the University of California, San Francisco (UCSF), and an author of the research, which was published on 8 August in the journal Obstetrics and Gynecology1. βSeeing this relationship is important because we are just starved for interventions that can make a difference.β
Public-health experts say that better treatment for pregnant women with serious sleep disorders could save babies' lives, and do so with approaches that avoid the use of medication. Every year, 15 million babies worldwide are born prematurely β more than three weeks before the typical full-term pregnancy of 40 weeks. These children have less time to develop in the womb, and 1.1 million will die from birth-related complications. Many others are left with hearing impairment, learning disabilities, cerebral palsy and other health issues.
The new study is part of the UCSF Preterm Birth Initiative, an ambitious US$100-million effort to study prematurity, focusing on California and East Africa. The researchers working on the effort plan to mine large quantities of historical data, ensuring that any findings are statistically significant. They hope to use these findings to identify medical and social interventions that could reduce preterm births, and test them in trials of pregnant women.The programme is funded by the Bill and Melinda Gates Foundation and philanthropists Lynne and Marc Benioff.
Forty winks for forty weeks
Jennifer Felder, a postdoctoral researcher in clinical psychology at UCSF who led the study, says that she had been troubled by the lack of research on sleep and pregnancy. Because pregnant women often have some difficulty sleeping, she suspects that doctors and researchers had not thought to examine the consequences of sleep disorders more closely.
Felder and her colleagues acquired the records of almost three million births that took place in California between 2007 and 2012, which were scrubbed of identifying information but linked to hospital-discharge papers from the women who had given birth. Each record contained a medical history of the mother and notes taken throughout her pregnancy and baby's delivery. Doctors had diagnosed about 2,300 of the women with a sleep disorder during their pregnancy. Insomnia and sleep apnoea were the main problems, although narcolepsy, excessive sleepiness and restless leg syndrome were also seen.
Insomnia, the researchers found, increased a woman's risk of preterm birth by 30%, while sleep apnoea increased the risk by 40%. Sleep disorders also increased the risk of very premature births: 5.3% of women with sleep issues delivered their babies at less than 34 weeks' pregnancy, compared to 2.9% for women without such a diagnosis.
Felder says that a lack of sleep is unlikely to be a direct cause of early births. But it could trigger other processes, such as inflammation, that eventually result in prematurity. A 2010 review of studies linked premature birth to the presence of the inflammatory proteins C-reactive protein and interleukin-6, in amniotic fluid2. To explore the idea, the UCSF initiative will soon begin to examine immune-system proteins in pregnant women using blood stored in a repository associated with Californiaβs department of public health. The scientists will compare samples with an attention to premature birth and insomnia.
And in the meantime, sleep troubles in expectant mothers can alert doctors to potential danger. βI counsel women on how to have the best pregnancy outcome,β says Louis Muglia, the director of the Center for Prevention of Preterm Birth at Cincinnati Childrenβs Hospital Medical Center in Ohio. βNow I might start asking, 'do you get a good nightβs sleep?'.β[/INST]β A new study suggests that one way to cut down on premature births is to make sure pregnant women get good sleep. The observational study, published in the journal Obstetrics & Gynecology, found that women diagnosed with some kind of sleep disorder were more likely to give birth early, reports the New York Times. Overall, 15% of such women had preemies, compared to 11% among women without a sleep disorder. More specifically, a diagnosis of insomnia raised the risk of having a pre-term birth by 30% and sleep apnea by 40%. Similarly, sleep disorders were associated with more births characterized as "very premature," reports Nature. The study found that 5.3% of women with such disorders delivered 34 weeks or earlier, compared with 2.9% for those without a disorder. βIt seems obvious, but strangely this study has not been done before,β says co-author Laura Jelliffe-Pawlowski, an epidemiologist at the University of California, San Francisco. "Seeing this relationship is important because we are just starved for interventions that can make a difference.β The authors make clear they're referring to women with diagnosed problems, not merely to women who occasionally have trouble sleeping while pregnant, which is fairly common. They found that sleep disorders are more common among women who are black, 35 or older, obese, and have other medical issues, reports Reuters. Based on the study, one piece of advice for women planning to have kids is to try to start the pregnancy at a healthy weight. (Some evidence supports therapy over pills to treat insomnia.)</s> |
we would like to express our gratitude to t. yanagida for making a chance to start this collaboration .
we thank k. kanaya for his help in preparing the manuscript .
the calculations were performed with ha - pacs computer at ccs , university of tsukuba and sr16000 at kek .
we would like to thank members of ccs and kek for their strong support for this work .
m. hayakawa , et al .
, pos lattice * 2010 * ( 2010 ) 325 .
m. a. clark and a. d. kennedy , phys .
* 98 * ( 2007 ) 051601 .
miransky , phys .
* d59 * ( 1999 ) 105003 ; l. del debbio and r. zwicky , phys . rev . *
d82 * 014502 .
ishikawa , y. iwasaki , yu nakayama and t. yoshie , to appear . | we give a new perspective on the dynamics of conformal theories realized in the su(@xmath0 ) gauge theory , when the number of flavors @xmath1 is within the conformal window .
motivated by the rg argument on conformal theories with a finite ir cutoff @xmath2 , we conjecture that the propagator of a meson @xmath3 on a lattice behaves at large @xmath4 as a power - law corrected yukawa - type decaying form @xmath5 instead of the exponentially decaying form @xmath6 , in the small quark mass region where @xmath7 : @xmath8 is the mass of the ground state hadron in the channel @xmath9 and @xmath10 is a constant of order 1 .
the transition between the `` conformal region '' and the confining region " is a first order transition .
our numerical results verify the predictions for the @xmath11 case and the @xmath12 case in the su(@xmath13 ) gauge theory with the fundamental representation .
conformal field theories are ubiquitous in nature and play important roles not only in particle physics beyond the standard model but also in condensed matter physics .
nonperturbative understanding of their dynamics in four - dimensional space - time is ardently desired . in this article
, we give a new perspective on the dynamics of conformal theories realized in the su(@xmath0 ) gauge theory when the number of flavors @xmath1 is within the conformal window @xcite by studying meson propagators with a finite infrared ( ir ) cutoff .
some preliminary results have been presented in @xcite .
our general argument that follows can be applied to any gauge theories with arbitrary representations as long as they are in the conformal window , but to be specific , we focus on su(3 ) gauge theories with @xmath1 fundamental fermions ( quarks " ) .
we define the conformal field theory in a constructive way @xcite : we employ the wilson quark action and the standard one - plaquette gauge action on the euclidean lattice of the size @xmath14 and @xmath15 with aspect ratio @xmath16 .
we impose periodic boundary conditions except for an anti - periodic boundary condition in the time direction for fermion fields .
we eventually take the continuum limit by sending the lattice space @xmath17 with @xmath18 keeping @xmath19 fixed .
when @xmath20 finite , the continuum limit defines a theory with an ir cutoff .
the theory is defined by two parameters ; the bare coupling constant @xmath21 and the bare degenerate quark mass @xmath22 at ultraviolet ( uv ) cutoff .
we also use , instead of @xmath21 and @xmath22 , @xmath23 and @xmath24 . for a later purpose
, we define the quark mass @xmath25 through ward - takahashi identities with renormalization constants being suppressed @xcite .
let us quickly remind ourselves of the renormalization group ( rg ) flow when @xmath1 is in the conformal window .
one important fact is finite size lattices in computer simulation always introduce an ir cutoff @xmath26 .
if the ir cutoff were zero , when quarks have tiny masses , the rg trajectory would stay close to the critical line , approaching the ir fixed point and finally would pass away from the ir fixed point to infinity .
therefore the ir behavior is governed by the `` confining region '' . only on the massless quark line the scale invariance
is realized at the ir fixed point .
see the left panel of fig . 1 .
when the cutoff @xmath2 is finite , the rg flow from uv to ir does stop evolving at the scale @xmath2 . when the typical mass scale ( e.g. that of a meson ) @xmath8 is smaller than @xmath27 , it is in the `` conformal region '' . on the other hand ,
when @xmath8 is larger than @xmath2 , the flow passes away from the ir fixed point to infinity with relevant variables integrated out , thus being in the `` confining region '' . see the right panel of fig . 1 .
this scenario implies that when physical quantities at ir ( e.g. hadron masses ) are mapped into a diagram in terms of physical parameters at uv ( e.g. the bare coupling constant and the bare quark mass ) , there will be gaps in the physical quantities along the boundary between the two phases .
there the phase transition will be a first order transition . to make the above rg argument more concrete
, we will study the propagator of the local meson operator @xmath28 when the theory is in the confining region " , it decays exponentially at large @xmath4 as @xmath29 due to the physical one - particle pole , where @xmath8 is the mass of the ground state hadron in the channel @xmath9 .
in contrast , we claim that in the conformal region " defined by @xmath30 where @xmath10 is a constant of order 1 which we will determine , the propagator @xmath31 behaves at large @xmath4 as @xmath32 which is a power - law corrected yukawa - type decaying form instead of the exponential decaying form ( eq.([exp ] ) ) observed in the confining region " .
we further claim that the boundary between the `` conformal region '' and the `` confining region '' is a first order transition .
we note that the behavior eq.([yukawa type ] ) is proposed based on the ads / cft correspondence with a softwall cutoff in the literature @xcite .
the meson propagator in the momentum space has a cut instead of a pole : @xmath33 .
the propagator in the position space ( after space integration ) takes the form eq.([yukawa type ] ) in the limit @xmath34 .
we distinguish @xmath35 in eq.([yukawa type ] ) from the pole mass @xmath8 in eq.([exp ] ) .
eq.([critical mass ] ) thus means the lower limit of @xmath8 is @xmath36 in the continuum limit with @xmath37 ( i.e. @xmath38 ) , the propagator on the massless quark line takes the form @xmath39 consistent with @xmath40 limit of eq .
( [ yukawa type ] ) .
if we take the coupling constant @xmath41 at the uv cutoff , @xmath42 takes a constant value , and the rg equation demands @xmath43 for the pseudo - scalar ( ps ) channel with @xmath44 being the anomalous mass dimension @xmath45 at @xmath46 .
the theory is scale invariant ( and shown to be conformal invariant within perturbation theory @xcite .
see also e.g. @xcite and references therein from ads / cft approach ) . when @xmath47 , @xmath42 depends slowly on @xmath4 as a solution of the rg equation . in the ir limit @xmath48
, we must retain @xmath49 .
the continuum limit with @xmath20 finite defines a continuum theory on @xmath50 which corresponds to a compact three - torus at finite temperature .
the ir cutoff @xmath51 is finite .
the propagator @xmath3 behaves at large @xmath4 as a power - law corrected yukawa type decaying form eq.([yukawa type ] ) .
the exponent @xmath42 in @xmath48 with @xmath52 takes the universal formula @xmath53 while with @xmath54 it takes a value depending on the dynamics , from which we can estimate the mass anomalous dimensions ( see @xcite ) .
[ exp_vs_yukawa ] [ expnf7nf16 ] now let us discuss the results of our numerical calculations .
we have performed simulations in the @xmath11 and @xmath12 cases , which we conjecture @xcite , are the boundaries of the conformal window .
the algorithms we employ are the blocked hmc algorithm @xcite for @xmath55 and the rhmc algorithm @xcite for @xmath56 in the case @xmath57 .
we specify the coupling constant @xmath58 for @xmath59 and @xmath60 for @xmath61 taking account of the fact that the ir fixed point for @xmath12 is @xmath62 in two - loop approximation .
we use the lattices of size @xmath63 and @xmath64 and vary the hopping parameter @xmath65 so that the quark mass takes the value from 0.40 to 0.0 : we simulate with 15 hopping parameters on the @xmath63 lattices , and 5 hopping parameters on the @xmath66 lattices .
we choose the run - parameters in such a way that the acceptance of the global metropolis test is about @xmath67 the statistics are 1,000 md trajectories for thermalization and 1,000 md trajectories or 500 md trajectories for the measurement .
we estimate the errors by the jack - knife method with a bin size corresponding to 100 hmc trajectories .
let us first discuss the results for the @xmath11 case on the @xmath63 lattices .
we define the effective mass @xmath68 by @xmath69 .
fig . 2 [ exp_vs_yukawa ] shows the @xmath4 dependence of the effective mass for the ps channel with three types of sources . on the left panel ,
we see the clear plateau of the effective mass at @xmath70 when quark mass is relatively large ; @xmath71 ( @xmath72 ) . on the other hand , on the right panel , we see the effective mass is slowly decreasing without no plateau up to @xmath73 when the quark mass is small ; @xmath74 ( @xmath75 ) , suggesting the power - law correction .
the effective masses for all cases with @xmath76 ( @xmath77 ) exhibit a similar behavior to the @xmath75 case .
we show the power - law corrected fit for the local - local data in the @xmath75 case with the fitting range @xmath78 $ ] on the left panel in fig .
3 .
the fit with @xmath79 reproduces the date very well .
in the case of @xmath12 , the effective masses on the @xmath63 lattices exhibit the power - law corrected yukawa - type decaying form for all cases when @xmath80 ( @xmath81 ) .
we show the power - law corrected fit for the local - local data in the @xmath82 case with the fitting range @xmath78 $ ] on the right panel in fig .
3 .
the fit with @xmath83 reproduces the data well .
we also report that the data on @xmath84 lattices for both cases of @xmath11 with @xmath85 and @xmath12 with @xmath81 clearly exhibit the power - law corrected yukawa type decaying form .
we obtain @xmath86 for @xmath75 in @xmath59 and @xmath87 for @xmath88 in @xmath89 , respectively .
thus we have confirmed that the propagators behaves as the power - law corrected yukawa type decaying form , when the quark mass is small enough .
we note in all cases the rho meson mass is degenerate with the pion mass within the one standard deviation .
this implies the phase is a chiral symmetric phase . in the remaining part of the article
, we try to identify the boundary between the `` conformal region '' and the `` confining region '' more precisely by investigating the transition region carefully with a small step of the value of @xmath65 for both of the @xmath11 and @xmath12 cases .
we present the results for @xmath25 and @xmath90 ( or @xmath91 ) in the @xmath11 case in fig . 4 .
we first note that the quark mass @xmath25 denoted by black points and line on the left panel is excellently proportional to @xmath92 in the whole region from @xmath93 to @xmath94 . for the propagators of the ps meson
, we observe the clear transition from the exponentially decaying form to the power - law corrected yukawa - type decaying form at @xmath95 . for @xmath96 , we present @xmath90 obtained from the fit to the exponentially decaying form with the fitting region [ 28:31 ] by green points and line .
for @xmath77 , we present @xmath91 obtained from the fit to the power - law corrected yukawa type decaying form with fitting range [ 15:31 ] by blue points and line .
the transition region is enlarged on the right panel in fig .
4 .
the values of @xmath90 and @xmath91 are different in the limit @xmath97 from smaller @xmath65 and from larger @xmath65 .
it should be noted that even if we had ignored the power - law corrections in yukawa type decay and had estimated the @xmath90 ( plotted in fig . 4 by black points ) by assuming exponential decay with the fitting range [ 28:31 ] , although no plateau is seen as shown on the right panel of fig 2 and in fig .
3 , there would have been a gap at the transition point .
it is worthwhile to stress that at @xmath98 and @xmath99 we observe two states , depending on the initial sate .
the existence of two states persists at least with 500 md trajectories .
we also note that the exponent @xmath42 does not vanish toward the transition point ; it rather increases up to @xmath100 thus the transition is a first order transition at @xmath101 these facts imply that there indeed exists a `` conformal region '' which is separated by a gap of physical quantities from the confining region " at finite quark mass .
the @xmath25 dependence of @xmath91 is rather complicated .
once @xmath91 becomes small at the transition point , it slightly increases as @xmath25 decreases , and then decreases at @xmath102 apparently the small @xmath91 region suffers from finite size effects . to verify the scaling relation @xcite for @xmath91 in terms of @xmath25 we have to control finite size effects . taking @xmath103 with @xmath104 ( @xmath105 ) , as the critical mass in eq.(3 )
, we estimate @xmath106 with our working definition of @xmath107 . in the @xmath12 case
we have observed similar results .
the @xmath25 dependence of @xmath91 is similarly complicated .
the transition occurs at @xmath108 with @xmath109 ( @xmath110 ) from which we estimate @xmath111 in the cases of @xmath84 lattices for both @xmath11 and @xmath12 cases , we have also observed the transition : in @xmath11 , we find exponential decay for @xmath112 ( @xmath113 ) and power - law corrected yukawa type decay for @xmath114 ( @xmath85 ) . in @xmath12 , we find power - law corrected yukawa type decay for @xmath80 ( @xmath81 ) .
the critical mass decreases compared with the @xmath63 lattices as expected since the ir cutoff decreases .
we conclude the paper with two main goals achieved in our study . we have given evidence that ( 1 ) : the meson propagator shows a transition from an exponentially decaying form to a power - law corrected yukawa - type decaying form at the critical hadron mass whose value is specified by the ir cutoff .
( 2 ) : the transition is first order . the existence of the conformal region we proposed gives a necessary ( but not sufficient ) condition for the conformal window , and the result for @xmath11 is consistent with our conjecture that @xmath11 is within the conformal window .
however we understand that we need more evidence to conclude that . in an accompanying publication @xcite
, we will discuss the physical interpretation of the power - law corrections in terms of the dynamics of the underlying conformal field theory by taking the continuum limit .
we also hope to report the physical applications of our findings in the near future . | <s>[INST]we would like to express our gratitude to t. yanagida for making a chance to start this collaboration .
we thank k. kanaya for his help in preparing the manuscript .
the calculations were performed with ha - pacs computer at ccs , university of tsukuba and sr16000 at kek .
we would like to thank members of ccs and kek for their strong support for this work .
m. hayakawa , et al .
, pos lattice * 2010 * ( 2010 ) 325 .
m. a. clark and a. d. kennedy , phys .
* 98 * ( 2007 ) 051601 .
miransky , phys .
* d59 * ( 1999 ) 105003 ; l. del debbio and r. zwicky , phys . rev . *
d82 * 014502 .
ishikawa , y. iwasaki , yu nakayama and t. yoshie , to appear .[/INST] we give a new perspective on the dynamics of conformal theories realized in the su(@xmath0 ) gauge theory , when the number of flavors @xmath1 is within the conformal window .
motivated by the rg argument on conformal theories with a finite ir cutoff @xmath2 , we conjecture that the propagator of a meson @xmath3 on a lattice behaves at large @xmath4 as a power - law corrected yukawa - type decaying form @xmath5 instead of the exponentially decaying form @xmath6 , in the small quark mass region where @xmath7 : @xmath8 is the mass of the ground state hadron in the channel @xmath9 and @xmath10 is a constant of order 1 .
the transition between the `` conformal region '' and the confining region " is a first order transition .
our numerical results verify the predictions for the @xmath11 case and the @xmath12 case in the su(@xmath13 ) gauge theory with the fundamental representation .
conformal field theories are ubiquitous in nature and play important roles not only in particle physics beyond the standard model but also in condensed matter physics .
nonperturbative understanding of their dynamics in four - dimensional space - time is ardently desired . in this article
, we give a new perspective on the dynamics of conformal theories realized in the su(@xmath0 ) gauge theory when the number of flavors @xmath1 is within the conformal window @xcite by studying meson propagators with a finite infrared ( ir ) cutoff .
some preliminary results have been presented in @xcite .
our general argument that follows can be applied to any gauge theories with arbitrary representations as long as they are in the conformal window , but to be specific , we focus on su(3 ) gauge theories with @xmath1 fundamental fermions ( quarks " ) .
we define the conformal field theory in a constructive way @xcite : we employ the wilson quark action and the standard one - plaquette gauge action on the euclidean lattice of the size @xmath14 and @xmath15 with aspect ratio @xmath16 .
we impose periodic boundary conditions except for an anti - periodic boundary condition in the time direction for fermion fields .
we eventually take the continuum limit by sending the lattice space @xmath17 with @xmath18 keeping @xmath19 fixed .
when @xmath20 finite , the continuum limit defines a theory with an ir cutoff .
the theory is defined by two parameters ; the bare coupling constant @xmath21 and the bare degenerate quark mass @xmath22 at ultraviolet ( uv ) cutoff .
we also use , instead of @xmath21 and @xmath22 , @xmath23 and @xmath24 . for a later purpose
, we define the quark mass @xmath25 through ward - takahashi identities with renormalization constants being suppressed @xcite .
let us quickly remind ourselves of the renormalization group ( rg ) flow when @xmath1 is in the conformal window .
one important fact is finite size lattices in computer simulation always introduce an ir cutoff @xmath26 .
if the ir cutoff were zero , when quarks have tiny masses , the rg trajectory would stay close to the critical line , approaching the ir fixed point and finally would pass away from the ir fixed point to infinity .
therefore the ir behavior is governed by the `` confining region '' . only on the massless quark line the scale invariance
is realized at the ir fixed point .
see the left panel of fig . 1 .
when the cutoff @xmath2 is finite , the rg flow from uv to ir does stop evolving at the scale @xmath2 . when the typical mass scale ( e.g. that of a meson ) @xmath8 is smaller than @xmath27 , it is in the `` conformal region '' . on the other hand ,
when @xmath8 is larger than @xmath2 , the flow passes away from the ir fixed point to infinity with relevant variables integrated out , thus being in the `` confining region '' . see the right panel of fig . 1 .
this scenario implies that when physical quantities at ir ( e.g. hadron masses ) are mapped into a diagram in terms of physical parameters at uv ( e.g. the bare coupling constant and the bare quark mass ) , there will be gaps in the physical quantities along the boundary between the two phases .
there the phase transition will be a first order transition . to make the above rg argument more concrete
, we will study the propagator of the local meson operator @xmath28 when the theory is in the confining region " , it decays exponentially at large @xmath4 as @xmath29 due to the physical one - particle pole , where @xmath8 is the mass of the ground state hadron in the channel @xmath9 .
in contrast , we claim that in the conformal region " defined by @xmath30 where @xmath10 is a constant of order 1 which we will determine , the propagator @xmath31 behaves at large @xmath4 as @xmath32 which is a power - law corrected yukawa - type decaying form instead of the exponential decaying form ( eq.([exp ] ) ) observed in the confining region " .
we further claim that the boundary between the `` conformal region '' and the `` confining region '' is a first order transition .
we note that the behavior eq.([yukawa type ] ) is proposed based on the ads / cft correspondence with a softwall cutoff in the literature @xcite .
the meson propagator in the momentum space has a cut instead of a pole : @xmath33 .
the propagator in the position space ( after space integration ) takes the form eq.([yukawa type ] ) in the limit @xmath34 .
we distinguish @xmath35 in eq.([yukawa type ] ) from the pole mass @xmath8 in eq.([exp ] ) .
eq.([critical mass ] ) thus means the lower limit of @xmath8 is @xmath36 in the continuum limit with @xmath37 ( i.e. @xmath38 ) , the propagator on the massless quark line takes the form @xmath39 consistent with @xmath40 limit of eq .
( [ yukawa type ] ) .
if we take the coupling constant @xmath41 at the uv cutoff , @xmath42 takes a constant value , and the rg equation demands @xmath43 for the pseudo - scalar ( ps ) channel with @xmath44 being the anomalous mass dimension @xmath45 at @xmath46 .
the theory is scale invariant ( and shown to be conformal invariant within perturbation theory @xcite .
see also e.g. @xcite and references therein from ads / cft approach ) . when @xmath47 , @xmath42 depends slowly on @xmath4 as a solution of the rg equation . in the ir limit @xmath48
, we must retain @xmath49 .
the continuum limit with @xmath20 finite defines a continuum theory on @xmath50 which corresponds to a compact three - torus at finite temperature .
the ir cutoff @xmath51 is finite .
the propagator @xmath3 behaves at large @xmath4 as a power - law corrected yukawa type decaying form eq.([yukawa type ] ) .
the exponent @xmath42 in @xmath48 with @xmath52 takes the universal formula @xmath53 while with @xmath54 it takes a value depending on the dynamics , from which we can estimate the mass anomalous dimensions ( see @xcite ) .
[ exp_vs_yukawa ] [ expnf7nf16 ] now let us discuss the results of our numerical calculations .
we have performed simulations in the @xmath11 and @xmath12 cases , which we conjecture @xcite , are the boundaries of the conformal window .
the algorithms we employ are the blocked hmc algorithm @xcite for @xmath55 and the rhmc algorithm @xcite for @xmath56 in the case @xmath57 .
we specify the coupling constant @xmath58 for @xmath59 and @xmath60 for @xmath61 taking account of the fact that the ir fixed point for @xmath12 is @xmath62 in two - loop approximation .
we use the lattices of size @xmath63 and @xmath64 and vary the hopping parameter @xmath65 so that the quark mass takes the value from 0.40 to 0.0 : we simulate with 15 hopping parameters on the @xmath63 lattices , and 5 hopping parameters on the @xmath66 lattices .
we choose the run - parameters in such a way that the acceptance of the global metropolis test is about @xmath67 the statistics are 1,000 md trajectories for thermalization and 1,000 md trajectories or 500 md trajectories for the measurement .
we estimate the errors by the jack - knife method with a bin size corresponding to 100 hmc trajectories .
let us first discuss the results for the @xmath11 case on the @xmath63 lattices .
we define the effective mass @xmath68 by @xmath69 .
fig . 2 [ exp_vs_yukawa ] shows the @xmath4 dependence of the effective mass for the ps channel with three types of sources . on the left panel ,
we see the clear plateau of the effective mass at @xmath70 when quark mass is relatively large ; @xmath71 ( @xmath72 ) . on the other hand , on the right panel , we see the effective mass is slowly decreasing without no plateau up to @xmath73 when the quark mass is small ; @xmath74 ( @xmath75 ) , suggesting the power - law correction .
the effective masses for all cases with @xmath76 ( @xmath77 ) exhibit a similar behavior to the @xmath75 case .
we show the power - law corrected fit for the local - local data in the @xmath75 case with the fitting range @xmath78 $ ] on the left panel in fig .
3 .
the fit with @xmath79 reproduces the date very well .
in the case of @xmath12 , the effective masses on the @xmath63 lattices exhibit the power - law corrected yukawa - type decaying form for all cases when @xmath80 ( @xmath81 ) .
we show the power - law corrected fit for the local - local data in the @xmath82 case with the fitting range @xmath78 $ ] on the right panel in fig .
3 .
the fit with @xmath83 reproduces the data well .
we also report that the data on @xmath84 lattices for both cases of @xmath11 with @xmath85 and @xmath12 with @xmath81 clearly exhibit the power - law corrected yukawa type decaying form .
we obtain @xmath86 for @xmath75 in @xmath59 and @xmath87 for @xmath88 in @xmath89 , respectively .
thus we have confirmed that the propagators behaves as the power - law corrected yukawa type decaying form , when the quark mass is small enough .
we note in all cases the rho meson mass is degenerate with the pion mass within the one standard deviation .
this implies the phase is a chiral symmetric phase . in the remaining part of the article
, we try to identify the boundary between the `` conformal region '' and the `` confining region '' more precisely by investigating the transition region carefully with a small step of the value of @xmath65 for both of the @xmath11 and @xmath12 cases .
we present the results for @xmath25 and @xmath90 ( or @xmath91 ) in the @xmath11 case in fig . 4 .
we first note that the quark mass @xmath25 denoted by black points and line on the left panel is excellently proportional to @xmath92 in the whole region from @xmath93 to @xmath94 . for the propagators of the ps meson
, we observe the clear transition from the exponentially decaying form to the power - law corrected yukawa - type decaying form at @xmath95 . for @xmath96 , we present @xmath90 obtained from the fit to the exponentially decaying form with the fitting region [ 28:31 ] by green points and line .
for @xmath77 , we present @xmath91 obtained from the fit to the power - law corrected yukawa type decaying form with fitting range [ 15:31 ] by blue points and line .
the transition region is enlarged on the right panel in fig .
4 .
the values of @xmath90 and @xmath91 are different in the limit @xmath97 from smaller @xmath65 and from larger @xmath65 .
it should be noted that even if we had ignored the power - law corrections in yukawa type decay and had estimated the @xmath90 ( plotted in fig . 4 by black points ) by assuming exponential decay with the fitting range [ 28:31 ] , although no plateau is seen as shown on the right panel of fig 2 and in fig .
3 , there would have been a gap at the transition point .
it is worthwhile to stress that at @xmath98 and @xmath99 we observe two states , depending on the initial sate .
the existence of two states persists at least with 500 md trajectories .
we also note that the exponent @xmath42 does not vanish toward the transition point ; it rather increases up to @xmath100 thus the transition is a first order transition at @xmath101 these facts imply that there indeed exists a `` conformal region '' which is separated by a gap of physical quantities from the confining region " at finite quark mass .
the @xmath25 dependence of @xmath91 is rather complicated .
once @xmath91 becomes small at the transition point , it slightly increases as @xmath25 decreases , and then decreases at @xmath102 apparently the small @xmath91 region suffers from finite size effects . to verify the scaling relation @xcite for @xmath91 in terms of @xmath25 we have to control finite size effects . taking @xmath103 with @xmath104 ( @xmath105 ) , as the critical mass in eq.(3 )
, we estimate @xmath106 with our working definition of @xmath107 . in the @xmath12 case
we have observed similar results .
the @xmath25 dependence of @xmath91 is similarly complicated .
the transition occurs at @xmath108 with @xmath109 ( @xmath110 ) from which we estimate @xmath111 in the cases of @xmath84 lattices for both @xmath11 and @xmath12 cases , we have also observed the transition : in @xmath11 , we find exponential decay for @xmath112 ( @xmath113 ) and power - law corrected yukawa type decay for @xmath114 ( @xmath85 ) . in @xmath12 , we find power - law corrected yukawa type decay for @xmath80 ( @xmath81 ) .
the critical mass decreases compared with the @xmath63 lattices as expected since the ir cutoff decreases .
we conclude the paper with two main goals achieved in our study . we have given evidence that ( 1 ) : the meson propagator shows a transition from an exponentially decaying form to a power - law corrected yukawa - type decaying form at the critical hadron mass whose value is specified by the ir cutoff .
( 2 ) : the transition is first order . the existence of the conformal region we proposed gives a necessary ( but not sufficient ) condition for the conformal window , and the result for @xmath11 is consistent with our conjecture that @xmath11 is within the conformal window .
however we understand that we need more evidence to conclude that . in an accompanying publication @xcite
, we will discuss the physical interpretation of the power - law corrections in terms of the dynamics of the underlying conformal field theory by taking the continuum limit .
we also hope to report the physical applications of our findings in the near future . </s> |
free energy is a central concept in thermodynamics and in modern works on biochemical and physical systems .
typical examples studied by computer simulations include the solvation free energies ( which is the free energy difference between a molecule _ in vacuo _ and its counterpart surrounded by solvent molecules ) and the binding free energy of two molecules ( which determines whether a new drug can have an efficient action on a given protein ) . in many applications , it is actually the free energy difference profile between the initial and the final state which is a quantity of paramount importance .
it is observed by practitioners that free energy barriers are a very important element to describe transition kinetics from one state to the other .
for instance , the chemical kinetics of reactions happening in solvent ( such as in the cells of our bodies ) are limited by free energy barriers , and can take place only when the free energy difference between the initial and the final state is negative , or at least less than the typical thermal energy .
it is therefore very important to accurately compute free energy differences in order to assess the likelihood of a certain physical event to happen . beside these physical motivations to compute free energy differences ,
a more abstract motivation is to overcome sampling barriers encountered when computing canonical averages ( see the discussion in ( * ? ? ?
* section 1.3.3 ) ) .
indeed , it is often the case in practice that the trajectories generated by the numerical methods at hand remain stuck for a long time in some region of the phase space , and hop only occasionally to another region , where they also remain stuck a behavior known as metastability .
chemical and physical intuitions may guide the practitioners of the field towards the choice of some slowly evolving degree of freedom , called _ reaction coordinate _ in the following , responsible for the metastable behavior of the system . in this case
, free energy techniques can be used to accelerate the sampling .
this viewpoint allows to consider applications which are not motivated by physical or biological problems , such as curing sampling issues in bayesian statistics @xcite . in this introductory section ,
we present the main results and give the outline of the paper , highlighting the three main contributions of this work .
we only briefly define the concepts we need in this general introduction , and refer the reader to the following sections ( in particular section [ sec : notation ] ) for further precisions on the mathematical objects at hand .
we consider mechanical systems with constraints .
the configuration of a classical @xmath0-body system is denoted by @xmath1 .
the results of the paper can be generalized _ mutatis mutandis _ to periodic boundary conditions ( @xmath2 , where @xmath3 denotes the one dimensional torus ) , or to systems with positions confined in a domain @xmath4 .
the mass matrix of the system is assumed to be a constant strictly positive symmetric matrix @xmath5 .
one could typically think of a diagonal matrix @xmath6 .
the interaction potential is a smooth function @xmath7 .
the hamiltonian of the system is assumed to be separable : @xmath8 in the present paper , the focus is on the canonical ensemble , which is the equilibrium probability distribution of microscopic states of a system at fixed temperature ( fixed average energy ) . for systems without constraints
, this ensemble is characterized by the probability distribution @xmath9 where @xmath10 is the normalizing constant is assumed to be such that @xmath11 . ] ensuring that @xmath12 is indeed a probability distribution , and @xmath13 is proportional to the inverse temperature .
one dynamics which admits the canonical measure as an invariant measure is the langevin dynamics ( see for instance ( * ? ? ?
* section 2.2.3 ) and references therein ) : @xmath14 where @xmath15 is a standard @xmath16-dimensional brownian motion , and @xmath17 are @xmath18 position dependent real matrices which are assumed to satisfy the fluctuation - dissipation identity @xmath19 the langevin dynamics can be seen as some modification of the hamiltonian dynamics with two added components : a damping term @xmath20 and a random forcing term @xmath21 . the energy dissipation due to the damping is compensated by the random forcing in such a way that the temperature of the system is @xmath22 ( with @xmath23 boltzmann s constant ) .
we will consider positions subject to a @xmath24-dimensional mechanical constraint denoted by @xmath25 as will become clear below , constrained systems appear in computational statistical physics in two kinds of contexts ( see _ e.g. _ ( * ? ? ?
* chapter 10 ) , and @xcite for applications to the computation of free energy differences , and @xcite for mathematical textbooks dealing with constrained hamiltonian dynamics ) : a. for free energy computations , where @xmath26 is a given reaction coordinate parameterizing a transition between states of interest ; b. when the system is subject to molecular constraints such as rigid covalent bonds , or rigid bond angles in molecular systems . in the sequel , @xmath26 may be thought of at first reading as a reaction coordinate ( case ( i ) ) .
section [ ti - sec : mc ] explains how to handle additional molecular constraints ( case ( ii ) ) within the same formalism . in any case
, the position of the system is constrained onto the submanifold of co - dimension @xmath24 : @xmath27 and the associated phase space is the cotangent bundle denoted by @xmath28 for a given @xmath29 , the set of cotangent momenta is denoted by @xmath30 the orthogonal projection on @xmath31 with respect to the scalar product induced by @xmath32 is denoted @xmath33 where @xmath34 is the gram matrix associated with the constraints @xmath35 throughout the paper , we assume that @xmath36 is invertible everywhere on @xmath37 ( for all @xmath38 ) .
it is easily checked that @xmath39 satisfies the projector property @xmath40 , and the orthogonality property @xmath41 for constrained systems , the associated canonical distribution is defined by @xmath42 where @xmath43 is the phase space liouville measure of @xmath44 , and @xmath45 the normalizing constant ( @xmath38 refers to the position constraint , and @xmath46 to the velocity or momentum constraint , see below ) .
see section [ sec : measures ] for precise definitions . a dynamics admitting the constrained canonical measure as an invariant equilibrium measure is the following langevin process ( `` cl '' stands for `` constrained langevin '' ) : for a given initial condition @xmath47 , @xmath48 \dps d p_{t } = -\nabla v(q_{t } ) \ , dt -\gamma(q_t ) m^{-1}p_t \ , dt + \sigma(q_t ) \ , d w_t + \nabla \xi(q_{t } ) \ , d \lambda_t , & \\[6pt ] \dps \xi(q_{t } ) = z , & ( c_q ) \end{cases}$}\ ] ] where the @xmath49-valued adapted process @xmath50 is the lagrange multiplier associated with the ( vectorial ) constraint @xmath51 , and @xmath17 are again assumed to satisfy .
note that @xmath52 for all @xmath53 .
then , averages of an observable @xmath54 with respect to the distribution can be obtained as longtime averages along any trajectory of the dynamics @xmath55 ( when @xmath56 is symmetric positive on @xmath37 ) : @xmath57 this is made precise in section [ sec : sampling ] .
several recent studies ( _ e.g. _ @xcite ) have analyzed dynamics similar to @xmath55 and some appropriate discretization of the process in order to approximate the left - hand side of . of our work
is to propose a simple discretization of the dynamics @xmath55 and to highlight its remarkable properties .
the numerical scheme is based on a splitting strategy between the hamiltonian and the thermostat part , see equations -- below ( in the spirit of the scheme proposed in @xcite in the unconstrained case ) .
the hamiltonian part is discretized using a verlet scheme with position and momentum constraints ( the so - called rattle scheme , see @xcite ) .
we show that this discretization enjoys the following properties : ( i ) for some choice of the parameters , an euler discretization of the _ overdamped _ langevin dynamics ( also called brownian dynamics ) with a projection step associated with the constraints is obtained ( see equation and proposition [ p : langtooverd ] ) ; ( ii ) it can be completed by a metropolis - hastings correction to obtain a generalized hybrid monte carlo ( ghmc ) method sampling _ exactly _ ( _ i.e. _ without any bias due to time - discretization ) the constrained canonical distribution ( see algorithm [ a : ghmcconst ] below ) .
the so - obtained numerical scheme is close to the ones proposed in @xcite .
see also @xcite for historic references on hybrid monte carlo methods , and @xcite for ghmc .
one output of this part is thus a new metropolization procedure for overdamped langevin dynamics to sample , without bias , measures with support a submanifold .
the free energy @xmath58 associated with the reaction coordinates @xmath59 is defined as @xmath60 times the log - density of the marginal probability distribution of the reaction coordinates @xmath26 under the canonical distribution .
explicitly , it is defined through the following relation : for any test function @xmath61 , @xmath62 in words , @xmath63 is the image of the measure @xmath12 by @xmath26 , and @xmath64 can be seen as an `` effective potential energy '' associated to @xmath26 . computing the free energy profile @xmath65 (
up to an additive constant independent of @xmath38 ) , or free energy differences between two states @xmath66 is a way to compare the relative probabilities of different states
parameterized by @xmath26 .
this is a very important calculation for practical applications , see @xcite .
a state should be understood here as the collection of all possible microscopic configurations @xmath67 , distributed according to the canonical measure , and satisfying the macroscopic constraint @xmath68 .
since we only focus on computing free energy differences , @xmath64 is defined up to an additive constant ( independent of @xmath38 , denoted by @xmath69 below , and whose value may vary from line to line ) and can be rewritten as : @xmath70 where @xmath71 denotes the conditional measure on @xmath37 verifying the following identity of measures in @xmath72 : @xmath73 ( see section [ sec : measures ] for more precisions on this relation ) .
however , when using constrained simulations in phase space , the momentum variable of the dynamical system is also constrained , and a modified free energy ( called `` rigid free energy '' in the sequel , see remark below for a justification of the term `` rigid '' ) is more naturally computed , see section [ sec : sampling ] . the latter is defined as @xmath74 the superscript @xmath5 indicates that this free energy depends on the considered mass matrix , even though this is not clear at this stage ( see below ) .
the above two definitions of free energy are related through the identity : @xmath75 where @xmath76 is the equilibrium distribution with constraints .
the relation , already proposed in @xcite ( see also @xcite for related formulas ) , is proved at the beginning of section [ sec : langti ] .
for any value of the reaction coordinate , the difference @xmath77 can then be easily computed with any method sampling the probability distribution @xmath76 , such as @xmath55 .
several methods have been suggested in the literature to compute either @xmath64 or @xmath78 from the lagrange multipliers of a constrained process similar to @xmath55 .
we refer for instance to @xcite ( and references therein ) for the hamiltonian case , and to @xcite ( and references therein ) for the overdamped case . of this paper
is twofold : ( i ) we rigorously prove that the longtime average of the lagrange multipliers in @xmath55 converges to the gradient of the rigid free energy ( the so - called _ mean force _ ) ; and ( ii ) we then show that the latter mean - force can be computed with second order accuracy ( _ i.e. _ up to @xmath79 error terms , where @xmath80 is the time - step ) using the lagrange multipliers involved in the hamiltonian part of the splitting scheme .
more precisely , the first point ( i ) amounts to showing that @xmath81 as compared to @xcite , where a formal proof for the hamiltonian case is proposed , we use an explicit calculation that does not require the use of the lagrangian structure of the problem , or a change of coordinates . once @xmath82 is obtained , @xmath83 can be computed ( up to an additive constant ) by integration .
this procedure is known as _ thermodynamic integration_. note that using and thermodynamic integration , together with , allows to obtain @xmath84 without computing second order derivatives of @xmath26 .
this is a desirable property since computing such high derivatives may be cumbersome for some reaction coordinates used in practice .
straightforward computations of the mean force using analytical expressions ( see for instance - ) usually involve such high order derivatives . the second point ( ii )
is then based on a discretization of a variant of , obtained by subtracting the martingale part of the lagrange multipliers .
this amounts to averaging the two lagrange multipliers involved in the rattle part of the scheme , see ) .
we also discuss how these techniques can be generalized to compute the free energy for systems with molecular constraints , see section [ ti - sec : mc ] .
the last part of this article is devoted to nonequilibrium methods for free energy computations , based on a hamiltonian or langevin dynamics with constraints subject to a predetermined time evolution .
such methods rely on a nonequilibrium fluctuation equality , the so - called jarzynski - crooks relation .
see @xcite for a pioneering work , as well as @xcite for an extension .
they are termed `` nonequilibrium '' since the transition from one value of the reaction coordinate @xmath26 to another one is imposed _ a priori _ , in a finite time@xmath85 , and with a given smooth deterministic schedule @xmath86
\mapsto z(t ) \in \mathbb{r}^\nc$ ] .
in particular , it may be arbitrarily fast
. therefore , even if the system starts at equilibrium , it does not remain at equilibrium .
the out - of - equilibrium langevin process we consider to this end is given by the following equations of motion ( `` scl '' stands for `` switched constrained langevin '' ) : @xmath87 d p_t & = -\nabla v ( q_t ) \,dt -\gamma_p(q_t ) m^{-1 } p_t \ , dt+ \sigma_p(q_t ) \,d w_t + \nabla
\xi(q_t ) \ , d \lambda_t , \\[6pt ] \xi(q_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.$}\ ] ] where @xmath88 is an adapted process enforcing the constraints @xmath89 ( the lagrange multipliers ) .
initial conditions are sampled from the phase - space canonical distribution defined by the constraints @xmath90 and @xmath91 ( see ) .
we restrict ourselves to projected fluctuation - dissipation matrices of the specific form @xmath92 where @xmath93 satisfy the fluctuation - dissipation identity .
note that @xmath94 also verify .
our analysis also applies to deterministic hamiltonian dynamics upon choosing @xmath95 .
the dynamics @xmath96 is a natural extension of the constrained langevin dynamics @xmath55 .
it is different from the dynamics proposed in @xcite , which is a langevin dynamics associated with a modified hamiltonian with projected momenta , driven by a forcing term along @xmath97 which acts directly on the position variable . as explained below ( see and the discussion following this equation ) , the specific choice ( rather than considering unprojected matrices @xmath93 ) leads to a simpler analysis and more natural numerical schemes , based again on a splitting procedure . as explained in section [ sec : jarz_lang_cons ] , it is possible to define the work associated with the constraints exerted on the system between time @xmath46 and @xmath98 as the displacement multiplied by the constraining force : @xmath99 of the present paper is twofold : ( i ) we derive a new general crooks - jarzynski relation ( see theorem [ th : crookslangcons ] below ) based on the nonequilibrium constrained dynamics @xmath96 and the associated work defined in ; and ( ii ) an original numerical scheme is proposed , which allows to compute free energy differences _ without time discretization error _ ( see theorem [ eq : jarz_disc ] below ) .
more precisely , concerning the first point , the main corollary is given by the following result .
consider the corrector @xmath100 where @xmath101 is the so - called fixman term due to the geometry of the position constraints ( see and remark [ rem : highosclang ] ) , and @xmath102 is the kinetic energy term due to the velocity of the switching .
then , the free energy profile can be computed through the following fluctuation identity ( see ):
@xmath103 } \right)}{\e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right),\ ] ] where the expectation is with respect to canonical ( equilibrium ) initial conditions and for all realizations of the dynamics @xmath96 . the numerical scheme mentioned in the second point ( ii ) above
is based on a modification of the splitting scheme used to discretize the constrained langevin dynamics @xmath55 .
this modification allows to take into account the evolving constraints . using the symplecticity of the modified rattle scheme
, we are able to prove a discrete - in - time version of the crooks relation , and of the associated jarzynski free energy estimator . moreover
, for some choice of the parameters , the latter scheme yields a jarzynski - crooks relation for an euler discretization of the overdamped langevin ( brownian ) dynamics with a projection step associated with the evolving constraints , without time discretization error .
this can be seen as an extension of the scheme formerly proposed in @xcite ( see equation and proposition [ p : langtooverd_jarz ] ) .
we also check the consistency of the various free energy estimators we introduce .
we start with an introduction to the mathematical concepts required for mechanically constrained systems in section [ sec : notation ] .
section [ sec : sampling ] is devoted to the properties and the discretization of mechanically constrained langevin processes defined by @xmath55 , and the problem of sampling the canonical distribution .
thermodynamic integration with constrained langevin processes is presented in section [ sec : langti ] .
section [ sec : lang_jarz ] discusses nonequilibrium constrained langevin processes @xmath96 and the associated jarzynski - crooks fluctuation identity .
finally , some technical lemmas are gathered in section [ sec : appendix ] .
after making precise our notation for matrices and matrix valued functions in section [ sec : matrix_notation ] , we introduce some additional concepts required to describe constrained systems in section [ sec : const_notation ] , and define the phase space measures with constraints in section [ sec : measures ] . throughout the paper ,
the following notation is used : * vectors and vector fields are by convention of column type .
when vectors are written as a line , they should be understood as the corresponding column version .
for instance , @xmath104 should be understood as @xmath105 , where @xmath106 are both column vectors .
* gradients in @xmath72 ( or @xmath107 ) of @xmath24-dimensional vector fields are by convention @xmath108-matrices , for instance : @xmath109 where @xmath110 is a column vector for any @xmath111 .
gradients in the space of constraints parameters @xmath112 or @xmath113 are denoted with the associated subscripts , namely @xmath114 and @xmath115 . * second order derivatives in @xmath72 of @xmath24-dimensional vector fields are characterized through the hessian bilinear form : @xmath116 where @xmath117 are test vectors . *
the canonical symplectic matrix is denoted by : @xmath118 for any smooth test functions @xmath119 and @xmath120 , the poisson bracket is the @xmath121 matrix @xmath122 * for two matrices @xmath123 , @xmath124 .
contrarily to what is often done in the literature , we avoid global changes of variables and the use of generalized coordinates .
we observe that global changes of variables are not required for the proofs of the theoretical results we present , and they are definitely to be avoided in practical numerical computations whenever possible
. two useful concepts to study constrained hamiltonian systems ( in particular , to use the co - area formula in phase space , as well as the poisson bracket formulation of the liouville equation ) are the effective velocity @xmath125 and the effective momentum @xmath126 associated with the constrained degrees of freedom @xmath26 : @xmath127 and @xmath128 the expression of the effective velocity is obtained by deriving the constraint @xmath26 along an unconstrained trajectory of the hamiltonian dynamics @xmath129
\dps \frac{d \tilde p_t}{dt } = -\nabla v(\tilde q_t ) , \end{cases}\ ] ] since @xmath130 the term @xmath131 in the expression of the effective momentum may be interpreted as the effective mass of @xmath26 .
this can be motivated by a decomposition of the kinetic energy of the system into tangential and orthogonal parts , using the projector for a given position @xmath132 :
@xmath133 the orthogonal part can be rewritten , for any @xmath1 , as : @xmath134 the last equations allow to consider @xmath135 as some effective mass .
the constraints on a mechanical system can also be reformulated in the more general form @xmath136 where either ( i ) the effective momentum is constrained , in which case @xmath137 and @xmath138 ; or ( ii ) the effective velocity is constrained , in which case @xmath139 and @xmath140 . the phase space associated with such constraints is denoted by @xmath141 a position @xmath142 being given , the affine space of constrained momenta verifying is then denoted by @xmath143 in the effective velocity case , and by @xmath144 in the effective momentum case .
this notation is very important for nonequilibrium methods where the constraints evolve in time according to a predefined schedule , see section [ sec : lang_jarz ] .
note that the phase space of mechanical constraints , defined by , is simply @xmath145 .
we can now define the skew - symmetric gram tensor of dimension @xmath146 associated with the constraints : @xmath147 the gram matrix @xmath148 associated with the generalized constraints can be explicitly computed by block . indeed , for @xmath149 , @xmath150 therefore , @xmath151 in this case .
in the case @xmath152 , the gram matrix reads @xmath153 and @xmath154 .
note that in both cases @xmath155 .
the constrained symplectic ( skew - symmetric ) matrix is now defined by @xmath156 and the poisson bracket associated with generalized constraints by : @xmath157 this poisson bracket is often called the dirac bracket in the literature ( in reference to the seminal work of dirac @xcite ) .
it is easily checked that @xmath158 verifies the characteristic properties of poisson brackets , namely the skew - symmetry , jacobi s identity , and leibniz rule .
therefore , the flow associated with the evolution equation @xmath159 defines a symplectic map .
recall that ( see ( * ? ? ?
* section vii.1.2 ) ) a map @xmath160 is symplectic if for any @xmath161 and @xmath162 , @xmath163 a consequence of the symplectic structure is the divergence formula relating the phase space measure @xmath164 on @xmath165 ( defined below ) , and the poisson bracket .
the reader is referred to chapter @xmath166 in @xcite , and section vii.@xmath167 in @xcite for more material on constrained systems .
it will be shown in proposition [ s : p : lconstgen ] below that the poisson system is equivalent to @xmath55 when @xmath168 .
the phase space measure ( also termed liouville measure ) on the phase space @xmath169 ( or more generally on @xmath165 ) of constrained mechanical systems is denoted by @xmath170 ( or more generally @xmath171 ) .
the latter is induced by the symplectic , or skew - symmetric @xmath172-form on @xmath107 defined by the canonical skew - symmetric matrix @xmath173 in @xmath107 .
more precisely , it can be defined through the volume form @xmath174 , where @xmath175 and @xmath176 is a basis of tangential vectors of the submanifold @xmath177 ( or @xmath165 ) at a given point @xmath67 .
surface measures induced by scalar products associated with general symmetric definite positive matrices will also be of interest .
we denote by @xmath178 the surface measure on @xmath37 induced by the scalar product @xmath179 on @xmath72 , and , for a given @xmath29 , by @xmath180 and @xmath181 the surface measures on the affine spaces @xmath144 and @xmath182 respectively , induced by the scalar product @xmath183 on @xmath72 . for more precise definitions of these measures ,
we refer to ( * ? ? ?
* sections 3.2.1 and 3.3.2 ) and the references therein .
it is now possible to define a generalization of the canonical distribution as follows : @xmath184 the distribution is associated with the generalized constraints @xmath185 , and is used in section [ sec : lang_jarz ] for nonequilibrium methods .
note that @xmath186 defined in .
the co - area formula ( see @xcite ) relates the phase space or surface measures , and the conditional measures .
conditional measures are defined in @xmath107 by the following conditioning formula : for any test function @xmath187 , @xmath188 in the same way in @xmath72 , conditional measures are defined , for any test function @xmath189 , by @xmath190 a more concise notation for the above equalities is @xmath191 and @xmath73 .
[ p : coareasympl ] let @xmath37 be the submanifold defined by the constraints @xmath68 , and assume that @xmath36 defined in is non - degenerate in a neighborhood of @xmath37 .
then , in the sense of measures on @xmath72 : @xmath192 let @xmath165 be the phase space defined by generalized constraints .
assume that @xmath193 defined in is non - degenerate in a neighborhood of @xmath165 .
then , in the sense of measures on @xmath107 : @xmath194 we refer for example to chapter @xmath195 in @xcite for an elementary proof
. an equivalent of - for momenta reads , for constrained effective momenta : @xmath196 and for constrained effective velocities : @xmath197 using the co - area formulas - , and the expressions of symplectic gram matrices - , we obtain the following expressions of the phase space measures : a. the phase space measure on @xmath198 can be identified with the conditional measure defined in : @xmath199 while the phase space measure on @xmath200 is related to the corresponding conditional measure as @xmath201 b. the phase space measures are given by the product of surface measures : @xmath202 and @xmath203 equations - are a consequence of the fact that @xmath204 ( and a similar relation for @xmath125 ) .
we end this section with an important formula , which is used to show the invariance of the canonical measure in the proof of proposition [ p : revcons ] .
[ p : divsympl ] consider the poisson bracket @xmath158 defined by , and an open neighborhood @xmath205 of @xmath206 where @xmath148 is invertible . then for any smooth test functions @xmath207 with compact support in @xmath205 , @xmath208
the divergence formula can be proved using darboux s theorem and internal coordinates , or directly using the co - area formula ( see section 3.3 in @xcite ) .
we will also need the classical divergence formula on affine spaces ( see for instance section 3.3 in @xcite ) : for a fixed @xmath132 , for any compactly supported smooth vector field @xmath209 , @xmath210
we first give some properties of the constrained langevin equation @xmath55 in section [ sec : sampling_gen ] , then propose some numerical schemes to discretize it in section [ sec : consnum ] , and finally consider the overdamped limit in section [ sec : ovd_limit_constraints ] .
we consider the dynamics @xmath55 : @xmath211 \dps d p_{t } = -\nabla v(q_{t } ) \ , dt -\gamma(q_t ) m^{-1}p_t \ , dt + \sigma(q_t ) \ , d w_t + \nabla \xi(q_{t } ) \ , d \lambda_t , & \\[6pt ] \dps \xi(q_{t } ) = z. & ( c_q ) \end{cases}\ ] ] by differentiating with respect to time the constraint @xmath212 , the lagrange multipliers can be computed explicitly ( see for instance section 3.3 in @xcite ) : @xmath213 \nonumber\\ & = \ , f_{\rm rgd}^m(q_t , p_t ) \ , dt + g_{m}^{-1}(q_t)\nabla \xi(q_t)^t m^{-1 } { \left(\gamma(q_{t } ) m^{-1}p_{t } \,dt - \sigma(q_{t } ) \,d w_t \right ) } , \label{eq : first_expression_lagrange}\end{aligned}\ ] ] where the constraining force @xmath214 is defined as : @xmath215 thus , using the fact that @xmath216 when @xmath217 , the dynamics @xmath55 can be recast in a more explicit form as @xmath218 d p_{t } & = -\nabla v(q_{t } ) \ , dt + \nabla \xi(q_t ) f_{\rm rgd}^m(q_t , p_t ) \ , dt -\gamma_p(q_t ) m^{-1 } p_{t}\ , dt \\ & \quad + \sigma_p(q_t ) \ , d w_t , \end{aligned } \right.\ ] ] where we introduced the notation @xmath219 .
the constraint therefore has two effects : ( i ) the matrices @xmath220 in the dissipation and fluctuation terms are replaced by their projected counterparts @xmath94 , and ( ii ) an orthogonal constraining force @xmath221 is introduced .
the generator of this stochastic langevin dynamics is the operator @xmath222 which appears in the kolmogorov evolution equation : for @xmath223 satisfying @xmath55 or , and for any smooth test function @xmath224 , @xmath225 the expression of @xmath222 can be obtained using it calculus , as made precise in the following proposition .
[ s : p : lconstgen ] consider either the effective momentum or the effective velocity , denoted with the general constraints @xmath226 or @xmath227 ( see ) .
the solution of the constrained dynamics @xmath55 ( or equivalently with an initial condition @xmath228 ) belongs to @xmath229 , and the generator of this markov process reads ( whatever the value of @xmath38 ) @xmath230 where the fluctuation - dissipation part is @xmath231 with @xmath232 defined in . using the fluctuation - dissipation relation ,
the generator @xmath233 can be rewritten more compactly as @xmath234 we perform the computation in two steps : ( i ) we compute the generator of the hamiltonian part of the constrained langevin dynamics , which is @xmath55 in the case @xmath235 ; ( ii ) we compute the generator of the thermostat part of @xmath55 , which is an ornstein - uhlenbeck process on momentum variable ( corresponding to the second equation in @xmath55 with @xmath236 ) .
let us first consider ( i ) , with @xmath226 ( the case @xmath227 being similar ) .
note that @xmath237 where the hessian operator @xmath238 is defined in .
now , implies that @xmath239 besides , @xmath240 along a trajectory , since @xmath52 .
therefore , @xmath241 where the notation @xmath242 is introduced in .
consider a test function @xmath243 , and remark that @xmath244 so that , for any @xmath245 , @xmath246 finally , for all @xmath247 , @xmath248 the operator is the generator of the hamiltonian part in .
we turn to ( ii ) .
the diffusive part arises from the fluctuation term @xmath249 in , and its expression @xmath250 is obtained directly from the standard it calculus .
similarly , the dissipation operator is @xmath251 the addition of these two contributions gives the expression of @xmath233 . with the expression of the generator at hand , it is easily checked that the process @xmath55 satisfies the following equilibrium properties : [ p : revcons ] when the fluctuation - dissipation relation holds , the constrained langevin dynamics @xmath55 on @xmath252 admits the boltzmann - gibbs distribution as a stationary measure , and is reversible up to momentum reversal with respect to : if @xmath253 , then , for any @xmath254 , @xmath255 moreover , if @xmath256 is everywhere strictly positive in the sense of symmetric matrices on @xmath257 , then the process @xmath55 is ergodic : for any smooth test function @xmath224 , @xmath258 the stationarity and reversibility properties follow from the following detailed balance condition up to momentum reversal ( see for instance section 2.2 in @xcite ) : for any test functions @xmath259 , @xmath260 , @xmath261 where @xmath262 is the momentum flip . in view of the expression of the generator , proving amounts to proving this property for the operators @xmath263 and @xmath233 . for the hamiltonian part @xmath263 , the expression yields @xmath264 which states the time symmetry under momentum reversal of the hamiltonian part of the equations of motion @xmath55 . on the other hand , @xmath265 so that @xmath266 and the divergence formula yields the balance condition for the hamiltonian part , in view of the invariance of the distribution @xmath170 under the momentum flip @xmath267 . for the thermostat part , it is easily checked , that @xmath268 for any smooth test function @xmath224 , so that the detailed balance condition up to momentum reversal follows from the following more general detailed balance condition , in the case @xmath269 ( @xmath270 being defined in ): @xmath271 it is interesting to prove for a general @xmath272 since it will be used in the proof of theorem [ th : crookslangcons ] below . consider the divergence formula in the affine space for the variable @xmath273 ( the position @xmath274 being fixed ) , with @xmath275 after integration in @xmath274 , using the formula for @xmath233 and , an expression symmetric in @xmath276 is obtained : @xmath277 hence the detailed balance condition .
ergodicity is a consequence of the hypo - ellipticity of the operator @xmath222 on @xmath278 ( hrmander s criterion is satisfied , see @xcite ) , which is itself a consequence of the fact that @xmath279 is strictly positive on each @xmath280 .
the proof can be carried out using local coordinates and the results from @xcite .
[ rem : highosclang ] we have considered in this section the langevin dynamics with constraints rigidly imposed by a projection onto the submanifold @xmath281 .
this dynamics samples the canonical distribution @xmath282 , with constraints on both positions and momenta .
the marginal on positions of this distribution is , in view of , proportional to @xmath283 this is what we call in the following rigidly imposed constraints .
the canonical distribution with rigid constraints is naturally associated to the rigid free energy ( and this is what justifies the qualification `` rigid '' ) , since , we recall , @xmath284 another way to impose some constraints on a system is to add a penalization term . in our context , this could be done by changing the potential energy @xmath285 to @xmath286 it is easy to check that , in the limit @xmath287 ( infinite stiffness limit ) , the canonical measure associated to this potential is the canonical distribution with positions conditioned by @xmath288 .
this distribution is proportional to @xmath289 and its marginal on positions is proportional to @xmath290 this is what we call in the following softly imposed constraints . the canonical distribution with soft constraints is naturally associated with the standard free energy , since , we recall , @xmath291 note that , in view of , the marginal on positions for softly imposed constraints can be written in terms of rigidly imposed constraints through a modification of the potential : @xmath292 where @xmath293 is sometimes called the fixman corrector ( see @xcite ) . thus ,
if @xmath223 satisfies with the modified potential @xmath294 then @xmath295 samples ( in the longtime limit ) the probability measure proportional to @xmath296 , and we thus refer to this dynamics as the softly constrained langevin dynamics .
these concepts will be used in section [ ti - sec : mc ] to describe the computation of free energy differences for systems with molecular constraints .
finally , let us mention that the infinite stiffness limit @xmath287 of the langevin dynamics with the potential @xmath297 is not ( except for very specific forms of constraints ) the softly constrained langevin dynamics , as one would expect .
we refer to [ 32 ] for example , where it is shown that adiabatic effective potentials ( derived from the conservation of the ratio of energy over frequency of fast modes ) are required to describe the limiting dynamics .
however , a formal argument based on `` over - damping '' the fast modes indeed leads to the softly constrained langevin dynamics .
we consider in this section a numerical scheme based on a splitting of the langevin dynamics @xmath55 into a hamiltonian part ( section [ sec : numhamiltonconst ] ) and a fluctuation - dissipation part acting only on the momentum ( section [ sec : numflucdissconst ] ) . such a splitting is standard for unconstrained systems , but other splitting strategies for the langevin equation can be considered as well ( see @xcite ) . for simplicity , we restrict ourselves to constant matrices @xmath298 and @xmath299 . generalizations to position dependent matrices are straightforward .
the hamiltonian part of the langevin dynamics @xmath55 ( namely @xmath55 with @xmath300 ) is discretized using a velocity - verlet scheme with constraints , which yields below .
the fluctuation - dissipation part on momentum variable in @xmath55 is the following ornstein - uhlenbeck process ( for a fixed given @xmath301 ) : @xmath302 which can be rewritten as ( see ) @xmath303 this equation can be explicitly integrated on @xmath304 $ ] to obtain : @xmath305 however , the matrix exponential @xmath306 may be difficult to compute in practice ( except for certain choices of @xmath298 and @xmath5 , see the discussion at the end of section [ sec : numflucdissconst ] ) .
instead of performing an exact integration , can be discretized using a midpoint euler scheme , which yields and below .
the numerical scheme we investigate , termed midpoint euler - verlet - midpoint euler splitting , is therefore the following : @xmath307 \nabla \xi(q^n)^{t } m^{-1 } p^{n+1/4 } = 0 , & ( c_p)\\ \end{cases } \label{eq : flucdiss1 } \\ & \begin{cases }
p^{n+1/2 } = \dps p^{n+1/4 } - \frac{\dt}{2 } \nabla v ( q^{n } ) + \nabla \xi(q^n ) \ , \lambda^{n+1/2 } , & \\[6pt ] q^{n+1 } = q^{n } + \dt \ ,
m^{-1 } \ , p^{n+1/2 } , \\[6pt ] \xi(q^{n+1 } ) = z , & ( c_q)\\[6pt ] p^{n+3/4 } = \dps p^{n+1/2 } - \frac{\dt}{2 } \nabla v ( q^{n+1 } ) + \nabla \xi(q^{n+1 } ) \ , \lambda^{n+3/4 } , & \\[6pt ] \nabla\xi ( q^{n+1})^{t } m^{-1 } p^{n+3/4 } = 0 , & ( c_p)\\ \end{cases } \label{eq : verletconst } \\ &
\begin{cases } \dps p^{n+1 } = p^{n+3/4 } -\frac{\dt}{4 } \gamma \ , m^{-1 } ( p^{n+3/4}+p^{n+1 } ) + \sqrt{\frac\dt2 } \ , \sigma \ , { \mathcal g}^{n+1/2 } \\
\phantom{p^{n+1 } = } + \nabla\xi(q^{n+1 } ) \ , \lambda^{n+1 } , & \\[6pt ] \nabla \xi(q^{n+1})^{t } m^{-1 } p^{n+1 } = 0 , & \hspace{-1 cm } ( c_p)\\ \end{cases } \label{eq : flucdiss2 } \end{aligned}\ ] ] where @xmath308 and @xmath309 are sequences of independently and identically distributed ( i.i.d . )
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
note that when @xmath311 and @xmath312 , the scheme -- becomes deterministic , and reduces to , which is a scheme for the deterministic hamiltonian equations of motion with position constraints @xmath68 .
the latter scheme is referred to as the hamiltonian scheme below .
the hamiltonian part of the scheme , often called rattle in the literature , is an explicit integrator , and is a modification of the classical shake algorithm ( see chapter vii.@xmath167 in @xcite , or chapter @xmath313 in @xcite for more precisions and historical references ) . in , @xmath314 are the lagrange multipliers associated with the position constraints @xmath315 , and @xmath316 are the lagrange multipliers associated with the velocity constraints @xmath317 . the nonlinear constraints @xmath315 are typically enforced using newton s algorithm . in ,
the ( linear ) momentum projection @xmath318 is always well defined since we assumed that the gram matrix @xmath34 is invertible . on the other hand ,
the nonlinear projection used to enforce the position constraints @xmath319 is in general well defined only on a subset of phase space .
the domain @xmath320 is defined as the set of configurations @xmath321 such that there is a unique solution @xmath322 verifying . solving the position constraints
@xmath51 consists in projecting onto @xmath37 a point in a @xmath80-neighborhood of @xmath323 . thus , by the implicit function theorem , the domain @xmath324
verifies : @xmath325 it may happen that there is no solution if the time - step is too large , and , even for small time - steps , that several projections exist , see for instance example @xmath172 in chapter @xmath313 of @xcite . in practice , @xmath324 can be chosen to be the set of @xmath326 such that the newton algorithm enforcing the constraints @xmath51 has converged within a given precision threshold and a limited number of iterations .
as for the verlet scheme in the unconstrained case , the associated numerical flow shares two important qualitative properties with the exact flow : it is time reversible and symplectic ( see @xcite ) .
this implies quasi - conservation of energy , in the sense that energy is conserved within a given precision threshold over exponentially long times , see @xcite .
the new momentum @xmath327 in ( or @xmath328 in ) may be obtained by first integrating the unconstrained dynamics with a midpoint scheme , and then computing the lagrange multiplier @xmath329 ( or @xmath330 ) by solving the following linear system implied by the constraints @xmath318 : @xmath331 = 0 . \end{aligned}\ ] ] a sufficient criteria for stability is @xmath332 besides , it can be checked ( see sections 2.3.2 and 3.3.5 in @xcite ) that the markov chain induced by the fluctuation - dissipation part of the scheme ( or ) verifies a detailed balance equation ( both in the plain sense and up to momentum reversal ) with respect to the stationary measure @xmath333 .
the latter is defined as the kinetic probability distribution @xmath334 and is the marginal in the @xmath273-variable of the canonical distribution @xmath335 conditioned by a given @xmath301 . moreover ,
if @xmath336 is strictly positive in the sense of symmetric linear transformations of @xmath337 , then the markov chain on momentum variable induced by ( or ) alone is ergodic with respect to @xmath333 .
finally , an important simplification occurs in the integration of in the special case when @xmath298 and @xmath5 are equal up to a multiplicative constant ( so that @xmath338 is proportional to identity ) .
indeed in this case the equality @xmath339 holds for any @xmath340 , and simplifies to @xmath341 the numerical integration of can thus be carried out in two steps : ( i ) exactly integrating without constraint , and then ( ii ) projecting the result onto @xmath342 .
usually , the invariant probability distribution sampled by the solution of a numerical scheme is biased by the time discretization .
relying on ( i ) the time symmetry ( up to momentum reversal ) and ( ii ) the preservation of the phase space measure @xmath343 by the solution of the rattle scheme , it is possible to eliminate the time discretization error in the splitting scheme -- by resorting to a generalized hybrid monte carlo algorithm .
[ a : ghmcconst ] consider an initial configuration @xmath344 , and a sequence @xmath345 of independently and identically distributed standard gaussian vectors .
iterate on @xmath340 : 1 .
evolve the momentum according to the midpoint euler scheme , and compute the energy @xmath346 of the new configuration ; 2 . integrate the hamiltonian part according to the rattle scheme , denote @xmath347 the resulting state , and set @xmath348 .
3 . accept the proposal @xmath349 with probability @xmath350 otherwise , reject and flip the momentum : @xmath351 .
4 . evolve the momentum according to the midpoint euler scheme . by construction ,
the ghmc algorithm with constraints leaves invariant the equilibrium distribution @xmath352 ( see section 3.3.5 in @xcite ) . to understand the momentum reversal required upon rejection , it is useful to write more explicitly the markov chain as the composition of a metropolis - hastings part , where the proposal is obtained by a rattle step followed by a momentum reversal ( the latter operation is needed to ensure the symmetry of the proposition ) , which is then accepted or rejected ; and another momentum reversal ( which leaves invariant the targeted probability measure @xmath352 ) .
when the proposal is accepted , the two momentum reversals cancel out each other . on the other hand , when the proposal is rejected , momenta are actually reversed .
see ( * ? ? ?
* section 2.1.4 ) for more background on generalized metropolis - hastings algorithms . in the above
, we implicitly assume that the rattle scheme is everywhere well defined . in practice
however , it is necessary to modify algorithm [ a : ghmcconst ] by restricting the sampled configurations to @xmath324 .
this can be achieved by introducing additional tests in steps ( 1 ) , ( 2 ) and ( 4 ) , and rejecting the states that have gone outside the set @xmath353 where the position constraint @xmath51 is well defined . by doing so
, the global algorithm has an invariant equilibrium distribution given by @xmath352 conditioned on the set of states @xmath324 .
this invariant distribution can be written explicitly as follows : @xmath354 alternatively , the rejection tests in steps ( 1 ) , ( 2 ) and ( 4 ) of algorithm [ a : ghmcconst ] can be performed with a cut - off parameter @xmath355 on the momentum variable , chosen so that the position constraint @xmath51 in is everywhere well defined when @xmath356 .
this can be achieved when there exists @xmath355 small enough so that @xmath357 .
since this is useful for later purposes ( see the discussion at the end of section [ sec : num_ti ] ) , we provide a rough estimate of @xmath358 in terms of @xmath80 , assuming for simplicity that @xmath37 is compact .
first , by the implicit function theorem , there exists @xmath359 such that , for all @xmath29 and @xmath360 with norm @xmath361 , there is a unique @xmath362 satisfying @xmath363 therefore , there exists @xmath364 small enough such that , when @xmath365 , the rattle scheme in is well defined , namely there exists a unique @xmath366 satisfying the constraint @xmath51 .
this shows that @xmath367 for some @xmath368 . the invariant probability distribution of the markov chain generated by ghmc with the additional rejection steps ensuring @xmath369 , is given by , and actually reads @xmath370 its marginal distribution in the position variable is then exactly given by : @xmath371 this is also the marginal distribution in the position variable of @xmath372 .
note however , that if @xmath358 is too small , only small momenta will be sampled in step ( 1 ) of algorithm [ a : ghmcconst ] , and the correlation time of the sampling will be large . in practice , the threshold @xmath358 should be tuned in preliminary computations so that : ( i ) @xmath358 is small enough so that the maximal number @xmath373 of iterations for the newton algorithm used to enforce @xmath51 in is never reached ; ( ii ) @xmath358 is large enough so that the correlation time of the sampling is as small as possible .
let us end this section with a warning : it is now known that the correction of the bias in discretizations of the langevin dynamics by a metropolization of the scheme may reduce the efficiency of the sampling , see for instance @xcite
. constrained overdamped langevin processes ( or brownian dynamics ) are solutions of the stochastic differential equation ( see also @xcite ) @xmath374 where @xmath375 is an adapted stochastic process .
equivalently , can be rewritten in the stratonovitch form as @xmath376 where @xmath377 denotes the stratonovitch integration , and @xmath378 is the projector defined by with the choice @xmath379 : @xmath380 it can be shown that verifies the detailed balance condition for ( and is ergodic with respect to ) the invariant distribution @xmath381 which is the marginal in the @xmath274-variable of the canonical distribution with constraints for the choice @xmath382 .
it is easy to generalize all our results to scalar products associated with a general symmetric definite positive matrix @xmath5 upon considering , see remark [ rmk : discrete_ovd_m ] below .
the constrained overdamped langevin process may be obtained from a scaling limit of the constrained langevin dynamics @xmath55 ( in the limit when either the mass goes to zero , or the damping @xmath298 goes to infinity ) , see propositions @xmath383 and @xmath384 in @xcite .
likewise , at the discrete level , an euler - maruyama discretization of the overdamped process can be obtained as a particular case of the numerical discretization -- for the langevin equation @xmath55 , yielding a markov chain @xmath385 on positions .
the condition that the mass goes to 0 is replaced by the condition that the mass is proportional to the time - step .
this is the content of the following proposition .
[ p : langtooverd ] suppose that the following relation is satisfied : @xmath386 with a slight abuse of notation , the mass matrix and the friction matrix are rewritten as @xmath387 and @xmath388 with @xmath389 .
then the splitting scheme -- yields the following euler scheme for the overdamped langevin constrained dynamics : @xmath390 \xi(q^{n+1 } ) = z , \end{cases}\ ] ] where @xmath391 are independent and identically distributed centered and normalized gaussian variables , and @xmath392 are the lagrange multipliers associated with the constraints @xmath393 .
moreover , the lagrange multipliers in verify : @xmath394 as well as @xmath395 where @xmath396 is defined in .
irrespective of @xmath397 , the choice in the scheme -- leads to @xmath398 where @xmath329 is associated with the constraints @xmath399 .
this gives @xmath400 where @xmath401 is such that @xmath402 .
the fluctuation - dissipation relation can be reformulated in this context as @xmath403 and the scheme is recovered by taking the associated lagrange multiplier equal to @xmath404 . finally , remarking that @xmath405 and computing explicitly @xmath401 and @xmath406 in yields -- .
this point of view allows to construct a metropolis correction to the euler scheme , using the generalized hybrid monte carlo scheme ( algorithm [ a : ghmcconst ] ) with the time - step chosen according to . in this way , assuming that the position constraint @xmath51 in is everywhere well defined , we obtain a markov chain @xmath407 discretizing the overdamped dynamics which _ exactly _ samples the invariant distribution .
deriving such a metropolis - hastings correction to the euler scheme without resorting to phase - space dynamics does not seem to be natural .
[ rmk : discrete_ovd_m ] proposition [ p : langtooverd ] can be seen as a discrete version of the zero - mass limit of the langevin dynamics .
it is also possible to obtain a discrete version of the overdamped limit ( @xmath408 ) of the langevin dynamics by assuming that the parameters satisfy the relation @xmath409 which is less restrictive than .
equation is then obtained with @xmath80 replaced by @xmath410 in this case , the effective discretization time - step @xmath411 for the overdamped langevin dynamics is thus different from the time - step @xmath412 originally used for the discretization of the langevin dynamics .
this is reminiscent of the fact that the overdamped limit ( at the continuous level ) of the langevin dynamics requires a change of timescale to obtain the overdamped langevin dynamics .
note also that in the more general case @xmath413 where @xmath5 is not supposed to be proportional to the identity , the following numerical scheme is obtained : @xmath414 \xi(q^{n+1 } ) = z , \end{cases}\ ] ] where @xmath415 .
this is a discretization of the overdamped dynamics @xmath416 which is a generalization of to a scalar product on @xmath417 induced by a general positive definite mass matrix @xmath5 .
in this section , we focus on the computation of the gradient of the rigid free energy @xmath418 using a numerical discretization of the constrained langevin process @xmath55 . as explained in the introduction
, we may indeed concentrate on the computation of the rigid free energy , since the standard free energy can be computed from the latter one using .
the relation can be proved with the co - area formula .
indeed , the free energy defined in can be rewritten as ( where c denotes a constant which may vary from line to line ) : @xmath419 hence @xmath420 where surface measures are defined in section [ sec : measures ] .
note that the rigid free energy @xmath78 indeed depends explicitly on the mass matrix since @xmath421 this section is organized as follows .
first , we show how systems with molecular constraints and systems with constrained values of the reaction coordinate can be treated in a unified framework ( section [ ti - sec : mc ] ) .
we then relate the lagrange multipliers arising in the constrained langevin dynamics , and the gradient of the rigid free energy ( the so - called mean force ) in section [ sec : lag ] .
we consider the numerical computation of the mean force in section [ sec : num_ti ] , where we prove consistency results for the corresponding approximation formulas .
finally , some numerical results on a model system illustrate the approach in section [ sec : simple_example_wca ] .
we discuss here how to generalize all the computations to systems with molecular constraints , generalizing thereby some results of @xcite . without loss of generality ,
we consider rigidly imposed molecular constraints , see remark [ rmk : choice_mc ] below for a discussion of this assumption .
this section can be considered as independent of the remainder of the paper and may therefore be omitted in a first reading . in practice , many systems are subject to molecular constraints , such as fixed lengths for covalent bonds , or fixed angles between covalent bonds .
the reader is referred to @xcite for practical aspects related to the simulation of molecular constraints . in the context of free energy computations , two types of constraints
are therefore considered : first , the molecular constraints , @xmath422 for @xmath423 , and second , the reaction coordinates denoted in this section by @xmath424 , with @xmath425 .
the submanifold of molecular constraints is denoted by @xmath426 and the submanifold associated with the reaction coordinates by @xmath427 it is assumed that the full gram matrix : @xmath428 is everywhere invertible on @xmath429 .
likewise , we denote @xmath430 and @xmath431 assuming rigid mechanical constraints on the molecular constraints @xmath432 ( see remark [ rmk : choice_mc ] below ) , we are led to considering the canonical distribution @xmath433 to describe systems with molecular constraints at a fixed temperature .
the measure @xmath434 denotes the phase space measure on @xmath435 , equal by to the conditional measure @xmath436 associated with the constraints @xmath437 , where @xmath438 is the effective momentum associated with @xmath432 .
[ rmk : choice_mc ] the distribution @xmath439 in is obtained by constraining rigidly @xmath440 to 0 , and not softly ( in which case @xmath441 would be replaced by @xmath442 , see also remark [ rem : highosclang ] ) . as explained in section [ sec : sampling ] , the distribution is the equilibrium distribution of a langevin process ( thermostated hamiltonian dynamics ) with rigid position constraints @xmath443 . choosing whether constraints should be soft or rigid is a modeling choice , and there is no clear consensus on this issue in the current literature .
note however that it is possible to rewrite the remainder of this section by considering the softly constrained potential rather than the rigidly constrained potential , up to an appropriate modification of below , with the help of some fixman corrective potential . by associativity of the conditioning of measures
, the distribution @xmath439 conditioned by a value of the reaction coordinates @xmath444 is given , up to a normalizing factor , by : @xmath445 therefore , considering the marginal probability distribution of the reaction coordinates @xmath446 leads to the following definition of the free energy associated with @xmath447 : @xmath448 the conditional distribution can be decomposed as follows , using the co - area formulas - and the definition of effective momentum : @xmath449 integrating out the momentum in the linear space @xmath450 with scalar product @xmath451 , the free energy can be rewritten as : @xmath452 as a consequence , the free energy @xmath453 can be computed from the generalized rigid free energy : @xmath454 using the following formula , similar to : @xmath455 in the above , @xmath456 is defined similarly to .
the case of molecular constraints can therefore be treated within the general framework considered in this paper , the sampling of the canonical measure @xmath456 and the computation of the rigid free energy being the problems at hand . for systems with molecular constraints ,
the measure sampled by the overdamped langevin dynamics with @xmath457 is the marginal distribution in the position variables of @xmath458 in the special case @xmath382 , namely @xmath459 the rigid free energy which is thus naturally computed with such a dynamics is @xmath460 and the actual free energy is thus recovered by a formula similar to , namely @xmath461 in this section , the average of the constraining force is related to the gradient of the rigid free energy ( or mean force ) .
we also give a similar result for the following generalized rigid free energy : @xmath462 [ p : meanforce ] the constraining force @xmath463 defined in as @xmath464 yields on average the rigid free energy derivative : @xmath465 moreover , for general constraints and the associated generalized free energy , the formula can be extended as follows : the generalized constraining force is @xmath466 where @xmath467 is defined in , and the rigid mean force is @xmath468 where @xmath469 , and @xmath470 is defined in . when @xmath67 verifies @xmath471 , then @xmath472 and @xmath473 .
formulas and are obtained directly by replacing @xmath224 by @xmath474 in lemma [ l : consint ] ( see the appendix ) . the fact that @xmath475 in the tangential case ( namely when @xmath471 ) is a consequence of .
the following lemma gives a momentum - averaged version of the constraining force ( a similar formula exists in the overdamped case , see equations ( 4.8)-(4.9 ) in @xcite , for example ) .
[ l : meanforce_av ] the rigid mean force can be rewritten as : @xmath476 where @xmath477 consider the gaussian distribution @xmath478 defined in : @xmath479 which is the marginal distribution in the momentum variable of the canonical distribution @xmath335 , conditioned by a given @xmath301 .
proving lemma [ l : meanforce_av ] amounts to showing that the average of the constraining force @xmath242 with respect to @xmath480 yields @xmath481 : @xmath482 first , we compute the covariance matrix @xmath483 of the gaussian distribution @xmath484 . since @xmath484 is a centered gaussian distribution , @xmath485 satisfies , for all @xmath486 , @xmath487 denoting @xmath488 , this yields @xmath489 so that @xmath490 this gives @xmath491 averaging over momenta thus leads to the desired result .
free energy derivatives can also be obtained from the lagrange multipliers of the langevin constrained process @xmath55 .
this is very useful in practice since it avoids the computation of second order derivatives of the reaction coordinates which appear in the expressions of @xmath492 and @xmath493 ( see the discussion at the beginning of section [ sec : avg_lagrange ] ) : consider the rigidly constrained langevin process solution of @xmath55 , with associated lagrange multipliers @xmath375 .
assume that @xmath97 , @xmath494 and @xmath299 are bounded functions on @xmath37 , and @xmath495 is strictly positive on @xmath496 ( in the sense of symmetric matrices ) .
then , the almost sure convergence claimed in the introduction holds : @xmath497 a similar result holds for the ` hamiltonian part ' of the lagrange multipliers , defined by : @xmath498 indeed , the following almost sure convergence holds : @xmath499 the estimator based on has a smaller variance than the estimator based on ( or above ) since only the bounded variation part is retained , and the martingale part due to the brownian increments and the dissipation term are subtracted out .
similar results on variance reduction where obtained in the overdamped case in @xcite .
recall the expression of the lagrange multipliers , which can be decomposed as the sum of the constraining force , a dissipation term and a martingale ( fluctuation ) term : @xmath500 the result follows from three facts .
first , the process is ergodic with respect to the equilibrium distribution @xmath335 and averaging @xmath242 yields the rigid free energy derivative in view of proposition [ p : meanforce ] .
this already shows .
second , the gaussian distribution of @xmath335 with respect to momentum variables is centered , which yields : @xmath501 third , the variance of the martingale term can be uniformly bounded as @xmath502 this implies the almost sure convergence @xmath503 see for example theorem 1.3.15 in @xcite .
the fact that averaging the lagrange multiplier in indeed yields the mean force may not be intuitive .
this is actually very much related to the cost interpretation of the lagrange multipliers in optimization , see ( * ? ? ?
* remark 3.29 ) .
estimates of the mean force based on either , or can be obtained .
free energy derivatives can be computed by averaging @xmath504 or @xmath505 with respect to the distribution @xmath335 , for instance using the estimators : @xmath506 or @xmath507 the functions @xmath504 and @xmath505 may thus be called `` rigid local mean forces '' .
note that using the momentum - averaged local mean force @xmath481 instead of the original @xmath242 reduces the variance since the fluctuations of the momentum variable have been averaged out analytically .
table [ tab : comparison_variance_langevin_ti ] below confirms this analysis , although the variance reduction appears to be small in our specific numerical experiment .
assuming the convergence of the constrained splitting scheme -- in the probability distribution sense to the limiting langevin process @xmath55 , the convergence of these estimators to @xmath508 is ensured , when taking first the limit @xmath509 with @xmath510 such that @xmath511 , and then @xmath512 .
free energy derivatives can also be computed using the lagrange multipliers of a langevin constrained process according to or .
this technique avoids the possibly cumbersome computation of second order derivatives @xmath513 of the reaction coordinate , which appear in the expressions of @xmath492 or @xmath481 . besides
, the lagrange multipliers are needed anyway for the numerical integration of the dynamics .
the computation can be performed as before with a longtime simulation of the splitting scheme -- discretizing the langevin process with constraints .
the following approximation formula can for instance be used : @xmath514 where @xmath515 are the lagrange multipliers in the hamiltonian part .
the consistency of this estimator is given by the following proposition .
[ p : consist ] the approximation formula is consistent .
more precisely , the lagrange multipliers @xmath516 in -- are both equivalent when @xmath509 to the constraining force defined in : @xmath517 moreover , the following second order consistency holds for the sum of the lagrange multipliers : @xmath518 together with the variant : @xmath519 the variant , which involves positions and momenta at the beginning and at the end of the hamiltonian steps only , is used in below to estimate the time discretization error in the thermodynamic integration method based on the estimator . for sufficiently small time - steps @xmath80 , the implicit function theorem ensures that the two projection steps associated with the nonlinear constraints in -- have a unique smooth solution .
a taylor expansion with respect to @xmath80 of the position constraints gives @xmath520 where @xmath521 denotes the order @xmath195 differential of @xmath26 computed at @xmath274 and evaluated with the vectors @xmath522 .
we denote @xmath523 then , the fact that @xmath524 and the identity @xmath525 yield the following expansion of @xmath526 in terms of @xmath527 : @xmath528 by time symmetry , the same computation holds for @xmath406 , starting from @xmath322 and by formally replacing @xmath80 by @xmath529 .
this can be double checked by taylor expanding with respect to @xmath80 the position constraints , as done above for @xmath401 .
it thus holds : @xmath530
the sum of the multipliers therefore reads @xmath531 which gives .
now , using the previous calculations , we remark that : @xmath532 \dps p^{n+1/2 } = p^{n+3/4 } + \frac{\dt}{2 } \nabla v ( q^{n+1 } ) - \frac{\dt}{2 } \nabla \xi ( q^{n+1 } ) f_{\rm rgd}^m(q^{n+1},p^{n+1/2 } ) + { \rm o}(\dt ^2 ) .
\end{cases}\ ] ] thus , it holds @xmath533 this gives the claimed second order consistency of the sum of the lagrange multipliers .
let us discuss the convergence of the approximation .
assuming again that the constrained splitting scheme -- converges in the probability distribution sense to the limiting langevin process @xmath55 , the following convergence in probability distribution occurs when @xmath509 and @xmath511 : @xmath534 this shows the convergence of the estimate of the mean force when taking first the limit @xmath509 and then @xmath512 .
when the scheme -- is complemented with a metropolis step ( see algorithm [ a : ghmcconst ] ) , it is possible to prove a result on the longtime limit of trajectorial averages ( _ i.e. _ letting first the number of iterations go to infinity , and then taking the limit @xmath509 ) , upon assuming the irreducibility of the numerical scheme .
indeed , let us consider the markov chain @xmath535 generated by the ghmc scheme in algorithm [ a : ghmcconst ] , and assume ( i ) the irreducibility of the markov chain , and ( ii ) that appropriate rejections outside the set @xmath536 are made in the steps ( 1)-(2)-(4 ) of the algorithm . in particular , the projection steps associated with the nonlinear constraints in step ( 2 ) of algorithm [ a : ghmcconst ] are well defined .
then , by ergodicity , an average of the analytic expression of the local rigid mean force @xmath481 given in yields an estimate of the free energy without time discretization error : @xmath537 if @xmath242 is used instead of @xmath481 , then the mean force is computed with some exponentially small error : almost surely , @xmath538 for some @xmath359 .
the error arising from replacing @xmath539 with @xmath169 is indeed exponentially small in view of ( namely @xmath540 ) and using the fact that the marginal distribution in the @xmath273-variable is gaussian . likewise , for estimates based on lagrange multipliers , the following longtime averaging holds : almost surely , @xmath541 where we have used the estimate on the lagrange multipliers .
the limit @xmath509 is obtained by a dominated convergence argument : @xmath542 note that , due to the metropolis correction in algorithm [ a : ghmcconst ] , the time discretization error in the sampling of the invariant measure is removed .
the only remaining time discretization errors come from ( i ) the approximation of the local mean force by the lagrange multipliers ( this is a second order error ) , and ( ii ) the integration domain being @xmath539 instead of @xmath169 ( as discussed above , this is an exponentially small error in @xmath80 ) . in conclusion
, the left - hand side of is an approximation of @xmath543 up to a @xmath544 error term .
finally , let us emphasize that free energy derivatives can be computed with the estimator within the overdamped langevin framework , using the scheme and the expressions -- of proposition [ p : langtooverd ] .
let us recall that the latter are equivalent to the scheme -- with fluctuation - dissipation matrices satisfying @xmath545 .
this leads to the original free energy estimator ( recall that , for the overdamped dynamics , @xmath72 is equipped with the scalar product associated with the identity matrix ) : @xmath546 which can be seen as a variant of the variance reduced estimator proposed directly for the overdamped scheme in @xcite : @xmath547 the rigorous justification of the consistency of in the limit @xmath509 follows from the results of @xcite .
see also section [ sec : time_continuous_limit_ovd ] below for similar results .
we consider a system composed of @xmath0 particles in a 2-dimensional periodic box of side length @xmath548 , interacting through the purely repulsive wca pair potential , which is a truncated lennard - jones potential : @xmath549 + \varepsilon & \quad { \rm if \ } r \leq r_0 , \\ 0 & \quad { \rm if \ } r > r_0 , \end{array } \right.\ ] ] where @xmath550 denotes the distance between two particles , @xmath551 and @xmath299 are two positive parameters and @xmath552 . among these particles ,
two ( numbered 1 and 2 in the following ) are designated to form a dimer while the others are solvent particles . instead of the above wca potential ,
the interaction potential between the two particles of the dimer is a double - well potential @xmath553 ^ 2,\ ] ] where @xmath554 and @xmath555 are two positive parameters .
the total energy of the system is therefore , for @xmath556 with @xmath557 , @xmath558 see @xcite for instance for other computational studies using this model .
the potential @xmath559 exhibits two energy minima , one corresponding to the compact state where the length of the dimer is @xmath560 , and one corresponding to the stretched state where this length is @xmath561 .
the energy barrier separating both states is @xmath554 .
the reaction coordinate used to describe the transition from the compact to the stretched state is the normalized bond length of the dimer molecule : @xmath562 where @xmath563 and @xmath564 are the positions of the two particles forming the dimer .
the compact state ( resp . the stretched state ) corresponds to the value @xmath565 ( resp .
@xmath566 ) of the reaction coordinate .
the inverse temperature is set to @xmath567 , with @xmath568 particles ( @xmath569 solvent particles and the dimer ) with solvent density @xmath570 , since there are @xmath569 solvent particles in a square box of side length @xmath571 with @xmath572 .
the parameters describing the wca interactions are set to @xmath573 and @xmath574 , and the additional parameters for the dimer are @xmath575 and @xmath576
. for this system , @xmath379 and @xmath577 is constant , so that the rigid free energy @xmath578 is equal to the free energy @xmath84 .
the mean force is estimated at the values @xmath579 , with @xmath580 , @xmath581 and @xmath582 , by ergodic averages obtained with the projected dynamics with metropolis correction ( algorithm [ a : ghmcconst ] , where in the simple case considered here , the fluctuation - dissipation part can be integrated exactly ) . for each value of @xmath38
, we integrate the dynamics on a time @xmath583 with a step size @xmath584 , using a scalar friction coefficient @xmath585 .
the resulting mean force profile is presented in figure [ fig : ti_lang_1 ] , together with the associated free energy profile .
top : estimated mean force .
bottom : corresponding free energy profile .
, title="fig:",width=340 ] top : estimated mean force .
bottom : corresponding free energy profile .
, title="fig:",width=340 ] figure [ fig : ti_lang_2 ] compares the analytical constraining force @xmath586 and the lagrange multipliers , see proposition [ p : consist ] . in figure
[ fig : ti_lang_2 ] , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
it can be seen that the difference between @xmath586 and the lagrange multipliers is small in any cases , though somewhat larger for the lowest values of @xmath26 .
top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] it can be checked numerically that the differences @xmath592 and @xmath593 are indeed of order @xmath594 , and that the difference @xmath595 is indeed of order @xmath596 ( by computing the average of these elementary differences for various step sizes ) .
the lagrange multipliers are in any case very good approximations to the constraining force @xmath492 .
let us finally discuss the efficiency of the different estimators of the mean force , in terms of their variances .
they can be written as the empirical average of the following random sequences : @xmath597 where @xmath598 are given by the numerical scheme -- .
the correlations in time ( between the iterates ) are very similar for the three methods , and we therefore simply compute the variance over all the samples .
table [ tab : comparison_variance_langevin_ti ] compares the so - obtained standard errors over @xmath588 time - steps with @xmath584 ( simulation time @xmath599 for each value of the reaction coordinate ) .
the results show that the different estimators are more or less equivalent .
this is related to the fact that the essential source of variance comes from the sampling of the positions , and not the sampling of the velocities .
note however that , for the smallest value of the reaction coordinate , the estimator based on the averaged local mean force @xmath600 appears to be better in terms of variance .
.standard error ( square - root of the variance ) of three mean force estimators , with correlations in time neglected , for different values @xmath38 of the reaction coordinate . [ cols="^,^,^,^ " , ]
this section presents nonequilibrium hamiltonian and langevin dynamics with time - evolving constraints .
we thus consider @xmath223 solution to the dynamics @xmath96 , which we recall for convenience : @xmath601 d p_t & = -\nabla v ( q_t ) \,dt -\gamma_p(q_t ) m^{-1 } p_t \ , dt+ \sigma_p(q_t ) \,d w_t + \nabla
\xi(q_t ) \ , d \lambda_t , \\[6pt ] \xi(q_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.\ ] ] we prove in particular the fluctuation identity , see below .
recall ( see ) that , for simplicity , we assume in this section that the fluctuation - dissipation matrices are assumed to be of the form @xmath602 with @xmath603 . at variance with the previous sections , we do _ not _ assume that @xmath495 is strictly positive .
actually , @xmath604 corresponds to an interesting case : the deterministic hamiltonian dynamics . to our knowledge
, the standard work fluctuations derived so far ( except for our previous work @xcite ) apply only to the case of time - dependent hamiltonians .
it is possible to consider transitions in the values of some reaction coordinate in this framework upon resorting to steered molecular dynamics techniques . in this case ,
a penalty term @xmath605 ( with @xmath551 small ) is used in the energy of the system to `` softly '' constrain the system to remain close to the submanifold @xmath606 at time @xmath607 .
however , it is observed in practice that the statistical fluctuations increase with smaller @xmath551 ( see @xcite ) .
we propose instead to replace the stiff constraining potential @xmath608 by a projection onto the submanifold @xmath417 .
this is reminiscent of the replacement of stiff constrained langevin dynamics by rigidly constrained ones , see remark [ rem : highosclang ] .
this section is organized as follows .
we first define the generalized free energy which is naturally computed with @xmath96 , and relate it to the standard free energy in section [ sec : langti_fe ] . then , we give some precisions on the nonequilibrium dynamics @xmath96 in section [ sec : generators_jarz ] .
next , we prove an appropriate version of the jarzynski - crooks fluctuation equality in section [ sec : jarz_lang_cons ] . a numerical discretization of the nonequilibrium dynamics is proposed in section [ sec : num_jarz ] , together with various approximations of the work .
in particular , we propose a numerical strategy to obtain a jarzynski - crooks identity without time discretization error ( see section [ sec : discrete_jarz ] ) .
we then consider the overdamped limit when the mass matrix @xmath5 goes to 0 ( see section [ sec : ovd_limit_disc ] ) . finally , in section [ sec : num_res_jarz ] , we present some numerical results for the model system already considered in section [ sec : simple_example_wca ] . for @xmath223 solution to the langevin dynamics @xmath96 ,
the reaction coordinate evolution @xmath609 implies that @xmath610 , so that , at each time @xmath53 , the system @xmath223 belongs to the state space @xmath611 . as a consequence ,
the free energy difference computed in this section by the jarzynski relation without correction ( see below ) is in fact the generalized rigid free energy @xmath612 defined in , in the special case @xmath152 : @xmath613 the latter free energy is associated to the normalization constant @xmath614 of the distribution @xmath615 defined by .
the generalized rigid free energy can be explicitly related to the usual free energy as follows .
first , remark that , for a fixed @xmath274 , @xmath616 in the above , the change of variable @xmath617 has been used , in the space @xmath618 note that @xmath619 can be interpreted as the kinetic energy of the reaction coordinate @xmath26 . using the decomposition of measures and the above calculations ,
an alternative expression of the generalized free energy is : @xmath620 where , as usual , @xmath621 denotes a generic constant ( independent of @xmath38 ) whose value may vary from line to line . as a consequence ,
the standard free energy is easily recovered from the generalized free energy , using relations similar to . indeed , using , and with computations similar to the ones leading to
, the difference of the two free energies writes : @xmath622 in practical nonequilibrium computations , the profile @xmath623 can then be computed by adding a corrector to the work value in the jarzynski estimator computing @xmath624 .
this yields the identity mentioned in the introduction and proved below ( see the discussion after theorem [ th : crookslangcons ] ) .
the explicit expression of the lagrange multipliers in @xmath96 is obtained by a computation similar to for the case without switching , by differentiating twice the constraints over time : @xmath625 in view of the special structure of @xmath232 , this leads to @xmath626 the expression does not depend on the fluctuation - dissipation tensors @xmath232 .
this leads to simplified computations and motivates the special form of the latter matrices .
the momentum evolution @xmath96 thus simplifies as @xmath627 let us denote by @xmath628 the generator of the forward dynamics @xmath629 defined in @xmath96 .
the latter has a backward switching version , @xmath630 obtained by using a time reversed switching @xmath631 , and by reversing the momentum first in the initial condition , and then reversing them back after the time evolution ( see @xcite for more general backward dynamics ) .
more precisely , the backward dynamics can be defined through its generator @xmath632 where @xmath633 is the generator of the forward process at time @xmath634 , and @xmath635 is the momentum flip operator with @xmath636 .
thus @xmath637 is solution of the forward evolution equation @xmath96 with a switching schedule @xmath631 .
therefore , the time evolution of the backward dynamics is given by @xmath638 d
p^{\rm b}_{t'}= \nabla v(q^{\rm b}_{t ' } ) \ , dt ' -\gamma_p(q^{\rm b}_{t ' } ) m^{-1 } p^{\rm b}_{t ' } \ , dt'+ \sigma_p(q^{\rm b}_{t ' } ) \
, d w_{t'}^{\rm b } + \nabla \xi(q^{\rm b}_{t ' } ) \
, d \lambda_{t'}^{\rm b } , \\[6pt ] \xi(q^{\rm b}_{t ' } ) = z(t - t ' ) .
\end{cases}\ ] ] in the following proposition , the expressions of @xmath628 and @xmath639 are explicitly written .
[ prop : generators_noneq ] consider @xmath640 .
then , the generator of the forward process @xmath96 at time @xmath86 $ ] reads : @xmath641 and the generator of the backward process at time @xmath642 $ ] reads : @xmath643 where @xmath644 is the fluctuation - dissipation operator defined in .
first , let us consider the terms in @xmath96 arising from the hamiltonian evolution and from the switching ( _ i.e. _ without fluctuation - dissipation , which amounts to setting @xmath645 and @xmath646 in @xmath96 ) .
since during this dynamics @xmath647 , yields : @xmath648 so that , using , @xmath649 with , we then obtain : @xmath650 now , the hamiltonian part of the switched dynamics @xmath96 ( see also ) can be recognized in , so that the generator @xmath651 when @xmath652 reads : for any smooth test function @xmath224 , @xmath653 the full expression of the generator @xmath654 is then obtained by adding the terms arising from the fluctuation - dissipation .
these terms are directly obtained from the terms involving @xmath495 and @xmath655 in , as in the proof of proposition [ s : p : lconstgen ] .
the generator of the backward switching process given by can be obtained from similar computations .
first , the thermostat parts in and in @xmath96 are the same .
consider now the hamiltonian part ( obtained by taking @xmath652 ) in the dynamics . by definition of the backward dynamics , and the expression of the forward dynamics , the hamiltonian part reads @xmath656 so that @xmath657 this gives . before stating the main result of this section ( theorem [ th : crookslangcons ] below ) , we need to introduce a notion of work .
this quantity is most conveniently defined for deterministic dynamics , but the corresponding definition is also valid for stochastic dynamics .
we define the work @xmath658 associated with the constraining force @xmath659 in @xmath96 as the physical displacement multiplied by the force : @xmath660 by convention , @xmath661 . in the above computations
, we used successively the fact that @xmath662 , and then @xmath663 are differentiable processes , so that stratonovitch and it integrations are equivalent .
let us introduce the deterministic version of the nonequilibrium process @xmath96 ( _ i.e. _ @xmath652 ) : @xmath664 d \tilde{p}_t & = -\nabla v ( \tilde{q}_t ) \,dt + \nabla \xi(\tilde{q}_t ) \ , d \tilde{\lambda}_t , \\[6pt ] \xi(\tilde{q}_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.\ ] ] and denote by @xmath665 the associated flow between time @xmath86 $ ] and @xmath666 $ ] .
the work can now be written out more explicitly using the following lemma : the infinitesimal variation of the work reads : @xmath667 where for all @xmath86 $ ] and all @xmath668 , @xmath669 the total exchanged work is then a time integral associated with the path @xmath629 , and is denoted by : @xmath670 note that the expression can be interpreted as the energy variation of the system during the switching when the stochastic thermostat is turned off .
the expression of the lagrange multipliers in yields : @xmath671 moreover , gives : @xmath672 where in the last line we have used @xmath673 .
this gives . to prove
, we compute the variations of the energy @xmath674 for @xmath675 solution of with initial condition @xmath67 : @xmath676 the last equality is obtained using the computation of the lagrange multipliers in .
this yields .
we are now in position to state the main result of this section .
[ th : crookslangcons ] consider the normalization @xmath614 for the canonical distribution @xmath615 defined in .
denote by @xmath677 the solution of the forward langevin dynamics @xmath96 with initial conditions distributed according to @xmath678 and by @xmath679 the solution of the backward langevin process with initial conditions distributed according to @xmath680 then , the following jarzynski - crooks identity holds on @xmath681 $ ] : for any bounded path functional @xmath682}$ ] , @xmath683}\left(\{q_t , p_t\}_{0 \leq t \leq t}\right ) \ ,
{ \rm e}^{-\beta\w_{0,t}\left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } \right ) } } { \e { \left ( \ph^{\rm r}_{[0,t]}\left(\{q^{\rm b}_{t'},p^{\rm b}_{t'}\}_{0 \leq t ' \leq t } \right ) \right ) } } , \ ] ] where @xmath684 denotes the composition with the operation of time reversal of paths : @xmath685}^{\rm r}\big(\ { q^{\rm b}_{t'},p^{\rm b}_{t'}\}_{0 \leq t ' \leq t}\big ) = \ph_{[0,t]}\big(\ { q^{\rm b}_{t - t},p^{\rm b}_{t - t } \}_{0 \leq t \leq t}\big).\ ] ] note that the theorem still holds in the hamiltonian case , _
i.e. _ when @xmath686 .
the choice @xmath682 } = 1 $ ] in leads to the following work fluctuation identity : @xmath687 } ) } \right ) \big].\ ] ] besides , upon choosing a path functional @xmath688 , it is possible to obtain a family of free energy estimators , parameterized by @xmath689 and where both forward and backward paths are weighted by the exponential of some work .
moreover , the standard crooks equality on ratios of probability density functions of work values is also a consequence of , see section 4.2.2 in @xcite .
note also that the choice @xmath682}(q , p ) = \phi(q_t , p_t)$ ] leads to the following representation of the canonical distribution @xmath690 : @xmath691}\right ) } } \right ) } } { \e { \left ( { \rm e}^{-\beta\w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } } \right ) } } = \int_{\manq_{\xi , v_\xi}(z(t),\dot{z}(t ) ) } \phi(q , p ) \ , \mu_{\manq_{\xi , v_\xi}(z(t),\dot{z}(t))}(dq\ , dp ) .\ ] ] the usual free energy profile @xmath65 can therefore be computed using the relations - presented in the introduction .
indeed , equation ( see below ) can be proved by combining and as follows : @xmath692 } ) } \right ) \big ] \nonumber \\ & = -\frac1\beta \ln \e { \left ( ( \det g_m(q_t ) ) ^{-1/2 } { \rm e}^{\frac{\beta}{2 } \dot{z}(t)^t g_m^{-1}(q_t ) \dot{z}(t)}\ , { \rm e}^{-\beta\w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } } \right ) } \nonumber \\ & \quad + \frac1\beta \ln \e { \left ( ( \det g_m(q_0 ) ) ^{-1/2 } { \rm e}^{\frac{\beta}{2 } \dot{z}(0)^t g_m^{-1}(q_0)\dot{z}(0 ) } \right ) } \nonumber \\ & = -\frac1\beta \ln \left ( \frac { \e\left(\rme^{-\beta \left [ \w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } + c(t , q_t ) \right ] } \right ) } { \e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right ) , \label{eq : identity_to_approximate}\end{aligned}\ ] ] where the corrector @xmath693 is defined in : @xmath694 this leads to the following relation : @xmath695 } \right)}{\e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right),\ ] ] estimators of the free energy based on can then be constructed , see chapter 4 in @xcite for a review . before turning to the proof of theorem [ th : crookslangcons ] , we first give the general lemma which enables to deduce the jarzynski - crooks fluctuation identity from a _ nonequilibrium detailed balance condition _
( similar to the one presented in @xcite for switchings arising from a time - dependence in the hamiltonian ) .
[ lem : jarz_gen ] let @xmath696 ( resp .
@xmath697 ) be a markov process with infinitesimal generator @xmath698 ( resp .
@xmath699 ) and initial conditions distributed according to ( resp . ) .
let us assume that the following nonequilibrium detailed balance condition is satisfied : for any two smooth test functions @xmath259 , @xmath260 , @xmath700 then the jarzynski - crooks fluctuation identity holds .
we use in this proof the short - hand notation @xmath701 , @xmath702 and @xmath703 for the partition function @xmath614 , the ( unnormalized ) distribution @xmath704 and the submanifold @xmath611 respectively .
let us introduce the following weighted transition operators : for any bounded test function @xmath224 , @xmath705 } \right ) } } \ , \big | \ , ( q_t , p_t ) = ( q , p ) \big ) , \label{eq : pfwd}\\ p^{\rm b}_{t',t}(\ph)(q , p ) & = \e\big(\ph(q^{\rm b}_{t},p^{\rm b}_{t})\ , \big | \ , ( q^{\rm b}_{t'},p^{\rm b}_{t'})=(q , p ) \big ) , \label{eq : pbwd}\end{aligned}\ ] ] where @xmath696 ( resp .
@xmath697 ) is a markov process with infinitesimal generator @xmath698 ( resp .
@xmath699 ) , and @xmath706 .
we assume that these operators are well defined and smooth with respect to time for sufficiently smooth test functions defined in an open neighborhood of @xmath611 and @xmath707 respectively ( for any @xmath708 $ ] ) .
the transition operators satisfy the following backward kolmogorov evolution equations : @xmath709 p^{\rm f}_{t , t } = { \rm i d } , \end{cases } \quad \begin{cases } \partial_{t ' } p^{\rm b}_{t',t } = -{\mathcal l}^{\rm b}_{t ' } p^{\rm b}_{t',t } , \\[6pt ] p^{\rm b}_{t , t } = { \rm id}. \end{cases}\ ] ] consider now two test functions @xmath710 and @xmath711 .
the balance condition implies @xmath712 integrating this equality on @xmath681 $ ] yields @xmath713 which is the crooks identity for path functionals of the form @xmath714}(q , p ) = \ph_0(q_0,p_0 ) \ , \ph_t(q_t , p_t).\ ] ] indeed ,
@xmath715 } ) } \big ] , \ ] ] while @xmath716.\ ] ] then , using the markov property of the forward and backward processes , crooks identity can be extended to finite - dimensional path functionals of the form : @xmath717}(q , p ) = \ph_0(q_{0},p_0 ) \dots \ph_k(q_{t_k},p_{t_k } ) \dots \ph_{k}(q_{t},p_t)\ ] ] with @xmath718 by repeatedly using a variant of on time subintervals @xmath719 $ ] ( see the proof of theorem 4.10 in @xcite for further precisions ) .
this allows to conclude since finite dimensional time marginal laws characterize the distribution on continuous paths , see for instance @xcite .
we are now in position to write the by lemma [ lem : jarz_gen ] , it is sufficient to prove the nonequilibrium detailed balance for the markov processes @xmath696 and @xmath697 , solutions to @xmath96 and respectively , with generators @xmath654 and @xmath720 defined by and .
first , using lemma [ l : consint ] , we compute the variation of the unnormalized canonical equilibrium distribution with constraints with respect to the switching : @xmath721 on the other hand , and proposition [ prop : generators_noneq ] give @xmath722 now , can be verified in two steps .
first , the last two terms in ( the thermostat terms ) cancel out after integration with respect to @xmath723 thanks to the detailed balance condition
. then , an integration of with respect to @xmath724 gives , in view of and , @xmath725 which is indeed .
note that the time - regularity on the evolution semi - groups - required to make these computations rigorous is proved in the overdamped case in the proof of theorem a.5 in @xcite .
a similar proof can be carried out for constrained langevin equations . in this section , a numerical scheme for the nonequilibrium dynamics @xmath96 and the associated free energy estimator
are presented . as for langevin processes with constraints ( section [ sec : consnum ] ) , a splitting between the hamiltonian part and the thermostat part of the dynamics @xmath96 leads to a simple and natural scheme ( see -- below ) .
note that a consistent numerical scheme in the case of hamiltonian dynamics can be obtained by considering only ( this corresponds to @xmath726 ) .
besides , we propose a discrete jarzynski - crooks identity without time discretization error , see section [ sec : discrete_jarz ]
. the reaction coordinate path is first discretized as @xmath727 where @xmath728 is the number of time - steps . for simplicity ,
equal time increments are used , so that @xmath729 and @xmath730 . the deterministic hamiltonian part in the equations of motion @xmath96 with switched position constraints
@xmath731 can be integrated by a velocity - verlet algorithm with constraints similar to .
the fluctuation - dissipation term in @xmath96 can be integrated similarly to the constrained case without switching - , using an ornstein - uhlenbeck process on the momentum variable approximated by a midpoint euler scheme . in conclusion ,
the splitting scheme for the langevin dynamics with time - evolving constraints reads as follows : take initial conditions @xmath732 distributed according to @xmath733 and iterate on @xmath734 : @xmath735 & \begin{cases } \dps p^{n+1/2 } = p^{n+1/4 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n } ) } + \nabla \xi(q^n ) \lambda^{n+1/2 } , & \\[6pt ] \dps q^{n+1 } = q^{n } + \dt \ m^{-1 } p^{n+1/2 } , & \\[6pt ] \dps \xi(q^{n+1 } ) = z(t_{n+1 } ) , & ( c_q ) \\[6pt ] \dps p^{n+3/4 } = p^{n+1/2 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n+1 } ) } + \nabla \xi(q^{n+1 } ) \lambda^{n+3/4},&\\[6pt ] \dps \nabla \xi ( q^{n+1})^{t } m^{-1 } p^{n+3/4 } = \frac { \dps z(t_{n+2})- z(t_{n+1})}{\dps \dt } , & ( c_p ) \end{cases}\label{eq : verletconstswitched}\\ & \begin{cases } \dps p^{n+1 } = p^{n+3/4 } -\frac{\dt}{4 } \gamma_p(q^{n+1 } ) m^{-1}(p^{n+3/4}+p^{n+1 } ) \\
\dps \phantom{p^{n+1 } = } + \sqrt{\frac{\dt}{2 } } \sigma_p(q^{n+1 } ) { \mathcal g}^{n+1/2 } , \end{cases}\label{eq : flucdissconstjarz2}\end{aligned}\ ] ] where @xmath736 and @xmath737 are sequences of i.i.d .
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
note that the momenta obtained from -- satisfy @xmath738 so that constraints on momenta are automatically enforced , and no lagrange multiplier is needed in and .
we comment in the subsequent sections on the different parts of the scheme .
the lagrange multipliers @xmath401 are associated with the position constraints @xmath315 , and the lagrange multipliers @xmath406 are associated with the velocity constraints @xmath317 . in @xmath318
, the velocity of the switching at time @xmath739 is discretized as : @xmath740 the latter choice is motivated by the following observation : the position after one step of an unconstrained motion , given by @xmath741 already satisfies @xmath315 up to error terms of order two with respect to @xmath80 .
indeed , using : @xmath742 this property is useful to ensure a fast convergence of the numerical algorithm solving the nonlinear constraints @xmath315 .
the numerical flow associated with is denoted in the sequel as @xmath743 ( q^n , p^{n+1/4 } ) & \mapsto & ( q^{n+1},p^{n+3/4 } ) \end{array}\right.\ ] ] it can be proven that @xmath744 is a symplectic map .
the proof is indeed exactly the same as for the symplecticity of the classical rattle scheme , see ( * ? ? ?
* sections vii.1.3 ) for an explicit computation for symplectic euler and ( * ? ? ?
* sections vii.1.4 ) for an extension to rattle . as a consequence
, @xmath744 transports the phase space measure @xmath745 to the phase space measure @xmath746 . in practice , may be rewritten in a form more suited to numerical computations . of course
, similar considerations hold for . since @xmath747 and @xmath748 ,
is equivalent to : @xmath749 where the lagrange multiplier @xmath329 is associated with the constraint @xmath318 .
the equivalence between and can be checked by multiplying by @xmath750 and using .
the lagrange multiplier @xmath329 in is obtained by multiplying the above equation by @xmath751 , and solving the following linear system : @xmath752 this system is well posed .
indeed , the matrix @xmath753 can be rewritten as @xmath754 with @xmath755 .
both @xmath5 and @xmath298 are symmetric and non - negative , so that @xmath267 is symmetric , positive and invertible .
finally , the invertibility of @xmath754 follows from the invertibility of @xmath34 . in the special case
when @xmath298 and @xmath5 are equal up to a multiplicative constant , the numerical integration can be simplified using the explicit formula and the method described below , which still holds for the tangential part of the momentum .
see section [ sec : num_res_jarz ] below for further precisions .
the splitting scheme for the backward langevin dynamics with time - evolving constraints reads as follows : denote @xmath756 , take initial conditions @xmath757 distributed according to @xmath758 and iterate on @xmath759 , @xmath760 &\begin{cases } \dps p^{{\rm b},n'+1/2 } = p^{{\rm b},n'+1/4 } + \displaystyle{\frac{\dt}{2 } \nabla v ( q^{{\rm b},n ' } ) } + \nabla \xi(q^{{\rm b},n ' } ) \lambda^{{\rm b},n'+1/2 } , & \\[6pt ] \dps q^{{\rm b},n'+1 } = q^{{\rm b},n ' } - \dt \ m^{-1 } p^{{\rm b},n'+1/2 } , \\[6pt ] \dps \xi(q^{{\rm b},n'+1 } ) = z(t_{n_t - n'-1 } ) , & ( c_q ) \\[6pt ] \dps p^{{\rm b},n'+3/4 } = p^{{\rm b},n'+1/2 } + \displaystyle{\frac{\dt}{2 } \nabla v ( q^{{\rm b},n'+1 } ) } + \nabla \xi(q^{{\rm b},n'+1 } ) \lambda^{{\rm b},n'+3/4},&\\[6pt ] \dps \nabla \xi ( q^{{\rm b},n'+1})^{t } m^{-1 } p^{{\rm b},n'+3/4 } = \frac { \dps z(t_{n_t - n ' } ) - z(t_{n_t - n ' - 1 } ) } { \dps \dt } , & ( c_p ) \end{cases}\label{eq : verletconstswitchedbck}\\ & \begin{cases } \dps p^{{\rm b},n'+1 } = p^{{\rm b},n'+3/4 } -\frac{\dt}{4 } \gamma_p(q^{{\rm b},n'+1 } ) m^{-1}(p^{{\rm b},n'+3/4}+p^{{\rm b},n'+1 } )
\\ \dps \phantom{p^{{\rm b},n'+1 } = } + \sqrt{\frac{\dt}{2 } } \sigma_p(q^{{\rm b},n'+1 } ) { \mathcal g}^{{\rm b},n'+1/2 } , \end{cases}\label{eq : flucdissconstjarzbck2}\end{aligned}\ ] ] where @xmath761 and @xmath762 are sequences of i.i.d .
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
the numerical flow associated with is denoted @xmath763 ( q^{{\rm b},n'},p^{{\rm b},n'+1/4 } ) & \mapsto & ( q^{{\rm b},n'+1},p^{{\rm b},n'+3/4 } ) \end{array}\right.\ ] ] where we recall @xmath764 .
assuming that the flow @xmath744 given by and @xmath765 are both well - defined , the following reversibility property is easily checked ( extending the symmetry property of the standard rattle scheme , see for instance ( * ? ? ?
* section vii.1.4 ) ) : @xmath766 the work can be approximated using the lagrange multipliers in : @xmath767 for @xmath768 . the ( formal ) consistency of the work discretization in the time continuous limit is a direct consequence of the work expression .
an estimator of the free energy profile is then obtained by using @xmath769 independent realizations of the switching process , computing the work @xmath770 for each realization @xmath771 ( with the numerical trajectories obtained from the numerical scheme -- and i.i.d .
initial conditions sampled according to @xmath733 ) , and approximating , rewritten up to an unimportant additive constant ( independent of @xmath98 ) , as @xmath772 } \right),\ ] ] with empirical averages such as @xmath773 \right).\ ] ] in the above , the discretization @xmath774 of the corrector is @xmath775 we refer to chapter 4 in @xcite for more background on free energy estimators for nonequilibrium dynamics . in particular , it is possible to compute a work associated with the backward switching from the lagrange multipliers in , and to resort to bridge estimators ( see section 4.2.3 in @xcite ) .
however , using approximations such as in the jarzynski - crooks identity introduces a time discretization error .
we show in the next section how to eliminate this error .
it turns out that a discrete version of the jarzynski - crooks identity can be obtained .
this enables the estimation of free energy differences using nonequilibrium simulation _ without time discretization error_. the discrete equality below may be seen as an extension of the corresponding equality obtained for transitions associated with time - dependent hamiltonians and performed with metropolis - hastings dynamics ( see @xcite and remark 4.5 in @xcite ) . for this purpose
, we consider a discretization of the work @xmath776 using the interpretation of the work as the energy variation of the hamiltonian part of the langevin dynamics .
this leads to the following definition of the work at the discrete level : @xmath777 for @xmath768 .
this work discretization leads to a jarzynski - crooks identity without time discretization error .
[ eq : jarz_disc ] consider the distribution @xmath615 and its normalization @xmath614 defined in .
denote by @xmath778 the solution of the forward discretized langevin dynamics -- with initial conditions distributed according to @xmath779 and by @xmath780 the solution of the discretized backward langevin dynamics -- distributed according to @xmath781 then , the following jarzynski - crooks identity holds on @xmath782 $ ] : for any bounded discrete path functional @xmath783}$ ] , @xmath784}\left(\{q^n , p^n\}_{0 \leq n \leq n_t}\right ) \ , { \rm e}^{-\beta\w^{n_t } } \right ) } } { \e { \left ( \ph^{\rm r}_{[0,n_t]}\left(\{q^ { { \rm b } , { n ' } } , p^ { { \rm b } , { n ' } } \}_{0 \leq n ' \leq n_t } \right ) \right ) } } , \ ] ] where @xmath785 is computed according to , and @xmath684 denotes the composition with the operation of time reversal of paths : @xmath786}^{\rm r}\big(\ { q^ { { \rm b},{n ' } } , p^{{\rm b } , { n ' } } \}_{0 \leq n ' \leq n_t}\big ) = \ph_{[0,n_t]}\big(\ { q^ { { \rm b},{n_t - n } } , p^{{\rm b } , { n_t - n } } \}_{0 \leq n \leq n_t}\big).\ ] ] the ( formal ) consistency of the work discretization in the time continuous limit is a direct consequence of the work expression .
free energy estimators based on the identity are obtained as described in section [ sec : work_discretization ] .
let us emphasize once again that there is no error related to the finiteness of the time - step @xmath80 in this estimator , and that the only source of approximation is due to the statistical error . with a slight abuse of notation ,
we denote in the same way the random variables @xmath787 , @xmath788 , etc . in -- or -- , and the integration variables in the definition of probability distributions .
we divide the proof into three steps .
step 1 : the phase space conservation of @xmath744 and @xmath765 and the reversibility property imply @xmath789 step 2 : the probability distribution of @xmath790 given @xmath787 in the discretization of the fluctuation - dissipation part is denoted @xmath791 .
the scheme is a mid - point discretization of an ornstein - uhlenbeck process , which can be rewritten by decomposing the orthogonal and tangential updates of the momentum : @xmath792 where @xmath793 , and @xmath794 .
the markov chain induced by the parallel part of the momentum is the same as the one induced by the scheme ( or ) defined in section [ sec : consnum ] .
the latter verifies a detailed balance equation ( both in the plain sense and up to momentum reversal ) with respect to the stationary measure @xmath333 defined by ( see sections 2.3.2 and 3.3.5 in @xcite ) .
we recall that this measure is defined as the kinetic probability distribution in the momentum variable of the canonical distribution @xmath335 on the tangential space , conditioned by a given @xmath301 . adding the ( invariant ) orthogonal part of the momentum , the following detailed balance condition is satisfied : @xmath795 step @xmath195 : denote by @xmath796 the probability distribution of the variables @xmath797 given the variables @xmath787 in the scheme -- ; and by @xmath798 the probability distribution of the variables @xmath799 given the variables @xmath800 in the scheme -- . the splitting structure yields : @xmath801 as well as @xmath802 combining the detailed balance conditions and of steps @xmath167 and @xmath172 , and using the decomposition of phase space measures
, it follows @xmath803 which can be seen as the jarzynski - crooks identity over one time - step . iterating the argument
, it is easy to obtain : @xmath804 which yields .
the splitting scheme -- can be used in the overdamped regime , using the method of proposition [ p : langtooverd ] , _ i.e. _ by choosing @xmath805 which implies @xmath806 and @xmath807 . for this choice of parameters , the continuous limit of the numerical scheme
is the following variant of the stochastic differential equation : @xmath808 where @xmath809 is an adapted stochastic process such that @xmath609 .
we then obtain the following jarzynski - crooks relation for discretized overdamped dynamics , _ without time discretization error_. [ p : langtooverd_jarz ] suppose that the relation is satisfied . with a slight abuse of notation ,
the mass matrix and the friction matrix are rewritten as @xmath387 and @xmath388 with @xmath389 . then the splitting scheme -- yields the following euler discretization of the overdamped langevin constrained dynamics : @xmath810 \xi(q^{n+1 } ) = z(t_{n+1 } ) , \end{cases}\ ] ] where @xmath391 are independent and identically distributed centered and normalized gaussian variables , and @xmath392 are the lagrange multipliers associated with the constraints @xmath811 . in the same way , the backward process -- yields the following euler scheme : @xmath812 \xi(q^{{\rm b},n'+1 } ) = z(t_{n_t - n'-1 } ) .
\end{cases}\ ] ] consider the work update @xmath813 for @xmath768 , where @xmath814 with @xmath815 , and the scheme is rewritten as : @xmath816 \dps q^{n+1 } = q^{n } + 2 p^{n+1/2 } , \\[6pt ] \dps \xi(q^{n+1 } ) = z(t_{n+1 } ) , \quad ( c_q ) \\[6pt ] \dps p^{n+3/4 } = p^{n+1/2 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n+1 } ) } + \nabla \xi(q^{n+1 } ) \lambda^{n+3/4},\\[6pt ] \dps \nabla \xi ( q^{n+1})^{t } p^{n+3/4 } = \frac { z(t_{n+2})- z(t_{n+1})}{2 } , \quad ( c_p ) \end{cases}\ ] ] then the jarzynski - crooks relation holds under the assumptions and on the initial conditions of the schemes and respectively .
the proof is a direct consequence of the reformulation of into , and a direct application of theorem [ eq : jarz_disc ] with the parameters .
note that the free energy estimator @xmath817 } \right),\ ] ] based on the work and the corrector @xmath818 is exact ( there is no time discretization error ) .
this free energy estimator can be seen as a variant of the estimator proposed in @xcite , which was derived directly for the scheme , and reads ( up to an unimportant additive constant ) : @xmath819 } \right),\ ] ] where the work is defined as @xmath820 with @xmath821 and the modified corrector is defined without the kinetic energy term : @xmath822 there is a bias due to the time discretization error in the estimator , which can be removed upon following the procedure described in proposition [ p : langtooverd_jarz ] . in this section , we would like to discuss the consistency of three free energy estimators introduced above : - ( based on the direct discretization of the overdamped dynamics proposed in @xcite ) , - ( which uses the lagrange multipliers to approximate the work ) and - ( based on the discrete jarzynski equality ) .
the limiting continuous - in - time version of the jarzynski relation is : @xmath823 where the work for the overdamped dynamics reads ( see @xcite ) : @xmath824 with @xmath825 the consistency of - with - was already proven in @xcite . concerning the consistency of @xmath826 with @xmath827 ( see and ) , note that in the overdamped scaling ( @xmath828 ) , the difference @xmath829 vanishes when @xmath509 .
this difference can therefore be neglected when analyzing the consistency of the scheme in the continuous - in - time limit .
we henceforth concentrate on the consistency of the works and with . in the sequel , we denote the anticipating stochastic integration of the integrand @xmath830 with respect to @xmath831 by @xmath832 where @xmath833 is the stratonovitch symmetric integration , and @xmath834 the it integration .
the symbol @xmath835 denotes the formal time continuous limit .
[ [ consistency - of . ] ] consistency of .
+ + + + + + + + + + + + + + + + let us justify the consistency of the work expression with .
remark that the lagrange multipliers in verify : @xmath836 \label{eq : lag_od_jarz_1}\ ] ] and @xmath837 as well as @xmath838 .
\label{eq : lag_od_jarz_3 } \end{aligned}\ ] ] the expressions and yield @xmath839 as well as @xmath840 moreover the constraints imply that @xmath841 so that @xmath401 and @xmath406 yield the same time continuous limit , that is to say @xmath842 eventually , implies @xmath843 the same holding true for @xmath844 . the work expression is thus formally consistent with .
this concludes the proof of the consistency of - with - .
[ [ consistency - of.-1 ] ] consistency of .
+ + + + + + + + + + + + + + + + we now prove the consistency of the work expression with .
define @xmath845 the expression yields using : @xmath846 where @xmath847 first , since @xmath848 and @xmath849 , the limit of the terms in is zero .
second , using the expressions and , and similarly to and , it holds @xmath850 \\ & - ( \nabla \xi g^{-1})(q^{n+1 } ) \big [ \nabla \xi ( q^{n+1})^t { \left(q^{n}-q^{n+1}\right ) } + ( z(t_{n+2})-z(t_{n+1 } ) ) + \dt \nabla \xi ( q^{n+1})^t \nabla v ( q^{n+1})\big ] \\ & + \frac\dt2 ( \nabla v(q^{n+1 } ) - \nabla v(q^n ) ) = \mathrm{o}(\dt ) \end{aligned}\ ] ] since @xmath851 by . expanding in higher order powers of @xmath80
, it can be checked that there exists two functions @xmath852 and @xmath853 such that @xmath854 therefore , since ( in the limit @xmath509 ) the martingale part of @xmath855 arises only from the term @xmath856 , one obtains @xmath857 since @xmath858
. in conclusion , the second term in has a zero contribution to the continuous - in - time limit . as a consequence ,
the formal time continuous limit of @xmath859 is the same as the one of @xmath860 .
computations similar to the one performed above yield @xmath861 indeed , @xmath862 as in , while @xmath863 .
the formal time continuous limit of @xmath860 is therefore the same as the limit of @xmath864 since implies @xmath865 we get in the end that the formal time continuous limit of @xmath860 and @xmath859 is the same as : @xmath866 where we have used .
this concludes the proof of the consistency of - with - .
we present some free energy profiles obtained with nonequilibrium switching dynamics for the model system and the parameters described in section [ sec : simple_example_wca ] .
the switching schedule reads @xmath867 with @xmath868 and @xmath869 .
the time - step is @xmath870 .
the initial conditions are obtained by first subsampling a constrained dynamics with @xmath871 and @xmath872 , with a time spacing @xmath873 ; and then adding the required component @xmath874 to the momentum variable ( with @xmath875 ) . in the specific case at hand , the corrector term is constant , and free energies differences are equal to differences of rigid free energies .
the dynamics used to integrate the nonequilibrium dynamics is based on a splitting strategy , analogous to -- , except that the midpoint integration of the ornstein - uhlenbeck part is replaced by an exact integration for the unconstrained dynamics , followed by a projection .
this can be done here since we choose a friction matrix of the form @xmath388 ( recall also that @xmath876 ) . more precisely , the corresponding scheme is obtained by replacing ( and likewise for ) with @xmath877 where @xmath878 , and setting @xmath879 with @xmath329 chosen such that @xmath880 free energy profiles .
the top curve corresponds to @xmath881 with @xmath882 , while the two other curves were obtained for @xmath883 with @xmath884 and @xmath885 with @xmath886 ( smoothest curve ) .
, width=275 ] figure [ fig : noneq_rc ] presents estimates obtained with @xmath5 independent realizations of the switching dynamics for different switching times @xmath98 , using the estimator presented in section [ sec : work_discretization ] with the work discretization . in all cases ,
the product @xmath887 is kept constant .
the free energy profile becomes closer to the reference curve as @xmath98 is increased , and the profile obtained for @xmath885 is in excellent agreement with the result obtained with thermodynamic integration .
when the switching time is small , more realizations should be considered to reduce the statistical errors and obtain estimates in better agreement with the reference profile .
the fact that the variance is very large when the switching time @xmath98 is too small is a well - known drawback of estimators based on the jarzynski - crooks identity , see the review in sections 4.1.4 and 4.1.5 in @xcite . roughly speaking
, the difficulty is related to the fact that the free energy difference is obtained as an average of @xmath888 , which requires a very good sampling of the small values of the work @xmath889 . as @xmath98 decreases , the width of the work distribution increases and the low tail part is more and more difficult to sample .
improved estimates can be obtained with estimators based on combinations of forward and backward trajectories , see for instance @xcite and section 4.2 in @xcite .
we give in this appendix two technical lemmas , used in the proof of proposition [ p : meanforce ] .
the first lemma can also be used to prove the divergence formula .
the proof relies on the following computation rules for any family of invertible square matrices @xmath892 : @xmath893 and @xmath894 fix @xmath895 .
first , using with @xmath896 replaced by @xmath148 and @xmath897 replaced by @xmath898 , we obtain @xmath899 so that by the skew - symmetry of @xmath900 and @xmath148 , @xmath901 jacobi s identity for poisson brackets and then yield @xmath902 since @xmath903 where @xmath904 is the kronecker symbol .
finally , the left hand and right hand sides of the last equality can be factorized as @xmath905 since @xmath906 and @xmath193 is invertible , it follows @xmath907 for all @xmath908 , which is .
consider a test function @xmath910 .
an integration by parts and the co - area formula give : @xmath911 where in the last line the following chain rule has been used : @xmath912 now an integration by parts with respect to @xmath913 , together with , leads to @xmath914 which gives the result .
w. e and e. vanden - eijnden , _ metastability , conformation dynamics , and transition pathways in complex systems _ , multiscale modelling and simulation ( s. attinger and p. koumoutsakos , eds . ) , lect . notes comput .
39 , springer , berlin , 2004 , pp . 3568 .
e. hairer , c. lubich , and g. wanner , _ geometric numerical integration : structure - preserving algorithms for ordinary differential equations _ , springer series in computational mathematics , vol .
31 , springer - verlag , 2006 .
t. lelivre , m. rousset , and g. stoltz , _ computation of free energy differences through nonequilibrium stochastic dynamics : the reaction coordinate case _ , j. comput
* 222 * ( 2007 ) , no . 2 , 624643 .
s. park , f. khalili - araghi , e. tajkhorshid , and k. schulten , _ free energy calculation from steered molecular dynamics simulations using jarzynski s equality _ , j. chem .
* 119 * ( 2003 ) , no . 6 , 35593566 . | in this paper , we consider langevin processes with mechanical constraints .
the latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences .
the results of this paper can be divided into three parts .
( i ) we propose a simple discretization of the constrained langevin process based on a splitting strategy .
we show how to correct the scheme so that it samples _ exactly _ the canonical measure restricted on a submanifold , using a metropolis - hastings correction in the spirit of the generalized hybrid monte carlo ( ghmc ) algorithm .
moreover , we obtain , in some limiting regime , a consistent discretization of the overdamped langevin ( brownian ) dynamics on a submanifold , also sampling exactly the correct canonical measure with constraints .
( ii ) for free energy computation using thermodynamic integration , we rigorously prove that the longtime average of the lagrange multipliers of the constrained langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints .
a second order time discretization using the lagrange multipliers is proposed .
( iii ) the jarzynski - crooks fluctuation relation is proved for langevin processes with mechanical constraints evolving in time .
an original numerical discretization without time discretization error is proposed , and its overdamped limit is studied .
numerical illustrations are provided for ( ii ) and ( iii ) . | <s>[INST]free energy is a central concept in thermodynamics and in modern works on biochemical and physical systems .
typical examples studied by computer simulations include the solvation free energies ( which is the free energy difference between a molecule _ in vacuo _ and its counterpart surrounded by solvent molecules ) and the binding free energy of two molecules ( which determines whether a new drug can have an efficient action on a given protein ) . in many applications , it is actually the free energy difference profile between the initial and the final state which is a quantity of paramount importance .
it is observed by practitioners that free energy barriers are a very important element to describe transition kinetics from one state to the other .
for instance , the chemical kinetics of reactions happening in solvent ( such as in the cells of our bodies ) are limited by free energy barriers , and can take place only when the free energy difference between the initial and the final state is negative , or at least less than the typical thermal energy .
it is therefore very important to accurately compute free energy differences in order to assess the likelihood of a certain physical event to happen . beside these physical motivations to compute free energy differences ,
a more abstract motivation is to overcome sampling barriers encountered when computing canonical averages ( see the discussion in ( * ? ? ?
* section 1.3.3 ) ) .
indeed , it is often the case in practice that the trajectories generated by the numerical methods at hand remain stuck for a long time in some region of the phase space , and hop only occasionally to another region , where they also remain stuck a behavior known as metastability .
chemical and physical intuitions may guide the practitioners of the field towards the choice of some slowly evolving degree of freedom , called _ reaction coordinate _ in the following , responsible for the metastable behavior of the system . in this case
, free energy techniques can be used to accelerate the sampling .
this viewpoint allows to consider applications which are not motivated by physical or biological problems , such as curing sampling issues in bayesian statistics @xcite . in this introductory section ,
we present the main results and give the outline of the paper , highlighting the three main contributions of this work .
we only briefly define the concepts we need in this general introduction , and refer the reader to the following sections ( in particular section [ sec : notation ] ) for further precisions on the mathematical objects at hand .
we consider mechanical systems with constraints .
the configuration of a classical @xmath0-body system is denoted by @xmath1 .
the results of the paper can be generalized _ mutatis mutandis _ to periodic boundary conditions ( @xmath2 , where @xmath3 denotes the one dimensional torus ) , or to systems with positions confined in a domain @xmath4 .
the mass matrix of the system is assumed to be a constant strictly positive symmetric matrix @xmath5 .
one could typically think of a diagonal matrix @xmath6 .
the interaction potential is a smooth function @xmath7 .
the hamiltonian of the system is assumed to be separable : @xmath8 in the present paper , the focus is on the canonical ensemble , which is the equilibrium probability distribution of microscopic states of a system at fixed temperature ( fixed average energy ) . for systems without constraints
, this ensemble is characterized by the probability distribution @xmath9 where @xmath10 is the normalizing constant is assumed to be such that @xmath11 . ] ensuring that @xmath12 is indeed a probability distribution , and @xmath13 is proportional to the inverse temperature .
one dynamics which admits the canonical measure as an invariant measure is the langevin dynamics ( see for instance ( * ? ? ?
* section 2.2.3 ) and references therein ) : @xmath14 where @xmath15 is a standard @xmath16-dimensional brownian motion , and @xmath17 are @xmath18 position dependent real matrices which are assumed to satisfy the fluctuation - dissipation identity @xmath19 the langevin dynamics can be seen as some modification of the hamiltonian dynamics with two added components : a damping term @xmath20 and a random forcing term @xmath21 . the energy dissipation due to the damping is compensated by the random forcing in such a way that the temperature of the system is @xmath22 ( with @xmath23 boltzmann s constant ) .
we will consider positions subject to a @xmath24-dimensional mechanical constraint denoted by @xmath25 as will become clear below , constrained systems appear in computational statistical physics in two kinds of contexts ( see _ e.g. _ ( * ? ? ?
* chapter 10 ) , and @xcite for applications to the computation of free energy differences , and @xcite for mathematical textbooks dealing with constrained hamiltonian dynamics ) : a. for free energy computations , where @xmath26 is a given reaction coordinate parameterizing a transition between states of interest ; b. when the system is subject to molecular constraints such as rigid covalent bonds , or rigid bond angles in molecular systems . in the sequel , @xmath26 may be thought of at first reading as a reaction coordinate ( case ( i ) ) .
section [ ti - sec : mc ] explains how to handle additional molecular constraints ( case ( ii ) ) within the same formalism . in any case
, the position of the system is constrained onto the submanifold of co - dimension @xmath24 : @xmath27 and the associated phase space is the cotangent bundle denoted by @xmath28 for a given @xmath29 , the set of cotangent momenta is denoted by @xmath30 the orthogonal projection on @xmath31 with respect to the scalar product induced by @xmath32 is denoted @xmath33 where @xmath34 is the gram matrix associated with the constraints @xmath35 throughout the paper , we assume that @xmath36 is invertible everywhere on @xmath37 ( for all @xmath38 ) .
it is easily checked that @xmath39 satisfies the projector property @xmath40 , and the orthogonality property @xmath41 for constrained systems , the associated canonical distribution is defined by @xmath42 where @xmath43 is the phase space liouville measure of @xmath44 , and @xmath45 the normalizing constant ( @xmath38 refers to the position constraint , and @xmath46 to the velocity or momentum constraint , see below ) .
see section [ sec : measures ] for precise definitions . a dynamics admitting the constrained canonical measure as an invariant equilibrium measure is the following langevin process ( `` cl '' stands for `` constrained langevin '' ) : for a given initial condition @xmath47 , @xmath48 \dps d p_{t } = -\nabla v(q_{t } ) \ , dt -\gamma(q_t ) m^{-1}p_t \ , dt + \sigma(q_t ) \ , d w_t + \nabla \xi(q_{t } ) \ , d \lambda_t , & \\[6pt ] \dps \xi(q_{t } ) = z , & ( c_q ) \end{cases}$}\ ] ] where the @xmath49-valued adapted process @xmath50 is the lagrange multiplier associated with the ( vectorial ) constraint @xmath51 , and @xmath17 are again assumed to satisfy .
note that @xmath52 for all @xmath53 .
then , averages of an observable @xmath54 with respect to the distribution can be obtained as longtime averages along any trajectory of the dynamics @xmath55 ( when @xmath56 is symmetric positive on @xmath37 ) : @xmath57 this is made precise in section [ sec : sampling ] .
several recent studies ( _ e.g. _ @xcite ) have analyzed dynamics similar to @xmath55 and some appropriate discretization of the process in order to approximate the left - hand side of . of our work
is to propose a simple discretization of the dynamics @xmath55 and to highlight its remarkable properties .
the numerical scheme is based on a splitting strategy between the hamiltonian and the thermostat part , see equations -- below ( in the spirit of the scheme proposed in @xcite in the unconstrained case ) .
the hamiltonian part is discretized using a verlet scheme with position and momentum constraints ( the so - called rattle scheme , see @xcite ) .
we show that this discretization enjoys the following properties : ( i ) for some choice of the parameters , an euler discretization of the _ overdamped _ langevin dynamics ( also called brownian dynamics ) with a projection step associated with the constraints is obtained ( see equation and proposition [ p : langtooverd ] ) ; ( ii ) it can be completed by a metropolis - hastings correction to obtain a generalized hybrid monte carlo ( ghmc ) method sampling _ exactly _ ( _ i.e. _ without any bias due to time - discretization ) the constrained canonical distribution ( see algorithm [ a : ghmcconst ] below ) .
the so - obtained numerical scheme is close to the ones proposed in @xcite .
see also @xcite for historic references on hybrid monte carlo methods , and @xcite for ghmc .
one output of this part is thus a new metropolization procedure for overdamped langevin dynamics to sample , without bias , measures with support a submanifold .
the free energy @xmath58 associated with the reaction coordinates @xmath59 is defined as @xmath60 times the log - density of the marginal probability distribution of the reaction coordinates @xmath26 under the canonical distribution .
explicitly , it is defined through the following relation : for any test function @xmath61 , @xmath62 in words , @xmath63 is the image of the measure @xmath12 by @xmath26 , and @xmath64 can be seen as an `` effective potential energy '' associated to @xmath26 . computing the free energy profile @xmath65 (
up to an additive constant independent of @xmath38 ) , or free energy differences between two states @xmath66 is a way to compare the relative probabilities of different states
parameterized by @xmath26 .
this is a very important calculation for practical applications , see @xcite .
a state should be understood here as the collection of all possible microscopic configurations @xmath67 , distributed according to the canonical measure , and satisfying the macroscopic constraint @xmath68 .
since we only focus on computing free energy differences , @xmath64 is defined up to an additive constant ( independent of @xmath38 , denoted by @xmath69 below , and whose value may vary from line to line ) and can be rewritten as : @xmath70 where @xmath71 denotes the conditional measure on @xmath37 verifying the following identity of measures in @xmath72 : @xmath73 ( see section [ sec : measures ] for more precisions on this relation ) .
however , when using constrained simulations in phase space , the momentum variable of the dynamical system is also constrained , and a modified free energy ( called `` rigid free energy '' in the sequel , see remark below for a justification of the term `` rigid '' ) is more naturally computed , see section [ sec : sampling ] . the latter is defined as @xmath74 the superscript @xmath5 indicates that this free energy depends on the considered mass matrix , even though this is not clear at this stage ( see below ) .
the above two definitions of free energy are related through the identity : @xmath75 where @xmath76 is the equilibrium distribution with constraints .
the relation , already proposed in @xcite ( see also @xcite for related formulas ) , is proved at the beginning of section [ sec : langti ] .
for any value of the reaction coordinate , the difference @xmath77 can then be easily computed with any method sampling the probability distribution @xmath76 , such as @xmath55 .
several methods have been suggested in the literature to compute either @xmath64 or @xmath78 from the lagrange multipliers of a constrained process similar to @xmath55 .
we refer for instance to @xcite ( and references therein ) for the hamiltonian case , and to @xcite ( and references therein ) for the overdamped case . of this paper
is twofold : ( i ) we rigorously prove that the longtime average of the lagrange multipliers in @xmath55 converges to the gradient of the rigid free energy ( the so - called _ mean force _ ) ; and ( ii ) we then show that the latter mean - force can be computed with second order accuracy ( _ i.e. _ up to @xmath79 error terms , where @xmath80 is the time - step ) using the lagrange multipliers involved in the hamiltonian part of the splitting scheme .
more precisely , the first point ( i ) amounts to showing that @xmath81 as compared to @xcite , where a formal proof for the hamiltonian case is proposed , we use an explicit calculation that does not require the use of the lagrangian structure of the problem , or a change of coordinates . once @xmath82 is obtained , @xmath83 can be computed ( up to an additive constant ) by integration .
this procedure is known as _ thermodynamic integration_. note that using and thermodynamic integration , together with , allows to obtain @xmath84 without computing second order derivatives of @xmath26 .
this is a desirable property since computing such high derivatives may be cumbersome for some reaction coordinates used in practice .
straightforward computations of the mean force using analytical expressions ( see for instance - ) usually involve such high order derivatives . the second point ( ii )
is then based on a discretization of a variant of , obtained by subtracting the martingale part of the lagrange multipliers .
this amounts to averaging the two lagrange multipliers involved in the rattle part of the scheme , see ) .
we also discuss how these techniques can be generalized to compute the free energy for systems with molecular constraints , see section [ ti - sec : mc ] .
the last part of this article is devoted to nonequilibrium methods for free energy computations , based on a hamiltonian or langevin dynamics with constraints subject to a predetermined time evolution .
such methods rely on a nonequilibrium fluctuation equality , the so - called jarzynski - crooks relation .
see @xcite for a pioneering work , as well as @xcite for an extension .
they are termed `` nonequilibrium '' since the transition from one value of the reaction coordinate @xmath26 to another one is imposed _ a priori _ , in a finite time@xmath85 , and with a given smooth deterministic schedule @xmath86
\mapsto z(t ) \in \mathbb{r}^\nc$ ] .
in particular , it may be arbitrarily fast
. therefore , even if the system starts at equilibrium , it does not remain at equilibrium .
the out - of - equilibrium langevin process we consider to this end is given by the following equations of motion ( `` scl '' stands for `` switched constrained langevin '' ) : @xmath87 d p_t & = -\nabla v ( q_t ) \,dt -\gamma_p(q_t ) m^{-1 } p_t \ , dt+ \sigma_p(q_t ) \,d w_t + \nabla
\xi(q_t ) \ , d \lambda_t , \\[6pt ] \xi(q_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.$}\ ] ] where @xmath88 is an adapted process enforcing the constraints @xmath89 ( the lagrange multipliers ) .
initial conditions are sampled from the phase - space canonical distribution defined by the constraints @xmath90 and @xmath91 ( see ) .
we restrict ourselves to projected fluctuation - dissipation matrices of the specific form @xmath92 where @xmath93 satisfy the fluctuation - dissipation identity .
note that @xmath94 also verify .
our analysis also applies to deterministic hamiltonian dynamics upon choosing @xmath95 .
the dynamics @xmath96 is a natural extension of the constrained langevin dynamics @xmath55 .
it is different from the dynamics proposed in @xcite , which is a langevin dynamics associated with a modified hamiltonian with projected momenta , driven by a forcing term along @xmath97 which acts directly on the position variable . as explained below ( see and the discussion following this equation ) , the specific choice ( rather than considering unprojected matrices @xmath93 ) leads to a simpler analysis and more natural numerical schemes , based again on a splitting procedure . as explained in section [ sec : jarz_lang_cons ] , it is possible to define the work associated with the constraints exerted on the system between time @xmath46 and @xmath98 as the displacement multiplied by the constraining force : @xmath99 of the present paper is twofold : ( i ) we derive a new general crooks - jarzynski relation ( see theorem [ th : crookslangcons ] below ) based on the nonequilibrium constrained dynamics @xmath96 and the associated work defined in ; and ( ii ) an original numerical scheme is proposed , which allows to compute free energy differences _ without time discretization error _ ( see theorem [ eq : jarz_disc ] below ) .
more precisely , concerning the first point , the main corollary is given by the following result .
consider the corrector @xmath100 where @xmath101 is the so - called fixman term due to the geometry of the position constraints ( see and remark [ rem : highosclang ] ) , and @xmath102 is the kinetic energy term due to the velocity of the switching .
then , the free energy profile can be computed through the following fluctuation identity ( see ):
@xmath103 } \right)}{\e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right),\ ] ] where the expectation is with respect to canonical ( equilibrium ) initial conditions and for all realizations of the dynamics @xmath96 . the numerical scheme mentioned in the second point ( ii ) above
is based on a modification of the splitting scheme used to discretize the constrained langevin dynamics @xmath55 .
this modification allows to take into account the evolving constraints . using the symplecticity of the modified rattle scheme
, we are able to prove a discrete - in - time version of the crooks relation , and of the associated jarzynski free energy estimator . moreover
, for some choice of the parameters , the latter scheme yields a jarzynski - crooks relation for an euler discretization of the overdamped langevin ( brownian ) dynamics with a projection step associated with the evolving constraints , without time discretization error .
this can be seen as an extension of the scheme formerly proposed in @xcite ( see equation and proposition [ p : langtooverd_jarz ] ) .
we also check the consistency of the various free energy estimators we introduce .
we start with an introduction to the mathematical concepts required for mechanically constrained systems in section [ sec : notation ] .
section [ sec : sampling ] is devoted to the properties and the discretization of mechanically constrained langevin processes defined by @xmath55 , and the problem of sampling the canonical distribution .
thermodynamic integration with constrained langevin processes is presented in section [ sec : langti ] .
section [ sec : lang_jarz ] discusses nonequilibrium constrained langevin processes @xmath96 and the associated jarzynski - crooks fluctuation identity .
finally , some technical lemmas are gathered in section [ sec : appendix ] .
after making precise our notation for matrices and matrix valued functions in section [ sec : matrix_notation ] , we introduce some additional concepts required to describe constrained systems in section [ sec : const_notation ] , and define the phase space measures with constraints in section [ sec : measures ] . throughout the paper ,
the following notation is used : * vectors and vector fields are by convention of column type .
when vectors are written as a line , they should be understood as the corresponding column version .
for instance , @xmath104 should be understood as @xmath105 , where @xmath106 are both column vectors .
* gradients in @xmath72 ( or @xmath107 ) of @xmath24-dimensional vector fields are by convention @xmath108-matrices , for instance : @xmath109 where @xmath110 is a column vector for any @xmath111 .
gradients in the space of constraints parameters @xmath112 or @xmath113 are denoted with the associated subscripts , namely @xmath114 and @xmath115 . * second order derivatives in @xmath72 of @xmath24-dimensional vector fields are characterized through the hessian bilinear form : @xmath116 where @xmath117 are test vectors . *
the canonical symplectic matrix is denoted by : @xmath118 for any smooth test functions @xmath119 and @xmath120 , the poisson bracket is the @xmath121 matrix @xmath122 * for two matrices @xmath123 , @xmath124 .
contrarily to what is often done in the literature , we avoid global changes of variables and the use of generalized coordinates .
we observe that global changes of variables are not required for the proofs of the theoretical results we present , and they are definitely to be avoided in practical numerical computations whenever possible
. two useful concepts to study constrained hamiltonian systems ( in particular , to use the co - area formula in phase space , as well as the poisson bracket formulation of the liouville equation ) are the effective velocity @xmath125 and the effective momentum @xmath126 associated with the constrained degrees of freedom @xmath26 : @xmath127 and @xmath128 the expression of the effective velocity is obtained by deriving the constraint @xmath26 along an unconstrained trajectory of the hamiltonian dynamics @xmath129
\dps \frac{d \tilde p_t}{dt } = -\nabla v(\tilde q_t ) , \end{cases}\ ] ] since @xmath130 the term @xmath131 in the expression of the effective momentum may be interpreted as the effective mass of @xmath26 .
this can be motivated by a decomposition of the kinetic energy of the system into tangential and orthogonal parts , using the projector for a given position @xmath132 :
@xmath133 the orthogonal part can be rewritten , for any @xmath1 , as : @xmath134 the last equations allow to consider @xmath135 as some effective mass .
the constraints on a mechanical system can also be reformulated in the more general form @xmath136 where either ( i ) the effective momentum is constrained , in which case @xmath137 and @xmath138 ; or ( ii ) the effective velocity is constrained , in which case @xmath139 and @xmath140 . the phase space associated with such constraints is denoted by @xmath141 a position @xmath142 being given , the affine space of constrained momenta verifying is then denoted by @xmath143 in the effective velocity case , and by @xmath144 in the effective momentum case .
this notation is very important for nonequilibrium methods where the constraints evolve in time according to a predefined schedule , see section [ sec : lang_jarz ] .
note that the phase space of mechanical constraints , defined by , is simply @xmath145 .
we can now define the skew - symmetric gram tensor of dimension @xmath146 associated with the constraints : @xmath147 the gram matrix @xmath148 associated with the generalized constraints can be explicitly computed by block . indeed , for @xmath149 , @xmath150 therefore , @xmath151 in this case .
in the case @xmath152 , the gram matrix reads @xmath153 and @xmath154 .
note that in both cases @xmath155 .
the constrained symplectic ( skew - symmetric ) matrix is now defined by @xmath156 and the poisson bracket associated with generalized constraints by : @xmath157 this poisson bracket is often called the dirac bracket in the literature ( in reference to the seminal work of dirac @xcite ) .
it is easily checked that @xmath158 verifies the characteristic properties of poisson brackets , namely the skew - symmetry , jacobi s identity , and leibniz rule .
therefore , the flow associated with the evolution equation @xmath159 defines a symplectic map .
recall that ( see ( * ? ? ?
* section vii.1.2 ) ) a map @xmath160 is symplectic if for any @xmath161 and @xmath162 , @xmath163 a consequence of the symplectic structure is the divergence formula relating the phase space measure @xmath164 on @xmath165 ( defined below ) , and the poisson bracket .
the reader is referred to chapter @xmath166 in @xcite , and section vii.@xmath167 in @xcite for more material on constrained systems .
it will be shown in proposition [ s : p : lconstgen ] below that the poisson system is equivalent to @xmath55 when @xmath168 .
the phase space measure ( also termed liouville measure ) on the phase space @xmath169 ( or more generally on @xmath165 ) of constrained mechanical systems is denoted by @xmath170 ( or more generally @xmath171 ) .
the latter is induced by the symplectic , or skew - symmetric @xmath172-form on @xmath107 defined by the canonical skew - symmetric matrix @xmath173 in @xmath107 .
more precisely , it can be defined through the volume form @xmath174 , where @xmath175 and @xmath176 is a basis of tangential vectors of the submanifold @xmath177 ( or @xmath165 ) at a given point @xmath67 .
surface measures induced by scalar products associated with general symmetric definite positive matrices will also be of interest .
we denote by @xmath178 the surface measure on @xmath37 induced by the scalar product @xmath179 on @xmath72 , and , for a given @xmath29 , by @xmath180 and @xmath181 the surface measures on the affine spaces @xmath144 and @xmath182 respectively , induced by the scalar product @xmath183 on @xmath72 . for more precise definitions of these measures ,
we refer to ( * ? ? ?
* sections 3.2.1 and 3.3.2 ) and the references therein .
it is now possible to define a generalization of the canonical distribution as follows : @xmath184 the distribution is associated with the generalized constraints @xmath185 , and is used in section [ sec : lang_jarz ] for nonequilibrium methods .
note that @xmath186 defined in .
the co - area formula ( see @xcite ) relates the phase space or surface measures , and the conditional measures .
conditional measures are defined in @xmath107 by the following conditioning formula : for any test function @xmath187 , @xmath188 in the same way in @xmath72 , conditional measures are defined , for any test function @xmath189 , by @xmath190 a more concise notation for the above equalities is @xmath191 and @xmath73 .
[ p : coareasympl ] let @xmath37 be the submanifold defined by the constraints @xmath68 , and assume that @xmath36 defined in is non - degenerate in a neighborhood of @xmath37 .
then , in the sense of measures on @xmath72 : @xmath192 let @xmath165 be the phase space defined by generalized constraints .
assume that @xmath193 defined in is non - degenerate in a neighborhood of @xmath165 .
then , in the sense of measures on @xmath107 : @xmath194 we refer for example to chapter @xmath195 in @xcite for an elementary proof
. an equivalent of - for momenta reads , for constrained effective momenta : @xmath196 and for constrained effective velocities : @xmath197 using the co - area formulas - , and the expressions of symplectic gram matrices - , we obtain the following expressions of the phase space measures : a. the phase space measure on @xmath198 can be identified with the conditional measure defined in : @xmath199 while the phase space measure on @xmath200 is related to the corresponding conditional measure as @xmath201 b. the phase space measures are given by the product of surface measures : @xmath202 and @xmath203 equations - are a consequence of the fact that @xmath204 ( and a similar relation for @xmath125 ) .
we end this section with an important formula , which is used to show the invariance of the canonical measure in the proof of proposition [ p : revcons ] .
[ p : divsympl ] consider the poisson bracket @xmath158 defined by , and an open neighborhood @xmath205 of @xmath206 where @xmath148 is invertible . then for any smooth test functions @xmath207 with compact support in @xmath205 , @xmath208
the divergence formula can be proved using darboux s theorem and internal coordinates , or directly using the co - area formula ( see section 3.3 in @xcite ) .
we will also need the classical divergence formula on affine spaces ( see for instance section 3.3 in @xcite ) : for a fixed @xmath132 , for any compactly supported smooth vector field @xmath209 , @xmath210
we first give some properties of the constrained langevin equation @xmath55 in section [ sec : sampling_gen ] , then propose some numerical schemes to discretize it in section [ sec : consnum ] , and finally consider the overdamped limit in section [ sec : ovd_limit_constraints ] .
we consider the dynamics @xmath55 : @xmath211 \dps d p_{t } = -\nabla v(q_{t } ) \ , dt -\gamma(q_t ) m^{-1}p_t \ , dt + \sigma(q_t ) \ , d w_t + \nabla \xi(q_{t } ) \ , d \lambda_t , & \\[6pt ] \dps \xi(q_{t } ) = z. & ( c_q ) \end{cases}\ ] ] by differentiating with respect to time the constraint @xmath212 , the lagrange multipliers can be computed explicitly ( see for instance section 3.3 in @xcite ) : @xmath213 \nonumber\\ & = \ , f_{\rm rgd}^m(q_t , p_t ) \ , dt + g_{m}^{-1}(q_t)\nabla \xi(q_t)^t m^{-1 } { \left(\gamma(q_{t } ) m^{-1}p_{t } \,dt - \sigma(q_{t } ) \,d w_t \right ) } , \label{eq : first_expression_lagrange}\end{aligned}\ ] ] where the constraining force @xmath214 is defined as : @xmath215 thus , using the fact that @xmath216 when @xmath217 , the dynamics @xmath55 can be recast in a more explicit form as @xmath218 d p_{t } & = -\nabla v(q_{t } ) \ , dt + \nabla \xi(q_t ) f_{\rm rgd}^m(q_t , p_t ) \ , dt -\gamma_p(q_t ) m^{-1 } p_{t}\ , dt \\ & \quad + \sigma_p(q_t ) \ , d w_t , \end{aligned } \right.\ ] ] where we introduced the notation @xmath219 .
the constraint therefore has two effects : ( i ) the matrices @xmath220 in the dissipation and fluctuation terms are replaced by their projected counterparts @xmath94 , and ( ii ) an orthogonal constraining force @xmath221 is introduced .
the generator of this stochastic langevin dynamics is the operator @xmath222 which appears in the kolmogorov evolution equation : for @xmath223 satisfying @xmath55 or , and for any smooth test function @xmath224 , @xmath225 the expression of @xmath222 can be obtained using it calculus , as made precise in the following proposition .
[ s : p : lconstgen ] consider either the effective momentum or the effective velocity , denoted with the general constraints @xmath226 or @xmath227 ( see ) .
the solution of the constrained dynamics @xmath55 ( or equivalently with an initial condition @xmath228 ) belongs to @xmath229 , and the generator of this markov process reads ( whatever the value of @xmath38 ) @xmath230 where the fluctuation - dissipation part is @xmath231 with @xmath232 defined in . using the fluctuation - dissipation relation ,
the generator @xmath233 can be rewritten more compactly as @xmath234 we perform the computation in two steps : ( i ) we compute the generator of the hamiltonian part of the constrained langevin dynamics , which is @xmath55 in the case @xmath235 ; ( ii ) we compute the generator of the thermostat part of @xmath55 , which is an ornstein - uhlenbeck process on momentum variable ( corresponding to the second equation in @xmath55 with @xmath236 ) .
let us first consider ( i ) , with @xmath226 ( the case @xmath227 being similar ) .
note that @xmath237 where the hessian operator @xmath238 is defined in .
now , implies that @xmath239 besides , @xmath240 along a trajectory , since @xmath52 .
therefore , @xmath241 where the notation @xmath242 is introduced in .
consider a test function @xmath243 , and remark that @xmath244 so that , for any @xmath245 , @xmath246 finally , for all @xmath247 , @xmath248 the operator is the generator of the hamiltonian part in .
we turn to ( ii ) .
the diffusive part arises from the fluctuation term @xmath249 in , and its expression @xmath250 is obtained directly from the standard it calculus .
similarly , the dissipation operator is @xmath251 the addition of these two contributions gives the expression of @xmath233 . with the expression of the generator at hand , it is easily checked that the process @xmath55 satisfies the following equilibrium properties : [ p : revcons ] when the fluctuation - dissipation relation holds , the constrained langevin dynamics @xmath55 on @xmath252 admits the boltzmann - gibbs distribution as a stationary measure , and is reversible up to momentum reversal with respect to : if @xmath253 , then , for any @xmath254 , @xmath255 moreover , if @xmath256 is everywhere strictly positive in the sense of symmetric matrices on @xmath257 , then the process @xmath55 is ergodic : for any smooth test function @xmath224 , @xmath258 the stationarity and reversibility properties follow from the following detailed balance condition up to momentum reversal ( see for instance section 2.2 in @xcite ) : for any test functions @xmath259 , @xmath260 , @xmath261 where @xmath262 is the momentum flip . in view of the expression of the generator , proving amounts to proving this property for the operators @xmath263 and @xmath233 . for the hamiltonian part @xmath263 , the expression yields @xmath264 which states the time symmetry under momentum reversal of the hamiltonian part of the equations of motion @xmath55 . on the other hand , @xmath265 so that @xmath266 and the divergence formula yields the balance condition for the hamiltonian part , in view of the invariance of the distribution @xmath170 under the momentum flip @xmath267 . for the thermostat part , it is easily checked , that @xmath268 for any smooth test function @xmath224 , so that the detailed balance condition up to momentum reversal follows from the following more general detailed balance condition , in the case @xmath269 ( @xmath270 being defined in ): @xmath271 it is interesting to prove for a general @xmath272 since it will be used in the proof of theorem [ th : crookslangcons ] below . consider the divergence formula in the affine space for the variable @xmath273 ( the position @xmath274 being fixed ) , with @xmath275 after integration in @xmath274 , using the formula for @xmath233 and , an expression symmetric in @xmath276 is obtained : @xmath277 hence the detailed balance condition .
ergodicity is a consequence of the hypo - ellipticity of the operator @xmath222 on @xmath278 ( hrmander s criterion is satisfied , see @xcite ) , which is itself a consequence of the fact that @xmath279 is strictly positive on each @xmath280 .
the proof can be carried out using local coordinates and the results from @xcite .
[ rem : highosclang ] we have considered in this section the langevin dynamics with constraints rigidly imposed by a projection onto the submanifold @xmath281 .
this dynamics samples the canonical distribution @xmath282 , with constraints on both positions and momenta .
the marginal on positions of this distribution is , in view of , proportional to @xmath283 this is what we call in the following rigidly imposed constraints .
the canonical distribution with rigid constraints is naturally associated to the rigid free energy ( and this is what justifies the qualification `` rigid '' ) , since , we recall , @xmath284 another way to impose some constraints on a system is to add a penalization term . in our context , this could be done by changing the potential energy @xmath285 to @xmath286 it is easy to check that , in the limit @xmath287 ( infinite stiffness limit ) , the canonical measure associated to this potential is the canonical distribution with positions conditioned by @xmath288 .
this distribution is proportional to @xmath289 and its marginal on positions is proportional to @xmath290 this is what we call in the following softly imposed constraints . the canonical distribution with soft constraints is naturally associated with the standard free energy , since , we recall , @xmath291 note that , in view of , the marginal on positions for softly imposed constraints can be written in terms of rigidly imposed constraints through a modification of the potential : @xmath292 where @xmath293 is sometimes called the fixman corrector ( see @xcite ) . thus ,
if @xmath223 satisfies with the modified potential @xmath294 then @xmath295 samples ( in the longtime limit ) the probability measure proportional to @xmath296 , and we thus refer to this dynamics as the softly constrained langevin dynamics .
these concepts will be used in section [ ti - sec : mc ] to describe the computation of free energy differences for systems with molecular constraints .
finally , let us mention that the infinite stiffness limit @xmath287 of the langevin dynamics with the potential @xmath297 is not ( except for very specific forms of constraints ) the softly constrained langevin dynamics , as one would expect .
we refer to [ 32 ] for example , where it is shown that adiabatic effective potentials ( derived from the conservation of the ratio of energy over frequency of fast modes ) are required to describe the limiting dynamics .
however , a formal argument based on `` over - damping '' the fast modes indeed leads to the softly constrained langevin dynamics .
we consider in this section a numerical scheme based on a splitting of the langevin dynamics @xmath55 into a hamiltonian part ( section [ sec : numhamiltonconst ] ) and a fluctuation - dissipation part acting only on the momentum ( section [ sec : numflucdissconst ] ) . such a splitting is standard for unconstrained systems , but other splitting strategies for the langevin equation can be considered as well ( see @xcite ) . for simplicity , we restrict ourselves to constant matrices @xmath298 and @xmath299 . generalizations to position dependent matrices are straightforward .
the hamiltonian part of the langevin dynamics @xmath55 ( namely @xmath55 with @xmath300 ) is discretized using a velocity - verlet scheme with constraints , which yields below .
the fluctuation - dissipation part on momentum variable in @xmath55 is the following ornstein - uhlenbeck process ( for a fixed given @xmath301 ) : @xmath302 which can be rewritten as ( see ) @xmath303 this equation can be explicitly integrated on @xmath304 $ ] to obtain : @xmath305 however , the matrix exponential @xmath306 may be difficult to compute in practice ( except for certain choices of @xmath298 and @xmath5 , see the discussion at the end of section [ sec : numflucdissconst ] ) .
instead of performing an exact integration , can be discretized using a midpoint euler scheme , which yields and below .
the numerical scheme we investigate , termed midpoint euler - verlet - midpoint euler splitting , is therefore the following : @xmath307 \nabla \xi(q^n)^{t } m^{-1 } p^{n+1/4 } = 0 , & ( c_p)\\ \end{cases } \label{eq : flucdiss1 } \\ & \begin{cases }
p^{n+1/2 } = \dps p^{n+1/4 } - \frac{\dt}{2 } \nabla v ( q^{n } ) + \nabla \xi(q^n ) \ , \lambda^{n+1/2 } , & \\[6pt ] q^{n+1 } = q^{n } + \dt \ ,
m^{-1 } \ , p^{n+1/2 } , \\[6pt ] \xi(q^{n+1 } ) = z , & ( c_q)\\[6pt ] p^{n+3/4 } = \dps p^{n+1/2 } - \frac{\dt}{2 } \nabla v ( q^{n+1 } ) + \nabla \xi(q^{n+1 } ) \ , \lambda^{n+3/4 } , & \\[6pt ] \nabla\xi ( q^{n+1})^{t } m^{-1 } p^{n+3/4 } = 0 , & ( c_p)\\ \end{cases } \label{eq : verletconst } \\ &
\begin{cases } \dps p^{n+1 } = p^{n+3/4 } -\frac{\dt}{4 } \gamma \ , m^{-1 } ( p^{n+3/4}+p^{n+1 } ) + \sqrt{\frac\dt2 } \ , \sigma \ , { \mathcal g}^{n+1/2 } \\
\phantom{p^{n+1 } = } + \nabla\xi(q^{n+1 } ) \ , \lambda^{n+1 } , & \\[6pt ] \nabla \xi(q^{n+1})^{t } m^{-1 } p^{n+1 } = 0 , & \hspace{-1 cm } ( c_p)\\ \end{cases } \label{eq : flucdiss2 } \end{aligned}\ ] ] where @xmath308 and @xmath309 are sequences of independently and identically distributed ( i.i.d . )
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
note that when @xmath311 and @xmath312 , the scheme -- becomes deterministic , and reduces to , which is a scheme for the deterministic hamiltonian equations of motion with position constraints @xmath68 .
the latter scheme is referred to as the hamiltonian scheme below .
the hamiltonian part of the scheme , often called rattle in the literature , is an explicit integrator , and is a modification of the classical shake algorithm ( see chapter vii.@xmath167 in @xcite , or chapter @xmath313 in @xcite for more precisions and historical references ) . in , @xmath314 are the lagrange multipliers associated with the position constraints @xmath315 , and @xmath316 are the lagrange multipliers associated with the velocity constraints @xmath317 . the nonlinear constraints @xmath315 are typically enforced using newton s algorithm . in ,
the ( linear ) momentum projection @xmath318 is always well defined since we assumed that the gram matrix @xmath34 is invertible . on the other hand ,
the nonlinear projection used to enforce the position constraints @xmath319 is in general well defined only on a subset of phase space .
the domain @xmath320 is defined as the set of configurations @xmath321 such that there is a unique solution @xmath322 verifying . solving the position constraints
@xmath51 consists in projecting onto @xmath37 a point in a @xmath80-neighborhood of @xmath323 . thus , by the implicit function theorem , the domain @xmath324
verifies : @xmath325 it may happen that there is no solution if the time - step is too large , and , even for small time - steps , that several projections exist , see for instance example @xmath172 in chapter @xmath313 of @xcite . in practice , @xmath324 can be chosen to be the set of @xmath326 such that the newton algorithm enforcing the constraints @xmath51 has converged within a given precision threshold and a limited number of iterations .
as for the verlet scheme in the unconstrained case , the associated numerical flow shares two important qualitative properties with the exact flow : it is time reversible and symplectic ( see @xcite ) .
this implies quasi - conservation of energy , in the sense that energy is conserved within a given precision threshold over exponentially long times , see @xcite .
the new momentum @xmath327 in ( or @xmath328 in ) may be obtained by first integrating the unconstrained dynamics with a midpoint scheme , and then computing the lagrange multiplier @xmath329 ( or @xmath330 ) by solving the following linear system implied by the constraints @xmath318 : @xmath331 = 0 . \end{aligned}\ ] ] a sufficient criteria for stability is @xmath332 besides , it can be checked ( see sections 2.3.2 and 3.3.5 in @xcite ) that the markov chain induced by the fluctuation - dissipation part of the scheme ( or ) verifies a detailed balance equation ( both in the plain sense and up to momentum reversal ) with respect to the stationary measure @xmath333 .
the latter is defined as the kinetic probability distribution @xmath334 and is the marginal in the @xmath273-variable of the canonical distribution @xmath335 conditioned by a given @xmath301 . moreover ,
if @xmath336 is strictly positive in the sense of symmetric linear transformations of @xmath337 , then the markov chain on momentum variable induced by ( or ) alone is ergodic with respect to @xmath333 .
finally , an important simplification occurs in the integration of in the special case when @xmath298 and @xmath5 are equal up to a multiplicative constant ( so that @xmath338 is proportional to identity ) .
indeed in this case the equality @xmath339 holds for any @xmath340 , and simplifies to @xmath341 the numerical integration of can thus be carried out in two steps : ( i ) exactly integrating without constraint , and then ( ii ) projecting the result onto @xmath342 .
usually , the invariant probability distribution sampled by the solution of a numerical scheme is biased by the time discretization .
relying on ( i ) the time symmetry ( up to momentum reversal ) and ( ii ) the preservation of the phase space measure @xmath343 by the solution of the rattle scheme , it is possible to eliminate the time discretization error in the splitting scheme -- by resorting to a generalized hybrid monte carlo algorithm .
[ a : ghmcconst ] consider an initial configuration @xmath344 , and a sequence @xmath345 of independently and identically distributed standard gaussian vectors .
iterate on @xmath340 : 1 .
evolve the momentum according to the midpoint euler scheme , and compute the energy @xmath346 of the new configuration ; 2 . integrate the hamiltonian part according to the rattle scheme , denote @xmath347 the resulting state , and set @xmath348 .
3 . accept the proposal @xmath349 with probability @xmath350 otherwise , reject and flip the momentum : @xmath351 .
4 . evolve the momentum according to the midpoint euler scheme . by construction ,
the ghmc algorithm with constraints leaves invariant the equilibrium distribution @xmath352 ( see section 3.3.5 in @xcite ) . to understand the momentum reversal required upon rejection , it is useful to write more explicitly the markov chain as the composition of a metropolis - hastings part , where the proposal is obtained by a rattle step followed by a momentum reversal ( the latter operation is needed to ensure the symmetry of the proposition ) , which is then accepted or rejected ; and another momentum reversal ( which leaves invariant the targeted probability measure @xmath352 ) .
when the proposal is accepted , the two momentum reversals cancel out each other . on the other hand , when the proposal is rejected , momenta are actually reversed .
see ( * ? ? ?
* section 2.1.4 ) for more background on generalized metropolis - hastings algorithms . in the above
, we implicitly assume that the rattle scheme is everywhere well defined . in practice
however , it is necessary to modify algorithm [ a : ghmcconst ] by restricting the sampled configurations to @xmath324 .
this can be achieved by introducing additional tests in steps ( 1 ) , ( 2 ) and ( 4 ) , and rejecting the states that have gone outside the set @xmath353 where the position constraint @xmath51 is well defined . by doing so
, the global algorithm has an invariant equilibrium distribution given by @xmath352 conditioned on the set of states @xmath324 .
this invariant distribution can be written explicitly as follows : @xmath354 alternatively , the rejection tests in steps ( 1 ) , ( 2 ) and ( 4 ) of algorithm [ a : ghmcconst ] can be performed with a cut - off parameter @xmath355 on the momentum variable , chosen so that the position constraint @xmath51 in is everywhere well defined when @xmath356 .
this can be achieved when there exists @xmath355 small enough so that @xmath357 .
since this is useful for later purposes ( see the discussion at the end of section [ sec : num_ti ] ) , we provide a rough estimate of @xmath358 in terms of @xmath80 , assuming for simplicity that @xmath37 is compact .
first , by the implicit function theorem , there exists @xmath359 such that , for all @xmath29 and @xmath360 with norm @xmath361 , there is a unique @xmath362 satisfying @xmath363 therefore , there exists @xmath364 small enough such that , when @xmath365 , the rattle scheme in is well defined , namely there exists a unique @xmath366 satisfying the constraint @xmath51 .
this shows that @xmath367 for some @xmath368 . the invariant probability distribution of the markov chain generated by ghmc with the additional rejection steps ensuring @xmath369 , is given by , and actually reads @xmath370 its marginal distribution in the position variable is then exactly given by : @xmath371 this is also the marginal distribution in the position variable of @xmath372 .
note however , that if @xmath358 is too small , only small momenta will be sampled in step ( 1 ) of algorithm [ a : ghmcconst ] , and the correlation time of the sampling will be large . in practice , the threshold @xmath358 should be tuned in preliminary computations so that : ( i ) @xmath358 is small enough so that the maximal number @xmath373 of iterations for the newton algorithm used to enforce @xmath51 in is never reached ; ( ii ) @xmath358 is large enough so that the correlation time of the sampling is as small as possible .
let us end this section with a warning : it is now known that the correction of the bias in discretizations of the langevin dynamics by a metropolization of the scheme may reduce the efficiency of the sampling , see for instance @xcite
. constrained overdamped langevin processes ( or brownian dynamics ) are solutions of the stochastic differential equation ( see also @xcite ) @xmath374 where @xmath375 is an adapted stochastic process .
equivalently , can be rewritten in the stratonovitch form as @xmath376 where @xmath377 denotes the stratonovitch integration , and @xmath378 is the projector defined by with the choice @xmath379 : @xmath380 it can be shown that verifies the detailed balance condition for ( and is ergodic with respect to ) the invariant distribution @xmath381 which is the marginal in the @xmath274-variable of the canonical distribution with constraints for the choice @xmath382 .
it is easy to generalize all our results to scalar products associated with a general symmetric definite positive matrix @xmath5 upon considering , see remark [ rmk : discrete_ovd_m ] below .
the constrained overdamped langevin process may be obtained from a scaling limit of the constrained langevin dynamics @xmath55 ( in the limit when either the mass goes to zero , or the damping @xmath298 goes to infinity ) , see propositions @xmath383 and @xmath384 in @xcite .
likewise , at the discrete level , an euler - maruyama discretization of the overdamped process can be obtained as a particular case of the numerical discretization -- for the langevin equation @xmath55 , yielding a markov chain @xmath385 on positions .
the condition that the mass goes to 0 is replaced by the condition that the mass is proportional to the time - step .
this is the content of the following proposition .
[ p : langtooverd ] suppose that the following relation is satisfied : @xmath386 with a slight abuse of notation , the mass matrix and the friction matrix are rewritten as @xmath387 and @xmath388 with @xmath389 .
then the splitting scheme -- yields the following euler scheme for the overdamped langevin constrained dynamics : @xmath390 \xi(q^{n+1 } ) = z , \end{cases}\ ] ] where @xmath391 are independent and identically distributed centered and normalized gaussian variables , and @xmath392 are the lagrange multipliers associated with the constraints @xmath393 .
moreover , the lagrange multipliers in verify : @xmath394 as well as @xmath395 where @xmath396 is defined in .
irrespective of @xmath397 , the choice in the scheme -- leads to @xmath398 where @xmath329 is associated with the constraints @xmath399 .
this gives @xmath400 where @xmath401 is such that @xmath402 .
the fluctuation - dissipation relation can be reformulated in this context as @xmath403 and the scheme is recovered by taking the associated lagrange multiplier equal to @xmath404 . finally , remarking that @xmath405 and computing explicitly @xmath401 and @xmath406 in yields -- .
this point of view allows to construct a metropolis correction to the euler scheme , using the generalized hybrid monte carlo scheme ( algorithm [ a : ghmcconst ] ) with the time - step chosen according to . in this way , assuming that the position constraint @xmath51 in is everywhere well defined , we obtain a markov chain @xmath407 discretizing the overdamped dynamics which _ exactly _ samples the invariant distribution .
deriving such a metropolis - hastings correction to the euler scheme without resorting to phase - space dynamics does not seem to be natural .
[ rmk : discrete_ovd_m ] proposition [ p : langtooverd ] can be seen as a discrete version of the zero - mass limit of the langevin dynamics .
it is also possible to obtain a discrete version of the overdamped limit ( @xmath408 ) of the langevin dynamics by assuming that the parameters satisfy the relation @xmath409 which is less restrictive than .
equation is then obtained with @xmath80 replaced by @xmath410 in this case , the effective discretization time - step @xmath411 for the overdamped langevin dynamics is thus different from the time - step @xmath412 originally used for the discretization of the langevin dynamics .
this is reminiscent of the fact that the overdamped limit ( at the continuous level ) of the langevin dynamics requires a change of timescale to obtain the overdamped langevin dynamics .
note also that in the more general case @xmath413 where @xmath5 is not supposed to be proportional to the identity , the following numerical scheme is obtained : @xmath414 \xi(q^{n+1 } ) = z , \end{cases}\ ] ] where @xmath415 .
this is a discretization of the overdamped dynamics @xmath416 which is a generalization of to a scalar product on @xmath417 induced by a general positive definite mass matrix @xmath5 .
in this section , we focus on the computation of the gradient of the rigid free energy @xmath418 using a numerical discretization of the constrained langevin process @xmath55 . as explained in the introduction
, we may indeed concentrate on the computation of the rigid free energy , since the standard free energy can be computed from the latter one using .
the relation can be proved with the co - area formula .
indeed , the free energy defined in can be rewritten as ( where c denotes a constant which may vary from line to line ) : @xmath419 hence @xmath420 where surface measures are defined in section [ sec : measures ] .
note that the rigid free energy @xmath78 indeed depends explicitly on the mass matrix since @xmath421 this section is organized as follows .
first , we show how systems with molecular constraints and systems with constrained values of the reaction coordinate can be treated in a unified framework ( section [ ti - sec : mc ] ) .
we then relate the lagrange multipliers arising in the constrained langevin dynamics , and the gradient of the rigid free energy ( the so - called mean force ) in section [ sec : lag ] .
we consider the numerical computation of the mean force in section [ sec : num_ti ] , where we prove consistency results for the corresponding approximation formulas .
finally , some numerical results on a model system illustrate the approach in section [ sec : simple_example_wca ] .
we discuss here how to generalize all the computations to systems with molecular constraints , generalizing thereby some results of @xcite . without loss of generality ,
we consider rigidly imposed molecular constraints , see remark [ rmk : choice_mc ] below for a discussion of this assumption .
this section can be considered as independent of the remainder of the paper and may therefore be omitted in a first reading . in practice , many systems are subject to molecular constraints , such as fixed lengths for covalent bonds , or fixed angles between covalent bonds .
the reader is referred to @xcite for practical aspects related to the simulation of molecular constraints . in the context of free energy computations , two types of constraints
are therefore considered : first , the molecular constraints , @xmath422 for @xmath423 , and second , the reaction coordinates denoted in this section by @xmath424 , with @xmath425 .
the submanifold of molecular constraints is denoted by @xmath426 and the submanifold associated with the reaction coordinates by @xmath427 it is assumed that the full gram matrix : @xmath428 is everywhere invertible on @xmath429 .
likewise , we denote @xmath430 and @xmath431 assuming rigid mechanical constraints on the molecular constraints @xmath432 ( see remark [ rmk : choice_mc ] below ) , we are led to considering the canonical distribution @xmath433 to describe systems with molecular constraints at a fixed temperature .
the measure @xmath434 denotes the phase space measure on @xmath435 , equal by to the conditional measure @xmath436 associated with the constraints @xmath437 , where @xmath438 is the effective momentum associated with @xmath432 .
[ rmk : choice_mc ] the distribution @xmath439 in is obtained by constraining rigidly @xmath440 to 0 , and not softly ( in which case @xmath441 would be replaced by @xmath442 , see also remark [ rem : highosclang ] ) . as explained in section [ sec : sampling ] , the distribution is the equilibrium distribution of a langevin process ( thermostated hamiltonian dynamics ) with rigid position constraints @xmath443 . choosing whether constraints should be soft or rigid is a modeling choice , and there is no clear consensus on this issue in the current literature .
note however that it is possible to rewrite the remainder of this section by considering the softly constrained potential rather than the rigidly constrained potential , up to an appropriate modification of below , with the help of some fixman corrective potential . by associativity of the conditioning of measures
, the distribution @xmath439 conditioned by a value of the reaction coordinates @xmath444 is given , up to a normalizing factor , by : @xmath445 therefore , considering the marginal probability distribution of the reaction coordinates @xmath446 leads to the following definition of the free energy associated with @xmath447 : @xmath448 the conditional distribution can be decomposed as follows , using the co - area formulas - and the definition of effective momentum : @xmath449 integrating out the momentum in the linear space @xmath450 with scalar product @xmath451 , the free energy can be rewritten as : @xmath452 as a consequence , the free energy @xmath453 can be computed from the generalized rigid free energy : @xmath454 using the following formula , similar to : @xmath455 in the above , @xmath456 is defined similarly to .
the case of molecular constraints can therefore be treated within the general framework considered in this paper , the sampling of the canonical measure @xmath456 and the computation of the rigid free energy being the problems at hand . for systems with molecular constraints ,
the measure sampled by the overdamped langevin dynamics with @xmath457 is the marginal distribution in the position variables of @xmath458 in the special case @xmath382 , namely @xmath459 the rigid free energy which is thus naturally computed with such a dynamics is @xmath460 and the actual free energy is thus recovered by a formula similar to , namely @xmath461 in this section , the average of the constraining force is related to the gradient of the rigid free energy ( or mean force ) .
we also give a similar result for the following generalized rigid free energy : @xmath462 [ p : meanforce ] the constraining force @xmath463 defined in as @xmath464 yields on average the rigid free energy derivative : @xmath465 moreover , for general constraints and the associated generalized free energy , the formula can be extended as follows : the generalized constraining force is @xmath466 where @xmath467 is defined in , and the rigid mean force is @xmath468 where @xmath469 , and @xmath470 is defined in . when @xmath67 verifies @xmath471 , then @xmath472 and @xmath473 .
formulas and are obtained directly by replacing @xmath224 by @xmath474 in lemma [ l : consint ] ( see the appendix ) . the fact that @xmath475 in the tangential case ( namely when @xmath471 ) is a consequence of .
the following lemma gives a momentum - averaged version of the constraining force ( a similar formula exists in the overdamped case , see equations ( 4.8)-(4.9 ) in @xcite , for example ) .
[ l : meanforce_av ] the rigid mean force can be rewritten as : @xmath476 where @xmath477 consider the gaussian distribution @xmath478 defined in : @xmath479 which is the marginal distribution in the momentum variable of the canonical distribution @xmath335 , conditioned by a given @xmath301 .
proving lemma [ l : meanforce_av ] amounts to showing that the average of the constraining force @xmath242 with respect to @xmath480 yields @xmath481 : @xmath482 first , we compute the covariance matrix @xmath483 of the gaussian distribution @xmath484 . since @xmath484 is a centered gaussian distribution , @xmath485 satisfies , for all @xmath486 , @xmath487 denoting @xmath488 , this yields @xmath489 so that @xmath490 this gives @xmath491 averaging over momenta thus leads to the desired result .
free energy derivatives can also be obtained from the lagrange multipliers of the langevin constrained process @xmath55 .
this is very useful in practice since it avoids the computation of second order derivatives of the reaction coordinates which appear in the expressions of @xmath492 and @xmath493 ( see the discussion at the beginning of section [ sec : avg_lagrange ] ) : consider the rigidly constrained langevin process solution of @xmath55 , with associated lagrange multipliers @xmath375 .
assume that @xmath97 , @xmath494 and @xmath299 are bounded functions on @xmath37 , and @xmath495 is strictly positive on @xmath496 ( in the sense of symmetric matrices ) .
then , the almost sure convergence claimed in the introduction holds : @xmath497 a similar result holds for the ` hamiltonian part ' of the lagrange multipliers , defined by : @xmath498 indeed , the following almost sure convergence holds : @xmath499 the estimator based on has a smaller variance than the estimator based on ( or above ) since only the bounded variation part is retained , and the martingale part due to the brownian increments and the dissipation term are subtracted out .
similar results on variance reduction where obtained in the overdamped case in @xcite .
recall the expression of the lagrange multipliers , which can be decomposed as the sum of the constraining force , a dissipation term and a martingale ( fluctuation ) term : @xmath500 the result follows from three facts .
first , the process is ergodic with respect to the equilibrium distribution @xmath335 and averaging @xmath242 yields the rigid free energy derivative in view of proposition [ p : meanforce ] .
this already shows .
second , the gaussian distribution of @xmath335 with respect to momentum variables is centered , which yields : @xmath501 third , the variance of the martingale term can be uniformly bounded as @xmath502 this implies the almost sure convergence @xmath503 see for example theorem 1.3.15 in @xcite .
the fact that averaging the lagrange multiplier in indeed yields the mean force may not be intuitive .
this is actually very much related to the cost interpretation of the lagrange multipliers in optimization , see ( * ? ? ?
* remark 3.29 ) .
estimates of the mean force based on either , or can be obtained .
free energy derivatives can be computed by averaging @xmath504 or @xmath505 with respect to the distribution @xmath335 , for instance using the estimators : @xmath506 or @xmath507 the functions @xmath504 and @xmath505 may thus be called `` rigid local mean forces '' .
note that using the momentum - averaged local mean force @xmath481 instead of the original @xmath242 reduces the variance since the fluctuations of the momentum variable have been averaged out analytically .
table [ tab : comparison_variance_langevin_ti ] below confirms this analysis , although the variance reduction appears to be small in our specific numerical experiment .
assuming the convergence of the constrained splitting scheme -- in the probability distribution sense to the limiting langevin process @xmath55 , the convergence of these estimators to @xmath508 is ensured , when taking first the limit @xmath509 with @xmath510 such that @xmath511 , and then @xmath512 .
free energy derivatives can also be computed using the lagrange multipliers of a langevin constrained process according to or .
this technique avoids the possibly cumbersome computation of second order derivatives @xmath513 of the reaction coordinate , which appear in the expressions of @xmath492 or @xmath481 . besides
, the lagrange multipliers are needed anyway for the numerical integration of the dynamics .
the computation can be performed as before with a longtime simulation of the splitting scheme -- discretizing the langevin process with constraints .
the following approximation formula can for instance be used : @xmath514 where @xmath515 are the lagrange multipliers in the hamiltonian part .
the consistency of this estimator is given by the following proposition .
[ p : consist ] the approximation formula is consistent .
more precisely , the lagrange multipliers @xmath516 in -- are both equivalent when @xmath509 to the constraining force defined in : @xmath517 moreover , the following second order consistency holds for the sum of the lagrange multipliers : @xmath518 together with the variant : @xmath519 the variant , which involves positions and momenta at the beginning and at the end of the hamiltonian steps only , is used in below to estimate the time discretization error in the thermodynamic integration method based on the estimator . for sufficiently small time - steps @xmath80 , the implicit function theorem ensures that the two projection steps associated with the nonlinear constraints in -- have a unique smooth solution .
a taylor expansion with respect to @xmath80 of the position constraints gives @xmath520 where @xmath521 denotes the order @xmath195 differential of @xmath26 computed at @xmath274 and evaluated with the vectors @xmath522 .
we denote @xmath523 then , the fact that @xmath524 and the identity @xmath525 yield the following expansion of @xmath526 in terms of @xmath527 : @xmath528 by time symmetry , the same computation holds for @xmath406 , starting from @xmath322 and by formally replacing @xmath80 by @xmath529 .
this can be double checked by taylor expanding with respect to @xmath80 the position constraints , as done above for @xmath401 .
it thus holds : @xmath530
the sum of the multipliers therefore reads @xmath531 which gives .
now , using the previous calculations , we remark that : @xmath532 \dps p^{n+1/2 } = p^{n+3/4 } + \frac{\dt}{2 } \nabla v ( q^{n+1 } ) - \frac{\dt}{2 } \nabla \xi ( q^{n+1 } ) f_{\rm rgd}^m(q^{n+1},p^{n+1/2 } ) + { \rm o}(\dt ^2 ) .
\end{cases}\ ] ] thus , it holds @xmath533 this gives the claimed second order consistency of the sum of the lagrange multipliers .
let us discuss the convergence of the approximation .
assuming again that the constrained splitting scheme -- converges in the probability distribution sense to the limiting langevin process @xmath55 , the following convergence in probability distribution occurs when @xmath509 and @xmath511 : @xmath534 this shows the convergence of the estimate of the mean force when taking first the limit @xmath509 and then @xmath512 .
when the scheme -- is complemented with a metropolis step ( see algorithm [ a : ghmcconst ] ) , it is possible to prove a result on the longtime limit of trajectorial averages ( _ i.e. _ letting first the number of iterations go to infinity , and then taking the limit @xmath509 ) , upon assuming the irreducibility of the numerical scheme .
indeed , let us consider the markov chain @xmath535 generated by the ghmc scheme in algorithm [ a : ghmcconst ] , and assume ( i ) the irreducibility of the markov chain , and ( ii ) that appropriate rejections outside the set @xmath536 are made in the steps ( 1)-(2)-(4 ) of the algorithm . in particular , the projection steps associated with the nonlinear constraints in step ( 2 ) of algorithm [ a : ghmcconst ] are well defined .
then , by ergodicity , an average of the analytic expression of the local rigid mean force @xmath481 given in yields an estimate of the free energy without time discretization error : @xmath537 if @xmath242 is used instead of @xmath481 , then the mean force is computed with some exponentially small error : almost surely , @xmath538 for some @xmath359 .
the error arising from replacing @xmath539 with @xmath169 is indeed exponentially small in view of ( namely @xmath540 ) and using the fact that the marginal distribution in the @xmath273-variable is gaussian . likewise , for estimates based on lagrange multipliers , the following longtime averaging holds : almost surely , @xmath541 where we have used the estimate on the lagrange multipliers .
the limit @xmath509 is obtained by a dominated convergence argument : @xmath542 note that , due to the metropolis correction in algorithm [ a : ghmcconst ] , the time discretization error in the sampling of the invariant measure is removed .
the only remaining time discretization errors come from ( i ) the approximation of the local mean force by the lagrange multipliers ( this is a second order error ) , and ( ii ) the integration domain being @xmath539 instead of @xmath169 ( as discussed above , this is an exponentially small error in @xmath80 ) . in conclusion
, the left - hand side of is an approximation of @xmath543 up to a @xmath544 error term .
finally , let us emphasize that free energy derivatives can be computed with the estimator within the overdamped langevin framework , using the scheme and the expressions -- of proposition [ p : langtooverd ] .
let us recall that the latter are equivalent to the scheme -- with fluctuation - dissipation matrices satisfying @xmath545 .
this leads to the original free energy estimator ( recall that , for the overdamped dynamics , @xmath72 is equipped with the scalar product associated with the identity matrix ) : @xmath546 which can be seen as a variant of the variance reduced estimator proposed directly for the overdamped scheme in @xcite : @xmath547 the rigorous justification of the consistency of in the limit @xmath509 follows from the results of @xcite .
see also section [ sec : time_continuous_limit_ovd ] below for similar results .
we consider a system composed of @xmath0 particles in a 2-dimensional periodic box of side length @xmath548 , interacting through the purely repulsive wca pair potential , which is a truncated lennard - jones potential : @xmath549 + \varepsilon & \quad { \rm if \ } r \leq r_0 , \\ 0 & \quad { \rm if \ } r > r_0 , \end{array } \right.\ ] ] where @xmath550 denotes the distance between two particles , @xmath551 and @xmath299 are two positive parameters and @xmath552 . among these particles ,
two ( numbered 1 and 2 in the following ) are designated to form a dimer while the others are solvent particles . instead of the above wca potential ,
the interaction potential between the two particles of the dimer is a double - well potential @xmath553 ^ 2,\ ] ] where @xmath554 and @xmath555 are two positive parameters .
the total energy of the system is therefore , for @xmath556 with @xmath557 , @xmath558 see @xcite for instance for other computational studies using this model .
the potential @xmath559 exhibits two energy minima , one corresponding to the compact state where the length of the dimer is @xmath560 , and one corresponding to the stretched state where this length is @xmath561 .
the energy barrier separating both states is @xmath554 .
the reaction coordinate used to describe the transition from the compact to the stretched state is the normalized bond length of the dimer molecule : @xmath562 where @xmath563 and @xmath564 are the positions of the two particles forming the dimer .
the compact state ( resp . the stretched state ) corresponds to the value @xmath565 ( resp .
@xmath566 ) of the reaction coordinate .
the inverse temperature is set to @xmath567 , with @xmath568 particles ( @xmath569 solvent particles and the dimer ) with solvent density @xmath570 , since there are @xmath569 solvent particles in a square box of side length @xmath571 with @xmath572 .
the parameters describing the wca interactions are set to @xmath573 and @xmath574 , and the additional parameters for the dimer are @xmath575 and @xmath576
. for this system , @xmath379 and @xmath577 is constant , so that the rigid free energy @xmath578 is equal to the free energy @xmath84 .
the mean force is estimated at the values @xmath579 , with @xmath580 , @xmath581 and @xmath582 , by ergodic averages obtained with the projected dynamics with metropolis correction ( algorithm [ a : ghmcconst ] , where in the simple case considered here , the fluctuation - dissipation part can be integrated exactly ) . for each value of @xmath38
, we integrate the dynamics on a time @xmath583 with a step size @xmath584 , using a scalar friction coefficient @xmath585 .
the resulting mean force profile is presented in figure [ fig : ti_lang_1 ] , together with the associated free energy profile .
top : estimated mean force .
bottom : corresponding free energy profile .
, title="fig:",width=340 ] top : estimated mean force .
bottom : corresponding free energy profile .
, title="fig:",width=340 ] figure [ fig : ti_lang_2 ] compares the analytical constraining force @xmath586 and the lagrange multipliers , see proposition [ p : consist ] . in figure
[ fig : ti_lang_2 ] , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
it can be seen that the difference between @xmath586 and the lagrange multipliers is small in any cases , though somewhat larger for the lowest values of @xmath26 .
top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] top : the constraining force @xmath586 ( pale line ) , and the difference between the constraining force and its estimate from the lagrange multipliers ( dark line ) .
middle : zoom on the difference between the constraining force and the lagrange multipliers .
note the difference of scales for the @xmath591-axis .
bottom : the schedule @xmath26 is piecewise constant . in all figures , the @xmath587-axis represents the blocks of @xmath588 simulation steps , concatenated for the @xmath589 different values of @xmath590 .
, title="fig:",width=340 ] it can be checked numerically that the differences @xmath592 and @xmath593 are indeed of order @xmath594 , and that the difference @xmath595 is indeed of order @xmath596 ( by computing the average of these elementary differences for various step sizes ) .
the lagrange multipliers are in any case very good approximations to the constraining force @xmath492 .
let us finally discuss the efficiency of the different estimators of the mean force , in terms of their variances .
they can be written as the empirical average of the following random sequences : @xmath597 where @xmath598 are given by the numerical scheme -- .
the correlations in time ( between the iterates ) are very similar for the three methods , and we therefore simply compute the variance over all the samples .
table [ tab : comparison_variance_langevin_ti ] compares the so - obtained standard errors over @xmath588 time - steps with @xmath584 ( simulation time @xmath599 for each value of the reaction coordinate ) .
the results show that the different estimators are more or less equivalent .
this is related to the fact that the essential source of variance comes from the sampling of the positions , and not the sampling of the velocities .
note however that , for the smallest value of the reaction coordinate , the estimator based on the averaged local mean force @xmath600 appears to be better in terms of variance .
.standard error ( square - root of the variance ) of three mean force estimators , with correlations in time neglected , for different values @xmath38 of the reaction coordinate . [ cols="^,^,^,^ " , ]
this section presents nonequilibrium hamiltonian and langevin dynamics with time - evolving constraints .
we thus consider @xmath223 solution to the dynamics @xmath96 , which we recall for convenience : @xmath601 d p_t & = -\nabla v ( q_t ) \,dt -\gamma_p(q_t ) m^{-1 } p_t \ , dt+ \sigma_p(q_t ) \,d w_t + \nabla
\xi(q_t ) \ , d \lambda_t , \\[6pt ] \xi(q_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.\ ] ] we prove in particular the fluctuation identity , see below .
recall ( see ) that , for simplicity , we assume in this section that the fluctuation - dissipation matrices are assumed to be of the form @xmath602 with @xmath603 . at variance with the previous sections , we do _ not _ assume that @xmath495 is strictly positive .
actually , @xmath604 corresponds to an interesting case : the deterministic hamiltonian dynamics . to our knowledge
, the standard work fluctuations derived so far ( except for our previous work @xcite ) apply only to the case of time - dependent hamiltonians .
it is possible to consider transitions in the values of some reaction coordinate in this framework upon resorting to steered molecular dynamics techniques . in this case ,
a penalty term @xmath605 ( with @xmath551 small ) is used in the energy of the system to `` softly '' constrain the system to remain close to the submanifold @xmath606 at time @xmath607 .
however , it is observed in practice that the statistical fluctuations increase with smaller @xmath551 ( see @xcite ) .
we propose instead to replace the stiff constraining potential @xmath608 by a projection onto the submanifold @xmath417 .
this is reminiscent of the replacement of stiff constrained langevin dynamics by rigidly constrained ones , see remark [ rem : highosclang ] .
this section is organized as follows .
we first define the generalized free energy which is naturally computed with @xmath96 , and relate it to the standard free energy in section [ sec : langti_fe ] . then , we give some precisions on the nonequilibrium dynamics @xmath96 in section [ sec : generators_jarz ] .
next , we prove an appropriate version of the jarzynski - crooks fluctuation equality in section [ sec : jarz_lang_cons ] . a numerical discretization of the nonequilibrium dynamics is proposed in section [ sec : num_jarz ] , together with various approximations of the work .
in particular , we propose a numerical strategy to obtain a jarzynski - crooks identity without time discretization error ( see section [ sec : discrete_jarz ] ) .
we then consider the overdamped limit when the mass matrix @xmath5 goes to 0 ( see section [ sec : ovd_limit_disc ] ) . finally , in section [ sec : num_res_jarz ] , we present some numerical results for the model system already considered in section [ sec : simple_example_wca ] . for @xmath223 solution to the langevin dynamics @xmath96 ,
the reaction coordinate evolution @xmath609 implies that @xmath610 , so that , at each time @xmath53 , the system @xmath223 belongs to the state space @xmath611 . as a consequence ,
the free energy difference computed in this section by the jarzynski relation without correction ( see below ) is in fact the generalized rigid free energy @xmath612 defined in , in the special case @xmath152 : @xmath613 the latter free energy is associated to the normalization constant @xmath614 of the distribution @xmath615 defined by .
the generalized rigid free energy can be explicitly related to the usual free energy as follows .
first , remark that , for a fixed @xmath274 , @xmath616 in the above , the change of variable @xmath617 has been used , in the space @xmath618 note that @xmath619 can be interpreted as the kinetic energy of the reaction coordinate @xmath26 . using the decomposition of measures and the above calculations ,
an alternative expression of the generalized free energy is : @xmath620 where , as usual , @xmath621 denotes a generic constant ( independent of @xmath38 ) whose value may vary from line to line . as a consequence ,
the standard free energy is easily recovered from the generalized free energy , using relations similar to . indeed , using , and with computations similar to the ones leading to
, the difference of the two free energies writes : @xmath622 in practical nonequilibrium computations , the profile @xmath623 can then be computed by adding a corrector to the work value in the jarzynski estimator computing @xmath624 .
this yields the identity mentioned in the introduction and proved below ( see the discussion after theorem [ th : crookslangcons ] ) .
the explicit expression of the lagrange multipliers in @xmath96 is obtained by a computation similar to for the case without switching , by differentiating twice the constraints over time : @xmath625 in view of the special structure of @xmath232 , this leads to @xmath626 the expression does not depend on the fluctuation - dissipation tensors @xmath232 .
this leads to simplified computations and motivates the special form of the latter matrices .
the momentum evolution @xmath96 thus simplifies as @xmath627 let us denote by @xmath628 the generator of the forward dynamics @xmath629 defined in @xmath96 .
the latter has a backward switching version , @xmath630 obtained by using a time reversed switching @xmath631 , and by reversing the momentum first in the initial condition , and then reversing them back after the time evolution ( see @xcite for more general backward dynamics ) .
more precisely , the backward dynamics can be defined through its generator @xmath632 where @xmath633 is the generator of the forward process at time @xmath634 , and @xmath635 is the momentum flip operator with @xmath636 .
thus @xmath637 is solution of the forward evolution equation @xmath96 with a switching schedule @xmath631 .
therefore , the time evolution of the backward dynamics is given by @xmath638 d
p^{\rm b}_{t'}= \nabla v(q^{\rm b}_{t ' } ) \ , dt ' -\gamma_p(q^{\rm b}_{t ' } ) m^{-1 } p^{\rm b}_{t ' } \ , dt'+ \sigma_p(q^{\rm b}_{t ' } ) \
, d w_{t'}^{\rm b } + \nabla \xi(q^{\rm b}_{t ' } ) \
, d \lambda_{t'}^{\rm b } , \\[6pt ] \xi(q^{\rm b}_{t ' } ) = z(t - t ' ) .
\end{cases}\ ] ] in the following proposition , the expressions of @xmath628 and @xmath639 are explicitly written .
[ prop : generators_noneq ] consider @xmath640 .
then , the generator of the forward process @xmath96 at time @xmath86 $ ] reads : @xmath641 and the generator of the backward process at time @xmath642 $ ] reads : @xmath643 where @xmath644 is the fluctuation - dissipation operator defined in .
first , let us consider the terms in @xmath96 arising from the hamiltonian evolution and from the switching ( _ i.e. _ without fluctuation - dissipation , which amounts to setting @xmath645 and @xmath646 in @xmath96 ) .
since during this dynamics @xmath647 , yields : @xmath648 so that , using , @xmath649 with , we then obtain : @xmath650 now , the hamiltonian part of the switched dynamics @xmath96 ( see also ) can be recognized in , so that the generator @xmath651 when @xmath652 reads : for any smooth test function @xmath224 , @xmath653 the full expression of the generator @xmath654 is then obtained by adding the terms arising from the fluctuation - dissipation .
these terms are directly obtained from the terms involving @xmath495 and @xmath655 in , as in the proof of proposition [ s : p : lconstgen ] .
the generator of the backward switching process given by can be obtained from similar computations .
first , the thermostat parts in and in @xmath96 are the same .
consider now the hamiltonian part ( obtained by taking @xmath652 ) in the dynamics . by definition of the backward dynamics , and the expression of the forward dynamics , the hamiltonian part reads @xmath656 so that @xmath657 this gives . before stating the main result of this section ( theorem [ th : crookslangcons ] below ) , we need to introduce a notion of work .
this quantity is most conveniently defined for deterministic dynamics , but the corresponding definition is also valid for stochastic dynamics .
we define the work @xmath658 associated with the constraining force @xmath659 in @xmath96 as the physical displacement multiplied by the force : @xmath660 by convention , @xmath661 . in the above computations
, we used successively the fact that @xmath662 , and then @xmath663 are differentiable processes , so that stratonovitch and it integrations are equivalent .
let us introduce the deterministic version of the nonequilibrium process @xmath96 ( _ i.e. _ @xmath652 ) : @xmath664 d \tilde{p}_t & = -\nabla v ( \tilde{q}_t ) \,dt + \nabla \xi(\tilde{q}_t ) \ , d \tilde{\lambda}_t , \\[6pt ] \xi(\tilde{q}_t ) & = z(t ) , \hspace{5 cm } ( c_q(t ) ) \end{aligned } \right.\ ] ] and denote by @xmath665 the associated flow between time @xmath86 $ ] and @xmath666 $ ] .
the work can now be written out more explicitly using the following lemma : the infinitesimal variation of the work reads : @xmath667 where for all @xmath86 $ ] and all @xmath668 , @xmath669 the total exchanged work is then a time integral associated with the path @xmath629 , and is denoted by : @xmath670 note that the expression can be interpreted as the energy variation of the system during the switching when the stochastic thermostat is turned off .
the expression of the lagrange multipliers in yields : @xmath671 moreover , gives : @xmath672 where in the last line we have used @xmath673 .
this gives . to prove
, we compute the variations of the energy @xmath674 for @xmath675 solution of with initial condition @xmath67 : @xmath676 the last equality is obtained using the computation of the lagrange multipliers in .
this yields .
we are now in position to state the main result of this section .
[ th : crookslangcons ] consider the normalization @xmath614 for the canonical distribution @xmath615 defined in .
denote by @xmath677 the solution of the forward langevin dynamics @xmath96 with initial conditions distributed according to @xmath678 and by @xmath679 the solution of the backward langevin process with initial conditions distributed according to @xmath680 then , the following jarzynski - crooks identity holds on @xmath681 $ ] : for any bounded path functional @xmath682}$ ] , @xmath683}\left(\{q_t , p_t\}_{0 \leq t \leq t}\right ) \ ,
{ \rm e}^{-\beta\w_{0,t}\left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } \right ) } } { \e { \left ( \ph^{\rm r}_{[0,t]}\left(\{q^{\rm b}_{t'},p^{\rm b}_{t'}\}_{0 \leq t ' \leq t } \right ) \right ) } } , \ ] ] where @xmath684 denotes the composition with the operation of time reversal of paths : @xmath685}^{\rm r}\big(\ { q^{\rm b}_{t'},p^{\rm b}_{t'}\}_{0 \leq t ' \leq t}\big ) = \ph_{[0,t]}\big(\ { q^{\rm b}_{t - t},p^{\rm b}_{t - t } \}_{0 \leq t \leq t}\big).\ ] ] note that the theorem still holds in the hamiltonian case , _
i.e. _ when @xmath686 .
the choice @xmath682 } = 1 $ ] in leads to the following work fluctuation identity : @xmath687 } ) } \right ) \big].\ ] ] besides , upon choosing a path functional @xmath688 , it is possible to obtain a family of free energy estimators , parameterized by @xmath689 and where both forward and backward paths are weighted by the exponential of some work .
moreover , the standard crooks equality on ratios of probability density functions of work values is also a consequence of , see section 4.2.2 in @xcite .
note also that the choice @xmath682}(q , p ) = \phi(q_t , p_t)$ ] leads to the following representation of the canonical distribution @xmath690 : @xmath691}\right ) } } \right ) } } { \e { \left ( { \rm e}^{-\beta\w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } } \right ) } } = \int_{\manq_{\xi , v_\xi}(z(t),\dot{z}(t ) ) } \phi(q , p ) \ , \mu_{\manq_{\xi , v_\xi}(z(t),\dot{z}(t))}(dq\ , dp ) .\ ] ] the usual free energy profile @xmath65 can therefore be computed using the relations - presented in the introduction .
indeed , equation ( see below ) can be proved by combining and as follows : @xmath692 } ) } \right ) \big ] \nonumber \\ & = -\frac1\beta \ln \e { \left ( ( \det g_m(q_t ) ) ^{-1/2 } { \rm e}^{\frac{\beta}{2 } \dot{z}(t)^t g_m^{-1}(q_t ) \dot{z}(t)}\ , { \rm e}^{-\beta\w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } } \right ) } \nonumber \\ & \quad + \frac1\beta \ln \e { \left ( ( \det g_m(q_0 ) ) ^{-1/2 } { \rm e}^{\frac{\beta}{2 } \dot{z}(0)^t g_m^{-1}(q_0)\dot{z}(0 ) } \right ) } \nonumber \\ & = -\frac1\beta \ln \left ( \frac { \e\left(\rme^{-\beta \left [ \w_{0,t } { \left({\left\{q_t , p_t\right\}}_{t\in [ 0,t]}\right ) } + c(t , q_t ) \right ] } \right ) } { \e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right ) , \label{eq : identity_to_approximate}\end{aligned}\ ] ] where the corrector @xmath693 is defined in : @xmath694 this leads to the following relation : @xmath695 } \right)}{\e\left(\rme^{-\beta c(0,q_0 ) } \right ) } \right),\ ] ] estimators of the free energy based on can then be constructed , see chapter 4 in @xcite for a review . before turning to the proof of theorem [ th : crookslangcons ] , we first give the general lemma which enables to deduce the jarzynski - crooks fluctuation identity from a _ nonequilibrium detailed balance condition _
( similar to the one presented in @xcite for switchings arising from a time - dependence in the hamiltonian ) .
[ lem : jarz_gen ] let @xmath696 ( resp .
@xmath697 ) be a markov process with infinitesimal generator @xmath698 ( resp .
@xmath699 ) and initial conditions distributed according to ( resp . ) .
let us assume that the following nonequilibrium detailed balance condition is satisfied : for any two smooth test functions @xmath259 , @xmath260 , @xmath700 then the jarzynski - crooks fluctuation identity holds .
we use in this proof the short - hand notation @xmath701 , @xmath702 and @xmath703 for the partition function @xmath614 , the ( unnormalized ) distribution @xmath704 and the submanifold @xmath611 respectively .
let us introduce the following weighted transition operators : for any bounded test function @xmath224 , @xmath705 } \right ) } } \ , \big | \ , ( q_t , p_t ) = ( q , p ) \big ) , \label{eq : pfwd}\\ p^{\rm b}_{t',t}(\ph)(q , p ) & = \e\big(\ph(q^{\rm b}_{t},p^{\rm b}_{t})\ , \big | \ , ( q^{\rm b}_{t'},p^{\rm b}_{t'})=(q , p ) \big ) , \label{eq : pbwd}\end{aligned}\ ] ] where @xmath696 ( resp .
@xmath697 ) is a markov process with infinitesimal generator @xmath698 ( resp .
@xmath699 ) , and @xmath706 .
we assume that these operators are well defined and smooth with respect to time for sufficiently smooth test functions defined in an open neighborhood of @xmath611 and @xmath707 respectively ( for any @xmath708 $ ] ) .
the transition operators satisfy the following backward kolmogorov evolution equations : @xmath709 p^{\rm f}_{t , t } = { \rm i d } , \end{cases } \quad \begin{cases } \partial_{t ' } p^{\rm b}_{t',t } = -{\mathcal l}^{\rm b}_{t ' } p^{\rm b}_{t',t } , \\[6pt ] p^{\rm b}_{t , t } = { \rm id}. \end{cases}\ ] ] consider now two test functions @xmath710 and @xmath711 .
the balance condition implies @xmath712 integrating this equality on @xmath681 $ ] yields @xmath713 which is the crooks identity for path functionals of the form @xmath714}(q , p ) = \ph_0(q_0,p_0 ) \ , \ph_t(q_t , p_t).\ ] ] indeed ,
@xmath715 } ) } \big ] , \ ] ] while @xmath716.\ ] ] then , using the markov property of the forward and backward processes , crooks identity can be extended to finite - dimensional path functionals of the form : @xmath717}(q , p ) = \ph_0(q_{0},p_0 ) \dots \ph_k(q_{t_k},p_{t_k } ) \dots \ph_{k}(q_{t},p_t)\ ] ] with @xmath718 by repeatedly using a variant of on time subintervals @xmath719 $ ] ( see the proof of theorem 4.10 in @xcite for further precisions ) .
this allows to conclude since finite dimensional time marginal laws characterize the distribution on continuous paths , see for instance @xcite .
we are now in position to write the by lemma [ lem : jarz_gen ] , it is sufficient to prove the nonequilibrium detailed balance for the markov processes @xmath696 and @xmath697 , solutions to @xmath96 and respectively , with generators @xmath654 and @xmath720 defined by and .
first , using lemma [ l : consint ] , we compute the variation of the unnormalized canonical equilibrium distribution with constraints with respect to the switching : @xmath721 on the other hand , and proposition [ prop : generators_noneq ] give @xmath722 now , can be verified in two steps .
first , the last two terms in ( the thermostat terms ) cancel out after integration with respect to @xmath723 thanks to the detailed balance condition
. then , an integration of with respect to @xmath724 gives , in view of and , @xmath725 which is indeed .
note that the time - regularity on the evolution semi - groups - required to make these computations rigorous is proved in the overdamped case in the proof of theorem a.5 in @xcite .
a similar proof can be carried out for constrained langevin equations . in this section , a numerical scheme for the nonequilibrium dynamics @xmath96 and the associated free energy estimator
are presented . as for langevin processes with constraints ( section [ sec : consnum ] ) , a splitting between the hamiltonian part and the thermostat part of the dynamics @xmath96 leads to a simple and natural scheme ( see -- below ) .
note that a consistent numerical scheme in the case of hamiltonian dynamics can be obtained by considering only ( this corresponds to @xmath726 ) .
besides , we propose a discrete jarzynski - crooks identity without time discretization error , see section [ sec : discrete_jarz ]
. the reaction coordinate path is first discretized as @xmath727 where @xmath728 is the number of time - steps . for simplicity ,
equal time increments are used , so that @xmath729 and @xmath730 . the deterministic hamiltonian part in the equations of motion @xmath96 with switched position constraints
@xmath731 can be integrated by a velocity - verlet algorithm with constraints similar to .
the fluctuation - dissipation term in @xmath96 can be integrated similarly to the constrained case without switching - , using an ornstein - uhlenbeck process on the momentum variable approximated by a midpoint euler scheme . in conclusion ,
the splitting scheme for the langevin dynamics with time - evolving constraints reads as follows : take initial conditions @xmath732 distributed according to @xmath733 and iterate on @xmath734 : @xmath735 & \begin{cases } \dps p^{n+1/2 } = p^{n+1/4 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n } ) } + \nabla \xi(q^n ) \lambda^{n+1/2 } , & \\[6pt ] \dps q^{n+1 } = q^{n } + \dt \ m^{-1 } p^{n+1/2 } , & \\[6pt ] \dps \xi(q^{n+1 } ) = z(t_{n+1 } ) , & ( c_q ) \\[6pt ] \dps p^{n+3/4 } = p^{n+1/2 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n+1 } ) } + \nabla \xi(q^{n+1 } ) \lambda^{n+3/4},&\\[6pt ] \dps \nabla \xi ( q^{n+1})^{t } m^{-1 } p^{n+3/4 } = \frac { \dps z(t_{n+2})- z(t_{n+1})}{\dps \dt } , & ( c_p ) \end{cases}\label{eq : verletconstswitched}\\ & \begin{cases } \dps p^{n+1 } = p^{n+3/4 } -\frac{\dt}{4 } \gamma_p(q^{n+1 } ) m^{-1}(p^{n+3/4}+p^{n+1 } ) \\
\dps \phantom{p^{n+1 } = } + \sqrt{\frac{\dt}{2 } } \sigma_p(q^{n+1 } ) { \mathcal g}^{n+1/2 } , \end{cases}\label{eq : flucdissconstjarz2}\end{aligned}\ ] ] where @xmath736 and @xmath737 are sequences of i.i.d .
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
note that the momenta obtained from -- satisfy @xmath738 so that constraints on momenta are automatically enforced , and no lagrange multiplier is needed in and .
we comment in the subsequent sections on the different parts of the scheme .
the lagrange multipliers @xmath401 are associated with the position constraints @xmath315 , and the lagrange multipliers @xmath406 are associated with the velocity constraints @xmath317 . in @xmath318
, the velocity of the switching at time @xmath739 is discretized as : @xmath740 the latter choice is motivated by the following observation : the position after one step of an unconstrained motion , given by @xmath741 already satisfies @xmath315 up to error terms of order two with respect to @xmath80 .
indeed , using : @xmath742 this property is useful to ensure a fast convergence of the numerical algorithm solving the nonlinear constraints @xmath315 .
the numerical flow associated with is denoted in the sequel as @xmath743 ( q^n , p^{n+1/4 } ) & \mapsto & ( q^{n+1},p^{n+3/4 } ) \end{array}\right.\ ] ] it can be proven that @xmath744 is a symplectic map .
the proof is indeed exactly the same as for the symplecticity of the classical rattle scheme , see ( * ? ? ?
* sections vii.1.3 ) for an explicit computation for symplectic euler and ( * ? ? ?
* sections vii.1.4 ) for an extension to rattle . as a consequence
, @xmath744 transports the phase space measure @xmath745 to the phase space measure @xmath746 . in practice , may be rewritten in a form more suited to numerical computations . of course
, similar considerations hold for . since @xmath747 and @xmath748 ,
is equivalent to : @xmath749 where the lagrange multiplier @xmath329 is associated with the constraint @xmath318 .
the equivalence between and can be checked by multiplying by @xmath750 and using .
the lagrange multiplier @xmath329 in is obtained by multiplying the above equation by @xmath751 , and solving the following linear system : @xmath752 this system is well posed .
indeed , the matrix @xmath753 can be rewritten as @xmath754 with @xmath755 .
both @xmath5 and @xmath298 are symmetric and non - negative , so that @xmath267 is symmetric , positive and invertible .
finally , the invertibility of @xmath754 follows from the invertibility of @xmath34 . in the special case
when @xmath298 and @xmath5 are equal up to a multiplicative constant , the numerical integration can be simplified using the explicit formula and the method described below , which still holds for the tangential part of the momentum .
see section [ sec : num_res_jarz ] below for further precisions .
the splitting scheme for the backward langevin dynamics with time - evolving constraints reads as follows : denote @xmath756 , take initial conditions @xmath757 distributed according to @xmath758 and iterate on @xmath759 , @xmath760 &\begin{cases } \dps p^{{\rm b},n'+1/2 } = p^{{\rm b},n'+1/4 } + \displaystyle{\frac{\dt}{2 } \nabla v ( q^{{\rm b},n ' } ) } + \nabla \xi(q^{{\rm b},n ' } ) \lambda^{{\rm b},n'+1/2 } , & \\[6pt ] \dps q^{{\rm b},n'+1 } = q^{{\rm b},n ' } - \dt \ m^{-1 } p^{{\rm b},n'+1/2 } , \\[6pt ] \dps \xi(q^{{\rm b},n'+1 } ) = z(t_{n_t - n'-1 } ) , & ( c_q ) \\[6pt ] \dps p^{{\rm b},n'+3/4 } = p^{{\rm b},n'+1/2 } + \displaystyle{\frac{\dt}{2 } \nabla v ( q^{{\rm b},n'+1 } ) } + \nabla \xi(q^{{\rm b},n'+1 } ) \lambda^{{\rm b},n'+3/4},&\\[6pt ] \dps \nabla \xi ( q^{{\rm b},n'+1})^{t } m^{-1 } p^{{\rm b},n'+3/4 } = \frac { \dps z(t_{n_t - n ' } ) - z(t_{n_t - n ' - 1 } ) } { \dps \dt } , & ( c_p ) \end{cases}\label{eq : verletconstswitchedbck}\\ & \begin{cases } \dps p^{{\rm b},n'+1 } = p^{{\rm b},n'+3/4 } -\frac{\dt}{4 } \gamma_p(q^{{\rm b},n'+1 } ) m^{-1}(p^{{\rm b},n'+3/4}+p^{{\rm b},n'+1 } )
\\ \dps \phantom{p^{{\rm b},n'+1 } = } + \sqrt{\frac{\dt}{2 } } \sigma_p(q^{{\rm b},n'+1 } ) { \mathcal g}^{{\rm b},n'+1/2 } , \end{cases}\label{eq : flucdissconstjarzbck2}\end{aligned}\ ] ] where @xmath761 and @xmath762 are sequences of i.i.d .
gaussian random variables of mean @xmath46 and covariance matrix @xmath310 .
the numerical flow associated with is denoted @xmath763 ( q^{{\rm b},n'},p^{{\rm b},n'+1/4 } ) & \mapsto & ( q^{{\rm b},n'+1},p^{{\rm b},n'+3/4 } ) \end{array}\right.\ ] ] where we recall @xmath764 .
assuming that the flow @xmath744 given by and @xmath765 are both well - defined , the following reversibility property is easily checked ( extending the symmetry property of the standard rattle scheme , see for instance ( * ? ? ?
* section vii.1.4 ) ) : @xmath766 the work can be approximated using the lagrange multipliers in : @xmath767 for @xmath768 . the ( formal ) consistency of the work discretization in the time continuous limit is a direct consequence of the work expression .
an estimator of the free energy profile is then obtained by using @xmath769 independent realizations of the switching process , computing the work @xmath770 for each realization @xmath771 ( with the numerical trajectories obtained from the numerical scheme -- and i.i.d .
initial conditions sampled according to @xmath733 ) , and approximating , rewritten up to an unimportant additive constant ( independent of @xmath98 ) , as @xmath772 } \right),\ ] ] with empirical averages such as @xmath773 \right).\ ] ] in the above , the discretization @xmath774 of the corrector is @xmath775 we refer to chapter 4 in @xcite for more background on free energy estimators for nonequilibrium dynamics . in particular , it is possible to compute a work associated with the backward switching from the lagrange multipliers in , and to resort to bridge estimators ( see section 4.2.3 in @xcite ) .
however , using approximations such as in the jarzynski - crooks identity introduces a time discretization error .
we show in the next section how to eliminate this error .
it turns out that a discrete version of the jarzynski - crooks identity can be obtained .
this enables the estimation of free energy differences using nonequilibrium simulation _ without time discretization error_. the discrete equality below may be seen as an extension of the corresponding equality obtained for transitions associated with time - dependent hamiltonians and performed with metropolis - hastings dynamics ( see @xcite and remark 4.5 in @xcite ) . for this purpose
, we consider a discretization of the work @xmath776 using the interpretation of the work as the energy variation of the hamiltonian part of the langevin dynamics .
this leads to the following definition of the work at the discrete level : @xmath777 for @xmath768 .
this work discretization leads to a jarzynski - crooks identity without time discretization error .
[ eq : jarz_disc ] consider the distribution @xmath615 and its normalization @xmath614 defined in .
denote by @xmath778 the solution of the forward discretized langevin dynamics -- with initial conditions distributed according to @xmath779 and by @xmath780 the solution of the discretized backward langevin dynamics -- distributed according to @xmath781 then , the following jarzynski - crooks identity holds on @xmath782 $ ] : for any bounded discrete path functional @xmath783}$ ] , @xmath784}\left(\{q^n , p^n\}_{0 \leq n \leq n_t}\right ) \ , { \rm e}^{-\beta\w^{n_t } } \right ) } } { \e { \left ( \ph^{\rm r}_{[0,n_t]}\left(\{q^ { { \rm b } , { n ' } } , p^ { { \rm b } , { n ' } } \}_{0 \leq n ' \leq n_t } \right ) \right ) } } , \ ] ] where @xmath785 is computed according to , and @xmath684 denotes the composition with the operation of time reversal of paths : @xmath786}^{\rm r}\big(\ { q^ { { \rm b},{n ' } } , p^{{\rm b } , { n ' } } \}_{0 \leq n ' \leq n_t}\big ) = \ph_{[0,n_t]}\big(\ { q^ { { \rm b},{n_t - n } } , p^{{\rm b } , { n_t - n } } \}_{0 \leq n \leq n_t}\big).\ ] ] the ( formal ) consistency of the work discretization in the time continuous limit is a direct consequence of the work expression .
free energy estimators based on the identity are obtained as described in section [ sec : work_discretization ] .
let us emphasize once again that there is no error related to the finiteness of the time - step @xmath80 in this estimator , and that the only source of approximation is due to the statistical error . with a slight abuse of notation ,
we denote in the same way the random variables @xmath787 , @xmath788 , etc . in -- or -- , and the integration variables in the definition of probability distributions .
we divide the proof into three steps .
step 1 : the phase space conservation of @xmath744 and @xmath765 and the reversibility property imply @xmath789 step 2 : the probability distribution of @xmath790 given @xmath787 in the discretization of the fluctuation - dissipation part is denoted @xmath791 .
the scheme is a mid - point discretization of an ornstein - uhlenbeck process , which can be rewritten by decomposing the orthogonal and tangential updates of the momentum : @xmath792 where @xmath793 , and @xmath794 .
the markov chain induced by the parallel part of the momentum is the same as the one induced by the scheme ( or ) defined in section [ sec : consnum ] .
the latter verifies a detailed balance equation ( both in the plain sense and up to momentum reversal ) with respect to the stationary measure @xmath333 defined by ( see sections 2.3.2 and 3.3.5 in @xcite ) .
we recall that this measure is defined as the kinetic probability distribution in the momentum variable of the canonical distribution @xmath335 on the tangential space , conditioned by a given @xmath301 . adding the ( invariant ) orthogonal part of the momentum , the following detailed balance condition is satisfied : @xmath795 step @xmath195 : denote by @xmath796 the probability distribution of the variables @xmath797 given the variables @xmath787 in the scheme -- ; and by @xmath798 the probability distribution of the variables @xmath799 given the variables @xmath800 in the scheme -- . the splitting structure yields : @xmath801 as well as @xmath802 combining the detailed balance conditions and of steps @xmath167 and @xmath172 , and using the decomposition of phase space measures
, it follows @xmath803 which can be seen as the jarzynski - crooks identity over one time - step . iterating the argument
, it is easy to obtain : @xmath804 which yields .
the splitting scheme -- can be used in the overdamped regime , using the method of proposition [ p : langtooverd ] , _ i.e. _ by choosing @xmath805 which implies @xmath806 and @xmath807 . for this choice of parameters , the continuous limit of the numerical scheme
is the following variant of the stochastic differential equation : @xmath808 where @xmath809 is an adapted stochastic process such that @xmath609 .
we then obtain the following jarzynski - crooks relation for discretized overdamped dynamics , _ without time discretization error_. [ p : langtooverd_jarz ] suppose that the relation is satisfied . with a slight abuse of notation ,
the mass matrix and the friction matrix are rewritten as @xmath387 and @xmath388 with @xmath389 . then the splitting scheme -- yields the following euler discretization of the overdamped langevin constrained dynamics : @xmath810 \xi(q^{n+1 } ) = z(t_{n+1 } ) , \end{cases}\ ] ] where @xmath391 are independent and identically distributed centered and normalized gaussian variables , and @xmath392 are the lagrange multipliers associated with the constraints @xmath811 . in the same way , the backward process -- yields the following euler scheme : @xmath812 \xi(q^{{\rm b},n'+1 } ) = z(t_{n_t - n'-1 } ) .
\end{cases}\ ] ] consider the work update @xmath813 for @xmath768 , where @xmath814 with @xmath815 , and the scheme is rewritten as : @xmath816 \dps q^{n+1 } = q^{n } + 2 p^{n+1/2 } , \\[6pt ] \dps \xi(q^{n+1 } ) = z(t_{n+1 } ) , \quad ( c_q ) \\[6pt ] \dps p^{n+3/4 } = p^{n+1/2 } - \displaystyle{\frac{\dt}{2 } \nabla v ( q^{n+1 } ) } + \nabla \xi(q^{n+1 } ) \lambda^{n+3/4},\\[6pt ] \dps \nabla \xi ( q^{n+1})^{t } p^{n+3/4 } = \frac { z(t_{n+2})- z(t_{n+1})}{2 } , \quad ( c_p ) \end{cases}\ ] ] then the jarzynski - crooks relation holds under the assumptions and on the initial conditions of the schemes and respectively .
the proof is a direct consequence of the reformulation of into , and a direct application of theorem [ eq : jarz_disc ] with the parameters .
note that the free energy estimator @xmath817 } \right),\ ] ] based on the work and the corrector @xmath818 is exact ( there is no time discretization error ) .
this free energy estimator can be seen as a variant of the estimator proposed in @xcite , which was derived directly for the scheme , and reads ( up to an unimportant additive constant ) : @xmath819 } \right),\ ] ] where the work is defined as @xmath820 with @xmath821 and the modified corrector is defined without the kinetic energy term : @xmath822 there is a bias due to the time discretization error in the estimator , which can be removed upon following the procedure described in proposition [ p : langtooverd_jarz ] . in this section , we would like to discuss the consistency of three free energy estimators introduced above : - ( based on the direct discretization of the overdamped dynamics proposed in @xcite ) , - ( which uses the lagrange multipliers to approximate the work ) and - ( based on the discrete jarzynski equality ) .
the limiting continuous - in - time version of the jarzynski relation is : @xmath823 where the work for the overdamped dynamics reads ( see @xcite ) : @xmath824 with @xmath825 the consistency of - with - was already proven in @xcite . concerning the consistency of @xmath826 with @xmath827 ( see and ) , note that in the overdamped scaling ( @xmath828 ) , the difference @xmath829 vanishes when @xmath509 .
this difference can therefore be neglected when analyzing the consistency of the scheme in the continuous - in - time limit .
we henceforth concentrate on the consistency of the works and with . in the sequel , we denote the anticipating stochastic integration of the integrand @xmath830 with respect to @xmath831 by @xmath832 where @xmath833 is the stratonovitch symmetric integration , and @xmath834 the it integration .
the symbol @xmath835 denotes the formal time continuous limit .
[ [ consistency - of . ] ] consistency of .
+ + + + + + + + + + + + + + + + let us justify the consistency of the work expression with .
remark that the lagrange multipliers in verify : @xmath836 \label{eq : lag_od_jarz_1}\ ] ] and @xmath837 as well as @xmath838 .
\label{eq : lag_od_jarz_3 } \end{aligned}\ ] ] the expressions and yield @xmath839 as well as @xmath840 moreover the constraints imply that @xmath841 so that @xmath401 and @xmath406 yield the same time continuous limit , that is to say @xmath842 eventually , implies @xmath843 the same holding true for @xmath844 . the work expression is thus formally consistent with .
this concludes the proof of the consistency of - with - .
[ [ consistency - of.-1 ] ] consistency of .
+ + + + + + + + + + + + + + + + we now prove the consistency of the work expression with .
define @xmath845 the expression yields using : @xmath846 where @xmath847 first , since @xmath848 and @xmath849 , the limit of the terms in is zero .
second , using the expressions and , and similarly to and , it holds @xmath850 \\ & - ( \nabla \xi g^{-1})(q^{n+1 } ) \big [ \nabla \xi ( q^{n+1})^t { \left(q^{n}-q^{n+1}\right ) } + ( z(t_{n+2})-z(t_{n+1 } ) ) + \dt \nabla \xi ( q^{n+1})^t \nabla v ( q^{n+1})\big ] \\ & + \frac\dt2 ( \nabla v(q^{n+1 } ) - \nabla v(q^n ) ) = \mathrm{o}(\dt ) \end{aligned}\ ] ] since @xmath851 by . expanding in higher order powers of @xmath80
, it can be checked that there exists two functions @xmath852 and @xmath853 such that @xmath854 therefore , since ( in the limit @xmath509 ) the martingale part of @xmath855 arises only from the term @xmath856 , one obtains @xmath857 since @xmath858
. in conclusion , the second term in has a zero contribution to the continuous - in - time limit . as a consequence ,
the formal time continuous limit of @xmath859 is the same as the one of @xmath860 .
computations similar to the one performed above yield @xmath861 indeed , @xmath862 as in , while @xmath863 .
the formal time continuous limit of @xmath860 is therefore the same as the limit of @xmath864 since implies @xmath865 we get in the end that the formal time continuous limit of @xmath860 and @xmath859 is the same as : @xmath866 where we have used .
this concludes the proof of the consistency of - with - .
we present some free energy profiles obtained with nonequilibrium switching dynamics for the model system and the parameters described in section [ sec : simple_example_wca ] .
the switching schedule reads @xmath867 with @xmath868 and @xmath869 .
the time - step is @xmath870 .
the initial conditions are obtained by first subsampling a constrained dynamics with @xmath871 and @xmath872 , with a time spacing @xmath873 ; and then adding the required component @xmath874 to the momentum variable ( with @xmath875 ) . in the specific case at hand , the corrector term is constant , and free energies differences are equal to differences of rigid free energies .
the dynamics used to integrate the nonequilibrium dynamics is based on a splitting strategy , analogous to -- , except that the midpoint integration of the ornstein - uhlenbeck part is replaced by an exact integration for the unconstrained dynamics , followed by a projection .
this can be done here since we choose a friction matrix of the form @xmath388 ( recall also that @xmath876 ) . more precisely , the corresponding scheme is obtained by replacing ( and likewise for ) with @xmath877 where @xmath878 , and setting @xmath879 with @xmath329 chosen such that @xmath880 free energy profiles .
the top curve corresponds to @xmath881 with @xmath882 , while the two other curves were obtained for @xmath883 with @xmath884 and @xmath885 with @xmath886 ( smoothest curve ) .
, width=275 ] figure [ fig : noneq_rc ] presents estimates obtained with @xmath5 independent realizations of the switching dynamics for different switching times @xmath98 , using the estimator presented in section [ sec : work_discretization ] with the work discretization . in all cases ,
the product @xmath887 is kept constant .
the free energy profile becomes closer to the reference curve as @xmath98 is increased , and the profile obtained for @xmath885 is in excellent agreement with the result obtained with thermodynamic integration .
when the switching time is small , more realizations should be considered to reduce the statistical errors and obtain estimates in better agreement with the reference profile .
the fact that the variance is very large when the switching time @xmath98 is too small is a well - known drawback of estimators based on the jarzynski - crooks identity , see the review in sections 4.1.4 and 4.1.5 in @xcite . roughly speaking
, the difficulty is related to the fact that the free energy difference is obtained as an average of @xmath888 , which requires a very good sampling of the small values of the work @xmath889 . as @xmath98 decreases , the width of the work distribution increases and the low tail part is more and more difficult to sample .
improved estimates can be obtained with estimators based on combinations of forward and backward trajectories , see for instance @xcite and section 4.2 in @xcite .
we give in this appendix two technical lemmas , used in the proof of proposition [ p : meanforce ] .
the first lemma can also be used to prove the divergence formula .
the proof relies on the following computation rules for any family of invertible square matrices @xmath892 : @xmath893 and @xmath894 fix @xmath895 .
first , using with @xmath896 replaced by @xmath148 and @xmath897 replaced by @xmath898 , we obtain @xmath899 so that by the skew - symmetry of @xmath900 and @xmath148 , @xmath901 jacobi s identity for poisson brackets and then yield @xmath902 since @xmath903 where @xmath904 is the kronecker symbol .
finally , the left hand and right hand sides of the last equality can be factorized as @xmath905 since @xmath906 and @xmath193 is invertible , it follows @xmath907 for all @xmath908 , which is .
consider a test function @xmath910 .
an integration by parts and the co - area formula give : @xmath911 where in the last line the following chain rule has been used : @xmath912 now an integration by parts with respect to @xmath913 , together with , leads to @xmath914 which gives the result .
w. e and e. vanden - eijnden , _ metastability , conformation dynamics , and transition pathways in complex systems _ , multiscale modelling and simulation ( s. attinger and p. koumoutsakos , eds . ) , lect . notes comput .
39 , springer , berlin , 2004 , pp . 3568 .
e. hairer , c. lubich , and g. wanner , _ geometric numerical integration : structure - preserving algorithms for ordinary differential equations _ , springer series in computational mathematics , vol .
31 , springer - verlag , 2006 .
t. lelivre , m. rousset , and g. stoltz , _ computation of free energy differences through nonequilibrium stochastic dynamics : the reaction coordinate case _ , j. comput
* 222 * ( 2007 ) , no . 2 , 624643 .
s. park , f. khalili - araghi , e. tajkhorshid , and k. schulten , _ free energy calculation from steered molecular dynamics simulations using jarzynski s equality _ , j. chem .
* 119 * ( 2003 ) , no . 6 , 35593566 .[/INST] in this paper , we consider langevin processes with mechanical constraints .
the latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences .
the results of this paper can be divided into three parts .
( i ) we propose a simple discretization of the constrained langevin process based on a splitting strategy .
we show how to correct the scheme so that it samples _ exactly _ the canonical measure restricted on a submanifold , using a metropolis - hastings correction in the spirit of the generalized hybrid monte carlo ( ghmc ) algorithm .
moreover , we obtain , in some limiting regime , a consistent discretization of the overdamped langevin ( brownian ) dynamics on a submanifold , also sampling exactly the correct canonical measure with constraints .
( ii ) for free energy computation using thermodynamic integration , we rigorously prove that the longtime average of the lagrange multipliers of the constrained langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints .
a second order time discretization using the lagrange multipliers is proposed .
( iii ) the jarzynski - crooks fluctuation relation is proved for langevin processes with mechanical constraints evolving in time .
an original numerical discretization without time discretization error is proposed , and its overdamped limit is studied .
numerical illustrations are provided for ( ii ) and ( iii ) . </s> |
many insights into the biological mechanisms of left ventricular ( lv ) remodeling and heart failure ( hf ) have been derived from small animals , particularly rodents such as mice . however , establishing direct analogies between rodents and humans can be problematic as there are considerable differences in cardiac physiology ( e.g. , heart rate , oxygen consumption , regulatory proteins , contractile proteins , stem cell characteristics , etc . ) between species .
validation and proper translation of fundamental discoveries into clinical utility necessitates the use of large animal models that more closely approximate human physiology [ 1 , 2 ] .
a recent advance in hf therapeutics consists of mechanical unloading with lv assist devices ( lvads ) .
a large animal disease model that mimics the human cardiovascular condition ( bovine or ovine ) is particularly critical for the rigorous evaluation of ( patho)physiological responses induced by lvads , as phylogenetically lower species can not physically accommodate implantable cardiac devices .
moreover , prolonged mechanical unloading with lvads can reverse remodeling of the human failing lv , with reports of myocardial recovery sufficient for lvad explantation in a subset of patients [ 5 , 6 ] .
meaningful assessment of the hemodynamic and molecular mechanisms of lvad - induced myocardial recovery and the influence of different strategies of mechanical unloading requires the use of a reliable large animal model of hf . in view of both anatomical size of the thoracic cavity and cardiovascular physiology ,
the current industry standard is to use normal calves to test safety , performance , and reliability of lvad systems .
however , evaluation of these devices in animals with chronic hf , with attendant differences in cardiac physiology and hemodynamics from the normal condition , has been extremely limited [ 79 ] . as myocardial recovery most often
has been reported in patients with idiopathic dilated cardiomyopathy , our objective in this study was to develop a nonischemic bovine model of cardiomyopathy to provide a substrate for studying device - based therapies for hf .
for this purpose , we used doxorubicin , a broad - spectrum antineoplastic drug with dose - dependent cardiotoxicity that has been used to induce chronic hf in several animal species that include sheep [ 10 , 11 ] and dogs [ 1217 ] .
all animals received humane care and were handled in accordance with national institutes of health and university of louisville animal care committee guidelines .
experimental procedures followed animal study protocols approved by the university of louisville institutional animal care and usage committee .
male jersey and mixed - breed calves ( n = 8 , 46 months old , 88 6 kg ) were used .
four animals were administered intravenous doxorubicin 1.2 mg / kg once weekly via the external jugular vein for seven weeks .
one animal that was relatively refractory to doxorubicin treatment received a dose of 1.5 mg / kg for the last two doses . for 48 hours following each injection ,
four animals were used as controls for myocardial blood flow , histological , and molecular analyses .
a separate group of 9 normal , age - matched calves from a previous study in our laboratory were used for hemodynamic comparison with the doxorubicin group .
serial venous blood samples were drawn from doxorubicin - treated animals at baseline , 14-day- , and 45-day - time points during the doxorubicin administration protocol .
transthoracic m - mode , 2d , and doppler echocardiograms were measured at baseline and weekly during the doxorubicin protocol with a phillips ie33 machine with s8 - 3 ultrasound probe .
prior to the final study and termination , open - chest epicardial echocardiography was performed .
modified parasternal and apical four - chamber views were used for imaging , and lv ejection fraction ( ef ) was determined using the modified simpson technique ( summation of discs ) .
target lv dysfunction was defined as an lvef of less than or equal to 35% . within 10 days of the final doxorubicin injection , a terminal study was performed to measure cardiovascular hemodynamics and to harvest tissues for myocardial blood flow , histology , and molecular analysis .
animals were preanesthetized with intravenous atropine ( 30 mg ) , anesthetized with inhaled isoflurane ( 35% ) , and anticoagulated with intravenous heparin ( 100 units / kg ) .
fluid - filled arterial and venous catheters were placed in the right carotid artery and jugular vein for blood sampling .
high - fidelity micromanometer catheters ( millar instruments ) were placed in the left atrium ( single - tip ) and across the aortic valve ( dual - tip ) for simultaneous measurement of left atrial ( la ) , lv , and aortic blood pressure .
transit - time ultrasonic flow probes ( transonics ) were placed around the pulmonary artery and left main coronary artery to measure cardiac output and volumetric coronary blood flow , respectively . a silicone catheter
( 7 fr ; access technologies ) was advanced 4 cm into the la appendage chamber .
this depth and the angle of catheter entry parallel to the surface of the atrial appendage ensured that the catheter did not interfere with mitral valve function .
the la catheter was used for injection of multiple colors of fluorescent - labeled 15 m microspheres into the systemic arterial circulation .
simultaneously , a reference blood sample was withdrawn at a known rate ( 15 ml / min ) from the aorta as previously described .
the microsphere technique enables the precise measurement of regional blood flow in vascular beds of interest .
microspheres injected into the la chamber mix with blood in the lv and are subsequently ejected into the aorta , from where they disseminate throughout the body and lodge within the smallest precapillary arterioles based on regional tissue blood flow distribution .
we have previously demonstrated that with the quantity used , 15 m spheres do not cause ischemia and do not induce pathology .
the aortic blood sample acts as a reference for later determination of flow in tissues of interest .
the number of counted microspheres in the reference blood sample ( known ) is compared to the number of microspheres that lodge and are counted in a tissue sample of interest ( known ) .
the ratio between the two sphere counts is equal to the ratio between the calibrated rate of aortic withdrawal ( known ) and flow in the tissue of interest ( unknown ) and provides accurate tissue - specific blood flow in ml / min / g [ 20 , 21 ] . at the completion of the study , while under anesthesia , euthanasia was performed with a single fatal bolus injection of beuthanasia - d special ( 1 ml/5 kg iv ) .
one- to two - gram tissue sections from the lv - free wall , right ventricular(rv)-free wall , and interventricular septum together with reference blood samples were sent to imt / stason laboratories ( irvine , ca ) for automated digestion and counting of fluorescent microspheres with flow cytometry and calculation of tissue - specific blood flows .
all pressure and flow transducers were pre- and postcalibrated against known physical standards to ensure measurement accuracy .
data were collected at 400 hz , signal conditioned , and a / d converted for digital analysis using our glp compliant data acquisition system . pressure and flow recordings were used to derive heart rate , cardiac output , mean arterial pressure , mean la pressure , lv peak systolic and end - diastolic pressure ( edp ) , peak dp / dt , lv external work , and mean diastolic coronary artery blood flow .
these parameters were calculated on a beat - to - beat basis for each 30-second data set with the hemodynamic evaluation and assessment research tool ( heart ) program developed in matlab ( version 6.5 , mathworks ) . all analyzed beats in each data set ( approximately 3050 beats )
paraffin - embedded tissue sections ( 4 m ) from the lv , rv , and interventricular septum were deparaffinized , rehydrated , and stained with masson 's trichrome ( for collagen ) with standard histological techniques as previously described . to determine myocyte cross - sectional area , fitc - conjugated wheat germ agglutinin ( molecular probes ) staining of cell membranes together with dapi ( molecular probes ) nuclear costaining
myocyte area determined from an average of 100150 cross - sectional cells with centrally located round nuclei and the total fibrotic area were assessed using metamorph imaging software .
apoptosis in cardiac tissue was determined with the deadend fluorometric tunel system ( promega ) , which catalytically incorporates fluorescein-12-dutp at dna strand breaks as previously described .
all sections were counterstained with dapi ( molecular probes ) at a final concentration of 2 m .
images were viewed with epifluorescence microscopy ( nikon te2000 ) within 24 hours and analyzed with metamorph imaging software .
mrna expression in the heart was quantified by real - time polymerase chain reaction ( pcr ) as previously described [ 23 , 25 ] .
briefly , total rna was isolated from lv tissue with trizol reagent ( invitrogen ) , and cdna was synthesized from 1 g rna with the iscript cdna synthesis kit ( biorad ) .
relative levels of mrna transcripts for atrial natriuretic factor ( anf ) , connective tissue growth factor ( ctgf ) , matrix metalloproteinase ( mmp)-2 , and mmp-9 were quantified by real - time pcr with the use of sybr green ( applied biosystems ) and the sense / antisense primer pairs listed in table 1 .
data were normalized to 18s ribosomal rna subunit expression using the ct comparative method , and the values from doxorubicin - treated hearts were expressed as a fold change over control .
plasma norepinephrine and epinephrine levels were determined by colorimetric quantitative competitive elisa with a commercially available kit ( rocky mountain diagnostics ) according to the manufacturer 's instructions .
briefly , the derivatized standards , test samples , and the solid phase bound analytes competed for a fixed number of antiserum binding sites .
after washing of the free antigen and the antigen - antiserum complexes , the antibody bound to the solid phase was detected by a peroxidase - conjugated secondary antibody .
serial echocardiographic and catecholamine data from the same animal at different time points during the doxorubicin protocol were compared using one - way anova with tukey posttest .
hemodynamic , myocardial blood flow , histological , and molecular comparisons between doxorubicin - treated animals and normal animals were performed with an unpaired t - test .
all four animals developed chronic coughing , three of four animals developed dyspnea on exertion , and one animal developed dyspnea at rest and severe ascites . during the duration of the study ,
the target lvef ( 35% ) was achieved in three animals , and diminished heart function was induced in the remaining animal treated with doxorubicin .
representative m - mode echocardiographic images from one animal at baseline and 60 days after initiating doxorubicin are shown in figure 1 .
mild lv dilitation was observed along with a much more profound reduction in systolic contraction and shortening fraction .
doxorubicin induced mild increases in lv end - diastolic volume ( edv ) that were not statistically significant , but significant ( p < 0.05 ) increases in lv end - systolic volume ( esv ) and worsening of lvef were observed .
these effects were more profound under isoflurane anesthesia . in the subset of animals that achieved target lvef , there was significant exacerbation of all echocardiographic parameters of interest ( baseline versus final anesthetized : lvedv 572 versus 71 29 ml ; lvesv 6 3 versus 52 15 ml ; lvef 89 6 versus 25 10% ; p < 0.05 )
.
table 3 depicts hemodynamic parameters measured 60 days after the initiation of doxorubicin . as compared to normal calves of somewhat smaller size ( n = 9 , mean weight : 76.1 kg ) that were previously studied in our laboratory , doxorubicin - treated calves exhibited hemodynamic changes indicative of lv contractile dysfunction with significantly ( p < 0.05 ) decreased cardiac output , mean arterial pressure , peak + dp / dt , and peak dp / dt , and a trend toward decreased lv peak systolic pressure ( p = 0.10 ) , lv external work ( p = 0.10 ) , and left main coronary artery blood flow ( p = 0.12 ) . interestingly , despite significant inotropic and lusitropic depression , filling pressures ( la pressure and lv end - diastolic pressure ) were comparable between the groups .
figure 2 demonstrates regional myocardial blood flow in the lv - free wall , interventricular septum , rv - free wall , and the transmural distribution in control animals and doxorubicin - treated animals at 60 days after initiation of doxorubicin .
there were statistically significant ( p < 0.05 ) reductions in myocardial blood flow in the lv- and rv - free walls and trends toward reduced blood flow in the septum ( p = 0.13 ) , epicardium ( p = 0.07 ) , midmyocardium ( p = 0.07 ) , and endocardium ( p = 0.13 ) .
gross heart weights were 518 82 g for control animals and 604 90 g for animals treated with doxorubicin and were not statistically different as a direct comparison ( p = 0.25 ) or normalized to body weight ( p = 0.88 ) and suggest the absence of doxorubicin - induced hypertrophy at the chamber level .
figure 3 demonstrates the degree of collagen deposition / fibrosis in the lv , rv , and interventricular septum as determined by masson 's trichrome staining . as
compared to control hearts , after doxorubicin treatment , connective tissue decreased or tended to decrease in each of the three regions ( lv p = 0.14 , septum p < 0.10 , rv p < 0.01 ) . moreover , as seen in the accompanying representative histomicrographs , the outline of individual myocytes and the interstitial space were well established and clearly visible in control hearts . in contrast , doxorubicin - treated hearts did not exhibit clear myocyte borders , and interstitial connective tissue volume was markedly diminished . to explore this further , we examined myocardial gene expression of ctgf , a profibrotic matrix - associated protein , and mmp-2 and -9 , which would be expected to augment collagen degradation ( figure 4 ) . as compared with control hearts ,
ctgf expression was unchanged in doxorubicin - treated hearts , whereas mmp-2 expression was significantly ( p < 0.05 ) upregulated .
mmp-9 expression tended toward a decrease ( p = 0.09 ) . the large increase in mmp-2
would be expected to favor collagen turnover and loss , which was consistent with the histological findings in figure 3 .
figure 5 shows representative wheat - germ agglutinin staining of cell membranes and corresponding myocyte size in the lv , rv , and interventricular septum from control and doxorubicin - treated hearts . as compared with control hearts , after doxorubicin treatment myocyte size increased in each of the three regions and indicated pathologic myocyte hypertrophy .
this increase was statistically significant ( p < 0.05 ) in the rv and septum but not statistically significant in the lv ( p = 0.29 ) . in control hearts ,
myocytes were of a uniform size and shape , and interstitial space was clearly visible as dark , variegated bands throughout the myocardium .
consistent with these histological findings of hypertrophy , mrna expression of anf , a hypertrophic marker , was increased 3.5-fold in doxorubicin - treated hearts as compared with control ( figure 4 ) .
one potential explanation for doxorubicin - induced myocyte hypertrophy without changes in lv chamber weight would be the concomitant enhancement of myocardial cell loss .
figure 6 demonstrates representative tunel stains from control and doxorubicin - treated hearts and the overall apoptotic rate in the lv , interventricular septum , and rv . as compared to controls ,
this increase was statistically significant in the left ventricle ( p < 0.01 ) , of borderline significance in the interventricular septum ( p = 0.10 ) , and not significant in the right ventricle ( p = 0.39 ) . staining morphology and
the proximity of cells to vascular structures suggested that the apoptotic cells were a mixture of myocytes , endothelial cells , and immune cells .
as shown in figure 7 , plasma norepinephrine levels were significantly increased 14 days into the doxorubicin administration protocol and subsequently returned to baseline at 45 days .
plasma epinephrine increased progressively during doxorubicin administration and was significantly increased over baseline at 45 days .
collectively , these data indicate heightened circulating catecholamines and adrenergic activation , a hallmark of cardiomyopathy and heart failure .
in this study , we report for the first time a stable model of doxorubicin - induced cardiomyopathy in the calf . specifically , weekly intravenous injections of doxorubicin induced ( 1 ) mild lv dilatation with impaired lv contraction and relaxation , ( 2 ) reductions in cardiac output without changes in lv filling pressure , ( 3 ) reductions in myocardial blood flow , ( 4 ) myocyte hypertrophy , ( 5 ) cardiac cell apoptosis , ( 6 ) loss of interstitial collagen , and ( 7 ) an increase in plasma catecholamines .
most of these phenotypic features are hallmarks of the failing human heart . given that the calf is generally used for preclinical testing of mechanical circulatory support devices
, this bovine model may be useful as a platform for testing acute and chronic pathophysiologic responses to lvads in the context of hf and for the development of adjunct therapies for myocardial recovery .
doxorubicin is a potent broad - spectrum antineoplastic drug with dose - dependent cardiotoxicity that clinically can manifest as cardiomyopathy and hf .
multiple pathological mechanisms have been proposed for doxorubicin - induced cardiomyopathy that include the generation of free radicals , oxidative stress - induced lipid peroxidation and mitochondrial damage , suppression of cardiac gene expression and protein synthesis , augmented release of catecholamines , and cardiomyocyte and endothelial cell apoptosis [ 2729 ] .
the large number of mitochondria in the heart and the strong affinity of anthracyclines for the inner mitochondrial membrane phospholipid cardiolipin contribute to the mitochondrial accumulation of doxorubicin and predispose cardiac myocytes to doxorubicin toxicity . as such ,
multiple investigators have used anthracyclines such as doxorubicin to induce cardiomyopathy and hf in a variety of large animal models that include dogs and sheep [ 1017 , 31 ] .
large animal studies that have used sequential weekly doxorubicin doses for a circumscribed period ( as was done in our study ) report a cardiomyopathy that is progressive over the long term without evidence of spontaneous improvement [ 1013 , 16 ] . in dogs and sheep , serial doxorubicin administration decreased cardiac output by 1532%
similarly , in our bovine model , cardiac output was 28% lower than normal animals .
moreover , significant contractile and lusitropic dysfunction was evident with 40% reduction in peak + dp / dt and 55% reduction in peak dp / dt .
interestingly , lv dilatation , a hallmark of anthracycline cardiotoxicity in rodents , was relatively modest in our calf model , and filling pressures were normal despite reduced cardiac output .
this suggests that pathological remodeling and hemodynamic decompensation may have become more pronounced upon larger doses of doxorubicin and/or a greater duration of followup .
alternatively , these less pronounced phenotypic features may be species - specific and distinguish doxorubicin - mediated responses in the calf in comparison with other animal species .
lvef dropped by 30% in the conscious state and 60% in the anesthetized state as compared with baseline .
interestingly , it is well documented that bovine hemodynamics differ between conscious and anesthetized conditions [ 33 , 34 ] . normal ejection fraction in calves
has been reported to be as high as 85 9% in the conscious state and 63 10% under anesthetized conditions . in our study , after seven weeks of doxorubicin , the calves exhibited an ejection fraction of 64 23% in the conscious state and 36 23% under isoflurane anesthesia .
lvef in the conscious state may have overestimated basal mechanical function in these animals , as they were uniformly anxious with attendant increase in stress - induced , catecholamine - mediated effects on cardiac performance . as a result
, echocardiographic measurements were performed in a hyperdynamic state as occurs during a stress echocardiogram .
both echocardiographic and hemodynamic measurement in the anesthetized state confirmed significant systolic dysfunction after doxorubicin administration .
moreover , doxorubicin - treated animals exhibited several characteristic histological , biochemical , and molecular features of pathological cardiac remodeling and myocyte hypertrophy .
myocardial apoptosis and microvascular insufficiency both contribute to myocardial dysfunction in anthracycline - induced hf [ 2729 , 36 ] .
indeed , doxorubicin - treated bovine hearts in our study exhibited both a 5 to 6-fold increase in apoptotic rate and profound reductions in myocardial blood flow as quantified by regional microsphere distribution .
as prior work has demonstrated that doxorubicin can induce apoptosis of cardiomyocytes and endothelial cells [ 2527 ] , these two phenomena may be interrelated .
specifically , endothelial cell death in the microvasculature may have contributed to the observed reductions in coronary blood flow .
indeed , we frequently observed foci of apoptotic nuclei in proximity to or within coronary arterioles in the heart , which suggests that at least some apoptotic cells were of vascular or endothelial origin . as cardiomyopathic hearts generally show augmented interstitial fibrosis and collagen deposition , our finding of reduced interstitial collagen volume in doxorubicin - treated hearts was surprising .
however , prior work has demonstrated that doxorubicin upregulates and activates matrix metalloproteinases in the heart and can also inhibit collagen synthesis ( both of which would favor collagen degradation ) .
indeed , in our study , the expression of profibrotic ctgf in the heart was not affected by doxorubicin , whereas mmp-2 ( which promotes collagen breakdown ) was upregulated , consistent with these prior observations . in a rat study of the cardiac matrix following a single injection of doxorubicin , a biphasic course of myocardial remodeling was observed .
the initial response ( up to 6 weeks after injection ) was loss of the myocardial collagen matrix . at later time points ,
hence , the interstitial remodeling after doxorubicin exposure may not be uniform and may depend on the stage of progression of doxorubicin - induced ventricular remodeling .
it is possible that in our animals , longer periods of treatment or followup may have augmented collagen deposition , and greater fibrosis may have been observed . moreover , as myocardial fibrosis increases , ventricular chamber stiffness increases .
the reduced collagen deposition that we observed may underlie the absence of diastolic filling pressure elevation in doxorubicin - treated hearts .
the decrease in matrix protein may have increased chamber compliance and thereby maintained lvedp at levels comparable to normal animals , despite the development of doxorubicin cardiomyopathy .
the depressed peak dp / dt and cardiac output in doxorubicin - treated animals despite equivalent lvedp ( preload ) indicated significant contractile dysfunction in these animals .
filling pressure elevation and further hemodynamic compensation would have likely occurred over longer time periods that allowed for further progression of pathological remodeling .
our results must be interpreted in light of potential study limitations . in our study ,
the one animal that was somewhat resistant to doxorubicin was a pure - breed jersey calf , whereas the other three animals were mixed breed .
reported in a canine model of doxorubicin cardiomyopathy that one animal in their medium dose cohort showed no cardiac impairment , whereas all others animals showed severe impairment or died of heart failure .
another study limitation was the small number of experimental animals , a situation that was mandated by unanticipated limitations in available resources for large animal maintenance .
the small sample size increased the risk of type i statistical error ( i.e. , that the observed effects may have been driven by chance findings in just one animal ) and type ii statistical error ( i.e. , finding no difference between groups due to a small number of observations when a difference truly exists ) . nonetheless , despite the study of only four animals , the observed hemodynamic , structural , histological , biochemical , and molecular changes were all sufficiently robust to establish the induction of lv dysfunction and pathological remodeling by doxorubicin .
moreover , the observed changes were consistent with multiple prior studies of doxorubicin - induced cardiomyopathy in other animal models ( described above ) , suggest that our results were experimentally valid and not simply the result of chance statistical variation .
these limitations notwithstanding , our results establish the validity and feasibility of a clinically relevant bovine model of doxorubicin - induced cardiomyopathy that shares many phenotypic similarities with human heart failure .
this model may prove useful assess the pathophysiological responses to lvads and associated adjunctive therapies in hf .
this work was supported in part by an american heart association scientist development grant no . | left ventricular assist devices ( lvads ) constitute a recent advance in heart failure ( hf ) therapeutics . as the rigorous experimental assessment of lvads in hf requires large animal models ,
our objective was to develop a bovine model of cardiomyopathy .
male calves ( n = 8) were used .
four animals received 1.2 mg / kg intravenous doxorubicin weekly for seven weeks and four separate animals were studied as controls .
doxorubicin - treated animals were followed with weekly echocardiography .
target lv dysfunction was defined as an ejection fraction 35% .
sixty days after initiating doxorubicin , a terminal study was performed to determine hemodynamic , histological , biochemical , and molecular parameters . all four doxorubicin - treated animals exhibited significant ( p < 0.05 ) contractile dysfunction , with target lv dysfunction achieved in three animals .
doxorubicin - treated hearts exhibited significantly reduced coronary blood flow and interstitial fibrosis and significantly increased apoptosis and myocyte size .
gene expression of atrial natriuretic factor increased more than 3-fold .
plasma norepinephrine and epinephrine levels were significantly increased early and late during the development of cardiomyopathy , respectively .
we conclude that sequential administration of intravenous doxorubicin in calves induces a cardiomyopathy with many phenotypic hallmarks of the failing human heart
. this clinically - relevant model may be useful for testing pathophysiologic responses to lvads in the context of hf . | <s>[INST]many insights into the biological mechanisms of left ventricular ( lv ) remodeling and heart failure ( hf ) have been derived from small animals , particularly rodents such as mice . however , establishing direct analogies between rodents and humans can be problematic as there are considerable differences in cardiac physiology ( e.g. , heart rate , oxygen consumption , regulatory proteins , contractile proteins , stem cell characteristics , etc . ) between species .
validation and proper translation of fundamental discoveries into clinical utility necessitates the use of large animal models that more closely approximate human physiology [ 1 , 2 ] .
a recent advance in hf therapeutics consists of mechanical unloading with lv assist devices ( lvads ) .
a large animal disease model that mimics the human cardiovascular condition ( bovine or ovine ) is particularly critical for the rigorous evaluation of ( patho)physiological responses induced by lvads , as phylogenetically lower species can not physically accommodate implantable cardiac devices .
moreover , prolonged mechanical unloading with lvads can reverse remodeling of the human failing lv , with reports of myocardial recovery sufficient for lvad explantation in a subset of patients [ 5 , 6 ] .
meaningful assessment of the hemodynamic and molecular mechanisms of lvad - induced myocardial recovery and the influence of different strategies of mechanical unloading requires the use of a reliable large animal model of hf . in view of both anatomical size of the thoracic cavity and cardiovascular physiology ,
the current industry standard is to use normal calves to test safety , performance , and reliability of lvad systems .
however , evaluation of these devices in animals with chronic hf , with attendant differences in cardiac physiology and hemodynamics from the normal condition , has been extremely limited [ 79 ] . as myocardial recovery most often
has been reported in patients with idiopathic dilated cardiomyopathy , our objective in this study was to develop a nonischemic bovine model of cardiomyopathy to provide a substrate for studying device - based therapies for hf .
for this purpose , we used doxorubicin , a broad - spectrum antineoplastic drug with dose - dependent cardiotoxicity that has been used to induce chronic hf in several animal species that include sheep [ 10 , 11 ] and dogs [ 1217 ] .
all animals received humane care and were handled in accordance with national institutes of health and university of louisville animal care committee guidelines .
experimental procedures followed animal study protocols approved by the university of louisville institutional animal care and usage committee .
male jersey and mixed - breed calves ( n = 8 , 46 months old , 88 6 kg ) were used .
four animals were administered intravenous doxorubicin 1.2 mg / kg once weekly via the external jugular vein for seven weeks .
one animal that was relatively refractory to doxorubicin treatment received a dose of 1.5 mg / kg for the last two doses . for 48 hours following each injection ,
four animals were used as controls for myocardial blood flow , histological , and molecular analyses .
a separate group of 9 normal , age - matched calves from a previous study in our laboratory were used for hemodynamic comparison with the doxorubicin group .
serial venous blood samples were drawn from doxorubicin - treated animals at baseline , 14-day- , and 45-day - time points during the doxorubicin administration protocol .
transthoracic m - mode , 2d , and doppler echocardiograms were measured at baseline and weekly during the doxorubicin protocol with a phillips ie33 machine with s8 - 3 ultrasound probe .
prior to the final study and termination , open - chest epicardial echocardiography was performed .
modified parasternal and apical four - chamber views were used for imaging , and lv ejection fraction ( ef ) was determined using the modified simpson technique ( summation of discs ) .
target lv dysfunction was defined as an lvef of less than or equal to 35% . within 10 days of the final doxorubicin injection , a terminal study was performed to measure cardiovascular hemodynamics and to harvest tissues for myocardial blood flow , histology , and molecular analysis .
animals were preanesthetized with intravenous atropine ( 30 mg ) , anesthetized with inhaled isoflurane ( 35% ) , and anticoagulated with intravenous heparin ( 100 units / kg ) .
fluid - filled arterial and venous catheters were placed in the right carotid artery and jugular vein for blood sampling .
high - fidelity micromanometer catheters ( millar instruments ) were placed in the left atrium ( single - tip ) and across the aortic valve ( dual - tip ) for simultaneous measurement of left atrial ( la ) , lv , and aortic blood pressure .
transit - time ultrasonic flow probes ( transonics ) were placed around the pulmonary artery and left main coronary artery to measure cardiac output and volumetric coronary blood flow , respectively . a silicone catheter
( 7 fr ; access technologies ) was advanced 4 cm into the la appendage chamber .
this depth and the angle of catheter entry parallel to the surface of the atrial appendage ensured that the catheter did not interfere with mitral valve function .
the la catheter was used for injection of multiple colors of fluorescent - labeled 15 m microspheres into the systemic arterial circulation .
simultaneously , a reference blood sample was withdrawn at a known rate ( 15 ml / min ) from the aorta as previously described .
the microsphere technique enables the precise measurement of regional blood flow in vascular beds of interest .
microspheres injected into the la chamber mix with blood in the lv and are subsequently ejected into the aorta , from where they disseminate throughout the body and lodge within the smallest precapillary arterioles based on regional tissue blood flow distribution .
we have previously demonstrated that with the quantity used , 15 m spheres do not cause ischemia and do not induce pathology .
the aortic blood sample acts as a reference for later determination of flow in tissues of interest .
the number of counted microspheres in the reference blood sample ( known ) is compared to the number of microspheres that lodge and are counted in a tissue sample of interest ( known ) .
the ratio between the two sphere counts is equal to the ratio between the calibrated rate of aortic withdrawal ( known ) and flow in the tissue of interest ( unknown ) and provides accurate tissue - specific blood flow in ml / min / g [ 20 , 21 ] . at the completion of the study , while under anesthesia , euthanasia was performed with a single fatal bolus injection of beuthanasia - d special ( 1 ml/5 kg iv ) .
one- to two - gram tissue sections from the lv - free wall , right ventricular(rv)-free wall , and interventricular septum together with reference blood samples were sent to imt / stason laboratories ( irvine , ca ) for automated digestion and counting of fluorescent microspheres with flow cytometry and calculation of tissue - specific blood flows .
all pressure and flow transducers were pre- and postcalibrated against known physical standards to ensure measurement accuracy .
data were collected at 400 hz , signal conditioned , and a / d converted for digital analysis using our glp compliant data acquisition system . pressure and flow recordings were used to derive heart rate , cardiac output , mean arterial pressure , mean la pressure , lv peak systolic and end - diastolic pressure ( edp ) , peak dp / dt , lv external work , and mean diastolic coronary artery blood flow .
these parameters were calculated on a beat - to - beat basis for each 30-second data set with the hemodynamic evaluation and assessment research tool ( heart ) program developed in matlab ( version 6.5 , mathworks ) . all analyzed beats in each data set ( approximately 3050 beats )
paraffin - embedded tissue sections ( 4 m ) from the lv , rv , and interventricular septum were deparaffinized , rehydrated , and stained with masson 's trichrome ( for collagen ) with standard histological techniques as previously described . to determine myocyte cross - sectional area , fitc - conjugated wheat germ agglutinin ( molecular probes ) staining of cell membranes together with dapi ( molecular probes ) nuclear costaining
myocyte area determined from an average of 100150 cross - sectional cells with centrally located round nuclei and the total fibrotic area were assessed using metamorph imaging software .
apoptosis in cardiac tissue was determined with the deadend fluorometric tunel system ( promega ) , which catalytically incorporates fluorescein-12-dutp at dna strand breaks as previously described .
all sections were counterstained with dapi ( molecular probes ) at a final concentration of 2 m .
images were viewed with epifluorescence microscopy ( nikon te2000 ) within 24 hours and analyzed with metamorph imaging software .
mrna expression in the heart was quantified by real - time polymerase chain reaction ( pcr ) as previously described [ 23 , 25 ] .
briefly , total rna was isolated from lv tissue with trizol reagent ( invitrogen ) , and cdna was synthesized from 1 g rna with the iscript cdna synthesis kit ( biorad ) .
relative levels of mrna transcripts for atrial natriuretic factor ( anf ) , connective tissue growth factor ( ctgf ) , matrix metalloproteinase ( mmp)-2 , and mmp-9 were quantified by real - time pcr with the use of sybr green ( applied biosystems ) and the sense / antisense primer pairs listed in table 1 .
data were normalized to 18s ribosomal rna subunit expression using the ct comparative method , and the values from doxorubicin - treated hearts were expressed as a fold change over control .
plasma norepinephrine and epinephrine levels were determined by colorimetric quantitative competitive elisa with a commercially available kit ( rocky mountain diagnostics ) according to the manufacturer 's instructions .
briefly , the derivatized standards , test samples , and the solid phase bound analytes competed for a fixed number of antiserum binding sites .
after washing of the free antigen and the antigen - antiserum complexes , the antibody bound to the solid phase was detected by a peroxidase - conjugated secondary antibody .
serial echocardiographic and catecholamine data from the same animal at different time points during the doxorubicin protocol were compared using one - way anova with tukey posttest .
hemodynamic , myocardial blood flow , histological , and molecular comparisons between doxorubicin - treated animals and normal animals were performed with an unpaired t - test .
all four animals developed chronic coughing , three of four animals developed dyspnea on exertion , and one animal developed dyspnea at rest and severe ascites . during the duration of the study ,
the target lvef ( 35% ) was achieved in three animals , and diminished heart function was induced in the remaining animal treated with doxorubicin .
representative m - mode echocardiographic images from one animal at baseline and 60 days after initiating doxorubicin are shown in figure 1 .
mild lv dilitation was observed along with a much more profound reduction in systolic contraction and shortening fraction .
doxorubicin induced mild increases in lv end - diastolic volume ( edv ) that were not statistically significant , but significant ( p < 0.05 ) increases in lv end - systolic volume ( esv ) and worsening of lvef were observed .
these effects were more profound under isoflurane anesthesia . in the subset of animals that achieved target lvef , there was significant exacerbation of all echocardiographic parameters of interest ( baseline versus final anesthetized : lvedv 572 versus 71 29 ml ; lvesv 6 3 versus 52 15 ml ; lvef 89 6 versus 25 10% ; p < 0.05 )
.
table 3 depicts hemodynamic parameters measured 60 days after the initiation of doxorubicin . as compared to normal calves of somewhat smaller size ( n = 9 , mean weight : 76.1 kg ) that were previously studied in our laboratory , doxorubicin - treated calves exhibited hemodynamic changes indicative of lv contractile dysfunction with significantly ( p < 0.05 ) decreased cardiac output , mean arterial pressure , peak + dp / dt , and peak dp / dt , and a trend toward decreased lv peak systolic pressure ( p = 0.10 ) , lv external work ( p = 0.10 ) , and left main coronary artery blood flow ( p = 0.12 ) . interestingly , despite significant inotropic and lusitropic depression , filling pressures ( la pressure and lv end - diastolic pressure ) were comparable between the groups .
figure 2 demonstrates regional myocardial blood flow in the lv - free wall , interventricular septum , rv - free wall , and the transmural distribution in control animals and doxorubicin - treated animals at 60 days after initiation of doxorubicin .
there were statistically significant ( p < 0.05 ) reductions in myocardial blood flow in the lv- and rv - free walls and trends toward reduced blood flow in the septum ( p = 0.13 ) , epicardium ( p = 0.07 ) , midmyocardium ( p = 0.07 ) , and endocardium ( p = 0.13 ) .
gross heart weights were 518 82 g for control animals and 604 90 g for animals treated with doxorubicin and were not statistically different as a direct comparison ( p = 0.25 ) or normalized to body weight ( p = 0.88 ) and suggest the absence of doxorubicin - induced hypertrophy at the chamber level .
figure 3 demonstrates the degree of collagen deposition / fibrosis in the lv , rv , and interventricular septum as determined by masson 's trichrome staining . as
compared to control hearts , after doxorubicin treatment , connective tissue decreased or tended to decrease in each of the three regions ( lv p = 0.14 , septum p < 0.10 , rv p < 0.01 ) . moreover , as seen in the accompanying representative histomicrographs , the outline of individual myocytes and the interstitial space were well established and clearly visible in control hearts . in contrast , doxorubicin - treated hearts did not exhibit clear myocyte borders , and interstitial connective tissue volume was markedly diminished . to explore this further , we examined myocardial gene expression of ctgf , a profibrotic matrix - associated protein , and mmp-2 and -9 , which would be expected to augment collagen degradation ( figure 4 ) . as compared with control hearts ,
ctgf expression was unchanged in doxorubicin - treated hearts , whereas mmp-2 expression was significantly ( p < 0.05 ) upregulated .
mmp-9 expression tended toward a decrease ( p = 0.09 ) . the large increase in mmp-2
would be expected to favor collagen turnover and loss , which was consistent with the histological findings in figure 3 .
figure 5 shows representative wheat - germ agglutinin staining of cell membranes and corresponding myocyte size in the lv , rv , and interventricular septum from control and doxorubicin - treated hearts . as compared with control hearts , after doxorubicin treatment myocyte size increased in each of the three regions and indicated pathologic myocyte hypertrophy .
this increase was statistically significant ( p < 0.05 ) in the rv and septum but not statistically significant in the lv ( p = 0.29 ) . in control hearts ,
myocytes were of a uniform size and shape , and interstitial space was clearly visible as dark , variegated bands throughout the myocardium .
consistent with these histological findings of hypertrophy , mrna expression of anf , a hypertrophic marker , was increased 3.5-fold in doxorubicin - treated hearts as compared with control ( figure 4 ) .
one potential explanation for doxorubicin - induced myocyte hypertrophy without changes in lv chamber weight would be the concomitant enhancement of myocardial cell loss .
figure 6 demonstrates representative tunel stains from control and doxorubicin - treated hearts and the overall apoptotic rate in the lv , interventricular septum , and rv . as compared to controls ,
this increase was statistically significant in the left ventricle ( p < 0.01 ) , of borderline significance in the interventricular septum ( p = 0.10 ) , and not significant in the right ventricle ( p = 0.39 ) . staining morphology and
the proximity of cells to vascular structures suggested that the apoptotic cells were a mixture of myocytes , endothelial cells , and immune cells .
as shown in figure 7 , plasma norepinephrine levels were significantly increased 14 days into the doxorubicin administration protocol and subsequently returned to baseline at 45 days .
plasma epinephrine increased progressively during doxorubicin administration and was significantly increased over baseline at 45 days .
collectively , these data indicate heightened circulating catecholamines and adrenergic activation , a hallmark of cardiomyopathy and heart failure .
in this study , we report for the first time a stable model of doxorubicin - induced cardiomyopathy in the calf . specifically , weekly intravenous injections of doxorubicin induced ( 1 ) mild lv dilatation with impaired lv contraction and relaxation , ( 2 ) reductions in cardiac output without changes in lv filling pressure , ( 3 ) reductions in myocardial blood flow , ( 4 ) myocyte hypertrophy , ( 5 ) cardiac cell apoptosis , ( 6 ) loss of interstitial collagen , and ( 7 ) an increase in plasma catecholamines .
most of these phenotypic features are hallmarks of the failing human heart . given that the calf is generally used for preclinical testing of mechanical circulatory support devices
, this bovine model may be useful as a platform for testing acute and chronic pathophysiologic responses to lvads in the context of hf and for the development of adjunct therapies for myocardial recovery .
doxorubicin is a potent broad - spectrum antineoplastic drug with dose - dependent cardiotoxicity that clinically can manifest as cardiomyopathy and hf .
multiple pathological mechanisms have been proposed for doxorubicin - induced cardiomyopathy that include the generation of free radicals , oxidative stress - induced lipid peroxidation and mitochondrial damage , suppression of cardiac gene expression and protein synthesis , augmented release of catecholamines , and cardiomyocyte and endothelial cell apoptosis [ 2729 ] .
the large number of mitochondria in the heart and the strong affinity of anthracyclines for the inner mitochondrial membrane phospholipid cardiolipin contribute to the mitochondrial accumulation of doxorubicin and predispose cardiac myocytes to doxorubicin toxicity . as such ,
multiple investigators have used anthracyclines such as doxorubicin to induce cardiomyopathy and hf in a variety of large animal models that include dogs and sheep [ 1017 , 31 ] .
large animal studies that have used sequential weekly doxorubicin doses for a circumscribed period ( as was done in our study ) report a cardiomyopathy that is progressive over the long term without evidence of spontaneous improvement [ 1013 , 16 ] . in dogs and sheep , serial doxorubicin administration decreased cardiac output by 1532%
similarly , in our bovine model , cardiac output was 28% lower than normal animals .
moreover , significant contractile and lusitropic dysfunction was evident with 40% reduction in peak + dp / dt and 55% reduction in peak dp / dt .
interestingly , lv dilatation , a hallmark of anthracycline cardiotoxicity in rodents , was relatively modest in our calf model , and filling pressures were normal despite reduced cardiac output .
this suggests that pathological remodeling and hemodynamic decompensation may have become more pronounced upon larger doses of doxorubicin and/or a greater duration of followup .
alternatively , these less pronounced phenotypic features may be species - specific and distinguish doxorubicin - mediated responses in the calf in comparison with other animal species .
lvef dropped by 30% in the conscious state and 60% in the anesthetized state as compared with baseline .
interestingly , it is well documented that bovine hemodynamics differ between conscious and anesthetized conditions [ 33 , 34 ] . normal ejection fraction in calves
has been reported to be as high as 85 9% in the conscious state and 63 10% under anesthetized conditions . in our study , after seven weeks of doxorubicin , the calves exhibited an ejection fraction of 64 23% in the conscious state and 36 23% under isoflurane anesthesia .
lvef in the conscious state may have overestimated basal mechanical function in these animals , as they were uniformly anxious with attendant increase in stress - induced , catecholamine - mediated effects on cardiac performance . as a result
, echocardiographic measurements were performed in a hyperdynamic state as occurs during a stress echocardiogram .
both echocardiographic and hemodynamic measurement in the anesthetized state confirmed significant systolic dysfunction after doxorubicin administration .
moreover , doxorubicin - treated animals exhibited several characteristic histological , biochemical , and molecular features of pathological cardiac remodeling and myocyte hypertrophy .
myocardial apoptosis and microvascular insufficiency both contribute to myocardial dysfunction in anthracycline - induced hf [ 2729 , 36 ] .
indeed , doxorubicin - treated bovine hearts in our study exhibited both a 5 to 6-fold increase in apoptotic rate and profound reductions in myocardial blood flow as quantified by regional microsphere distribution .
as prior work has demonstrated that doxorubicin can induce apoptosis of cardiomyocytes and endothelial cells [ 2527 ] , these two phenomena may be interrelated .
specifically , endothelial cell death in the microvasculature may have contributed to the observed reductions in coronary blood flow .
indeed , we frequently observed foci of apoptotic nuclei in proximity to or within coronary arterioles in the heart , which suggests that at least some apoptotic cells were of vascular or endothelial origin . as cardiomyopathic hearts generally show augmented interstitial fibrosis and collagen deposition , our finding of reduced interstitial collagen volume in doxorubicin - treated hearts was surprising .
however , prior work has demonstrated that doxorubicin upregulates and activates matrix metalloproteinases in the heart and can also inhibit collagen synthesis ( both of which would favor collagen degradation ) .
indeed , in our study , the expression of profibrotic ctgf in the heart was not affected by doxorubicin , whereas mmp-2 ( which promotes collagen breakdown ) was upregulated , consistent with these prior observations . in a rat study of the cardiac matrix following a single injection of doxorubicin , a biphasic course of myocardial remodeling was observed .
the initial response ( up to 6 weeks after injection ) was loss of the myocardial collagen matrix . at later time points ,
hence , the interstitial remodeling after doxorubicin exposure may not be uniform and may depend on the stage of progression of doxorubicin - induced ventricular remodeling .
it is possible that in our animals , longer periods of treatment or followup may have augmented collagen deposition , and greater fibrosis may have been observed . moreover , as myocardial fibrosis increases , ventricular chamber stiffness increases .
the reduced collagen deposition that we observed may underlie the absence of diastolic filling pressure elevation in doxorubicin - treated hearts .
the decrease in matrix protein may have increased chamber compliance and thereby maintained lvedp at levels comparable to normal animals , despite the development of doxorubicin cardiomyopathy .
the depressed peak dp / dt and cardiac output in doxorubicin - treated animals despite equivalent lvedp ( preload ) indicated significant contractile dysfunction in these animals .
filling pressure elevation and further hemodynamic compensation would have likely occurred over longer time periods that allowed for further progression of pathological remodeling .
our results must be interpreted in light of potential study limitations . in our study ,
the one animal that was somewhat resistant to doxorubicin was a pure - breed jersey calf , whereas the other three animals were mixed breed .
reported in a canine model of doxorubicin cardiomyopathy that one animal in their medium dose cohort showed no cardiac impairment , whereas all others animals showed severe impairment or died of heart failure .
another study limitation was the small number of experimental animals , a situation that was mandated by unanticipated limitations in available resources for large animal maintenance .
the small sample size increased the risk of type i statistical error ( i.e. , that the observed effects may have been driven by chance findings in just one animal ) and type ii statistical error ( i.e. , finding no difference between groups due to a small number of observations when a difference truly exists ) . nonetheless , despite the study of only four animals , the observed hemodynamic , structural , histological , biochemical , and molecular changes were all sufficiently robust to establish the induction of lv dysfunction and pathological remodeling by doxorubicin .
moreover , the observed changes were consistent with multiple prior studies of doxorubicin - induced cardiomyopathy in other animal models ( described above ) , suggest that our results were experimentally valid and not simply the result of chance statistical variation .
these limitations notwithstanding , our results establish the validity and feasibility of a clinically relevant bovine model of doxorubicin - induced cardiomyopathy that shares many phenotypic similarities with human heart failure .
this model may prove useful assess the pathophysiological responses to lvads and associated adjunctive therapies in hf .
this work was supported in part by an american heart association scientist development grant no .[/INST]left ventricular assist devices ( lvads ) constitute a recent advance in heart failure ( hf ) therapeutics . as the rigorous experimental assessment of lvads in hf requires large animal models ,
our objective was to develop a bovine model of cardiomyopathy .
male calves ( n = 8) were used .
four animals received 1.2 mg / kg intravenous doxorubicin weekly for seven weeks and four separate animals were studied as controls .
doxorubicin - treated animals were followed with weekly echocardiography .
target lv dysfunction was defined as an ejection fraction 35% .
sixty days after initiating doxorubicin , a terminal study was performed to determine hemodynamic , histological , biochemical , and molecular parameters . all four doxorubicin - treated animals exhibited significant ( p < 0.05 ) contractile dysfunction , with target lv dysfunction achieved in three animals .
doxorubicin - treated hearts exhibited significantly reduced coronary blood flow and interstitial fibrosis and significantly increased apoptosis and myocyte size .
gene expression of atrial natriuretic factor increased more than 3-fold .
plasma norepinephrine and epinephrine levels were significantly increased early and late during the development of cardiomyopathy , respectively .
we conclude that sequential administration of intravenous doxorubicin in calves induces a cardiomyopathy with many phenotypic hallmarks of the failing human heart
. this clinically - relevant model may be useful for testing pathophysiologic responses to lvads in the context of hf .</s> |
the first trans - neptunian binary ( tnb ) was identified in 1978 with the discovery of charon , pluto s moon ( christy and harrington 1978 ) .
the first binary kuiper - belt object , , was announced in 2001 ( veillet 2001 ) , though it has since been identified in images taken as early as november 1998 ( veillet et al .
more discoveries have followed in rapid succession ( table 1 ) so that , as of february 2002 , a total of six trans - neptunian binaries were known .
the discovery of tnbs opens up a significant new tool for physical study of trans - neptunian objects ( tno ) . through analysis of the orbit ,
it offers the only direct means of determining the mass of these distant objects for the forseeable future .
when combined with optical and thermal wavelength photometry , density can also be determined .
both mass and density have _ a priori _ uncertainties of at least an order of magnitude for tnos , so the value of direct observations can not be underestimated .
binaries offer further opportunities for physical study through mutual occultations .
the series of pluto - charon mutual events that occurred soon after the discovery of charon led to surface albedo maps and separate spectra , revealing the very distinct surface compositions of pluto and its satellite ( buie et al .
1987 , fink & disanti 1988 , buie et al .
1992 , young et al .
veillet et al . (
2002 ) suggest that will begin a series of mutual events in approximately 50 years .
tnos have periods of 250 years or more so it will be necessary to discover and determine the orbits of approximately 10 tnbs before it will be likely to find one having mutual occultations within the next decade .
two tnos , and , are the focus of this work . was discovered at mauna kea observatory by chen et al .
( 1997 ) and was discovered at kitt peak national observatory by the deep ecliptic survey team ( millis , et al .
both objects are classical tnos in orbits of small eccentricity and low inclination . in this paper
we describe the discovery of binary companions to and , making them the seventh and eighth known tnbs ( noll and stephens 2002 , noll et al .
and were observed as part of a large photometric survey of tnos that we are carrying out using the hubble space telescope .
the data were dark - subtracted , flat - fielded , and flux calibrated using standard stsci on - the - fly pipeline calibration steps including up - to - date dark files .
cosmic ray hits were removed by combining pairs of filtered observations with the standard crrej routine found in the stsdas iraf software package ( baggett et al .
2002 ) .
we used the wfall aperture , centered at pixel 133 , 149 on the wf3 chip ( biretta et al .
2001 ) , for all observations in our photometric survey .
this is the corner of the wf3 chip nearest the x and y readout registers , a position that reduces the magnitude of the charge transfer efficiency correction required ( whitmore et al .
1999 , dolphin 2000 ) . the wfall aperture was also chosen to increase the likelihood of finding objects with uncertain ephemeris positions .
the telescope was tracked during all observations correcting both for the proper motion of the tno and the parallax induced by hubble s orbital motion . in followup observations of we placed the target on the pc chip to take advantage of the better sampling on that detector .
as with the other observations , the telescope was tracked at the apparent rate of the tno .
[ [ section ] ] was first imaged by us from 6:44 to 7:22 ut on 17 november 2001 when it was at a distance of 41.85 au from the earth .
we obtained images with the wfpc2 camera on the hubble space telescope ( hst ) in three broad band filters approximating v ( f555w ) , r ( f675w ) , and i ( f814w ) bands .
there were two 160 second exposures in each filter .
the sequence started with a single f555w exposure , followed by two each in f675w and f814w , and ended with a second single f555w .
we identified in our images both by its lack of motion relative to tracking and by its position at 66,92 on the wf3 chip , 8.76 arcsec from the predicted position .
stars and galaxies in the field moved by a total of 0.46 arcsec between the first and last exposure .
as shown in figure 1 , the image of is clearly elongated .
the orientation of the spacecraft was such that north is approximately 30 degrees from the vertical in our images as indicated by the long arrow .
the axis of the elongation is rotated by 16@xmath04 degrees east of north relative to the brighter of the two components , component @xmath1 .
the elongation appears in all six individual images at a similar angle and separation .
we note that the direction of the elongation is almost perpendicular to the apparent motion of stars and galaxies which moved diagonally from east to west in the images as shown .
we also examined engineering data that tracks jitter during the observations .
no unusual jitter was seen , ruling this out as a possible source of error .
based on this visual evidence , we concluded that is a probable binary and proceeded to obtain confirming images .
three additional sets of observations of were made from 7:30 to 8:26 ut on 18 june 2002 , 3:09 to 4:05 ut on 30 june 2002 , and 3:39 - 4:35 ut on 12 july 2002 . on each date we obtained three 800 second exposures in the f814w filter with the on the pc chip .
in all three cases the binary was easily detected and clearly resolved , as shown in figure 1 .
the higher resolution of the pc , the better s / n resulting from longer integrations , and obvious presence of the two components on four separate dates leaves no doubt about the binarity of .
[ [ section-1 ] ] was observed in two filters , the f555w and f814w , on 12 january 2002 from 1:12 to 1:49 ut . as with
, the observing sequence began and ended with an f555w exposure .
a pair of f814w exposures occurred between the f555ws . because is fainter
, we exposed this object in only two filters with two 260 second exposures per filter .
the brighter component of , component @xmath1 , was found 0.58 arcsec from the wfall aperture at pixel 133,155 . a second , fainter object , component @xmath2 ,
can be seen to the east in figure 2 at pixel 138 , 161 .
@xmath1 and @xmath2 were stationary during the observations .
stars and galaxies were trailed , moving a total of 1.1 arcsec from the first to last exposure .
as shown in figure 2 , the two components of are cleanly separated by an angular distance of [email protected] arcsec at a position angle of [email protected] degrees measured from @xmath1 .
was subsequently observed from the keck i telescope ( fig . 3 , romanishin et al . 2002 ) .
on the night of 11 april 2002 ( ut ) was observed in four ten - minute integrations simultaneously in b and r bands using the lris instrument in imaging mode .
the images were individually bias - subtracted and flat - fielded and then combined into a single image . for the combined image shown in figure 3 ,
the individual exposures were shifted to align the images of which was moving at -0.235 arcsec / hr in ra and 0.00 arcsec / hr in dec . as can be seen in figure 3 ,
appears elongated in the east - west direction with the fainter component to the east .
romanishin et al .
report a separation of [email protected] arcsec at a position angle of 103@xmath05 degrees .
this matches the orientation seen in the wfpc2 image and confirms the presence of the companion .
[ [ section-2 ] ] in order to determine the separation and to obtain separate photometric magnitudes for the two components of in the november data we fit the observed image by iteratively combining scaled synthetic point - spread functions ( psf ) generated by the tinytim software tool ( krist et al .
an example is shown in figure 4 .
both the separation and the relative magnitude of the components were allowed to vary . after finding a preliminary fit
, we repeated the procedure over a finer grid .
a best fit was determined by finding the parameters that yielded a minimum in the least squares residuals between the model and observed data .
errors were estimated from the residuals . from the iterative fit we determined a mean separation of [email protected] arcsec on 17 november 2001 .
we note that this is 0.04 arcsec larger than reported by noll & stephens ( 2002 ) because the separation of the psf centers is slightly larger than the separation of the peaks in the brightness distribution .
this separation is near the resolution limit of the wide field portion of wfpc2 where the pixel scale is 0.1 arcsec / pixel , though it is sufficiently large that the two components can be reliably resolved .
we applied the same technique to determine separations in the june / july 2002 data , even though the objects are clearly resolved and separate .
positional information is summarized in table 2 .
magnitudes are converted to the standard johnson - cousins system using the synphot software package .
details of our photometric pipeline are described in more detail in a forthcoming paper .
we measure a johnson v magnitude of v = [email protected] and cousins r and i magnitudes of r = [email protected] , i = [email protected] for the component @xmath1 .
component @xmath2 was found to have v = [email protected] , r = [email protected] , and i = [email protected] ( table 3 ) .
the photometry we obtained in june / july 2002 is generally consistent with the i band magnitudes determined in november 2001 as detailed in table 3 .
the one exception is the unusually faint magnitude recorded for the component @xmath1 on 18 june 2002 .
the faintness initially caused us to misidentify the components in this image , but when combined with the other images and possible mutual orbits , it is clear that on 18 june @xmath1 is almost a full magnitude fainter than on the other three dates when we measured it .
note , in particular , that the observations in june and july 2002 were each separated by approximately 12 days .
this is far shorter than any plausible period for the binary as discussed below .
and there is essentially no change between the 30 june and 12 july magnitudes for either component . finally , the measured magnitude of component @xmath2 is almost identical in all four observations .
it is possible that the unusually low measured magnitude for component @xmath1 is due to some unrecognized observational error .
it is also possible that @xmath1 has an intrinsic lightcurve with a large amplitude .
further observations to set limits on lightcurves would be valuable .
the discovery of binaries is valuable because it offers the possibility of determining the mass and density of the objects , basic physical parameters that would otherwise require spacecraft to measure .
we have not yet determined the orbits for either of the binaries that we have detected .
it is possible , however , to make estimates of diameter and mass by making assumptions about the albedo and density of the objects and using measured magnitudes .
if we assume an albedo of q=0.04 as is customarily done for tnos , we find that the two components of have diameters of d(a)=220 km and d(b)=200 km following the formalism of romanishin and tegler ( 1999 ) .
if we further assume a bulk density of 1 g @xmath3 , we calculate a combined mass of 9.76@xmath4 g , or 1/1500th the mass of pluto and charon .
it is also possible to make educated guesses about possible orbital periods as we discuss separately below . on january 12 , 2002 ,
was 41.30 au from the earth . at this distance ,
the angular separation we observed , 0.78 arcsec , corresponds to a minimum separation of 23,360 km .
because of the wide separation , we were able to measure individual magnitudes for each component of the binary with standard aperture photometry using the iraf phot routine .
we used an aperture radius of 3 pixels and a background annulus with inner diameter of 20 pixels and a thickness of 20 pixels .
an aperture correction factor was calculated using synthetic psfs .
we determined v = 24.25@xmath0 0.11 and i = 22.99@xmath0 0.08 for the brighter component @xmath1 and v = 25.12@xmath0 0.24 and i = 23.55@xmath0 0.13 for the component @xmath2 ( table 3 ) .
the uncertainties are relatively large , especially for the fainter component @xmath2 , because of the faintness of these objects .
@xmath1 is one of the faintest tnos we have observed and the @xmath2 is more than a magnitude fainter than the nominal magnitude limit we used for target selection .
significantly fainter companions would not be detected by our relatively short integrations .
romanishin et al .
( 2002 ) report that the two components of differ by [email protected] mags in the r band , consistent with hst relative photometry .
absolute photometry with the keck data has not been reported .
using the same procedure as we did for , we estimate diameters for the two components to be d(@xmath1)=170 km and d(@xmath2)=120 km for an albedo of 0.04 . assuming a density of @xmath5 = 1 g @xmath3 we find a combined mass of 3.48@xmath4 g , 4200 times less than pluto and charon .
it is possible to estimate the period of tnbs using kepler s third law by making an assumption about the semimajor axis and eccentricity of the orbit .
this exercise is necessary in order to plan followup observations and is also useful as a yardstick for comparison with the actual orbit once it is known .
we note that of the two tnbs with measured orbits , one , pluto / charon is nearly circular , while the other , has an eccentricity of e=0.8 ( veillet et al .
2002 ) . for our initial
guess we assumed that e=0 and that the observed separation in november 2001 , a=6070 km , is the semimajor axis . for this set of assumptions
we derive an orbital period of 42.6 days .
we used this value to plan our followup observations in june and july 2002 .
the separation we observed in june / july 2002 was larger , an average of 10,200 km . using the same assumptions
, this would yield a period of 92 days .
the four epochs of observation allow us to determine some basic facts about the orbit of .
as can be seen in table 2 , on the dates in june and july 2002 , each separated by approximately 12 days , the position angle measured from component @xmath1 to @xmath2 increases steadily .
the average rate over the nearly 24 days from 18 june to 12 july 2002 is 0.281 degrees / day .
however , the average rate from 17 november to 18 june , a period of 212.85 days , must be significantly higher , averaging 1.494 degrees / day .
we have insufficient data to resolve these discrepant rates .
it is apparent , however , that the orbital plane is inclined relative to our line of sight and/or the orbit is significantly eccentric .
additional observations will be required to determine the orbit of .
if we perform the same exercise for we find an orbital period for a circular orbit would be 539 days , comparable to the 547 day period of ( veillet et al . 2002 ) and significantly longer than the apparent period of .
the similarity of position angles observed in january and april 2002 is consistent with a long period , though the uncertainties are sufficiently large that nothing more quantitative can be said .
the v - i color index can be computed for each binary component from the measured v and i photometry .
color can , in principle , be used to infer the surface composition and resurfacing history of tnos ( c.f .
jewitt & luu 2001 ) . in the 75 objects surveyed by us ,
v - i ranges from 0.8 to 1.6 , which is to be compared to v - i(sun)=0.71 .
that is , tno colors range from neutral to extremely red , as has been noted before ( luu & jewitt 1996 ) .
the colors of and are listed in table 3 .
the brighter @xmath1 components of both binaries have colors , v - i @xmath6 1.25 , that are average for classical tnos observed in our survey .
their companions differ by about 1-sigma , more neutral in the case of @xmath2 and redder in the case of @xmath2 .
unfortunately , the uncertainties in the colors are sufficiently large that we can not reach conclusions beyond stating that @xmath2 is unlikely to have neutral colors while @xmath2 is not significantly more red than @xmath1 . future observations that reduce the photometric uncertainties will be required to reach stronger conclusions .
we have observed 75 tnos so far in our photometric survey using hst and have examined all of these for possible binary companions .
of those 75 , we have detected companions to 3 , , , and the previously known binary .
this statistic applies to companions with separations greater than @xmath60.15 arcsec and v - band differences of less than @xmath61 mag .
although was identified as a binary prior to its inclusion in our target list , the magnitude of and the precision of its orbit determination matched the criteria for inclusion and it would have been added even if the binary were not known .
also , the order in which snapshot targets are scheduled is random and outside the control of the observers .
the probablility that would have been observed at this point in our observing program is approximately 50% .
given these considerations , we believe it is proper to consider as part of an unbiased sample .
we then conclude that the frequency of binaries consistent with the limits above is simply 3/75 or @xmath7% .
we note that , because of the large statistical uncertainty , the exclusion of from the sample would not alter this conclusion substantially .
a frequency of @xmath7% is in marginal agreement with the detection of 8 tnbs out of a total of more than 500 tnos detected to date .
however , the uneven sampling and data quality of this larger population complicates any statistical conclusions from this larger sample .
many of the objects have been observed only a few times and some are effectively lost .
many of the detected binaries , for example , could not be detected by most ground - based systems including those equipped with adaptive optics .
is just detectable with ground - based systems , and indeed has been verified as binary from the ground ( romanishin & tegler et al .
furthermore , the magnitude limit and angular resolution in individual observations of tnos is a strong function of equipment and observing conditions .
nevertheless , the overall detection rate of @xmath8% supports the rate inferred from our more uniform survey .
it is worth noting that half of known tnbs , four of eight , have been discovered with hst ( trujillo and brown 2002 , brown and trujillo 2002 , noll and stephens 2002 , noll et al .
since far more observations of tnos are made by groundbased telescopes than by hst , this fact would appear to imply that tnbs separated by more than an arcsecond are less frequent than more closely spaced companions , an assertion borne out by table 1 when one considers that 1 arcsec at 40 au is a physical distance of 29,000 km .
we also note that all three of the binaries detected by us and five of the eight objects in table 1 are classical tnos .
two are in the 3:2 resonance and one is possibly a scattered object . of the 75 objects observed in our program so far ,
65% are classical tnos with low eccentricity and inclination , 24% are plutinos , and 11% are scattered disk objects
. there does not seem to be sufficient evidence at present to make any conclusions about the relative frequency of binaries in the different dynamical populations , though eventually this information may be useful in determining the origin and history of tnbs and the dynamical classes in the kuiper belt .
finally , it is worthwhile to make a comparison between tnbs and binaries found in the main belt and near - earth populations .
a total of 6 binaries have been identified out of a sample of 300 main - belt targets by merline et al .
( 2001 ) , a rate , at first glance , roughly similar to that being found in the kuiper belt .
however , it must be noted that the relative sizes and separations of main belt and kuiper belt binaries appear to be significantly different ( margot 2002 ) . if a population of tnbs with faint and close - in companions , similar to the main belt binaries , exists , the fraction of tnbs could be significantly higher than our current estimate .
if collisions are the main source of binaries in both populations , the frequency of binaries , and their orbital and size distribution can be used to probe the efficiency of binary formation from such events .
the near - earth asteroid ( nea ) population has a higher frequency of binaries , as high as 16% for objects over 200 m in diameter ( margot et al .
however , mechanisms other than collisions , e.g. tidal breakup , may be responsible for this larger number among the neas and this population may be less relevant for comparison to tnbs . | images of the trans - neptunian objects and obtained with the hubble space telescope s wfpc2 camera show them to be binary .
the two components of were separated in our images by [email protected] arsec in november 2001 and by [email protected] arcsec in june / july 2002 .
the corresponding minimum physical distances are 6100 km and 10,200 km .
the companion to was [email protected] arcsec from the primary , at least 23,400 km .
six other objects in the trans - neptunian region , including pluto and its moon charon , are known to be binaries ; and are the seventh and eighth known pair .
binarity appears to be a not - uncommon characteristic in this region of the solar system , with detectable companions present in 4@xmath02% of the objects we have examined .
[ 0.5in=1 ] | <s>[INST]the first trans - neptunian binary ( tnb ) was identified in 1978 with the discovery of charon , pluto s moon ( christy and harrington 1978 ) .
the first binary kuiper - belt object , , was announced in 2001 ( veillet 2001 ) , though it has since been identified in images taken as early as november 1998 ( veillet et al .
more discoveries have followed in rapid succession ( table 1 ) so that , as of february 2002 , a total of six trans - neptunian binaries were known .
the discovery of tnbs opens up a significant new tool for physical study of trans - neptunian objects ( tno ) . through analysis of the orbit ,
it offers the only direct means of determining the mass of these distant objects for the forseeable future .
when combined with optical and thermal wavelength photometry , density can also be determined .
both mass and density have _ a priori _ uncertainties of at least an order of magnitude for tnos , so the value of direct observations can not be underestimated .
binaries offer further opportunities for physical study through mutual occultations .
the series of pluto - charon mutual events that occurred soon after the discovery of charon led to surface albedo maps and separate spectra , revealing the very distinct surface compositions of pluto and its satellite ( buie et al .
1987 , fink & disanti 1988 , buie et al .
1992 , young et al .
veillet et al . (
2002 ) suggest that will begin a series of mutual events in approximately 50 years .
tnos have periods of 250 years or more so it will be necessary to discover and determine the orbits of approximately 10 tnbs before it will be likely to find one having mutual occultations within the next decade .
two tnos , and , are the focus of this work . was discovered at mauna kea observatory by chen et al .
( 1997 ) and was discovered at kitt peak national observatory by the deep ecliptic survey team ( millis , et al .
both objects are classical tnos in orbits of small eccentricity and low inclination . in this paper
we describe the discovery of binary companions to and , making them the seventh and eighth known tnbs ( noll and stephens 2002 , noll et al .
and were observed as part of a large photometric survey of tnos that we are carrying out using the hubble space telescope .
the data were dark - subtracted , flat - fielded , and flux calibrated using standard stsci on - the - fly pipeline calibration steps including up - to - date dark files .
cosmic ray hits were removed by combining pairs of filtered observations with the standard crrej routine found in the stsdas iraf software package ( baggett et al .
2002 ) .
we used the wfall aperture , centered at pixel 133 , 149 on the wf3 chip ( biretta et al .
2001 ) , for all observations in our photometric survey .
this is the corner of the wf3 chip nearest the x and y readout registers , a position that reduces the magnitude of the charge transfer efficiency correction required ( whitmore et al .
1999 , dolphin 2000 ) . the wfall aperture was also chosen to increase the likelihood of finding objects with uncertain ephemeris positions .
the telescope was tracked during all observations correcting both for the proper motion of the tno and the parallax induced by hubble s orbital motion . in followup observations of we placed the target on the pc chip to take advantage of the better sampling on that detector .
as with the other observations , the telescope was tracked at the apparent rate of the tno .
[ [ section ] ] was first imaged by us from 6:44 to 7:22 ut on 17 november 2001 when it was at a distance of 41.85 au from the earth .
we obtained images with the wfpc2 camera on the hubble space telescope ( hst ) in three broad band filters approximating v ( f555w ) , r ( f675w ) , and i ( f814w ) bands .
there were two 160 second exposures in each filter .
the sequence started with a single f555w exposure , followed by two each in f675w and f814w , and ended with a second single f555w .
we identified in our images both by its lack of motion relative to tracking and by its position at 66,92 on the wf3 chip , 8.76 arcsec from the predicted position .
stars and galaxies in the field moved by a total of 0.46 arcsec between the first and last exposure .
as shown in figure 1 , the image of is clearly elongated .
the orientation of the spacecraft was such that north is approximately 30 degrees from the vertical in our images as indicated by the long arrow .
the axis of the elongation is rotated by 16@xmath04 degrees east of north relative to the brighter of the two components , component @xmath1 .
the elongation appears in all six individual images at a similar angle and separation .
we note that the direction of the elongation is almost perpendicular to the apparent motion of stars and galaxies which moved diagonally from east to west in the images as shown .
we also examined engineering data that tracks jitter during the observations .
no unusual jitter was seen , ruling this out as a possible source of error .
based on this visual evidence , we concluded that is a probable binary and proceeded to obtain confirming images .
three additional sets of observations of were made from 7:30 to 8:26 ut on 18 june 2002 , 3:09 to 4:05 ut on 30 june 2002 , and 3:39 - 4:35 ut on 12 july 2002 . on each date we obtained three 800 second exposures in the f814w filter with the on the pc chip .
in all three cases the binary was easily detected and clearly resolved , as shown in figure 1 .
the higher resolution of the pc , the better s / n resulting from longer integrations , and obvious presence of the two components on four separate dates leaves no doubt about the binarity of .
[ [ section-1 ] ] was observed in two filters , the f555w and f814w , on 12 january 2002 from 1:12 to 1:49 ut . as with
, the observing sequence began and ended with an f555w exposure .
a pair of f814w exposures occurred between the f555ws . because is fainter
, we exposed this object in only two filters with two 260 second exposures per filter .
the brighter component of , component @xmath1 , was found 0.58 arcsec from the wfall aperture at pixel 133,155 . a second , fainter object , component @xmath2 ,
can be seen to the east in figure 2 at pixel 138 , 161 .
@xmath1 and @xmath2 were stationary during the observations .
stars and galaxies were trailed , moving a total of 1.1 arcsec from the first to last exposure .
as shown in figure 2 , the two components of are cleanly separated by an angular distance of [email protected] arcsec at a position angle of [email protected] degrees measured from @xmath1 .
was subsequently observed from the keck i telescope ( fig . 3 , romanishin et al . 2002 ) .
on the night of 11 april 2002 ( ut ) was observed in four ten - minute integrations simultaneously in b and r bands using the lris instrument in imaging mode .
the images were individually bias - subtracted and flat - fielded and then combined into a single image . for the combined image shown in figure 3 ,
the individual exposures were shifted to align the images of which was moving at -0.235 arcsec / hr in ra and 0.00 arcsec / hr in dec . as can be seen in figure 3 ,
appears elongated in the east - west direction with the fainter component to the east .
romanishin et al .
report a separation of [email protected] arcsec at a position angle of 103@xmath05 degrees .
this matches the orientation seen in the wfpc2 image and confirms the presence of the companion .
[ [ section-2 ] ] in order to determine the separation and to obtain separate photometric magnitudes for the two components of in the november data we fit the observed image by iteratively combining scaled synthetic point - spread functions ( psf ) generated by the tinytim software tool ( krist et al .
an example is shown in figure 4 .
both the separation and the relative magnitude of the components were allowed to vary . after finding a preliminary fit
, we repeated the procedure over a finer grid .
a best fit was determined by finding the parameters that yielded a minimum in the least squares residuals between the model and observed data .
errors were estimated from the residuals . from the iterative fit we determined a mean separation of [email protected] arcsec on 17 november 2001 .
we note that this is 0.04 arcsec larger than reported by noll & stephens ( 2002 ) because the separation of the psf centers is slightly larger than the separation of the peaks in the brightness distribution .
this separation is near the resolution limit of the wide field portion of wfpc2 where the pixel scale is 0.1 arcsec / pixel , though it is sufficiently large that the two components can be reliably resolved .
we applied the same technique to determine separations in the june / july 2002 data , even though the objects are clearly resolved and separate .
positional information is summarized in table 2 .
magnitudes are converted to the standard johnson - cousins system using the synphot software package .
details of our photometric pipeline are described in more detail in a forthcoming paper .
we measure a johnson v magnitude of v = [email protected] and cousins r and i magnitudes of r = [email protected] , i = [email protected] for the component @xmath1 .
component @xmath2 was found to have v = [email protected] , r = [email protected] , and i = [email protected] ( table 3 ) .
the photometry we obtained in june / july 2002 is generally consistent with the i band magnitudes determined in november 2001 as detailed in table 3 .
the one exception is the unusually faint magnitude recorded for the component @xmath1 on 18 june 2002 .
the faintness initially caused us to misidentify the components in this image , but when combined with the other images and possible mutual orbits , it is clear that on 18 june @xmath1 is almost a full magnitude fainter than on the other three dates when we measured it .
note , in particular , that the observations in june and july 2002 were each separated by approximately 12 days .
this is far shorter than any plausible period for the binary as discussed below .
and there is essentially no change between the 30 june and 12 july magnitudes for either component . finally , the measured magnitude of component @xmath2 is almost identical in all four observations .
it is possible that the unusually low measured magnitude for component @xmath1 is due to some unrecognized observational error .
it is also possible that @xmath1 has an intrinsic lightcurve with a large amplitude .
further observations to set limits on lightcurves would be valuable .
the discovery of binaries is valuable because it offers the possibility of determining the mass and density of the objects , basic physical parameters that would otherwise require spacecraft to measure .
we have not yet determined the orbits for either of the binaries that we have detected .
it is possible , however , to make estimates of diameter and mass by making assumptions about the albedo and density of the objects and using measured magnitudes .
if we assume an albedo of q=0.04 as is customarily done for tnos , we find that the two components of have diameters of d(a)=220 km and d(b)=200 km following the formalism of romanishin and tegler ( 1999 ) .
if we further assume a bulk density of 1 g @xmath3 , we calculate a combined mass of 9.76@xmath4 g , or 1/1500th the mass of pluto and charon .
it is also possible to make educated guesses about possible orbital periods as we discuss separately below . on january 12 , 2002 ,
was 41.30 au from the earth . at this distance ,
the angular separation we observed , 0.78 arcsec , corresponds to a minimum separation of 23,360 km .
because of the wide separation , we were able to measure individual magnitudes for each component of the binary with standard aperture photometry using the iraf phot routine .
we used an aperture radius of 3 pixels and a background annulus with inner diameter of 20 pixels and a thickness of 20 pixels .
an aperture correction factor was calculated using synthetic psfs .
we determined v = 24.25@xmath0 0.11 and i = 22.99@xmath0 0.08 for the brighter component @xmath1 and v = 25.12@xmath0 0.24 and i = 23.55@xmath0 0.13 for the component @xmath2 ( table 3 ) .
the uncertainties are relatively large , especially for the fainter component @xmath2 , because of the faintness of these objects .
@xmath1 is one of the faintest tnos we have observed and the @xmath2 is more than a magnitude fainter than the nominal magnitude limit we used for target selection .
significantly fainter companions would not be detected by our relatively short integrations .
romanishin et al .
( 2002 ) report that the two components of differ by [email protected] mags in the r band , consistent with hst relative photometry .
absolute photometry with the keck data has not been reported .
using the same procedure as we did for , we estimate diameters for the two components to be d(@xmath1)=170 km and d(@xmath2)=120 km for an albedo of 0.04 . assuming a density of @xmath5 = 1 g @xmath3 we find a combined mass of 3.48@xmath4 g , 4200 times less than pluto and charon .
it is possible to estimate the period of tnbs using kepler s third law by making an assumption about the semimajor axis and eccentricity of the orbit .
this exercise is necessary in order to plan followup observations and is also useful as a yardstick for comparison with the actual orbit once it is known .
we note that of the two tnbs with measured orbits , one , pluto / charon is nearly circular , while the other , has an eccentricity of e=0.8 ( veillet et al .
2002 ) . for our initial
guess we assumed that e=0 and that the observed separation in november 2001 , a=6070 km , is the semimajor axis . for this set of assumptions
we derive an orbital period of 42.6 days .
we used this value to plan our followup observations in june and july 2002 .
the separation we observed in june / july 2002 was larger , an average of 10,200 km . using the same assumptions
, this would yield a period of 92 days .
the four epochs of observation allow us to determine some basic facts about the orbit of .
as can be seen in table 2 , on the dates in june and july 2002 , each separated by approximately 12 days , the position angle measured from component @xmath1 to @xmath2 increases steadily .
the average rate over the nearly 24 days from 18 june to 12 july 2002 is 0.281 degrees / day .
however , the average rate from 17 november to 18 june , a period of 212.85 days , must be significantly higher , averaging 1.494 degrees / day .
we have insufficient data to resolve these discrepant rates .
it is apparent , however , that the orbital plane is inclined relative to our line of sight and/or the orbit is significantly eccentric .
additional observations will be required to determine the orbit of .
if we perform the same exercise for we find an orbital period for a circular orbit would be 539 days , comparable to the 547 day period of ( veillet et al . 2002 ) and significantly longer than the apparent period of .
the similarity of position angles observed in january and april 2002 is consistent with a long period , though the uncertainties are sufficiently large that nothing more quantitative can be said .
the v - i color index can be computed for each binary component from the measured v and i photometry .
color can , in principle , be used to infer the surface composition and resurfacing history of tnos ( c.f .
jewitt & luu 2001 ) . in the 75 objects surveyed by us ,
v - i ranges from 0.8 to 1.6 , which is to be compared to v - i(sun)=0.71 .
that is , tno colors range from neutral to extremely red , as has been noted before ( luu & jewitt 1996 ) .
the colors of and are listed in table 3 .
the brighter @xmath1 components of both binaries have colors , v - i @xmath6 1.25 , that are average for classical tnos observed in our survey .
their companions differ by about 1-sigma , more neutral in the case of @xmath2 and redder in the case of @xmath2 .
unfortunately , the uncertainties in the colors are sufficiently large that we can not reach conclusions beyond stating that @xmath2 is unlikely to have neutral colors while @xmath2 is not significantly more red than @xmath1 . future observations that reduce the photometric uncertainties will be required to reach stronger conclusions .
we have observed 75 tnos so far in our photometric survey using hst and have examined all of these for possible binary companions .
of those 75 , we have detected companions to 3 , , , and the previously known binary .
this statistic applies to companions with separations greater than @xmath60.15 arcsec and v - band differences of less than @xmath61 mag .
although was identified as a binary prior to its inclusion in our target list , the magnitude of and the precision of its orbit determination matched the criteria for inclusion and it would have been added even if the binary were not known .
also , the order in which snapshot targets are scheduled is random and outside the control of the observers .
the probablility that would have been observed at this point in our observing program is approximately 50% .
given these considerations , we believe it is proper to consider as part of an unbiased sample .
we then conclude that the frequency of binaries consistent with the limits above is simply 3/75 or @xmath7% .
we note that , because of the large statistical uncertainty , the exclusion of from the sample would not alter this conclusion substantially .
a frequency of @xmath7% is in marginal agreement with the detection of 8 tnbs out of a total of more than 500 tnos detected to date .
however , the uneven sampling and data quality of this larger population complicates any statistical conclusions from this larger sample .
many of the objects have been observed only a few times and some are effectively lost .
many of the detected binaries , for example , could not be detected by most ground - based systems including those equipped with adaptive optics .
is just detectable with ground - based systems , and indeed has been verified as binary from the ground ( romanishin & tegler et al .
furthermore , the magnitude limit and angular resolution in individual observations of tnos is a strong function of equipment and observing conditions .
nevertheless , the overall detection rate of @xmath8% supports the rate inferred from our more uniform survey .
it is worth noting that half of known tnbs , four of eight , have been discovered with hst ( trujillo and brown 2002 , brown and trujillo 2002 , noll and stephens 2002 , noll et al .
since far more observations of tnos are made by groundbased telescopes than by hst , this fact would appear to imply that tnbs separated by more than an arcsecond are less frequent than more closely spaced companions , an assertion borne out by table 1 when one considers that 1 arcsec at 40 au is a physical distance of 29,000 km .
we also note that all three of the binaries detected by us and five of the eight objects in table 1 are classical tnos .
two are in the 3:2 resonance and one is possibly a scattered object . of the 75 objects observed in our program so far ,
65% are classical tnos with low eccentricity and inclination , 24% are plutinos , and 11% are scattered disk objects
. there does not seem to be sufficient evidence at present to make any conclusions about the relative frequency of binaries in the different dynamical populations , though eventually this information may be useful in determining the origin and history of tnbs and the dynamical classes in the kuiper belt .
finally , it is worthwhile to make a comparison between tnbs and binaries found in the main belt and near - earth populations .
a total of 6 binaries have been identified out of a sample of 300 main - belt targets by merline et al .
( 2001 ) , a rate , at first glance , roughly similar to that being found in the kuiper belt .
however , it must be noted that the relative sizes and separations of main belt and kuiper belt binaries appear to be significantly different ( margot 2002 ) . if a population of tnbs with faint and close - in companions , similar to the main belt binaries , exists , the fraction of tnbs could be significantly higher than our current estimate .
if collisions are the main source of binaries in both populations , the frequency of binaries , and their orbital and size distribution can be used to probe the efficiency of binary formation from such events .
the near - earth asteroid ( nea ) population has a higher frequency of binaries , as high as 16% for objects over 200 m in diameter ( margot et al .
however , mechanisms other than collisions , e.g. tidal breakup , may be responsible for this larger number among the neas and this population may be less relevant for comparison to tnbs .[/INST] images of the trans - neptunian objects and obtained with the hubble space telescope s wfpc2 camera show them to be binary .
the two components of were separated in our images by [email protected] arsec in november 2001 and by [email protected] arcsec in june / july 2002 .
the corresponding minimum physical distances are 6100 km and 10,200 km .
the companion to was [email protected] arcsec from the primary , at least 23,400 km .
six other objects in the trans - neptunian region , including pluto and its moon charon , are known to be binaries ; and are the seventh and eighth known pair .
binarity appears to be a not - uncommon characteristic in this region of the solar system , with detectable companions present in 4@xmath02% of the objects we have examined .
[ 0.5in=1 ] </s> |
the recent released third catalog of high - energy @xmath1-ray sources by the egret telescope on the compton gamma - ray observatory contains 66 high - confidence identifications of blazars and 27 lower - confidence potential blazar identifications ( hartman et al .
the @xmath1-ray blazars are relativistically beamed and have strong jet components .
the inverse compton scattering is the most promising process responsible for the @xmath1-ray emission ( marscher & gear 1985 ; bloom & marscher 1996 ; ghisellini & madau 1996 ; bttcher & dermer 1998 ) .
all @xmath1-ray agns identified by egret are radio - loud with flat spectrum , but not all flat - spectrum agns are detectable @xmath1-ray sources .
one possibility is that the beaming cone for @xmath1-ray emission is narrower than that for radio emission . in this case
, the @xmath1-ray emission could be beamed away from the line of sight , but the radio emission is still doppler boosted due to a wider beaming cone ( von montigny et al .
1995 ) .
the apparent position angle difference @xmath0pa between parsec and kilo - parsec jets can be related to the bending properties of the jets .
many authors have investigated the misalignment angle distributions for the different samples of radio sources ( pearson & readhead 1988 ; conway & murphy 1993 ; appl et al .
1996 ; tingay et al .
if the angle between the relativistic jet and the line of the sight is small , the projection effect of beaming can amplify the intrinsic bend of the jet ( conway & murphy 1993 ) .
several effects such as motion of the host galaxy , collision of the jet with clouds , or precession of the central engine , can thereby cause the bend .
recently , the concept of jet - disc symbiosis was introduced and the inhomogeneous jet model plus mass and energy conservation in the jet - disc system was applied to study the relation between disc and jet luminosities ( falcke & biermann 1995 ; falcke et al . 1995 ; falcke & biermann 1999 ) .
an effective approach to study the link between these two phenomena is to explore the relationship between luminosity in line emission and kinetic power of jets in different scales ( rawlings & saunders 1991 ; celotti , padovani & ghisellini 1997 ) .
rawlings & saunders ( 1991 ) derived the total jet kinetic power @xmath2 and found a correlation between @xmath2 and the narrow line luminosity @xmath3 . similar correlations between line and radio emission have also been found by some authors ( cao & jiang 1999 ; xu et al .
1999 ; willott et al .
the optical line region is photoionized by a nuclear source ( probably radiation from the disk ) , so the optical line emission is a better accretion power indicator than the optical continuum radiation may be enhanced by relativistically beamed synchrotron radiation for some flat - spectrum quasars ( celotti et al .
the extended radio emission which is not affected by beaming may reflect the jet power @xmath2 .
thus , the ratio of extended radio to broad - line flux reflects the ratio of jet power to accretion power . in this work
, we present correlations between the misalignment @xmath0pa and the ratio of radio to broad - line emission for a sample of @xmath1-ray blazars . in sect .
2 , we describe the sample of sources .
the results are contained in sect .
the last section includes the discussion .
[ cols="^,^,^,^ , < , < , > , > , > , < " , ] notes for the table 2 .
@xmath4 : lower - confidence blazar identification . + column ( 1 ) : iau source name .
column ( 2)-(4 ) : vlbi observation frequences ( in ghz ) and core flux density(in jansky ) . column
( 6 ) : references for core flux density .
column ( 7 ) and ( 8) : position angles ( degree ) for kilo - parsec and parsec jet components .
column ( 9 ) : references for position angles .
column ( 10 ) and ( 11 ) : difference of position angle ( degree ) between kilo - parsec and parsec jet components and the reference in which the @xmath0pa is given .
+ references : a96 : appl et al .
( 1996 ) , au85 : antonucci & ulvestad ( 1985 ) , b82 : browne et al .
( 1982 ) , b87 : browne ( 1987 ) , cm93 : conway & murphy ( 1993 ) , f96 : fey et al .
( 1996 ) , fc97 : fey & charlot ( 1997 ) , g92 : gabuzda et al ( 1992 ) , h92 : hummel et al .
( 1992 ) , ho92a : hooimeyer et al .
( 1992a ) , ho92b : hooimeyer et al .
( 1992b ) , h98 : hong et al .
( 1998 ) , k86 : keel ( 1986 ) , k92 : kollgaard et al .
( 1992 ) , k98 : kellermann et al . (
1998 ) , l90 : linfield et al .
( 1990 ) , m86 : morabito et al .
( 1986 ) , m87 : madau et al .
( 1987 ) , m90 : mutel ( 1990 ) , m93 : murphy et al .
( 1993 ) , mo96 : moellenbrock et al .
( 1996 ) , p82 : perley ( 1982 ) , p84 : pauliny - toth et al .
( 1984 ) , p85 : preston et al . ( 1985 ) , p95 : polatidis et al . ( 1995 ) , pr88 : pearson & readhead ( 1988 ) , r84 : romney et al .
( 1984 ) , r87 : roberts et al .
( 1987 ) , r88 : rusk ( 1988 ) , s97 : shen et al .
( 1997 ) , s98 : shen et al .
( 1998 ) , t96 : tingay et al .
( 1996 ) , t98 : tingay et al .
( 1998 ) , u87 : unwin ( 1987 ) , w90 : wardle et al .
( 1990 ) , w92 : wehrle et al .
( 1992 ) , x95 : xu et al .
zb90 : zhang & baath ( 1990 ) .
complete information on the line spectra is available for very few sources in our sample , since different lines are observed for the sources at different redshifts . we have to estimate the total broad - line flux from the available observational data .
there is not a solidly established procedure to derive the total broad - line flux and we therefore adopt the method proposed by celotti et al .
the following lines : ly@xmath5 , civ , mgii , h@xmath1 , h@xmath6 and h@xmath5 , which contribute the major parts in the total broad - line emissions , are used in our estimate .
we use the line ratios reported by francis et al .
( 1991 ) and add the contribution from line h@xmath5 to derive the total broad - line flux ( see celotti et al .
1997 for details ) .
we then search the literature to collect data on broad - line fluxes .
we only consider values of line fluxes ( or luminosities ) given directly or the equivalent width and the continuum flux density at the corresponding line frequency which are reported together in the literature . when more than one value of the same line flux was found in the literature , we take the most recent reference .
we start with the @xmath1-ray blazars identified by hartman et al.(1999 ) including lower - confidence blazars .
there are 79 agns with available redshifts in the third egret catalog . among these sources ,
we search the literature extensively and find 44 sources with sufficient line data to estimate the total broad - line flux .
the remainder of the sources that lack broad - line flux data include 9 bl lac objects and 26 quasars .
the broad - line fluxes have not been measured due to weak line emission for the bl lac objects .
the situation for the quasars is quite different from the bl lac objects .
we note that the spectroscopic observations for most of these 26 quasars have been performed .
however , the line data of these quasars are usually incomplete , i.e. , only the equivalent width , line profile or line - to - continuum ratio is given , but the continuum flux density at the given frequency is not available probably due to the specific purpose of the literature or the problem of calibration .
only a bit more than half of the @xmath1-ray sources with known redshifts have sufficient data , such that the total broad - line flux can be estimated .
this is similar to the situation in cao & jiang ( 1999 ) . in their work ,
198 sources within the starting sample of 378 sources have suitable data to derive the total broad - line flux .
no evidence shows that the lack of broad - line flux for these sources would affect the main results of present analyses , though it leads to a highly incomplete sample for present study .
the further spectroscopic observations on these sources would be helpful .
we collect the data of all sources with both the broad - line flux and the misalignment angle @xmath0pa between parsec and kilo - parsec jets , which leads to a sample of 34 blazars ( we add the tev @xmath1-ray objects : mkn501 to the sample , which is not listed in the egret catalog ) .
there are 26 quasars and 8 bl lac objects in this sample , in which 7 sources are lower - confidence potential blazar identifications and two tev @xmath1-ray objects : mkn421 and mkn501 .
the broad - line data are listed in table 1 .
we compile the data of the extended radio flux density at 5 ghz in the rest frame of the source in column ( 9 ) of table 1 .
the data given at the wavelength other than 5 ghz are k - corrected to 5 ghz in the rest frame of the source assuming @xmath7 ( @xmath8 ) .
we also give the core flux density data at two different frequencies for each source in the sample , and a two - point spectral index is then derived for the core of the source .
the core flux density at 5 ghz in the rest frame of the source is available by k - correction .
the misalignment between kilo - parsec and parsec jets @xmath0pa are taken from the literature .
for a few sources , different values of @xmath0pa are given by different authors usually due to the complex jet structures .
we take the minimum @xmath0pa for these sources .
all data of the core flux density and the misalignment angle @xmath0pa are given in table 2 .
the misalignment angle @xmath0pa is given by the comparison between the vla and vlbi maps .
we note that only one position angle ( vla or vlbi ) is available for some sources .
only the vla position angle is available for the sources 0414@xmath9189 and 0954 + 556 .
there are five sources : 0454@xmath9234 , 1504@xmath9166 , 1741@xmath9038 , 2200 + 420 and 2320@xmath9035 ,
of which only the vlbi position angle is available .
one reason is that these sources are too compact .
high dynamic range vla maps of many sources sufficient to reveal weak kilo - parsec structure are not available .
therefore , further radio observations on these sources might reveal their misalignment information .
further spectroscopic observations are also necessary to complete the sample .
the distribution of @xmath0pa of the sample is plotted in fig . 1 and appears bimodal , which is similar to that given by pearson & readhead ( 1988 ) .
such distribution can be explained by projection of the helical jet ( conway & murphy 1993 ) . in fig .
2 we plot the relation between the apparent misalignment @xmath0pa and the ratio of the total radio flux at 5 ghz to the broad - line flux .
the radio flux density is k - corrected to the rest frame of the source .
a correlation is found at 99.9 per cent significant level for the whole sample using spearman s correlation coefficient @xmath10 .
a slightly less significant correlation is present for quasars in the sample .
we also find a significant correlation between @xmath0pa and the ratio of the vlbi core flux to the broad - line flux at the level 99.99 per cent , where the vlbi core flux density is also k - corrected to the rest frame of the source at 5 ghz ( see fig .
3 ) . in fig .
4 we plot the relation between the apparent misalignment @xmath0pa and the ratio of the extended radio flux at 5 ghz in the rest frame of the source to the broad - line flux .
a weak correlation at 90 per cent significance shows that a trend for sources with higher ratios have larger misalignment @xmath0pa . in present sample ,
there are two tev @xmath1-ray sources : mkn421 ( 1101 + 384 ) and mkn501 ( 1652 + 398 ) . we know that the three tev @xmath1-ray objects are quite different from other @xmath1-ray sources ( coppi & aharonian 1999a , b ) .
only mkn421 is listed in the third egret catalog ( hartman et al .
however , we can not find obvious different behaviours for these two tev @xmath1-ray objects from the remains in the sample ( see figs .
2 @xmath9 4 , labeled by large squares ) .
the redshifts of the sources in our sample ranges from 0.031 to 2.286 , which means that the spatial resolution of vla and vlbi are very different .
however , the angular resolution is about same for these sources , which would probably affect the correlation analyses ( appl et al .
we therefore group the sources into low ( [email protected] ) and high ( [email protected] ) redshift objects . for the latter , the angular to linear
scale mapping is approximately constant .
we re - analyze the correlations and find a correlation between @xmath0pa and the ratio of the radio core flux to the broad - line flux at 99.94 per cent significant level for the 24 objects with [email protected] .
recently , serjeant et al . ( 1998 ) found a correlation between radio and optical continuum emission for a sample of steep - spectrum radio quasars that is evidence for a link between accretion process and jet power their sample is limited to the steep - spectrum quasars to reduce the doppler beaming effect in the optical waveband .
a similar correlation is given by carballo et al ( 1999 ) for the b3-vla sample .
cao & jiang ( 1999 ) present a correlation between radio and broad - line emission for a sample of radio quasars including both flat - spectrum and steep - spectrum quasars .
they adopted the broad - line emission instead of the optical continuum in their investigation to avoid the beaming effect on optical emission .
the jet power @xmath2 is proportional to the bulk lorentz factor of the jet , and also depends on the size of the jet and the particle density in the jet ( celotti & fabian 1993 ) .
the apparent misalignment may be affected by the angle between the direction of vlbi jet and the sight line if the angle is small ( conway & murphy 1993 ) .
the total radio flux density and vlbi core flux density are both strongly increased by beaming in core - dominated radio blazars .
the sources with higher ratio may therefore have higher doppler factors .
so , the correlations between @xmath0pa and @xmath13 or @xmath14 can be explained by the beaming effects .
impey et al .
( 1991 ) found that the sources with higher fractional optical polarization tend to have relatively larger misalignment @xmath0pa between vlbi and parsec structures , which is consistent with both large apparent misalignments and optical fractional polarization being correlated with large beaming and small angles to the line of sight .
the extended radio emission may also be correlated to the jet power @xmath2 ( see fig .
4 ) . if this is true , the ratio of the extended radio flux to the broad - line flux may reflect the ratio of the jet power to the disk luminosity : @xmath15 .
the weak correlation between @xmath0pa and the ratio of extended radio to broad - line flux might imply that the intrinsic bend of the jet is related with the ratio of jet mechanical power to accretion power .
jets in quasars may be powered by rotating black holes in the nuclei ( blandford & znajek 1977 ; moderski et al .
the jet power @xmath2 is then related to the rotational energy of the black hole according to the bz mechanism .
hence , the ratio of radio to broad - line flux might be related to the angular momentum of the black hole to some extent . also , we know that the variation of the rotation axis of the black hole caused by the lense - thirring effect can result in a change of the orientation of the nuclei jet ( bardeen & petterson 1975 ; scheuer & feiler 1996 ) , which may lead to the different ejected orientations between small and large scale jets .
the faster rotating black hole may cause the jet ejected orientation changing more rapidly , which leads to a larger intrinsic bend of the jet .
more recently , ghosh & abramowicz ( 1997 ) , livio et al .
( 1999 ) have shown that the electromagnetic output from the inner disc is generally expected to dominate over that from the hole .
if this is the case for the @xmath1-ray agns , the jet power @xmath2 from the disc is mainly determined by the poloidal magnetic field @xmath16 at the disc surface . a tentative explanation on the relation in fig .
is that both bending and the jet power could be increased by having large magnetic fields in the accretion disk .
the further study on this problem for a larger sample of core - dominated radio quasars will be in our future work , and we can then check whether the correlations are properties only of egret sources or of all blazars in general .
antonucci r.r.j .
, ulvestad j.s . , 1985 , apj 294 158 ( au85 ) appl s. , sol h. , vicente l. , 1996 , a&a 310 , 419 ( a96 ) baldwin j.a . , wampler e.j .
, gaskell c.m . , 1989 , apj 338 , 630(b89 ) bardeen j.m . , petterson j.a . , 1975 , apj 195 , l65 bergeron j. , kunth d. , 1984 , mnras 207 , 263(bk84 ) blandford r.d . ,
znajek r.l . , 1977 , mnras 179 , 433 bloom s.d . , marscher a.p . , 1996 , apj 461 , 657 bttcher m. , dermer c.d . , 1998 ,
apj 501 , l51 browne i.w.a .
, 1987 , superluminal radio sources , j.a .
zensus & t.j .
pearson , eds .
, cambridge univ . press , p. 129
( b87 ) browne i.w.a . ,
clark r.r .
, moore p.k .
et al . , 1982 ,
nat 299 , 788 ( b82 ) browne i.w.a . ,
murphy d.w . , 1987 ,
mnras 226 , 601 ( bm87 ) browne i.w.a .
, perley r.a . , 1986 ,
mnras 222 , 149 ( bp86 ) cao x. , jiang d.r .
, 1999 , mnras 307 , 802 carballo r. , gonzalez - serrano j.i . , benn c.r . ,
sanchez s.f . , vigotti m. , 1999 , mnras 306 , 137 celotti a. , fabian a.c . , 1993 ,
mnras 264 , 228 celotti a. , padovani p. , ghisellini g. , 1997 , mnras 286 , 416 conway j.e . , murphy d.w .
, 1993 , apj 411 , 89 ( cm93 ) coppi p.s .
, aharonian f.a .
, 1999a , apj 521 , l33 coppi p.s .
, aharonian f.a . , 1999b , astro - ph .
9903160 di serego alighieri s. , danziger i.j . , morganti r. et al . , 1994 , mnras 269 , 998(d94 ) falcke h. , biermann p.l . , 1995 , a&a 293 , 665 falcke h. , biermann p.l . , 1999 , a&a 342 , 49 falcke h. , malkan m.a . , biermann p.l . , 1995 ,
a&a 298 , 375 fey a.l . , charlot p. , 1997
, apjs 111 , 95 ( fc97 ) fey a.l . ,
clegg a.w . ,
fomalont e.b . , 1996 ,
apjs 105 , 299 ( f96 ) francis p.j . , hewett p.c .
, foltz c.b .
et al . , 1991 ,
apj 373 , 465 gabuzda d.c . ,
cawthorne t.v .
, roberts d.h .
et al . , 1992 , apj 388 , 40 ( g92 ) ghisellini g. , madau p. , 1996
, mnras 280 , 67 ghosh p. , abramowicz m.a . , 1997 , mnras 292 , 887 hartman r.c . , bertsch d.l .
, bloom s.d .
et al . , 1999 ,
apjs 123 , 79 hintzen p , ulvestad j. , owen f. , 1983 , aj 88 , 709 ( h83 ) hong x.y . , jiang d.r .
, shen z.q . , 1998 , a&a 330 , l45 ( h98 ) hooimeyer j.r.a . , barthel p.d .
, schilizzi r.t .
et al . , 1992 ,
a&a 261 , 18 ( ho92a ) hooimeyer j.r.a .
, schilizzi r.t . ,
miley g.k .
et al . , 1992 , a&a 261 , 25 ( ho92b ) hummel c.a .
, muxlow t.w.b .
, krichbaum t.p .
et al . , 1992 ,
a&a 266 , 93 ( h92 ) impey c.d . , lawrence c.r . , tapia s. , 1991 , apj 375 , 46 jackson n. , browne j.w.a .
, 1991 , mnras 250 , 414(jb91 ) junkkarinen v. , 1984 , pasp 96 , 539 ( j84 ) keel w.c .
, 1986 , apj 302 , 296 ( k86 ) kellermann k.i . , vermeulen r.c .
, zensus j.a .
et al . , 1998 , aj 115 , 1295 ( k98 ) kollgaard r.i . , wandle j.f.c . , roberts d.h .
et al . , 1992 , aj 104 , 1687 ( k92 ) lawrence c.r . , zucker j.r .
, readhead a.c.s .
et al . , 1996 ,
apjs 107 , 541(l96 ) linfield r.p . , levy g.s . , edwards c.d .
et al . , 1990 ,
apj 358 , 350 ( l90 ) livio m. , ogilvie g.i . , pringle j.e . , 1999 ,
apj 512 , 100 madau p. , ghisellini g. , persic m. , 1987 , mnras 224 , 257 ( m87 ) marscher a.p . ,
gear w.k . , 1985 ,
apj 298 , 114 marziani p. , sulentic j.w .
, dultzin - hacyan d. et al . , 1996 , apjs 104 , 37(ma96 ) moderski r. , sikora m. , lasota j.p . , 1998 ,
mnras 301 , 142 moellenbrock g.a . , fujisawa k. , preston r.a .
et al . , 1996 , aj 111 , 2174 ( mo96 ) morabito d.d . , niell a.e .
, preston r.a .
et al . , 1986 aj 91 , 1038 ( m86 ) morganti r. , ulrich m.h . , tadhunter c.n .
et al . , 1992 ,
mnras 254 , 546 ( m92 ) murphy d.w . ,
browne i.w.a . ,
perley r.a .
, 1993 , mnras 264 , 298 ( m93 ) mutel r.l .
, 1990 , in parsec - scale radio jets , j.a .
zensus , t.j .
pearson , eds .
, cambridge univ . press ,
( m90 ) neugebauer g. , oke j.b . , beckline e.e .
et al . , 1979 , apj 230 , 79(n79 ) osmer p.s . , porter a.c . , green r.f . , 1994 , apj 436 , 678(o94 ) pauliny - toth i.i.k
, porcas r.w .
, zensus j.a .
et al . , in iau symposium 110 : vlbi and compact radio sources , r. fanti , k.i .
kellermann , s. setti , eds .
, dordrecht : reidel , p. 149
( p84 ) pearson t.j . ,
readhead a.c.s . , 1988 , apj 328 , 114 ( pr88 )
perley r.a . , 1982 , aj 87 , 859 ( p82 ) polatidis a.g . , wilkinson p.n . , xu w. et al . , 1995 ,
apjs 98 , 1 ( p95 ) preston r.a . ,
morabito d.d .
, williams j.g .
et al . , 1985 ,
aj 90 , 1599 ( p85 ) rawlings s.g . , saunders r.d.e . , 1991 , nat 349 , 138 richstone d.o .
, schmidt m. , 1980 , apj 235 , 361(rs80 ) roberts d.h .
, gabuzda d.c .
, wardle j.f.c . , 1987 , apj 323 , 536 ( r87 ) rumney j. , padrielli l. , barthel n. et al . , 1984 ,
a&a 135 , 289 ( r84 ) rudy r.j . , 1984 ,
apj 284 , 33 ( r84 ) rusk r.e . , 1988 , ph .
d. thesis , univ .
toronto ( r88 ) scarpa r. , falomo r. , pian e. et al .
, 1995 , a&a 303 , 730 ( s95 ) scheuer p.a.g .
, feiler r. , 1996 , mnras 282 , 291 serjeant s. , rawlings s. , maddox s.j .
et al . , 1998 ,
mnras 294 , 494 shen z.q .
, wan t.s .
, moran j.m .
et al . , 1997 , aj 114 , 1999 ( s97 )
shen z.q . , wan t.s . , moran j.m .
et al . , 1998 , aj 115 , 1357 ( s98 ) stickel m. , fried w. , khr h. , 1989 , a&as 80 , 103 ( s89 ) stickel m. , fried w. , khr h. , 1993a , a&as 98 , 393 ( s93a ) stickel m. , khr h. , 1993 , a&as 101 , 521 ( sk93 ) stickel m. , khr h. , fried w. , 1993b , a&as 97 , 483 ( s93b ) stockton a. , mackenty j.w . , 1987 ,
apj 316 , 584 ( sm87 ) tadhunter c.n .
, morganti r. , alighieri s. et al . , 1993 ,
mnras 263 , 999(t93 ) tingay s.j . ,
edwards p.g .
, costa m.e .
et al . , 1996 , apj 464 , 170 ( t96 )
tingay s.j . ,
murphy d.w .
, edwards p.g . , 1998 ,
apj 500 , 673 ( t98 ) unwin s.c . , 1987 , superluminal radio sources , j.a .
zensus & t.j .
pearson , eds .
, cambridge univ . press , p. 34
( u87 ) von montigny c. , bertsch d.l .
, chiang j. et al . , 1995 , a&a 299 , 680 wampler e.j . , gaskell c.m . , burke w.l . , 1984 , apj 276 , 403(w84 ) wardle j.f.c . , roberts d.h . , brown l.f .
et al . , 1990 , in parsec - scale radio jets , j.a .
zensus , t.j .
pearson , eds .
, cambridge univ .
press , p. 98
( w90 ) wehrle a.e . ,
cohen m.h .
, unwin s.c .
et al . , 1992 , apj 391
, 589 ( w92 ) wills b.j .
, pollock j.t . , aller h.d .
et al . , 1983 , apj 274 , 62 ( w83 ) wills b.j . , thompson k.l .
, han m. et al . , 1995 ,
apj 447 , 139(w95 ) xu c. , livio m. , baum s. , 1999 , aj 118 ,
1169 xu w. , readhead a.c.s . , pearson t.j .
et al . , 1995 ,
apjs 99 , 297 ( x95 ) zhang f.j . ,
baath l.b . , 1990 , a&a 236 , 47 ( zb90 ) | the apparent position angle difference @xmath0pa between parsec and kilo - parsec jets in blazars can be related to the bending properties of the jets .
we present correlations between the misalignment @xmath0pa and the ratio of radio to broad - line emission for a sample of @xmath1-ray blazars .
the present study is limited to egret sources due to uniform data for the radio and optical properties of these sources being easily available .
the broad - line emission is known to be a good indicator of the accretion power for both steep and flat - spectrum quasars .
we find significant correlations between @xmath0pa and the ratio of radio flux ( total and radio core flux respectively ) to broad - line flux , which is consistent with the beaming scenario .
a weak correlation between @xmath0pa and the ratio of extended radio to broad - line flux might imply that the intrinsic bend of the jet is related with the ratio of jet mechanical power to accretion power .
galaxies : active galaxies : jets quasars : emission lines accretion , accretion disks | <s>[INST]the recent released third catalog of high - energy @xmath1-ray sources by the egret telescope on the compton gamma - ray observatory contains 66 high - confidence identifications of blazars and 27 lower - confidence potential blazar identifications ( hartman et al .
the @xmath1-ray blazars are relativistically beamed and have strong jet components .
the inverse compton scattering is the most promising process responsible for the @xmath1-ray emission ( marscher & gear 1985 ; bloom & marscher 1996 ; ghisellini & madau 1996 ; bttcher & dermer 1998 ) .
all @xmath1-ray agns identified by egret are radio - loud with flat spectrum , but not all flat - spectrum agns are detectable @xmath1-ray sources .
one possibility is that the beaming cone for @xmath1-ray emission is narrower than that for radio emission . in this case
, the @xmath1-ray emission could be beamed away from the line of sight , but the radio emission is still doppler boosted due to a wider beaming cone ( von montigny et al .
1995 ) .
the apparent position angle difference @xmath0pa between parsec and kilo - parsec jets can be related to the bending properties of the jets .
many authors have investigated the misalignment angle distributions for the different samples of radio sources ( pearson & readhead 1988 ; conway & murphy 1993 ; appl et al .
1996 ; tingay et al .
if the angle between the relativistic jet and the line of the sight is small , the projection effect of beaming can amplify the intrinsic bend of the jet ( conway & murphy 1993 ) .
several effects such as motion of the host galaxy , collision of the jet with clouds , or precession of the central engine , can thereby cause the bend .
recently , the concept of jet - disc symbiosis was introduced and the inhomogeneous jet model plus mass and energy conservation in the jet - disc system was applied to study the relation between disc and jet luminosities ( falcke & biermann 1995 ; falcke et al . 1995 ; falcke & biermann 1999 ) .
an effective approach to study the link between these two phenomena is to explore the relationship between luminosity in line emission and kinetic power of jets in different scales ( rawlings & saunders 1991 ; celotti , padovani & ghisellini 1997 ) .
rawlings & saunders ( 1991 ) derived the total jet kinetic power @xmath2 and found a correlation between @xmath2 and the narrow line luminosity @xmath3 . similar correlations between line and radio emission have also been found by some authors ( cao & jiang 1999 ; xu et al .
1999 ; willott et al .
the optical line region is photoionized by a nuclear source ( probably radiation from the disk ) , so the optical line emission is a better accretion power indicator than the optical continuum radiation may be enhanced by relativistically beamed synchrotron radiation for some flat - spectrum quasars ( celotti et al .
the extended radio emission which is not affected by beaming may reflect the jet power @xmath2 .
thus , the ratio of extended radio to broad - line flux reflects the ratio of jet power to accretion power . in this work
, we present correlations between the misalignment @xmath0pa and the ratio of radio to broad - line emission for a sample of @xmath1-ray blazars . in sect .
2 , we describe the sample of sources .
the results are contained in sect .
the last section includes the discussion .
[ cols="^,^,^,^ , < , < , > , > , > , < " , ] notes for the table 2 .
@xmath4 : lower - confidence blazar identification . + column ( 1 ) : iau source name .
column ( 2)-(4 ) : vlbi observation frequences ( in ghz ) and core flux density(in jansky ) . column
( 6 ) : references for core flux density .
column ( 7 ) and ( 8) : position angles ( degree ) for kilo - parsec and parsec jet components .
column ( 9 ) : references for position angles .
column ( 10 ) and ( 11 ) : difference of position angle ( degree ) between kilo - parsec and parsec jet components and the reference in which the @xmath0pa is given .
+ references : a96 : appl et al .
( 1996 ) , au85 : antonucci & ulvestad ( 1985 ) , b82 : browne et al .
( 1982 ) , b87 : browne ( 1987 ) , cm93 : conway & murphy ( 1993 ) , f96 : fey et al .
( 1996 ) , fc97 : fey & charlot ( 1997 ) , g92 : gabuzda et al ( 1992 ) , h92 : hummel et al .
( 1992 ) , ho92a : hooimeyer et al .
( 1992a ) , ho92b : hooimeyer et al .
( 1992b ) , h98 : hong et al .
( 1998 ) , k86 : keel ( 1986 ) , k92 : kollgaard et al .
( 1992 ) , k98 : kellermann et al . (
1998 ) , l90 : linfield et al .
( 1990 ) , m86 : morabito et al .
( 1986 ) , m87 : madau et al .
( 1987 ) , m90 : mutel ( 1990 ) , m93 : murphy et al .
( 1993 ) , mo96 : moellenbrock et al .
( 1996 ) , p82 : perley ( 1982 ) , p84 : pauliny - toth et al .
( 1984 ) , p85 : preston et al . ( 1985 ) , p95 : polatidis et al . ( 1995 ) , pr88 : pearson & readhead ( 1988 ) , r84 : romney et al .
( 1984 ) , r87 : roberts et al .
( 1987 ) , r88 : rusk ( 1988 ) , s97 : shen et al .
( 1997 ) , s98 : shen et al .
( 1998 ) , t96 : tingay et al .
( 1996 ) , t98 : tingay et al .
( 1998 ) , u87 : unwin ( 1987 ) , w90 : wardle et al .
( 1990 ) , w92 : wehrle et al .
( 1992 ) , x95 : xu et al .
zb90 : zhang & baath ( 1990 ) .
complete information on the line spectra is available for very few sources in our sample , since different lines are observed for the sources at different redshifts . we have to estimate the total broad - line flux from the available observational data .
there is not a solidly established procedure to derive the total broad - line flux and we therefore adopt the method proposed by celotti et al .
the following lines : ly@xmath5 , civ , mgii , h@xmath1 , h@xmath6 and h@xmath5 , which contribute the major parts in the total broad - line emissions , are used in our estimate .
we use the line ratios reported by francis et al .
( 1991 ) and add the contribution from line h@xmath5 to derive the total broad - line flux ( see celotti et al .
1997 for details ) .
we then search the literature to collect data on broad - line fluxes .
we only consider values of line fluxes ( or luminosities ) given directly or the equivalent width and the continuum flux density at the corresponding line frequency which are reported together in the literature . when more than one value of the same line flux was found in the literature , we take the most recent reference .
we start with the @xmath1-ray blazars identified by hartman et al.(1999 ) including lower - confidence blazars .
there are 79 agns with available redshifts in the third egret catalog . among these sources ,
we search the literature extensively and find 44 sources with sufficient line data to estimate the total broad - line flux .
the remainder of the sources that lack broad - line flux data include 9 bl lac objects and 26 quasars .
the broad - line fluxes have not been measured due to weak line emission for the bl lac objects .
the situation for the quasars is quite different from the bl lac objects .
we note that the spectroscopic observations for most of these 26 quasars have been performed .
however , the line data of these quasars are usually incomplete , i.e. , only the equivalent width , line profile or line - to - continuum ratio is given , but the continuum flux density at the given frequency is not available probably due to the specific purpose of the literature or the problem of calibration .
only a bit more than half of the @xmath1-ray sources with known redshifts have sufficient data , such that the total broad - line flux can be estimated .
this is similar to the situation in cao & jiang ( 1999 ) . in their work ,
198 sources within the starting sample of 378 sources have suitable data to derive the total broad - line flux .
no evidence shows that the lack of broad - line flux for these sources would affect the main results of present analyses , though it leads to a highly incomplete sample for present study .
the further spectroscopic observations on these sources would be helpful .
we collect the data of all sources with both the broad - line flux and the misalignment angle @xmath0pa between parsec and kilo - parsec jets , which leads to a sample of 34 blazars ( we add the tev @xmath1-ray objects : mkn501 to the sample , which is not listed in the egret catalog ) .
there are 26 quasars and 8 bl lac objects in this sample , in which 7 sources are lower - confidence potential blazar identifications and two tev @xmath1-ray objects : mkn421 and mkn501 .
the broad - line data are listed in table 1 .
we compile the data of the extended radio flux density at 5 ghz in the rest frame of the source in column ( 9 ) of table 1 .
the data given at the wavelength other than 5 ghz are k - corrected to 5 ghz in the rest frame of the source assuming @xmath7 ( @xmath8 ) .
we also give the core flux density data at two different frequencies for each source in the sample , and a two - point spectral index is then derived for the core of the source .
the core flux density at 5 ghz in the rest frame of the source is available by k - correction .
the misalignment between kilo - parsec and parsec jets @xmath0pa are taken from the literature .
for a few sources , different values of @xmath0pa are given by different authors usually due to the complex jet structures .
we take the minimum @xmath0pa for these sources .
all data of the core flux density and the misalignment angle @xmath0pa are given in table 2 .
the misalignment angle @xmath0pa is given by the comparison between the vla and vlbi maps .
we note that only one position angle ( vla or vlbi ) is available for some sources .
only the vla position angle is available for the sources 0414@xmath9189 and 0954 + 556 .
there are five sources : 0454@xmath9234 , 1504@xmath9166 , 1741@xmath9038 , 2200 + 420 and 2320@xmath9035 ,
of which only the vlbi position angle is available .
one reason is that these sources are too compact .
high dynamic range vla maps of many sources sufficient to reveal weak kilo - parsec structure are not available .
therefore , further radio observations on these sources might reveal their misalignment information .
further spectroscopic observations are also necessary to complete the sample .
the distribution of @xmath0pa of the sample is plotted in fig . 1 and appears bimodal , which is similar to that given by pearson & readhead ( 1988 ) .
such distribution can be explained by projection of the helical jet ( conway & murphy 1993 ) . in fig .
2 we plot the relation between the apparent misalignment @xmath0pa and the ratio of the total radio flux at 5 ghz to the broad - line flux .
the radio flux density is k - corrected to the rest frame of the source .
a correlation is found at 99.9 per cent significant level for the whole sample using spearman s correlation coefficient @xmath10 .
a slightly less significant correlation is present for quasars in the sample .
we also find a significant correlation between @xmath0pa and the ratio of the vlbi core flux to the broad - line flux at the level 99.99 per cent , where the vlbi core flux density is also k - corrected to the rest frame of the source at 5 ghz ( see fig .
3 ) . in fig .
4 we plot the relation between the apparent misalignment @xmath0pa and the ratio of the extended radio flux at 5 ghz in the rest frame of the source to the broad - line flux .
a weak correlation at 90 per cent significance shows that a trend for sources with higher ratios have larger misalignment @xmath0pa . in present sample ,
there are two tev @xmath1-ray sources : mkn421 ( 1101 + 384 ) and mkn501 ( 1652 + 398 ) . we know that the three tev @xmath1-ray objects are quite different from other @xmath1-ray sources ( coppi & aharonian 1999a , b ) .
only mkn421 is listed in the third egret catalog ( hartman et al .
however , we can not find obvious different behaviours for these two tev @xmath1-ray objects from the remains in the sample ( see figs .
2 @xmath9 4 , labeled by large squares ) .
the redshifts of the sources in our sample ranges from 0.031 to 2.286 , which means that the spatial resolution of vla and vlbi are very different .
however , the angular resolution is about same for these sources , which would probably affect the correlation analyses ( appl et al .
we therefore group the sources into low ( [email protected] ) and high ( [email protected] ) redshift objects . for the latter , the angular to linear
scale mapping is approximately constant .
we re - analyze the correlations and find a correlation between @xmath0pa and the ratio of the radio core flux to the broad - line flux at 99.94 per cent significant level for the 24 objects with [email protected] .
recently , serjeant et al . ( 1998 ) found a correlation between radio and optical continuum emission for a sample of steep - spectrum radio quasars that is evidence for a link between accretion process and jet power their sample is limited to the steep - spectrum quasars to reduce the doppler beaming effect in the optical waveband .
a similar correlation is given by carballo et al ( 1999 ) for the b3-vla sample .
cao & jiang ( 1999 ) present a correlation between radio and broad - line emission for a sample of radio quasars including both flat - spectrum and steep - spectrum quasars .
they adopted the broad - line emission instead of the optical continuum in their investigation to avoid the beaming effect on optical emission .
the jet power @xmath2 is proportional to the bulk lorentz factor of the jet , and also depends on the size of the jet and the particle density in the jet ( celotti & fabian 1993 ) .
the apparent misalignment may be affected by the angle between the direction of vlbi jet and the sight line if the angle is small ( conway & murphy 1993 ) .
the total radio flux density and vlbi core flux density are both strongly increased by beaming in core - dominated radio blazars .
the sources with higher ratio may therefore have higher doppler factors .
so , the correlations between @xmath0pa and @xmath13 or @xmath14 can be explained by the beaming effects .
impey et al .
( 1991 ) found that the sources with higher fractional optical polarization tend to have relatively larger misalignment @xmath0pa between vlbi and parsec structures , which is consistent with both large apparent misalignments and optical fractional polarization being correlated with large beaming and small angles to the line of sight .
the extended radio emission may also be correlated to the jet power @xmath2 ( see fig .
4 ) . if this is true , the ratio of the extended radio flux to the broad - line flux may reflect the ratio of the jet power to the disk luminosity : @xmath15 .
the weak correlation between @xmath0pa and the ratio of extended radio to broad - line flux might imply that the intrinsic bend of the jet is related with the ratio of jet mechanical power to accretion power .
jets in quasars may be powered by rotating black holes in the nuclei ( blandford & znajek 1977 ; moderski et al .
the jet power @xmath2 is then related to the rotational energy of the black hole according to the bz mechanism .
hence , the ratio of radio to broad - line flux might be related to the angular momentum of the black hole to some extent . also , we know that the variation of the rotation axis of the black hole caused by the lense - thirring effect can result in a change of the orientation of the nuclei jet ( bardeen & petterson 1975 ; scheuer & feiler 1996 ) , which may lead to the different ejected orientations between small and large scale jets .
the faster rotating black hole may cause the jet ejected orientation changing more rapidly , which leads to a larger intrinsic bend of the jet .
more recently , ghosh & abramowicz ( 1997 ) , livio et al .
( 1999 ) have shown that the electromagnetic output from the inner disc is generally expected to dominate over that from the hole .
if this is the case for the @xmath1-ray agns , the jet power @xmath2 from the disc is mainly determined by the poloidal magnetic field @xmath16 at the disc surface . a tentative explanation on the relation in fig .
is that both bending and the jet power could be increased by having large magnetic fields in the accretion disk .
the further study on this problem for a larger sample of core - dominated radio quasars will be in our future work , and we can then check whether the correlations are properties only of egret sources or of all blazars in general .
antonucci r.r.j .
, ulvestad j.s . , 1985 , apj 294 158 ( au85 ) appl s. , sol h. , vicente l. , 1996 , a&a 310 , 419 ( a96 ) baldwin j.a . , wampler e.j .
, gaskell c.m . , 1989 , apj 338 , 630(b89 ) bardeen j.m . , petterson j.a . , 1975 , apj 195 , l65 bergeron j. , kunth d. , 1984 , mnras 207 , 263(bk84 ) blandford r.d . ,
znajek r.l . , 1977 , mnras 179 , 433 bloom s.d . , marscher a.p . , 1996 , apj 461 , 657 bttcher m. , dermer c.d . , 1998 ,
apj 501 , l51 browne i.w.a .
, 1987 , superluminal radio sources , j.a .
zensus & t.j .
pearson , eds .
, cambridge univ . press , p. 129
( b87 ) browne i.w.a . ,
clark r.r .
, moore p.k .
et al . , 1982 ,
nat 299 , 788 ( b82 ) browne i.w.a . ,
murphy d.w . , 1987 ,
mnras 226 , 601 ( bm87 ) browne i.w.a .
, perley r.a . , 1986 ,
mnras 222 , 149 ( bp86 ) cao x. , jiang d.r .
, 1999 , mnras 307 , 802 carballo r. , gonzalez - serrano j.i . , benn c.r . ,
sanchez s.f . , vigotti m. , 1999 , mnras 306 , 137 celotti a. , fabian a.c . , 1993 ,
mnras 264 , 228 celotti a. , padovani p. , ghisellini g. , 1997 , mnras 286 , 416 conway j.e . , murphy d.w .
, 1993 , apj 411 , 89 ( cm93 ) coppi p.s .
, aharonian f.a .
, 1999a , apj 521 , l33 coppi p.s .
, aharonian f.a . , 1999b , astro - ph .
9903160 di serego alighieri s. , danziger i.j . , morganti r. et al . , 1994 , mnras 269 , 998(d94 ) falcke h. , biermann p.l . , 1995 , a&a 293 , 665 falcke h. , biermann p.l . , 1999 , a&a 342 , 49 falcke h. , malkan m.a . , biermann p.l . , 1995 ,
a&a 298 , 375 fey a.l . , charlot p. , 1997
, apjs 111 , 95 ( fc97 ) fey a.l . ,
clegg a.w . ,
fomalont e.b . , 1996 ,
apjs 105 , 299 ( f96 ) francis p.j . , hewett p.c .
, foltz c.b .
et al . , 1991 ,
apj 373 , 465 gabuzda d.c . ,
cawthorne t.v .
, roberts d.h .
et al . , 1992 , apj 388 , 40 ( g92 ) ghisellini g. , madau p. , 1996
, mnras 280 , 67 ghosh p. , abramowicz m.a . , 1997 , mnras 292 , 887 hartman r.c . , bertsch d.l .
, bloom s.d .
et al . , 1999 ,
apjs 123 , 79 hintzen p , ulvestad j. , owen f. , 1983 , aj 88 , 709 ( h83 ) hong x.y . , jiang d.r .
, shen z.q . , 1998 , a&a 330 , l45 ( h98 ) hooimeyer j.r.a . , barthel p.d .
, schilizzi r.t .
et al . , 1992 ,
a&a 261 , 18 ( ho92a ) hooimeyer j.r.a .
, schilizzi r.t . ,
miley g.k .
et al . , 1992 , a&a 261 , 25 ( ho92b ) hummel c.a .
, muxlow t.w.b .
, krichbaum t.p .
et al . , 1992 ,
a&a 266 , 93 ( h92 ) impey c.d . , lawrence c.r . , tapia s. , 1991 , apj 375 , 46 jackson n. , browne j.w.a .
, 1991 , mnras 250 , 414(jb91 ) junkkarinen v. , 1984 , pasp 96 , 539 ( j84 ) keel w.c .
, 1986 , apj 302 , 296 ( k86 ) kellermann k.i . , vermeulen r.c .
, zensus j.a .
et al . , 1998 , aj 115 , 1295 ( k98 ) kollgaard r.i . , wandle j.f.c . , roberts d.h .
et al . , 1992 , aj 104 , 1687 ( k92 ) lawrence c.r . , zucker j.r .
, readhead a.c.s .
et al . , 1996 ,
apjs 107 , 541(l96 ) linfield r.p . , levy g.s . , edwards c.d .
et al . , 1990 ,
apj 358 , 350 ( l90 ) livio m. , ogilvie g.i . , pringle j.e . , 1999 ,
apj 512 , 100 madau p. , ghisellini g. , persic m. , 1987 , mnras 224 , 257 ( m87 ) marscher a.p . ,
gear w.k . , 1985 ,
apj 298 , 114 marziani p. , sulentic j.w .
, dultzin - hacyan d. et al . , 1996 , apjs 104 , 37(ma96 ) moderski r. , sikora m. , lasota j.p . , 1998 ,
mnras 301 , 142 moellenbrock g.a . , fujisawa k. , preston r.a .
et al . , 1996 , aj 111 , 2174 ( mo96 ) morabito d.d . , niell a.e .
, preston r.a .
et al . , 1986 aj 91 , 1038 ( m86 ) morganti r. , ulrich m.h . , tadhunter c.n .
et al . , 1992 ,
mnras 254 , 546 ( m92 ) murphy d.w . ,
browne i.w.a . ,
perley r.a .
, 1993 , mnras 264 , 298 ( m93 ) mutel r.l .
, 1990 , in parsec - scale radio jets , j.a .
zensus , t.j .
pearson , eds .
, cambridge univ . press ,
( m90 ) neugebauer g. , oke j.b . , beckline e.e .
et al . , 1979 , apj 230 , 79(n79 ) osmer p.s . , porter a.c . , green r.f . , 1994 , apj 436 , 678(o94 ) pauliny - toth i.i.k
, porcas r.w .
, zensus j.a .
et al . , in iau symposium 110 : vlbi and compact radio sources , r. fanti , k.i .
kellermann , s. setti , eds .
, dordrecht : reidel , p. 149
( p84 ) pearson t.j . ,
readhead a.c.s . , 1988 , apj 328 , 114 ( pr88 )
perley r.a . , 1982 , aj 87 , 859 ( p82 ) polatidis a.g . , wilkinson p.n . , xu w. et al . , 1995 ,
apjs 98 , 1 ( p95 ) preston r.a . ,
morabito d.d .
, williams j.g .
et al . , 1985 ,
aj 90 , 1599 ( p85 ) rawlings s.g . , saunders r.d.e . , 1991 , nat 349 , 138 richstone d.o .
, schmidt m. , 1980 , apj 235 , 361(rs80 ) roberts d.h .
, gabuzda d.c .
, wardle j.f.c . , 1987 , apj 323 , 536 ( r87 ) rumney j. , padrielli l. , barthel n. et al . , 1984 ,
a&a 135 , 289 ( r84 ) rudy r.j . , 1984 ,
apj 284 , 33 ( r84 ) rusk r.e . , 1988 , ph .
d. thesis , univ .
toronto ( r88 ) scarpa r. , falomo r. , pian e. et al .
, 1995 , a&a 303 , 730 ( s95 ) scheuer p.a.g .
, feiler r. , 1996 , mnras 282 , 291 serjeant s. , rawlings s. , maddox s.j .
et al . , 1998 ,
mnras 294 , 494 shen z.q .
, wan t.s .
, moran j.m .
et al . , 1997 , aj 114 , 1999 ( s97 )
shen z.q . , wan t.s . , moran j.m .
et al . , 1998 , aj 115 , 1357 ( s98 ) stickel m. , fried w. , khr h. , 1989 , a&as 80 , 103 ( s89 ) stickel m. , fried w. , khr h. , 1993a , a&as 98 , 393 ( s93a ) stickel m. , khr h. , 1993 , a&as 101 , 521 ( sk93 ) stickel m. , khr h. , fried w. , 1993b , a&as 97 , 483 ( s93b ) stockton a. , mackenty j.w . , 1987 ,
apj 316 , 584 ( sm87 ) tadhunter c.n .
, morganti r. , alighieri s. et al . , 1993 ,
mnras 263 , 999(t93 ) tingay s.j . ,
edwards p.g .
, costa m.e .
et al . , 1996 , apj 464 , 170 ( t96 )
tingay s.j . ,
murphy d.w .
, edwards p.g . , 1998 ,
apj 500 , 673 ( t98 ) unwin s.c . , 1987 , superluminal radio sources , j.a .
zensus & t.j .
pearson , eds .
, cambridge univ . press , p. 34
( u87 ) von montigny c. , bertsch d.l .
, chiang j. et al . , 1995 , a&a 299 , 680 wampler e.j . , gaskell c.m . , burke w.l . , 1984 , apj 276 , 403(w84 ) wardle j.f.c . , roberts d.h . , brown l.f .
et al . , 1990 , in parsec - scale radio jets , j.a .
zensus , t.j .
pearson , eds .
, cambridge univ .
press , p. 98
( w90 ) wehrle a.e . ,
cohen m.h .
, unwin s.c .
et al . , 1992 , apj 391
, 589 ( w92 ) wills b.j .
, pollock j.t . , aller h.d .
et al . , 1983 , apj 274 , 62 ( w83 ) wills b.j . , thompson k.l .
, han m. et al . , 1995 ,
apj 447 , 139(w95 ) xu c. , livio m. , baum s. , 1999 , aj 118 ,
1169 xu w. , readhead a.c.s . , pearson t.j .
et al . , 1995 ,
apjs 99 , 297 ( x95 ) zhang f.j . ,
baath l.b . , 1990 , a&a 236 , 47 ( zb90 )[/INST] the apparent position angle difference @xmath0pa between parsec and kilo - parsec jets in blazars can be related to the bending properties of the jets .
we present correlations between the misalignment @xmath0pa and the ratio of radio to broad - line emission for a sample of @xmath1-ray blazars .
the present study is limited to egret sources due to uniform data for the radio and optical properties of these sources being easily available .
the broad - line emission is known to be a good indicator of the accretion power for both steep and flat - spectrum quasars .
we find significant correlations between @xmath0pa and the ratio of radio flux ( total and radio core flux respectively ) to broad - line flux , which is consistent with the beaming scenario .
a weak correlation between @xmath0pa and the ratio of extended radio to broad - line flux might imply that the intrinsic bend of the jet is related with the ratio of jet mechanical power to accretion power .
galaxies : active galaxies : jets quasars : emission lines accretion , accretion disks </s> |
the description of perturbative quantum field theory in terms of hopf algebras @xcite ( cf .
@xcite ) has led to a better understanding of the combinatorial structure of renormalization . at the same time
, it provided a beautiful interaction of quantum field theory with several parts of mathematics .
although the hopf algebra was modelled on a scalar quantum field theory , it can be generalized to any quantum field theory .
however , subtleties appear in the case of quantum gauge theories .
gauge theories are field theories that are invariant under a certain group , known as the gauge group . in the process of renormalization
, one has to deal with the ` overcounting ' due to the gauge degrees of freedom .
furthermore , one has to understand how the gauge symmetries manifest themselves in the quantum field theory .
important here are the so - called ward - takahashi ( or slavnov - taylor ) identities . the first example of a gauge theory is quantum electrodynamics ( qed ) , which has the abelian group @xmath1 as a gauge group .
the hopf algebraic structure of feynman graphs in qed was desrcibed in @xcite and more recently in @xcite .
a slightly different approach is taken in @xcite , where hopf algebras on planar binary trees were considered .
the anatomy of a gauge theory with gauge group @xmath2 ( known as quantum chromodynamics ) has been discussed in the hopf algebra setting in @xcite , with a central role played by the dyson - schwinger equations ( see also @xcite ) . however , a full understanding of renormalization of general gauge theories is still incomplete .
this paper is a modest attempt towards understanding this by working out explicitly the hopf algebraic structure underlying renormalization of quantum electrodynamics , thereby implementing the ward - takahashi identities in a compatible way .
we start in section [ sect : hopf ] by defining the commutative hopf algebra @xmath3 of feynman graphs for quantum electrodynamics . the approach we take differs from the one in @xcite where a noncommutative hopf algebra was considered .
this was motivated by the fact that in qed , feynman amplitudes are ( noncommuting ) matrices .
instead , we work with a commutative hopf algebra and encode the matricial form of the feynman amplitudes into the distributions giving the external structure of the graph .
our approach has the advantage of still being able to use the duality between commutative hopf algebras and affine group schemes in the formulation of the bphz - procedure . in section [
sect : birkhoff ] , we associate a feynman amplitude to a feynman graph , as dictated by the feynman rules .
the bphz - formula of renormalization is obtained as a special case of the birkhoff decomposition for affine group schemes @xcite .
then in section [ sect : wt ] , we incorporate the ward - takahashi ( wt ) identities as relations between graphs , much as was done by t hooft and veltman in @xcite .
we show that these relations are compatible with the coproduct in the hopf algebra @xmath3 , so that they define a hopf ideal .
this reflects the physical fact that wt - identities are compatible with renormalization ( in the dimensional regularization and minimal subtraction scheme ) .
the feynman amplitudes can now be defined on the quotient hopf algebra of @xmath3 by this ideal , and we conclude that the counterterms as well as the renormalized feynman amplitudes satisfy the wt - identities in the physical sense ( i.e. , between feynman amplitudes ) . in particular , we arrive at the well - known identity @xmath0 as derived by ward in @xcite .
quantum electrodynamics in 4 dimensions is given by the following classical lagrangian , @xmath4 where @xmath5 is the _ field strength _ of the _ gauge potential _ @xmath6 , @xmath7 is the spinor describing the electron with mass @xmath8 and electric charge @xmath9 and @xmath10 are the @xmath11 dirac matrices .
finally , the real parameter @xmath12 is the _ gauge - fixing parameter_. the lagrangian @xmath13 describes the dynamics and the interaction as well as the gauge fixing : we can write @xmath14 , where the free , interaction and gauge fixing parts are @xmath15 the adjective `` quantum '' for electrodynamics is justified when this lagrangian is used in computing probability amplitudes . in perturbation theory , one expands such amplitudes in terms of feynman diagrams which are the graphs constructed from the following vertices , as dictated by the form of the lagrangian : ( 60,60 ) ( 60,60 ) ( 60,60 ) [ rem : el - mass ] in fact , we will also need the 2-point vertex ( 40,10 ) , associated to the electron mass term , similar to @xcite .
we will focus on the so - called _ one - particle irreducible _ ( 1pi ) _ graphs _ , which are graphs that are not trees , and that can not be disconnected by cutting a single internal edge . in qed , there are three types of 1pi graphs that are of interest in renormalization theory : the vacuum polarization , the electron self - energy and the full vertex graphs : ( 60,60 ) + ( 60,60 ) + ( 60,60 ) here the blob stands for any 1pi graph of the type dictated by the external lines .
we now describe the _ external structure _ of a feynman graph @xmath16 , assigning ( among other data ) momenta to the external legs . in physics ,
the feynman amplitude of @xmath16 ( dictated by the feynman rules , see below ) is evaluated with respect to this external structure ( see below ) .
mathematically , the external structure is a distribution on the space of feynman amplitudes , understood as test functions on a suitable space .
more explicitly , in the case of qed the ( euclidean ) feynman amplitudes @xmath17 are functions in @xmath18 where @xmath19 with @xmath20 the set of indices labelling the external photon lines of @xmath16 with spatial index @xmath21 respectively , and @xmath22 is the set of its external electron lines .
the factor @xmath23 can be understood from the fact that in qed , feynman amplitudes are matrix - valued functions on @xmath24 . for qed , the external structure
is thus given by an element in the space of distributions on @xmath18 ; we denote this space by @xmath25 .
for example , for the above full vertex graph @xmath16 , @xmath26 and a typical distribution is given by @xmath27 in terms of a dirac mass and the ( standard ) dual basis @xmath28 of @xmath29 .
evaluation on the feynman amplitude @xmath30 is then given by the pairing @xmath31 note that @xmath32 is translated in the diagram by a reversal of the corresponding arrow with associated momentum @xmath33 .
we will be interested in the following special external structures for the different graphs introduced above .
a full vertex graph @xmath34 at zero momentum transfer ( meaning @xmath35 ) can be written in terms of the two form factors @xmath36 ( cf .
* section 6.2 ) ) @xmath37 where @xmath38 .
only the first form factor @xmath39 requires renormalization ; therefore , we define the following external structure : @xmath40 where the normalization comes from @xmath41 . for the ward - takahashi identities , we will also need the following external structure , @xmath42 which puts finite momentum @xmath43 on the ingoing and outgoing electron lines , but zero momentum on the external photon line ( zero - momentum transfer ) .
this external structure allows us to treat ward - takahashi identities in massless qed as well .
the form factors @xmath39 and @xmath44 can also be recovered separately by using the following two distributions @xcite , @xmath45 for an electron self - energy graph @xmath46 , we have @xmath47 and the corresponding feynman amplitude is written in terms of two form factors : @xmath48 correspondingly , there are two distributions , which we choose of the form , @xmath49 for all @xmath50 . also , there is an external structure which puts finite momentum on the ingoing and outgoing electron lines , @xmath51 finally , for a vacuum polarization graph @xmath16 , @xmath52 , we let @xmath53 be the external structure that satisfies @xmath54 for all @xmath55 .
the labelling of the external structures by @xmath56 and @xmath57 differs from the one in @xcite , where they were labelled by @xmath58 and @xmath59 . here
we follow @xcite , so that the labels correspond to the renormalization constants @xmath60 , as they appear in the lagrangian , @xmath61 the precise correspondence will be given in equation below .
let @xmath3 be the free commutative algebra generated by pairs @xmath62 with @xmath16 a 1pi graph and @xmath63 a distribution encoding its external structure .
the product in @xmath3 can be understood as the union of graphs , with induced external structure .
more precisely , for two 1pi graphs @xmath64 and @xmath65 , the product @xmath66 is the graph @xmath67 with external structure given by @xmath68 .
the algebra @xmath3 is a ( positively ) graded algebra @xmath69 , with the grading given by the loop number of the graph . in the following
, we will also write @xmath64 for the pair @xmath70 , and sometimes even @xmath16 . we will shorten the notation for graphs equipped with the special external structures defined above by writing @xmath71 .
we define a coproduct @xmath72 as follows ; if @xmath16 is a 1pi graph , then one sets @xmath73 here @xmath74 is a proper subset of the graph @xmath75 formed by the internal edges of @xmath16 ( i.e. @xmath76 ) .
the connected components @xmath77 of @xmath74 are 1pi graphs with the property that the set of edges of @xmath16 that meet @xmath77 have two or three elements .
the sum runs over all multi - indices @xmath78 , one index for each 1pi connected component of @xmath74 , and one denotes by @xmath79 the 1pi graph that has external structure as defined in equation - , with @xmath80 in the case of a vacuum polarization , @xmath81 for a full vertex graph and @xmath82 or @xmath83 in the case of an electron self - energy . in equation
, @xmath84 denotes the disjoint union of all graphs @xmath79 associated to the connected components of @xmath74 and the graph @xmath85 is the graph @xmath16 ( with the same external structure ) with each @xmath77 reduced to a vertex of type @xmath86 .
more explicitly , if @xmath87 ( 30,11 ) , then for @xmath88 one replaces this graph in @xmath16 by the line ( 20,11 ) @xmath89 ( 20,11 ) , and for @xmath82 by ( 20,11 ) @xmath90 ( 20,11 ) ( cf .
remark [ rem : el - mass ] ) . in the case of the vacuum polarization and the full vertex graph ,
one replaces @xmath77 by the corresponding vertex . by complete analogy with @xcite
, we find that with this coproduct , @xmath3 becomes a connected graded hopf algebra , i.e. @xmath91 , @xmath92 and @xmath93 indeed , @xmath94 consists of complex multiples of the empty graph , which is the unit in @xmath3 , so that @xmath95 .
moreover , from general results on graded hopf algebras , we obtain the antipode inductively , @xmath96 where @xmath97 .
we give a few examples in order to clarify the coproduct .
@xmath98 @xmath99 + \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph * } } _ { { ( 0 ) } } \otimes \parbox{50pt } { \begin{fmfgraph*}(50,20 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v2,v3,v5,v6,r } \fmf{photon , left , tension=0}{v1,v5 } \fmf{photon , right , tension=0}{v2,v6 } \fmfdot{v3 } \end{fmfgraph * } } + \parbox{50pt}{\begin{fmfgraph*}(50,20 ) \fmfforce{(.33w,0h)}{b } \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v3,v5,v6,v7,r } \fmffreeze \fmf{photon}{b , v3 } \fmf{photon , left , tension=0}{v5,v6 } \fmf{photon , left , tension=0}{v1,v7 } \end{fmfgraph * } } _ { { ( 1 ) } } \otimes \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph * } } + \parbox{50pt}{\begin{fmfgraph*}(50,20 ) \fmfforce{(.66w,0h)}{b } \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v2,v3,v6,v7,r } \fmffreeze \fmf{photon}{b , v6 } \fmf{photon , left , tension=0}{v2,v3 } \fmf{photon , left , tension=0}{v1,v7 } \end{fmfgraph * } } _ { { ( 1 ) } } \otimes \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph*}}\end{gathered}\ ] ]
in @xcite , connes and kreimer understood renormalization of perturbative quantum field theory in terms of a birkhoff decomposition .
in particular , using the dimensional regularization ( dim - reg ) and minimal subtraction scheme , they have proved that the bphz - formula is a special case of the birkhoff decomposition of a loop on a small circle in the complex plane , centered at the dimension of the theory , and taking values in a pro - unipotent lie group . before applying this to the case of qed , we briefly recall the birkhoff decomposition , while referring to @xcite and @xcite for more details .
the birkhoff decomposition provides a procedure to extract a finite value from a singular expression .
more precisely , let @xmath100 be a smooth simple curve and let @xmath101 denote its two complements with @xmath102 .
the birkhoff decomposition of a loop @xmath103 , taking values in a complex lie group @xmath104 , is a factorization of the form @xmath105 where @xmath106 are boundary values of holomorphic maps ( denoted by the same symbol ) @xmath107 the normalization @xmath108 ensures uniqueness of the decomposition ( if it exists ) .
the evaluation @xmath109 is a natural principle to extract a finite value from the ( possibly ) singular expression @xmath110 .
this gives a multiplicative removal of the pole part for a meromorphic loop @xmath74 , when we let @xmath111 be an infinitesimal circle centered at @xmath112 .
existence of the birkhoff decomposition has been established for prounipotent complex lie groups in @xcite , and , more generally , in @xcite in the setting of affine group schemes .
recall that affine group schemes are dual to commutative hopf algebras in the following sense . for a commutative hopf algebra @xmath3 , we understand an affine group scheme as a functor @xmath113 from the category of commutative algebras to the category of groups in the following way . for a given algebra @xmath114
, one defines the group @xmath115 to be the set of all homomorphisms from @xmath3 to @xmath114 , with product , inverse and unit given as the duals with respect to the coproduct , antipode and counit @xmath116 respectively , i.e. @xmath117 the following result is the algebraic translation of the birkhoff decomposition to ( pro - unipotent ) affine group schemes , expressed in terms of the commutative ( connected graded ) hopf algebra @xmath3 underlying this affine group scheme . its proof can be found in @xcite ( see also @xcite ) .
we assume that @xmath111 is an infinitesimal circle centered at @xmath118 and denote by @xmath119 the field of convergent laurent series , with arbitrary radius of convergence and by @xmath120 the ring of convergent power series .
furthermore , we set @xmath121)$ ] .
[ birkhoff ] let @xmath122 be an algebra homomorphism from a commutative connected graded hopf algebra @xmath3 to the field @xmath119 defined above .
the birkhoff decomposition of the corresponding loop is obtained recursively from the equalities , @xmath123 where we have written @xmath124 for @xmath125 and @xmath126 is the projection on the pole part in @xmath127 , and @xmath128 , or explicitly , @xmath129 the maps @xmath130 and @xmath131 are homomorphisms from @xmath3 to @xmath132 and @xmath120 respectively .
the loop @xmath133 defined in terms of @xmath134 by @xmath135 therefore factorizes as @xmath136 where @xmath137 are defined in like manner in terms of @xmath138 .
the fact that they are holomorphic maps on @xmath139 and @xmath140 , respectively , follows from the properties that @xmath131 maps to @xmath120 whereas @xmath130 maps to @xmath132 .
let us see how this applies in the case of quantum electrodynamics and in particular , how it gives the bphz procedure of renormalization of it .
let us start by giving the feynman rules for the graphs in our hopf algebra , allowing us to associate a feynman amplitude to a graph @xmath16 .
we will use dim - reg ( see ( * ? ? ? * ch.4 ) ) and obtain the regularized ( bare ) feynman amplitudes as integrals @xmath141 if we work in the euclidean setting , the integrand is given by the following feynman rules : 1 . assign a factor @xmath142 to each internal photon line
assign a factor @xmath143 to each internal electron line .
assign a factor @xmath144 to each 3-point vertex .
the apparent dependence on the index @xmath145 is resolved by summing over @xmath145 in combination with the attached photon line ( having also an index @xmath145 ) .
4 . assign a factor @xmath8 to the 2-point vertex .
assign a momentum conservation rule to each vertex . in rules
_ 1 . _ and _ 2 .
_ , we have introduced the ir - regulators @xmath146 in order to resolve divergences at small momenta .
consider the following electron self - energy graph + ( 150,60 ) according to the feynman rules , the integrand for this graph is @xmath147 with summation over repeated indices understood .
as can be seen from equation , a feynman amplitude @xmath148 corresponding to a 1pi graph @xmath16 is an element in @xmath149 , and a map @xmath150 can be defined by setting @xmath151 the factor @xmath152 is introduced in order to keep track of the loop number of the graph in terms of powers of @xmath153 . indeed , with @xmath154 the number of external edges of @xmath16 , the power of @xmath153 appearing in the above expression is exactly the loop number @xmath155 of @xmath16 .
the counterterm @xmath156 for a graph @xmath16 is given as the negative part of the birkhoff decomposition of @xmath157 applied to @xmath16 and the renormalized value @xmath158 as the positive part .
indeed , in this case , the above formul give precisely the recursive bphz - procedure of subtracting divergences , dealing with possible subdivergences recursively , so that @xmath159 and @xmath160 .
more explicitly , @xmath161 the relation between the renormalization constants in the lagrangian ( see equation ) and the counterterms , was given by dyson in @xcite . in terms of an expansion of feynman graphs of the specified type , they read ( compare with equation ( 73)-(76 ) in @xcite ) @xmath162
in quantum electrodynamics , the ward - takahashi identities give relations between feynman amplitudes for full vertex graphs and electron self - energy graphs .
our goal is to translate these identities into relations on the hopf algebra @xmath3 , thus giving relations between feynman graphs .
more precisely , we consider a quotient of the hopf algebra @xmath3 by a hopf ideal generated by so - called _ ward - takahashi ( wt ) elements _ , thereby establishing the well - known fact ( see for example @xcite ) that the wt - identities are compatible with renormalization .
first , we introduce the following notation .
let @xmath16 be an electron self - energy graph , and number the internal electron lines that are not part of an electron loop by @xmath163 .
we define @xmath164 to be the graph @xmath16 with insertion of a photon line on the @xmath163th electron line . for every electron self - energy graph @xmath16
, we define the ward - takahashi element @xmath165 associated to @xmath16 by @xmath166 the first term is understood as the pair @xmath167 , with external structure given by the distribution @xmath168 .
moreover , we set @xmath169 and @xmath170 ; in other words @xmath171 in what follows , we will suppress the matrix indices @xmath172 in @xmath173 for notational convenience .
the following notation due to t hooft and veltman of double headed photon lines provides a compact way to denote the above external structure in terms of diagrams : @xmath174\end{aligned}\ ] ] in diagrams , this leads to the familiar expressions for the wt - identities ( see for example ( * ? ? ?
7 ) ) , @xmath175 w_\mu'(\gamma)(p)&= \sum_{\parbox{40pt}{\centering \tiny{insertion\\ points } } } \parbox{60pt } { \begin{fmfgraph*}(60,60 ) \fmfleft{l } \fmfright{r1,r2 } \fmflabel{$p$}{r1 } \fmf{photon , label=$(\noexpand 0,,\noexpand \mu)$}{l , v } \fmf{fermion}{r1,v } \fmf{fermion}{v , r2 } \fmfblob{.25w}{v } \end{fmfgraph * } } + \frac{\partial}{\partial p_\mu}~ \parbox{60pt } { \begin{fmfgraph*}(60,60 ) \fmfleft{l } \fmfright{r } \fmf{fermion , label=$p$}{l , v } \fmf{fermion}{v , r } \fmfblob{.25w}{v } \end{fmfgraph * } } \\[5 mm ] w''(\gamma)&= \sum_{\parbox{40pt}{\centering \tiny{insertion\\ points } } } \parbox{40pt } { \begin{fmfgraph*}(40,40 ) \fmfleft{l } \fmfright{r1,r2 } \fmf{photon}{l , v } \fmf{plain}{r1,v } \fmf{plain}{v , r2 } \fmfblob{.25w}{v } \end{fmfgraph*}}_{{(1 ) } } + \parbox{40pt } { \begin{fmfgraph*}(40,30 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v } \fmf{plain}{v , r } \fmfblob{.25w}{v } \end{fmfgraph*}}_{{(2)}}\end{aligned}\ ] ] for @xmath176 ( 40,11 ) any electron self - energy graph .
[ thm : wt ] the ideal generated ( in @xmath3 ) by @xmath173 , @xmath177 and @xmath178 for all 1pi electron self - energy graphs @xmath16 is a hopf ideal . before stating the proof of this , we remark that it is thus possible to define the quotient hopf algebra @xmath179 of @xmath3 , with the induced coproduct , counit and antipode .
recall that an ideal @xmath180 in a hopf algebra @xmath3 is called a hopf ideal if @xmath181 in our case of a connected graded hopf algebra @xmath3 , the last property follows from the first . indeed , since @xmath182 is given inductively by equation , we find that @xmath183 .
we set @xmath184 and denote the ideal generated by the wt - identities by @xmath180 .
clearly , it is enough to establish @xmath185 .
moreover , since @xmath186 is an algebra map by definition , it is enough to establish @xmath187 and the analogous expressions for @xmath188 and @xmath178 for any electron self - energy graph @xmath16 .
let us start by illustrating the general argument in the following special case of the self - energy graph @xmath16 displayed in figure [ figure - blocks ] .
( 90,60 ) we label the internal electron lines from left to right , from 1 to 9 .
let us consider the first term in @xmath173 , and split its image under @xmath189 in a term in which @xmath74 contains the electron line @xmath163 and a term in which it does not : @xmath190 with @xmath191 and @xmath192 .
for example , if @xmath193 forms the ` block ' of concatenated electron self - energy graphs inside @xmath16 , we find , @xmath194 where for @xmath195 , @xmath196 denotes the electron self - energy graph @xmath197 with an external photon line attached to its internal electron line and @xmath198 is the electron line that corresponds to @xmath197 in the quotient @xmath199 .
on the other hand , @xmath200 here we wrote explicitly the external structure @xmath201 for the electron self - energy graph in @xmath74 for which an external photon line is attached to its incoming electron line ( i.e. for @xmath202 if @xmath203 and for @xmath204 if @xmath205 ) .
also , in the last line we used a labelling of the internal electron lines of the quotient @xmath199 in terms of the electron lines of @xmath16 when @xmath206 .
the first two terms of @xmath207 combine with @xmath208 forming the wt - elements @xmath209 , and also the last three terms of @xmath207 combine to give , @xmath210 using for the last term the fact that the quotient @xmath211 gives rise to a 2-point vertex , and thus to a new internal electron line .
it is easy to see that the first two terms in the above equation are in @xmath212 .
the two other terms in @xmath213 are of the form @xmath214 and combine , for fixed @xmath193 as above , with the last term in the previous equation to give precisely @xmath215 .
we conclude that the term in @xmath213 arising from the subgraph @xmath216 is an element in @xmath217 .
similar arguments show that such relations hold for all subgraphs of @xmath16 .
let us now turn to the proof of the claim that @xmath187 for any electron self - energy graph @xmath16 .
for the first term in @xmath173 we have @xmath218 where @xmath78 is a multi - index labelling the external structure on the connected components of @xmath74 and @xmath163 runs over all internal electron lines of @xmath16 that are not part of a loop . also , we suppressed the external structure of @xmath164 as it appears in @xmath219 .
in general , @xmath74 can be written as a union @xmath220 , where @xmath221 consists of electron self - energy graphs , @xmath222 of full vertex graphs , @xmath223 of vacuum polarization graphs and @xmath224 of electron self - energy graphs with a photon line inserted at the @xmath163th electron line ( with this labelling inherited from @xmath16 ) .
graphs of the type @xmath225 and @xmath226 do not appear in the sum , because there are no corresponding vertices of valence 3 and 4 in qed .
note that the multi - index @xmath78 only affects the subgraphs in @xmath221 , for each of which it can take the values @xmath227 and @xmath83 .
we split the above sum in a term in which @xmath228 contains the electron line @xmath163 as an internal line and those in which it does not : @xmath229 where @xmath230 .
we will write @xmath231 for the two terms appearing in equation . before examining the terms @xmath111 and @xmath232 , we note that for each @xmath74 , @xmath221 can be split into ` blocks ' each of which appear in the graph @xmath16 by concatenation of electron self - energy graphs ( as in figure [ figure - blocks ] ) .
we will denote such blocks by @xmath233 and write @xmath208 as @xmath234 where @xmath198 is the electron line corresponding to @xmath197 in the quotient @xmath199 . in words
, we separated the sum over the internal electron lines @xmath163 of @xmath221 into a sum over all blocks @xmath235 in @xmath221 , together with a sum over its connected components @xmath197 and a sum over the internal electron lines that are part of @xmath197 .
then , with @xmath236 , the quotient @xmath237 is given by the replacement of @xmath197 by a 3-vertex , followed by the quotient by the other graphs that constitute @xmath74 , and with external structure inherited from @xmath164 .
note that since @xmath238 is a full vertex graph , there is only the external structure @xmath239 .
this fixes @xmath240 inside the multi - index @xmath78 to be @xmath83 , and by a slight abuse of notation , we let @xmath78 also denote the external structures of the elements in @xmath241 .
the term @xmath207 can be split in a sum over @xmath163 of electron lines that are external edges for @xmath221 and those that are not , @xmath242 again , we will write this in terms of the blocks @xmath235 forming @xmath221 : @xmath243 where the first term arises from @xmath163 being the ingoing line of @xmath197 for @xmath244 and the second term from @xmath163 being the outgoing line for @xmath245 , thus equal to the sum of all external edges in @xmath235 .
writing explicitly the two terms for @xmath246 one obtains , @xmath247 where in the first line , we have used the fact that @xmath248 , in the above notation .
since each vertex ( 20,11 ) adds an electron line to @xmath16 , we can combine the last three terms to obtain @xmath249 thus , we obtain for the sum of @xmath111 and @xmath232 , @xmath250 where we recognize the wt - element @xmath209 for each 1pi self - energy graph @xmath251 , @xmath252 combining the second term in equation with the two other terms in @xmath213 ( which involve the coproduct @xmath253 , it follows that @xmath254 so that @xmath255 .
the other inclusions @xmath256 and @xmath257 follow from the latter equation by the definitions of @xmath177 and @xmath178 in terms of @xmath173 .
we have shown that the ward - takahashi identities can be implemented on the hopf algebra of feynman graphs of qed as relations that define a hopf ideal .
the quotient hopf algebra @xmath179 by this hopf ideal is still commutative but has the wt - identities ` built in ' .
the feynman amplitudes @xmath157 on @xmath179 defined by equation therefore automatically satisfy the wt - identities in the physical sense ( i.e. between feynman amplitudes )
. moreover , theorem [ birkhoff ] applies and shows that the counterterms and the renormalized feynman amplitudes are given in terms of the algebra maps @xmath258 and @xmath259 , respectively . in particular , the counterterms as well as the renormalized feynman amplitudes
satisfy the wt - identities .
the well - known relation @xmath0 between the renormalization constants as derived by ward in @xcite is now an easy consequence of their definition in , @xmath260 in the first line we have used the fact that the contribution @xmath261 vanishes whenever @xmath163 is part of an electron loop , as follows by explicit computation using the feynman rules ( cf .
i would like to thank matilde marcolli for discussion and remarks , and zgr ceyhan for several comments . | we report on the hopf algebraic description of renormalization theory of quantum electrodynamics .
the ward - takahashi identities are implemented as linear relations on the ( commutative ) hopf algebra of feynman graphs of qed .
compatibility of these relations with the hopf algebra structure is the mathematical formulation of the physical fact that wt - identities are compatible with renormalization . as a result , the counterterms and the renormalized feynman amplitudes automatically satisfy the wt - identities , which leads in particular to the well - known identity @xmath0
. graphs | <s>[INST]the description of perturbative quantum field theory in terms of hopf algebras @xcite ( cf .
@xcite ) has led to a better understanding of the combinatorial structure of renormalization . at the same time
, it provided a beautiful interaction of quantum field theory with several parts of mathematics .
although the hopf algebra was modelled on a scalar quantum field theory , it can be generalized to any quantum field theory .
however , subtleties appear in the case of quantum gauge theories .
gauge theories are field theories that are invariant under a certain group , known as the gauge group . in the process of renormalization
, one has to deal with the ` overcounting ' due to the gauge degrees of freedom .
furthermore , one has to understand how the gauge symmetries manifest themselves in the quantum field theory .
important here are the so - called ward - takahashi ( or slavnov - taylor ) identities . the first example of a gauge theory is quantum electrodynamics ( qed ) , which has the abelian group @xmath1 as a gauge group .
the hopf algebraic structure of feynman graphs in qed was desrcibed in @xcite and more recently in @xcite .
a slightly different approach is taken in @xcite , where hopf algebras on planar binary trees were considered .
the anatomy of a gauge theory with gauge group @xmath2 ( known as quantum chromodynamics ) has been discussed in the hopf algebra setting in @xcite , with a central role played by the dyson - schwinger equations ( see also @xcite ) . however , a full understanding of renormalization of general gauge theories is still incomplete .
this paper is a modest attempt towards understanding this by working out explicitly the hopf algebraic structure underlying renormalization of quantum electrodynamics , thereby implementing the ward - takahashi identities in a compatible way .
we start in section [ sect : hopf ] by defining the commutative hopf algebra @xmath3 of feynman graphs for quantum electrodynamics . the approach we take differs from the one in @xcite where a noncommutative hopf algebra was considered .
this was motivated by the fact that in qed , feynman amplitudes are ( noncommuting ) matrices .
instead , we work with a commutative hopf algebra and encode the matricial form of the feynman amplitudes into the distributions giving the external structure of the graph .
our approach has the advantage of still being able to use the duality between commutative hopf algebras and affine group schemes in the formulation of the bphz - procedure . in section [
sect : birkhoff ] , we associate a feynman amplitude to a feynman graph , as dictated by the feynman rules .
the bphz - formula of renormalization is obtained as a special case of the birkhoff decomposition for affine group schemes @xcite .
then in section [ sect : wt ] , we incorporate the ward - takahashi ( wt ) identities as relations between graphs , much as was done by t hooft and veltman in @xcite .
we show that these relations are compatible with the coproduct in the hopf algebra @xmath3 , so that they define a hopf ideal .
this reflects the physical fact that wt - identities are compatible with renormalization ( in the dimensional regularization and minimal subtraction scheme ) .
the feynman amplitudes can now be defined on the quotient hopf algebra of @xmath3 by this ideal , and we conclude that the counterterms as well as the renormalized feynman amplitudes satisfy the wt - identities in the physical sense ( i.e. , between feynman amplitudes ) . in particular , we arrive at the well - known identity @xmath0 as derived by ward in @xcite .
quantum electrodynamics in 4 dimensions is given by the following classical lagrangian , @xmath4 where @xmath5 is the _ field strength _ of the _ gauge potential _ @xmath6 , @xmath7 is the spinor describing the electron with mass @xmath8 and electric charge @xmath9 and @xmath10 are the @xmath11 dirac matrices .
finally , the real parameter @xmath12 is the _ gauge - fixing parameter_. the lagrangian @xmath13 describes the dynamics and the interaction as well as the gauge fixing : we can write @xmath14 , where the free , interaction and gauge fixing parts are @xmath15 the adjective `` quantum '' for electrodynamics is justified when this lagrangian is used in computing probability amplitudes . in perturbation theory , one expands such amplitudes in terms of feynman diagrams which are the graphs constructed from the following vertices , as dictated by the form of the lagrangian : ( 60,60 ) ( 60,60 ) ( 60,60 ) [ rem : el - mass ] in fact , we will also need the 2-point vertex ( 40,10 ) , associated to the electron mass term , similar to @xcite .
we will focus on the so - called _ one - particle irreducible _ ( 1pi ) _ graphs _ , which are graphs that are not trees , and that can not be disconnected by cutting a single internal edge . in qed , there are three types of 1pi graphs that are of interest in renormalization theory : the vacuum polarization , the electron self - energy and the full vertex graphs : ( 60,60 ) + ( 60,60 ) + ( 60,60 ) here the blob stands for any 1pi graph of the type dictated by the external lines .
we now describe the _ external structure _ of a feynman graph @xmath16 , assigning ( among other data ) momenta to the external legs . in physics ,
the feynman amplitude of @xmath16 ( dictated by the feynman rules , see below ) is evaluated with respect to this external structure ( see below ) .
mathematically , the external structure is a distribution on the space of feynman amplitudes , understood as test functions on a suitable space .
more explicitly , in the case of qed the ( euclidean ) feynman amplitudes @xmath17 are functions in @xmath18 where @xmath19 with @xmath20 the set of indices labelling the external photon lines of @xmath16 with spatial index @xmath21 respectively , and @xmath22 is the set of its external electron lines .
the factor @xmath23 can be understood from the fact that in qed , feynman amplitudes are matrix - valued functions on @xmath24 . for qed , the external structure
is thus given by an element in the space of distributions on @xmath18 ; we denote this space by @xmath25 .
for example , for the above full vertex graph @xmath16 , @xmath26 and a typical distribution is given by @xmath27 in terms of a dirac mass and the ( standard ) dual basis @xmath28 of @xmath29 .
evaluation on the feynman amplitude @xmath30 is then given by the pairing @xmath31 note that @xmath32 is translated in the diagram by a reversal of the corresponding arrow with associated momentum @xmath33 .
we will be interested in the following special external structures for the different graphs introduced above .
a full vertex graph @xmath34 at zero momentum transfer ( meaning @xmath35 ) can be written in terms of the two form factors @xmath36 ( cf .
* section 6.2 ) ) @xmath37 where @xmath38 .
only the first form factor @xmath39 requires renormalization ; therefore , we define the following external structure : @xmath40 where the normalization comes from @xmath41 . for the ward - takahashi identities , we will also need the following external structure , @xmath42 which puts finite momentum @xmath43 on the ingoing and outgoing electron lines , but zero momentum on the external photon line ( zero - momentum transfer ) .
this external structure allows us to treat ward - takahashi identities in massless qed as well .
the form factors @xmath39 and @xmath44 can also be recovered separately by using the following two distributions @xcite , @xmath45 for an electron self - energy graph @xmath46 , we have @xmath47 and the corresponding feynman amplitude is written in terms of two form factors : @xmath48 correspondingly , there are two distributions , which we choose of the form , @xmath49 for all @xmath50 . also , there is an external structure which puts finite momentum on the ingoing and outgoing electron lines , @xmath51 finally , for a vacuum polarization graph @xmath16 , @xmath52 , we let @xmath53 be the external structure that satisfies @xmath54 for all @xmath55 .
the labelling of the external structures by @xmath56 and @xmath57 differs from the one in @xcite , where they were labelled by @xmath58 and @xmath59 . here
we follow @xcite , so that the labels correspond to the renormalization constants @xmath60 , as they appear in the lagrangian , @xmath61 the precise correspondence will be given in equation below .
let @xmath3 be the free commutative algebra generated by pairs @xmath62 with @xmath16 a 1pi graph and @xmath63 a distribution encoding its external structure .
the product in @xmath3 can be understood as the union of graphs , with induced external structure .
more precisely , for two 1pi graphs @xmath64 and @xmath65 , the product @xmath66 is the graph @xmath67 with external structure given by @xmath68 .
the algebra @xmath3 is a ( positively ) graded algebra @xmath69 , with the grading given by the loop number of the graph . in the following
, we will also write @xmath64 for the pair @xmath70 , and sometimes even @xmath16 . we will shorten the notation for graphs equipped with the special external structures defined above by writing @xmath71 .
we define a coproduct @xmath72 as follows ; if @xmath16 is a 1pi graph , then one sets @xmath73 here @xmath74 is a proper subset of the graph @xmath75 formed by the internal edges of @xmath16 ( i.e. @xmath76 ) .
the connected components @xmath77 of @xmath74 are 1pi graphs with the property that the set of edges of @xmath16 that meet @xmath77 have two or three elements .
the sum runs over all multi - indices @xmath78 , one index for each 1pi connected component of @xmath74 , and one denotes by @xmath79 the 1pi graph that has external structure as defined in equation - , with @xmath80 in the case of a vacuum polarization , @xmath81 for a full vertex graph and @xmath82 or @xmath83 in the case of an electron self - energy . in equation
, @xmath84 denotes the disjoint union of all graphs @xmath79 associated to the connected components of @xmath74 and the graph @xmath85 is the graph @xmath16 ( with the same external structure ) with each @xmath77 reduced to a vertex of type @xmath86 .
more explicitly , if @xmath87 ( 30,11 ) , then for @xmath88 one replaces this graph in @xmath16 by the line ( 20,11 ) @xmath89 ( 20,11 ) , and for @xmath82 by ( 20,11 ) @xmath90 ( 20,11 ) ( cf .
remark [ rem : el - mass ] ) . in the case of the vacuum polarization and the full vertex graph ,
one replaces @xmath77 by the corresponding vertex . by complete analogy with @xcite
, we find that with this coproduct , @xmath3 becomes a connected graded hopf algebra , i.e. @xmath91 , @xmath92 and @xmath93 indeed , @xmath94 consists of complex multiples of the empty graph , which is the unit in @xmath3 , so that @xmath95 .
moreover , from general results on graded hopf algebras , we obtain the antipode inductively , @xmath96 where @xmath97 .
we give a few examples in order to clarify the coproduct .
@xmath98 @xmath99 + \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph * } } _ { { ( 0 ) } } \otimes \parbox{50pt } { \begin{fmfgraph*}(50,20 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v2,v3,v5,v6,r } \fmf{photon , left , tension=0}{v1,v5 } \fmf{photon , right , tension=0}{v2,v6 } \fmfdot{v3 } \end{fmfgraph * } } + \parbox{50pt}{\begin{fmfgraph*}(50,20 ) \fmfforce{(.33w,0h)}{b } \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v3,v5,v6,v7,r } \fmffreeze \fmf{photon}{b , v3 } \fmf{photon , left , tension=0}{v5,v6 } \fmf{photon , left , tension=0}{v1,v7 } \end{fmfgraph * } } _ { { ( 1 ) } } \otimes \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph * } } + \parbox{50pt}{\begin{fmfgraph*}(50,20 ) \fmfforce{(.66w,0h)}{b } \fmfleft{l } \fmfright{r } \fmf{plain}{l , v1,v2,v3,v6,v7,r } \fmffreeze \fmf{photon}{b , v6 } \fmf{photon , left , tension=0}{v2,v3 } \fmf{photon , left , tension=0}{v1,v7 } \end{fmfgraph * } } _ { { ( 1 ) } } \otimes \parbox{40pt } { \begin{fmfgraph*}(40,11 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v3,v4,r } \fmf{photon , left , tension=0}{v3,v4 } \end{fmfgraph*}}\end{gathered}\ ] ]
in @xcite , connes and kreimer understood renormalization of perturbative quantum field theory in terms of a birkhoff decomposition .
in particular , using the dimensional regularization ( dim - reg ) and minimal subtraction scheme , they have proved that the bphz - formula is a special case of the birkhoff decomposition of a loop on a small circle in the complex plane , centered at the dimension of the theory , and taking values in a pro - unipotent lie group . before applying this to the case of qed , we briefly recall the birkhoff decomposition , while referring to @xcite and @xcite for more details .
the birkhoff decomposition provides a procedure to extract a finite value from a singular expression .
more precisely , let @xmath100 be a smooth simple curve and let @xmath101 denote its two complements with @xmath102 .
the birkhoff decomposition of a loop @xmath103 , taking values in a complex lie group @xmath104 , is a factorization of the form @xmath105 where @xmath106 are boundary values of holomorphic maps ( denoted by the same symbol ) @xmath107 the normalization @xmath108 ensures uniqueness of the decomposition ( if it exists ) .
the evaluation @xmath109 is a natural principle to extract a finite value from the ( possibly ) singular expression @xmath110 .
this gives a multiplicative removal of the pole part for a meromorphic loop @xmath74 , when we let @xmath111 be an infinitesimal circle centered at @xmath112 .
existence of the birkhoff decomposition has been established for prounipotent complex lie groups in @xcite , and , more generally , in @xcite in the setting of affine group schemes .
recall that affine group schemes are dual to commutative hopf algebras in the following sense . for a commutative hopf algebra @xmath3 , we understand an affine group scheme as a functor @xmath113 from the category of commutative algebras to the category of groups in the following way . for a given algebra @xmath114
, one defines the group @xmath115 to be the set of all homomorphisms from @xmath3 to @xmath114 , with product , inverse and unit given as the duals with respect to the coproduct , antipode and counit @xmath116 respectively , i.e. @xmath117 the following result is the algebraic translation of the birkhoff decomposition to ( pro - unipotent ) affine group schemes , expressed in terms of the commutative ( connected graded ) hopf algebra @xmath3 underlying this affine group scheme . its proof can be found in @xcite ( see also @xcite ) .
we assume that @xmath111 is an infinitesimal circle centered at @xmath118 and denote by @xmath119 the field of convergent laurent series , with arbitrary radius of convergence and by @xmath120 the ring of convergent power series .
furthermore , we set @xmath121)$ ] .
[ birkhoff ] let @xmath122 be an algebra homomorphism from a commutative connected graded hopf algebra @xmath3 to the field @xmath119 defined above .
the birkhoff decomposition of the corresponding loop is obtained recursively from the equalities , @xmath123 where we have written @xmath124 for @xmath125 and @xmath126 is the projection on the pole part in @xmath127 , and @xmath128 , or explicitly , @xmath129 the maps @xmath130 and @xmath131 are homomorphisms from @xmath3 to @xmath132 and @xmath120 respectively .
the loop @xmath133 defined in terms of @xmath134 by @xmath135 therefore factorizes as @xmath136 where @xmath137 are defined in like manner in terms of @xmath138 .
the fact that they are holomorphic maps on @xmath139 and @xmath140 , respectively , follows from the properties that @xmath131 maps to @xmath120 whereas @xmath130 maps to @xmath132 .
let us see how this applies in the case of quantum electrodynamics and in particular , how it gives the bphz procedure of renormalization of it .
let us start by giving the feynman rules for the graphs in our hopf algebra , allowing us to associate a feynman amplitude to a graph @xmath16 .
we will use dim - reg ( see ( * ? ? ? * ch.4 ) ) and obtain the regularized ( bare ) feynman amplitudes as integrals @xmath141 if we work in the euclidean setting , the integrand is given by the following feynman rules : 1 . assign a factor @xmath142 to each internal photon line
assign a factor @xmath143 to each internal electron line .
assign a factor @xmath144 to each 3-point vertex .
the apparent dependence on the index @xmath145 is resolved by summing over @xmath145 in combination with the attached photon line ( having also an index @xmath145 ) .
4 . assign a factor @xmath8 to the 2-point vertex .
assign a momentum conservation rule to each vertex . in rules
_ 1 . _ and _ 2 .
_ , we have introduced the ir - regulators @xmath146 in order to resolve divergences at small momenta .
consider the following electron self - energy graph + ( 150,60 ) according to the feynman rules , the integrand for this graph is @xmath147 with summation over repeated indices understood .
as can be seen from equation , a feynman amplitude @xmath148 corresponding to a 1pi graph @xmath16 is an element in @xmath149 , and a map @xmath150 can be defined by setting @xmath151 the factor @xmath152 is introduced in order to keep track of the loop number of the graph in terms of powers of @xmath153 . indeed , with @xmath154 the number of external edges of @xmath16 , the power of @xmath153 appearing in the above expression is exactly the loop number @xmath155 of @xmath16 .
the counterterm @xmath156 for a graph @xmath16 is given as the negative part of the birkhoff decomposition of @xmath157 applied to @xmath16 and the renormalized value @xmath158 as the positive part .
indeed , in this case , the above formul give precisely the recursive bphz - procedure of subtracting divergences , dealing with possible subdivergences recursively , so that @xmath159 and @xmath160 .
more explicitly , @xmath161 the relation between the renormalization constants in the lagrangian ( see equation ) and the counterterms , was given by dyson in @xcite . in terms of an expansion of feynman graphs of the specified type , they read ( compare with equation ( 73)-(76 ) in @xcite ) @xmath162
in quantum electrodynamics , the ward - takahashi identities give relations between feynman amplitudes for full vertex graphs and electron self - energy graphs .
our goal is to translate these identities into relations on the hopf algebra @xmath3 , thus giving relations between feynman graphs .
more precisely , we consider a quotient of the hopf algebra @xmath3 by a hopf ideal generated by so - called _ ward - takahashi ( wt ) elements _ , thereby establishing the well - known fact ( see for example @xcite ) that the wt - identities are compatible with renormalization .
first , we introduce the following notation .
let @xmath16 be an electron self - energy graph , and number the internal electron lines that are not part of an electron loop by @xmath163 .
we define @xmath164 to be the graph @xmath16 with insertion of a photon line on the @xmath163th electron line . for every electron self - energy graph @xmath16
, we define the ward - takahashi element @xmath165 associated to @xmath16 by @xmath166 the first term is understood as the pair @xmath167 , with external structure given by the distribution @xmath168 .
moreover , we set @xmath169 and @xmath170 ; in other words @xmath171 in what follows , we will suppress the matrix indices @xmath172 in @xmath173 for notational convenience .
the following notation due to t hooft and veltman of double headed photon lines provides a compact way to denote the above external structure in terms of diagrams : @xmath174\end{aligned}\ ] ] in diagrams , this leads to the familiar expressions for the wt - identities ( see for example ( * ? ? ?
7 ) ) , @xmath175 w_\mu'(\gamma)(p)&= \sum_{\parbox{40pt}{\centering \tiny{insertion\\ points } } } \parbox{60pt } { \begin{fmfgraph*}(60,60 ) \fmfleft{l } \fmfright{r1,r2 } \fmflabel{$p$}{r1 } \fmf{photon , label=$(\noexpand 0,,\noexpand \mu)$}{l , v } \fmf{fermion}{r1,v } \fmf{fermion}{v , r2 } \fmfblob{.25w}{v } \end{fmfgraph * } } + \frac{\partial}{\partial p_\mu}~ \parbox{60pt } { \begin{fmfgraph*}(60,60 ) \fmfleft{l } \fmfright{r } \fmf{fermion , label=$p$}{l , v } \fmf{fermion}{v , r } \fmfblob{.25w}{v } \end{fmfgraph * } } \\[5 mm ] w''(\gamma)&= \sum_{\parbox{40pt}{\centering \tiny{insertion\\ points } } } \parbox{40pt } { \begin{fmfgraph*}(40,40 ) \fmfleft{l } \fmfright{r1,r2 } \fmf{photon}{l , v } \fmf{plain}{r1,v } \fmf{plain}{v , r2 } \fmfblob{.25w}{v } \end{fmfgraph*}}_{{(1 ) } } + \parbox{40pt } { \begin{fmfgraph*}(40,30 ) \fmfleft{l } \fmfright{r } \fmf{plain}{l , v } \fmf{plain}{v , r } \fmfblob{.25w}{v } \end{fmfgraph*}}_{{(2)}}\end{aligned}\ ] ] for @xmath176 ( 40,11 ) any electron self - energy graph .
[ thm : wt ] the ideal generated ( in @xmath3 ) by @xmath173 , @xmath177 and @xmath178 for all 1pi electron self - energy graphs @xmath16 is a hopf ideal . before stating the proof of this , we remark that it is thus possible to define the quotient hopf algebra @xmath179 of @xmath3 , with the induced coproduct , counit and antipode .
recall that an ideal @xmath180 in a hopf algebra @xmath3 is called a hopf ideal if @xmath181 in our case of a connected graded hopf algebra @xmath3 , the last property follows from the first . indeed , since @xmath182 is given inductively by equation , we find that @xmath183 .
we set @xmath184 and denote the ideal generated by the wt - identities by @xmath180 .
clearly , it is enough to establish @xmath185 .
moreover , since @xmath186 is an algebra map by definition , it is enough to establish @xmath187 and the analogous expressions for @xmath188 and @xmath178 for any electron self - energy graph @xmath16 .
let us start by illustrating the general argument in the following special case of the self - energy graph @xmath16 displayed in figure [ figure - blocks ] .
( 90,60 ) we label the internal electron lines from left to right , from 1 to 9 .
let us consider the first term in @xmath173 , and split its image under @xmath189 in a term in which @xmath74 contains the electron line @xmath163 and a term in which it does not : @xmath190 with @xmath191 and @xmath192 .
for example , if @xmath193 forms the ` block ' of concatenated electron self - energy graphs inside @xmath16 , we find , @xmath194 where for @xmath195 , @xmath196 denotes the electron self - energy graph @xmath197 with an external photon line attached to its internal electron line and @xmath198 is the electron line that corresponds to @xmath197 in the quotient @xmath199 .
on the other hand , @xmath200 here we wrote explicitly the external structure @xmath201 for the electron self - energy graph in @xmath74 for which an external photon line is attached to its incoming electron line ( i.e. for @xmath202 if @xmath203 and for @xmath204 if @xmath205 ) .
also , in the last line we used a labelling of the internal electron lines of the quotient @xmath199 in terms of the electron lines of @xmath16 when @xmath206 .
the first two terms of @xmath207 combine with @xmath208 forming the wt - elements @xmath209 , and also the last three terms of @xmath207 combine to give , @xmath210 using for the last term the fact that the quotient @xmath211 gives rise to a 2-point vertex , and thus to a new internal electron line .
it is easy to see that the first two terms in the above equation are in @xmath212 .
the two other terms in @xmath213 are of the form @xmath214 and combine , for fixed @xmath193 as above , with the last term in the previous equation to give precisely @xmath215 .
we conclude that the term in @xmath213 arising from the subgraph @xmath216 is an element in @xmath217 .
similar arguments show that such relations hold for all subgraphs of @xmath16 .
let us now turn to the proof of the claim that @xmath187 for any electron self - energy graph @xmath16 .
for the first term in @xmath173 we have @xmath218 where @xmath78 is a multi - index labelling the external structure on the connected components of @xmath74 and @xmath163 runs over all internal electron lines of @xmath16 that are not part of a loop . also , we suppressed the external structure of @xmath164 as it appears in @xmath219 .
in general , @xmath74 can be written as a union @xmath220 , where @xmath221 consists of electron self - energy graphs , @xmath222 of full vertex graphs , @xmath223 of vacuum polarization graphs and @xmath224 of electron self - energy graphs with a photon line inserted at the @xmath163th electron line ( with this labelling inherited from @xmath16 ) .
graphs of the type @xmath225 and @xmath226 do not appear in the sum , because there are no corresponding vertices of valence 3 and 4 in qed .
note that the multi - index @xmath78 only affects the subgraphs in @xmath221 , for each of which it can take the values @xmath227 and @xmath83 .
we split the above sum in a term in which @xmath228 contains the electron line @xmath163 as an internal line and those in which it does not : @xmath229 where @xmath230 .
we will write @xmath231 for the two terms appearing in equation . before examining the terms @xmath111 and @xmath232 , we note that for each @xmath74 , @xmath221 can be split into ` blocks ' each of which appear in the graph @xmath16 by concatenation of electron self - energy graphs ( as in figure [ figure - blocks ] ) .
we will denote such blocks by @xmath233 and write @xmath208 as @xmath234 where @xmath198 is the electron line corresponding to @xmath197 in the quotient @xmath199 . in words
, we separated the sum over the internal electron lines @xmath163 of @xmath221 into a sum over all blocks @xmath235 in @xmath221 , together with a sum over its connected components @xmath197 and a sum over the internal electron lines that are part of @xmath197 .
then , with @xmath236 , the quotient @xmath237 is given by the replacement of @xmath197 by a 3-vertex , followed by the quotient by the other graphs that constitute @xmath74 , and with external structure inherited from @xmath164 .
note that since @xmath238 is a full vertex graph , there is only the external structure @xmath239 .
this fixes @xmath240 inside the multi - index @xmath78 to be @xmath83 , and by a slight abuse of notation , we let @xmath78 also denote the external structures of the elements in @xmath241 .
the term @xmath207 can be split in a sum over @xmath163 of electron lines that are external edges for @xmath221 and those that are not , @xmath242 again , we will write this in terms of the blocks @xmath235 forming @xmath221 : @xmath243 where the first term arises from @xmath163 being the ingoing line of @xmath197 for @xmath244 and the second term from @xmath163 being the outgoing line for @xmath245 , thus equal to the sum of all external edges in @xmath235 .
writing explicitly the two terms for @xmath246 one obtains , @xmath247 where in the first line , we have used the fact that @xmath248 , in the above notation .
since each vertex ( 20,11 ) adds an electron line to @xmath16 , we can combine the last three terms to obtain @xmath249 thus , we obtain for the sum of @xmath111 and @xmath232 , @xmath250 where we recognize the wt - element @xmath209 for each 1pi self - energy graph @xmath251 , @xmath252 combining the second term in equation with the two other terms in @xmath213 ( which involve the coproduct @xmath253 , it follows that @xmath254 so that @xmath255 .
the other inclusions @xmath256 and @xmath257 follow from the latter equation by the definitions of @xmath177 and @xmath178 in terms of @xmath173 .
we have shown that the ward - takahashi identities can be implemented on the hopf algebra of feynman graphs of qed as relations that define a hopf ideal .
the quotient hopf algebra @xmath179 by this hopf ideal is still commutative but has the wt - identities ` built in ' .
the feynman amplitudes @xmath157 on @xmath179 defined by equation therefore automatically satisfy the wt - identities in the physical sense ( i.e. between feynman amplitudes )
. moreover , theorem [ birkhoff ] applies and shows that the counterterms and the renormalized feynman amplitudes are given in terms of the algebra maps @xmath258 and @xmath259 , respectively . in particular , the counterterms as well as the renormalized feynman amplitudes
satisfy the wt - identities .
the well - known relation @xmath0 between the renormalization constants as derived by ward in @xcite is now an easy consequence of their definition in , @xmath260 in the first line we have used the fact that the contribution @xmath261 vanishes whenever @xmath163 is part of an electron loop , as follows by explicit computation using the feynman rules ( cf .
i would like to thank matilde marcolli for discussion and remarks , and zgr ceyhan for several comments .[/INST] we report on the hopf algebraic description of renormalization theory of quantum electrodynamics .
the ward - takahashi identities are implemented as linear relations on the ( commutative ) hopf algebra of feynman graphs of qed .
compatibility of these relations with the hopf algebra structure is the mathematical formulation of the physical fact that wt - identities are compatible with renormalization . as a result , the counterterms and the renormalized feynman amplitudes automatically satisfy the wt - identities , which leads in particular to the well - known identity @xmath0
. graphs </s> |
wormholes are hypothetical tunnels in spacetime , possibly through which observers may freely traverse . however , it is important to emphasize that these solutions are primarily useful as `` gedanken - experiments '' and as a theoretician s probe of the foundations of general relativity ( gr ) . in classical general relativity ,
wormholes are supported by exotic matter , which involves a stress - energy tensor that violates the null energy condition ( nec ) @xcite .
note that the nec is given by @xmath1 , where @xmath2 is _ any _ null vector .
thus , it is an important and intriguing challenge in wormhole physics to find a realistic matter source that will support these exotic spacetimes .
several candidates have been proposed in the literature , amongst which we refer to solutions in higher dimensions , for instance in einstein - gauss - bonnet theory @xcite , wormholes on the brane @xcite ; solutions in brans - dicke theory @xcite ; wormhole solutions in semi - classical gravity ( see ref . @xcite and references therein ) ; exact wormhole solutions using a more systematic geometric approach were found @xcite ; geometries supported by equations of state responsible for the cosmic acceleration @xcite , and solutions in conformal weyl gravity were also found @xcite , etc ( see refs .
@xcite for more details and @xcite for a recent review ) . in this work , instead of further exploring wormholes in some extension of gr , we rather analyse the possibility of having tunneling solutions in general relativistic solutions with negatively curved spatial surfaces which might be considered the analogue of wormholes .
indeed , we consider a largely ignored metric which belongs to a class of vacuum solutions referred as degenerate solutions of class a class a @xcite by ehlers and kundt , which are axisymmetric solutions and thus also belong to weyl s class @xcite , given by @xmath3 where the usual 2@xmath4 spheres are replaced by pseudo - spheres , @xmath5 , hence by surfaces of negative , constant curvature .
these are still surfaces of revolution around an axis , and @xmath6 represents the corresponding rotation angle .
the specific case of @xmath7 is of particular interest , where @xmath8 is a constant . in our opinion
this metric can be seen as an anti - schwarzschild in the same way the de sitter model with negative curvature is an anti - de sitter model .
we immediately see that the static solution holds for @xmath9 and that there is a coordinate singularity at @xmath10 ( note that @xmath11 neither vanishes nor becomes @xmath12 at @xmath10)@xcite .
this is the complementary domain of the exterior schwarzschild solution in the region outside the schwarzchild horizon . in the domain @xmath13 , as with the latter solution , the @xmath14 and @xmath15 metric coefficients swap signs . defining @xmath16 and @xmath17
, we obtain @xmath18 with the following parametric definitions @xmath19 , @xmath20 and @xmath21 , which is a particular case of a bianchi iii axisymetric universe .
using pseudo - spherical coordinates @xmath22 , the spatial part of the metric ( [ metric_constnc ] ) can be related to the hyperboloid @xmath23 embedded in a 4-dimensional flat space .
we then have @xmath24\,{\rm d}r^2 + \nonumber \\ & & r^2 \left ( { \rm d}u^2+\sinh^2u\ , { \rm d}v^2 \right ) \ ; .\end{aligned}\ ] ] where the prime stands for differentiation with respect to @xmath25 , and @xmath26 .
we can recast metric ( [ metric_constnc ] ) into the following @xmath27 \,{\rm d}\tau^2 + \left(\frac{2\mu}{\bar r}\right)^2\ , \cos ^4\left[\ln\left ( \bar r\right)^{\mp 1}\right]\times\nonumber \\ & \times\ , \left[{\rm d}\bar{r}^2\,+ \bar r^2\,({\rm d}u^2 + \sinh^2{u}\,{\rm d}v^2 ) \right]\ ; , \label{isotrop3}\end{aligned}\ ] ] which is the analogue of the isotropic form of the schwarzschild solution .
in the neighborhood of @xmath28 , i.e. , for @xmath29 , we can cast the metric of the 2-dimensional hyperbolic solid angle as @xmath30 so that it confounds itself with the tangent space to the spherically symmetric @xmath31 surfaces in neighborhood of the poles . the apparent arbitrariness of the locus @xmath28 ,
is overcome simply by transforming it to another location by means of a hyperbolic rotation , as in the case of the spherically symmetries case where the poles are defined up to a spherical rotation ( so(3 ) group ) .
thus , the spatial surfaces are conformally flat .
however , we can not recover the usual newtonian weak - field limit for large @xmath25 , because of the change of signature that takes place at @xmath10 .
analyzing the `` radial '' motion of test particles , we have the following equation @xmath32 where @xmath33 and @xmath34 are constants of motion defined by @xmath35 and @xmath36 , for fixed @xmath37 .
the former and latter constants represent the energy and angular momentum per unit mass , respectively .
we thus define the potential @xmath38 this potential is manifestly repulsive , crosses the @xmath25-axis at @xmath10 , and for sufficiently high values of @xmath34 it has a minimum at @xmath39 .
however this minimum falls outside the @xmath10 divide .
so a test particle is subject to a repulsive potential forcing it to inevitably cross the event horizon at @xmath10 attracted either by some mass at the minimum or by masses at infinity . in it
is hinted that the non - existence of a clear newtonian analogue is related to the existence of mass sources at @xmath12 , but no definite conclusions were drawn .
a more detailed analysis of the physical properties and characteristics of this intriguing solution is presently underway @xcite , as well as an application to the cosmological features of the model , namely the study of negatively curved spacetimes in order to understand the ultimate stages of underdensities @xcite .
here we shall study the extension of the solution ( [ metric_constnc - antiscwarz ] ) which arises from adding exotic matter to analyze the possibility of tunneling in hyperbolic spacetimes .
these would add to other non - spherically symmetric wormholes which have already been considered in the literature .
for instance , extending the spherically symmetric morris - thorne wormholes @xcite and motivated by the aim of minimizing the violation of the energy conditions , polyhedral solutions and , in particular , cubic wormholes were constructed in ref .
@xcite . in ref .
@xcite , the static spherically symmetric traversable wormhole solution was generalized to that of a ( non - planar ) torus - like topology @xcite , denoted as a ringhole . in ref .
@xcite , solutions of plane symmetric wormholes in the presence of a negative cosmological constant by matching an interior spacetime to the exterior anti - de sitter vacuum solution were constructed .
it is interesting to note that the construction of these plane symmetric wormholes does not alter the topology of the background spacetime ( i.e. , spacetime is not multiply - connected ) , so that these solutions can instead be considered domain walls .
the dynamic stability analysis of plane symmetric wormholes was further analyzed in ref .
@xcite .
thus , it is the purpose of this paper to study static and _ pseudo_-spherically symmetric counterparts to the usual wormholes by adding exotic matter to the vacuum degenerate solution of class @xmath0 , given by ( [ metric_constnc ] ) .
the physical properties and characteristics of these intriguing solutions are explored , and through the mathematics of embedding it is shown that particular constraints are placed on the shape function , that differ radically from the morris - thorne wormhole .
in particular , it is shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions are also presented by considering various equations of state , and by imposing restricted choices for the shape function or the redshift function .
this paper is organized in the following manner : in sec .
[ sec : ii ] , the spacetime metric , the field equations and the mathematics of embedding of these pseudo - spherically symmetric geometries are analyzed in detail . in sec .
[ sec : iii ] , specific solutions are found by considering several equations of state .
we conclude in sec .
[ sec : conclusion ] .
consider the following _ pseudo_-spherically symmetric and static solution @xmath40 where the coordinates @xmath41 and @xmath6 have the following range @xmath42 and @xmath43 .
the @xmath25 coordinate yields the curvature radius of the 2-dimensional pseudo - spherical surfaces that thread the spacetime : @xmath44 , and , hence , is a generalised radial coordinate .
@xmath45 and @xmath46 are arbitrary functions of the radial coordinate @xmath25 . as in the morris - thorne wormhole @xcite
, we denote @xmath45 the redshift function , for it is related to the gravitational redshift , and @xmath46 the shape function , as will be shown below by embedding diagrams , determines the shape of the tunnel ( in analogy to the analysis considered in @xcite ) .
the coordinate @xmath25 is non - monotonic in that it decreases from a constant value @xmath47 to a minimum value @xmath48 , representing the location of the throat of the wormhole , where @xmath49 , and then it increases from @xmath48 back to the value @xmath47 .
note that the condition @xmath50 imposes that @xmath51 , contrary to the morris - thorne counterpart . the einstein field equation , @xmath52 , provides the following stress - energy scenario @xmath53 \label{radialpwh}\,,\\ p_t(r)&=&\frac{1}{8\pi } \left(\frac{b}{r}-1\right)\bigg[\phi ' ' + ( \phi')^2 + \frac{b'r+b - r}{2r(b - r)}\phi ' \nonumber \\ & & + \frac{b'r - b}{2r^2(b - r ) } \bigg ] \label{lateralpwh}\,.\end{aligned}\ ] ] in which @xmath54 is the energy density
, @xmath55 is the radial pressure , @xmath56 is the pressure measured in the tangential directions , orthogonal to the radial direction . assuming that the redshift function is finite @xmath57 , note that the radial pressure is always positive at the throat , i.e , @xmath58 , contrary to the morris - thorne wormhole , where a radial tension at the throat is needed to sustain the wormhole .
in addition to this , we also show below that @xmath59 at the throat , which implies a negative energy density at the throat .
this condition is another significant difference to the morris - thorne wormhole , where the existence of negative energy densities at the throat is not a necessary condition . by taking the derivative with respect to the radial coordinate @xmath25 , of eq .
( [ radialpwh ] ) , and eliminating @xmath60 and @xmath61 , given in eq .
( [ rhowh ] ) and eq .
( [ lateralpwh ] ) , respectively , we obtain the following equation @xmath62 equation ( [ tauderivative ] ) is the relativistic euler equation , or the hydrostatic equation for equilibrium for the material threading the hyperbolic spacetime tunnel .
we now have a system of three equations , namely , eqs . ( [ rhowh])-([lateralpwh ] ) , with five unknown functions of @xmath25 , i.e. , the stress - energy components , @xmath54 , @xmath55 and @xmath56 , and the metric fields , @xmath46 and @xmath45 . to construct specific solutions , we may adopt several approaches , and in this work we shall mainly use the strategy of considering a specific equation of state given by @xmath63 , and restricted choices for @xmath46 or @xmath45 .
one may also impose a specific form for the stress - energy components and through the field equations and the equation of state , @xmath63 , determine @xmath46 and @xmath45 .
we will show below , through the embedding analysis , that @xmath59 , so that throughout this paper we only consider the cases of a negative energy density at the throat , @xmath64 , .
the embedding diagrams are useful to represent the geometry of the tunnelling solution and extract some useful information for the choice of the shape function , @xmath46 @xcite . due to the _ pseudo_-spherically symmetric nature of the problem , without a significant loss of generality consider a slice with the specific value of @xmath65 which imposes @xmath66 .
the respective line element , considering a fixed moment of time , @xmath67 , is given by @xmath68 to visualize this slice , one embeds this metric into three - dimensional euclidean space @xcite , in which the metric can be written in cylindrical coordinates , @xmath69 , as @xmath70 now , in the three - dimensional euclidean space the embedded surface has equation @xmath71 , and thus the metric of the surface can be written as , @xmath72 { \rm d}r^2+r^2 \ , { \rm d}v ^2 \ , .
\label{surface2}\ ] ] comparing eq .
( [ surface2 ] ) with ( [ surface1 ] ) , we have the equation for the embedding surface , given by @xmath73^{1/2 } \label{lift}\,.\ ] ] to be a solution of a spacetime tunnel , the geometry has a minimum radius , @xmath74 , denoted as the throat , at which the embedded surface is vertical , i.e. , @xmath75 , see figure [ fig : embed2 ] .
note also that contrary to the morris - thorne traversable wormhole , the shape function is constrained in the present case . more specifically , taking into account that @xmath51 , then the embedding surface ( [ lift ] ) also imposes the condition @xmath76 .
thus , the shape function is restricted to lie within the following range : @xmath77 .
, @xmath78 ) of a tunnel in spacetime.,width=268 ] in addition to this , to be a solution of a tunnel in spacetime , one needs to impose that the throat flares out , as in figure [ fig : embed2 ] .
mathematically , this flaring - out condition entails that the inverse of the embedding function @xmath79 , must satisfy @xmath80 at or near the throat @xmath81 .
differentiating @xmath82 with respect to @xmath83 , we have @xmath84 at the throat we verify that the shape function satisfies the condition @xmath59 , also contrary to its morris - thorne counterpart .
this condition plays a fundamental role in the analysis of the violation of the energy conditions . in particular
, considering the nec , i.e. , @xmath85 , the term @xmath86 , taking into account the field equations ( [ rhowh ] ) and ( [ radialpwh ] ) , is given by @xmath87 \,.\ ] ] at the throat , we have @xmath88 which implies the important condition @xmath59 at the throat , contrary to the morris - thorne counterpart . as mentioned above , this implies that the energy density , at the throat , is always negative for these exotic hyperbolic , tunneling geometries .
in this section , we find exact solutions by considering several appropriate equations of state , @xmath63 , and by imposing specific shape functions or specific redshift functions . to this effect ,
an adequate shape function is the following case : @xmath89 taking the radial derivative , we have @xmath90 which at the throat implies @xmath91 . from the condition @xmath92 , one has @xmath93 .
thus , we have the following conditions : @xmath94 we verify that one may have an arbitrary large tunnel by imposing the condition @xmath95 .
consider the linear equation of state @xmath96 , in which wormhole solutions were extensively analyzed in ref .
@xcite , and consequently denoted as `` phantom wormhole '' .
now , using the above - mentioned equation of state and taking into account eqs .
( [ rhowh])-([radialpwh ] ) , one deduces the following expression @xmath97 } \ , , \label{diffeq}\ ] ] which is the relationship governing what may be considered the hyperbolic analogue of the `` phantom wormhole '' .
note that the nec violation , and taking into account @xmath64 , imposes that @xmath98 , contrary to its spherically symmetric counterpart . by imposing a specific redshift function ,
one finds the general solution for the shape function @xmath99\,.\ ] ] however , one also deduces an adequate solution by imposing the shape function given by eq .
( [ specform ] ) . using relationship ( [ diffeq ] ) ,
the redshift function is provided by @xmath100+c_1\,,\ ] ] where @xmath101 is an integration constant .
now , to avoid an event horizon at @xmath48 , one needs to impose that @xmath102 , so that the redshift function simplifies to @xmath103 .
one may also further restrict the parameters by considering certain traversability conditions in analogy to the morris - thorne wormhole @xcite .
in particular , it is important that an observer traversing through the hyperbolic tunnel should not be ripped apart by enormous tidal forces .
thus , the tidal traversability condition requires that the tidal accelerations felt by the traveller should not exceed , for instance , the earth s gravitational acceleration , @xmath104 , which is translated by the following inequalities @xmath105 \right | & \leq & g_\oplus \ , , \label{radialtidalconstraint }
\\ \left | \frac{\gamma ^2}{r^2 } \left [ v^2\left ( \frac{b}{r}-b ' \right ) + 2(b - r)\phi ' \right ] \right | & \leq & g_\oplus \ , . \label{lateraltidalconstraint}\end{aligned}\ ] ] we refer the reader to @xcite for details in deducing these relationships . the radial tidal constraint , eq .
( [ radialtidalconstraint ] ) , constrains the redshift function , and the lateral tidal constraint , eq .
( [ lateraltidalconstraint ] ) , constrains the velocity with which observers traverse the tunnel .
these inequalities are particularly simple at the throat , @xmath48 , @xmath106 in particular , considering non - relativistic velocities , i.e. , @xmath107 and @xmath108 , using the shape function given by ( [ specform ] ) and @xmath103 , one readily verifies that the radial tidal constraint is satisfied .
the lateral tidal constraint provides the condition @xmath109 , which essentially depends on the values taken for the parameter @xmath110 . in alternative , by specifying the traversal velocity , we find a restriction placed on @xmath110 given by @xmath111 .
it is also adequate to find solutions by considering a specific redshift function .
consider the redshift function given by @xmath112 .
using expression ( [ diffeq ] ) , one deduces the shape function given by @xmath113 where @xmath114 is an integration constant and , for notational simplicity , the function @xmath115 is defined as @xmath116 and @xmath117 and @xmath118 are the gamma and the incomplete gamma functions , respectively .
note that the constant of integration @xmath114 may be found by taking into account the condition @xmath49 , and is given by the following relationship @xmath119\,.\ ] ] in cosmology , the equation of state representing the generalized chaplygin gas ( gcg ) is given by @xmath120 , where @xmath0 and @xmath121 are positive constants , and the latter lies in the range @xmath122 @xcite .
the particular case of @xmath123 corresponds to the chaplygin gas .
an attractive feature of this model is that at early times the energy density behaves as matter , @xmath124 , where @xmath125 is the scale factor , and as a cosmological constant at a later stage , i.e. , @xmath126 . in a cosmological context , at a late stage dominated by an accelerated expansion of the universe , the cosmological constant may be given by @xmath127 .
this dual behavior is responsible for the interpretation that the gcg model is a candidate of a unified model of dark matter and dark energy @xcite .
it was noted in ref .
@xcite that the gcg equation of state is that of a polytropic gas with a negative polytropic index , and thus suggested that one could analyze astrophysical implications of the model . in this context
, the construction of traversable wormholes , possibly arising from a density fluctuation in the gcg cosmological background was explored in @xcite .
these latter solutions were denoted chaplygin wormholes . as in ref .
@xcite , it was considered that the pressure in the gcg equation of state is a radial pressure , and the tangential pressure can be determined from the einstein equations , in particular , eq .
( [ lateralpwh ] ) . to compare to the spherically symmetric chaplygin wormholes ,
we construct their pseudo - spherically symmetric duplicates .
thus , taking into account the gcg equation of state in the form @xmath128 , and using eqs .
( [ rhowh])-([radialpwh ] ) , we have the following condition @xmath129\big/\left(\frac{b}{r } -1\right ) \ , . \label{eoscondition}\ ] ] solutions of the metric ( [ metricwormhole ] ) , satisfying eq .
( [ eoscondition ] ) may be considered as the analogues of `` chaplygin wormholes '' analyzed in @xcite . as shown above , to be a spacetime tunnel ,
the condition @xmath59 is imposed .
now , using the gcg equation of state , evaluated at the throat , and taking into account eq .
( [ radialpwh ] ) , we verify that the energy density at @xmath48 is given by @xmath130 . finally , using eq .
( [ rhowh ] ) , and the condition @xmath59 , we verify that for these solutions , the following condition is imposed @xmath131 , contrary to its spherically symmetric counterpart @xcite .
we consider next a specific example , by taking into account the shape function given by eq .
( [ specform ] ) .
thus , the differential equation ( [ eoscondition ] ) provides the following redshift function @xmath132 \nonumber \\ & & % -a(8\pi)^{1+\alpha}\left[\delta\left(\frac{r}{r_0}\right)^{\delta-1 } \right ] r^{2\alpha+3 } \times \nonumber \\ % & & \hspace{-1 cm } & & \times { \rm lerchphi}\left[\left(\frac{r}{r_0}\right)^{\delta-1},1 , \frac{3\alpha+2-\alpha\delta}{\delta-1}\right ] \nonumber \\ % & & -r\ln\left[\left(\frac{r}{r_0}\right)^{\delta-1}-1\right ] \bigg\}/\left[(\delta-1)r\right]+c_3\,,\end{aligned}\ ] ] where @xmath133 is a constant of integration ; and lerchphi is the general lerch phi function , defined as @xmath134 .
it is interesting to consider the specific case of @xmath135 and @xmath123 ( this latter value corresponds to the chaplygin gas equation of state ) , which yields the following simpler solution @xmath136 note the existence of an event horizon at the throat , rendering the hyperbolic tunnel non - traversable .
thus , to avoid this we impose the condition @xmath137 , so that the above solution simplifies to @xmath138 yielding a traversable geometry .
another case that lends itself to our analysis , is that of the van der waals quintessence equation of state , which seems to provide a solution to the puzzle of dark energy , without the presence of exotic fluids or modifications of the friedmann equations . in ref .
@xcite , the construction of inhomogeneous compact spheres supported by a van der waals equation of state was explored .
these relativistic stellar configurations were denoted as _ van der waals quintessence stars_. despite the fact that , in a cosmological context , the van der waals fluid is considered homogeneous , inhomogeneities may arise through gravitational instabilities . thus , these solutions may possibly originate from density fluctuations in the cosmological background .
exact solutions were found , and their respective characteristics and physical properties were further explored in ref .
@xcite .
the van der waals equation of state is given by @xmath139 where @xmath140 is the energy density and @xmath141 the pressure of the vdw fluid .
the accelerated and decelerated periods depend on the parameters , @xmath121 , @xmath142 and @xmath143 of the equation of state , and in the limiting case @xmath144 , one recovers the dark energy equation of state , with @xmath145 @xcite . as in the previous exact solutions , we may also consider the counterpart of the static and spherically symmetric van der waals wormhole . thus , taking into account the specific shape function given by eq .
( [ specform ] ) , with the parameter @xmath135 , and considering that @xmath141 is a radial pressure ( see @xcite for details ) , we have the following solution @xmath146+c_4 \,,\end{aligned}\ ] ] where @xmath147 is a constant of integration , and we have considered the following definitions for notational simplicity : @xmath148 note the presence of an event horizon , due to the term @xmath149 .
thus , to avoid this , we impose the following condition @xmath150 so the redshift function reduces to @xmath151 using the simplified relationship ( [ vdwredshift ] ) , one may find a restriction from the lateral tidal acceleration constraint ( [ lateraltidalconstraint2 ] ) , provided by @xmath152 summary , discussion and future outlook --------------------------------------
traversable wormholes possess a peculiar property , namely `` exotic matter '' , involving a stress - energy tensor that violates the null energy condition . in this work ,
we have constructed exact solutions of static and _ pseudo_-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class @xmath0 .
the usual 2-dimensional spheres are replaced by pseudo - spheres , which are still surfaces of revolution around an axis , but now consist of a negative and constant curvature . the physical properties and characteristics of these intriguing
, hyperbolic solutions were further explored , and through the mathematics of embedding it was shown that particular constraints are placed on the shape function , that differ radically from the morris - thorne wormhole .
in particular , it was shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions were also presented by considering several different equations of state , and by imposing restricted choices for the shape function or the redshift function .
standard definitions of a wormhole usually require either asymptotic flatness with a localized bridge to another asymptotically flat region , or the ability to identify a compact region that can usefully be thought of as a throat .
the geometries considered in the current article also exhibit asymptotic flatness and share the possibility of having localized tunnels , with throats , bridging different spacetime regions .
however the spatial hypersurfaces of the asymptotic flat limit of the hyperbolic spacetime under consideration here is peculiar in that it is not euclidean , but rather pseudo - euclidean ( it is a 3-dimensional lorentzian space ) .
hence , rather than denote the exotic geometric objects analyzed in this work as wormholes , we prefer the term hyperbolic tunnels .
they should indeed be understood as a theoretician s probe of the foundations of general relativity , on the same grounds as in the case of the morris - thorne wormhole .
the authors are thankful to reza tavakol for helpful comments , and gratefully acknowledge the grants ptdc / fis/102742/2008 and cern / fp/109381/2009 from fct . 99 m. s. morris and k. s. thorne , `` wormholes in space - time and their use for interstellar travel : a tool for teaching general relativity , '' am .
j. phys .
* 56 * , 395 ( 1988 ) .
m. visser , _ loretzian wormholes : from einstein to hawking _
aip press ( 1995 ) .
g. dotti , j. oliva , and r. troncoso , `` static wormhole solution for higher - dimensional gravity in vacuum , '' phys .
d * 75 * , 024002 ( 2007 ) [ arxiv : hep - th/0607062 ] . l. a. anchordoqui and s. e. p bergliaffa , `` wormhole surgery and cosmology on the brane : the world is not enough , '' phys .
d * 62 * , 067502 ( 2000 ) [ arxiv : gr - qc/0001019 ] ; k. a. bronnikov and s .- w .
kim , `` possible wormholes in a brane world , '' phys .
d * 67 * , 064027 ( 2003 ) [ arxiv : gr - qc/0212112 ] ; m. la camera , `` wormhole solutions in the randall - sundrum scenario , '' phys .
* b573 * , 27 - 32 ( 2003 ) [ arxiv : gr - qc/0306017 ] . f. s. n. lobo , `` general class of braneworld wormholes , '' phys .
rev . * d75 * , 064027 ( 2007 ) [ arxiv : gr - qc/0701133 ]
. k. k. nandi , b. bhattacharjee , s. m. k. alam and j. evans , `` brans - dicke wormholes in the jordan and einstein frames , '' phys .
d * 57 * , 823 ( 1998 ) ; f. s. n. lobo and m. a. oliveira , phys .
d * 81 * , 067501 ( 2010 ) ; f. s. n. lobo and m. a. oliveira , phys .
d * 80 * , 104012 ( 2009 ) .
r. garattini and f. s. n. lobo , `` self sustained phantom wormholes in semi - classical gravity , '' class .
* 24 * , 2401 ( 2007 ) [ arxiv : gr - qc/0701020 ] ; r. garattini and f. s. n. lobo , `` self - sustained traversable wormholes in noncommutative geometry , '' phys .
b * 671 * , 146 ( 2009 ) [ arxiv:0811.0919 [ gr - qc ] ] . c. g. boehmer , t. harko and f. s. n. lobo , `` conformally symmetric traversable wormholes , '' phys .
d * 76 * , 084014 ( 2007 ) [ arxiv:0708.1537 [ gr - qc ] ] ; c. g. boehmer , t. harko and f. s. n. lobo , `` wormhole geometries with conformal motions , '' class .
grav . * 25 * , 075016 ( 2008 ) [ arxiv:0711.2424 [ gr - qc ] ] .
s. sushkov , `` wormholes supported by a phantom energy , '' phys
d * 71 * , 043520 ( 2005 ) [ arxiv : gr - qc/0502084 ] ; f. s. n. lobo , `` phantom energy traversable wormholes , '' phys .
* d71 * , 084011 ( 2005 ) [ arxiv : gr - qc/0502099 ] ; f. s. n. lobo , `` stability of phantom wormholes , '' phys .
* d71 * , 124022 ( 2005 ) [ arxiv : gr - qc/0506001 ]
. f. s. n. lobo , `` chaplygin traversable wormholes , '' phys .
* d73 * , 064028 ( 2006 ) [ arxiv : gr - qc/0511003 ] .
f. s. n. lobo , `` van der waals quintessence stars , '' phys . rev .
d * 75 * , 024023 ( 2007 ) [ arxiv : gr - qc/0610118 ] . f. s. n. lobo , `` general class of wormhole geometries in conformal weyl gravity , '' class .
* 25 * , 175006 ( 2008 ) [ arxiv:0801.4401 [ gr - qc ] ] .
j. p. s. lemos , f. s. n. lobo and s. quinet de oliveira , `` morris - thorne wormholes with a cosmological constant , '' phys .
d * 68 * , 064004 ( 2003 ) [ arxiv : gr - qc/0302049 ] .
f. s. n. lobo , `` exotic solutions in general relativity : traversable wormholes and warp drive spacetimes , '' arxiv:0710.4474 [ gr - qc ] .
h. stephani , d. kramer , m. a. h. maccallum , c. hoenselaers and e. herlt , _ cambridge , uk : univ . pr .
( 2003 ) 701 p _
t. levi - civita , ren .
lincei 27 , 183 ( 1017 ) .
h. weyl , annalen phys .
* 54 * ( 1917 ) 117
. w. b. bonnor and m- a. p.
martins , classical and quantum gravity , 8 , 727 ( 1991 ) .
m. a. p. martins , gen .
28 ( 1996 ) 1309 .
l. a. anchordoqui , j. d. edelstein , c. nunez and g. s. birman , arxiv : gr - qc/9509018 .
j. p. s. lemos and f. s. n. lobo , `` plane symmetric traversable wormholes in an anti - de sitter background , '' phys .
d * 69 * , 104007 ( 2004 ) [ arxiv : gr - qc/0402099 ] . j. p. s. lemos and f. s. n. lobo , `` plane symmetric thin - shell wormholes : solutions and stability , '' phys .
d * 78 * , 044030 ( 2008 ) [ arxiv:0806.4459 [ gr - qc ] ] .
d. hochberg and m. visser , `` the null energy condition in dynamic wormholes , '' phys .
* 81 * , 746 ( 1998 ) [ arxiv : gr - qc/9802048 ] ; d. hochberg and m. visser , `` dynamic wormholes , anti - trapped surfaces , and energy conditions , '' phys .
d * 58 * , 044021 ( 1998 ) [ arxiv : gr - qc/9802046 ] ; s. kar , `` evolving wormholes and the weak energy condition , '' phys .
d * 49 * , 862 ( 1994 ) ; s. kar and d. sahdev , `` evolving lorentzian wormholes , '' phys .
d * 53 * , 722 ( 1996 ) [ arxiv : gr - qc/9506094 ] ; s. w. kim , `` the cosmological model with traversable wormhole , '' phys .
d * 53 * , 6889 ( 1996 ) ; a. v. b. arellano and f. s. n. lobo , `` evolving wormhole geometries within nonlinear electrodynamics , '' class .
* 23 * , 5811 ( 2006 ) [ arxiv : gr - qc/0608003 ] .
m. s. morris , k. s. thorne and u. yurtsever , `` wormholes , time machines and the weak energy condition , '' phy . rev . lett . * 61 * , 1446 ( 1988 ) .
s. capozziello , v. f. cardone , s. carloni , d. de martino , m. falanga , a. troisi and m. bruni , `` constraining van der waals quintessence by observations , '' jcap 0504 , 005 ( 2005 ) , [ arxiv : astro - ph/0410503 ] .
p. j. e. peebles , ap .
j , 557 , 495 ( 2001 ) ; v. g. gurzadyan and a. a. kocharyan , astron . astrophys .
* 493 * ( 2009 ) l61 [ arxiv:0807.1239 [ astro - ph ] ] ; t. clifton , p. g. ferreira and k. land , phys .
* 101 * ( 2008 ) 131302 [ arxiv:0807.1443 [ astro - ph ] ] . | traversable wormhole are primarily useful as `` gedanken - experiments '' and as a theoretician s probe of the foundations of general relativity . in this work ,
we analyse the possibility of having tunnels in a hyperbolic spacetime .
we obtain exact solutions of static and _ pseudo_-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class @xmath0 .
the physical properties and characteristics of these intriguing solutions are explored , and through the mathematics of embedding it is shown that particular constraints are placed on the shape function , that differ significantly from the morris - thorne wormhole .
in particular , it is shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions are also presented by considering several equations of state , and by imposing restricted choices for the shape function or the redshift function . | <s>[INST]wormholes are hypothetical tunnels in spacetime , possibly through which observers may freely traverse . however , it is important to emphasize that these solutions are primarily useful as `` gedanken - experiments '' and as a theoretician s probe of the foundations of general relativity ( gr ) . in classical general relativity ,
wormholes are supported by exotic matter , which involves a stress - energy tensor that violates the null energy condition ( nec ) @xcite .
note that the nec is given by @xmath1 , where @xmath2 is _ any _ null vector .
thus , it is an important and intriguing challenge in wormhole physics to find a realistic matter source that will support these exotic spacetimes .
several candidates have been proposed in the literature , amongst which we refer to solutions in higher dimensions , for instance in einstein - gauss - bonnet theory @xcite , wormholes on the brane @xcite ; solutions in brans - dicke theory @xcite ; wormhole solutions in semi - classical gravity ( see ref . @xcite and references therein ) ; exact wormhole solutions using a more systematic geometric approach were found @xcite ; geometries supported by equations of state responsible for the cosmic acceleration @xcite , and solutions in conformal weyl gravity were also found @xcite , etc ( see refs .
@xcite for more details and @xcite for a recent review ) . in this work , instead of further exploring wormholes in some extension of gr , we rather analyse the possibility of having tunneling solutions in general relativistic solutions with negatively curved spatial surfaces which might be considered the analogue of wormholes .
indeed , we consider a largely ignored metric which belongs to a class of vacuum solutions referred as degenerate solutions of class a class a @xcite by ehlers and kundt , which are axisymmetric solutions and thus also belong to weyl s class @xcite , given by @xmath3 where the usual 2@xmath4 spheres are replaced by pseudo - spheres , @xmath5 , hence by surfaces of negative , constant curvature .
these are still surfaces of revolution around an axis , and @xmath6 represents the corresponding rotation angle .
the specific case of @xmath7 is of particular interest , where @xmath8 is a constant . in our opinion
this metric can be seen as an anti - schwarzschild in the same way the de sitter model with negative curvature is an anti - de sitter model .
we immediately see that the static solution holds for @xmath9 and that there is a coordinate singularity at @xmath10 ( note that @xmath11 neither vanishes nor becomes @xmath12 at @xmath10)@xcite .
this is the complementary domain of the exterior schwarzschild solution in the region outside the schwarzchild horizon . in the domain @xmath13 , as with the latter solution , the @xmath14 and @xmath15 metric coefficients swap signs . defining @xmath16 and @xmath17
, we obtain @xmath18 with the following parametric definitions @xmath19 , @xmath20 and @xmath21 , which is a particular case of a bianchi iii axisymetric universe .
using pseudo - spherical coordinates @xmath22 , the spatial part of the metric ( [ metric_constnc ] ) can be related to the hyperboloid @xmath23 embedded in a 4-dimensional flat space .
we then have @xmath24\,{\rm d}r^2 + \nonumber \\ & & r^2 \left ( { \rm d}u^2+\sinh^2u\ , { \rm d}v^2 \right ) \ ; .\end{aligned}\ ] ] where the prime stands for differentiation with respect to @xmath25 , and @xmath26 .
we can recast metric ( [ metric_constnc ] ) into the following @xmath27 \,{\rm d}\tau^2 + \left(\frac{2\mu}{\bar r}\right)^2\ , \cos ^4\left[\ln\left ( \bar r\right)^{\mp 1}\right]\times\nonumber \\ & \times\ , \left[{\rm d}\bar{r}^2\,+ \bar r^2\,({\rm d}u^2 + \sinh^2{u}\,{\rm d}v^2 ) \right]\ ; , \label{isotrop3}\end{aligned}\ ] ] which is the analogue of the isotropic form of the schwarzschild solution .
in the neighborhood of @xmath28 , i.e. , for @xmath29 , we can cast the metric of the 2-dimensional hyperbolic solid angle as @xmath30 so that it confounds itself with the tangent space to the spherically symmetric @xmath31 surfaces in neighborhood of the poles . the apparent arbitrariness of the locus @xmath28 ,
is overcome simply by transforming it to another location by means of a hyperbolic rotation , as in the case of the spherically symmetries case where the poles are defined up to a spherical rotation ( so(3 ) group ) .
thus , the spatial surfaces are conformally flat .
however , we can not recover the usual newtonian weak - field limit for large @xmath25 , because of the change of signature that takes place at @xmath10 .
analyzing the `` radial '' motion of test particles , we have the following equation @xmath32 where @xmath33 and @xmath34 are constants of motion defined by @xmath35 and @xmath36 , for fixed @xmath37 .
the former and latter constants represent the energy and angular momentum per unit mass , respectively .
we thus define the potential @xmath38 this potential is manifestly repulsive , crosses the @xmath25-axis at @xmath10 , and for sufficiently high values of @xmath34 it has a minimum at @xmath39 .
however this minimum falls outside the @xmath10 divide .
so a test particle is subject to a repulsive potential forcing it to inevitably cross the event horizon at @xmath10 attracted either by some mass at the minimum or by masses at infinity . in it
is hinted that the non - existence of a clear newtonian analogue is related to the existence of mass sources at @xmath12 , but no definite conclusions were drawn .
a more detailed analysis of the physical properties and characteristics of this intriguing solution is presently underway @xcite , as well as an application to the cosmological features of the model , namely the study of negatively curved spacetimes in order to understand the ultimate stages of underdensities @xcite .
here we shall study the extension of the solution ( [ metric_constnc - antiscwarz ] ) which arises from adding exotic matter to analyze the possibility of tunneling in hyperbolic spacetimes .
these would add to other non - spherically symmetric wormholes which have already been considered in the literature .
for instance , extending the spherically symmetric morris - thorne wormholes @xcite and motivated by the aim of minimizing the violation of the energy conditions , polyhedral solutions and , in particular , cubic wormholes were constructed in ref .
@xcite . in ref .
@xcite , the static spherically symmetric traversable wormhole solution was generalized to that of a ( non - planar ) torus - like topology @xcite , denoted as a ringhole . in ref .
@xcite , solutions of plane symmetric wormholes in the presence of a negative cosmological constant by matching an interior spacetime to the exterior anti - de sitter vacuum solution were constructed .
it is interesting to note that the construction of these plane symmetric wormholes does not alter the topology of the background spacetime ( i.e. , spacetime is not multiply - connected ) , so that these solutions can instead be considered domain walls .
the dynamic stability analysis of plane symmetric wormholes was further analyzed in ref .
@xcite .
thus , it is the purpose of this paper to study static and _ pseudo_-spherically symmetric counterparts to the usual wormholes by adding exotic matter to the vacuum degenerate solution of class @xmath0 , given by ( [ metric_constnc ] ) .
the physical properties and characteristics of these intriguing solutions are explored , and through the mathematics of embedding it is shown that particular constraints are placed on the shape function , that differ radically from the morris - thorne wormhole .
in particular , it is shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions are also presented by considering various equations of state , and by imposing restricted choices for the shape function or the redshift function .
this paper is organized in the following manner : in sec .
[ sec : ii ] , the spacetime metric , the field equations and the mathematics of embedding of these pseudo - spherically symmetric geometries are analyzed in detail . in sec .
[ sec : iii ] , specific solutions are found by considering several equations of state .
we conclude in sec .
[ sec : conclusion ] .
consider the following _ pseudo_-spherically symmetric and static solution @xmath40 where the coordinates @xmath41 and @xmath6 have the following range @xmath42 and @xmath43 .
the @xmath25 coordinate yields the curvature radius of the 2-dimensional pseudo - spherical surfaces that thread the spacetime : @xmath44 , and , hence , is a generalised radial coordinate .
@xmath45 and @xmath46 are arbitrary functions of the radial coordinate @xmath25 . as in the morris - thorne wormhole @xcite
, we denote @xmath45 the redshift function , for it is related to the gravitational redshift , and @xmath46 the shape function , as will be shown below by embedding diagrams , determines the shape of the tunnel ( in analogy to the analysis considered in @xcite ) .
the coordinate @xmath25 is non - monotonic in that it decreases from a constant value @xmath47 to a minimum value @xmath48 , representing the location of the throat of the wormhole , where @xmath49 , and then it increases from @xmath48 back to the value @xmath47 .
note that the condition @xmath50 imposes that @xmath51 , contrary to the morris - thorne counterpart . the einstein field equation , @xmath52 , provides the following stress - energy scenario @xmath53 \label{radialpwh}\,,\\ p_t(r)&=&\frac{1}{8\pi } \left(\frac{b}{r}-1\right)\bigg[\phi ' ' + ( \phi')^2 + \frac{b'r+b - r}{2r(b - r)}\phi ' \nonumber \\ & & + \frac{b'r - b}{2r^2(b - r ) } \bigg ] \label{lateralpwh}\,.\end{aligned}\ ] ] in which @xmath54 is the energy density
, @xmath55 is the radial pressure , @xmath56 is the pressure measured in the tangential directions , orthogonal to the radial direction . assuming that the redshift function is finite @xmath57 , note that the radial pressure is always positive at the throat , i.e , @xmath58 , contrary to the morris - thorne wormhole , where a radial tension at the throat is needed to sustain the wormhole .
in addition to this , we also show below that @xmath59 at the throat , which implies a negative energy density at the throat .
this condition is another significant difference to the morris - thorne wormhole , where the existence of negative energy densities at the throat is not a necessary condition . by taking the derivative with respect to the radial coordinate @xmath25 , of eq .
( [ radialpwh ] ) , and eliminating @xmath60 and @xmath61 , given in eq .
( [ rhowh ] ) and eq .
( [ lateralpwh ] ) , respectively , we obtain the following equation @xmath62 equation ( [ tauderivative ] ) is the relativistic euler equation , or the hydrostatic equation for equilibrium for the material threading the hyperbolic spacetime tunnel .
we now have a system of three equations , namely , eqs . ( [ rhowh])-([lateralpwh ] ) , with five unknown functions of @xmath25 , i.e. , the stress - energy components , @xmath54 , @xmath55 and @xmath56 , and the metric fields , @xmath46 and @xmath45 . to construct specific solutions , we may adopt several approaches , and in this work we shall mainly use the strategy of considering a specific equation of state given by @xmath63 , and restricted choices for @xmath46 or @xmath45 .
one may also impose a specific form for the stress - energy components and through the field equations and the equation of state , @xmath63 , determine @xmath46 and @xmath45 .
we will show below , through the embedding analysis , that @xmath59 , so that throughout this paper we only consider the cases of a negative energy density at the throat , @xmath64 , .
the embedding diagrams are useful to represent the geometry of the tunnelling solution and extract some useful information for the choice of the shape function , @xmath46 @xcite . due to the _ pseudo_-spherically symmetric nature of the problem , without a significant loss of generality consider a slice with the specific value of @xmath65 which imposes @xmath66 .
the respective line element , considering a fixed moment of time , @xmath67 , is given by @xmath68 to visualize this slice , one embeds this metric into three - dimensional euclidean space @xcite , in which the metric can be written in cylindrical coordinates , @xmath69 , as @xmath70 now , in the three - dimensional euclidean space the embedded surface has equation @xmath71 , and thus the metric of the surface can be written as , @xmath72 { \rm d}r^2+r^2 \ , { \rm d}v ^2 \ , .
\label{surface2}\ ] ] comparing eq .
( [ surface2 ] ) with ( [ surface1 ] ) , we have the equation for the embedding surface , given by @xmath73^{1/2 } \label{lift}\,.\ ] ] to be a solution of a spacetime tunnel , the geometry has a minimum radius , @xmath74 , denoted as the throat , at which the embedded surface is vertical , i.e. , @xmath75 , see figure [ fig : embed2 ] .
note also that contrary to the morris - thorne traversable wormhole , the shape function is constrained in the present case . more specifically , taking into account that @xmath51 , then the embedding surface ( [ lift ] ) also imposes the condition @xmath76 .
thus , the shape function is restricted to lie within the following range : @xmath77 .
, @xmath78 ) of a tunnel in spacetime.,width=268 ] in addition to this , to be a solution of a tunnel in spacetime , one needs to impose that the throat flares out , as in figure [ fig : embed2 ] .
mathematically , this flaring - out condition entails that the inverse of the embedding function @xmath79 , must satisfy @xmath80 at or near the throat @xmath81 .
differentiating @xmath82 with respect to @xmath83 , we have @xmath84 at the throat we verify that the shape function satisfies the condition @xmath59 , also contrary to its morris - thorne counterpart .
this condition plays a fundamental role in the analysis of the violation of the energy conditions . in particular
, considering the nec , i.e. , @xmath85 , the term @xmath86 , taking into account the field equations ( [ rhowh ] ) and ( [ radialpwh ] ) , is given by @xmath87 \,.\ ] ] at the throat , we have @xmath88 which implies the important condition @xmath59 at the throat , contrary to the morris - thorne counterpart . as mentioned above , this implies that the energy density , at the throat , is always negative for these exotic hyperbolic , tunneling geometries .
in this section , we find exact solutions by considering several appropriate equations of state , @xmath63 , and by imposing specific shape functions or specific redshift functions . to this effect ,
an adequate shape function is the following case : @xmath89 taking the radial derivative , we have @xmath90 which at the throat implies @xmath91 . from the condition @xmath92 , one has @xmath93 .
thus , we have the following conditions : @xmath94 we verify that one may have an arbitrary large tunnel by imposing the condition @xmath95 .
consider the linear equation of state @xmath96 , in which wormhole solutions were extensively analyzed in ref .
@xcite , and consequently denoted as `` phantom wormhole '' .
now , using the above - mentioned equation of state and taking into account eqs .
( [ rhowh])-([radialpwh ] ) , one deduces the following expression @xmath97 } \ , , \label{diffeq}\ ] ] which is the relationship governing what may be considered the hyperbolic analogue of the `` phantom wormhole '' .
note that the nec violation , and taking into account @xmath64 , imposes that @xmath98 , contrary to its spherically symmetric counterpart . by imposing a specific redshift function ,
one finds the general solution for the shape function @xmath99\,.\ ] ] however , one also deduces an adequate solution by imposing the shape function given by eq .
( [ specform ] ) . using relationship ( [ diffeq ] ) ,
the redshift function is provided by @xmath100+c_1\,,\ ] ] where @xmath101 is an integration constant .
now , to avoid an event horizon at @xmath48 , one needs to impose that @xmath102 , so that the redshift function simplifies to @xmath103 .
one may also further restrict the parameters by considering certain traversability conditions in analogy to the morris - thorne wormhole @xcite .
in particular , it is important that an observer traversing through the hyperbolic tunnel should not be ripped apart by enormous tidal forces .
thus , the tidal traversability condition requires that the tidal accelerations felt by the traveller should not exceed , for instance , the earth s gravitational acceleration , @xmath104 , which is translated by the following inequalities @xmath105 \right | & \leq & g_\oplus \ , , \label{radialtidalconstraint }
\\ \left | \frac{\gamma ^2}{r^2 } \left [ v^2\left ( \frac{b}{r}-b ' \right ) + 2(b - r)\phi ' \right ] \right | & \leq & g_\oplus \ , . \label{lateraltidalconstraint}\end{aligned}\ ] ] we refer the reader to @xcite for details in deducing these relationships . the radial tidal constraint , eq .
( [ radialtidalconstraint ] ) , constrains the redshift function , and the lateral tidal constraint , eq .
( [ lateraltidalconstraint ] ) , constrains the velocity with which observers traverse the tunnel .
these inequalities are particularly simple at the throat , @xmath48 , @xmath106 in particular , considering non - relativistic velocities , i.e. , @xmath107 and @xmath108 , using the shape function given by ( [ specform ] ) and @xmath103 , one readily verifies that the radial tidal constraint is satisfied .
the lateral tidal constraint provides the condition @xmath109 , which essentially depends on the values taken for the parameter @xmath110 . in alternative , by specifying the traversal velocity , we find a restriction placed on @xmath110 given by @xmath111 .
it is also adequate to find solutions by considering a specific redshift function .
consider the redshift function given by @xmath112 .
using expression ( [ diffeq ] ) , one deduces the shape function given by @xmath113 where @xmath114 is an integration constant and , for notational simplicity , the function @xmath115 is defined as @xmath116 and @xmath117 and @xmath118 are the gamma and the incomplete gamma functions , respectively .
note that the constant of integration @xmath114 may be found by taking into account the condition @xmath49 , and is given by the following relationship @xmath119\,.\ ] ] in cosmology , the equation of state representing the generalized chaplygin gas ( gcg ) is given by @xmath120 , where @xmath0 and @xmath121 are positive constants , and the latter lies in the range @xmath122 @xcite .
the particular case of @xmath123 corresponds to the chaplygin gas .
an attractive feature of this model is that at early times the energy density behaves as matter , @xmath124 , where @xmath125 is the scale factor , and as a cosmological constant at a later stage , i.e. , @xmath126 . in a cosmological context , at a late stage dominated by an accelerated expansion of the universe , the cosmological constant may be given by @xmath127 .
this dual behavior is responsible for the interpretation that the gcg model is a candidate of a unified model of dark matter and dark energy @xcite .
it was noted in ref .
@xcite that the gcg equation of state is that of a polytropic gas with a negative polytropic index , and thus suggested that one could analyze astrophysical implications of the model . in this context
, the construction of traversable wormholes , possibly arising from a density fluctuation in the gcg cosmological background was explored in @xcite .
these latter solutions were denoted chaplygin wormholes . as in ref .
@xcite , it was considered that the pressure in the gcg equation of state is a radial pressure , and the tangential pressure can be determined from the einstein equations , in particular , eq .
( [ lateralpwh ] ) . to compare to the spherically symmetric chaplygin wormholes ,
we construct their pseudo - spherically symmetric duplicates .
thus , taking into account the gcg equation of state in the form @xmath128 , and using eqs .
( [ rhowh])-([radialpwh ] ) , we have the following condition @xmath129\big/\left(\frac{b}{r } -1\right ) \ , . \label{eoscondition}\ ] ] solutions of the metric ( [ metricwormhole ] ) , satisfying eq .
( [ eoscondition ] ) may be considered as the analogues of `` chaplygin wormholes '' analyzed in @xcite . as shown above , to be a spacetime tunnel ,
the condition @xmath59 is imposed .
now , using the gcg equation of state , evaluated at the throat , and taking into account eq .
( [ radialpwh ] ) , we verify that the energy density at @xmath48 is given by @xmath130 . finally , using eq .
( [ rhowh ] ) , and the condition @xmath59 , we verify that for these solutions , the following condition is imposed @xmath131 , contrary to its spherically symmetric counterpart @xcite .
we consider next a specific example , by taking into account the shape function given by eq .
( [ specform ] ) .
thus , the differential equation ( [ eoscondition ] ) provides the following redshift function @xmath132 \nonumber \\ & & % -a(8\pi)^{1+\alpha}\left[\delta\left(\frac{r}{r_0}\right)^{\delta-1 } \right ] r^{2\alpha+3 } \times \nonumber \\ % & & \hspace{-1 cm } & & \times { \rm lerchphi}\left[\left(\frac{r}{r_0}\right)^{\delta-1},1 , \frac{3\alpha+2-\alpha\delta}{\delta-1}\right ] \nonumber \\ % & & -r\ln\left[\left(\frac{r}{r_0}\right)^{\delta-1}-1\right ] \bigg\}/\left[(\delta-1)r\right]+c_3\,,\end{aligned}\ ] ] where @xmath133 is a constant of integration ; and lerchphi is the general lerch phi function , defined as @xmath134 .
it is interesting to consider the specific case of @xmath135 and @xmath123 ( this latter value corresponds to the chaplygin gas equation of state ) , which yields the following simpler solution @xmath136 note the existence of an event horizon at the throat , rendering the hyperbolic tunnel non - traversable .
thus , to avoid this we impose the condition @xmath137 , so that the above solution simplifies to @xmath138 yielding a traversable geometry .
another case that lends itself to our analysis , is that of the van der waals quintessence equation of state , which seems to provide a solution to the puzzle of dark energy , without the presence of exotic fluids or modifications of the friedmann equations . in ref .
@xcite , the construction of inhomogeneous compact spheres supported by a van der waals equation of state was explored .
these relativistic stellar configurations were denoted as _ van der waals quintessence stars_. despite the fact that , in a cosmological context , the van der waals fluid is considered homogeneous , inhomogeneities may arise through gravitational instabilities . thus , these solutions may possibly originate from density fluctuations in the cosmological background .
exact solutions were found , and their respective characteristics and physical properties were further explored in ref .
@xcite .
the van der waals equation of state is given by @xmath139 where @xmath140 is the energy density and @xmath141 the pressure of the vdw fluid .
the accelerated and decelerated periods depend on the parameters , @xmath121 , @xmath142 and @xmath143 of the equation of state , and in the limiting case @xmath144 , one recovers the dark energy equation of state , with @xmath145 @xcite . as in the previous exact solutions , we may also consider the counterpart of the static and spherically symmetric van der waals wormhole . thus , taking into account the specific shape function given by eq .
( [ specform ] ) , with the parameter @xmath135 , and considering that @xmath141 is a radial pressure ( see @xcite for details ) , we have the following solution @xmath146+c_4 \,,\end{aligned}\ ] ] where @xmath147 is a constant of integration , and we have considered the following definitions for notational simplicity : @xmath148 note the presence of an event horizon , due to the term @xmath149 .
thus , to avoid this , we impose the following condition @xmath150 so the redshift function reduces to @xmath151 using the simplified relationship ( [ vdwredshift ] ) , one may find a restriction from the lateral tidal acceleration constraint ( [ lateraltidalconstraint2 ] ) , provided by @xmath152 summary , discussion and future outlook --------------------------------------
traversable wormholes possess a peculiar property , namely `` exotic matter '' , involving a stress - energy tensor that violates the null energy condition . in this work ,
we have constructed exact solutions of static and _ pseudo_-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class @xmath0 .
the usual 2-dimensional spheres are replaced by pseudo - spheres , which are still surfaces of revolution around an axis , but now consist of a negative and constant curvature . the physical properties and characteristics of these intriguing
, hyperbolic solutions were further explored , and through the mathematics of embedding it was shown that particular constraints are placed on the shape function , that differ radically from the morris - thorne wormhole .
in particular , it was shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions were also presented by considering several different equations of state , and by imposing restricted choices for the shape function or the redshift function .
standard definitions of a wormhole usually require either asymptotic flatness with a localized bridge to another asymptotically flat region , or the ability to identify a compact region that can usefully be thought of as a throat .
the geometries considered in the current article also exhibit asymptotic flatness and share the possibility of having localized tunnels , with throats , bridging different spacetime regions .
however the spatial hypersurfaces of the asymptotic flat limit of the hyperbolic spacetime under consideration here is peculiar in that it is not euclidean , but rather pseudo - euclidean ( it is a 3-dimensional lorentzian space ) .
hence , rather than denote the exotic geometric objects analyzed in this work as wormholes , we prefer the term hyperbolic tunnels .
they should indeed be understood as a theoretician s probe of the foundations of general relativity , on the same grounds as in the case of the morris - thorne wormhole .
the authors are thankful to reza tavakol for helpful comments , and gratefully acknowledge the grants ptdc / fis/102742/2008 and cern / fp/109381/2009 from fct . 99 m. s. morris and k. s. thorne , `` wormholes in space - time and their use for interstellar travel : a tool for teaching general relativity , '' am .
j. phys .
* 56 * , 395 ( 1988 ) .
m. visser , _ loretzian wormholes : from einstein to hawking _
aip press ( 1995 ) .
g. dotti , j. oliva , and r. troncoso , `` static wormhole solution for higher - dimensional gravity in vacuum , '' phys .
d * 75 * , 024002 ( 2007 ) [ arxiv : hep - th/0607062 ] . l. a. anchordoqui and s. e. p bergliaffa , `` wormhole surgery and cosmology on the brane : the world is not enough , '' phys .
d * 62 * , 067502 ( 2000 ) [ arxiv : gr - qc/0001019 ] ; k. a. bronnikov and s .- w .
kim , `` possible wormholes in a brane world , '' phys .
d * 67 * , 064027 ( 2003 ) [ arxiv : gr - qc/0212112 ] ; m. la camera , `` wormhole solutions in the randall - sundrum scenario , '' phys .
* b573 * , 27 - 32 ( 2003 ) [ arxiv : gr - qc/0306017 ] . f. s. n. lobo , `` general class of braneworld wormholes , '' phys .
rev . * d75 * , 064027 ( 2007 ) [ arxiv : gr - qc/0701133 ]
. k. k. nandi , b. bhattacharjee , s. m. k. alam and j. evans , `` brans - dicke wormholes in the jordan and einstein frames , '' phys .
d * 57 * , 823 ( 1998 ) ; f. s. n. lobo and m. a. oliveira , phys .
d * 81 * , 067501 ( 2010 ) ; f. s. n. lobo and m. a. oliveira , phys .
d * 80 * , 104012 ( 2009 ) .
r. garattini and f. s. n. lobo , `` self sustained phantom wormholes in semi - classical gravity , '' class .
* 24 * , 2401 ( 2007 ) [ arxiv : gr - qc/0701020 ] ; r. garattini and f. s. n. lobo , `` self - sustained traversable wormholes in noncommutative geometry , '' phys .
b * 671 * , 146 ( 2009 ) [ arxiv:0811.0919 [ gr - qc ] ] . c. g. boehmer , t. harko and f. s. n. lobo , `` conformally symmetric traversable wormholes , '' phys .
d * 76 * , 084014 ( 2007 ) [ arxiv:0708.1537 [ gr - qc ] ] ; c. g. boehmer , t. harko and f. s. n. lobo , `` wormhole geometries with conformal motions , '' class .
grav . * 25 * , 075016 ( 2008 ) [ arxiv:0711.2424 [ gr - qc ] ] .
s. sushkov , `` wormholes supported by a phantom energy , '' phys
d * 71 * , 043520 ( 2005 ) [ arxiv : gr - qc/0502084 ] ; f. s. n. lobo , `` phantom energy traversable wormholes , '' phys .
* d71 * , 084011 ( 2005 ) [ arxiv : gr - qc/0502099 ] ; f. s. n. lobo , `` stability of phantom wormholes , '' phys .
* d71 * , 124022 ( 2005 ) [ arxiv : gr - qc/0506001 ]
. f. s. n. lobo , `` chaplygin traversable wormholes , '' phys .
* d73 * , 064028 ( 2006 ) [ arxiv : gr - qc/0511003 ] .
f. s. n. lobo , `` van der waals quintessence stars , '' phys . rev .
d * 75 * , 024023 ( 2007 ) [ arxiv : gr - qc/0610118 ] . f. s. n. lobo , `` general class of wormhole geometries in conformal weyl gravity , '' class .
* 25 * , 175006 ( 2008 ) [ arxiv:0801.4401 [ gr - qc ] ] .
j. p. s. lemos , f. s. n. lobo and s. quinet de oliveira , `` morris - thorne wormholes with a cosmological constant , '' phys .
d * 68 * , 064004 ( 2003 ) [ arxiv : gr - qc/0302049 ] .
f. s. n. lobo , `` exotic solutions in general relativity : traversable wormholes and warp drive spacetimes , '' arxiv:0710.4474 [ gr - qc ] .
h. stephani , d. kramer , m. a. h. maccallum , c. hoenselaers and e. herlt , _ cambridge , uk : univ . pr .
( 2003 ) 701 p _
t. levi - civita , ren .
lincei 27 , 183 ( 1017 ) .
h. weyl , annalen phys .
* 54 * ( 1917 ) 117
. w. b. bonnor and m- a. p.
martins , classical and quantum gravity , 8 , 727 ( 1991 ) .
m. a. p. martins , gen .
28 ( 1996 ) 1309 .
l. a. anchordoqui , j. d. edelstein , c. nunez and g. s. birman , arxiv : gr - qc/9509018 .
j. p. s. lemos and f. s. n. lobo , `` plane symmetric traversable wormholes in an anti - de sitter background , '' phys .
d * 69 * , 104007 ( 2004 ) [ arxiv : gr - qc/0402099 ] . j. p. s. lemos and f. s. n. lobo , `` plane symmetric thin - shell wormholes : solutions and stability , '' phys .
d * 78 * , 044030 ( 2008 ) [ arxiv:0806.4459 [ gr - qc ] ] .
d. hochberg and m. visser , `` the null energy condition in dynamic wormholes , '' phys .
* 81 * , 746 ( 1998 ) [ arxiv : gr - qc/9802048 ] ; d. hochberg and m. visser , `` dynamic wormholes , anti - trapped surfaces , and energy conditions , '' phys .
d * 58 * , 044021 ( 1998 ) [ arxiv : gr - qc/9802046 ] ; s. kar , `` evolving wormholes and the weak energy condition , '' phys .
d * 49 * , 862 ( 1994 ) ; s. kar and d. sahdev , `` evolving lorentzian wormholes , '' phys .
d * 53 * , 722 ( 1996 ) [ arxiv : gr - qc/9506094 ] ; s. w. kim , `` the cosmological model with traversable wormhole , '' phys .
d * 53 * , 6889 ( 1996 ) ; a. v. b. arellano and f. s. n. lobo , `` evolving wormhole geometries within nonlinear electrodynamics , '' class .
* 23 * , 5811 ( 2006 ) [ arxiv : gr - qc/0608003 ] .
m. s. morris , k. s. thorne and u. yurtsever , `` wormholes , time machines and the weak energy condition , '' phy . rev . lett . * 61 * , 1446 ( 1988 ) .
s. capozziello , v. f. cardone , s. carloni , d. de martino , m. falanga , a. troisi and m. bruni , `` constraining van der waals quintessence by observations , '' jcap 0504 , 005 ( 2005 ) , [ arxiv : astro - ph/0410503 ] .
p. j. e. peebles , ap .
j , 557 , 495 ( 2001 ) ; v. g. gurzadyan and a. a. kocharyan , astron . astrophys .
* 493 * ( 2009 ) l61 [ arxiv:0807.1239 [ astro - ph ] ] ; t. clifton , p. g. ferreira and k. land , phys .
* 101 * ( 2008 ) 131302 [ arxiv:0807.1443 [ astro - ph ] ] .[/INST] traversable wormhole are primarily useful as `` gedanken - experiments '' and as a theoretician s probe of the foundations of general relativity . in this work ,
we analyse the possibility of having tunnels in a hyperbolic spacetime .
we obtain exact solutions of static and _ pseudo_-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class @xmath0 .
the physical properties and characteristics of these intriguing solutions are explored , and through the mathematics of embedding it is shown that particular constraints are placed on the shape function , that differ significantly from the morris - thorne wormhole .
in particular , it is shown that the energy density is always negative and the radial pressure is positive , at the throat , contrary to the morris - thorne counterpart .
specific solutions are also presented by considering several equations of state , and by imposing restricted choices for the shape function or the redshift function . </s> |
We've detected that JavaScript is disabled in your browser. Would you like to proceed to legacy Twitter?
Yes ||||| Romney rebukes 'numbskull' advisers
On Twitter, Mitt Romney backs off a feud with Palin:
TIME says unnamed advisors disparaged @SarahPalinUSA. Anonymous numbskulls. Sheβs proven her smarts; theyβve disproven theirs.
The dynamic here: People who want to be the Republican nominee may not expect Palin to run, but they do want her supporters to like them. ||||| From left: Mark Humphrey / AP; Tim Sloan / AFP / Getty Images Minnesota Governor Tim Pawlenty, left, and former governor Mitt Romney
Sarah Palin's recent Web video making a pitch to conservative women may have again shifted the political spotlight to the former governor of Alaska, but more than a half-dozen other GOP hopefuls are toying seriously this summer with a presidential run.
Unlike four years ago, when presidential hopefuls from both parties were already halfway out of the gate, with conspicuous trips to New Hampshire and Iowa, competitive staffing and heavy courting of donors and party chiefs, Republicans are mostly staying true to their public pledges to focus on the midterms. Given the unusually late start, therefore, Palin isn't falling meaningfully behind the organizational efforts of her potential rivals. And after Election Day, when the male candidates begin to seriously consider their options and announce their intentions, they will once again be reminded of Palin's capacity to dominate the stage with her Internet communiquΓ©s, book-promotional efforts and TV appearances. (See photos of Sarah Palin's life since the 2008 election.)
Some of the other would-be candidates and their senior advisers have known Palin over the years, primarily from her days as governor, but most have never met her or had a substantive talk with her. That is a strange situation, to say the least; it forces them to evaluate her without any direct insight into her strengths and weaknesses. But from afar, they increasingly believe she will either become a candidate for President or play a major role in the nominating process. (See photos of the fashion looks of Sarah Palin.)
Still, few express much regard for Palin's ultimate chances. An adviser to Mitt Romney, the former Massachusetts governor and, by traditional standards, the putative 2012 front runner, says of Palin, "She's not a serious human being." Another Romney intimate warns, "If she's standing up there in a debate and the answers are more than 15 seconds long, she's in trouble."
One of the most experienced Republican national political operatives in the country suggests that while Palin might be envied and sleek, she lacks the endurance required for a protracted nomination fight. "She's like a cheetah. She can run really fast but not really long." In the end, according to this school of thought about Palin, she is too polarizing to be seen as likely to beat Barack Obama, and Republicans will be too hungry in 2012 to risk nominating someone who could cost the party the White House Β maybe even losing in a landslide. (See the top 10 postelection Sarah Palin quips.)
If the traditional path to the nomination is still valid in 2012, despite the advent of Facebook, the Tea Party and Twitter, then Romney has as good a chance as anyone else to be the Republican standard bearer; no one is more likely to make the race and show up with the required table stakes. Although he launched a splashy book tour for his own New York Times best-selling tome and has written the occasional newspaper essay assailing Obama, Romney has purposely lain low most of the year. He has stayed off network television and campaigned below the radar for midterm candidates in 20 states, dispensing money to Republicans from his PAC funds, while engaging in intense private courtship of party donors and quiet recruitment of potential backing for his campaign-in-waiting.
Still, there remain serious doubts within the party about Romney's numerous policy flip-flops, remote personal style and support for Obama-style health care reform in Massachusetts during his governorship, as well as concern over potential prejudice against his Mormon faith. Romney advisers claim to be confident that all of those vulnerabilities can be addressed. Most of the candidate's 2008 team plans to sign up for another go-round, and all say they see in their man a more relaxed figure who has well learned the lessons of his second-place finish to McCain. Most important: rather than shape his campaign in an effort to dominate the social-conservative vote in the nomination fight, as he did in 2008, Romney will present himself as an experienced manager of state government with private-sector experience and a rhetorical emphasis on fiscal restraint. That is the background that establishment figures in both parties believe would match up best against the incumbent.
Romney might be following the old-school candidate handbook, but it is Indiana Governor Mitch Daniels who has attracted the backing of many party elders, including George W. Bush and Dick Cheney. Daniels, like Romney, fits the profile that Obama White House advisers and experienced Republicans believe would give the GOP the best chance to beat Obama in 2012. If voters think Washington is broken and spending is out of control, Daniels, like Romney, could effectively run as a Mr. Fix-It, ready to make the hard choices that conservatives believe Obama has dodged.
See TIME's special "After Alaska: Sarah Palin's Year of Living Large." | β Time quoted anonymous advisers to Mitt Romney dissing Sarah Palin in this article yesterday, and today Romney himself came to her defense. On Twitter, no less: "TIME says unnamed advisors disparaged @SarahPalinUSA. Anonymous numbskulls. She's proven her smarts; they've disproven theirs." Consider their feud over, Ben Smith blogs for Politico. "The dynamic here: People who want to be the Republican nominee may not expect Palin to run, but they do want her supporters to like them." | <s>[INST]We've detected that JavaScript is disabled in your browser. Would you like to proceed to legacy Twitter?
Yes ||||| Romney rebukes 'numbskull' advisers
On Twitter, Mitt Romney backs off a feud with Palin:
TIME says unnamed advisors disparaged @SarahPalinUSA. Anonymous numbskulls. Sheβs proven her smarts; theyβve disproven theirs.
The dynamic here: People who want to be the Republican nominee may not expect Palin to run, but they do want her supporters to like them. ||||| From left: Mark Humphrey / AP; Tim Sloan / AFP / Getty Images Minnesota Governor Tim Pawlenty, left, and former governor Mitt Romney
Sarah Palin's recent Web video making a pitch to conservative women may have again shifted the political spotlight to the former governor of Alaska, but more than a half-dozen other GOP hopefuls are toying seriously this summer with a presidential run.
Unlike four years ago, when presidential hopefuls from both parties were already halfway out of the gate, with conspicuous trips to New Hampshire and Iowa, competitive staffing and heavy courting of donors and party chiefs, Republicans are mostly staying true to their public pledges to focus on the midterms. Given the unusually late start, therefore, Palin isn't falling meaningfully behind the organizational efforts of her potential rivals. And after Election Day, when the male candidates begin to seriously consider their options and announce their intentions, they will once again be reminded of Palin's capacity to dominate the stage with her Internet communiquΓ©s, book-promotional efforts and TV appearances. (See photos of Sarah Palin's life since the 2008 election.)
Some of the other would-be candidates and their senior advisers have known Palin over the years, primarily from her days as governor, but most have never met her or had a substantive talk with her. That is a strange situation, to say the least; it forces them to evaluate her without any direct insight into her strengths and weaknesses. But from afar, they increasingly believe she will either become a candidate for President or play a major role in the nominating process. (See photos of the fashion looks of Sarah Palin.)
Still, few express much regard for Palin's ultimate chances. An adviser to Mitt Romney, the former Massachusetts governor and, by traditional standards, the putative 2012 front runner, says of Palin, "She's not a serious human being." Another Romney intimate warns, "If she's standing up there in a debate and the answers are more than 15 seconds long, she's in trouble."
One of the most experienced Republican national political operatives in the country suggests that while Palin might be envied and sleek, she lacks the endurance required for a protracted nomination fight. "She's like a cheetah. She can run really fast but not really long." In the end, according to this school of thought about Palin, she is too polarizing to be seen as likely to beat Barack Obama, and Republicans will be too hungry in 2012 to risk nominating someone who could cost the party the White House Β maybe even losing in a landslide. (See the top 10 postelection Sarah Palin quips.)
If the traditional path to the nomination is still valid in 2012, despite the advent of Facebook, the Tea Party and Twitter, then Romney has as good a chance as anyone else to be the Republican standard bearer; no one is more likely to make the race and show up with the required table stakes. Although he launched a splashy book tour for his own New York Times best-selling tome and has written the occasional newspaper essay assailing Obama, Romney has purposely lain low most of the year. He has stayed off network television and campaigned below the radar for midterm candidates in 20 states, dispensing money to Republicans from his PAC funds, while engaging in intense private courtship of party donors and quiet recruitment of potential backing for his campaign-in-waiting.
Still, there remain serious doubts within the party about Romney's numerous policy flip-flops, remote personal style and support for Obama-style health care reform in Massachusetts during his governorship, as well as concern over potential prejudice against his Mormon faith. Romney advisers claim to be confident that all of those vulnerabilities can be addressed. Most of the candidate's 2008 team plans to sign up for another go-round, and all say they see in their man a more relaxed figure who has well learned the lessons of his second-place finish to McCain. Most important: rather than shape his campaign in an effort to dominate the social-conservative vote in the nomination fight, as he did in 2008, Romney will present himself as an experienced manager of state government with private-sector experience and a rhetorical emphasis on fiscal restraint. That is the background that establishment figures in both parties believe would match up best against the incumbent.
Romney might be following the old-school candidate handbook, but it is Indiana Governor Mitch Daniels who has attracted the backing of many party elders, including George W. Bush and Dick Cheney. Daniels, like Romney, fits the profile that Obama White House advisers and experienced Republicans believe would give the GOP the best chance to beat Obama in 2012. If voters think Washington is broken and spending is out of control, Daniels, like Romney, could effectively run as a Mr. Fix-It, ready to make the hard choices that conservatives believe Obama has dodged.
See TIME's special "After Alaska: Sarah Palin's Year of Living Large."[/INST]β Time quoted anonymous advisers to Mitt Romney dissing Sarah Palin in this article yesterday, and today Romney himself came to her defense. On Twitter, no less: "TIME says unnamed advisors disparaged @SarahPalinUSA. Anonymous numbskulls. She's proven her smarts; they've disproven theirs." Consider their feud over, Ben Smith blogs for Politico. "The dynamic here: People who want to be the Republican nominee may not expect Palin to run, but they do want her supporters to like them."</s> |
the collider detector at fermilab ( cdf ) @xcite operating at the runii tevatron collider is a complex general purpose detector and has many subsystems . for the simulation of each subdetector
, one needs geometry , a digitizer to generate hits , a menu to change digitizer s configuration , and an object to keep a simulated event .
the simulation framework allows to plug these pieces into the existing software system and hides complicated details of their interaction from the user . to achieve these goals ,
the framework design is based upon a mixture of generic programming and object oriented principles .
this mix , rather than a pure object oriented solution , allows the framework to be easily expandable while retaining as much time efficiency as possible .
the cdf detector simulation framework is integrated into an ac++ @xcite application used to process events at the cdf experiment .
the tracking of particles through matter is performed by the geant3 @xcite package .
the cdf software uses the same geometry for event reconstruction and simulation .
the cdf geometry package provides the volume description and geometry tree creation .
the cdf geometry was designed to allow seamless transition to geant4 if desired .
it can be converted to a geant3 or geant4 geometry .
an output event of the simulation contains data in the same format as raw detector data plus monte carlo truth information .
the main simulation executable , cdfsim , allows generation of physics events with different generators such as herwig v6.5 , pythia v6.2 , isajet v7.51 , wgrad , wbbgen , grappa ( grace for @xmath0 ) , vecbos , bgenerator , minbiasgenerator , singleparticle .
les houches accords - a universal interface between matrix element generators and parton shower mc programs - is implemented in herwig , pythia and grappa .
in addition to decay routines internal to each mc generator , particle decays can be simulated by three decay packages - qq v9.1 , evtgen and tauola .
the cdfsim executable may be used with different configurations of subdetectors , different geometry levels , and physics processes depending on desired accuracy versus time efficiency .
the following sub - detectors are simulated : * silicon detectors ( svx , isl ) * central outer tracker ( cot ) * muon systems * time - of - flight system ( tof ) * calorimeters * cherenkov luminosity counters ( clc ) * forward detectors ( miniplug , bsc , rps ) in addition , the cdf geometry contains a detailed description of passive material elements , in particular within the silicon detectors .
the flow diagram in figure [ sim - f1 ] shows how the various generators are incorporated within the ac++ framework .
the ac++ modules are shown in order of execution from top to bottom .
a hepevt common block is used for communication between different generators and decay packages .
the geninputmanager module creates an instance of the cdfrn class which interfaces to the clhep random number generators .
cdf unified the usage of the various random number generators used throughout the simulation code including all generator packages .
this ensures statistically independent production of large monte carlo samples on the cdf production farms .
cdfrn manages the random engines of its clients and allows restoring and saving of current engine configurations .
the geninputmanager and randomgenmanager are followed by a sequence of generator modules and decay modules .
the combination of enabled modules from this sequence is checked at the ac++ framework level for user setup errors .
each module has an interface to the generator / decay package controlling the access to the underlying fortran routines .
the generator or decay package modifies the hepevt common block .
after the event has been processed by all enabled generators and decay packages , the hepevt common block is converted into a persistent object and added to the event record .
after this step , a sequence of generator level filters can be evoked to reject events based on user chosen selection criteria .
finally , the position of the primary interaction vertex is generated by the genprimvert module which allows to take beam line information from the cdf data base depending on a chosen run number .
this information is also added to the event record .
the diagram in figure [ sim - f2 ] shows the relationship between different components of the simulation framework .
the boxes represent ac++ modules in order of execution from top to bottom .
an instance of the cdf geometry is created by the geometrymanager module at the beginning of the job .
the siminitmanager module initializes geant3 , passes the cdf geometry to geant3 , and obtains the information which simulation configuration is used .
the simulationcontrol module instantiates the simulation elements requested by the siminitmanager .
the simulation elements are processed by a simulation base which is implemented as an abstract factory owned by simulationcontrol .
each simulation element consists of a geometry , a configuration menu , a digitizer , and an object to keep the monte carlo event data . during the event processing the simulationcontrol module interacts with geant3 and
passes to it the monte carlo particles from the generator .
inside an active detector volume , geant3 calls a user defined stepping routine and control is passed to the digitizer of the corresponding simulation element .
this action is dispatched by the simulation base .
the digitizer creates hits , depending on the configuration menu , and adds the information to the monte carlo event data .
after tracing of particles with geant3 is finished , the hit information from the mc event data object is converted into the persistent object and added to the event record . at the beginning of each simulation
run , information from the cdf data base may be accessed to obtain noise , calibrations or alignment constants used for the simulation job .
in the following subsections the current status of the simulation of the different subdetectors is described including a discussion of the simulation performance compared to collision data .
the runii silicon detector consists of seven double sided layers and one single sided layer mounted on the beampipe covering a total radial area from 1.5 - 28 cm .
the silicon vertex detector covers the full tevatron luminous region and allows for standalone silicon tracking up to a pseudo - rapidity @xmath1 .
the geometry of the silicon detectors has been implemented in great details in the simulation including passive materials and allows for detector misalignment .
the main purpose of simulating the silicon detector is to describe the charge deposition of traversing tracks on the silicon strips well enough to evaluate silicon tracking performance .
the basic distributions to model are the number of strips included in a charge cluster and the cluster shape .
three charge deposition models ( cdm ) are implemented in the simulation framework : geometric , parametric and physical .
the geometric model is based purely on geometry .
the total amount of charge deposited on a sensor is calculated by geant3 based on an unrestricted landau distribution .
the amount of charge deposited on each strip is a fraction of the entire charge proportional to the path length of the particle in the vicinity of the strip .
the result of this method is that for tracks at a certain incident angle , all strips in the cluster have the same amount of charge deposited .
the cluster length and shape in silicon data is considerably more complicated due to various physics effects such as @xmath2-rays .
the parametric model is based on the physics effects simulated by geant3 .
however , the geant3 results have been parameterized into template distributions to increase the speed of the code .
the important effects that are included in this model are energy deposition using a restricted landau distribution with @xmath2-ray production above a cutoff value , capacitive charge sharing between strips , and noise .
this cdm has been further tuned to data .
the physical model simulates the physics of charge deposition from first principals .
the basic idea is to have the capability of monitoring , predicting and comparing the electrical behavior of the real detector with the expectations from theory .
the physics described by this model includes continuous energy loss using a restricted landau distribution with @xmath2-ray production , convolution of landau fluctuations with a gaussian , magnetic field effects , diffusion of electrons , holes , and noise .
in addition to these effects , the charge inversion of a sensor can be simulated . in figure [ svx - f1 ]
cdf silicon data are compared with simulation using the parametric cdm .
the cluster length ( left ) and cluster profile ( right ) are compared for both the axial side ( top ) and stereo side ( bottom ) of layer1 .
the intrinsic silicon resolution is displayed in figure [ svx - f1 ] .
unbiased axial residuals ( layer2 ) are compared between data and mc .
silicon simulation and data are in good agreement .
cdf s central outer tracker contains 30,200 sense wires arranged in 96 layers combined into four axial and four stereo superlayers .
it also provides d@xmath3/d@xmath4 information for particle identification .
the default drift model used in the cot simulation is based on the garfield package @xcite , a general drift chamber simulation program .
the default garfield parameters are scaled to describe the data .
an example of the performance of cot simulation is displayed in figure [ cot - f1 ] which shows a comparison of track residuals between data and mc .
the track residual is calculated as the hit displacement minus track displacement after applying track quality cuts .
the simulation ( histogram ) is in a good agreement with the data ( points ) .
figure [ cot - f2 ] is a comparison of @xmath5 events generated with pythia to @xmath6 data obtained from an inclusive high @xmath7 muon data set with a muon trigger threshold of 18 gev/@xmath8 .
shown is the distribution of signed track curvature ( charge/@xmath7 ) for primary tracks with impact parameter @xmath9 mm . the data ( points ) are reasonably well described by the monte carlo ( histogram ) . ) for primary tracks with impact parameter @xmath9 mm in @xmath10 data ( points ) and mc events ( histogram).,width=302 ] one of the new devices in the cdfii detector is a time - of - flight system with a resolution of about 100 ps .
it employs 216 three - meter - long scintillator bars with photomultiplier tubes ( pmt s ) at each end located between the outer radius of the cot and the superconducting solenoid ( see figure [ tof - f1 ] ) .
the time - of - flight system is designed for the identification of kaons with a 2@xmath11-separation between @xmath12 and @xmath13 for @xmath14 gev/@xmath8 .
the energy deposition of the incident particle as well as the time at entry and exit points are simulated by geant3 .
this information is translated into tdc and adc counts .
three response parameterizations with different levels of detail in the parameterization are implemented .
one of the models uses a simple analytic form to parametrize time and adc count .
two other models use calibration parameters from tof data .
figure [ tof - f2 ] shows a comparison of the time distribution between collision data and simulated events .
crosses with error bars denote data and the histogram represents the simulation .
the upper ( lower ) plots are a comparison of the time distribution for the east ( west ) channels before ( top ) and after ( bottom ) time - walk correction .
the comparison indicates reasonable agreement between data and simulation allowing for further tuning of the simulation .
there are four muon sub - systems in cdf : central muon detector ( cmu ) , central muon upgrade detector ( cmp ) , central muon extension ( cmx ) , and intermediate muon detector ( imu ) .
figure [ muon - f1 ] shows the location of the muon systems in azimuth @xmath15 and pseudorapidity @xmath16 . and pseudorapidity @xmath16 . , width=302 ] the central calorimeters act as a hadron absorber for the muon detection system .
the cmu consisting of four layers of planar drift chambers is located directly outside the central calorimeters .
the cmu system covers @xmath17 and can be reached by muons with @xmath7 in excess of 1.4 gev/@xmath8 . to reduce the probability of misidentifying penetrating hadrons as muon candidates in the central detector region
, four additional layers of drift chambers ( cmp ) are located behind 0.6 m of steel outside the cmu system . to reach these two detectors , particles produced at the primary interaction vertex
must traverse material totaling 5.4 and 8.4 pion interaction lengths , respectively .
the cmx is located in the pseudorapidity interval @xmath18 extending the polar acceptance of the muon system .
this detector consists of free - standing conical sections at the four corners of the central detector with eight 15 degree wedges .
the imu identifies muons over the rapidity range @xmath19 by a 4-layer barrel of drift tubes ( bmu ) and scintillators ( wsu , bsu , tsu ) .
all muon systems have adc / tdc read - out .
the runii upgrades to the muon system almost double the central muon coverage compared to runi and extent it up to @xmath20 .
the most challenging part in the muon simulation is the description of the complicated geometry of the muon systems , while tuning of the digitization to muon trigger data is straight forward .
special efforts were made to compare simulation to real data with the aim of checking the geometry description .
the study was done for cmp , cmu , and cmx using muons from @xmath5 and @xmath21 in data and simulation .
the overall description of the data is good . as an example of the numerous studies , figure [ muon - f2 ] shows a comparison of simulation and data for the number of muons per stack in the north wall .
the cherenkov luminosity counters @xcite are used to measure the tevatron luminosity at cdf .
the clc acceptance for @xmath0 inelastic processes is estimated from the simulation and adds a major contribution to the luminosity uncertainty .
an excellent clc simulation performance is therefore critical .
the generation and propagation of cherenkov photons is fully simulated by geant3 and then corrected for photo - cathode efficiencies .
the hit count in the clc is sensitive to the material traversed by particles between the interaction point and the clc counters .
therefore , the detector geometry in front of and in the vicinity ( back - scattering ) of the clc needs to be described with high accuracy .
monte carlo and data are in good agreement as can be seen in figure [ clc - f1 ] .
it shows a comparison of amplitude distributions in the three layers of the clc counters .
dots are monte carlo ( pythia ) , the red ( west ) and blue ( east ) histograms are minimum bias data .
the distributions are normalized to the single particle peak .
the resulting uncertainty on the cdf luminosity calculation due to the clc simulation is less than @xmath22 .
the cdf calorimeters @xcite provide separate electromagnetic ( em ) and hadronic ( had ) measurements as shown in figure [ cal - f1 ] .
the central electromagnetic ( cem ) and hadronic ( cha ) calorimeters ( @xmath23 ) employ a projective tower geometry back to the nominal interaction point with a segmentation of @xmath24 .
the sampling medium is composed of scintillators layered with lead absorbers in the electromagnetic calorimeter and steel in the cha .
the energy resolution for the cdf central calorimeter is @xmath25^{1/2}$ ] for electromagnetic showers and @xmath26^{1/2}$ ] for hadrons with @xmath27 measured in gev .
a layer of proportional chambers ( ces ) , with wire and strip readout , is located six radiation lengths deep in the cem calorimeter , approximately near shower maximum for electromagnetic showers .
the ces provides a measurement of electromagnetic shower profiles in both the @xmath15- and @xmath28-directions .
proportional chambers located between the solenoid and the cem comprise the central preradiator detector ( cpr ) , which samples the early development of electromagnetic showers in the material of the solenoid coil , providing information in @xmath29-@xmath15 only .
in addition , the forward calorimeters have been replaced in runii by a new scintillator tile based plug calorimeter which covers the range @xmath30 and gives good electron identification up to @xmath31 .
the plug electromagnetic calorimeter also has fine grained shower profile detectors at electron shower maximum , and preshower pulse height detectors at approximately @xmath32 depth .
the calorimeter cell segmentation is summarized in table [ calseg ] .
a comparison of the central and plug calorimeters is given in table [ plugcomp ] .
l|c|c @xmath33 range & @xmath34 & @xmath35 + 0 . - 1.1 ( 1.2 h ) & @xmath36 & @xmath37 + 1.1 ( 1.2 h ) - 1.8 & @xmath38 & @xmath37 + 1.8 - 2.1 & @xmath38 & @xmath39 + 2.1 - 3.64 & @xmath36 & 0.2 @xmath40 0.6 + l|c|c & central & plug + em : & & + thickness & @xmath41 & @xmath42 + sample ( pb ) & @xmath43 & @xmath44 + sample ( scint . ) & 5 mm & 4.5 mm + wls & sheet & fiber + light yield & @xmath45 pe / gev & @xmath46 pe / gev + sampling res .
& @xmath47 & @xmath48 + stoch
@xmath49 & @xmath50 + shower max .
( cm ) & 1.4@xmath51(1.6 - 2.0 ) z & @xmath52 uv + pre - shower seg .
( cm ) & @xmath53 z & by tower + hadron : & & + thickness & @xmath54 & @xmath55 + sample ( fe)&1 to 2 in . & 2 in . + sample ( scint . ) & 10 mm & 6 mm + wls & finger & fiber + light yield & @xmath56 pe / gev & @xmath57 pe / gev + the main objective for the calorimeter simulation is speed .
the simulation of the cdf calorimeters is based on the gflash @xcite parameterization package interfaced with the geant3 simulation .
the simulation of em and had showers in gflash is initiated when particles undergo inelastic interactions inside the calorimeter volume .
gflash uses a mixture - level geant3 geometry description for the cdf calorimeters .
it handles the spatial distribution of the deposited energy and the energy loss of particles inside the geometry volumes .
the gflash parameters are tuned .
the basic idea of the tuning process is first to bring the response of the electromagnetic calorimeter into agreement with data and then tune the hadron response by adjusting gflash parameters to match pion testbeam data and @xmath58 collision data .
the tuning of gflash is split according to the two sets of parameters that control the fraction of visible energy produced in the active medium , and the energy and depth dependent spatial distribution of the various components of the shower model . to tune em showers , 8 - 227
gev electrons from test beam data were used .
the energy scale and resolution for electrons was verified using @xmath59 .
the hadronic shower shape was tuned to test beam data and minimum bias data .
high @xmath7 tuning was done using high @xmath7 pions test beam data in the energy range 7 - 227 gev ( mainly 57 gev ) for cha and 8 - 227 gev for pha .
the low @xmath7 tuning process uses isolated low @xmath7 tracks from minimum bias data .
the minimum - ionizing - particle ( mip ) peak is measured in the em compartments with pions . the hadronic energy scale in the tuning procedure
is set by the response of 57 gev pions in the central and plug calorimeters .
since there are no test beam data available for the wall calorimeter , the energy scale of wha is set to cha .
once the mip distribution and the hadron energy scale are set , the logarithmic energy dependence of the calorimeter response can be tuned .
finally , for the tuning of the lateral shower profile , tracks obtained from minimum bias events measured in the central part of the cdf detector are used .
the available energy range was 0.5 - 2.5 gev .
distributions between simulation and testbeam as well as collision data for different particle momenta . , width=302 ] figure [ cal - f3 ] ( top ) and 40 gev@xmath60 ( bottom ) muons .
, width=302 ] figure [ cal - f2 ] shows a comparison of the @xmath59 distributions between simulation and testbeam as well as collision data at low @xmath61 for different particle momenta . the calorimeter response in the simulation yields excellent agreement with data . as
another example of calorimeter simulation performance , compares the energy deposition of muons in the cdf calorimeter .
data are shown as dashed lines and mc as solid .
the two top plots show the energy distributions for 4 gev@xmath60 muons from @xmath62 in the hadronic ( left ) and electromagnetic ( right ) calorimeters .
the two bottom plots show these distributions for 40 gev@xmath60 muons from @xmath63 decays . again
, excellent agreement is seen between data and monte carlo .
the gflash based calorimeter simulation is about one hundred times faster then the geant3 shower simulation for a typical top quark event .
we described the overall design of the cdf detector simulation framework which is based on the geant3 package and integrated into an ac++ application used to process events in the cdf experiment .
the cdf simulation framework is shown to be flexible , easily extensible , and efficient .
it is hiding complex infrastructure details from a user and suitable for large scale monte carlo production .
subdetectors are successfully implemented within the cdf simulation framework .
we discussed details of the simulation of specific detector components and in particular the performance of the cdf simulation which shows good agreement with @xmath58 collider data .
a further upgrade to geant4 is possible through the low level api without affecting the client s code .
the cdf detector simulation project is the summary of a collective effort of cdf institutions working on implementing and tuning simulation for the many cdf subdetectors .
the authors would like to thank all the members of the cdf simulation group for their support and fruitful discussion .
this work is supported by the u.s .
department of energy under grant de - fg02 - 91er40682 . | the cdf detector simulation framework is integrated into an ac++ application used to process events in the cdf experiment .
the simulation framework is based on the geant3 package .
it holds the detector element geometry descriptions , allows configuration of digitizers at run - time and manages the generated data .
the design is based on generic programming which allows for easy extension of the simulation framework .
the overall design , details of specific detector components and in particular the performance of the cdf simulation compared to collider data are described . | <s>[INST]the collider detector at fermilab ( cdf ) @xcite operating at the runii tevatron collider is a complex general purpose detector and has many subsystems . for the simulation of each subdetector
, one needs geometry , a digitizer to generate hits , a menu to change digitizer s configuration , and an object to keep a simulated event .
the simulation framework allows to plug these pieces into the existing software system and hides complicated details of their interaction from the user . to achieve these goals ,
the framework design is based upon a mixture of generic programming and object oriented principles .
this mix , rather than a pure object oriented solution , allows the framework to be easily expandable while retaining as much time efficiency as possible .
the cdf detector simulation framework is integrated into an ac++ @xcite application used to process events at the cdf experiment .
the tracking of particles through matter is performed by the geant3 @xcite package .
the cdf software uses the same geometry for event reconstruction and simulation .
the cdf geometry package provides the volume description and geometry tree creation .
the cdf geometry was designed to allow seamless transition to geant4 if desired .
it can be converted to a geant3 or geant4 geometry .
an output event of the simulation contains data in the same format as raw detector data plus monte carlo truth information .
the main simulation executable , cdfsim , allows generation of physics events with different generators such as herwig v6.5 , pythia v6.2 , isajet v7.51 , wgrad , wbbgen , grappa ( grace for @xmath0 ) , vecbos , bgenerator , minbiasgenerator , singleparticle .
les houches accords - a universal interface between matrix element generators and parton shower mc programs - is implemented in herwig , pythia and grappa .
in addition to decay routines internal to each mc generator , particle decays can be simulated by three decay packages - qq v9.1 , evtgen and tauola .
the cdfsim executable may be used with different configurations of subdetectors , different geometry levels , and physics processes depending on desired accuracy versus time efficiency .
the following sub - detectors are simulated : * silicon detectors ( svx , isl ) * central outer tracker ( cot ) * muon systems * time - of - flight system ( tof ) * calorimeters * cherenkov luminosity counters ( clc ) * forward detectors ( miniplug , bsc , rps ) in addition , the cdf geometry contains a detailed description of passive material elements , in particular within the silicon detectors .
the flow diagram in figure [ sim - f1 ] shows how the various generators are incorporated within the ac++ framework .
the ac++ modules are shown in order of execution from top to bottom .
a hepevt common block is used for communication between different generators and decay packages .
the geninputmanager module creates an instance of the cdfrn class which interfaces to the clhep random number generators .
cdf unified the usage of the various random number generators used throughout the simulation code including all generator packages .
this ensures statistically independent production of large monte carlo samples on the cdf production farms .
cdfrn manages the random engines of its clients and allows restoring and saving of current engine configurations .
the geninputmanager and randomgenmanager are followed by a sequence of generator modules and decay modules .
the combination of enabled modules from this sequence is checked at the ac++ framework level for user setup errors .
each module has an interface to the generator / decay package controlling the access to the underlying fortran routines .
the generator or decay package modifies the hepevt common block .
after the event has been processed by all enabled generators and decay packages , the hepevt common block is converted into a persistent object and added to the event record .
after this step , a sequence of generator level filters can be evoked to reject events based on user chosen selection criteria .
finally , the position of the primary interaction vertex is generated by the genprimvert module which allows to take beam line information from the cdf data base depending on a chosen run number .
this information is also added to the event record .
the diagram in figure [ sim - f2 ] shows the relationship between different components of the simulation framework .
the boxes represent ac++ modules in order of execution from top to bottom .
an instance of the cdf geometry is created by the geometrymanager module at the beginning of the job .
the siminitmanager module initializes geant3 , passes the cdf geometry to geant3 , and obtains the information which simulation configuration is used .
the simulationcontrol module instantiates the simulation elements requested by the siminitmanager .
the simulation elements are processed by a simulation base which is implemented as an abstract factory owned by simulationcontrol .
each simulation element consists of a geometry , a configuration menu , a digitizer , and an object to keep the monte carlo event data . during the event processing the simulationcontrol module interacts with geant3 and
passes to it the monte carlo particles from the generator .
inside an active detector volume , geant3 calls a user defined stepping routine and control is passed to the digitizer of the corresponding simulation element .
this action is dispatched by the simulation base .
the digitizer creates hits , depending on the configuration menu , and adds the information to the monte carlo event data .
after tracing of particles with geant3 is finished , the hit information from the mc event data object is converted into the persistent object and added to the event record . at the beginning of each simulation
run , information from the cdf data base may be accessed to obtain noise , calibrations or alignment constants used for the simulation job .
in the following subsections the current status of the simulation of the different subdetectors is described including a discussion of the simulation performance compared to collision data .
the runii silicon detector consists of seven double sided layers and one single sided layer mounted on the beampipe covering a total radial area from 1.5 - 28 cm .
the silicon vertex detector covers the full tevatron luminous region and allows for standalone silicon tracking up to a pseudo - rapidity @xmath1 .
the geometry of the silicon detectors has been implemented in great details in the simulation including passive materials and allows for detector misalignment .
the main purpose of simulating the silicon detector is to describe the charge deposition of traversing tracks on the silicon strips well enough to evaluate silicon tracking performance .
the basic distributions to model are the number of strips included in a charge cluster and the cluster shape .
three charge deposition models ( cdm ) are implemented in the simulation framework : geometric , parametric and physical .
the geometric model is based purely on geometry .
the total amount of charge deposited on a sensor is calculated by geant3 based on an unrestricted landau distribution .
the amount of charge deposited on each strip is a fraction of the entire charge proportional to the path length of the particle in the vicinity of the strip .
the result of this method is that for tracks at a certain incident angle , all strips in the cluster have the same amount of charge deposited .
the cluster length and shape in silicon data is considerably more complicated due to various physics effects such as @xmath2-rays .
the parametric model is based on the physics effects simulated by geant3 .
however , the geant3 results have been parameterized into template distributions to increase the speed of the code .
the important effects that are included in this model are energy deposition using a restricted landau distribution with @xmath2-ray production above a cutoff value , capacitive charge sharing between strips , and noise .
this cdm has been further tuned to data .
the physical model simulates the physics of charge deposition from first principals .
the basic idea is to have the capability of monitoring , predicting and comparing the electrical behavior of the real detector with the expectations from theory .
the physics described by this model includes continuous energy loss using a restricted landau distribution with @xmath2-ray production , convolution of landau fluctuations with a gaussian , magnetic field effects , diffusion of electrons , holes , and noise .
in addition to these effects , the charge inversion of a sensor can be simulated . in figure [ svx - f1 ]
cdf silicon data are compared with simulation using the parametric cdm .
the cluster length ( left ) and cluster profile ( right ) are compared for both the axial side ( top ) and stereo side ( bottom ) of layer1 .
the intrinsic silicon resolution is displayed in figure [ svx - f1 ] .
unbiased axial residuals ( layer2 ) are compared between data and mc .
silicon simulation and data are in good agreement .
cdf s central outer tracker contains 30,200 sense wires arranged in 96 layers combined into four axial and four stereo superlayers .
it also provides d@xmath3/d@xmath4 information for particle identification .
the default drift model used in the cot simulation is based on the garfield package @xcite , a general drift chamber simulation program .
the default garfield parameters are scaled to describe the data .
an example of the performance of cot simulation is displayed in figure [ cot - f1 ] which shows a comparison of track residuals between data and mc .
the track residual is calculated as the hit displacement minus track displacement after applying track quality cuts .
the simulation ( histogram ) is in a good agreement with the data ( points ) .
figure [ cot - f2 ] is a comparison of @xmath5 events generated with pythia to @xmath6 data obtained from an inclusive high @xmath7 muon data set with a muon trigger threshold of 18 gev/@xmath8 .
shown is the distribution of signed track curvature ( charge/@xmath7 ) for primary tracks with impact parameter @xmath9 mm . the data ( points ) are reasonably well described by the monte carlo ( histogram ) . ) for primary tracks with impact parameter @xmath9 mm in @xmath10 data ( points ) and mc events ( histogram).,width=302 ] one of the new devices in the cdfii detector is a time - of - flight system with a resolution of about 100 ps .
it employs 216 three - meter - long scintillator bars with photomultiplier tubes ( pmt s ) at each end located between the outer radius of the cot and the superconducting solenoid ( see figure [ tof - f1 ] ) .
the time - of - flight system is designed for the identification of kaons with a 2@xmath11-separation between @xmath12 and @xmath13 for @xmath14 gev/@xmath8 .
the energy deposition of the incident particle as well as the time at entry and exit points are simulated by geant3 .
this information is translated into tdc and adc counts .
three response parameterizations with different levels of detail in the parameterization are implemented .
one of the models uses a simple analytic form to parametrize time and adc count .
two other models use calibration parameters from tof data .
figure [ tof - f2 ] shows a comparison of the time distribution between collision data and simulated events .
crosses with error bars denote data and the histogram represents the simulation .
the upper ( lower ) plots are a comparison of the time distribution for the east ( west ) channels before ( top ) and after ( bottom ) time - walk correction .
the comparison indicates reasonable agreement between data and simulation allowing for further tuning of the simulation .
there are four muon sub - systems in cdf : central muon detector ( cmu ) , central muon upgrade detector ( cmp ) , central muon extension ( cmx ) , and intermediate muon detector ( imu ) .
figure [ muon - f1 ] shows the location of the muon systems in azimuth @xmath15 and pseudorapidity @xmath16 . and pseudorapidity @xmath16 . , width=302 ] the central calorimeters act as a hadron absorber for the muon detection system .
the cmu consisting of four layers of planar drift chambers is located directly outside the central calorimeters .
the cmu system covers @xmath17 and can be reached by muons with @xmath7 in excess of 1.4 gev/@xmath8 . to reduce the probability of misidentifying penetrating hadrons as muon candidates in the central detector region
, four additional layers of drift chambers ( cmp ) are located behind 0.6 m of steel outside the cmu system . to reach these two detectors , particles produced at the primary interaction vertex
must traverse material totaling 5.4 and 8.4 pion interaction lengths , respectively .
the cmx is located in the pseudorapidity interval @xmath18 extending the polar acceptance of the muon system .
this detector consists of free - standing conical sections at the four corners of the central detector with eight 15 degree wedges .
the imu identifies muons over the rapidity range @xmath19 by a 4-layer barrel of drift tubes ( bmu ) and scintillators ( wsu , bsu , tsu ) .
all muon systems have adc / tdc read - out .
the runii upgrades to the muon system almost double the central muon coverage compared to runi and extent it up to @xmath20 .
the most challenging part in the muon simulation is the description of the complicated geometry of the muon systems , while tuning of the digitization to muon trigger data is straight forward .
special efforts were made to compare simulation to real data with the aim of checking the geometry description .
the study was done for cmp , cmu , and cmx using muons from @xmath5 and @xmath21 in data and simulation .
the overall description of the data is good . as an example of the numerous studies , figure [ muon - f2 ] shows a comparison of simulation and data for the number of muons per stack in the north wall .
the cherenkov luminosity counters @xcite are used to measure the tevatron luminosity at cdf .
the clc acceptance for @xmath0 inelastic processes is estimated from the simulation and adds a major contribution to the luminosity uncertainty .
an excellent clc simulation performance is therefore critical .
the generation and propagation of cherenkov photons is fully simulated by geant3 and then corrected for photo - cathode efficiencies .
the hit count in the clc is sensitive to the material traversed by particles between the interaction point and the clc counters .
therefore , the detector geometry in front of and in the vicinity ( back - scattering ) of the clc needs to be described with high accuracy .
monte carlo and data are in good agreement as can be seen in figure [ clc - f1 ] .
it shows a comparison of amplitude distributions in the three layers of the clc counters .
dots are monte carlo ( pythia ) , the red ( west ) and blue ( east ) histograms are minimum bias data .
the distributions are normalized to the single particle peak .
the resulting uncertainty on the cdf luminosity calculation due to the clc simulation is less than @xmath22 .
the cdf calorimeters @xcite provide separate electromagnetic ( em ) and hadronic ( had ) measurements as shown in figure [ cal - f1 ] .
the central electromagnetic ( cem ) and hadronic ( cha ) calorimeters ( @xmath23 ) employ a projective tower geometry back to the nominal interaction point with a segmentation of @xmath24 .
the sampling medium is composed of scintillators layered with lead absorbers in the electromagnetic calorimeter and steel in the cha .
the energy resolution for the cdf central calorimeter is @xmath25^{1/2}$ ] for electromagnetic showers and @xmath26^{1/2}$ ] for hadrons with @xmath27 measured in gev .
a layer of proportional chambers ( ces ) , with wire and strip readout , is located six radiation lengths deep in the cem calorimeter , approximately near shower maximum for electromagnetic showers .
the ces provides a measurement of electromagnetic shower profiles in both the @xmath15- and @xmath28-directions .
proportional chambers located between the solenoid and the cem comprise the central preradiator detector ( cpr ) , which samples the early development of electromagnetic showers in the material of the solenoid coil , providing information in @xmath29-@xmath15 only .
in addition , the forward calorimeters have been replaced in runii by a new scintillator tile based plug calorimeter which covers the range @xmath30 and gives good electron identification up to @xmath31 .
the plug electromagnetic calorimeter also has fine grained shower profile detectors at electron shower maximum , and preshower pulse height detectors at approximately @xmath32 depth .
the calorimeter cell segmentation is summarized in table [ calseg ] .
a comparison of the central and plug calorimeters is given in table [ plugcomp ] .
l|c|c @xmath33 range & @xmath34 & @xmath35 + 0 . - 1.1 ( 1.2 h ) & @xmath36 & @xmath37 + 1.1 ( 1.2 h ) - 1.8 & @xmath38 & @xmath37 + 1.8 - 2.1 & @xmath38 & @xmath39 + 2.1 - 3.64 & @xmath36 & 0.2 @xmath40 0.6 + l|c|c & central & plug + em : & & + thickness & @xmath41 & @xmath42 + sample ( pb ) & @xmath43 & @xmath44 + sample ( scint . ) & 5 mm & 4.5 mm + wls & sheet & fiber + light yield & @xmath45 pe / gev & @xmath46 pe / gev + sampling res .
& @xmath47 & @xmath48 + stoch
@xmath49 & @xmath50 + shower max .
( cm ) & 1.4@xmath51(1.6 - 2.0 ) z & @xmath52 uv + pre - shower seg .
( cm ) & @xmath53 z & by tower + hadron : & & + thickness & @xmath54 & @xmath55 + sample ( fe)&1 to 2 in . & 2 in . + sample ( scint . ) & 10 mm & 6 mm + wls & finger & fiber + light yield & @xmath56 pe / gev & @xmath57 pe / gev + the main objective for the calorimeter simulation is speed .
the simulation of the cdf calorimeters is based on the gflash @xcite parameterization package interfaced with the geant3 simulation .
the simulation of em and had showers in gflash is initiated when particles undergo inelastic interactions inside the calorimeter volume .
gflash uses a mixture - level geant3 geometry description for the cdf calorimeters .
it handles the spatial distribution of the deposited energy and the energy loss of particles inside the geometry volumes .
the gflash parameters are tuned .
the basic idea of the tuning process is first to bring the response of the electromagnetic calorimeter into agreement with data and then tune the hadron response by adjusting gflash parameters to match pion testbeam data and @xmath58 collision data .
the tuning of gflash is split according to the two sets of parameters that control the fraction of visible energy produced in the active medium , and the energy and depth dependent spatial distribution of the various components of the shower model . to tune em showers , 8 - 227
gev electrons from test beam data were used .
the energy scale and resolution for electrons was verified using @xmath59 .
the hadronic shower shape was tuned to test beam data and minimum bias data .
high @xmath7 tuning was done using high @xmath7 pions test beam data in the energy range 7 - 227 gev ( mainly 57 gev ) for cha and 8 - 227 gev for pha .
the low @xmath7 tuning process uses isolated low @xmath7 tracks from minimum bias data .
the minimum - ionizing - particle ( mip ) peak is measured in the em compartments with pions . the hadronic energy scale in the tuning procedure
is set by the response of 57 gev pions in the central and plug calorimeters .
since there are no test beam data available for the wall calorimeter , the energy scale of wha is set to cha .
once the mip distribution and the hadron energy scale are set , the logarithmic energy dependence of the calorimeter response can be tuned .
finally , for the tuning of the lateral shower profile , tracks obtained from minimum bias events measured in the central part of the cdf detector are used .
the available energy range was 0.5 - 2.5 gev .
distributions between simulation and testbeam as well as collision data for different particle momenta . , width=302 ] figure [ cal - f3 ] ( top ) and 40 gev@xmath60 ( bottom ) muons .
, width=302 ] figure [ cal - f2 ] shows a comparison of the @xmath59 distributions between simulation and testbeam as well as collision data at low @xmath61 for different particle momenta . the calorimeter response in the simulation yields excellent agreement with data . as
another example of calorimeter simulation performance , compares the energy deposition of muons in the cdf calorimeter .
data are shown as dashed lines and mc as solid .
the two top plots show the energy distributions for 4 gev@xmath60 muons from @xmath62 in the hadronic ( left ) and electromagnetic ( right ) calorimeters .
the two bottom plots show these distributions for 40 gev@xmath60 muons from @xmath63 decays . again
, excellent agreement is seen between data and monte carlo .
the gflash based calorimeter simulation is about one hundred times faster then the geant3 shower simulation for a typical top quark event .
we described the overall design of the cdf detector simulation framework which is based on the geant3 package and integrated into an ac++ application used to process events in the cdf experiment .
the cdf simulation framework is shown to be flexible , easily extensible , and efficient .
it is hiding complex infrastructure details from a user and suitable for large scale monte carlo production .
subdetectors are successfully implemented within the cdf simulation framework .
we discussed details of the simulation of specific detector components and in particular the performance of the cdf simulation which shows good agreement with @xmath58 collider data .
a further upgrade to geant4 is possible through the low level api without affecting the client s code .
the cdf detector simulation project is the summary of a collective effort of cdf institutions working on implementing and tuning simulation for the many cdf subdetectors .
the authors would like to thank all the members of the cdf simulation group for their support and fruitful discussion .
this work is supported by the u.s .
department of energy under grant de - fg02 - 91er40682 .[/INST] the cdf detector simulation framework is integrated into an ac++ application used to process events in the cdf experiment .
the simulation framework is based on the geant3 package .
it holds the detector element geometry descriptions , allows configuration of digitizers at run - time and manages the generated data .
the design is based on generic programming which allows for easy extension of the simulation framework .
the overall design , details of specific detector components and in particular the performance of the cdf simulation compared to collider data are described . </s> |
Russian explorers headed home Thursday after proving it is possible to drive from Russia to Canada across the North Pole, in buses with bloated tires over drifting ice, using a pickaxe to clear the way.
Their two-and-a-half-month hitherto untried odyssey aimed to road test the hand-crafted vehicles on ice and water, conduct a few scientific experiments, and bring together a band of adventurers drawn to the vast and pristine Arctic, expedition leader Vassili Ielaguine said during a stopover in Ottawa.
At the "speed of a (farm) tractor" or about 10 kilometers per hour (6.2 miles/h) and carrying three tonnes of donated diesel fuel and supplies, they traveled more than 4,000 kilometers (2,485 miles) in 70 days from the Russian archipelago Severnaya Zemlya (or Earth North), after being dropped off by a Russian icebreaker, to the pole and then to Resolute Bay in Canada's far north.
Their two bright red vehicles were built around two-liter Toyota diesel engines and using old parts from prototypes that some of the team had used back in 2009 to drive from Russia to the North Pole and double back.
During this trip, the seven men came across a handful of polar bears, which "did not appear to be aggressive," said Ielaguine, as well as seals. But it was a group of mustachioed walruses on the Canadian side that left the biggest impression on the wary travelers.
They also had an opportunity to see "exceptional aurora borealis light up the entire sky," he said.
At one point "Heaven helped us," said Ielaguine, describing coming upon a wide chasm that appeared too dangerous to cross and almost forced them to take a long detour, risking that they might run out of fuel.
Suddenly the ice floes shifted beneath their feet and closed over the open waters ahead of them. They kicked the vans in gear and drove, but barely two minutes after crossing to the other side the gap opened up again.
Although the vehicles' fat tires would keep them afloat, Ielaguine said: "We don't like falling in the water, because you have to clean the suspension, which gets completely covered in ice."
In such emergencies, a rope is tied between the vehicles allowing one van to drag the other out of danger.
Similarly, the trekkers never walked alone on the ice because falling through a patch of thin ice into the icy waters of the Arctic Ocean wearing heavy parkas would mean certain death, as they would be unable to climb out before paralyzing hypothermia set in.
In Resolute Bay, they were given a warm welcome, and a garage to store their trucks while the team flew home to rest and prepare for another leg of their grand adventure.
The vehicles are to be retrieved next February and driven West across the Bering Straight and back to Russia.
Dubbed "Iemelia" after a lazy character in a Russian fable who travels on a magic stove the vehicles could eventually see commercial success. When he arrives in Moscow, Ielaguine said he is meeting with investors interested in manufacturing them.
Explore further: Explorer Amundsen's polar ship to return to Norway ||||| A group of Russian explorers left Russia in February to drive to the North Pole and then on to Resolute, Nunavut, in specialized amphibious trucks. The group says the trucks are designed to minimize damage to the tundra and ice in the Arctic. (Yemelya)
A group of Russian explorers have driven across the North Pole and are heading to Resolute, Nunavut, in specialized amphibious trucks.
The expedition sponsored by the Russian Geographic Society left Russiaβs northern coast in February in two of the large trucks. They reached the geographical North Pole on April 6 and expect to reach the Nunavut hamlet in June.
The trip is part of the Marine Live-Ice Automobile Expedition.
βThese are specially designed vehicles made to travel over ice and open water with an extra light aluminum body, six tires per vehicle with low pressure intended to cause little damage to the tundra,β said Natalia Babikova, who is co-ordinating the expedition from Moscow.
Babikova said it's the second time in the history of the worldβs automobile industry that cars have reached that area.
The vehicles are powered and heated by diesel fuel.
Now, the team is on its way to Ward Hunt Island, then on to Resolute where residents are used to seeing all sorts of adventurers in the community.
"Good for them! I mean, they have a new technology that they're test-proofing over the North Pole, which is probably the toughest ice there can be," said resident Wayne Davidson.
"It is a wonderful achievement in engineering and also a wonderful achievement in daring."
The Russians plan to leave the vehicles in Resolute until next winter. They will then try to get from there to the Bering Sea, and then back to Russia. | β Talk about a road trip: Russian explorers spent the past two-and-a-half months driving from Russia to Canada via the North Pole. But instead of car bingo and the alphabet game, they passed their time clearing the route with a pickaxe, gazing upon the aurora borealis, and spotting the occasional polar bear. The 2,485-mile journey from Russian archipelago Severnaya Zemlya to Resolute Bay in Canada's far north took 70 days at a speed of about 6.2mphβabout farm-tractor speed, PhysOrg reports. The team flew back to Russia on Thursday, leaving their vehicles in a garage; they'll be driven back to Russia across the Bering Straight next February. Speaking of those vehicles, they're pretty bizarre: CBC describes them as "amphibious trucks," while PhysOrg calls them "buses with bloated tires." They were able to carry the explorers over drifting ice floes and would have kept them afloat, had they fallen into the Arctic Ocean (which they almost did at one point). The expedition leader is planning to meet with investors who are interested in manufacturing them, which should perhaps concern Canada: As Next Big Future points out in its headline, "Russians have proven a land invasion of Canada is feasible by driving over the North Pole." | <s>[INST]Russian explorers headed home Thursday after proving it is possible to drive from Russia to Canada across the North Pole, in buses with bloated tires over drifting ice, using a pickaxe to clear the way.
Their two-and-a-half-month hitherto untried odyssey aimed to road test the hand-crafted vehicles on ice and water, conduct a few scientific experiments, and bring together a band of adventurers drawn to the vast and pristine Arctic, expedition leader Vassili Ielaguine said during a stopover in Ottawa.
At the "speed of a (farm) tractor" or about 10 kilometers per hour (6.2 miles/h) and carrying three tonnes of donated diesel fuel and supplies, they traveled more than 4,000 kilometers (2,485 miles) in 70 days from the Russian archipelago Severnaya Zemlya (or Earth North), after being dropped off by a Russian icebreaker, to the pole and then to Resolute Bay in Canada's far north.
Their two bright red vehicles were built around two-liter Toyota diesel engines and using old parts from prototypes that some of the team had used back in 2009 to drive from Russia to the North Pole and double back.
During this trip, the seven men came across a handful of polar bears, which "did not appear to be aggressive," said Ielaguine, as well as seals. But it was a group of mustachioed walruses on the Canadian side that left the biggest impression on the wary travelers.
They also had an opportunity to see "exceptional aurora borealis light up the entire sky," he said.
At one point "Heaven helped us," said Ielaguine, describing coming upon a wide chasm that appeared too dangerous to cross and almost forced them to take a long detour, risking that they might run out of fuel.
Suddenly the ice floes shifted beneath their feet and closed over the open waters ahead of them. They kicked the vans in gear and drove, but barely two minutes after crossing to the other side the gap opened up again.
Although the vehicles' fat tires would keep them afloat, Ielaguine said: "We don't like falling in the water, because you have to clean the suspension, which gets completely covered in ice."
In such emergencies, a rope is tied between the vehicles allowing one van to drag the other out of danger.
Similarly, the trekkers never walked alone on the ice because falling through a patch of thin ice into the icy waters of the Arctic Ocean wearing heavy parkas would mean certain death, as they would be unable to climb out before paralyzing hypothermia set in.
In Resolute Bay, they were given a warm welcome, and a garage to store their trucks while the team flew home to rest and prepare for another leg of their grand adventure.
The vehicles are to be retrieved next February and driven West across the Bering Straight and back to Russia.
Dubbed "Iemelia" after a lazy character in a Russian fable who travels on a magic stove the vehicles could eventually see commercial success. When he arrives in Moscow, Ielaguine said he is meeting with investors interested in manufacturing them.
Explore further: Explorer Amundsen's polar ship to return to Norway ||||| A group of Russian explorers left Russia in February to drive to the North Pole and then on to Resolute, Nunavut, in specialized amphibious trucks. The group says the trucks are designed to minimize damage to the tundra and ice in the Arctic. (Yemelya)
A group of Russian explorers have driven across the North Pole and are heading to Resolute, Nunavut, in specialized amphibious trucks.
The expedition sponsored by the Russian Geographic Society left Russiaβs northern coast in February in two of the large trucks. They reached the geographical North Pole on April 6 and expect to reach the Nunavut hamlet in June.
The trip is part of the Marine Live-Ice Automobile Expedition.
βThese are specially designed vehicles made to travel over ice and open water with an extra light aluminum body, six tires per vehicle with low pressure intended to cause little damage to the tundra,β said Natalia Babikova, who is co-ordinating the expedition from Moscow.
Babikova said it's the second time in the history of the worldβs automobile industry that cars have reached that area.
The vehicles are powered and heated by diesel fuel.
Now, the team is on its way to Ward Hunt Island, then on to Resolute where residents are used to seeing all sorts of adventurers in the community.
"Good for them! I mean, they have a new technology that they're test-proofing over the North Pole, which is probably the toughest ice there can be," said resident Wayne Davidson.
"It is a wonderful achievement in engineering and also a wonderful achievement in daring."
The Russians plan to leave the vehicles in Resolute until next winter. They will then try to get from there to the Bering Sea, and then back to Russia.[/INST]β Talk about a road trip: Russian explorers spent the past two-and-a-half months driving from Russia to Canada via the North Pole. But instead of car bingo and the alphabet game, they passed their time clearing the route with a pickaxe, gazing upon the aurora borealis, and spotting the occasional polar bear. The 2,485-mile journey from Russian archipelago Severnaya Zemlya to Resolute Bay in Canada's far north took 70 days at a speed of about 6.2mphβabout farm-tractor speed, PhysOrg reports. The team flew back to Russia on Thursday, leaving their vehicles in a garage; they'll be driven back to Russia across the Bering Straight next February. Speaking of those vehicles, they're pretty bizarre: CBC describes them as "amphibious trucks," while PhysOrg calls them "buses with bloated tires." They were able to carry the explorers over drifting ice floes and would have kept them afloat, had they fallen into the Arctic Ocean (which they almost did at one point). The expedition leader is planning to meet with investors who are interested in manufacturing them, which should perhaps concern Canada: As Next Big Future points out in its headline, "Russians have proven a land invasion of Canada is feasible by driving over the North Pole."</s> |
the standard model ( sm ) of electroweak interactions has been tested to high accuracy with the precision experiments at the z - resonance at lep @xcite . with these experiments
the sm in its perturbative formulation has been tested also beyond the tree approximation .
for this reason an extensive calculation of 1-loop processes and also 2-loop processes has been carried out in the past years ( see @xcite for a review and references therein ) and compared to the experimental results .
a careful analysis shows that the theoretical predictions and the experiments are in excellent agreement with each other @xcite .
a necessary prerequisite for carrying out precision tests of the sm is the consistent mathematical and physical formulation in the framework of its perturbative construction . due to the fact that parity is broken by weak interactions ,
higher orders in quantum field theory can not be treated by referring to an invariant regularization scheme . in ref .
@xcite we have carried out the renormalization of the electroweak sm to all orders by applying the algebraic method .
it allows to prove renormalizability in a scheme - independent way just by using general properties of renormalized perturbation theory ( see @xcite for a review to the algebraic method ) . the algebraic method has been first applied to gauge theories with simple or semisimple groups @xcite , later on it has been extended to gauge theories with non - semisimple groups with several @xmath0-factors @xcite .
the results obtained therein are only partially applicable to the sm due to the fact , that all particles are assumed to be massive , but it gives a complete discussion of anomalies in gauge theories with non - semisimple groups . in the section 2 of the paper we outline the procedure of algebraic renormalization and
present the basic ingredients of the method , scheme dependence of counterterms and the quantum action principle . in section 3
we discuss the characterization of invariant counterterms to the sm green functions .
there we direct our attention to three important results : the construction of the abelian ward identity , the definition of symmetry operators in the on - shell schemes and consequences of rigid symmetry in the gauge - fixing and ghost sector of the action .
starting point for the construction is the brs - symmetric classical action of the electroweak sm .
( we do not include strong interactions in the present analysis , but assume the quarks to be color vectors of global @xmath1 . )
it consists of the @xmath2-gauge invariant action @xmath3 and the brs - invariant gauge - fixing @xmath4 and ghost action @xmath5 .
@xmath6 here @xmath7 denotes the nilpotent brs - transformations ( @xmath8 ) .
the glashow - salam - weinberg action @xmath3 includes the massive gauge bosons of weak interactions , @xmath9 , and the massless photon @xmath10 , the leptons @xmath11 , the quarks @xmath12 , the physical higgs @xmath13 and the unphysical scalar bosons @xmath14 and @xmath15 .
masses of gauge bosons , fermions and the higgs are generated by spontaneous breaking of gauge symmetry to the electromagnetic subgroup .
we do not consider mixing of different fermion families and assume cp - invariance throughout .
free parameters of the model are the masses and one coupling constant , which in the qed - like parametrization is chosen to be the electromagnetic coupling . for ensuring renormalizability and off - shell infrared existence by power counting we choose the restricted linear @xmath16 gauge in the tree approximation .
it contains two gauge parameters @xmath17 and @xmath18 and turns out to be compatible with rigid symmetry : @xmath19 the gauge - fixing action breaks gauge invariance . introducing the faddeev - popov ghosts @xmath20 and the corresponding antighosts @xmath21 the gauge - fixing action is complemented by the ghost action in such a way that the complete action is brs - invariant . in perturbation
theory the green functions are formally defined from the classical action by the gell - mann - low formula and by wick s theorem or equivalently by the feynman diagrams and feynman rules .
( feynman rules of the sm are given in several publications , see e.g. @xcite . )
the loop corrections to green functions are plagued with divergencies , which have to be consistently removed in the procedure of renormalization .
then one has to prove that the symmetries of the tree approximation can be established in the course of renormalization and that these symmetries uniquely fix the green functions , if one imposes a finite number of normalization conditions . for renormalization
only the 1pi green functions are relevant , which are summarized in the functional of 1pi green functions @xmath22 .
the lowest order of @xmath22 is the classical action , @xmath23 . for proceeding to higher orders the symmetry transformations have to be rewritten into functional form .
the functional form of brs - symmetry is the slavnov - taylor ( st ) identity . by introducing an external scalar doublet @xmath24
we are able to maintain rigid @xmath25-symmetry and spontaneously broken @xmath0-gauge symmetry for the special choice of gauge parameters ( [ f_a ] ) and to establish the respective ward identities : @xmath26 the local ward identity is crucial for the unique construction of higher orders .
the symmetry operators depend explicitly on the free parameters of the theory . with the gauge choice ( [ f_a ] ) they depend on the mass ratio @xmath27 in the tree approximation @xcite .
we now assume that we have already calculated the 1-loop order in a specific scheme of renormalization and denote the finite green functions by @xmath28 .
regardless of special properties of the scheme we can apply the action principle in its quantized version to the green functions @xcite , in order to get information of the possible breakings at 1-loop order . applied to the symmetries of the tree approximation it tells that in the 1-loop order the symmetries are at most broken by _
field polynomials with a definite uv and ir degree of power counting . taking the most important example , the st identity
, it reads @xmath29 the breakings include in a first step all local field polynomials compatible with the uv and ir dimension .
they are restricted if one takes into account that the renormalization schemes do not break global symmetries such as charge conservation , and discrete symmetries such as cp - invariance .
for example @xmath30 has faddeev - popov charge 1 , is neutral with respect to electromagnetic charge and is even with respect to cp - transformations . in the next step
we have to prove that the breakings of the st identity can be absorbed into counterterms to the classical action : for doing this one has to note that green functions , when they are computed in a specific scheme , are only defined up to local counterterms .
these counterterms are restricted by the global symmetries and the discrete symmetries of the sm . in order to maintain the properties of power counting renormalizability
their uv and ir degree has to agree with the one of the classical action @xmath31 combining both the quantum action principle ( [ qap ] ) and the scheme dependence of counterterms ( [ ct ] ) we get @xmath32 and a similar expression for rigid ward identities
. eventually we have to prove that breakings of the st identity can be written as @xmath33-variations of counterterms to the classical action , i.e. @xmath34 up to this point we did only use properties of renormalized perturbation theory .
finally one has to characterize both the counterterms and the breakings in terms of the symmetries : first , counterterms have to be decomposed into invariant and non - invariant counterterms @xmath35 the coefficients of invariants are not determined by the symmetries but have to be fixed by normalization conditions .
second , one restricts the breakings by using algebraic properties of the symmetry operators , as e.g. nilpotency of the st operator : @xmath36 applying the @xmath33-operator to eq .
( [ st1loop ] ) one obtains from ( [ brsnil ] ) that @xmath37 is @xmath33-invariant @xmath38 @xmath39 is invariant under the @xmath33-transformation whenever it is a variation of the counterterms , i.e. if eq .
( [ brsct ] ) is fulfilled .
if there is only one field polynomial which is @xmath33-invariant , but not a variation of counterterms , one has an anomaly , and symmetries can not be established by adjusting counterterms . in this way
one has achieved an algebraic characterization of scheme dependent breakings and anomalies .
the proof to all orders proceeds by induction , passing through the same steps as above from order @xmath40 to @xmath41 in the sm the algebraic characterization of breakings can be proven to be the same as in the symmetric @xmath2 theory and does not depend on the specific form of spontaneous symmetry breaking .
in @xcite it has been shown that there are only the well - known adler - bardeen anomalies .
their coefficients vanish in the sm , if we include lepton and colored quark doublets .
the difficult and indeed specific part is the classification of invariant counterterms and of appropriate normalization conditions . here mixing effects between neutral massless / massive fields have to be carefully analysed from the point of view of off - shell infrared existence . in the next section we present three important results of this analysis .
invariant counterterms are determined if one solves the st identity and the ward identities for the most general action compatible with power counting renormalizability : @xmath42 in the sm one finds as solution an action , which contains in addition to the free parameters of the tree approximation two further undetermined couplings in each fermion family .
they are couplings of abelian currents to the abelian component of vector fields and are not determined by the st identity , but have to be fixed by a local gauge ward identity .
( in @xcite these couplings are fixed by an antighost equation . from there
the local ward identity is defined by using the consistency with the st identity . ) in the sm classically we have three types of abelian currents , the currents of lepton and quark family number conservation , @xmath43 and @xmath44 , and the sum of the electromagnetic and neutral current of weak interactions .
being more specific we find as a special solution of eq .
( [ gagencl ] ) @xmath45 where @xmath46 is the classical action ( [ gacl ] ) . in order to identify the action ( [ gacl ] ) as solution of symmetry identities , one has to impose the local @xmath0-ward identity as given in ( [ funid ] ) .
the abelian local ward operator is to all orders fixed to be the sum of the non - integrated neutral @xmath25 ward operator and of the electromagnetic charge operator @xmath47 = 0\ ] ] in fact the local abelian ward identity ( [ funid ] ) with the abelian operator ( [ w4q ] ) is the functional generalization of the classical gell - mann - nishijima relation .
we want to point out that the abelian ward identity has to be characterized to be abelian by its commutation relations with ward operators of rigid @xmath25-symmetry . for this reason it is crucial to establish rigid symmetry in addition to the st identity .
we did already mention that the symmetry operators depend explicitly on the mass ratio @xmath48 in the tree approximation .
solving eq .
( [ gagencl ] ) by inserting the tree operators we are not able to fix all mass parameters by normalization conditions and especially we are not able to diagonalize the mass matrix of neutral vector bosons on - shell at the same time : @xmath49 mass diagonalization at @xmath50 is crucial for obtaining infrared finite expression for off - shell green functions and are implemented in the bphzl scheme by the ir power counting . in order to fulfill the normalization conditions ( [ onshell ] ) one has to introduce a non - diagonal wave - function renormalization for the neutral vector bosons .
if we carry out such field redefinitions also in the symmetry operators , the symmetry operators are renormalized and get higher order corrections , i.e. @xmath51 these corrections are in agreement with the algebra .
for this reason one can not fix the symmetry operators to their tree form but one has to take the most general ones compatible with the algebraic properties of the tree approximation ( see ( [ brsnil ] ) ) , when one solves eqs .
( [ gagencl ] ) .
then one has indeed the same number of free parameters as normalization conditions even in the complete on - shell scheme . requiring rigid symmetry
has important restrictions on the gauge fixing .
as we have already mentioned the choice ( [ f_a ] ) is covariant under rigid @xmath2-transformations and can be constructed as being invariant under rigid transformation by introducing the external scalar field @xmath24 . in this special gauge
the ghost mass ratio is equivalent to the vector mass ratio , @xmath52 but it turns out to be differently renormalized from the vector mass ratio in higher orders .
for this reason we have to introduce the ghost mass ratio as an independent parameter of the model .
however , if one takes arbitrary gauge parameters @xmath53 and @xmath54 in the in the gauge - fixing functions @xmath55 and @xmath56 without changing @xmath57 ( [ f_a ] ) , one breaks rigid symmetry by the gauge fixing and can not derive ward identities of rigid and local @xmath0 symmetry .
consequently we loose the control about the gauged abelian currents in higher orders , namely we are not able to identify the electromagnetic current by means of a local ward identity . taking for the gauge fixing @xmath58 the gauge fixing is compatible with rigid symmetry and allows at the same time to treat the ghost mass ratio as an independent parameter of the theory . in order to avoid
non - diagonal ghost mass terms brs - transformations have to be generalized to @xmath59 and @xmath60 differs from the unit matrix by @xmath61 with this modification the ghost mass matrix is diagonal , and can be achieved to be diagonal on - shell in higher orders by adjusting the free parameters in the matrix @xmath62
. then also the faddeev - popov part is free from off - shell infrared divergencies .
contrary to simple gauge groups we have introduced not only independent wave function renormalizations for ghosts and vectors , but have also an independent wave function renormalization for antighosts . | the algebraic method of renormalization is applied to the standard model of electroweak interactions .
we present the most important modifications compared to theories with simple groups .
bn - th-98 - 15 + hep - th/9807102 + july 1998 + + + * elisabeth kraus * + [ 3 mm ] _ physikalisches
institut , universitt bonn _
+ _ nuallee 12 , d53115 bonn , germany _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the algebraic method of renormalization is applied to the standard model of electroweak interactions .
we present the most important modifications compared to theories with simple groups . _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | <s>[INST]the standard model ( sm ) of electroweak interactions has been tested to high accuracy with the precision experiments at the z - resonance at lep @xcite . with these experiments
the sm in its perturbative formulation has been tested also beyond the tree approximation .
for this reason an extensive calculation of 1-loop processes and also 2-loop processes has been carried out in the past years ( see @xcite for a review and references therein ) and compared to the experimental results .
a careful analysis shows that the theoretical predictions and the experiments are in excellent agreement with each other @xcite .
a necessary prerequisite for carrying out precision tests of the sm is the consistent mathematical and physical formulation in the framework of its perturbative construction . due to the fact that parity is broken by weak interactions ,
higher orders in quantum field theory can not be treated by referring to an invariant regularization scheme . in ref .
@xcite we have carried out the renormalization of the electroweak sm to all orders by applying the algebraic method .
it allows to prove renormalizability in a scheme - independent way just by using general properties of renormalized perturbation theory ( see @xcite for a review to the algebraic method ) . the algebraic method has been first applied to gauge theories with simple or semisimple groups @xcite , later on it has been extended to gauge theories with non - semisimple groups with several @xmath0-factors @xcite .
the results obtained therein are only partially applicable to the sm due to the fact , that all particles are assumed to be massive , but it gives a complete discussion of anomalies in gauge theories with non - semisimple groups . in the section 2 of the paper we outline the procedure of algebraic renormalization and
present the basic ingredients of the method , scheme dependence of counterterms and the quantum action principle . in section 3
we discuss the characterization of invariant counterterms to the sm green functions .
there we direct our attention to three important results : the construction of the abelian ward identity , the definition of symmetry operators in the on - shell schemes and consequences of rigid symmetry in the gauge - fixing and ghost sector of the action .
starting point for the construction is the brs - symmetric classical action of the electroweak sm .
( we do not include strong interactions in the present analysis , but assume the quarks to be color vectors of global @xmath1 . )
it consists of the @xmath2-gauge invariant action @xmath3 and the brs - invariant gauge - fixing @xmath4 and ghost action @xmath5 .
@xmath6 here @xmath7 denotes the nilpotent brs - transformations ( @xmath8 ) .
the glashow - salam - weinberg action @xmath3 includes the massive gauge bosons of weak interactions , @xmath9 , and the massless photon @xmath10 , the leptons @xmath11 , the quarks @xmath12 , the physical higgs @xmath13 and the unphysical scalar bosons @xmath14 and @xmath15 .
masses of gauge bosons , fermions and the higgs are generated by spontaneous breaking of gauge symmetry to the electromagnetic subgroup .
we do not consider mixing of different fermion families and assume cp - invariance throughout .
free parameters of the model are the masses and one coupling constant , which in the qed - like parametrization is chosen to be the electromagnetic coupling . for ensuring renormalizability and off - shell infrared existence by power counting we choose the restricted linear @xmath16 gauge in the tree approximation .
it contains two gauge parameters @xmath17 and @xmath18 and turns out to be compatible with rigid symmetry : @xmath19 the gauge - fixing action breaks gauge invariance . introducing the faddeev - popov ghosts @xmath20 and the corresponding antighosts @xmath21 the gauge - fixing action is complemented by the ghost action in such a way that the complete action is brs - invariant . in perturbation
theory the green functions are formally defined from the classical action by the gell - mann - low formula and by wick s theorem or equivalently by the feynman diagrams and feynman rules .
( feynman rules of the sm are given in several publications , see e.g. @xcite . )
the loop corrections to green functions are plagued with divergencies , which have to be consistently removed in the procedure of renormalization .
then one has to prove that the symmetries of the tree approximation can be established in the course of renormalization and that these symmetries uniquely fix the green functions , if one imposes a finite number of normalization conditions . for renormalization
only the 1pi green functions are relevant , which are summarized in the functional of 1pi green functions @xmath22 .
the lowest order of @xmath22 is the classical action , @xmath23 . for proceeding to higher orders the symmetry transformations have to be rewritten into functional form .
the functional form of brs - symmetry is the slavnov - taylor ( st ) identity . by introducing an external scalar doublet @xmath24
we are able to maintain rigid @xmath25-symmetry and spontaneously broken @xmath0-gauge symmetry for the special choice of gauge parameters ( [ f_a ] ) and to establish the respective ward identities : @xmath26 the local ward identity is crucial for the unique construction of higher orders .
the symmetry operators depend explicitly on the free parameters of the theory . with the gauge choice ( [ f_a ] ) they depend on the mass ratio @xmath27 in the tree approximation @xcite .
we now assume that we have already calculated the 1-loop order in a specific scheme of renormalization and denote the finite green functions by @xmath28 .
regardless of special properties of the scheme we can apply the action principle in its quantized version to the green functions @xcite , in order to get information of the possible breakings at 1-loop order . applied to the symmetries of the tree approximation it tells that in the 1-loop order the symmetries are at most broken by _
field polynomials with a definite uv and ir degree of power counting . taking the most important example , the st identity
, it reads @xmath29 the breakings include in a first step all local field polynomials compatible with the uv and ir dimension .
they are restricted if one takes into account that the renormalization schemes do not break global symmetries such as charge conservation , and discrete symmetries such as cp - invariance .
for example @xmath30 has faddeev - popov charge 1 , is neutral with respect to electromagnetic charge and is even with respect to cp - transformations . in the next step
we have to prove that the breakings of the st identity can be absorbed into counterterms to the classical action : for doing this one has to note that green functions , when they are computed in a specific scheme , are only defined up to local counterterms .
these counterterms are restricted by the global symmetries and the discrete symmetries of the sm . in order to maintain the properties of power counting renormalizability
their uv and ir degree has to agree with the one of the classical action @xmath31 combining both the quantum action principle ( [ qap ] ) and the scheme dependence of counterterms ( [ ct ] ) we get @xmath32 and a similar expression for rigid ward identities
. eventually we have to prove that breakings of the st identity can be written as @xmath33-variations of counterterms to the classical action , i.e. @xmath34 up to this point we did only use properties of renormalized perturbation theory .
finally one has to characterize both the counterterms and the breakings in terms of the symmetries : first , counterterms have to be decomposed into invariant and non - invariant counterterms @xmath35 the coefficients of invariants are not determined by the symmetries but have to be fixed by normalization conditions .
second , one restricts the breakings by using algebraic properties of the symmetry operators , as e.g. nilpotency of the st operator : @xmath36 applying the @xmath33-operator to eq .
( [ st1loop ] ) one obtains from ( [ brsnil ] ) that @xmath37 is @xmath33-invariant @xmath38 @xmath39 is invariant under the @xmath33-transformation whenever it is a variation of the counterterms , i.e. if eq .
( [ brsct ] ) is fulfilled .
if there is only one field polynomial which is @xmath33-invariant , but not a variation of counterterms , one has an anomaly , and symmetries can not be established by adjusting counterterms . in this way
one has achieved an algebraic characterization of scheme dependent breakings and anomalies .
the proof to all orders proceeds by induction , passing through the same steps as above from order @xmath40 to @xmath41 in the sm the algebraic characterization of breakings can be proven to be the same as in the symmetric @xmath2 theory and does not depend on the specific form of spontaneous symmetry breaking .
in @xcite it has been shown that there are only the well - known adler - bardeen anomalies .
their coefficients vanish in the sm , if we include lepton and colored quark doublets .
the difficult and indeed specific part is the classification of invariant counterterms and of appropriate normalization conditions . here mixing effects between neutral massless / massive fields have to be carefully analysed from the point of view of off - shell infrared existence . in the next section we present three important results of this analysis .
invariant counterterms are determined if one solves the st identity and the ward identities for the most general action compatible with power counting renormalizability : @xmath42 in the sm one finds as solution an action , which contains in addition to the free parameters of the tree approximation two further undetermined couplings in each fermion family .
they are couplings of abelian currents to the abelian component of vector fields and are not determined by the st identity , but have to be fixed by a local gauge ward identity .
( in @xcite these couplings are fixed by an antighost equation . from there
the local ward identity is defined by using the consistency with the st identity . ) in the sm classically we have three types of abelian currents , the currents of lepton and quark family number conservation , @xmath43 and @xmath44 , and the sum of the electromagnetic and neutral current of weak interactions .
being more specific we find as a special solution of eq .
( [ gagencl ] ) @xmath45 where @xmath46 is the classical action ( [ gacl ] ) . in order to identify the action ( [ gacl ] ) as solution of symmetry identities , one has to impose the local @xmath0-ward identity as given in ( [ funid ] ) .
the abelian local ward operator is to all orders fixed to be the sum of the non - integrated neutral @xmath25 ward operator and of the electromagnetic charge operator @xmath47 = 0\ ] ] in fact the local abelian ward identity ( [ funid ] ) with the abelian operator ( [ w4q ] ) is the functional generalization of the classical gell - mann - nishijima relation .
we want to point out that the abelian ward identity has to be characterized to be abelian by its commutation relations with ward operators of rigid @xmath25-symmetry . for this reason it is crucial to establish rigid symmetry in addition to the st identity .
we did already mention that the symmetry operators depend explicitly on the mass ratio @xmath48 in the tree approximation .
solving eq .
( [ gagencl ] ) by inserting the tree operators we are not able to fix all mass parameters by normalization conditions and especially we are not able to diagonalize the mass matrix of neutral vector bosons on - shell at the same time : @xmath49 mass diagonalization at @xmath50 is crucial for obtaining infrared finite expression for off - shell green functions and are implemented in the bphzl scheme by the ir power counting . in order to fulfill the normalization conditions ( [ onshell ] ) one has to introduce a non - diagonal wave - function renormalization for the neutral vector bosons .
if we carry out such field redefinitions also in the symmetry operators , the symmetry operators are renormalized and get higher order corrections , i.e. @xmath51 these corrections are in agreement with the algebra .
for this reason one can not fix the symmetry operators to their tree form but one has to take the most general ones compatible with the algebraic properties of the tree approximation ( see ( [ brsnil ] ) ) , when one solves eqs .
( [ gagencl ] ) .
then one has indeed the same number of free parameters as normalization conditions even in the complete on - shell scheme . requiring rigid symmetry
has important restrictions on the gauge fixing .
as we have already mentioned the choice ( [ f_a ] ) is covariant under rigid @xmath2-transformations and can be constructed as being invariant under rigid transformation by introducing the external scalar field @xmath24 . in this special gauge
the ghost mass ratio is equivalent to the vector mass ratio , @xmath52 but it turns out to be differently renormalized from the vector mass ratio in higher orders .
for this reason we have to introduce the ghost mass ratio as an independent parameter of the model .
however , if one takes arbitrary gauge parameters @xmath53 and @xmath54 in the in the gauge - fixing functions @xmath55 and @xmath56 without changing @xmath57 ( [ f_a ] ) , one breaks rigid symmetry by the gauge fixing and can not derive ward identities of rigid and local @xmath0 symmetry .
consequently we loose the control about the gauged abelian currents in higher orders , namely we are not able to identify the electromagnetic current by means of a local ward identity . taking for the gauge fixing @xmath58 the gauge fixing is compatible with rigid symmetry and allows at the same time to treat the ghost mass ratio as an independent parameter of the theory . in order to avoid
non - diagonal ghost mass terms brs - transformations have to be generalized to @xmath59 and @xmath60 differs from the unit matrix by @xmath61 with this modification the ghost mass matrix is diagonal , and can be achieved to be diagonal on - shell in higher orders by adjusting the free parameters in the matrix @xmath62
. then also the faddeev - popov part is free from off - shell infrared divergencies .
contrary to simple gauge groups we have introduced not only independent wave function renormalizations for ghosts and vectors , but have also an independent wave function renormalization for antighosts .[/INST] the algebraic method of renormalization is applied to the standard model of electroweak interactions .
we present the most important modifications compared to theories with simple groups .
bn - th-98 - 15 + hep - th/9807102 + july 1998 + + + * elisabeth kraus * + [ 3 mm ] _ physikalisches
institut , universitt bonn _
+ _ nuallee 12 , d53115 bonn , germany _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the algebraic method of renormalization is applied to the standard model of electroweak interactions .
we present the most important modifications compared to theories with simple groups . _
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ </s> |
in a previous issue of critical care a comparison was made between metrics of transpulmonary thermodilution ( tpt ) and the pulmonary artery catheter ( pac ) in patients with acute heart failure ( ahf ) and sepsis .
the results showed acceptable correlation between metrics derived from the two techniques and showed that tpt allowed identification of heart dysfunction in both heart failure and sepsis .
this study , while small and retrospective , adds to mounting evidence that routine use of the pac is probably no longer warranted in ahf and many other conditions .
it appears that a grand chapter in the intensive care medicine story may be coming to an end .
the pac first came into widespread use after its introduction by swan and ganz in 1970 . their balloon - tipped , flow - directed catheter allowed clinicians for the first time to assess advanced parameters of hemodynamics and gas exchange at the bedside - and it was an overnight success .
in fact , the catheter was so enthusiastically adopted that it helped define the modern intensive care unit for the coming decades . but the device was introduced without clinical trials establishing benefit , and in the ensuing years much debate as regards its safety and efficacy has occurred .
opponents of the device state that it has never been shown to improve major clinical outcomes [ 3 - 10 ] , and in fact might increase mortality and morbidity .
both the left ventricular stroke work index ( lvswi ) and cardiac power ( cp ) , however , have been found to be excellent prognosticators in cardiac surgery and ahf , and many feel that the pulmonary artery occlusion pressure may provide useful information on the function of the left ventricle . as such , the pac device is still recommended in patients with heart failure . since the introduction of the pac
one such device , the picco ( pulsion medical systems , munich , germany ) , uses the tpt method to assess preload , cardiac output , filling volumes , extravascular lung water and parameters of cardiac function .
the technique requires only central venous access and an arterial line , and therefore may be safer than the pac .
but many tpt metrics remain relatively untested with regards to gold standard techniques in the assessment and treatment of heart failure .
the study by ritter and colleagues retrospectively compared metrics of cardiac function in patients with sepsis and ahf as determined by the picco and by the pac .
they compared the cardiac function index and the global ejection fraction - picco metrics - with the lvswi and the cp calculated from measurements taken by the pac .
patients with ahf had a lower cardiac index , a lower lvswi , a lower cp and a higher pulmonary artery occlusion pressure as determined by the pac .
these same patients had a lower cardiac function index and global ejection fraction as determined by the picco. reasonable correlation of the cardiac function index to the lvswi and cp was observed . additionally , the cardiac function index allowed identification of patients with cardiac dysfunction in both heart failure and severe sepsis .
the authors , however , used repeated measures over steady - state periods in two very distinct patient populations and showed good correlation in measurements of cardiac function over the treatment course , which helped to compensate for some of these limitations . given that there are now reliable less invasive alternatives to the pac that can accurately determine cardiac output , preload status , fluid responsiveness , and the etiology of shock , the need for routine use of the pac in sepsis , in acute respiratory distress syndrome , and in most surgical settings has already been called into question .
it now appears in light of this present study and others that the pac is not needed in the assessment of or the treatment of ahf or sepsis - related cardiomyopathy .
but what devices should we be using , and in what diseases ? to effectively answer these questions , as the authors themselves have stated , we must now demonstrate efficacy of newer devices such as the picco as compared with the pac in large prospective outcome studies .
the studies should be based on current treatment recommendations and/or new algorithmic approaches , since it is not just the device but also how it is used that potentially changes outcome . but should we continue to use the pac until we have further proof ? for the time being there appears to be enough evidence to say that the pac adds little to information attainable by less invasive measures and should probably no longer be a part of routine management for conditions other than right heart failure , disorders causing abnormalities of pulmonary arterial pressure , and congenital heart disease .
ahf : acute heart failure ; cp : cardiac power ; lvswi : left ventricular stroke work index ; pac : pulmonary artery catheter ; picco : pulse contour cardiac output ; tpt : transpulmonary thermodilution .
crp is a member of the medical advisory board of pulsion medical systems ag ( munich , germany ) and has received honoraria for presenting lectures . | whereas the pulmonary artery catheter ( pac ) is still widely used in guiding assessment and treatment of heart failure , controversy surrounding its safety and efficacy has prompted development of newer , less invasive techniques .
for these purposes , the transpulmonary thermodilution technique allows assessment of preload , cardiac output , filling volumes , and metrics of contractility without the need to pass a catheter through the right heart . in a previous issue of critical care , ritter and colleagues compare metrics of transpulmonary thermodilution with the pac in patients with acute heart failure and severe sepsis .
the results add to a growing body of evidence that the pac adds little to information attainable by less invasive methods in many conditions , including acute heart failure . whether newer devices improve outcome needs to be tested in well - controlled prospective trials . | <s>[INST]in a previous issue of critical care a comparison was made between metrics of transpulmonary thermodilution ( tpt ) and the pulmonary artery catheter ( pac ) in patients with acute heart failure ( ahf ) and sepsis .
the results showed acceptable correlation between metrics derived from the two techniques and showed that tpt allowed identification of heart dysfunction in both heart failure and sepsis .
this study , while small and retrospective , adds to mounting evidence that routine use of the pac is probably no longer warranted in ahf and many other conditions .
it appears that a grand chapter in the intensive care medicine story may be coming to an end .
the pac first came into widespread use after its introduction by swan and ganz in 1970 . their balloon - tipped , flow - directed catheter allowed clinicians for the first time to assess advanced parameters of hemodynamics and gas exchange at the bedside - and it was an overnight success .
in fact , the catheter was so enthusiastically adopted that it helped define the modern intensive care unit for the coming decades . but the device was introduced without clinical trials establishing benefit , and in the ensuing years much debate as regards its safety and efficacy has occurred .
opponents of the device state that it has never been shown to improve major clinical outcomes [ 3 - 10 ] , and in fact might increase mortality and morbidity .
both the left ventricular stroke work index ( lvswi ) and cardiac power ( cp ) , however , have been found to be excellent prognosticators in cardiac surgery and ahf , and many feel that the pulmonary artery occlusion pressure may provide useful information on the function of the left ventricle . as such , the pac device is still recommended in patients with heart failure . since the introduction of the pac
one such device , the picco ( pulsion medical systems , munich , germany ) , uses the tpt method to assess preload , cardiac output , filling volumes , extravascular lung water and parameters of cardiac function .
the technique requires only central venous access and an arterial line , and therefore may be safer than the pac .
but many tpt metrics remain relatively untested with regards to gold standard techniques in the assessment and treatment of heart failure .
the study by ritter and colleagues retrospectively compared metrics of cardiac function in patients with sepsis and ahf as determined by the picco and by the pac .
they compared the cardiac function index and the global ejection fraction - picco metrics - with the lvswi and the cp calculated from measurements taken by the pac .
patients with ahf had a lower cardiac index , a lower lvswi , a lower cp and a higher pulmonary artery occlusion pressure as determined by the pac .
these same patients had a lower cardiac function index and global ejection fraction as determined by the picco. reasonable correlation of the cardiac function index to the lvswi and cp was observed . additionally , the cardiac function index allowed identification of patients with cardiac dysfunction in both heart failure and severe sepsis .
the authors , however , used repeated measures over steady - state periods in two very distinct patient populations and showed good correlation in measurements of cardiac function over the treatment course , which helped to compensate for some of these limitations . given that there are now reliable less invasive alternatives to the pac that can accurately determine cardiac output , preload status , fluid responsiveness , and the etiology of shock , the need for routine use of the pac in sepsis , in acute respiratory distress syndrome , and in most surgical settings has already been called into question .
it now appears in light of this present study and others that the pac is not needed in the assessment of or the treatment of ahf or sepsis - related cardiomyopathy .
but what devices should we be using , and in what diseases ? to effectively answer these questions , as the authors themselves have stated , we must now demonstrate efficacy of newer devices such as the picco as compared with the pac in large prospective outcome studies .
the studies should be based on current treatment recommendations and/or new algorithmic approaches , since it is not just the device but also how it is used that potentially changes outcome . but should we continue to use the pac until we have further proof ? for the time being there appears to be enough evidence to say that the pac adds little to information attainable by less invasive measures and should probably no longer be a part of routine management for conditions other than right heart failure , disorders causing abnormalities of pulmonary arterial pressure , and congenital heart disease .
ahf : acute heart failure ; cp : cardiac power ; lvswi : left ventricular stroke work index ; pac : pulmonary artery catheter ; picco : pulse contour cardiac output ; tpt : transpulmonary thermodilution .
crp is a member of the medical advisory board of pulsion medical systems ag ( munich , germany ) and has received honoraria for presenting lectures .[/INST]whereas the pulmonary artery catheter ( pac ) is still widely used in guiding assessment and treatment of heart failure , controversy surrounding its safety and efficacy has prompted development of newer , less invasive techniques .
for these purposes , the transpulmonary thermodilution technique allows assessment of preload , cardiac output , filling volumes , and metrics of contractility without the need to pass a catheter through the right heart . in a previous issue of critical care , ritter and colleagues compare metrics of transpulmonary thermodilution with the pac in patients with acute heart failure and severe sepsis .
the results add to a growing body of evidence that the pac adds little to information attainable by less invasive methods in many conditions , including acute heart failure . whether newer devices improve outcome needs to be tested in well - controlled prospective trials .</s> |
the family cucurbitaceae comprises many vegetable and fruit crops including cucumbers , squashes , luffas , melons , and watermelons .
squash ( cucurbita pepo ) is a major vegetable crop grown all over the world from the cold region to the tropical one .
the world production of squash reported by fao statistics for 2002 exceeded 17.7 million tons from 2.4 million ha .
china is the most important producer on the world , while in africa egypt is one of the 10 top producers ranking as the eighth country from the world production of squash depending on last report of fao 2012 .
there are many pests that significantly affect the yield and fruit quality of squash . among these diseases ,
geminiviridae represents the largest family of plant dna viruses that infect a broad range of plants causing severe losses in the yield of economically important crops within tropical and subtropical regions .
geminiviruses are single - stranded circular dna viruses that cause severe damage to wide range of economically important crops worldwide .
they are characterized by twinned icosahedra particles and have emerged globally as one of the most economically important pathogens .
begomovirus is the largest genus of the geminiviridae family whose genus has two types classified depending on their genome into monopartite and bipartite .
bipartite begomoviruses genome has either one or two circular single strand dna named components a and b ; each one of them has its specific role in the virus life cycle .
component a contains 5 genes named replication associated protein ( rep or ac1 ) , replication enhancer protein ( ren or ac3 ) , transcription activator protein ( trap or ac2 ) , ac4 , and coat protein ( cp or av1 ) .
component b contains 2 genes named movement protein ( mp or bc1 ) and nuclear shuttle protein ( nsp or bv1 ) .
nsp and mp genes play significant role in virus movement either from the nucleus to the cytoplasm or from cell to cell through plasmodesmata , respectively .
squash leaf curl virus ( sqlcv ) is transmitted by its whitefly vector bemisia tabaci and it induces severe stunting and leaf curling in squash plants and causes severe losses in cucurbit production .
the first record of sqlcv in the middle east was in israel in 2003 ; subsequently it has spread to neighbor countries such as egypt , jordan , palestine , and lebanon .
the spreading of the sqlcv within egypt was quickly as it took 5 years to spread from one governorate to another [ 6 , 10 , 11 ] .
restriction enzymes of rca products combined with a cloning strategy showed being a very efficient method to obtain full genome sequences .
this technique allowed the easy detection , cloning , and sequencing of a mixed infection and the identification of the respective begomoviruses on the same sample [ 1214 ] .
the small interference rna ( sirna ) or posttranscriptional gene silencing ( ptgs ) occurs naturally in plants and acts as an antiviral defense mechanism .
the sirna has been widely used as a method to engineer resistance against viruses in plants , including nuclear - replicating geminiviruses , which have no double - stranded rna phase in their replication cycle .
the produced virus specific sirna from the breakdown of dsrna induces the degradation of homologous mrna sequences , resulting in hindering the virus form expressing its genes , thus limiting virus replication process . in this
study the two viral components of the egyptian sqlcv noubaria isolate were cloned and their sequences were submitted to the genbank , from the cloned viral genome two regions , one from early and one from late expressed genes which were used to trigger ptgs against sqlcv using agroinfiltration as a transient experiment method .
the second one represents the gene bc1 , which has an important role in virus spreading from cell to cell causing systemic infection .
geminivirus - infected squash plants were collected from different cultivated open fields of noubaria village at beheira governorate .
the collected plant samples showed symptoms of squash leaf curl virus ( sqlcv ) such as severe systemic stunting and leaf curling .
nonviruliferous whiteflies ( bemisia tabaci ) were obtained from rearing whiteflies on healthy cotton plants in an isolated insectary for at least a month .
whiteflies were fed for a month on infected squash plants collected from the field to acquire the virus and used to infect healthy squash plants .
preliminary pcr for viral detection was carried out using the degenerate primers v324 ( + ) primer 5-gccyatrtayagraagcc mag-3 and c889 ( ) primer 5-ggrttdgargcatghgtacatg-3 specific for whitefly transmitted geminiviruses to amplify 570 bp fragment . for cloning the complete viral genome ,
total dna extracted from infected squash plants was subjected to 29 amplification essentially according to the manufacturer 's instructions ( fermentas ) .
the amplified products were denatured at 65c for 10 min and run on a 1% agarose gel to confirm amplification .
the ampliphi product was digested independently with selected restriction enzymes , that is , ecori , hindiii , bamhi , sali , saci , psti , xbai , bglii , kpni , ncoi , xmai , xho1 , smai , sphi , and swai ( fermentas , fast digest ) and separated in an agarose gel .
the enzymes that could cut at a single site in the genome generating genome size fragment was selected for further cloning in pbluescript ii sk ( ) .
sequencing was carried out and was subjected to genbank ( genbank accession a : kp795975 ; b : kp795976 ) . to assess silencing effect of the selected viral fragments potentially useful in the control of sqlcv
, two fragments were selected from the viral sequences to cover partial rep / trap and full bc1 genes .
two sets of primers were designed to amplify the selected regions by using vector nti software .
rep / trap primer sequences are 5-cccacataattacttgagcggccat-3 and 5-ttagcaatcctgtgctgtgctttga-3 , while bc1 gene primer pairs are 5-atgggttctcaattagttccaccc-3 and 5-gcttagggattttggagtgctcggg-3. restriction sites xhoi and xmai added to the forward primers and asci and bamhi to the reverse primers to facilitate cloning in sense and antisense forms in the binary vector pfgc5041 within the intron region .
the expected sizes of the selected regions were 348 bp and 879 bp for cloned viral genome to amplify the selected region .
the sizes of the selected fragments were 348 bp and 879 bp for rep / trap and bc1 genes , respectively .
cloned viral genome was used as a template in pcr reaction with a concentration of 100 ng , 5 l of 5x flexi gotaq buffer , 2 l of 25 mm mgcl2 , 0.5 l of 10 mm dntps , 0.5 l 10 pmol of each primer , 0.25 l gotaq enzyme , and ddh2o to reach a total volume of 25 l ; the amplification was carried out in a biorad t100 usa .
the reaction was performed with an initial cycle at 94c for 4 min , followed by 30 cycles of denaturation step at 94c for 1 min , annealing at 50c for 30 sec , and an extension cycle at 72c for 1 min followed by a final cycle at 72c for 7 min .
the amplified fragments were cloned initially into pgem-teasy vector system ; subsequently rep / trap and bc1 fragments were digested using xhoi and xmai and asci and bamhi for cloning in pfgc5041 silencing binary vector ( supplied by richared jorgensen , university of arizona , usa ) .
each fragment was cloned into the expression vector pfgc5041 , in which the transgene is cloned in both orientations separated within the chsa intron and under the control of the 35s promoter and the osc terminator .
the cloning of amplified fragments has been carried out in two steps by using the inner restriction sites on the primers .
double digestion with fastdigest enzymes xmai and bamhi was used for the sense orientation into the plant vector pfgc5041 ; the outer restriction enzymes pair xhoi and asci were used to clone the antisense orientation .
all enzymes used for cloning were fastdigest restriction enzymes supplied from thermo scientific. after confirming the presence of the gene fragments by sequencing , pfgc - rep / trap and pfgc - bc1 were transformed to electrocompetent agrobacterium lb4404 by electroporation .
electroporation was carried out using biorad gene pulser set at 25 f , 200 , and 2.5 kv .
eskandrani ) were grown in the biocontainment greenhouse in the agriculture genetic engineering research institute ( ageri ) at 28c with 16 hr light/8 hr dark . for each treatment
infiltration media were prepared as follows : 5 ml overnight culture was used to inoculate 50 ml of lb medium containing 1 : 1 kanamycin and 0.5 : 1 streptomycin and incubated overnight at 28c . upon centrifugation of the 50 ml overnight culture
, it has been resuspended in infiltration media containing 10 mm mgcl2 , 10 mm , mes , and 20 m acetosyringone and then was incubated at room temperature for 2 hr till its od600 reached 2.0 .
agrobacterium harboring sense / antisense rep / trap construct and sense / antisense bc1 construct infiltrated employing needleless 5 ml syringe using the syringe spotted technique developed by johansen and carrington .
after 1 week from infiltration viruliferous whiteflies feed on infiltrated plant for 48 hr inoculation access period .
the treated plants were sprayed with imidacloprid ( confidor , bayer , leverkusen , germany ) to get rid of the whiteflies .
plants infiltrated with silencing constructs were assayed for positive inoculation with specific pcr primers for each fragment .
the accumulation of viral dna in infected agrobacterium plants was determined by rt - qpcr using the ( leaves weight : 0.51.01 g ) total dna extracted from upper leaves .
the fragment of bc1 amplified by 5-cggatttgaccagtcttctctc-3 and 5-gggcaccgacagtaaagatac-3 as forward and reverse primer , respectively , resulted in fragment with length 102 bp . in case of rep / trap
a fragment with length 105 bp was produced by those primers 5-tatccaaggtgcgatgttcc-3 as forward and 5-atgttcctctctggccattc-3 as reverse one .
annealing temperature was 60c for both fragments , while 18s rrna was used as internal control for gene expression .
squash plants were kept for 10 days after virus infection ; then samples were collected for rt - qpcr detection , and total rna was extracted using sv total rna isolation system .
the rt - qpcr was performed in a ab7300 real - time pcr system ( applied biosystems , usa ) using sybr premix extaqii from takara ( catalog number rr82sw , takara , japan ) ; rt - qpcr analysis was performed as described by manufacturer . in real - time pcr
, primers were tested using conventional pcr resulting in the amplification of fragments monitored at the expected size , where rep primers gave a 105 bp fragment while bc1 gave a 102 bp fragment , with no primer dimer development .
all plant samples from different fields gave the expected band with pcr using the degenerate primer of cp core region , indicating that these samples were infected with geminivirus ( figure 1 ) .
the digestion of amplified products resulted in 4 unique cuts with enzymes ecori , bglii , bamhi , and sali ( figure 2 ) while only xba1 enzyme cut twice ( figure 3 ) .
linearized fragments with the expected size were cloned in the corresponding site into the e. coli vector psk .
three constructed plasmids from cloning of the linearized genome with ecori , bamhi , and sali were sent for sequencing and the sequences were confirmed by similarity search using blast at national center for biotechnology information ( ncbi ) .
results showed that ecori gave component b while sali and bamhi gave component a. identity ratio showed high similarity results reaching 99% homology to component a with other sqlcv isolates .
component b showed less similarity than component a but the identity ratio is still high giving 99% homology with cairo isolate ( dq285020.1 ) , 98% homology with palestine isolate ( kc441466.1 ) , jordon isolates ( jx444574.1 and jx131282.1 ) , israel isolate ( hq184437.1 ) , and lebanon ( hm368374.1 ) , 96% homology with kaliobeya isolate ( kj579954.1 ) , and 95% homology with california isolate ( dq285017.1 ) and arizona isolate ( dq285018.1 ) . to study sqlcv resistance using sirna strategy on squash plants ,
two putatively effective fragments from the whole virus genome of the sqlcva noubaria were chosen to form short dsrna structure for enhancing posttranscriptional gene silencing ( figure 4 ) .
the first fragment was designed targeting the rep / trap with a length of 347 bp , while the second fragment was designed to contain the full bc1 gene with length of 849 bp .
pcr analysis was carried out to amplify both fragments giving the expected band size as showed in figure 5 .
the insertion of the first fragment in the antisense orientation into the pfgc5041 vector was confirmed by restriction digestion using xhoi and asci enzymes , while bamhi and xmai enzymes were used to confirm the insertion of the second fragment in the sense orientation .
the full rnai cassette expression was driven by the e35s promoter and the osc 3 terminator ( figure 6 ) .
positive clones of transformed agrobacterium lb4404 with constructs pfgc5041-rep and pfgc5041-bc1 were screened using colony pcr technique ( data not shown ) . to assess the expression of silencing fragments , c. pepo plant leaves were infiltrated in a transient manner .
plants were then left for a week and subsequently subjected to infection with viruliferous whiteflies raised on infected squash plants with sqlcv . to detect the presence of viral genome in infiltrated plants ,
primers of sqlcv coat protein gene were used in confirming pcr as a positive control .
after the 7th day after infection noninfiltrated control plants gave positive results in pcr ; however pfgc - rep / trap and pfgc - bc1 infiltrated plants gave negative results in pcr . to monitor quantitative viral accumulation in infiltrated squash plants
all noninfiltrated squash plants inoculated with viruliferous whiteflies carrying the sqlcv developed typical viral symptoms with severe yellowing , leaf curling , and a reduced leaflet size .
such plants ceased to grow , failing to flower and produce fruits , while the untreated plants remained the negative control ( figure 7(a ) ) .
one month after inoculation by the pfgc - rep / trap vector all plants were symptomless , while after two months only 1 plant of the total 5 plants gave mild symptoms = + ( figure 7(c ) ) .
meanwhile , in the case of infiltrating the plants with pfgc - bc1 construct , one month after inoculation , plants produced 2 symptomless plants and 3 plants with mild symptoms . by the end of the second month
only 1 plant showed being symptomless , 3 with mild symptoms , and 1 with moderate symptoms = + + ( figure 7(d ) ) ( table 1 ) .
control plants treated with empty pfgc5041 showed early symptoms after two weeks and severe symptoms after one month of inoculation ( figure 7(b ) ) .
quantitative analysis using rt - qpcr assay was carried out to study the level of the expression of the two viral genes , rep / trap and bc1 in the infiltrated squash .
total rna extracted from infiltrated plants was used to synthesize cdna and was subjected to rt - qpcr . in addition , rt - qpcr was performed from infected c. pepo plants as a positive control reaction and nontemplate dna reaction that represent negative control which had ct values equivalent to the total number of cycles used in the rt - qpcr experiment , resulting in curves that did not achieve the threshold level , thus indicating that these reactions contained no detectable viral dna .
the level of virus detection was significantly lower in all infiltrated plants than in the control plants .
infiltrated plants with pfgc - rep / trap construct showed significant shifting in ct value compared with the control .
average ct resulting from re pfgc - rep / trap treatment was 29.51 while an average ct value of control plants was 24.29 .
in pfgc - rep / trap samples the fold of change is calculated using the ct and it showed a 32-fold decrease thus silencing percent was calculated to reach 97% .
also , pfgc - bc1 construct displayed a slight shifting in ct values compared with that in the control .
treated samples ct values average was 29.58 while control ct values average was 27.48 resulting in a decrease 4.7-fold ( table 2 ) .
the calculated expression of bc1 gene has decreased by 79% giving showing a good degree of plant resistance against the respected virus but not as efficient as pfgc - rep / trap construct ( figure 8) .
sqlcv has become a major concern for cultivation of squash in the middle east region .
thus , it is important to study the vast diversity of sqlcv and also the epidemic implications .
small circular dna is preferentially amplified by rca , which makes the ssdna genome of the geminiviruses ideal substrate for rca .
in addition , during viral replication , through complementary strand synthesis ( csr ) of the circular ssdna , rolling circle replication ( rcr ) , and recombination - dependent replication ( rdr ) , various dna intermediates are produced . in this work ,
the rolling circle amplification ( rca ) technology was used for molecular cloning of the sqlcv genome , because of its simplicity , high sensitivity , and proofreading against misincorporation of nucleotides .
it can be used to amplify sequences without the necessity of previous knowledge of it [ 12 , 23 ] .
the sequence of the sqlcv - noubaria isolate obtained in this work showed high similarities to other isolates in the region .
the low sequence variation observed among sqlcv isolates in the middle east region was explained by lapidot et al . .
they predict that uncontrolled movement of viruliferous whiteflies among countries causes viruses readily moved across country boundaries in this region , preventing strong genetic differentiation of these viruses among neighbor countries .
studies on crops harboring virus resistance indicated the possibility of engineering the resistance by different transgene - based approaches . during the past decade
there has been considerable evidence for the successful using of sirna to protect plants against viruses in plum , papaya , watermelon , and potato , which has led to the development of virus - resistant transgenic crops [ 2630 ] . in this
study the same technology has been used by the incorporation of sense and antisense fragments separated in pfgc5041 vector within the chsa intron to be transcribed and hybridized with itself to form a hairpin structure . however , rna silencing degree induced in infiltrated plants could be diverse according to the gene used
. two regions of squash leaf curl viral genome were selected for cloning , the first was rep / trap , and the second was the full length of bc1 gene .
the selected region rep / trap fragment was chosen according to its location representing the end of the rep gene and the beginning of trap in overlapping manner , which may be putatively stronger than one of them alone as it could lead to the silencing of both of them , while in case of bc1 gene it was selected because of its important function in systemic spreading of viral genome through the plasmodesmata , as its silencing attempt is expected to limit the infection and inhibit virus transmission from cell to cell .
the two constructed plasmids , pfgc - rep / trap and pfgc - bc1 , were prepared and used to infiltrate squash plants .
resistance was measured either by monitoring symptoms development or by real - time pcr . in real - time pcr , three replicates from each construct were tested , whereas detection of gene expression was measured by threshold cycle ( ct ) .
thus , higher ct value means less amount of template in the sample , which indicates fewer titrations of virus particles . depending on previous studies using the same virus ,
18s rrna was chosen to be used as the reference gene in real - time pcr . to calculate relative gene expression ct method was used , where target gene expression was normalized to reference gene expression within the same sample to correct any variation that could affect the study .
results of rep / trap fragment in real - time pcr have proved that there is a vital role for this fragment on the rep gene expression as it has been decreased 32-fold and a silencing of 97% has been achieved through this construct .
this significant result could be due to the key role of the rep protein , which is the most essential protein for viral replication .
in addition , transcription activator protein gene is overlapped with rep gene by 50 bp at its 3 end ; this overlapping has played a significant role in silencing of both genes and gave more efficient silencing percent ; this could be clear because the transcription activator protein alone is acting as a gene silencing suppressor so its early silencing may help the plants to resist higher . the construct that contains
the movement protein gene showed a degree of resistance accomplishment but being less efficient than the rep / trap construct .
a decrease in the virus quantity 4.7-fold has been achieved ; this may be due to the late expression of this gene in the virus machinery or it may be due to the effect of its longer fragment size
. in former studies fragments size showed efficient silencing ranged from ~110 to 550 bp [ 36 , 37 ] , while in the case of bc1 gene used in this study it was 879 bp so it might be a factor that affect the silencing percentage .
symptoms developed in all treated plants in each treatment completed the story with the real - time pcr results by giving ratio in plant resistance in case of pfgc - rep / trap construct more than pfgc - bc1 construct .
we have demonstrated that hairpin constructs expressing either 348 bp of the rep / trap gene or 879 bp for the bc1 genes can control sqlcv .
however , sirna produced from using the rep / trap construct proved to be more efficient in controlling the virus than bc1 construct .
it is clear from several studies that the sirna strategy is more efficient at the 5 and 3 ends of the gene .
both the rt - pcr and the symptoms screening at the greenhouse showed that the expression level of the rep gene , as one of the early genes , could play the most significant role in silencing when it is employed as a posttranscriptional gene silencing and tool for controlling the squash leaf curl virus . the bc1 gene could also give a degree silencing but we proved that it is less effective than the rep gene .
therefore , the 3 end fragment of the rep gene for producing stable transformation should be used to measure effect of construct on the transgenic c. pepo plants and reach high level of resistance to sqlcv on large populations in the field . | squash leaf curl virus ( sqlcv ) is a bipartite begomovirus affecting squash plants .
it is transmitted by whitefly bemisia tabaci biotype b causing severe leaf curling , vein banding , and molting ending by stunting . in this study full - length genomic clone of sqlcv
egyptian isolated and posttranscriptional gene silencing ( ptgs ) has been induced to develop virus resistance . the noubaria sqlcv has more than 95% homology with jordon , israel , lebanon , palestine , and cairo isolates .
two genes fragment from sqlcv introduced in sense and antisense orientations using pfgc5049 vector to be expressed as hairpin rna .
the first fragment was 348 bp from replication associated protein gene ( rep ) .
the second fragment was 879 bp representing the full sequence of the movement protein gene ( bc1 ) .
using real - time pcr , a silencing record of 97% has been recorded to rep / trap construct ; as a result it has prevented the appearance of viral symptoms in most tested plants up to two months after infection , while construct containing the bc1 gene scored a reduction in the accumulation of viral genome expression as appearing in real - time pcr results 4.6-fold giving a silencing of 79% , which had a positive effect on symptoms development in most tested plants . | <s>[INST]the family cucurbitaceae comprises many vegetable and fruit crops including cucumbers , squashes , luffas , melons , and watermelons .
squash ( cucurbita pepo ) is a major vegetable crop grown all over the world from the cold region to the tropical one .
the world production of squash reported by fao statistics for 2002 exceeded 17.7 million tons from 2.4 million ha .
china is the most important producer on the world , while in africa egypt is one of the 10 top producers ranking as the eighth country from the world production of squash depending on last report of fao 2012 .
there are many pests that significantly affect the yield and fruit quality of squash . among these diseases ,
geminiviridae represents the largest family of plant dna viruses that infect a broad range of plants causing severe losses in the yield of economically important crops within tropical and subtropical regions .
geminiviruses are single - stranded circular dna viruses that cause severe damage to wide range of economically important crops worldwide .
they are characterized by twinned icosahedra particles and have emerged globally as one of the most economically important pathogens .
begomovirus is the largest genus of the geminiviridae family whose genus has two types classified depending on their genome into monopartite and bipartite .
bipartite begomoviruses genome has either one or two circular single strand dna named components a and b ; each one of them has its specific role in the virus life cycle .
component a contains 5 genes named replication associated protein ( rep or ac1 ) , replication enhancer protein ( ren or ac3 ) , transcription activator protein ( trap or ac2 ) , ac4 , and coat protein ( cp or av1 ) .
component b contains 2 genes named movement protein ( mp or bc1 ) and nuclear shuttle protein ( nsp or bv1 ) .
nsp and mp genes play significant role in virus movement either from the nucleus to the cytoplasm or from cell to cell through plasmodesmata , respectively .
squash leaf curl virus ( sqlcv ) is transmitted by its whitefly vector bemisia tabaci and it induces severe stunting and leaf curling in squash plants and causes severe losses in cucurbit production .
the first record of sqlcv in the middle east was in israel in 2003 ; subsequently it has spread to neighbor countries such as egypt , jordan , palestine , and lebanon .
the spreading of the sqlcv within egypt was quickly as it took 5 years to spread from one governorate to another [ 6 , 10 , 11 ] .
restriction enzymes of rca products combined with a cloning strategy showed being a very efficient method to obtain full genome sequences .
this technique allowed the easy detection , cloning , and sequencing of a mixed infection and the identification of the respective begomoviruses on the same sample [ 1214 ] .
the small interference rna ( sirna ) or posttranscriptional gene silencing ( ptgs ) occurs naturally in plants and acts as an antiviral defense mechanism .
the sirna has been widely used as a method to engineer resistance against viruses in plants , including nuclear - replicating geminiviruses , which have no double - stranded rna phase in their replication cycle .
the produced virus specific sirna from the breakdown of dsrna induces the degradation of homologous mrna sequences , resulting in hindering the virus form expressing its genes , thus limiting virus replication process . in this
study the two viral components of the egyptian sqlcv noubaria isolate were cloned and their sequences were submitted to the genbank , from the cloned viral genome two regions , one from early and one from late expressed genes which were used to trigger ptgs against sqlcv using agroinfiltration as a transient experiment method .
the second one represents the gene bc1 , which has an important role in virus spreading from cell to cell causing systemic infection .
geminivirus - infected squash plants were collected from different cultivated open fields of noubaria village at beheira governorate .
the collected plant samples showed symptoms of squash leaf curl virus ( sqlcv ) such as severe systemic stunting and leaf curling .
nonviruliferous whiteflies ( bemisia tabaci ) were obtained from rearing whiteflies on healthy cotton plants in an isolated insectary for at least a month .
whiteflies were fed for a month on infected squash plants collected from the field to acquire the virus and used to infect healthy squash plants .
preliminary pcr for viral detection was carried out using the degenerate primers v324 ( + ) primer 5-gccyatrtayagraagcc mag-3 and c889 ( ) primer 5-ggrttdgargcatghgtacatg-3 specific for whitefly transmitted geminiviruses to amplify 570 bp fragment . for cloning the complete viral genome ,
total dna extracted from infected squash plants was subjected to 29 amplification essentially according to the manufacturer 's instructions ( fermentas ) .
the amplified products were denatured at 65c for 10 min and run on a 1% agarose gel to confirm amplification .
the ampliphi product was digested independently with selected restriction enzymes , that is , ecori , hindiii , bamhi , sali , saci , psti , xbai , bglii , kpni , ncoi , xmai , xho1 , smai , sphi , and swai ( fermentas , fast digest ) and separated in an agarose gel .
the enzymes that could cut at a single site in the genome generating genome size fragment was selected for further cloning in pbluescript ii sk ( ) .
sequencing was carried out and was subjected to genbank ( genbank accession a : kp795975 ; b : kp795976 ) . to assess silencing effect of the selected viral fragments potentially useful in the control of sqlcv
, two fragments were selected from the viral sequences to cover partial rep / trap and full bc1 genes .
two sets of primers were designed to amplify the selected regions by using vector nti software .
rep / trap primer sequences are 5-cccacataattacttgagcggccat-3 and 5-ttagcaatcctgtgctgtgctttga-3 , while bc1 gene primer pairs are 5-atgggttctcaattagttccaccc-3 and 5-gcttagggattttggagtgctcggg-3. restriction sites xhoi and xmai added to the forward primers and asci and bamhi to the reverse primers to facilitate cloning in sense and antisense forms in the binary vector pfgc5041 within the intron region .
the expected sizes of the selected regions were 348 bp and 879 bp for cloned viral genome to amplify the selected region .
the sizes of the selected fragments were 348 bp and 879 bp for rep / trap and bc1 genes , respectively .
cloned viral genome was used as a template in pcr reaction with a concentration of 100 ng , 5 l of 5x flexi gotaq buffer , 2 l of 25 mm mgcl2 , 0.5 l of 10 mm dntps , 0.5 l 10 pmol of each primer , 0.25 l gotaq enzyme , and ddh2o to reach a total volume of 25 l ; the amplification was carried out in a biorad t100 usa .
the reaction was performed with an initial cycle at 94c for 4 min , followed by 30 cycles of denaturation step at 94c for 1 min , annealing at 50c for 30 sec , and an extension cycle at 72c for 1 min followed by a final cycle at 72c for 7 min .
the amplified fragments were cloned initially into pgem-teasy vector system ; subsequently rep / trap and bc1 fragments were digested using xhoi and xmai and asci and bamhi for cloning in pfgc5041 silencing binary vector ( supplied by richared jorgensen , university of arizona , usa ) .
each fragment was cloned into the expression vector pfgc5041 , in which the transgene is cloned in both orientations separated within the chsa intron and under the control of the 35s promoter and the osc terminator .
the cloning of amplified fragments has been carried out in two steps by using the inner restriction sites on the primers .
double digestion with fastdigest enzymes xmai and bamhi was used for the sense orientation into the plant vector pfgc5041 ; the outer restriction enzymes pair xhoi and asci were used to clone the antisense orientation .
all enzymes used for cloning were fastdigest restriction enzymes supplied from thermo scientific. after confirming the presence of the gene fragments by sequencing , pfgc - rep / trap and pfgc - bc1 were transformed to electrocompetent agrobacterium lb4404 by electroporation .
electroporation was carried out using biorad gene pulser set at 25 f , 200 , and 2.5 kv .
eskandrani ) were grown in the biocontainment greenhouse in the agriculture genetic engineering research institute ( ageri ) at 28c with 16 hr light/8 hr dark . for each treatment
infiltration media were prepared as follows : 5 ml overnight culture was used to inoculate 50 ml of lb medium containing 1 : 1 kanamycin and 0.5 : 1 streptomycin and incubated overnight at 28c . upon centrifugation of the 50 ml overnight culture
, it has been resuspended in infiltration media containing 10 mm mgcl2 , 10 mm , mes , and 20 m acetosyringone and then was incubated at room temperature for 2 hr till its od600 reached 2.0 .
agrobacterium harboring sense / antisense rep / trap construct and sense / antisense bc1 construct infiltrated employing needleless 5 ml syringe using the syringe spotted technique developed by johansen and carrington .
after 1 week from infiltration viruliferous whiteflies feed on infiltrated plant for 48 hr inoculation access period .
the treated plants were sprayed with imidacloprid ( confidor , bayer , leverkusen , germany ) to get rid of the whiteflies .
plants infiltrated with silencing constructs were assayed for positive inoculation with specific pcr primers for each fragment .
the accumulation of viral dna in infected agrobacterium plants was determined by rt - qpcr using the ( leaves weight : 0.51.01 g ) total dna extracted from upper leaves .
the fragment of bc1 amplified by 5-cggatttgaccagtcttctctc-3 and 5-gggcaccgacagtaaagatac-3 as forward and reverse primer , respectively , resulted in fragment with length 102 bp . in case of rep / trap
a fragment with length 105 bp was produced by those primers 5-tatccaaggtgcgatgttcc-3 as forward and 5-atgttcctctctggccattc-3 as reverse one .
annealing temperature was 60c for both fragments , while 18s rrna was used as internal control for gene expression .
squash plants were kept for 10 days after virus infection ; then samples were collected for rt - qpcr detection , and total rna was extracted using sv total rna isolation system .
the rt - qpcr was performed in a ab7300 real - time pcr system ( applied biosystems , usa ) using sybr premix extaqii from takara ( catalog number rr82sw , takara , japan ) ; rt - qpcr analysis was performed as described by manufacturer . in real - time pcr
, primers were tested using conventional pcr resulting in the amplification of fragments monitored at the expected size , where rep primers gave a 105 bp fragment while bc1 gave a 102 bp fragment , with no primer dimer development .
all plant samples from different fields gave the expected band with pcr using the degenerate primer of cp core region , indicating that these samples were infected with geminivirus ( figure 1 ) .
the digestion of amplified products resulted in 4 unique cuts with enzymes ecori , bglii , bamhi , and sali ( figure 2 ) while only xba1 enzyme cut twice ( figure 3 ) .
linearized fragments with the expected size were cloned in the corresponding site into the e. coli vector psk .
three constructed plasmids from cloning of the linearized genome with ecori , bamhi , and sali were sent for sequencing and the sequences were confirmed by similarity search using blast at national center for biotechnology information ( ncbi ) .
results showed that ecori gave component b while sali and bamhi gave component a. identity ratio showed high similarity results reaching 99% homology to component a with other sqlcv isolates .
component b showed less similarity than component a but the identity ratio is still high giving 99% homology with cairo isolate ( dq285020.1 ) , 98% homology with palestine isolate ( kc441466.1 ) , jordon isolates ( jx444574.1 and jx131282.1 ) , israel isolate ( hq184437.1 ) , and lebanon ( hm368374.1 ) , 96% homology with kaliobeya isolate ( kj579954.1 ) , and 95% homology with california isolate ( dq285017.1 ) and arizona isolate ( dq285018.1 ) . to study sqlcv resistance using sirna strategy on squash plants ,
two putatively effective fragments from the whole virus genome of the sqlcva noubaria were chosen to form short dsrna structure for enhancing posttranscriptional gene silencing ( figure 4 ) .
the first fragment was designed targeting the rep / trap with a length of 347 bp , while the second fragment was designed to contain the full bc1 gene with length of 849 bp .
pcr analysis was carried out to amplify both fragments giving the expected band size as showed in figure 5 .
the insertion of the first fragment in the antisense orientation into the pfgc5041 vector was confirmed by restriction digestion using xhoi and asci enzymes , while bamhi and xmai enzymes were used to confirm the insertion of the second fragment in the sense orientation .
the full rnai cassette expression was driven by the e35s promoter and the osc 3 terminator ( figure 6 ) .
positive clones of transformed agrobacterium lb4404 with constructs pfgc5041-rep and pfgc5041-bc1 were screened using colony pcr technique ( data not shown ) . to assess the expression of silencing fragments , c. pepo plant leaves were infiltrated in a transient manner .
plants were then left for a week and subsequently subjected to infection with viruliferous whiteflies raised on infected squash plants with sqlcv . to detect the presence of viral genome in infiltrated plants ,
primers of sqlcv coat protein gene were used in confirming pcr as a positive control .
after the 7th day after infection noninfiltrated control plants gave positive results in pcr ; however pfgc - rep / trap and pfgc - bc1 infiltrated plants gave negative results in pcr . to monitor quantitative viral accumulation in infiltrated squash plants
all noninfiltrated squash plants inoculated with viruliferous whiteflies carrying the sqlcv developed typical viral symptoms with severe yellowing , leaf curling , and a reduced leaflet size .
such plants ceased to grow , failing to flower and produce fruits , while the untreated plants remained the negative control ( figure 7(a ) ) .
one month after inoculation by the pfgc - rep / trap vector all plants were symptomless , while after two months only 1 plant of the total 5 plants gave mild symptoms = + ( figure 7(c ) ) .
meanwhile , in the case of infiltrating the plants with pfgc - bc1 construct , one month after inoculation , plants produced 2 symptomless plants and 3 plants with mild symptoms . by the end of the second month
only 1 plant showed being symptomless , 3 with mild symptoms , and 1 with moderate symptoms = + + ( figure 7(d ) ) ( table 1 ) .
control plants treated with empty pfgc5041 showed early symptoms after two weeks and severe symptoms after one month of inoculation ( figure 7(b ) ) .
quantitative analysis using rt - qpcr assay was carried out to study the level of the expression of the two viral genes , rep / trap and bc1 in the infiltrated squash .
total rna extracted from infiltrated plants was used to synthesize cdna and was subjected to rt - qpcr . in addition , rt - qpcr was performed from infected c. pepo plants as a positive control reaction and nontemplate dna reaction that represent negative control which had ct values equivalent to the total number of cycles used in the rt - qpcr experiment , resulting in curves that did not achieve the threshold level , thus indicating that these reactions contained no detectable viral dna .
the level of virus detection was significantly lower in all infiltrated plants than in the control plants .
infiltrated plants with pfgc - rep / trap construct showed significant shifting in ct value compared with the control .
average ct resulting from re pfgc - rep / trap treatment was 29.51 while an average ct value of control plants was 24.29 .
in pfgc - rep / trap samples the fold of change is calculated using the ct and it showed a 32-fold decrease thus silencing percent was calculated to reach 97% .
also , pfgc - bc1 construct displayed a slight shifting in ct values compared with that in the control .
treated samples ct values average was 29.58 while control ct values average was 27.48 resulting in a decrease 4.7-fold ( table 2 ) .
the calculated expression of bc1 gene has decreased by 79% giving showing a good degree of plant resistance against the respected virus but not as efficient as pfgc - rep / trap construct ( figure 8) .
sqlcv has become a major concern for cultivation of squash in the middle east region .
thus , it is important to study the vast diversity of sqlcv and also the epidemic implications .
small circular dna is preferentially amplified by rca , which makes the ssdna genome of the geminiviruses ideal substrate for rca .
in addition , during viral replication , through complementary strand synthesis ( csr ) of the circular ssdna , rolling circle replication ( rcr ) , and recombination - dependent replication ( rdr ) , various dna intermediates are produced . in this work ,
the rolling circle amplification ( rca ) technology was used for molecular cloning of the sqlcv genome , because of its simplicity , high sensitivity , and proofreading against misincorporation of nucleotides .
it can be used to amplify sequences without the necessity of previous knowledge of it [ 12 , 23 ] .
the sequence of the sqlcv - noubaria isolate obtained in this work showed high similarities to other isolates in the region .
the low sequence variation observed among sqlcv isolates in the middle east region was explained by lapidot et al . .
they predict that uncontrolled movement of viruliferous whiteflies among countries causes viruses readily moved across country boundaries in this region , preventing strong genetic differentiation of these viruses among neighbor countries .
studies on crops harboring virus resistance indicated the possibility of engineering the resistance by different transgene - based approaches . during the past decade
there has been considerable evidence for the successful using of sirna to protect plants against viruses in plum , papaya , watermelon , and potato , which has led to the development of virus - resistant transgenic crops [ 2630 ] . in this
study the same technology has been used by the incorporation of sense and antisense fragments separated in pfgc5041 vector within the chsa intron to be transcribed and hybridized with itself to form a hairpin structure . however , rna silencing degree induced in infiltrated plants could be diverse according to the gene used
. two regions of squash leaf curl viral genome were selected for cloning , the first was rep / trap , and the second was the full length of bc1 gene .
the selected region rep / trap fragment was chosen according to its location representing the end of the rep gene and the beginning of trap in overlapping manner , which may be putatively stronger than one of them alone as it could lead to the silencing of both of them , while in case of bc1 gene it was selected because of its important function in systemic spreading of viral genome through the plasmodesmata , as its silencing attempt is expected to limit the infection and inhibit virus transmission from cell to cell .
the two constructed plasmids , pfgc - rep / trap and pfgc - bc1 , were prepared and used to infiltrate squash plants .
resistance was measured either by monitoring symptoms development or by real - time pcr . in real - time pcr , three replicates from each construct were tested , whereas detection of gene expression was measured by threshold cycle ( ct ) .
thus , higher ct value means less amount of template in the sample , which indicates fewer titrations of virus particles . depending on previous studies using the same virus ,
18s rrna was chosen to be used as the reference gene in real - time pcr . to calculate relative gene expression ct method was used , where target gene expression was normalized to reference gene expression within the same sample to correct any variation that could affect the study .
results of rep / trap fragment in real - time pcr have proved that there is a vital role for this fragment on the rep gene expression as it has been decreased 32-fold and a silencing of 97% has been achieved through this construct .
this significant result could be due to the key role of the rep protein , which is the most essential protein for viral replication .
in addition , transcription activator protein gene is overlapped with rep gene by 50 bp at its 3 end ; this overlapping has played a significant role in silencing of both genes and gave more efficient silencing percent ; this could be clear because the transcription activator protein alone is acting as a gene silencing suppressor so its early silencing may help the plants to resist higher . the construct that contains
the movement protein gene showed a degree of resistance accomplishment but being less efficient than the rep / trap construct .
a decrease in the virus quantity 4.7-fold has been achieved ; this may be due to the late expression of this gene in the virus machinery or it may be due to the effect of its longer fragment size
. in former studies fragments size showed efficient silencing ranged from ~110 to 550 bp [ 36 , 37 ] , while in the case of bc1 gene used in this study it was 879 bp so it might be a factor that affect the silencing percentage .
symptoms developed in all treated plants in each treatment completed the story with the real - time pcr results by giving ratio in plant resistance in case of pfgc - rep / trap construct more than pfgc - bc1 construct .
we have demonstrated that hairpin constructs expressing either 348 bp of the rep / trap gene or 879 bp for the bc1 genes can control sqlcv .
however , sirna produced from using the rep / trap construct proved to be more efficient in controlling the virus than bc1 construct .
it is clear from several studies that the sirna strategy is more efficient at the 5 and 3 ends of the gene .
both the rt - pcr and the symptoms screening at the greenhouse showed that the expression level of the rep gene , as one of the early genes , could play the most significant role in silencing when it is employed as a posttranscriptional gene silencing and tool for controlling the squash leaf curl virus . the bc1 gene could also give a degree silencing but we proved that it is less effective than the rep gene .
therefore , the 3 end fragment of the rep gene for producing stable transformation should be used to measure effect of construct on the transgenic c. pepo plants and reach high level of resistance to sqlcv on large populations in the field .[/INST]squash leaf curl virus ( sqlcv ) is a bipartite begomovirus affecting squash plants .
it is transmitted by whitefly bemisia tabaci biotype b causing severe leaf curling , vein banding , and molting ending by stunting . in this study full - length genomic clone of sqlcv
egyptian isolated and posttranscriptional gene silencing ( ptgs ) has been induced to develop virus resistance . the noubaria sqlcv has more than 95% homology with jordon , israel , lebanon , palestine , and cairo isolates .
two genes fragment from sqlcv introduced in sense and antisense orientations using pfgc5049 vector to be expressed as hairpin rna .
the first fragment was 348 bp from replication associated protein gene ( rep ) .
the second fragment was 879 bp representing the full sequence of the movement protein gene ( bc1 ) .
using real - time pcr , a silencing record of 97% has been recorded to rep / trap construct ; as a result it has prevented the appearance of viral symptoms in most tested plants up to two months after infection , while construct containing the bc1 gene scored a reduction in the accumulation of viral genome expression as appearing in real - time pcr results 4.6-fold giving a silencing of 79% , which had a positive effect on symptoms development in most tested plants .</s> |
in the last years many papers have been devoted to experimental and theoretical studies of bose - einstein interference effects @xcite in multiparticle production .
it has been argued that these studies may allow for the reconstruction of space - time development of the interactions . in particular
, different possibilities of implementing interference effects into monte carlo generators used for high energy hadroproduction processes were discussed . in this note
we add some points to this discussion .
we present in detail some aspects of the weight method of implementing be effect in the mc generators .
in particular , we try to establish to what extent one may reconstruct the two - particle weight function ( related to the wigner function ) from the data on be effect . for this purpose
we use the data on multiparticle production with highest statistics available - the hadronic decays of @xmath0 s produced in @xmath1 collisions .
a short summary of various methods of implementing interference effects into monte carlo generators is presented in the next section . in the third section
we discuss the data from different lep experiments on two - particle correlations from @xmath0 hadronic decays which were used for analyzing the bose - einstein effect .
section 4 is devoted to the analysis of data in terms of the weight model . in particular , various choices of two - particle weight factors used in this method
are compared .
last section contains some conclusions and outlook for further investigations .
the standard discussion of the be effect in multiparticle production @xcite starts from the classical space - time source emitting identical bosons with known momenta .
thus the most natural procedure is to treat the original monte carlo generator as the model for the source and to symmetrize the final state wave function @xcite .
this may be done in a more proper way using the formalism of wigner functions @xcite . in any case , however , the monte carlo generator should yield both the momenta of produced particles and the space - time coordinates of their creation ( or last interaction ) points . even if we avoid troubles with the uncertainty principle by using the wigner function approach
, such a generator seems reliable only for heavy ion collisions .
it has been constructed also for the @xmath2 collisions @xcite , but localizing the hadron creation point in the parton - based monte carlo program for lepton and/or hadron collisions is a rather arbitrary procedure , and it is hard to say what does one really test comparing such a model with data .
it seems to be the best procedure to take into account the interference effects before generating events .
unfortunately , this was done till now only for the jetset generator for a single lund string @xcite , and a generalization for multi - string processes is not obvious .
no similar modifications were yet proposed for other generators .
the most popular approach , applied since years to the description of be effect in various processes , is to shift the final state momenta of events generated by the pythia/ + jetset generators @xcite .
the prescription for a shift is such as to reproduce the experimentallly observed enhancement in the ratio @xmath3 which is a function of a single invariant variable @xmath4 .
the value of this function is close to one for the default jetset / pythia generator .
one parametrizes often this ratio by @xmath5 where @xmath6 and @xmath7 are parameters interpreted as the source radius and `` incoherence strength '' , respectively . after performing the shifts , all the cm 3-momenta of final state particles
are rescaled to restore the original energy . in more recent versions of the procedure
@xcite `` local rescaling '' is used instead of the global one . in any case , each event is modified and the resulting generated sample exhibits now the `` be enhancement '' : the ratio ( [ eq : ratio ] ) is no longer close to one , and may be parametrized as in ( [ eq : factor ] ) . there is no theoretical justification for this procedure , so it should be regarded as an imitation rather than implementation of the be effect .
its success or failure in describing data is the only relevant feature .
unfortunately , whereas the method is very useful for the description of two - particle inclusive spectra , it fails to reproduce ( with the same fit parameters @xmath6 and @xmath7 ) the three - particle spectra @xcite and the semi - inclusive data @xcite .
this could be certainly cured , e.g. , by modifying the shifting procedure and fitting the parameters separately for each semi - inclusive sample of data . however , the fitted values of parameters needed in the input factor ( [ eq : factor ] ) used to calculate shifts are quite different from the values one would get fitting the resulting ratio ( [ eq : ratio ] ) to the same form @xcite .
this was shown recently in a much more detailed study @xcite .
thus it seems to be very difficult to learn something reliable on the space - time structure of the source from the values of fit parameters in this procedure .
all this has led to the revival of weight methods , known for quite a long time @xcite , but plagued with many practical problems .
the method is clearly justified within the formalism of the wigner functions , which allows to represent ( after some simplifying assumptions ) any distribution with the be effect built in as a product of the original distribution ( without the be effect ) and the weight factor , depending on the final state momenta @xcite . with an extra assumption of factorization in momentum space , we may write the weight factor for the final state with @xmath8 identical bosons as @xmath9 where the sum extends over all permutations @xmath10 of @xmath8 elements , and @xmath11 is a two - particle weight factor reflecting the effective source size .
a commonly used simple parametrization of this factor for a lorentz symmetric source is @xmath12 , \label{eq : wf}\ ] ] the only free parameter is now @xmath13 , representing the inverse of the effective source size .
in fact , the full weight given to each event should be a product of factors ( [ eq : weight ] ) calculated for all kinds of bosons ; in practice , pions of all signs should be taken into account . only direct pions and the decay products of @xmath14 and @xmath15 should be taken into account , since for other pairs much bigger @xmath6 should be used , resulting in negligible contributions .
the main problem of the weight methods is that weights do change not only the bose - einstein ratio ( [ eq : ratio ] ) , but also many other distributions .
thus with the default values of free parameters ( fitted to the data without weights ) we find inevitably some discrepancies with data after introducing weights .
we want to make clear that this can not be taken as a flaw of the weight method .
there is no measurable world `` without the be effect '' , and it makes not much sense to ask , if this effect changes e.g. the multiplicity distributions . if any model is compared to the data without taking the be effect into account , the fitted values of its free parameters are simply not correct .
they should be refitted with weights , and then the weights recalculated in an iterative procedure .
this , however , may be a rather tedious task .
therefore we use a simple rescaling method proposed by jadach and zalewski @xcite . instead of refitting the free parameters of the mc generator , we rescale the be weights ( calculated according to the procedure outlined above ) with a simple factor @xmath16 , where @xmath8 is the global multiplicity of `` direct '' pions , and @xmath17 and @xmath18 are fit parameters .
their values are fitted to minimize @xmath19 ^ 2/n^0(n ) \label{eq : chi2}\ ] ] where @xmath20 is the number of events for the multiplicity @xmath8 without weights , and @xmath21 is the weighted number of events .
this rescaling restores the original multiplicity distribution @xcite .
in addition , the single longitudinal and transverse momentum spectra are also restored by this rescaling @xcite .
obviously , for a more detailed analysis of the final states , single rescaling may be not enough .
e.g. , since different parameters govern the average number of jets and the average multiplicity of a single jet , both should be rescaled separately to avoid discrepancy with data .
let us stress once again that such problems arise due to the use of generators with improperly fitted free parameters , and do not suggest any flaw of the weight method .
another problem is that our formula for weights ( [ eq : weight ] ) is derived using some approximations , which are rather difficult to control @xcite .
we can justify them only _ a posteriori _ from the phenomenological successes of the weight method .
last but not least , the main practical difficulty with formula ( [ eq : weight ] ) is the factorial increase of the number of terms in the sum with increasing multiplicity of identical pions @xmath8 . for high energies , when @xmath8 often exceeds 20 , a straightforward application of formula ( [ eq : weight ] ) is impractical @xcite , and some authors @xcite replaced it with simpler expresssions , motivated by some models .
it is , however , rather difficult to estimate their reliability .
we have recently proposed two ways of dealing with this problem .
one method consists of a truncation of the sum ( 3 ) up to terms , for which the permutation @xmath22 moves no more than 5 particles from their places @xcite .
however , it is difficult to claim a priori that such a truncation does not change the results which would be obtained using the full series ( 2 ) . therefore a second way of an approximate calculation of the sum ( 2 ) was proposed @xcite . since this sum , called a permanent of a matrix built from weight factors @xmath23 , is quite familiar in field theory , one may use a known integral representation and approximate the integral by the saddle point method .
however , this method is reliable only if in each row ( and column ) of the matrix there is at least one non - diagonal element significantly different from zero .
thus the prescription should not be applied to the full events , but to the clusters , in which each momentum is not far from at least one other momentum .
the full weight is then a product of weights calculated for clusters , in which the full event is divided .
the considerations presented above suggested the necessity of combining these two methods .
after dividing the final state momenta of identical particles into clusters , we used for small clusters exact formulae presented in @xcite . for large clusters
( with more than five particles ) we compared two approximations ( truncated series and the integral representation ) to estimate their reliability and the sensitivity of the final results to the method .
obviously , the results depend also on the clustering algorithm : if we restrict each cluster to particles very close in momentum space , the neglected contributions to the sum ( [ eq : weight ] ) from permutations exchanging pions from different clusters may be non - negligible , and if the cluster definition is very loose , the saddle point approximation may be unreliable .
this was then also checked to optimize the algorithm used .
we found that the truncated series approximation was sufficient in all cases we checked on @xcite .
our method was already applied to the analysis of @xmath24 production @xcite .
extremely high statistics collected in lep for the hadronic decays of @xmath0-s produced in the @xmath1 collisions allowed to investigate in detail many interesting effects . in particular , the interference effects due to the bose - einstein statistics for pions were analyzed in several experiments .
the notorious difficulty in measuring the bose - einstein interference effects ( be effects ) in the multiparticle production is the proper choice of reference sample . in the early investigations
the ratio of numbers of `` like - to - unlike '' charged pion pairs was analyzed as a function of three- or four - momentum difference squared @xmath25d^3p_1 d^3p_2}{\int\rho_2^{+-}(p_1,p_2)\delta[(p_1-p2)^2+q^2]d^3p_1d^3p_2 } \label{eq:6}\ ] ] obviously , the denominator has breit - wigner peaks around the values of @xmath26 corresponding to masses of resonances in the @xmath27system ( and other peaks due to the maxima in mass spectra from 3-pion resonances ) which are absent in the numerator .
to estimate properly the be effects one should subtract these maxima , or to exclude the `` resonance regions '' from the @xmath26 range used in fitting @xmath28 to the chosen function . therefore recently a more common choice for the denominator
was the `` uncorrelated background '' formed e.g. by choosing pairs of `` like sign '' pions from different events , which led to the definition presented in the former section ( [ eq : ratio ] ) . here
the main problem comes from neglecting the energy - momentum conservation effects ( present in the numerator and absent in the denominator ) .
however , for high energies and restricted range of momenta ( e.g. the `` central region '' , often used for the analysis ) such effects are expected to be rather small .
this method is easy to apply for hadronic or heavy ion collisions , where the initial momenta form the natural symmetry axis in the cm frame . for @xmath0
decays the typical events are not aligned with the momenta of the initial @xmath1 pair .
thus the momenta chosen from different events should be rotated to the same symmetry axis before calculating @xmath26 .
unfortunately , such a procedure is not well - defined : using sphericity , thrust or other variables one obtains different values of rotation angles .
moreover , the three- and many - jet events do not have well - defined symmetry axis , and limiting the analysis to the two - jet events would be rather arbitrary ( and dependent on the jet definition ) . * fig.1 . * _ a ) the be ratio @xmath28 ( 6 ) from the opal data ( black points ) and from the jetset mc without be effect ( open points ) ; b ) the double ratio @xmath29 ( 7 ) from the same data .
solid lines are fits to the form ( 8) [ 25 ] .
_ therefore the best strategy seems to be using monte carlo generators , which are rather reliable for the process under discussion . instead of analyzing the be ratio
@xmath28 one considers the `` double ratio '' , i.e. the ratio of @xmath30 given by the data and @xmath31 computed from the mc generated events @xmath32 analogous `` double ratio '' has been defined also for the first definition of the `` be ratio '' ( [ eq : ratio ] ) @xcite .
the results obtained for two double ratios are inconsistent . in the following we use only the definition ( [ eq:7 ] ) , preferred recently by the experimental groups @xcite .
the data with largest statistics has been presented by the opal group both for @xmath29 and for @xmath28 .
they compared the parameter values from the fits ( with resonance regions excluded ) to the function @xmath33(1+\alpha x^2 ) .
\label{eq:8}\ ] ] the data ( based on 3.6 milion of events ) were shown for @xmath34 and for @xmath35 @xcite .
we remind here in fig.1 the data and fits for @xmath36 and @xmath37 .
the values of @xmath7 and r differ quite significantly , as shown in table i. table i. fits to opal data .
[ cols="<,^,^,^",options="header " , ] @xmath13 is not a best measure of `` width in momentum space '' when one compares different shapes of the weight factor .
it seems more natural to use @xmath38 , which is just the average value of @xmath4 for a given weight factor @xmath39 if we define @xmath40 as the `` effective source size '' we find a close relation between the fitted values of @xmath6 and the input values of @xmath41 .
the ratio @xmath42 , quoted in the last column of table ii , is in the range @xmath43 for almost all values of @xmath13 and all shapes of the weight factor . the first obvious conclusion from fig .
4 is that the fits to the two experimental sets of data are strongly different .
this is partly due to the gamow correction for the effect of electromagnetic final state interactions , which was used by opal and neglected by aleph .
since it has been recently argued that this correction badly overestimates the effect @xcite , we have shown also an estimate for the opal point without gamow correction ( obtained using the values for correction quoted in ref .
now the two data points are much closer , but still they differ significantly .
the values resulting from our generated samples cover quite a wide range both in @xmath7 and r. certainly it is possible to reproduce any of the experimental values by a suitable choice of the form and free parameters of our weight factors .
however , we do not think it would give a valuable information on the `` proper '' choice of the weight factor reflecting the `` real '' space - time structure of the source .
there are a few reasons for such scepticism .
first , as noted in the previous section , the shape of `` experimental '' @xmath29 strongly depends on the quality of `` reference mc '' . since we know that already at @xmath44 the influence of ( poorly described ) @xmath45 and @xmath46 contributions
distorts the shape , the fitted values of @xmath6 around @xmath47 are not very reliable .
the situation is even less clear if one fits wider range of q using a more elaborate ansatz for @xmath29 ( e.g. ( [ eq:8 ] ) ) . here
the choice of `` cut out resonance region '' may influence quite significantly the fit results .
moreover , the method of implementing the be effect may influence the resonance contribution . for our method
the absence of peaks or bumps in the double ratio for `` mc with weights '' over `` mc without weights '' ( as seen , e.g. , in fig .
3 ) suggests that this is not the case ( the oscillations shown in fig .
2 ) of ref . @xcite may result from lower statistics ) .
this should be also checked for any other method .
second , the choice of `` direct '' pions affected by the be effects described in section 2 ( although the same in our method and in the sjoestrand s momentum shift method ) is by no means unique .
in fact , even for the fastest - decaying resonances the effective `` source radius '' for the decay products should not be exactly the same as for the `` real direct pions '' .
thus the choice of a single value of @xmath13 in our weight factor is certainly an oversimplification .
the total exclusion of the decay products of long - living resonances is also an approximation : some of them may be born quite close to the collision point and contribute to the visible be effect .
the selection and treatment of `` direct '' pions included in calculating weights ( or subject to the momentum shift in the sjestrand s method ) influences strongly the resulting value of @xmath7 .
third , the standard fitting method of be ratios or double ratios is also a subject of criticism @xcite .
more plausible methods suggest bigger uncertainties of the fit parameters
. the situation would not improve if we add the other published data , which used much lower statistics @xcite or different form of the fitted function @xcite .
one may shortly summarize that it is too early to deduce details of the source space - time structure from the existing data , even if we assume the applicability of all the assumptions used in formulating the weight method .
another interesting feature is the relative stability of our results with respect to the detailed shape of two - particle weight factor .
the fitted values of @xmath7 fall in the range of values 0.2 - 0.5 for all the functions considered .
they are highest for the step function , lower for `` diffuse step function '' , still lower for a gaussian and lowest for the exponent .
one may summarize that for the same `` half width '' of the weight factor function one gets higher value of @xmath7 if the function stays longer near the value of 1 at small q. as already noted , @xmath7 depends much stronger on the percentage of pions counted as `` direct '' .
the values of @xmath7 below 1 reflect mainly the percentage of direct like - sign pion pairs , which was already observed when using sjstrand s method of be effect implementation @xcite .
a new result is the observed relative insensitivity of the results on the oscillations in the two - particle weight factor .
in fact , the oscillation half - period serves as an effective range of correlations if it is smaller than @xmath13 .
therefore @xmath41 is almost the same for all the values of @xmath13 quoted in the table ii .
the non - positive oscillating values of weight factor for larger q do not result in the values of @xmath29 oscillating around 1 , as one could naively expect ; averaging over many pairs in each event and over many events kills any trace of oscillations .
this is quite important , as many simple forms of weight factor in space - time ( e.g. the step function ) results in oscillating form in momentum space . on the other hand , there is an obvious dependence of fitted values of r on the parameter @xmath13 ( or @xmath41 ) , which determine how fast the weight factor decreases with increasing q. @xmath42 has quite similar values for various shapes of the weight factors and various values of @xmath13 .
thus in our method r reflects in some sense the `` source size '' , as expected . as already noted ,
this is true also for the oscillations in momentum space . increasing @xmath13
one increases also fitted values of @xmath7 , but this effect is weaker .
we have analyzed the data on be effect in multihadron states obtained from @xmath0 decays within the framework of the weight method of implementing the effect .
we show that the resonance contributions are not satisfactorily described by the standard mc generators , which makes the analysis of `` double ratio '' data quite difficult . in particular , the choice of the `` proper '' two particle weight factor which would describe the data best is obviously dependent on the way the data are processed
. thus one should improve ( if possible ) the quality of mc generators before drawing any serious conclusion on the agreement or disagreement between the models and data on the be effect .
the alternative is to elaborate better methods of preparing the `` reference sample '' using only the like - sign pairs , which are much less affected by the resonance effects . on the other hand
, we found that the analysis makes no great difference between the positively defined and oscillating weight factors in momentum space , provided they correspond to similar `` half - width '' .
this means that the results are not too strongly dependent on the `` sharpness of the source boundary '' in space - time ; one may hope to recover the proper `` source size '' in our method .
let us stress that the analysis presented in this paper is just the first step : we do not discuss the anisotropy of source nor the time dependence reflected in the be effect . also , we do not consider here the possibilities of comparing the effect for selected classes of events ( defined i.e. by multiplicity , by event shape parameters or by some special triggers ) . in our opinion ,
the weight method is well suited to discuss these subjects and we hope to consider them in near future .
the authors are grateful to a. biaas for useful remarks . the financial support from kbn grants no 2 p03b 086 14 and no 2 p03b 010 15 are acknowledged .
a. gagatek provided patient assistance with figure preparations .
99 r. hanbury - brown and r.q .
twiss , _ nature _ * 178 * ( 1956 ) 1046 .
boal , c .- k .
gelbke and b.k .
jennings , _ rev
* 62 * ( 1990 ) 553 ; r.m .
weiner , e - print hep - ph/9904389 .
j.p . sullivan _
_ , _ phys .
_ * 70 * ( 1993 ) 3000 .
q.h . zhang _
_ b * 407 * ( 1997 ) 33 .
j. ellis and k. geiger , _ phys .
_ d * 54 * ( 1996 ) 1967 ; k. geiger , j. ellis , u. heinz and u.a .
wiedemann , e - print hep - ph/9811270 .
b. andersson and m. ringnr , _ nucl .
_ b * 513 * ( 1998 ) 627 .
b. andersson and m. ringnr , _ phys .
_ b * 421 * ( 1998 ) 283 .
s. todorova - nov and j. rames , e - print hep - ph/9710280 .
j. hkkinen and m. ringnr , _ eur .
c * 5 * ( 1998 ) 275 .
t. sjstrand and m. bengtsson , _ comp .
* 43 * ( 1987 ) 367 ; t. sjstrand , _ comp .
* 82 * ( 1994 ) 74 .
l. lnnblad and t. sjstrand , _ phys .
_ b * 351 * ( 1995 ) 293 .
l. lnnblad and t. sjstrand , _ eur .
c * 2 * ( 1998 ) 165 .
et al . _ , in _ proc .
cracow workshop on multiparticle production `` soft physics and fluctuations '' _ , ed .
a. biaas _
_ , p.22 , world sci . , singapore 1994 .
_ , _ phys .
_ b * 332 * ( 1994 ) 458 .
k. fiakowski and r. wit , _ z. phys .
_ c * 74 * ( 1997 ) 145 .
o. smirnova , b. lrstad , r. murean , proceedings of the 8th int .
workshop on multiparticle prod .
, _ correlations and fluctuations 98 _ ( mtrahza , hungary ) , ed .
t. csrg , s. hegyi , g. jancs and r.c .
hwa , p.20 , world sci .
singapore 1999 .
s. pratt , _ phys .
_ * 53 * ( 1984 ) 1219 .
a. biaas and a. krzywicki , _ phys .
_ b * 354 * ( 1995 ) 134 .
s. haywood , rutherford lab .
report ral-94 - 074
. s. jadach and k. zalewski , _ acta phys . pol .
b * 28 * ( 1997 ) 1363 . v. kartvelishvili , r. kvatadze and r. mller , _ phys .
_ b * 408 * ( 1997 ) 331 .
k. fiakowski and r. wit , _ eur .
c * 2 * ( 1998 ) 691 .
j. wosiek , _ phys .
_ b * 399 * ( 1997 ) 130 .
k. fiakowski , r. wit and j. wosiek , _ phys .
_ d * 57 * ( 1998 ) 094013 .
k. fiakowski and r. wit , _ phys .
_ b * 438 * ( 1998 ) 154 .
aleph collaboration , d. decamp _
et al.__z .
_ c * 54 * ( 1992 ) 75 .
opal collaboration , g. alexander _
_ z. phys .
_ c * 72 * ( 1996 ) 389 .
the aleph collaboration , collaboration report aleph 99 - 027 , contribution conf 99 - 021 to the 1999 winter conferences .
bowler , _ phys
_ b * 270 * ( 1991 ) 69 ; m.biyajima _ et al .
_ _ phys . lett .
_ b * 353 * ( 1995 ) 340 ; g.baym and p. braun - munzinger , _ nucl .
phys . _ a * 610 * ( 1996 ) 286c ; h. merlitz and d. pelte , _ phys
_ b * 415 * ( 1997 ) 411 .
a. de angelis and l. vitale , cern preprint cern - open 98 - 020 , e - print hep - ex/9808002 .
delphi collaboration , p. abreu _ at al _ , _ phys .
_ b * 286 * ( 1992 ) 201 .
delphi collaboration , p. abreu _ at al _ , _
_ c * 63 * ( 1994 ) 17 . | we discuss the bose - einstein interference effect in multiparticle production . after a short review of various methods of implementation of this effect into monte carlo generators
the weight method is presented in more detail and used to analyze the data for hadronic @xmath0 decays . in particular
, we consider the possibility of deducing the two - particle weight factor from the experimental data . 23.0 cm 16.0 cm -1.0 cm 0.0 cm 0.0 cm k. fiakowski , r. wit _ m. smoluchowski institute of physics + jagellonian university + 30 - 059 krakw , ul.reymonta 4 , poland _
pacs : 13.85.-t , 13.90.+i + _ keywords : _ monte carlo , bose - einstein correlations , @xmath0 decay + august , 1999 + | <s>[INST]in the last years many papers have been devoted to experimental and theoretical studies of bose - einstein interference effects @xcite in multiparticle production .
it has been argued that these studies may allow for the reconstruction of space - time development of the interactions . in particular
, different possibilities of implementing interference effects into monte carlo generators used for high energy hadroproduction processes were discussed . in this note
we add some points to this discussion .
we present in detail some aspects of the weight method of implementing be effect in the mc generators .
in particular , we try to establish to what extent one may reconstruct the two - particle weight function ( related to the wigner function ) from the data on be effect . for this purpose
we use the data on multiparticle production with highest statistics available - the hadronic decays of @xmath0 s produced in @xmath1 collisions .
a short summary of various methods of implementing interference effects into monte carlo generators is presented in the next section . in the third section
we discuss the data from different lep experiments on two - particle correlations from @xmath0 hadronic decays which were used for analyzing the bose - einstein effect .
section 4 is devoted to the analysis of data in terms of the weight model . in particular , various choices of two - particle weight factors used in this method
are compared .
last section contains some conclusions and outlook for further investigations .
the standard discussion of the be effect in multiparticle production @xcite starts from the classical space - time source emitting identical bosons with known momenta .
thus the most natural procedure is to treat the original monte carlo generator as the model for the source and to symmetrize the final state wave function @xcite .
this may be done in a more proper way using the formalism of wigner functions @xcite . in any case , however , the monte carlo generator should yield both the momenta of produced particles and the space - time coordinates of their creation ( or last interaction ) points . even if we avoid troubles with the uncertainty principle by using the wigner function approach
, such a generator seems reliable only for heavy ion collisions .
it has been constructed also for the @xmath2 collisions @xcite , but localizing the hadron creation point in the parton - based monte carlo program for lepton and/or hadron collisions is a rather arbitrary procedure , and it is hard to say what does one really test comparing such a model with data .
it seems to be the best procedure to take into account the interference effects before generating events .
unfortunately , this was done till now only for the jetset generator for a single lund string @xcite , and a generalization for multi - string processes is not obvious .
no similar modifications were yet proposed for other generators .
the most popular approach , applied since years to the description of be effect in various processes , is to shift the final state momenta of events generated by the pythia/ + jetset generators @xcite .
the prescription for a shift is such as to reproduce the experimentallly observed enhancement in the ratio @xmath3 which is a function of a single invariant variable @xmath4 .
the value of this function is close to one for the default jetset / pythia generator .
one parametrizes often this ratio by @xmath5 where @xmath6 and @xmath7 are parameters interpreted as the source radius and `` incoherence strength '' , respectively . after performing the shifts , all the cm 3-momenta of final state particles
are rescaled to restore the original energy . in more recent versions of the procedure
@xcite `` local rescaling '' is used instead of the global one . in any case , each event is modified and the resulting generated sample exhibits now the `` be enhancement '' : the ratio ( [ eq : ratio ] ) is no longer close to one , and may be parametrized as in ( [ eq : factor ] ) . there is no theoretical justification for this procedure , so it should be regarded as an imitation rather than implementation of the be effect .
its success or failure in describing data is the only relevant feature .
unfortunately , whereas the method is very useful for the description of two - particle inclusive spectra , it fails to reproduce ( with the same fit parameters @xmath6 and @xmath7 ) the three - particle spectra @xcite and the semi - inclusive data @xcite .
this could be certainly cured , e.g. , by modifying the shifting procedure and fitting the parameters separately for each semi - inclusive sample of data . however , the fitted values of parameters needed in the input factor ( [ eq : factor ] ) used to calculate shifts are quite different from the values one would get fitting the resulting ratio ( [ eq : ratio ] ) to the same form @xcite .
this was shown recently in a much more detailed study @xcite .
thus it seems to be very difficult to learn something reliable on the space - time structure of the source from the values of fit parameters in this procedure .
all this has led to the revival of weight methods , known for quite a long time @xcite , but plagued with many practical problems .
the method is clearly justified within the formalism of the wigner functions , which allows to represent ( after some simplifying assumptions ) any distribution with the be effect built in as a product of the original distribution ( without the be effect ) and the weight factor , depending on the final state momenta @xcite . with an extra assumption of factorization in momentum space , we may write the weight factor for the final state with @xmath8 identical bosons as @xmath9 where the sum extends over all permutations @xmath10 of @xmath8 elements , and @xmath11 is a two - particle weight factor reflecting the effective source size .
a commonly used simple parametrization of this factor for a lorentz symmetric source is @xmath12 , \label{eq : wf}\ ] ] the only free parameter is now @xmath13 , representing the inverse of the effective source size .
in fact , the full weight given to each event should be a product of factors ( [ eq : weight ] ) calculated for all kinds of bosons ; in practice , pions of all signs should be taken into account . only direct pions and the decay products of @xmath14 and @xmath15 should be taken into account , since for other pairs much bigger @xmath6 should be used , resulting in negligible contributions .
the main problem of the weight methods is that weights do change not only the bose - einstein ratio ( [ eq : ratio ] ) , but also many other distributions .
thus with the default values of free parameters ( fitted to the data without weights ) we find inevitably some discrepancies with data after introducing weights .
we want to make clear that this can not be taken as a flaw of the weight method .
there is no measurable world `` without the be effect '' , and it makes not much sense to ask , if this effect changes e.g. the multiplicity distributions . if any model is compared to the data without taking the be effect into account , the fitted values of its free parameters are simply not correct .
they should be refitted with weights , and then the weights recalculated in an iterative procedure .
this , however , may be a rather tedious task .
therefore we use a simple rescaling method proposed by jadach and zalewski @xcite . instead of refitting the free parameters of the mc generator , we rescale the be weights ( calculated according to the procedure outlined above ) with a simple factor @xmath16 , where @xmath8 is the global multiplicity of `` direct '' pions , and @xmath17 and @xmath18 are fit parameters .
their values are fitted to minimize @xmath19 ^ 2/n^0(n ) \label{eq : chi2}\ ] ] where @xmath20 is the number of events for the multiplicity @xmath8 without weights , and @xmath21 is the weighted number of events .
this rescaling restores the original multiplicity distribution @xcite .
in addition , the single longitudinal and transverse momentum spectra are also restored by this rescaling @xcite .
obviously , for a more detailed analysis of the final states , single rescaling may be not enough .
e.g. , since different parameters govern the average number of jets and the average multiplicity of a single jet , both should be rescaled separately to avoid discrepancy with data .
let us stress once again that such problems arise due to the use of generators with improperly fitted free parameters , and do not suggest any flaw of the weight method .
another problem is that our formula for weights ( [ eq : weight ] ) is derived using some approximations , which are rather difficult to control @xcite .
we can justify them only _ a posteriori _ from the phenomenological successes of the weight method .
last but not least , the main practical difficulty with formula ( [ eq : weight ] ) is the factorial increase of the number of terms in the sum with increasing multiplicity of identical pions @xmath8 . for high energies , when @xmath8 often exceeds 20 , a straightforward application of formula ( [ eq : weight ] ) is impractical @xcite , and some authors @xcite replaced it with simpler expresssions , motivated by some models .
it is , however , rather difficult to estimate their reliability .
we have recently proposed two ways of dealing with this problem .
one method consists of a truncation of the sum ( 3 ) up to terms , for which the permutation @xmath22 moves no more than 5 particles from their places @xcite .
however , it is difficult to claim a priori that such a truncation does not change the results which would be obtained using the full series ( 2 ) . therefore a second way of an approximate calculation of the sum ( 2 ) was proposed @xcite . since this sum , called a permanent of a matrix built from weight factors @xmath23 , is quite familiar in field theory , one may use a known integral representation and approximate the integral by the saddle point method .
however , this method is reliable only if in each row ( and column ) of the matrix there is at least one non - diagonal element significantly different from zero .
thus the prescription should not be applied to the full events , but to the clusters , in which each momentum is not far from at least one other momentum .
the full weight is then a product of weights calculated for clusters , in which the full event is divided .
the considerations presented above suggested the necessity of combining these two methods .
after dividing the final state momenta of identical particles into clusters , we used for small clusters exact formulae presented in @xcite . for large clusters
( with more than five particles ) we compared two approximations ( truncated series and the integral representation ) to estimate their reliability and the sensitivity of the final results to the method .
obviously , the results depend also on the clustering algorithm : if we restrict each cluster to particles very close in momentum space , the neglected contributions to the sum ( [ eq : weight ] ) from permutations exchanging pions from different clusters may be non - negligible , and if the cluster definition is very loose , the saddle point approximation may be unreliable .
this was then also checked to optimize the algorithm used .
we found that the truncated series approximation was sufficient in all cases we checked on @xcite .
our method was already applied to the analysis of @xmath24 production @xcite .
extremely high statistics collected in lep for the hadronic decays of @xmath0-s produced in the @xmath1 collisions allowed to investigate in detail many interesting effects . in particular , the interference effects due to the bose - einstein statistics for pions were analyzed in several experiments .
the notorious difficulty in measuring the bose - einstein interference effects ( be effects ) in the multiparticle production is the proper choice of reference sample . in the early investigations
the ratio of numbers of `` like - to - unlike '' charged pion pairs was analyzed as a function of three- or four - momentum difference squared @xmath25d^3p_1 d^3p_2}{\int\rho_2^{+-}(p_1,p_2)\delta[(p_1-p2)^2+q^2]d^3p_1d^3p_2 } \label{eq:6}\ ] ] obviously , the denominator has breit - wigner peaks around the values of @xmath26 corresponding to masses of resonances in the @xmath27system ( and other peaks due to the maxima in mass spectra from 3-pion resonances ) which are absent in the numerator .
to estimate properly the be effects one should subtract these maxima , or to exclude the `` resonance regions '' from the @xmath26 range used in fitting @xmath28 to the chosen function . therefore recently a more common choice for the denominator
was the `` uncorrelated background '' formed e.g. by choosing pairs of `` like sign '' pions from different events , which led to the definition presented in the former section ( [ eq : ratio ] ) . here
the main problem comes from neglecting the energy - momentum conservation effects ( present in the numerator and absent in the denominator ) .
however , for high energies and restricted range of momenta ( e.g. the `` central region '' , often used for the analysis ) such effects are expected to be rather small .
this method is easy to apply for hadronic or heavy ion collisions , where the initial momenta form the natural symmetry axis in the cm frame . for @xmath0
decays the typical events are not aligned with the momenta of the initial @xmath1 pair .
thus the momenta chosen from different events should be rotated to the same symmetry axis before calculating @xmath26 .
unfortunately , such a procedure is not well - defined : using sphericity , thrust or other variables one obtains different values of rotation angles .
moreover , the three- and many - jet events do not have well - defined symmetry axis , and limiting the analysis to the two - jet events would be rather arbitrary ( and dependent on the jet definition ) . * fig.1 . * _ a ) the be ratio @xmath28 ( 6 ) from the opal data ( black points ) and from the jetset mc without be effect ( open points ) ; b ) the double ratio @xmath29 ( 7 ) from the same data .
solid lines are fits to the form ( 8) [ 25 ] .
_ therefore the best strategy seems to be using monte carlo generators , which are rather reliable for the process under discussion . instead of analyzing the be ratio
@xmath28 one considers the `` double ratio '' , i.e. the ratio of @xmath30 given by the data and @xmath31 computed from the mc generated events @xmath32 analogous `` double ratio '' has been defined also for the first definition of the `` be ratio '' ( [ eq : ratio ] ) @xcite .
the results obtained for two double ratios are inconsistent . in the following we use only the definition ( [ eq:7 ] ) , preferred recently by the experimental groups @xcite .
the data with largest statistics has been presented by the opal group both for @xmath29 and for @xmath28 .
they compared the parameter values from the fits ( with resonance regions excluded ) to the function @xmath33(1+\alpha x^2 ) .
\label{eq:8}\ ] ] the data ( based on 3.6 milion of events ) were shown for @xmath34 and for @xmath35 @xcite .
we remind here in fig.1 the data and fits for @xmath36 and @xmath37 .
the values of @xmath7 and r differ quite significantly , as shown in table i. table i. fits to opal data .
[ cols="<,^,^,^",options="header " , ] @xmath13 is not a best measure of `` width in momentum space '' when one compares different shapes of the weight factor .
it seems more natural to use @xmath38 , which is just the average value of @xmath4 for a given weight factor @xmath39 if we define @xmath40 as the `` effective source size '' we find a close relation between the fitted values of @xmath6 and the input values of @xmath41 .
the ratio @xmath42 , quoted in the last column of table ii , is in the range @xmath43 for almost all values of @xmath13 and all shapes of the weight factor . the first obvious conclusion from fig .
4 is that the fits to the two experimental sets of data are strongly different .
this is partly due to the gamow correction for the effect of electromagnetic final state interactions , which was used by opal and neglected by aleph .
since it has been recently argued that this correction badly overestimates the effect @xcite , we have shown also an estimate for the opal point without gamow correction ( obtained using the values for correction quoted in ref .
now the two data points are much closer , but still they differ significantly .
the values resulting from our generated samples cover quite a wide range both in @xmath7 and r. certainly it is possible to reproduce any of the experimental values by a suitable choice of the form and free parameters of our weight factors .
however , we do not think it would give a valuable information on the `` proper '' choice of the weight factor reflecting the `` real '' space - time structure of the source .
there are a few reasons for such scepticism .
first , as noted in the previous section , the shape of `` experimental '' @xmath29 strongly depends on the quality of `` reference mc '' . since we know that already at @xmath44 the influence of ( poorly described ) @xmath45 and @xmath46 contributions
distorts the shape , the fitted values of @xmath6 around @xmath47 are not very reliable .
the situation is even less clear if one fits wider range of q using a more elaborate ansatz for @xmath29 ( e.g. ( [ eq:8 ] ) ) . here
the choice of `` cut out resonance region '' may influence quite significantly the fit results .
moreover , the method of implementing the be effect may influence the resonance contribution . for our method
the absence of peaks or bumps in the double ratio for `` mc with weights '' over `` mc without weights '' ( as seen , e.g. , in fig .
3 ) suggests that this is not the case ( the oscillations shown in fig .
2 ) of ref . @xcite may result from lower statistics ) .
this should be also checked for any other method .
second , the choice of `` direct '' pions affected by the be effects described in section 2 ( although the same in our method and in the sjoestrand s momentum shift method ) is by no means unique .
in fact , even for the fastest - decaying resonances the effective `` source radius '' for the decay products should not be exactly the same as for the `` real direct pions '' .
thus the choice of a single value of @xmath13 in our weight factor is certainly an oversimplification .
the total exclusion of the decay products of long - living resonances is also an approximation : some of them may be born quite close to the collision point and contribute to the visible be effect .
the selection and treatment of `` direct '' pions included in calculating weights ( or subject to the momentum shift in the sjestrand s method ) influences strongly the resulting value of @xmath7 .
third , the standard fitting method of be ratios or double ratios is also a subject of criticism @xcite .
more plausible methods suggest bigger uncertainties of the fit parameters
. the situation would not improve if we add the other published data , which used much lower statistics @xcite or different form of the fitted function @xcite .
one may shortly summarize that it is too early to deduce details of the source space - time structure from the existing data , even if we assume the applicability of all the assumptions used in formulating the weight method .
another interesting feature is the relative stability of our results with respect to the detailed shape of two - particle weight factor .
the fitted values of @xmath7 fall in the range of values 0.2 - 0.5 for all the functions considered .
they are highest for the step function , lower for `` diffuse step function '' , still lower for a gaussian and lowest for the exponent .
one may summarize that for the same `` half width '' of the weight factor function one gets higher value of @xmath7 if the function stays longer near the value of 1 at small q. as already noted , @xmath7 depends much stronger on the percentage of pions counted as `` direct '' .
the values of @xmath7 below 1 reflect mainly the percentage of direct like - sign pion pairs , which was already observed when using sjstrand s method of be effect implementation @xcite .
a new result is the observed relative insensitivity of the results on the oscillations in the two - particle weight factor .
in fact , the oscillation half - period serves as an effective range of correlations if it is smaller than @xmath13 .
therefore @xmath41 is almost the same for all the values of @xmath13 quoted in the table ii .
the non - positive oscillating values of weight factor for larger q do not result in the values of @xmath29 oscillating around 1 , as one could naively expect ; averaging over many pairs in each event and over many events kills any trace of oscillations .
this is quite important , as many simple forms of weight factor in space - time ( e.g. the step function ) results in oscillating form in momentum space . on the other hand , there is an obvious dependence of fitted values of r on the parameter @xmath13 ( or @xmath41 ) , which determine how fast the weight factor decreases with increasing q. @xmath42 has quite similar values for various shapes of the weight factors and various values of @xmath13 .
thus in our method r reflects in some sense the `` source size '' , as expected . as already noted ,
this is true also for the oscillations in momentum space . increasing @xmath13
one increases also fitted values of @xmath7 , but this effect is weaker .
we have analyzed the data on be effect in multihadron states obtained from @xmath0 decays within the framework of the weight method of implementing the effect .
we show that the resonance contributions are not satisfactorily described by the standard mc generators , which makes the analysis of `` double ratio '' data quite difficult . in particular , the choice of the `` proper '' two particle weight factor which would describe the data best is obviously dependent on the way the data are processed
. thus one should improve ( if possible ) the quality of mc generators before drawing any serious conclusion on the agreement or disagreement between the models and data on the be effect .
the alternative is to elaborate better methods of preparing the `` reference sample '' using only the like - sign pairs , which are much less affected by the resonance effects . on the other hand
, we found that the analysis makes no great difference between the positively defined and oscillating weight factors in momentum space , provided they correspond to similar `` half - width '' .
this means that the results are not too strongly dependent on the `` sharpness of the source boundary '' in space - time ; one may hope to recover the proper `` source size '' in our method .
let us stress that the analysis presented in this paper is just the first step : we do not discuss the anisotropy of source nor the time dependence reflected in the be effect . also , we do not consider here the possibilities of comparing the effect for selected classes of events ( defined i.e. by multiplicity , by event shape parameters or by some special triggers ) . in our opinion ,
the weight method is well suited to discuss these subjects and we hope to consider them in near future .
the authors are grateful to a. biaas for useful remarks . the financial support from kbn grants no 2 p03b 086 14 and no 2 p03b 010 15 are acknowledged .
a. gagatek provided patient assistance with figure preparations .
99 r. hanbury - brown and r.q .
twiss , _ nature _ * 178 * ( 1956 ) 1046 .
boal , c .- k .
gelbke and b.k .
jennings , _ rev
* 62 * ( 1990 ) 553 ; r.m .
weiner , e - print hep - ph/9904389 .
j.p . sullivan _
_ , _ phys .
_ * 70 * ( 1993 ) 3000 .
q.h . zhang _
_ b * 407 * ( 1997 ) 33 .
j. ellis and k. geiger , _ phys .
_ d * 54 * ( 1996 ) 1967 ; k. geiger , j. ellis , u. heinz and u.a .
wiedemann , e - print hep - ph/9811270 .
b. andersson and m. ringnr , _ nucl .
_ b * 513 * ( 1998 ) 627 .
b. andersson and m. ringnr , _ phys .
_ b * 421 * ( 1998 ) 283 .
s. todorova - nov and j. rames , e - print hep - ph/9710280 .
j. hkkinen and m. ringnr , _ eur .
c * 5 * ( 1998 ) 275 .
t. sjstrand and m. bengtsson , _ comp .
* 43 * ( 1987 ) 367 ; t. sjstrand , _ comp .
* 82 * ( 1994 ) 74 .
l. lnnblad and t. sjstrand , _ phys .
_ b * 351 * ( 1995 ) 293 .
l. lnnblad and t. sjstrand , _ eur .
c * 2 * ( 1998 ) 165 .
et al . _ , in _ proc .
cracow workshop on multiparticle production `` soft physics and fluctuations '' _ , ed .
a. biaas _
_ , p.22 , world sci . , singapore 1994 .
_ , _ phys .
_ b * 332 * ( 1994 ) 458 .
k. fiakowski and r. wit , _ z. phys .
_ c * 74 * ( 1997 ) 145 .
o. smirnova , b. lrstad , r. murean , proceedings of the 8th int .
workshop on multiparticle prod .
, _ correlations and fluctuations 98 _ ( mtrahza , hungary ) , ed .
t. csrg , s. hegyi , g. jancs and r.c .
hwa , p.20 , world sci .
singapore 1999 .
s. pratt , _ phys .
_ * 53 * ( 1984 ) 1219 .
a. biaas and a. krzywicki , _ phys .
_ b * 354 * ( 1995 ) 134 .
s. haywood , rutherford lab .
report ral-94 - 074
. s. jadach and k. zalewski , _ acta phys . pol .
b * 28 * ( 1997 ) 1363 . v. kartvelishvili , r. kvatadze and r. mller , _ phys .
_ b * 408 * ( 1997 ) 331 .
k. fiakowski and r. wit , _ eur .
c * 2 * ( 1998 ) 691 .
j. wosiek , _ phys .
_ b * 399 * ( 1997 ) 130 .
k. fiakowski , r. wit and j. wosiek , _ phys .
_ d * 57 * ( 1998 ) 094013 .
k. fiakowski and r. wit , _ phys .
_ b * 438 * ( 1998 ) 154 .
aleph collaboration , d. decamp _
et al.__z .
_ c * 54 * ( 1992 ) 75 .
opal collaboration , g. alexander _
_ z. phys .
_ c * 72 * ( 1996 ) 389 .
the aleph collaboration , collaboration report aleph 99 - 027 , contribution conf 99 - 021 to the 1999 winter conferences .
bowler , _ phys
_ b * 270 * ( 1991 ) 69 ; m.biyajima _ et al .
_ _ phys . lett .
_ b * 353 * ( 1995 ) 340 ; g.baym and p. braun - munzinger , _ nucl .
phys . _ a * 610 * ( 1996 ) 286c ; h. merlitz and d. pelte , _ phys
_ b * 415 * ( 1997 ) 411 .
a. de angelis and l. vitale , cern preprint cern - open 98 - 020 , e - print hep - ex/9808002 .
delphi collaboration , p. abreu _ at al _ , _ phys .
_ b * 286 * ( 1992 ) 201 .
delphi collaboration , p. abreu _ at al _ , _
_ c * 63 * ( 1994 ) 17 .[/INST] we discuss the bose - einstein interference effect in multiparticle production . after a short review of various methods of implementation of this effect into monte carlo generators
the weight method is presented in more detail and used to analyze the data for hadronic @xmath0 decays . in particular
, we consider the possibility of deducing the two - particle weight factor from the experimental data . 23.0 cm 16.0 cm -1.0 cm 0.0 cm 0.0 cm k. fiakowski , r. wit _ m. smoluchowski institute of physics + jagellonian university + 30 - 059 krakw , ul.reymonta 4 , poland _
pacs : 13.85.-t , 13.90.+i + _ keywords : _ monte carlo , bose - einstein correlations , @xmath0 decay + august , 1999 + </s> |
2.7 million people are estimated to have diabetes in saudi arabia , with estimated prevalence of 16.2% .
fear of hypoglycaemia and gain in body weight are barriers for initiation of insulin therapy .
modern insulin analogues are a convenient new approach or tool to glycaemic control , associated with low number of hypoglycaemia and favourable weight change .
a1chieve , a multinational , 24-week , non - interventional study , assessed the safety and effectiveness of insulin analogues in people with t2 dm ( n = 66,726 ) in routine clinical care .
please refer to editorial titled : the a1chieve study : mapping the ibn battuta trail .
the patient characteristics for the entire cohort divided as insulin - nave and insulin users is shown in the table 1 .
other groups were insulin aspart ( n = 21 ) , basal insulin plus insulin aspart ( n = 280 ) , biphasic insulin aspart ( n = 121 ) and other insulin combinations ( n = 17 ) . overall demographic data after 24 weeks of treatment , overall hypoglycaemic events or episodes reduced from 5.3 events / patient - year to 1.9 events / patient - year in insulin user group whereas overall hypoglycaemia increased from 0.8 events / patient - year to 1.8 events / patient - year in the insulin nave group . however , this hypoglycaemia incidence in insulin naive group at 24 weeks was still lower than that observed in insulin users at baseline .
blood pressure and lipid profile improved after 24 weeks in the total cohort [ tables 2 and 3 ] .
all parameters of glycaemic control improved from baseline to study end in the total cohort [ table 4 ] .
overall efficacy data of the total cohort , 987 patients started on biphasic insulin aspart ogld , of which 483 ( 48.9% ) were insulin nave and 504 ( 51.1% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events or episodes reduced from 4.2 events / patient - year to 1.8 events / patient - year in insulin user group whereas hypoglycaemia increased from 0.8 events / patient - year to 1.7 events / patient - year in insulin nave group .
biphasic insulin aspartoral glucose - lowering drug safety data all aspects of glycaemic control improved from baseline to study end in those who started on or were switched to biphasic insulin aspart for both insulin nave and insulin user groups [ table 7 ] .
biphasic insulin aspartoral glucose - lowering drug efficacy data of the total cohort , 280 patients started on basal + insulin aspart ogld , of which 70 ( 25% ) were insulin nave and 210 ( 75% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events reduced from 1.9 events / patient - year to 1.0 events / patient - year in insulin nave group and from 6.7 events / patient - year to 2.5 events / patient - year in insulin user group .
body weight decreased after 24 weeks in insulin nave group [ tables 8 and 9 ] .
basal+insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to basal + insulin aspart oglds for both insulin nave and insulin user groups [ table 10 ] .
basal+insulin aspartoral glucose - lowering drug efficacy data of the total cohort , 1121 patients started on insulin detemir ogld , of which 982 ( 87.6% ) were insulin nave and 139 ( 12.4% ) were insulin users .
after 24 weeks of starting or switching to insulin detemir , hypoglycaemia reduced from 3.6 events / patient - year to 1.3 events / patient - year in insulin user group while hypoglycaemic events increased from 0.7 events / patient - year to 2.1 events / patient - year in insulin nave group . a slight decrease in body weight
was observed for both the groups at the end of 24 weeks [ table 11 ] .
insulin detemiroral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin detemir oglds for both insulin - nave and insulin user groups [ table 13 ] .
insulin detemiroral glucose - lowering drug efficacy data of the total cohort , 21 patients started on insulin aspart ogld of which 17 ( 80.9% ) were insulin nave and 4 ( 19.1% ) were insulin users .
after 24 weeks of treatment , a decrease in body weight was observed in the insulin nave group [ table 14 ] .
insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin aspart oglds for insulin nave group [ table 16 ] .
of the total cohort , 987 patients started on biphasic insulin aspart ogld , of which 483 ( 48.9% ) were insulin nave and 504 ( 51.1% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events or episodes reduced from 4.2 events / patient - year to 1.8 events / patient - year in insulin user group whereas hypoglycaemia increased from 0.8 events / patient - year to 1.7 events / patient - year in insulin nave group .
biphasic insulin aspartoral glucose - lowering drug safety data all aspects of glycaemic control improved from baseline to study end in those who started on or were switched to biphasic insulin aspart for both insulin nave and insulin user groups [ table 7 ] .
of the total cohort , 280 patients started on basal + insulin aspart ogld , of which 70 ( 25% ) were insulin nave and 210 ( 75% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events reduced from 1.9 events / patient - year to 1.0 events / patient - year in insulin nave group and from 6.7 events / patient - year to 2.5 events / patient - year in insulin user group .
body weight decreased after 24 weeks in insulin nave group [ tables 8 and 9 ] .
basal+insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to basal + insulin aspart oglds for both insulin nave and insulin user groups [ table 10 ] .
of the total cohort , 1121 patients started on insulin detemir ogld , of which 982 ( 87.6% ) were insulin nave and 139 ( 12.4% ) were insulin users .
after 24 weeks of starting or switching to insulin detemir , hypoglycaemia reduced from 3.6 events / patient - year to 1.3 events / patient - year in insulin user group while hypoglycaemic events increased from 0.7 events / patient - year to 2.1 events / patient - year in insulin nave group . a slight decrease in body weight
was observed for both the groups at the end of 24 weeks [ table 11 ] .
insulin detemiroral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin detemir oglds for both insulin - nave and insulin user groups [ table 13 ] .
of the total cohort , 21 patients started on insulin aspart ogld of which 17 ( 80.9% ) were insulin nave and 4 ( 19.1% ) were insulin users .
after 24 weeks of treatment , a decrease in body weight was observed in the insulin nave group [ table 14 ] .
insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin aspart oglds for insulin nave group [ table 16 ] .
our study reports improved glycaemic control following 24 weeks of treatment with any of the insulin analogues ( biphasic insulin aspart ; basal + insulin aspart ; insulin detemir ; insulin aspart ) with or without ogld .
though the findings are limited by number of patients , still the trend indicates that insulin analogues can be considered effective and possess a safe profile for treating type 2 diabetes in southwest saudi arabia . | background : the a1chieve , a multicentric ( 28 countries ) , 24-week , non - interventional study evaluated the safety and effectiveness of insulin detemir , biphasic insulin aspart and insulin aspart in people with t2 dm ( n = 66,726 ) in routine clinical care across four continents.materials and methods : data was collected at baseline , at 12 weeks and at 24 weeks . this short communication presents the results for patients enrolled from southwest saudi arabia.results:a total of 2561 patients were enrolled in the study .
four different insulin analogue regimens were used in the study .
study patients had started on or were switched to biphasic insulin aspart ( n = 987 ) , insulin detemir ( n = 1121 ) , insulin aspart ( n = 21 ) , basal insulin plus insulin aspart ( n = 280 ) and missing or other insulin combinations ( n = 152 ) . at baseline glycaemic control was poor for both insulin nave ( mean hba1c : 9.9% ) and insulin user ( mean hba1c : 9.5% ) groups .
after 24 weeks of treatment , both the study groups showed improvement in hba1c ( insulin nave : 2.5% , insulin users : 2.2% ) .
major hypoglycaemic events did not occur in any of the study patients .
sadrs were reported in 0.1% of insulin nave and 0.1% of insulin user groups.conclusion:starting or switching to insulin analogues was associated with improvement in glycaemic control with a low rate of hypoglycaemia . | <s>[INST]2.7 million people are estimated to have diabetes in saudi arabia , with estimated prevalence of 16.2% .
fear of hypoglycaemia and gain in body weight are barriers for initiation of insulin therapy .
modern insulin analogues are a convenient new approach or tool to glycaemic control , associated with low number of hypoglycaemia and favourable weight change .
a1chieve , a multinational , 24-week , non - interventional study , assessed the safety and effectiveness of insulin analogues in people with t2 dm ( n = 66,726 ) in routine clinical care .
please refer to editorial titled : the a1chieve study : mapping the ibn battuta trail .
the patient characteristics for the entire cohort divided as insulin - nave and insulin users is shown in the table 1 .
other groups were insulin aspart ( n = 21 ) , basal insulin plus insulin aspart ( n = 280 ) , biphasic insulin aspart ( n = 121 ) and other insulin combinations ( n = 17 ) . overall demographic data after 24 weeks of treatment , overall hypoglycaemic events or episodes reduced from 5.3 events / patient - year to 1.9 events / patient - year in insulin user group whereas overall hypoglycaemia increased from 0.8 events / patient - year to 1.8 events / patient - year in the insulin nave group . however , this hypoglycaemia incidence in insulin naive group at 24 weeks was still lower than that observed in insulin users at baseline .
blood pressure and lipid profile improved after 24 weeks in the total cohort [ tables 2 and 3 ] .
all parameters of glycaemic control improved from baseline to study end in the total cohort [ table 4 ] .
overall efficacy data of the total cohort , 987 patients started on biphasic insulin aspart ogld , of which 483 ( 48.9% ) were insulin nave and 504 ( 51.1% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events or episodes reduced from 4.2 events / patient - year to 1.8 events / patient - year in insulin user group whereas hypoglycaemia increased from 0.8 events / patient - year to 1.7 events / patient - year in insulin nave group .
biphasic insulin aspartoral glucose - lowering drug safety data all aspects of glycaemic control improved from baseline to study end in those who started on or were switched to biphasic insulin aspart for both insulin nave and insulin user groups [ table 7 ] .
biphasic insulin aspartoral glucose - lowering drug efficacy data of the total cohort , 280 patients started on basal + insulin aspart ogld , of which 70 ( 25% ) were insulin nave and 210 ( 75% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events reduced from 1.9 events / patient - year to 1.0 events / patient - year in insulin nave group and from 6.7 events / patient - year to 2.5 events / patient - year in insulin user group .
body weight decreased after 24 weeks in insulin nave group [ tables 8 and 9 ] .
basal+insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to basal + insulin aspart oglds for both insulin nave and insulin user groups [ table 10 ] .
basal+insulin aspartoral glucose - lowering drug efficacy data of the total cohort , 1121 patients started on insulin detemir ogld , of which 982 ( 87.6% ) were insulin nave and 139 ( 12.4% ) were insulin users .
after 24 weeks of starting or switching to insulin detemir , hypoglycaemia reduced from 3.6 events / patient - year to 1.3 events / patient - year in insulin user group while hypoglycaemic events increased from 0.7 events / patient - year to 2.1 events / patient - year in insulin nave group . a slight decrease in body weight
was observed for both the groups at the end of 24 weeks [ table 11 ] .
insulin detemiroral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin detemir oglds for both insulin - nave and insulin user groups [ table 13 ] .
insulin detemiroral glucose - lowering drug efficacy data of the total cohort , 21 patients started on insulin aspart ogld of which 17 ( 80.9% ) were insulin nave and 4 ( 19.1% ) were insulin users .
after 24 weeks of treatment , a decrease in body weight was observed in the insulin nave group [ table 14 ] .
insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin aspart oglds for insulin nave group [ table 16 ] .
of the total cohort , 987 patients started on biphasic insulin aspart ogld , of which 483 ( 48.9% ) were insulin nave and 504 ( 51.1% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events or episodes reduced from 4.2 events / patient - year to 1.8 events / patient - year in insulin user group whereas hypoglycaemia increased from 0.8 events / patient - year to 1.7 events / patient - year in insulin nave group .
biphasic insulin aspartoral glucose - lowering drug safety data all aspects of glycaemic control improved from baseline to study end in those who started on or were switched to biphasic insulin aspart for both insulin nave and insulin user groups [ table 7 ] .
of the total cohort , 280 patients started on basal + insulin aspart ogld , of which 70 ( 25% ) were insulin nave and 210 ( 75% ) were insulin users .
after 24 weeks of treatment , hypoglycaemic events reduced from 1.9 events / patient - year to 1.0 events / patient - year in insulin nave group and from 6.7 events / patient - year to 2.5 events / patient - year in insulin user group .
body weight decreased after 24 weeks in insulin nave group [ tables 8 and 9 ] .
basal+insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to basal + insulin aspart oglds for both insulin nave and insulin user groups [ table 10 ] .
of the total cohort , 1121 patients started on insulin detemir ogld , of which 982 ( 87.6% ) were insulin nave and 139 ( 12.4% ) were insulin users .
after 24 weeks of starting or switching to insulin detemir , hypoglycaemia reduced from 3.6 events / patient - year to 1.3 events / patient - year in insulin user group while hypoglycaemic events increased from 0.7 events / patient - year to 2.1 events / patient - year in insulin nave group . a slight decrease in body weight
was observed for both the groups at the end of 24 weeks [ table 11 ] .
insulin detemiroral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin detemir oglds for both insulin - nave and insulin user groups [ table 13 ] .
of the total cohort , 21 patients started on insulin aspart ogld of which 17 ( 80.9% ) were insulin nave and 4 ( 19.1% ) were insulin users .
after 24 weeks of treatment , a decrease in body weight was observed in the insulin nave group [ table 14 ] .
insulin aspartoral glucose - lowering drug safety data all parameters of glycaemic control improved from baseline to study end in those who started on or were switched to insulin aspart oglds for insulin nave group [ table 16 ] .
our study reports improved glycaemic control following 24 weeks of treatment with any of the insulin analogues ( biphasic insulin aspart ; basal + insulin aspart ; insulin detemir ; insulin aspart ) with or without ogld .
though the findings are limited by number of patients , still the trend indicates that insulin analogues can be considered effective and possess a safe profile for treating type 2 diabetes in southwest saudi arabia .[/INST]background : the a1chieve , a multicentric ( 28 countries ) , 24-week , non - interventional study evaluated the safety and effectiveness of insulin detemir , biphasic insulin aspart and insulin aspart in people with t2 dm ( n = 66,726 ) in routine clinical care across four continents.materials and methods : data was collected at baseline , at 12 weeks and at 24 weeks . this short communication presents the results for patients enrolled from southwest saudi arabia.results:a total of 2561 patients were enrolled in the study .
four different insulin analogue regimens were used in the study .
study patients had started on or were switched to biphasic insulin aspart ( n = 987 ) , insulin detemir ( n = 1121 ) , insulin aspart ( n = 21 ) , basal insulin plus insulin aspart ( n = 280 ) and missing or other insulin combinations ( n = 152 ) . at baseline glycaemic control was poor for both insulin nave ( mean hba1c : 9.9% ) and insulin user ( mean hba1c : 9.5% ) groups .
after 24 weeks of treatment , both the study groups showed improvement in hba1c ( insulin nave : 2.5% , insulin users : 2.2% ) .
major hypoglycaemic events did not occur in any of the study patients .
sadrs were reported in 0.1% of insulin nave and 0.1% of insulin user groups.conclusion:starting or switching to insulin analogues was associated with improvement in glycaemic control with a low rate of hypoglycaemia .</s> |
AS SHE swept a friend's make-up brush across her face, Warwick woman Jo Gilchrist could never have imagined she was triggering a battle that would force her to fight for her life.
The bristles of that brush gently glided over a pimple on her face and are most likely how a staph infection invaded her body.
The insidious bacteria eventually travelled to and attacked her spine, leaving her writhing in pain and her body going numb.
YOU MIGHT ALSO LIKE:
Just over a month since the onset, the young mum of one is now wheelchair-bound and will call the spinal ward of the Princess Alexandra Hospital home for at least the next three months.
Initially told she would never walk again, her best-case outlook is she may one day be able to walk an hour or two a day.
But she will be in a wheelchair for the rest of her life.
She will never again have control of her bowel or bladder and has no sexual function.
Never again will she chase her two-year-old son Tommy around the yard.
Her life has been thrown into turmoil since that day in February when she noticed something was seriously wrong.
"It started as a dull ache and I thought it was my bad posture but it got worse and worse and got to the point I had to call one of those doctors who come to you because I couldn't get out of bed," she said.
"I rate the pain worse than childbirth; I literally thought I was going to die."
Days later things took a turn for the worst when Jo started to lose the feeling in her legs.
"They told me if it went up my arms and chest I would have to learn to breathe again and it would be my parents' decision to turn the machines off," she said.
"It was horrible when I heard that but I also got this incredible fight for life. I knew I had to keep fighting because I didn't want to not be able to see my son grow up. Before I got airlifted out I could feel (the paralysis) going up my arms and I was trying to fight it and keep my arms moving."
Jo later learned she contracted community-associated MRSA, an antibiotic-resistant form of golden staph.
She was told it had damaged her spine and she would be restricted to a wheelchair for the rest of her life.
But she kept fighting.
"They first said I would never walk again but I got a wiggle out of my toes and I just kept fighting," she said.
"This has been a real wake-up call. Before this I was just going through the motions and existing but now I have a huge fight for life. If someone tells me I can't do something, I keep going because just the look on their faces when I do it is worth it."
On top of dealing with the huge physical trauma and changes her body is going through, single mum Jo is fighting the emotional battle of being away from her son.
The little boy who is too young to understand his mummy can't come home.
"He hates it and I don't see him very often because he is in Warwick," she said.
"I can't talk to him on the phone because he throws tantrums and won't say goodbye but won't hang up.
"When he comes here he screams when he has to leave and it is heartbreaking to see him leave like that."
ABOVE: A visit with her friend, Bec Bolzan. Contributed
Jo now faces Easter, Mother's Day and her son's third birthday away from the main man in her life.
"I would rather him not be here on those days because I want him to be happy all day and not upset when he has to say goodbye," she said.
Although devastated by being away from her son, Jo reminds herself there are better days ahead.
"I have pictures of him and his drawings all over the walls and I look at them every day," she said.
"It will feel like a lifetime but at least I will get to go home to him in July and it will be OK.
"This is the best possible place for me."
This week Jo was on a high after mastering a "wheelie" in her wheelchair, a skill she had to master before being able to venture out on trips in her chair.
She is trying to remain positive about her future.
"There are so many people worse off than me - I am lucky really," she said.
"There are people in here who are in automatic chairs because they can't use their hands.
"I think it's a good thing I am in a wheelchair because I am a bit of speed demon - I'm pretty good."
As she works on her recovery, Jo's friends have been working on their own project. Trying to boost her spirits, they reached out to Jo's favourite musician Seth Sentry to visit her in hospital.
Although he was busy on a tour, Seth sent a personal message to the Warwick mum and passed on his best wishes in her recovery. "Even if he hadn't sent the message, it was just so amazing to know that people tried to help," Jo said.
To follow Jo's progress search #jolovessethsentry on Facebook and who knows, maybe Seth might visit Jo after all.
MRSA
About one-third of healthy people carry staph bacteria on their skin or in their nose.
Drug-resistant strains are known as MRSA
MRSA strains can cause skin and soft tissue infections, however can also become serious and life-threatening ||||| Jo Gilchrist
For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around! I have fought with everything I have to lead to this. Surprise! β€ β€ xx
#jolovessethsentry For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around! I have fought with everything I have to lead to this. Surprise!xx ||||| A young Australian mother could not have imagined that fixing a spot on her face with her best friendβs make up brush could have likely caused her to contract an infection which has left her paralysed.
Jo Gilchrist, 27, who has a two-year-old son, believes the staphylococcus, or staph, bacteria entered her body and attacked her spine, after she used he friendβs makeup kit.
Medics at the Princess Alexandra Hospital in Brisbane are still attempting to rid her body of the bacteria, almost three months after she became ill.
She must now spend the next three months in hospital, where she will be administered with strong antibiotics, her hometown newspaper the Warwick Daily News.
Staph bacteria are often found in the nose or on the skin, and they generally do not cause any symptoms - a phenomenon known as colonisation, according to the NHS.
Ms Gilchrist told Daily Mail Australia that she first put βa little acheβ down to βbad postureβ, but that eventually progressed to become βworse than childbirthβ.
βI literally thought I was going to die,β she told the Warwick Daily News.
Read more Researchers map pathogens on the New York subway
Doctors could not pinpoint the cause of Ms Gilchristβs pain as her body started to go numb and she lost the feeling in her legs.
She was then airlifted to hospital, given emergency surgery, and put into an induced coma.
Hospital staff told her when she woke up that she had contracted community-associated MRSA β a form of staph.
Gilchrist believes she caught the infection because her friend had a staph infection on her face, and her immune was not strong enough to tackle the bacteria.
It has damaged her spine so severely that she will never walk again, and will never regain control over her bowel or bladder function.
However, Gilchrist is remaining positive after she managed to wiggle her toes, and doctors told her she may be able to walk for an hour or two a day, the Warwick Daily News reported. ||||| A young mother in Australia is fighting to recover from a virulent staph infection that threatened her life and left her partially paralyzed. She caught it from a seemingly innocuous source: borrowing a friend's makeup brush.
The Daily Mail Australia reports Jo Gilchrist started feeling pain in her back on Valentine's Day and it rapidly got worse -- "worse than childbirth," she said. She lost all feeling in her legs and lower body and had to be airlifted to a hospital in Brisbane for emergency surgery.
It turned out to be an infection caused by a drug-resistant strain of staph called MRSA (Methicillin-resistant Staphylococcus aureus) that she apparently contracted when she used a friend's makeup brush to hide a pimple.
Jo Gilchrist, 27, was left paralyzed by a MRSA infection she contracted from a friend's makeup brush. Jo Gilchrist/Facebook
'The only thing we can put it down to is the makeup brush," she told the paper. "My friend did have a staph infection on her face and I was using her brush just before. I had no idea that could even happen, I used to share with my friends all the time."
The infection damaged her spine, and doctors said she might never walk again. But Gilchrist, 27, has been working to prove them wrong, getting back on her feet in physical therapy.
"It's been the hardest struggle I've ever faced," she wrote on Facebook. "There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around!"
Intensive treatment and therapy have helped. Gilchrist posted a short video of herself last week slowly moving her legs, standing and taking a few steps during physical therapy. "I have fought with everything I have to lead to this," she wrote.
For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of... Posted by Jo Gilchrist on Monday, March 30, 2015
Now doctors say her prognosis looks better. "Two weeks ago they said I might be able to walk for an hour or two a day -- like grocery shopping, washing up and hanging the washing out," Gilchrist told the Daily Mail. "I'm happy with that. I honestly didn't even expect that."
While her case sounds like a freak occurrence, health officials warn of the risks of spreading MRSA by sharing personal items like towels or razors that have touched infected skin. The U.S. Centers for Disease Control and Prevention says about a third of the population carries staph bacteria, usually without showing any symptoms, and about 2 percent of people are carriers for MRSA. The bug is often a source of outbreaks among hospital patients with weaker immune systems, but it can spread in the community as well.
Initial symptoms of a MRSA infection can include a red, swollen or painful skin inflammation and a fever; the sore spot may feel warm to the touch or develop pus. The CDC says anyone who experiences symptoms should wash and bandage the area and see a doctor. MRSA can be life-threatening if the infection spreads to the bloodstream or into the lungs, causing pneumonia. | β Jo Gilchrist borrowed a friend's makeup brush recently, using it to sweep makeup onto her faceβincluding over a pimple. Soon after, in February, she noticed a "dull ache" in her body. Initially unconcerned, the 27-year-old Australian called a doctor when she was in such pain she couldn't get out of bed. Ultimately she learned that she had contracted MRSA, an antibiotic-resistant staph infection; the bacteria had likely gotten in via the makeup brush and the pimple. As the Warwick Daily News explains, about a third of healthy people have staph bacteria on their skin; the Independent notes that for those people, the bacteria typically "colonize" without causing any symptoms. CBS News says 2% of people are carriers of the antibiotic-resistant version. Doctors told Gilchrist her immune system simply couldn't fight off the infection. Days after her first doctor visit, Gilchrist started losing feeling in her legs. Doctors told her the infection had damaged her spine and would leave her unable to walk, but she says she's managed to get "a wiggle out of my toes" and is determined to prove them wrong, though she's currently wheelchair-bound and will likely reside in Princess Alexandra Hospital's spinal ward for at least three more monthsβduring which her son will turn 3. "It will feel like a lifetime, but at least I will get to go home to him in July and it will be OK," she says. A video posted on her Facebook page on March 30 shows her moving her legs and briefly standing and walking with support, and she notes in the description, "As hard as it has been [I'm] so lucky to have muscle power and no feeling [rather] than the other way around!" (This mom was killed in a freak driveway accident.) | <s>[INST]AS SHE swept a friend's make-up brush across her face, Warwick woman Jo Gilchrist could never have imagined she was triggering a battle that would force her to fight for her life.
The bristles of that brush gently glided over a pimple on her face and are most likely how a staph infection invaded her body.
The insidious bacteria eventually travelled to and attacked her spine, leaving her writhing in pain and her body going numb.
YOU MIGHT ALSO LIKE:
Just over a month since the onset, the young mum of one is now wheelchair-bound and will call the spinal ward of the Princess Alexandra Hospital home for at least the next three months.
Initially told she would never walk again, her best-case outlook is she may one day be able to walk an hour or two a day.
But she will be in a wheelchair for the rest of her life.
She will never again have control of her bowel or bladder and has no sexual function.
Never again will she chase her two-year-old son Tommy around the yard.
Her life has been thrown into turmoil since that day in February when she noticed something was seriously wrong.
"It started as a dull ache and I thought it was my bad posture but it got worse and worse and got to the point I had to call one of those doctors who come to you because I couldn't get out of bed," she said.
"I rate the pain worse than childbirth; I literally thought I was going to die."
Days later things took a turn for the worst when Jo started to lose the feeling in her legs.
"They told me if it went up my arms and chest I would have to learn to breathe again and it would be my parents' decision to turn the machines off," she said.
"It was horrible when I heard that but I also got this incredible fight for life. I knew I had to keep fighting because I didn't want to not be able to see my son grow up. Before I got airlifted out I could feel (the paralysis) going up my arms and I was trying to fight it and keep my arms moving."
Jo later learned she contracted community-associated MRSA, an antibiotic-resistant form of golden staph.
She was told it had damaged her spine and she would be restricted to a wheelchair for the rest of her life.
But she kept fighting.
"They first said I would never walk again but I got a wiggle out of my toes and I just kept fighting," she said.
"This has been a real wake-up call. Before this I was just going through the motions and existing but now I have a huge fight for life. If someone tells me I can't do something, I keep going because just the look on their faces when I do it is worth it."
On top of dealing with the huge physical trauma and changes her body is going through, single mum Jo is fighting the emotional battle of being away from her son.
The little boy who is too young to understand his mummy can't come home.
"He hates it and I don't see him very often because he is in Warwick," she said.
"I can't talk to him on the phone because he throws tantrums and won't say goodbye but won't hang up.
"When he comes here he screams when he has to leave and it is heartbreaking to see him leave like that."
ABOVE: A visit with her friend, Bec Bolzan. Contributed
Jo now faces Easter, Mother's Day and her son's third birthday away from the main man in her life.
"I would rather him not be here on those days because I want him to be happy all day and not upset when he has to say goodbye," she said.
Although devastated by being away from her son, Jo reminds herself there are better days ahead.
"I have pictures of him and his drawings all over the walls and I look at them every day," she said.
"It will feel like a lifetime but at least I will get to go home to him in July and it will be OK.
"This is the best possible place for me."
This week Jo was on a high after mastering a "wheelie" in her wheelchair, a skill she had to master before being able to venture out on trips in her chair.
She is trying to remain positive about her future.
"There are so many people worse off than me - I am lucky really," she said.
"There are people in here who are in automatic chairs because they can't use their hands.
"I think it's a good thing I am in a wheelchair because I am a bit of speed demon - I'm pretty good."
As she works on her recovery, Jo's friends have been working on their own project. Trying to boost her spirits, they reached out to Jo's favourite musician Seth Sentry to visit her in hospital.
Although he was busy on a tour, Seth sent a personal message to the Warwick mum and passed on his best wishes in her recovery. "Even if he hadn't sent the message, it was just so amazing to know that people tried to help," Jo said.
To follow Jo's progress search #jolovessethsentry on Facebook and who knows, maybe Seth might visit Jo after all.
MRSA
About one-third of healthy people carry staph bacteria on their skin or in their nose.
Drug-resistant strains are known as MRSA
MRSA strains can cause skin and soft tissue infections, however can also become serious and life-threatening ||||| Jo Gilchrist
For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around! I have fought with everything I have to lead to this. Surprise! β€ β€ xx
#jolovessethsentry For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around! I have fought with everything I have to lead to this. Surprise!xx ||||| A young Australian mother could not have imagined that fixing a spot on her face with her best friendβs make up brush could have likely caused her to contract an infection which has left her paralysed.
Jo Gilchrist, 27, who has a two-year-old son, believes the staphylococcus, or staph, bacteria entered her body and attacked her spine, after she used he friendβs makeup kit.
Medics at the Princess Alexandra Hospital in Brisbane are still attempting to rid her body of the bacteria, almost three months after she became ill.
She must now spend the next three months in hospital, where she will be administered with strong antibiotics, her hometown newspaper the Warwick Daily News.
Staph bacteria are often found in the nose or on the skin, and they generally do not cause any symptoms - a phenomenon known as colonisation, according to the NHS.
Ms Gilchrist told Daily Mail Australia that she first put βa little acheβ down to βbad postureβ, but that eventually progressed to become βworse than childbirthβ.
βI literally thought I was going to die,β she told the Warwick Daily News.
Read more Researchers map pathogens on the New York subway
Doctors could not pinpoint the cause of Ms Gilchristβs pain as her body started to go numb and she lost the feeling in her legs.
She was then airlifted to hospital, given emergency surgery, and put into an induced coma.
Hospital staff told her when she woke up that she had contracted community-associated MRSA β a form of staph.
Gilchrist believes she caught the infection because her friend had a staph infection on her face, and her immune was not strong enough to tackle the bacteria.
It has damaged her spine so severely that she will never walk again, and will never regain control over her bowel or bladder function.
However, Gilchrist is remaining positive after she managed to wiggle her toes, and doctors told her she may be able to walk for an hour or two a day, the Warwick Daily News reported. ||||| A young mother in Australia is fighting to recover from a virulent staph infection that threatened her life and left her partially paralyzed. She caught it from a seemingly innocuous source: borrowing a friend's makeup brush.
The Daily Mail Australia reports Jo Gilchrist started feeling pain in her back on Valentine's Day and it rapidly got worse -- "worse than childbirth," she said. She lost all feeling in her legs and lower body and had to be airlifted to a hospital in Brisbane for emergency surgery.
It turned out to be an infection caused by a drug-resistant strain of staph called MRSA (Methicillin-resistant Staphylococcus aureus) that she apparently contracted when she used a friend's makeup brush to hide a pimple.
Jo Gilchrist, 27, was left paralyzed by a MRSA infection she contracted from a friend's makeup brush. Jo Gilchrist/Facebook
'The only thing we can put it down to is the makeup brush," she told the paper. "My friend did have a staph infection on her face and I was using her brush just before. I had no idea that could even happen, I used to share with my friends all the time."
The infection damaged her spine, and doctors said she might never walk again. But Gilchrist, 27, has been working to prove them wrong, getting back on her feet in physical therapy.
"It's been the hardest struggle I've ever faced," she wrote on Facebook. "There's been lots of sleepless nights and days spent sleeping. There's been vomiting, tremendous pain. Tears for the unknown and tears for all the accidents. As hard as it has been Im so lucky to have muscle power and no feeling than the other way around!"
Intensive treatment and therapy have helped. Gilchrist posted a short video of herself last week slowly moving her legs, standing and taking a few steps during physical therapy. "I have fought with everything I have to lead to this," she wrote.
For all the kind words and love I thank you, it's been the hardest struggle I've ever faced. There's been lots of... Posted by Jo Gilchrist on Monday, March 30, 2015
Now doctors say her prognosis looks better. "Two weeks ago they said I might be able to walk for an hour or two a day -- like grocery shopping, washing up and hanging the washing out," Gilchrist told the Daily Mail. "I'm happy with that. I honestly didn't even expect that."
While her case sounds like a freak occurrence, health officials warn of the risks of spreading MRSA by sharing personal items like towels or razors that have touched infected skin. The U.S. Centers for Disease Control and Prevention says about a third of the population carries staph bacteria, usually without showing any symptoms, and about 2 percent of people are carriers for MRSA. The bug is often a source of outbreaks among hospital patients with weaker immune systems, but it can spread in the community as well.
Initial symptoms of a MRSA infection can include a red, swollen or painful skin inflammation and a fever; the sore spot may feel warm to the touch or develop pus. The CDC says anyone who experiences symptoms should wash and bandage the area and see a doctor. MRSA can be life-threatening if the infection spreads to the bloodstream or into the lungs, causing pneumonia.[/INST]β Jo Gilchrist borrowed a friend's makeup brush recently, using it to sweep makeup onto her faceβincluding over a pimple. Soon after, in February, she noticed a "dull ache" in her body. Initially unconcerned, the 27-year-old Australian called a doctor when she was in such pain she couldn't get out of bed. Ultimately she learned that she had contracted MRSA, an antibiotic-resistant staph infection; the bacteria had likely gotten in via the makeup brush and the pimple. As the Warwick Daily News explains, about a third of healthy people have staph bacteria on their skin; the Independent notes that for those people, the bacteria typically "colonize" without causing any symptoms. CBS News says 2% of people are carriers of the antibiotic-resistant version. Doctors told Gilchrist her immune system simply couldn't fight off the infection. Days after her first doctor visit, Gilchrist started losing feeling in her legs. Doctors told her the infection had damaged her spine and would leave her unable to walk, but she says she's managed to get "a wiggle out of my toes" and is determined to prove them wrong, though she's currently wheelchair-bound and will likely reside in Princess Alexandra Hospital's spinal ward for at least three more monthsβduring which her son will turn 3. "It will feel like a lifetime, but at least I will get to go home to him in July and it will be OK," she says. A video posted on her Facebook page on March 30 shows her moving her legs and briefly standing and walking with support, and she notes in the description, "As hard as it has been [I'm] so lucky to have muscle power and no feeling [rather] than the other way around!" (This mom was killed in a freak driveway accident.)</s> |
Potesters try to topple a Confederate monument with a chain Sunday, Aug. 13, 2017, at Piedmont Park in Atlanta. The peace monument at the 14th Street entrance depicts an angel of peace stilling the hand... (Associated Press)
CHARLOTTESVILLE, Va. (AP) β The Latest on violent protesting in Virginia and related developments around the nation (all times local):
___
A judge has denied bond for an Ohio man accused of plowing his car into a crowd at a white nationalist rally.
Judge Robert Downer said during a bond hearing Monday he would appoint a lawyer for James Alex Fields Jr.
Fields is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others.
The rally was held by white nationalists and others who oppose a plan to remove from a Charlottesville park of a statue of Confederate Gen. Robert E. Lee.
Fields has been in custody since Saturday.
A high school teacher said Fields was fascinated with Nazism, idolized Adolf Hitler and had been singled out by school officials in the 9th grade for his "deeply held, radical" convictions on race.
___
9:45 a.m.
A group that hosts a ceremony every year to re-dedicate an Atlanta monument depicting a Confederate soldier vows that it will be repaired after protesters spray-painted it and broke a chunk from it.
John Green, past commandant of the Old Guard of the Gate City Guard, said Monday it appears his group must now raise money to repair the 105-year-old statue damaged during a Sunday protest after the deadly weekend violence in Virginia.
City officials haven't commented on any plans for repairs or whether city funds would be used for that.
Green said removing the statue from Piedmont Park, a city park, is not an option.
He said the angel standing over the soldier represents peace, and it was created to help bring the nation back together after the Civil War.
___
7:40 a.m.
A prominent white nationalist website that promoted a Virginia rally that ended in deadly violence Saturday is losing its internet domain host.
GoDaddy tweeted late Sunday night that it has given the Daily Stormer 24 hours to move its domain to another provider because the site has violated GoDaddy's terms of service.
GoDaddy spokesman Dan Race tells the New York Daily News that the Daily Stormer violated its terms of service by labeling a woman killed in an attack at the event in Charlottesville "fat" and "childless." Heather Heyer was killed Saturday when police say a man plowed his car into a group of demonstrators protesting the white nationalist rally.
Shortly after GoDaddy tweeted its decision, the site posted an article claiming it had been hacked and would be shut down.
___
7:25 a.m.
Protesters spray-painted and broke a chunk off a statue depicting a Confederate soldier at an Atlanta park after they marched through the city to protest the weekend violence in Charlottesville, Virginia.
The Atlanta Journal-Constitution reports that a lone policeman at Piedmont Park on Sunday night was surrounded by black-clad protesters shouting "pig" as demonstrators used chains to try and destroy the Peace Monument.
The statue depicts a winged angel standing over a Confederate soldier.
Video from local news outlets showed red spray paint covering much of the monument following the demonstration.
The Atlanta protest was among several around the nation over the weekend that were organized after a chaotic white supremacist rally in Virginia ended with deadly violence.
___
7:25 a.m.
The German government is condemning the white nationalist rally in Virginia that turned violent Saturday, expressing solidarity with peaceful counter-protesters.
Chancellor Angela Merkel's spokesman Steffen Seibert told reporters Monday that it was an "absolutely repulsive scene at this extreme-right march."
He said "there was outrageous racism, anti-Semitism and hate in its most despicable form to be seen, and whenever it comes to such speech or such images it is repugnant."
He added that it's "completely contrary to what the chancellor and the German government works for politically, and we are in solidarity with those who stand peacefully against such aggressive extreme-right opinions."
Seibert says Merkel also regrets the death of a counter-protester and sent her sympathies to those injured.
___
3 a.m.
An Ohio man accused of plowing his car into counter-protesters at a white nationalist rally in Virginia is set to make his first court appearance.
Col. Martin Kumer, superintendent at the Albemarle-Charlottesville Regional Jail, says 20-year-old James Alex Fields Jr. has a bond hearing Monday morning.
Fields is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others.
Fields has been in custody since Saturday. Jail officials told The Associated Press they don't know if he's obtained an attorney.
A high school teacher said Fields was fascinated with Nazism, idolized Adolf Hitler and had been singled out by school officials in the 9th grade for his "deeply held, radical" convictions on race. ||||| Attorney General Jeff Sessions said a driver's ramming a car into a crowd of demonstrators in Charlottesville, Virginia, on Saturday, which killed a young woman and sent 19 other people to hospitals, "does meet the definition of domestic terrorism" under U.S. law.
"It does meet the definition of domestic terrorism in our statute," Sessions told ABC News' David Muir on "Good Morning America" today. "We are pursuing it in the [Department of Justice] in every way that we can make a case."
"You can be sure we will charge and advance the investigation towards the most serious charges that can be brought, because this is unequivocally an unacceptable, evil attack," he said. "Terrorism investigators from the FBI are working on the case as well as civil rights division FBI agents."
The ramming occurred shortly after authorities in Charlottesville called off a planned white nationalist rally, titled Unite the Right, and ordered crowds to disperse after violent clashes between rally attendees and counterprotesters.
Heather Heyer, 32, who was with a group protesting the white nationalist gathering, was killed when the car plowed into the crowd.
The suspected driver, 20-year-old James Alex Fields Jr. of Ohio, was arrested and charged with second-degree murder.
President Trump drew criticism when, after the ramming, he condemned "hatred, bigotry and violence on many sides," which some commentators said appeared to draw a moral equivalence between the white nationalists rallying in Charlottesville and the counterprotesters.
But Sessions said on "GMA" that the president "explicitly condemned the kind of ideology behind these movements of Nazism, white supremacy, the KKK. That is his unequivocal position, he totally opposes those kind of values."
The attorney general added, "The president, I suspect, will be talking to the country again soon, maybe today. I plan to meet with him today, and the FBI today will be meeting with him to brief him on this case. He takes this exceedingly seriously." | β A judge in Charlottesville, Va., has denied bond for an Ohio man accused of plowing his car into a crowd at a white nationalist rally, reports the AP. Judge Robert Downer said during a bond hearing Monday he would appoint a lawyer for James Alex Fields Jr. The 20-year-old is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others. Also on Monday, Attorney General Jeff Sessions called the attack that killed 32-year-old Heather Heyer "domestic terrorism." "It does meet the definition of domestic terrorism in our statute," Sessions said on Good Morning America, per ABC News. "You can be sure we will charge and advance the investigation towards the most serious charges that can be brought, because this is unequivocally an unacceptable, evil attack." Sessions also defended President Trump's public response to the violence. The president, he said, "explicitly condemned the kind of ideology behind these movements of Nazism, white supremacy, the KKK. That is his unequivocal position, he totally opposes those kind of values." He predicted that Trump would address the nation on the subject soon. | <s>[INST]Potesters try to topple a Confederate monument with a chain Sunday, Aug. 13, 2017, at Piedmont Park in Atlanta. The peace monument at the 14th Street entrance depicts an angel of peace stilling the hand... (Associated Press)
CHARLOTTESVILLE, Va. (AP) β The Latest on violent protesting in Virginia and related developments around the nation (all times local):
___
A judge has denied bond for an Ohio man accused of plowing his car into a crowd at a white nationalist rally.
Judge Robert Downer said during a bond hearing Monday he would appoint a lawyer for James Alex Fields Jr.
Fields is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others.
The rally was held by white nationalists and others who oppose a plan to remove from a Charlottesville park of a statue of Confederate Gen. Robert E. Lee.
Fields has been in custody since Saturday.
A high school teacher said Fields was fascinated with Nazism, idolized Adolf Hitler and had been singled out by school officials in the 9th grade for his "deeply held, radical" convictions on race.
___
9:45 a.m.
A group that hosts a ceremony every year to re-dedicate an Atlanta monument depicting a Confederate soldier vows that it will be repaired after protesters spray-painted it and broke a chunk from it.
John Green, past commandant of the Old Guard of the Gate City Guard, said Monday it appears his group must now raise money to repair the 105-year-old statue damaged during a Sunday protest after the deadly weekend violence in Virginia.
City officials haven't commented on any plans for repairs or whether city funds would be used for that.
Green said removing the statue from Piedmont Park, a city park, is not an option.
He said the angel standing over the soldier represents peace, and it was created to help bring the nation back together after the Civil War.
___
7:40 a.m.
A prominent white nationalist website that promoted a Virginia rally that ended in deadly violence Saturday is losing its internet domain host.
GoDaddy tweeted late Sunday night that it has given the Daily Stormer 24 hours to move its domain to another provider because the site has violated GoDaddy's terms of service.
GoDaddy spokesman Dan Race tells the New York Daily News that the Daily Stormer violated its terms of service by labeling a woman killed in an attack at the event in Charlottesville "fat" and "childless." Heather Heyer was killed Saturday when police say a man plowed his car into a group of demonstrators protesting the white nationalist rally.
Shortly after GoDaddy tweeted its decision, the site posted an article claiming it had been hacked and would be shut down.
___
7:25 a.m.
Protesters spray-painted and broke a chunk off a statue depicting a Confederate soldier at an Atlanta park after they marched through the city to protest the weekend violence in Charlottesville, Virginia.
The Atlanta Journal-Constitution reports that a lone policeman at Piedmont Park on Sunday night was surrounded by black-clad protesters shouting "pig" as demonstrators used chains to try and destroy the Peace Monument.
The statue depicts a winged angel standing over a Confederate soldier.
Video from local news outlets showed red spray paint covering much of the monument following the demonstration.
The Atlanta protest was among several around the nation over the weekend that were organized after a chaotic white supremacist rally in Virginia ended with deadly violence.
___
7:25 a.m.
The German government is condemning the white nationalist rally in Virginia that turned violent Saturday, expressing solidarity with peaceful counter-protesters.
Chancellor Angela Merkel's spokesman Steffen Seibert told reporters Monday that it was an "absolutely repulsive scene at this extreme-right march."
He said "there was outrageous racism, anti-Semitism and hate in its most despicable form to be seen, and whenever it comes to such speech or such images it is repugnant."
He added that it's "completely contrary to what the chancellor and the German government works for politically, and we are in solidarity with those who stand peacefully against such aggressive extreme-right opinions."
Seibert says Merkel also regrets the death of a counter-protester and sent her sympathies to those injured.
___
3 a.m.
An Ohio man accused of plowing his car into counter-protesters at a white nationalist rally in Virginia is set to make his first court appearance.
Col. Martin Kumer, superintendent at the Albemarle-Charlottesville Regional Jail, says 20-year-old James Alex Fields Jr. has a bond hearing Monday morning.
Fields is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others.
Fields has been in custody since Saturday. Jail officials told The Associated Press they don't know if he's obtained an attorney.
A high school teacher said Fields was fascinated with Nazism, idolized Adolf Hitler and had been singled out by school officials in the 9th grade for his "deeply held, radical" convictions on race. ||||| Attorney General Jeff Sessions said a driver's ramming a car into a crowd of demonstrators in Charlottesville, Virginia, on Saturday, which killed a young woman and sent 19 other people to hospitals, "does meet the definition of domestic terrorism" under U.S. law.
"It does meet the definition of domestic terrorism in our statute," Sessions told ABC News' David Muir on "Good Morning America" today. "We are pursuing it in the [Department of Justice] in every way that we can make a case."
"You can be sure we will charge and advance the investigation towards the most serious charges that can be brought, because this is unequivocally an unacceptable, evil attack," he said. "Terrorism investigators from the FBI are working on the case as well as civil rights division FBI agents."
The ramming occurred shortly after authorities in Charlottesville called off a planned white nationalist rally, titled Unite the Right, and ordered crowds to disperse after violent clashes between rally attendees and counterprotesters.
Heather Heyer, 32, who was with a group protesting the white nationalist gathering, was killed when the car plowed into the crowd.
The suspected driver, 20-year-old James Alex Fields Jr. of Ohio, was arrested and charged with second-degree murder.
President Trump drew criticism when, after the ramming, he condemned "hatred, bigotry and violence on many sides," which some commentators said appeared to draw a moral equivalence between the white nationalists rallying in Charlottesville and the counterprotesters.
But Sessions said on "GMA" that the president "explicitly condemned the kind of ideology behind these movements of Nazism, white supremacy, the KKK. That is his unequivocal position, he totally opposes those kind of values."
The attorney general added, "The president, I suspect, will be talking to the country again soon, maybe today. I plan to meet with him today, and the FBI today will be meeting with him to brief him on this case. He takes this exceedingly seriously."[/INST]β A judge in Charlottesville, Va., has denied bond for an Ohio man accused of plowing his car into a crowd at a white nationalist rally, reports the AP. Judge Robert Downer said during a bond hearing Monday he would appoint a lawyer for James Alex Fields Jr. The 20-year-old is charged with second-degree murder and other counts after authorities say he drove into the crowd, fatally injuring one woman and hurting 19 others. Also on Monday, Attorney General Jeff Sessions called the attack that killed 32-year-old Heather Heyer "domestic terrorism." "It does meet the definition of domestic terrorism in our statute," Sessions said on Good Morning America, per ABC News. "You can be sure we will charge and advance the investigation towards the most serious charges that can be brought, because this is unequivocally an unacceptable, evil attack." Sessions also defended President Trump's public response to the violence. The president, he said, "explicitly condemned the kind of ideology behind these movements of Nazism, white supremacy, the KKK. That is his unequivocal position, he totally opposes those kind of values." He predicted that Trump would address the nation on the subject soon.</s> |
one of the biggest surprises in the exoplanet field was the discovery of gas giant planets orbiting very close to their host star .
these hot jupiter planets represent one extreme of the galaxy s population of planets , and they provide important constraints to guide our nascent ideas about the formation and evolution of planetary systems .
the probability of transit for close - in giant planets is @xmath0 @xcite , and through the analysis of transit light curves the ratio of the stellar and planetary radii can be deduced . through the significant uncertainties in the mass and radius of any particular star ,
our characterisation of exoplanets is limited by that of their host stars ( e.g. * ? ? ?
for this reason , it is important to directly measure the properties of planet hosting stars , particularly in cases where we expect the presence of planets may have influenced the properties of the star through star - planet interactions .
one of the most extreme hot jupiter exoplanets is wasp-12b , a gas giant planet orbiting only 0.023au from a late f - type host star @xcite .
wasp-12b s orbit is , therefore , only about 1.5 stellar diameters from the photosphere of the star . at such proximity ,
interactions between the star and the planet must occur .
near - uv observations of wasp-12 covering the wavelengths of many resonance lines reveal that wasp-12b is surrounded by an exosphere which appears to overfill its roche lobe @xcite
. this exospheric gas may be the consequence of tidal disruption of the planet s convective envelope as recently suggested by @xcite , but it could also be entrained material from the stellar corona .
a planet orbiting as close as wasp-12b might be expected to interact magnetically with its host star , c.f .
@xcite , @xcite , and @xcite .
a first step to search for such interactions is to detect and quantify the stellar magnetic field by spectropolarimetry , e.g. @xcite .
the presence of a magnetic field belonging to wasp-12 would provide a precious piece of information needed to establish which mechanism controls the structure and the evolution of the disk @xcite .
the solar system s giant planets have enhanced metal abundances relative to the sun @xcite and high atmospheric metal abundances have been suggested as a contributing factor in the inflated radii of planets such as wasp-12b @xcite .
intriguingly , @xcite detected a wealth of metallic atoms and ions in the exospheric gas surrounding wasp-12b .
if this gas is indeed accreting onto the host star as suggested by @xcite , this could lead to abundance anomalies in the photosphere of wasp-12 . since wasp-12 is expected to have a very shallow surface convection zone
, any accreted gas will remain close to the surface rendering any pollution of the surface composition relatively easy to detect . in this paper , we report on spectropolarimetric observations of wasp-12 which we use to probe the stellar magnetic field , fundamental parameters and abundance pattern of the star . in sect .
[ obs ] we describe our observations and data reduction . sect .
[ model ] and sect .
[ parameters ] provide a description of the adopted model atmosphere including methods and results of the stellar parameter determination and abundance analysis . in sect .
[ mag.field ] we provide the results of our stellar magnetic field search .
our results are finally discussed in sect .
[ discussion ] , while in sect .
[ conclusions ] we gather our conclusions .
we observed wasp-12 using the ( echelle spectropolarimetric device for observations of stars ) spectropolarimeter at the canada - france - hawaii telescope ( cfht ) on the 3rd and 5th of january 2010 .
the observations were performed in polarimetric " mode .
consists of a table - top cross - dispersed echelle spectrograph fed via a double optical fiber directly from a cassegrain - mounted polarisation analysis module . beside the natural intensity @xmath1 , in polarimetric mode
the instrument can acquire a stokes @xmath2 ( or @xmath3 or @xmath4 ) profile throughout the spectral range 370010400 with a resolving power of about 65000 .
a complete polarimetric observation consists of a sequence of 4 sub - exposures @xcite .
each of the four sub - exposures was 1290seconds long , with a total amount of integration time of 1.5hrs , each night .
the spectra were reduced using the libre - esprit package @xcite .
the stokes @xmath1 spectra have a signal - to - noise ratio ( snr ) per pixel of @xmath5126 and @xmath5158 in the continuum , on the first and second nights respectively ; both values calculated at 5000 . to increase the snr of the stokes @xmath1 spectrum we averaged the two available spectra , obtaining a single spectrum with a snr of @xmath5200 , normalised by fitting a low order polynomial to carefully selected continuum points .
the effective temperature ( ) was determined ( see sect . [ parameters ] ) from our data and two spectra of wasp-12 obtained at the isaac newton telescope ( int ) with the intermediate dispersion spectrograph ( ids ) .
the spectra cover the region of the h@xmath6 line with a spectral resolution of @xmath7=8000 ( see * ? ? ? * for more details ) .
we also used near - uv observations obtained with the hst cosmic origin spectrograph ( cos ) @xcite for the analysis of the spectral energy distribution .
the spectra , calibrated in flux , cover three non - contiguous wavelength ranges in the near - uv with a resolution of @xmath820000 .
these observations are described in detail in @xcite .
to compute model atmospheres of wasp-12 we employed the stellar model atmosphere code @xcite .
for all the calculations local thermodynamical equilibrium ( lte ) and plane - parallel geometry were assumed .
we used the database @xcite as a source of atomic line parameters for opacity calculations .
the recent vald compilation contains information for about @xmath9 atomic transitions , most of them coming from the latest theoretical calculations performed by r. kurucz .
convection was implemented according to the @xcite model of convection ( see * ? ? ? * for more details ) .
@xcite derived the fundamental parameters of wasp-12 from the analysis of low and mid - resolution spectra , obtaining = 6300@xmath10150k , = [email protected] , and adopting a value of 0.85 for the microturbulence velocity ( ) .
we used these values as our starting point in an iterative process to gradually improve the parameters using different spectroscopic indicators . in our analysis ,
every time any of , , or abundances changed during the iteration process , we recalculated a new model with the implementation of the last measured quantities .
similarly the derived abundances were treated iteratively : while the results of the abundance analysis depend upon the assumed model atmosphere , the atmospheric temperature - pressure structure itself depends upon the adopted abundances , so we recalculated the model atmosphere every time abundances were changed , even if the other model parameters were fixed .
this ensures the model structure is consistent with the assumed abundances .
we determined by fitting synthetic line profiles , calculated with @xcite , to the observed profiles of two hydrogen lines : h@xmath6 ( from the ids spectrograph ) and h@xmath11 ( from the spectropolarimeter ) .
we discarded the other hydrogen lines observed with because of the uncertainties in the continuum normalisation .
in the temperature range expected for wasp-12 , hydrogen lines are extremely sensitive to temperature variations and insensitive to variations , and are therefore good temperature indicators .
we found = 6250@xmath10100k , in good agreement with @xcite .
the uncertainty estimate considered both the quality of the observations and the uncertainties in the normalisation .
figure [ hydrogen ] shows the comparison between the observed h@xmath6 line profile and the synthetic profiles calculated with the adopted of 6250@xmath10100k .
the poor fit of the hydrogen line core is due to the adopted lte approximation ( see e.g. * ? ? ?
line profile observed with the ids spectrograph ( black solid line ) and synthetic profiles calculated with the final adopted of 6250k ( red solid line ) , and uncertainty ( dashed lines ) . ] another spectroscopic indicator for is given by the analysis of metallic lines , that we performed on the spectrum .
in particular , is determined by eliminating the correlation between abundance and excitation potential ( ) for the selected lines of a given ion / element .
the top panel of fig .
[ equilibria ] shows the correlation between abundance and for all measured lines of , , , , and .
figure [ equilibria ] , produced using the final adopted fundamental parameters , shows no significant correlation between abundance and for all ions , except , for which we registered a slightly positive correlation ( [email protected] ) , that would be eliminated by a higher .
what we found here for resambles what remarked by @xcite for hd 49933 and hd 32115 ( both stars have a slightly higher than wasp-12 ) : an effective temperature determination based only on the analysis of lines leads systematically to a that is substantially higher ( by about 5% ) , compared to the one obtained with other ions and in particular with other temperature indicators , such as hydrogen lines .
for this reason , we decided to use the analysis of the metallic lines only as consistency check of derived from the hydrogen lines .
in addition to the ions shown in fig .
[ equilibria ] , we included in the consistency check also , , , , , , , , , , and , obtaining the requested equilibrium for all of them .
the number of lines adopted to measure the abundance- correlation for each ion is the same as the one we used to derive the final ion abundance , and it is listed in table [ abundance ] . 0.01270 , consistent with zero .
bottom panel : abundance obtained for each measured line of the ions given in the top panel , as a function of the measured line equivalent width .
the effective temperature from metallic lines is derived eliminating the correlation shown in the top panel , while is determined eliminating the correlation shown in the bottom panel . ]
the surface gravity was derived from two independent methods based on ( _ i _ ) line profile fitting of gravity - sensitive metal lines with developed wings and ( _ ii _ ) ionisation balance for several elements .
the first method is described in @xcite and uses the fact that the wings of the lines at @xmath125167 , 5172 and 5183 are very sensitive to variations . in practice
we first derived the mg abundance from other lines without developed wings , such as @xmath125711 and 5785 , and then we fit the wings of the gravity indicator lines by tuning the value . to apply this method , very accurate values and van der waals ( log@xmath13 ) damping constants
are required for all the lines .
we adopted the set of line parameters used by @xcite and included the uncertainty in these parameters in the uncertainty in .
we obtained a value of [email protected] , in good agreement with @xcite .
our line profile fit of the lines with developed wings is shown in fig .
[ mglines ] . 0.2 .
we adopted the same combination of and van der waals damping constants as in @xcite : oscillator strengths from @xcite and damping constants from @xcite . ] the second method , the ionisation equilibrium , is often used to derive the surface gravity , but this method is extremely sensitive to the effects present for each ion / element , while mg lines with developed wings ( less sensitive to effects ) are more suitable as indicators @xcite .
for this reason we decided to keep the mg lines as our primary indicator , and checked the result with the ionisation equilibrium . adopting the value obtained from the analysis of the lines with developed wings and taking into account the abundance uncertainties , we satisfied the ionisation equilibrium for every element with two analysed ions .
our main source for the atomic parameters of spectral lines is the database with the default configuration .
lte abundance analysis was based on equivalent widths , analysed with a modified version @xcite of the width9 code @xcite . for all analysed elements / ions we used almost all unblended spectral lines with accurate atomic parameters available in the wavelength range 42409900 , except lines in spectral regions where the continuum normalisation was too uncertain . for blended lines , lines subjected to hyperfine splitting ( ) , lines situated in the wings of the hydrogen lines or for very shallow lines of specific ions we derived the line abundance by performing synthetic spectrum calculations with the code .
the constants for abundance calculations were taken from @xcite for lines and from @xcite for the line at @xmath126707 .
for the barium abundance we used the lines at @xmath125853.7 and 6496.9 for which we do not expect any relevant effect @xcite .
a line - by - line abundance list with the equivalent width measurements , adopted oscillator strengths , and their sources is given in table [ linelist ] ( see the online material for the complete version of the table ) .
.linelist of the lines used for the abundance analysis .
the first and second columns list respectively the ( in ev ) and the value for each line .
columns five and six list the equivalent width in m and the abundance for each line , while the last column gives the reference for the value .
spectral lines for which the abundance was measured with synthetic spectra , instead of equivalent widths , present an
s `` instead of the equivalent width value .
lines marked with * '' are subject to hyperfine structure , discussed in detail in the main text , while lines marked with # " are multiplets ( doublets or triplets ) and in these cases we listed only the strongest line .
the entire table can be viewed in the electronic version of the journal .
[ cols="^,^,^ , > , > , > " , ] one of the main purpose of this work is to search for chemical peculiarities that could be connected with pollution of the stellar atmosphere by material lost by the planet .
this can be done in different ways , as also shown in the extensive salient literature present ( see e.g. * ? ? ?
* and references therein ) .
wasp-12 is a promising target for signs of atmospheric pollution : wasp-12b is most likely currently losing material @xcite ; this material is believed to be forming a circumstellar disk that is accreting onto the star , polluting the stellar photosphere @xcite .
classical ways of looking for atmospheric pollution are by searching : ( _ i _ ) chemical peculiarities of single elements , such as li and be ( e.g. * ? ? ?
* ) ; ( _ ii _ ) a trend in the element abundance against the condensation temperature ( t@xmath14 ; see e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) ; ( _ iii _ ) chemical peculiarities of the abundance pattern in comparison to reference stars ( both planet hosting and non - planet hosting ) .
when searching for small effects on the stellar atmospheric abundances it is important to determine whether a certain star belongs to the thin or thick galactic disk population .
to do so we performed both a kinematic and chemical analysis of wasp-12 .
we calculated the galactic velocity vectors ( u , v , w ) corrected to the local standard of rest ( lsr ) using the formalism of @xcite , instead defining u as positive towards the galactic anti - centre . as done by @xcite , wasp-12 was then placed on the toomre diagram of the @xcite stellar sample , indicating that wasp-12 has a peculiar velocity less than 85 , strongly indicative of thin disk membership . from the wasp-12 abundances , we then compared our values of [ @xmath6/fe ] ( @xmath150.15dex ) and [ fe / h ] ( @xmath160.28dex ) , where [ @xmath6/fe ] is defined as 0.25([mg
/ fe]+[si / fe]+[ca / fe]+[ti / fe ] ) , with the @xcite sample , obtaining that wasp-12 is again consistent with the properties of the thin disk population .
in our analysis we are not able to look for chemical peculiarities of both li and be . as shown in fig .
[ fig.lithium ] , our spectra do not have the snr and the resolution necessary to perform a precise analysis of the li@xmath17/li@xmath18 ratio , but we can compare the lithium abundance obtained for wasp-12 with that of other planet hosting stars . @xcite and
@xcite published lithium abundances of stars hosting a giant planet or a brown dwarf and compared them to a set of non - planet hosting stars .
the lithium abundance we obtained for wasp-12 matches that of both set of stars , showing clearly that li is not peculiar in wasp-12 .
our spectra do not include the region around @xmath123130 covering the two lines usually adopted to measure the be abundance .
an effective way to check whether a stellar photosphere is polluted by accretion of metal - rich material is to examine the correlation between the relative abundance of various elements and their t@xmath14 . in accreting metal - rich material
the refractory elements tend to form dust grains that are blown away by the stellar wind .
thus the star accretes more volatile than refractory elements , as happens , for example , in @xmath12 bootis stars @xcite .
our wasp-12 ion abundance are shown against condensation temperature ( taken from * ? ? ?
* ) in fig .
[ fig.condtemp ] . .
] the correlation obtained between the ion abundances relative to the sun @xcite and t@xmath14 is not statistically significant : [email protected]@xmath1910@xmath20 . in the past years
several authors ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) looked for the same kind of correlation in several planet hosting stars , without having found any .
the trend we obtain for wasp-12 is also indicative of a null result .
@xcite , applying a differential analysis on the sun and solar twins , discovered that the sun shows a highly significant correlation of the abundances ( relative to the mean abundance of the solar twins ) in respect to the condensation temperature .
in addition this correlation shows a significant break at t@xmath211200k . @xcite and @xcite came to the conclusion that this correlation is likely connected to the presence of planets around the sun .
the detection of this kind of correlation requires very high precision abundances ( error bars @xmath22 0.05dex and free from systematic differences ) , attainable only with a differential analysis .
the application of this method to wasp-12 would require observations of stars that can be considered twins of wasp-12 ( similar , metallicity , age , and population ) .
the choice of the wasp-12 twins will be of crucial importance because effects such as diffusion , more prevalent for f - type stars than g - type stars , are strongly age and dependent , and consequently could easily hide or mimic pollution signatures .
our analysis does not lead to a firm conclusion about the atmospheric pollution of wasp-12 . to check whether wasp-12 has a peculiar abundance pattern we compared the abundances with those obtained by other authors on a large number of stars with a similar .
in particular we took into account the results of the abundance analysis on stars that are not known planet hosts , in the temperature range 60006500k , and with a [ fe / h]@xmath230.0dex .
we decided to use such a small temperature range to decrease the effect of possible systematics , such as effects .
in addition , since we are interested in looking for a peculiar pattern , we decided to use only the stars with an over - solar iron abundance and to subdivide the sample of comparison stars according to their iron abundance : 0.0@xmath22[fe
/ h]@xmath240.1 , 0.1@xmath22[fe / h]@xmath240.2 , and [ fe / h]@xmath230.2 . to have a better statistical view of each subsample we decided to plot in our comparisons not only the mean abundance and relative standard deviation for the comparison stars , but also their abundance range . to accomplish all these requirements
, we needed to have a large set of non - planet hosting stars , such as the one provided by @xcite .
@xcite performed a parameter determination and lte abundance analysis of more than 1000 late - type main sequence stars . for each star they derived the abundances of na ,
si , ti , fe , and ni . this sample provided us with comparison abundances for 59 stars with 0.0@xmath22[fe / h]@xmath240.1dex , 36 stars with 0.1@xmath22[fe / h]@xmath240.2dex , and 22 stars with [ fe / h]@xmath230.2dex .
the comparison between our wasp-12 abundances and the ones from the sample of @xcite is shown in fig .
[ fig.valenti ] .
[ fe / h]@xmath240.1dex ( open upside triangles ) , 0.1@xmath22[fe / h]@xmath240.2dex ( open squares ) , and [ fe / h]@xmath230.2dex ( open downside triangles ) .
the shaded areas show the abundance range , while the error bars of the comparison sample give the standard deviation from the mean abundance .
the uncertainties on the abundances of wasp-12 are as in fig .
[ fig.abn ] . ]
figure [ fig.valenti ] shows that the abundances of ti and fe are clearly comparable to the ones of the higher metallicity subsample , as expected given the fact that [ fe / h ] of wasp-12 is about 0.3 .
the na abundance of wasp-12 falls within the abundance range of the high - metallicity stars of the comparison sample , due to the large range covered by the na abundance , while ni shows a mean abundance that is just outside the abundance range .
the si abundance looks definitely more similar to the one of the set of stars with 0.1@xmath22[fe / h]@xmath240.2dex , but the large uncertainty on this abundance does not allow any firm conclusion . in summary
the abundances of ti and fe follow the pattern of the high - metallicity stars , while na , si , and ni seem to follow more the abundance pattern of the set of comparison stars with [ fe / h ] between 0.1 and 0.2dex . the information gathered from this comparison lead to the conclusion that there is the possibility that the wasp-12 abundances of na , si , and ni do not really match the abundance pattern that the wasp-12 iron abundance would suggest .
but it has to be taken into account that the comparison is not free from systematic differences in the fundamental parameters and abundance determinations , and in the set of adopted atomic line parameters . for a further search of possible abundance peculiarities in the atmosphere of wasp-12 we decided to compare our results with those of several other authors
@xcite have obtained in planet hosting and non - planet hosting stars . in this way
we should also be able to partially remove possible systematic differences in case a peculiar pattern becomes evident in the comparisons with several different authors .
the wasp-12 abundances we derived for o , ca , sc , mn , zn , y , zr , nd , and eu match very well the ones previously obtained by other authors in planet hosting and non - planet hosting stars , while abundances of al , v , and cu appear to be clearly below the values previously obtained by more than 0.2dex .
for the other compared elements ( c , n , na , mg , si , s , ti , cr , co , and ni ) we obtained just a satisfactory agreement , since we register a tendency of the wasp-12 abundances of these elements to lay always in the lower margin of the comparison samples , in particular when the abundances are put in relation to the iron abundance .
this result follows what previously obtained , strengthening the possibility of an increased fe abundance in comparison to the one of some other elements .
in addition we compared our si , ti , and ni wasp-12 abundances with the ones obtained by @xcite in a set of planet hosting and non - planet hosting stars .
we obtained a good agreement for ti , but both si and ni appear to be depleted in wasp-12 , compared to the abundances obtained by @xcite in a set of planet hosting stars , therefore we can not confirm their conclusion of a systematic enrichment of si and ni in planet hosting compared to non - planet hosting stars
. the circumstellar disk , predicted by @xcite and tentatively observed by @xcite , could be detectable in the infrared .
for this reason we decided to compare the calibrated near - uv cos fluxes of wasp-12 and the available photometry ( johnson and 2mass photometry ) with synthetic fluxes obtained with adopting the fundamental parameters and the abundances derived from the data , looking for an infrared excess in the 2mass photometry . for this comparison , shown in fig .
[ fig.flux ] , we took into account a reddening e(b - v)=0.126mag @xcite , that was calculated assuming the stellar distance obtained in sect .
[ age ] .
photometry ( full points ) and 2mass photometry ( full triangles ) . the error bars on the photometry have the same size of the symbols .
the model fluxes and the cos spectra were convolved to have approximately a spectral resolution of 800 , for display reasons . ]
figure [ fig.flux ] shows a very good agreement between the model fluxes and the observations , demonstrating also the quality of both the adopted fundamental parameters and interstellar reddening .
figure [ fig.flux ] does not show any clear infrared excess in the 2mass photometry that could be interpreted as : ( _ i _ ) there is no interstellar disk around the star or ( _ ii _ ) the interstellar disk is not visible because either the emission is not strong enough or the emission peaks at much longer wavelengths .
@xcite suggested that the disk emission should peak at @xmath52.3@xmath25 m , inside the wavelength range covered by the @xmath26 band 2mass photometry .
therefore , to look for an interstellar disk around wasp-12 it would be necessary to observe the system with a very high precision @xcite and at longer wavelengths , both accessible with the herschel satellite @xcite .
on january 3rd and 5th 2010 we observed the planet hosting star wasp-12 with the spectropolarimeter with the aim of looking for a global magnetic field , derive the stellar parameters and perform a precise abundance analysis .
the wasp-12 fundamental parameters and iron abundance we obtained are in agreement with what previously published by @xcite : = 6250@xmath10100k , = [email protected] , = [email protected] , and [ fe / h][email protected] .
is less than [email protected] , while lays within the range [email protected] .
dedicated observations to measure the amplitude of the rm effect are necessary to derive the real stellar .
the resultant metallicity of wasp-12 is @[email protected] . a detailed analysis of the hr diagram , with the use of isochrones and evolutionary tracks allowed to derive more accurate ranges for the stellar age , mass and distance : the age of wasp-12 is between 1.0gyr @xcite and 2.65gyr
, the mass is between 1.23 and 1.49 ( the last value comes from * ? ? ? * ) , and the distance to wasp-12 is between 295 and 465pc .
our measurement of the li abundance allowed us just to conclude that wasp-12 is older than 500myr .
we performed a magnetic field search adopting the lsd technique revealing that the star does not show any magnetic field signature in stokes @xmath2 .
a detailed analysis of the possible star - planet magnetic interaction would require a time - dependent analysis of particular spectral lines , such as the ca h & k lines @xcite and the uv resonance lines , but it has to be taken into account that wasp-12 shows a remarkably low stellar activity @xcite , that will be analysed in detail in a forthcoming paper .
given recent theoretical predictions @xcite and discoveries @xcite , the wasp-12 system seems to be an ideal target to detect the presence of atmospheric pollution , due to the material lost by the planet .
therefore we looked for hints of pollution by looking for a correlation between the atmospheric element abundances and the condensation temperature , and by comparing the wasp-12 abundance pattern with the one of other planet hosting and non - planet hosting stars , previously published by several other authors .
our analysis revealed just the presence of hints of atmospheric pollution , although only a differential analysis would allow to obtain firm evidences .
one must also take into account the fact that it is not clear whether wasp-12 would show the same kind of atmospheric pollution shown by the sun @xcite : the material coming from wasp-12b and falling onto the star is in a gas / plasma state and only a detailed modeling of the temperature and density structure of the accretion disk would show whether the material is condensing in dust grains .
if dust grains are forming it is likely that a differential analysis would reveal the kind of pollution signatures obtained for the sun , otherwise all the material lost by the planet would fall onto the star , making then the pollution signature dependent to the unknown hydrogen content of the planet . with the use of the available hst calibrated spectra and of visible and infrared photometry
, we looked for the presence of a circumstellar disk around wasp-12 , but without success .
probably high precision far infrared measurements , such as those possible with the hershel satellite , may reveal the presence of a circumstellar disk .
this work is based on observations obtained at the canada - france - hawaii telescope ( cfht ) , which is operated by the national research council of canada , the institut national des sciences de lunivers of the centre national de la rechereche scientifique of france , and the university of hawaii .
this work is also based on observations made with the nasa / esa hubble space telescope , obtained from mast at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc .
, under nasa contract nas 5 - 26555 .
these observations are associated with program # 11651 to which support was provided by nasa through a grant from the space telescope science institute .
this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation .
this work is supported by an stfc rolling grant ( l.f . , a.e . ) .
o.k . is a royal swedish academy of sciences research fellow supported by grants from the knut and alice wallenberg foundation and the swedish research council .
d.s . acknowledges support received from the deutsche forschungsgemeinschaft ( dfg ) research grant re1664/7 - 1 .
l.f . is deeply in debt with dr .
tanya ryabchikova for the tremendous help she gave with the values references , dr .
gregg wade for his help during the preparation of the observing proposal , and dr .
berry smalley for the information regarding the determination of the wasp-12 distance .
we thank also the cfht staff , dr .
nadine manset and the cfht director , dr .
christian veillet , for their help and speed in obtaining the observations .
_ facilities : _ , , .
aldenius , m. , tanner , j.d . , johansson , s. , lundberg , h. , & ryan , s.g .
2007 , , 461 , 767 amres , e. b. , & lpine , j. r. d. 2005 , , 130 , 679 asplund , m. , grevesse , n. , & sauval , a. j. 2005 , astronomical society of the pacific conference series , 336 , 25 bard , a. , & kock , m. 1994 , , 282 , 1014 bard , a. , kock , a. , & kock , m. 1991 , , 248 , 315 berry , h.g . , bromander , j. , curtis , l.j . , & buchta , r. 1971 , phys .
, 3 , 125 bielski , a. 1975 , jqsrt , 15 , 463 biemont e. , quinet p. , & zeippen c.j .
1993 , , 102 , 435 bizzarri , a. , et al .
1993 , , 273 , 707 blackwell , d. e. , shallis , m. j. , & selby , m. j. 1979 , , 188 , 847 blanco , f. , botho , b. , & campos , j. 1995 , phys .
, 52 , 628 bond , j. c. , et al .
2008 , , 682 , 1234 bhm - vitense , e. 1958 , zeitschrift fur astrophysik , 46 , 108 burrows , a. , hubeny , i. , budaj , j. , & hubbard , w. b. 2007 , , 661 , 502 canuto , v. m. , & mazzitelli , i. 1991 , , 370 , 295 canuto , v. m. , & mazzitelli , i. 1992 , , 389 , 724 cowley , c.r . , & bord , d.j .
1998 , in the scientific impact of the goddard high resolution spectrograph , eds .
brandt , t.b .
ake , and c.c .
petersen , asp conf .
143 , 346 cowley , c. r. , & corliss , c. h. 1983 , , 203 , 651 den hartog , e.a . ,
lawler , j.e .
, sneden , c. , & cowan , j.j .
2003 , , 148 , 543 donati , j .- f . ,
semel , m. , carter , b. d. , rees , d. e. , & collier cameron , a. 1997 , , 291 , 658 donati , j .- f .
, et al . 2007 , , 380 , 1297 ecuvillon , a. , et al . 2004 , , 426 , 619 ecuvillon , a. , israelian , g. , santos , n. c. , mayor , m. , & gilli , g. 2006 , , 449 , 809 fares , r. , et al .
2010 ( arxiv:1003.6027 ) fossati , l. , et al .
2009 , , 503 , 945 fossati , l. , et al .
2010 , , 714l , 222 fuhr , j.r . ,
martin , g.a . , & wiese , w.l .
1988 , j.phys.chem.ref.data , 17 , suppl .
4 . fuhrmann , k. , pfeiffer , m. , frank , c. , reetz , j. , & gehren , t. 1997 , , 323 , 909 gilli , g. , israelian , g. , ecuvillon , a. , santos , n. c. , & mayor , m. 2006 , , 449 , 723 girardi , l. , bressan , a. , bertelli , g. , & chiosi , c. 2000 , , 141 , 371 gonzalez , g. , carlson , m. k. , & tobin , r. w. 2010 , , 403 , 1368 gonzalez , g. , carlson , m. k. , & tobin , r. w. 2010 , , tmp , 843 ( arxiv : 1004.3313 ) green , j. c. , et al .
2010 , baas , 41 , 501 guillot , t. 2005 , annual review of earth and planetary sciences , 33 , 493 hannaford , p. , lowe , r.m . , grevesse , n. , biemont , e. , & whaling , w. 1982 , , 261 , 736 hebb , l. , et al .
2009 , , 693 , 1920 heiter , u. , et al .
2002 , , 392 , 619 husnoo , n. , pont , f. , hebrard , g. , et al .
2010 , , submitted ( arxiv : 1004.1809 ) israelian , g. , santos , n. c. , mayor , m. , & rebolo , r. 2004 , , 414 , 601 johnson , d. r. h. , & soderblom , d. r. 1987 , , 93 , 864 knutson , h. a. , howard , a. w. , & isaacson , h. 2010 , , submitted ( arxiv : 1004.2702 ) kochukhov , o. 2007 , spectrum synthesis for magnetic , chemically stratified stellar atmospheres , physics of magnetic stars , 109 , 118 kupka , f. , piskunov , n. , ryabchikova , t. a. , stempels , h. c. , & weiss , w. w. 1999 , , 138 , 119 kurucz , r.l .
1988 , trans .
iau , xxb , m. mcnally , ed .
, dordrecht : kluwer , 168 - 172 kurucz , r. 1993 , atlas9 : stellar atmosphere programs and 2 km / s grid .
kurucz cd - rom no .
13 ( cambridge : smithsonian astrophysical observatory ) kurucz , r.l . 1993 , sao , cambridge , cdrom 20 - 22 kurucz , r.l . , & peytremann , e. 1975 , sao special report , 362 lai , d. , helling , c. , & van den heuvel , e. p. j. 2010 , , submitted ( arxiv : 1005.4497 ) lambert , d.l . , mallia , e.a . , &
warner , b. 1969 , , 142 , 71 lawler , j.e .
, & dakin , j.t .
1989 , josa , b6 , 1457 lawler , j.e . , bonvallet , g. , & sneden , c. 2001 , , 556 , 452 lawler , j.e . ,
wickliffe , m.e . ,
den hartog , e.a . , & sneden , c. 2001 , , 563 , 1075 lawler , j.e . , den hartog , e.a . ,
sneden , c. , & cowan , j.j .
2006 , , 162 , 227 lawler , j.e . , sneden , c. , cowan , j.j . ,
ivans , i.i . , &
den hartog , e.a .
2009 , , 182 , 51 li , s. , miller , n. , lin , d. n. c. , & fortney , j. j. 2010 , , 463 , 1054 lincke , r. , & ziegenbein , g. 1971 , z. phyzik , 241 , 369 ljung g. , nilsson h. , asplund m. , & johansson s. 2006 , , 456 , 1181 lodders , k. 2003 , , 591 , 1220 marigo , p. , et al .
2008 , , 482 , 883 martin , g.a . ,
fuhr , j.r . , & wiese , w.l .
1988 , j.phys.chem.ref.data , 17 , suppl .
3 . martnez - galarza , j. r. , et al .
2009 , , 694 , 165 mashonkina , l. , & zhao , g. 2006 , , 456 , 313 mashonkina , l. i. , vinogradova , a. b. , ptitsyn , d. a. , khokhlova , v. s. , & chernetsova , t. a. 2007 , astronomy reports , 51 , 903 mashonkina , l. i. 2009 , phis .
scr . , t134 , 014004 melndez , j. , asplund , m. , gustafsson , b. , & yong , d. 2009 , , 704 , l66 miles , b.m . , & wiese , w.l .
1969 , wsg technical note 474 neves , v. , santos , n. c. , sousa , s. g. , correia , a. c. m. , & israelian , g. 2009 , , 497 , 563 nitz , d.e . ,
wickliffe , m.e . , & lawler , j.e .
1998 , , 117 , 313 obrian , t.r . ,
wickliffe , m.e . ,
lawler , j.e . , whaling , w. , & brault , j.w .
1991 , josa , b8 , 1185 osterman , s. , et al .
2010 , baas , 41 , 502 pickering , j.c . ,
thorne , a.p . , & perez , r. 2001 , , 132 , 403 pilbratt , g. l. , et al .
2010 , , accepted ( arxiv : 1005.5331 ) piskunov , n. e. , kupka , f. , ryabchikova , t. a. , weiss , w. w. , & jeffery , c. s. 1995 , , 112 , 525 raassen , a.j.j .
, & uylings , p.h.m .
1998 , , 340 , 300 , ( ftp://ftp.wins.uva.nl/pub/orth ) ralchenko , yu . ,
kramida , a.e . ,
reader , j. , & nist asd team .
2008 , nist atomic spectra database ( version 3.1.5 ) , available : http://physics.nist.gov/asd3 , nist , gaithersburg , md robinson , s. e. , laughlin , g. , bodenheimer , p. , & fischer , d. 2006 , , 643 , 484 ryabchikova , t. a. , piskunov , n. e. , stempels , h. c. , kupka , f. , & weiss , w. w. 1999 , phis .
, t83 , 162 ryabchikova , t. a. , fossati , l. , & shulyak , d. 2009 , , 506 , 203 sadakane , k. , et al .
2002 , , 54 , 911 santos , n. c. , et al .
2006 , , 458 , 997 seager , s. , whitney , b. a. , & sasselov , d. d. 2000 , , 540 , 504 seaton , m.j . , mihalas , d. , & pradhan , a.k .
1994 , , 266 , 805 sestito , p. , & randich , s. 2005 , , 442 , 615 shkolnik , e. , walker , g. a. h. , & bohlender , d. a. 2003 , , 597 , 1092 shkolnik , e. , walker , g. a. h. , bohlender , d. a. , gu , p .-
g . , & krster , m. 2005 , , 622 , 1075 shkolnik , e. , bohlender , d. a. , walker , g. a. h. , & collier cameron , a. 2008 , , 676 , 628 shulyak , d. , tsymbal , v. , ryabchikova , t. , sttz ch . , & weiss , w. w. 2004 , , 428 , 993 smith , g. , & oneil , j.a .
1975 , , 38 , 1 smith , g. , & raggett , d.st.j . 1981 , j. phys .
b , 14 , 4015 smith , v. v. , lambert , d. l. , & nissen , p. e. 1998 , , 506 , 405 smith , g. 1988 , j. phys .
phys . , 21 , 2827 soubiran , c. , & girard , p. 2005
, , 438 , 139 southworth , j. 2009 , , 394 , 272 sozzetti , a. , et al .
2006 , , 131 , 2274 takeda , y. , kato , k .-
i . , watanabe , y. , & sadakane , k. 1996 , , 48 , 511 takeda , y. , et al .
2002 , , 53 , 1211 tsymbal , v. v. 1996 , in asp conf .
108 , model atmospheres and spectral synthesis , ed .
s. j. , adelman , f. , kupka , & w. w. , weiss , 198 valenti , j. a. , & fisher , d. a. 2005 , , 159 , 141 wade , g. a. , donati , j .- f .
, landstreet , j. d. , & shorlin , s. l. s. 2000 , , 313 , 823 warner , b. 1968 , , 139 , 115 wickliffe , m.e . , & lawler , j.e .
1997 , , 110 , 163 wiese , w.l . ,
fuhr , j.r . , & deters , t.m .
1996 , aip press , a critical data compilation , j. phys .
chem . ref .
data , monograph no .
7 , melville , ny , pp . 532 wiese , w.l . ,
smith , m.w .
, & miles , b.m .
1969 , nsrds - nbs , 22 wiese , w.l . , smith , m.w . , & miles , b.m .
1969 , nsrds - wsg , 22 zhao , g. , & gehren , t. 2000 , , 362 , 1077 | the knowledge of accurate stellar parameters is paramount in several fields of stellar astrophysics , particularly in the study of extrasolar planets , where often the star is the only visible component and therefore used to infer the planet s fundamental parameters .
another important aspect of the analysis of planetary systems is the stellar activity and the possible star - planet interaction . here
we present a self - consistent abundance analysis of the planet hosting star wasp-12 and a high - precision search for a structured stellar magnetic field on the basis of spectropolarimetric observations obtained with the spectropolarimeter .
our results show that the star does not have a structured magnetic field , and that the obtained fundamental parameters are in good agreement with what was previously published .
in addition we derive improved constraints on the stellar age ( 1.02.65gyr ) , mass ( 1.231.49 ) , and distance ( 295465pc ) .
wasp-12 is an ideal object to look for pollution signatures in the stellar atmosphere .
we analyse the wasp-12 abundances as a function of the condensation temperature and compare them with those published by several other authors on planet hosting and non - planet hosting stars .
we find hints of atmospheric pollution in wasp-12 s photosphere , but are unable to reach firm conclusions with our present data .
we conclude that a differential analysis based on wasp-12 twins will probably clarify if an atmospheric pollution is present , the nature of this pollution and its implications in the planet formation and evolution .
we attempt also the direct detection of the circumstellar disk through infrared excess , but without success . | <s>[INST]one of the biggest surprises in the exoplanet field was the discovery of gas giant planets orbiting very close to their host star .
these hot jupiter planets represent one extreme of the galaxy s population of planets , and they provide important constraints to guide our nascent ideas about the formation and evolution of planetary systems .
the probability of transit for close - in giant planets is @xmath0 @xcite , and through the analysis of transit light curves the ratio of the stellar and planetary radii can be deduced . through the significant uncertainties in the mass and radius of any particular star ,
our characterisation of exoplanets is limited by that of their host stars ( e.g. * ? ? ?
for this reason , it is important to directly measure the properties of planet hosting stars , particularly in cases where we expect the presence of planets may have influenced the properties of the star through star - planet interactions .
one of the most extreme hot jupiter exoplanets is wasp-12b , a gas giant planet orbiting only 0.023au from a late f - type host star @xcite .
wasp-12b s orbit is , therefore , only about 1.5 stellar diameters from the photosphere of the star . at such proximity ,
interactions between the star and the planet must occur .
near - uv observations of wasp-12 covering the wavelengths of many resonance lines reveal that wasp-12b is surrounded by an exosphere which appears to overfill its roche lobe @xcite
. this exospheric gas may be the consequence of tidal disruption of the planet s convective envelope as recently suggested by @xcite , but it could also be entrained material from the stellar corona .
a planet orbiting as close as wasp-12b might be expected to interact magnetically with its host star , c.f .
@xcite , @xcite , and @xcite .
a first step to search for such interactions is to detect and quantify the stellar magnetic field by spectropolarimetry , e.g. @xcite .
the presence of a magnetic field belonging to wasp-12 would provide a precious piece of information needed to establish which mechanism controls the structure and the evolution of the disk @xcite .
the solar system s giant planets have enhanced metal abundances relative to the sun @xcite and high atmospheric metal abundances have been suggested as a contributing factor in the inflated radii of planets such as wasp-12b @xcite .
intriguingly , @xcite detected a wealth of metallic atoms and ions in the exospheric gas surrounding wasp-12b .
if this gas is indeed accreting onto the host star as suggested by @xcite , this could lead to abundance anomalies in the photosphere of wasp-12 . since wasp-12 is expected to have a very shallow surface convection zone
, any accreted gas will remain close to the surface rendering any pollution of the surface composition relatively easy to detect . in this paper , we report on spectropolarimetric observations of wasp-12 which we use to probe the stellar magnetic field , fundamental parameters and abundance pattern of the star . in sect .
[ obs ] we describe our observations and data reduction . sect .
[ model ] and sect .
[ parameters ] provide a description of the adopted model atmosphere including methods and results of the stellar parameter determination and abundance analysis . in sect .
[ mag.field ] we provide the results of our stellar magnetic field search .
our results are finally discussed in sect .
[ discussion ] , while in sect .
[ conclusions ] we gather our conclusions .
we observed wasp-12 using the ( echelle spectropolarimetric device for observations of stars ) spectropolarimeter at the canada - france - hawaii telescope ( cfht ) on the 3rd and 5th of january 2010 .
the observations were performed in polarimetric " mode .
consists of a table - top cross - dispersed echelle spectrograph fed via a double optical fiber directly from a cassegrain - mounted polarisation analysis module . beside the natural intensity @xmath1 , in polarimetric mode
the instrument can acquire a stokes @xmath2 ( or @xmath3 or @xmath4 ) profile throughout the spectral range 370010400 with a resolving power of about 65000 .
a complete polarimetric observation consists of a sequence of 4 sub - exposures @xcite .
each of the four sub - exposures was 1290seconds long , with a total amount of integration time of 1.5hrs , each night .
the spectra were reduced using the libre - esprit package @xcite .
the stokes @xmath1 spectra have a signal - to - noise ratio ( snr ) per pixel of @xmath5126 and @xmath5158 in the continuum , on the first and second nights respectively ; both values calculated at 5000 . to increase the snr of the stokes @xmath1 spectrum we averaged the two available spectra , obtaining a single spectrum with a snr of @xmath5200 , normalised by fitting a low order polynomial to carefully selected continuum points .
the effective temperature ( ) was determined ( see sect . [ parameters ] ) from our data and two spectra of wasp-12 obtained at the isaac newton telescope ( int ) with the intermediate dispersion spectrograph ( ids ) .
the spectra cover the region of the h@xmath6 line with a spectral resolution of @xmath7=8000 ( see * ? ? ? * for more details ) .
we also used near - uv observations obtained with the hst cosmic origin spectrograph ( cos ) @xcite for the analysis of the spectral energy distribution .
the spectra , calibrated in flux , cover three non - contiguous wavelength ranges in the near - uv with a resolution of @xmath820000 .
these observations are described in detail in @xcite .
to compute model atmospheres of wasp-12 we employed the stellar model atmosphere code @xcite .
for all the calculations local thermodynamical equilibrium ( lte ) and plane - parallel geometry were assumed .
we used the database @xcite as a source of atomic line parameters for opacity calculations .
the recent vald compilation contains information for about @xmath9 atomic transitions , most of them coming from the latest theoretical calculations performed by r. kurucz .
convection was implemented according to the @xcite model of convection ( see * ? ? ? * for more details ) .
@xcite derived the fundamental parameters of wasp-12 from the analysis of low and mid - resolution spectra , obtaining = 6300@xmath10150k , = [email protected] , and adopting a value of 0.85 for the microturbulence velocity ( ) .
we used these values as our starting point in an iterative process to gradually improve the parameters using different spectroscopic indicators . in our analysis ,
every time any of , , or abundances changed during the iteration process , we recalculated a new model with the implementation of the last measured quantities .
similarly the derived abundances were treated iteratively : while the results of the abundance analysis depend upon the assumed model atmosphere , the atmospheric temperature - pressure structure itself depends upon the adopted abundances , so we recalculated the model atmosphere every time abundances were changed , even if the other model parameters were fixed .
this ensures the model structure is consistent with the assumed abundances .
we determined by fitting synthetic line profiles , calculated with @xcite , to the observed profiles of two hydrogen lines : h@xmath6 ( from the ids spectrograph ) and h@xmath11 ( from the spectropolarimeter ) .
we discarded the other hydrogen lines observed with because of the uncertainties in the continuum normalisation .
in the temperature range expected for wasp-12 , hydrogen lines are extremely sensitive to temperature variations and insensitive to variations , and are therefore good temperature indicators .
we found = 6250@xmath10100k , in good agreement with @xcite .
the uncertainty estimate considered both the quality of the observations and the uncertainties in the normalisation .
figure [ hydrogen ] shows the comparison between the observed h@xmath6 line profile and the synthetic profiles calculated with the adopted of 6250@xmath10100k .
the poor fit of the hydrogen line core is due to the adopted lte approximation ( see e.g. * ? ? ?
line profile observed with the ids spectrograph ( black solid line ) and synthetic profiles calculated with the final adopted of 6250k ( red solid line ) , and uncertainty ( dashed lines ) . ] another spectroscopic indicator for is given by the analysis of metallic lines , that we performed on the spectrum .
in particular , is determined by eliminating the correlation between abundance and excitation potential ( ) for the selected lines of a given ion / element .
the top panel of fig .
[ equilibria ] shows the correlation between abundance and for all measured lines of , , , , and .
figure [ equilibria ] , produced using the final adopted fundamental parameters , shows no significant correlation between abundance and for all ions , except , for which we registered a slightly positive correlation ( [email protected] ) , that would be eliminated by a higher .
what we found here for resambles what remarked by @xcite for hd 49933 and hd 32115 ( both stars have a slightly higher than wasp-12 ) : an effective temperature determination based only on the analysis of lines leads systematically to a that is substantially higher ( by about 5% ) , compared to the one obtained with other ions and in particular with other temperature indicators , such as hydrogen lines .
for this reason , we decided to use the analysis of the metallic lines only as consistency check of derived from the hydrogen lines .
in addition to the ions shown in fig .
[ equilibria ] , we included in the consistency check also , , , , , , , , , , and , obtaining the requested equilibrium for all of them .
the number of lines adopted to measure the abundance- correlation for each ion is the same as the one we used to derive the final ion abundance , and it is listed in table [ abundance ] . 0.01270 , consistent with zero .
bottom panel : abundance obtained for each measured line of the ions given in the top panel , as a function of the measured line equivalent width .
the effective temperature from metallic lines is derived eliminating the correlation shown in the top panel , while is determined eliminating the correlation shown in the bottom panel . ]
the surface gravity was derived from two independent methods based on ( _ i _ ) line profile fitting of gravity - sensitive metal lines with developed wings and ( _ ii _ ) ionisation balance for several elements .
the first method is described in @xcite and uses the fact that the wings of the lines at @xmath125167 , 5172 and 5183 are very sensitive to variations . in practice
we first derived the mg abundance from other lines without developed wings , such as @xmath125711 and 5785 , and then we fit the wings of the gravity indicator lines by tuning the value . to apply this method , very accurate values and van der waals ( log@xmath13 ) damping constants
are required for all the lines .
we adopted the set of line parameters used by @xcite and included the uncertainty in these parameters in the uncertainty in .
we obtained a value of [email protected] , in good agreement with @xcite .
our line profile fit of the lines with developed wings is shown in fig .
[ mglines ] . 0.2 .
we adopted the same combination of and van der waals damping constants as in @xcite : oscillator strengths from @xcite and damping constants from @xcite . ] the second method , the ionisation equilibrium , is often used to derive the surface gravity , but this method is extremely sensitive to the effects present for each ion / element , while mg lines with developed wings ( less sensitive to effects ) are more suitable as indicators @xcite .
for this reason we decided to keep the mg lines as our primary indicator , and checked the result with the ionisation equilibrium . adopting the value obtained from the analysis of the lines with developed wings and taking into account the abundance uncertainties , we satisfied the ionisation equilibrium for every element with two analysed ions .
our main source for the atomic parameters of spectral lines is the database with the default configuration .
lte abundance analysis was based on equivalent widths , analysed with a modified version @xcite of the width9 code @xcite . for all analysed elements / ions we used almost all unblended spectral lines with accurate atomic parameters available in the wavelength range 42409900 , except lines in spectral regions where the continuum normalisation was too uncertain . for blended lines , lines subjected to hyperfine splitting ( ) , lines situated in the wings of the hydrogen lines or for very shallow lines of specific ions we derived the line abundance by performing synthetic spectrum calculations with the code .
the constants for abundance calculations were taken from @xcite for lines and from @xcite for the line at @xmath126707 .
for the barium abundance we used the lines at @xmath125853.7 and 6496.9 for which we do not expect any relevant effect @xcite .
a line - by - line abundance list with the equivalent width measurements , adopted oscillator strengths , and their sources is given in table [ linelist ] ( see the online material for the complete version of the table ) .
.linelist of the lines used for the abundance analysis .
the first and second columns list respectively the ( in ev ) and the value for each line .
columns five and six list the equivalent width in m and the abundance for each line , while the last column gives the reference for the value .
spectral lines for which the abundance was measured with synthetic spectra , instead of equivalent widths , present an
s `` instead of the equivalent width value .
lines marked with * '' are subject to hyperfine structure , discussed in detail in the main text , while lines marked with # " are multiplets ( doublets or triplets ) and in these cases we listed only the strongest line .
the entire table can be viewed in the electronic version of the journal .
[ cols="^,^,^ , > , > , > " , ] one of the main purpose of this work is to search for chemical peculiarities that could be connected with pollution of the stellar atmosphere by material lost by the planet .
this can be done in different ways , as also shown in the extensive salient literature present ( see e.g. * ? ? ?
* and references therein ) .
wasp-12 is a promising target for signs of atmospheric pollution : wasp-12b is most likely currently losing material @xcite ; this material is believed to be forming a circumstellar disk that is accreting onto the star , polluting the stellar photosphere @xcite .
classical ways of looking for atmospheric pollution are by searching : ( _ i _ ) chemical peculiarities of single elements , such as li and be ( e.g. * ? ? ?
* ) ; ( _ ii _ ) a trend in the element abundance against the condensation temperature ( t@xmath14 ; see e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) ; ( _ iii _ ) chemical peculiarities of the abundance pattern in comparison to reference stars ( both planet hosting and non - planet hosting ) .
when searching for small effects on the stellar atmospheric abundances it is important to determine whether a certain star belongs to the thin or thick galactic disk population .
to do so we performed both a kinematic and chemical analysis of wasp-12 .
we calculated the galactic velocity vectors ( u , v , w ) corrected to the local standard of rest ( lsr ) using the formalism of @xcite , instead defining u as positive towards the galactic anti - centre . as done by @xcite , wasp-12 was then placed on the toomre diagram of the @xcite stellar sample , indicating that wasp-12 has a peculiar velocity less than 85 , strongly indicative of thin disk membership . from the wasp-12 abundances , we then compared our values of [ @xmath6/fe ] ( @xmath150.15dex ) and [ fe / h ] ( @xmath160.28dex ) , where [ @xmath6/fe ] is defined as 0.25([mg
/ fe]+[si / fe]+[ca / fe]+[ti / fe ] ) , with the @xcite sample , obtaining that wasp-12 is again consistent with the properties of the thin disk population .
in our analysis we are not able to look for chemical peculiarities of both li and be . as shown in fig .
[ fig.lithium ] , our spectra do not have the snr and the resolution necessary to perform a precise analysis of the li@xmath17/li@xmath18 ratio , but we can compare the lithium abundance obtained for wasp-12 with that of other planet hosting stars . @xcite and
@xcite published lithium abundances of stars hosting a giant planet or a brown dwarf and compared them to a set of non - planet hosting stars .
the lithium abundance we obtained for wasp-12 matches that of both set of stars , showing clearly that li is not peculiar in wasp-12 .
our spectra do not include the region around @xmath123130 covering the two lines usually adopted to measure the be abundance .
an effective way to check whether a stellar photosphere is polluted by accretion of metal - rich material is to examine the correlation between the relative abundance of various elements and their t@xmath14 . in accreting metal - rich material
the refractory elements tend to form dust grains that are blown away by the stellar wind .
thus the star accretes more volatile than refractory elements , as happens , for example , in @xmath12 bootis stars @xcite .
our wasp-12 ion abundance are shown against condensation temperature ( taken from * ? ? ?
* ) in fig .
[ fig.condtemp ] . .
] the correlation obtained between the ion abundances relative to the sun @xcite and t@xmath14 is not statistically significant : [email protected]@xmath1910@xmath20 . in the past years
several authors ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) looked for the same kind of correlation in several planet hosting stars , without having found any .
the trend we obtain for wasp-12 is also indicative of a null result .
@xcite , applying a differential analysis on the sun and solar twins , discovered that the sun shows a highly significant correlation of the abundances ( relative to the mean abundance of the solar twins ) in respect to the condensation temperature .
in addition this correlation shows a significant break at t@xmath211200k . @xcite and @xcite came to the conclusion that this correlation is likely connected to the presence of planets around the sun .
the detection of this kind of correlation requires very high precision abundances ( error bars @xmath22 0.05dex and free from systematic differences ) , attainable only with a differential analysis .
the application of this method to wasp-12 would require observations of stars that can be considered twins of wasp-12 ( similar , metallicity , age , and population ) .
the choice of the wasp-12 twins will be of crucial importance because effects such as diffusion , more prevalent for f - type stars than g - type stars , are strongly age and dependent , and consequently could easily hide or mimic pollution signatures .
our analysis does not lead to a firm conclusion about the atmospheric pollution of wasp-12 . to check whether wasp-12 has a peculiar abundance pattern we compared the abundances with those obtained by other authors on a large number of stars with a similar .
in particular we took into account the results of the abundance analysis on stars that are not known planet hosts , in the temperature range 60006500k , and with a [ fe / h]@xmath230.0dex .
we decided to use such a small temperature range to decrease the effect of possible systematics , such as effects .
in addition , since we are interested in looking for a peculiar pattern , we decided to use only the stars with an over - solar iron abundance and to subdivide the sample of comparison stars according to their iron abundance : 0.0@xmath22[fe
/ h]@xmath240.1 , 0.1@xmath22[fe / h]@xmath240.2 , and [ fe / h]@xmath230.2 . to have a better statistical view of each subsample we decided to plot in our comparisons not only the mean abundance and relative standard deviation for the comparison stars , but also their abundance range . to accomplish all these requirements
, we needed to have a large set of non - planet hosting stars , such as the one provided by @xcite .
@xcite performed a parameter determination and lte abundance analysis of more than 1000 late - type main sequence stars . for each star they derived the abundances of na ,
si , ti , fe , and ni . this sample provided us with comparison abundances for 59 stars with 0.0@xmath22[fe / h]@xmath240.1dex , 36 stars with 0.1@xmath22[fe / h]@xmath240.2dex , and 22 stars with [ fe / h]@xmath230.2dex .
the comparison between our wasp-12 abundances and the ones from the sample of @xcite is shown in fig .
[ fig.valenti ] .
[ fe / h]@xmath240.1dex ( open upside triangles ) , 0.1@xmath22[fe / h]@xmath240.2dex ( open squares ) , and [ fe / h]@xmath230.2dex ( open downside triangles ) .
the shaded areas show the abundance range , while the error bars of the comparison sample give the standard deviation from the mean abundance .
the uncertainties on the abundances of wasp-12 are as in fig .
[ fig.abn ] . ]
figure [ fig.valenti ] shows that the abundances of ti and fe are clearly comparable to the ones of the higher metallicity subsample , as expected given the fact that [ fe / h ] of wasp-12 is about 0.3 .
the na abundance of wasp-12 falls within the abundance range of the high - metallicity stars of the comparison sample , due to the large range covered by the na abundance , while ni shows a mean abundance that is just outside the abundance range .
the si abundance looks definitely more similar to the one of the set of stars with 0.1@xmath22[fe / h]@xmath240.2dex , but the large uncertainty on this abundance does not allow any firm conclusion . in summary
the abundances of ti and fe follow the pattern of the high - metallicity stars , while na , si , and ni seem to follow more the abundance pattern of the set of comparison stars with [ fe / h ] between 0.1 and 0.2dex . the information gathered from this comparison lead to the conclusion that there is the possibility that the wasp-12 abundances of na , si , and ni do not really match the abundance pattern that the wasp-12 iron abundance would suggest .
but it has to be taken into account that the comparison is not free from systematic differences in the fundamental parameters and abundance determinations , and in the set of adopted atomic line parameters . for a further search of possible abundance peculiarities in the atmosphere of wasp-12 we decided to compare our results with those of several other authors
@xcite have obtained in planet hosting and non - planet hosting stars . in this way
we should also be able to partially remove possible systematic differences in case a peculiar pattern becomes evident in the comparisons with several different authors .
the wasp-12 abundances we derived for o , ca , sc , mn , zn , y , zr , nd , and eu match very well the ones previously obtained by other authors in planet hosting and non - planet hosting stars , while abundances of al , v , and cu appear to be clearly below the values previously obtained by more than 0.2dex .
for the other compared elements ( c , n , na , mg , si , s , ti , cr , co , and ni ) we obtained just a satisfactory agreement , since we register a tendency of the wasp-12 abundances of these elements to lay always in the lower margin of the comparison samples , in particular when the abundances are put in relation to the iron abundance .
this result follows what previously obtained , strengthening the possibility of an increased fe abundance in comparison to the one of some other elements .
in addition we compared our si , ti , and ni wasp-12 abundances with the ones obtained by @xcite in a set of planet hosting and non - planet hosting stars .
we obtained a good agreement for ti , but both si and ni appear to be depleted in wasp-12 , compared to the abundances obtained by @xcite in a set of planet hosting stars , therefore we can not confirm their conclusion of a systematic enrichment of si and ni in planet hosting compared to non - planet hosting stars
. the circumstellar disk , predicted by @xcite and tentatively observed by @xcite , could be detectable in the infrared .
for this reason we decided to compare the calibrated near - uv cos fluxes of wasp-12 and the available photometry ( johnson and 2mass photometry ) with synthetic fluxes obtained with adopting the fundamental parameters and the abundances derived from the data , looking for an infrared excess in the 2mass photometry . for this comparison , shown in fig .
[ fig.flux ] , we took into account a reddening e(b - v)=0.126mag @xcite , that was calculated assuming the stellar distance obtained in sect .
[ age ] .
photometry ( full points ) and 2mass photometry ( full triangles ) . the error bars on the photometry have the same size of the symbols .
the model fluxes and the cos spectra were convolved to have approximately a spectral resolution of 800 , for display reasons . ]
figure [ fig.flux ] shows a very good agreement between the model fluxes and the observations , demonstrating also the quality of both the adopted fundamental parameters and interstellar reddening .
figure [ fig.flux ] does not show any clear infrared excess in the 2mass photometry that could be interpreted as : ( _ i _ ) there is no interstellar disk around the star or ( _ ii _ ) the interstellar disk is not visible because either the emission is not strong enough or the emission peaks at much longer wavelengths .
@xcite suggested that the disk emission should peak at @xmath52.3@xmath25 m , inside the wavelength range covered by the @xmath26 band 2mass photometry .
therefore , to look for an interstellar disk around wasp-12 it would be necessary to observe the system with a very high precision @xcite and at longer wavelengths , both accessible with the herschel satellite @xcite .
on january 3rd and 5th 2010 we observed the planet hosting star wasp-12 with the spectropolarimeter with the aim of looking for a global magnetic field , derive the stellar parameters and perform a precise abundance analysis .
the wasp-12 fundamental parameters and iron abundance we obtained are in agreement with what previously published by @xcite : = 6250@xmath10100k , = [email protected] , = [email protected] , and [ fe / h][email protected] .
is less than [email protected] , while lays within the range [email protected] .
dedicated observations to measure the amplitude of the rm effect are necessary to derive the real stellar .
the resultant metallicity of wasp-12 is @[email protected] . a detailed analysis of the hr diagram , with the use of isochrones and evolutionary tracks allowed to derive more accurate ranges for the stellar age , mass and distance : the age of wasp-12 is between 1.0gyr @xcite and 2.65gyr
, the mass is between 1.23 and 1.49 ( the last value comes from * ? ? ? * ) , and the distance to wasp-12 is between 295 and 465pc .
our measurement of the li abundance allowed us just to conclude that wasp-12 is older than 500myr .
we performed a magnetic field search adopting the lsd technique revealing that the star does not show any magnetic field signature in stokes @xmath2 .
a detailed analysis of the possible star - planet magnetic interaction would require a time - dependent analysis of particular spectral lines , such as the ca h & k lines @xcite and the uv resonance lines , but it has to be taken into account that wasp-12 shows a remarkably low stellar activity @xcite , that will be analysed in detail in a forthcoming paper .
given recent theoretical predictions @xcite and discoveries @xcite , the wasp-12 system seems to be an ideal target to detect the presence of atmospheric pollution , due to the material lost by the planet .
therefore we looked for hints of pollution by looking for a correlation between the atmospheric element abundances and the condensation temperature , and by comparing the wasp-12 abundance pattern with the one of other planet hosting and non - planet hosting stars , previously published by several other authors .
our analysis revealed just the presence of hints of atmospheric pollution , although only a differential analysis would allow to obtain firm evidences .
one must also take into account the fact that it is not clear whether wasp-12 would show the same kind of atmospheric pollution shown by the sun @xcite : the material coming from wasp-12b and falling onto the star is in a gas / plasma state and only a detailed modeling of the temperature and density structure of the accretion disk would show whether the material is condensing in dust grains .
if dust grains are forming it is likely that a differential analysis would reveal the kind of pollution signatures obtained for the sun , otherwise all the material lost by the planet would fall onto the star , making then the pollution signature dependent to the unknown hydrogen content of the planet . with the use of the available hst calibrated spectra and of visible and infrared photometry
, we looked for the presence of a circumstellar disk around wasp-12 , but without success .
probably high precision far infrared measurements , such as those possible with the hershel satellite , may reveal the presence of a circumstellar disk .
this work is based on observations obtained at the canada - france - hawaii telescope ( cfht ) , which is operated by the national research council of canada , the institut national des sciences de lunivers of the centre national de la rechereche scientifique of france , and the university of hawaii .
this work is also based on observations made with the nasa / esa hubble space telescope , obtained from mast at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc .
, under nasa contract nas 5 - 26555 .
these observations are associated with program # 11651 to which support was provided by nasa through a grant from the space telescope science institute .
this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation .
this work is supported by an stfc rolling grant ( l.f . , a.e . ) .
o.k . is a royal swedish academy of sciences research fellow supported by grants from the knut and alice wallenberg foundation and the swedish research council .
d.s . acknowledges support received from the deutsche forschungsgemeinschaft ( dfg ) research grant re1664/7 - 1 .
l.f . is deeply in debt with dr .
tanya ryabchikova for the tremendous help she gave with the values references , dr .
gregg wade for his help during the preparation of the observing proposal , and dr .
berry smalley for the information regarding the determination of the wasp-12 distance .
we thank also the cfht staff , dr .
nadine manset and the cfht director , dr .
christian veillet , for their help and speed in obtaining the observations .
_ facilities : _ , , .
aldenius , m. , tanner , j.d . , johansson , s. , lundberg , h. , & ryan , s.g .
2007 , , 461 , 767 amres , e. b. , & lpine , j. r. d. 2005 , , 130 , 679 asplund , m. , grevesse , n. , & sauval , a. j. 2005 , astronomical society of the pacific conference series , 336 , 25 bard , a. , & kock , m. 1994 , , 282 , 1014 bard , a. , kock , a. , & kock , m. 1991 , , 248 , 315 berry , h.g . , bromander , j. , curtis , l.j . , & buchta , r. 1971 , phys .
, 3 , 125 bielski , a. 1975 , jqsrt , 15 , 463 biemont e. , quinet p. , & zeippen c.j .
1993 , , 102 , 435 bizzarri , a. , et al .
1993 , , 273 , 707 blackwell , d. e. , shallis , m. j. , & selby , m. j. 1979 , , 188 , 847 blanco , f. , botho , b. , & campos , j. 1995 , phys .
, 52 , 628 bond , j. c. , et al .
2008 , , 682 , 1234 bhm - vitense , e. 1958 , zeitschrift fur astrophysik , 46 , 108 burrows , a. , hubeny , i. , budaj , j. , & hubbard , w. b. 2007 , , 661 , 502 canuto , v. m. , & mazzitelli , i. 1991 , , 370 , 295 canuto , v. m. , & mazzitelli , i. 1992 , , 389 , 724 cowley , c.r . , & bord , d.j .
1998 , in the scientific impact of the goddard high resolution spectrograph , eds .
brandt , t.b .
ake , and c.c .
petersen , asp conf .
143 , 346 cowley , c. r. , & corliss , c. h. 1983 , , 203 , 651 den hartog , e.a . ,
lawler , j.e .
, sneden , c. , & cowan , j.j .
2003 , , 148 , 543 donati , j .- f . ,
semel , m. , carter , b. d. , rees , d. e. , & collier cameron , a. 1997 , , 291 , 658 donati , j .- f .
, et al . 2007 , , 380 , 1297 ecuvillon , a. , et al . 2004 , , 426 , 619 ecuvillon , a. , israelian , g. , santos , n. c. , mayor , m. , & gilli , g. 2006 , , 449 , 809 fares , r. , et al .
2010 ( arxiv:1003.6027 ) fossati , l. , et al .
2009 , , 503 , 945 fossati , l. , et al .
2010 , , 714l , 222 fuhr , j.r . ,
martin , g.a . , & wiese , w.l .
1988 , j.phys.chem.ref.data , 17 , suppl .
4 . fuhrmann , k. , pfeiffer , m. , frank , c. , reetz , j. , & gehren , t. 1997 , , 323 , 909 gilli , g. , israelian , g. , ecuvillon , a. , santos , n. c. , & mayor , m. 2006 , , 449 , 723 girardi , l. , bressan , a. , bertelli , g. , & chiosi , c. 2000 , , 141 , 371 gonzalez , g. , carlson , m. k. , & tobin , r. w. 2010 , , 403 , 1368 gonzalez , g. , carlson , m. k. , & tobin , r. w. 2010 , , tmp , 843 ( arxiv : 1004.3313 ) green , j. c. , et al .
2010 , baas , 41 , 501 guillot , t. 2005 , annual review of earth and planetary sciences , 33 , 493 hannaford , p. , lowe , r.m . , grevesse , n. , biemont , e. , & whaling , w. 1982 , , 261 , 736 hebb , l. , et al .
2009 , , 693 , 1920 heiter , u. , et al .
2002 , , 392 , 619 husnoo , n. , pont , f. , hebrard , g. , et al .
2010 , , submitted ( arxiv : 1004.1809 ) israelian , g. , santos , n. c. , mayor , m. , & rebolo , r. 2004 , , 414 , 601 johnson , d. r. h. , & soderblom , d. r. 1987 , , 93 , 864 knutson , h. a. , howard , a. w. , & isaacson , h. 2010 , , submitted ( arxiv : 1004.2702 ) kochukhov , o. 2007 , spectrum synthesis for magnetic , chemically stratified stellar atmospheres , physics of magnetic stars , 109 , 118 kupka , f. , piskunov , n. , ryabchikova , t. a. , stempels , h. c. , & weiss , w. w. 1999 , , 138 , 119 kurucz , r.l .
1988 , trans .
iau , xxb , m. mcnally , ed .
, dordrecht : kluwer , 168 - 172 kurucz , r. 1993 , atlas9 : stellar atmosphere programs and 2 km / s grid .
kurucz cd - rom no .
13 ( cambridge : smithsonian astrophysical observatory ) kurucz , r.l . 1993 , sao , cambridge , cdrom 20 - 22 kurucz , r.l . , & peytremann , e. 1975 , sao special report , 362 lai , d. , helling , c. , & van den heuvel , e. p. j. 2010 , , submitted ( arxiv : 1005.4497 ) lambert , d.l . , mallia , e.a . , &
warner , b. 1969 , , 142 , 71 lawler , j.e .
, & dakin , j.t .
1989 , josa , b6 , 1457 lawler , j.e . , bonvallet , g. , & sneden , c. 2001 , , 556 , 452 lawler , j.e . ,
wickliffe , m.e . ,
den hartog , e.a . , & sneden , c. 2001 , , 563 , 1075 lawler , j.e . , den hartog , e.a . ,
sneden , c. , & cowan , j.j .
2006 , , 162 , 227 lawler , j.e . , sneden , c. , cowan , j.j . ,
ivans , i.i . , &
den hartog , e.a .
2009 , , 182 , 51 li , s. , miller , n. , lin , d. n. c. , & fortney , j. j. 2010 , , 463 , 1054 lincke , r. , & ziegenbein , g. 1971 , z. phyzik , 241 , 369 ljung g. , nilsson h. , asplund m. , & johansson s. 2006 , , 456 , 1181 lodders , k. 2003 , , 591 , 1220 marigo , p. , et al .
2008 , , 482 , 883 martin , g.a . ,
fuhr , j.r . , & wiese , w.l .
1988 , j.phys.chem.ref.data , 17 , suppl .
3 . martnez - galarza , j. r. , et al .
2009 , , 694 , 165 mashonkina , l. , & zhao , g. 2006 , , 456 , 313 mashonkina , l. i. , vinogradova , a. b. , ptitsyn , d. a. , khokhlova , v. s. , & chernetsova , t. a. 2007 , astronomy reports , 51 , 903 mashonkina , l. i. 2009 , phis .
scr . , t134 , 014004 melndez , j. , asplund , m. , gustafsson , b. , & yong , d. 2009 , , 704 , l66 miles , b.m . , & wiese , w.l .
1969 , wsg technical note 474 neves , v. , santos , n. c. , sousa , s. g. , correia , a. c. m. , & israelian , g. 2009 , , 497 , 563 nitz , d.e . ,
wickliffe , m.e . , & lawler , j.e .
1998 , , 117 , 313 obrian , t.r . ,
wickliffe , m.e . ,
lawler , j.e . , whaling , w. , & brault , j.w .
1991 , josa , b8 , 1185 osterman , s. , et al .
2010 , baas , 41 , 502 pickering , j.c . ,
thorne , a.p . , & perez , r. 2001 , , 132 , 403 pilbratt , g. l. , et al .
2010 , , accepted ( arxiv : 1005.5331 ) piskunov , n. e. , kupka , f. , ryabchikova , t. a. , weiss , w. w. , & jeffery , c. s. 1995 , , 112 , 525 raassen , a.j.j .
, & uylings , p.h.m .
1998 , , 340 , 300 , ( ftp://ftp.wins.uva.nl/pub/orth ) ralchenko , yu . ,
kramida , a.e . ,
reader , j. , & nist asd team .
2008 , nist atomic spectra database ( version 3.1.5 ) , available : http://physics.nist.gov/asd3 , nist , gaithersburg , md robinson , s. e. , laughlin , g. , bodenheimer , p. , & fischer , d. 2006 , , 643 , 484 ryabchikova , t. a. , piskunov , n. e. , stempels , h. c. , kupka , f. , & weiss , w. w. 1999 , phis .
, t83 , 162 ryabchikova , t. a. , fossati , l. , & shulyak , d. 2009 , , 506 , 203 sadakane , k. , et al .
2002 , , 54 , 911 santos , n. c. , et al .
2006 , , 458 , 997 seager , s. , whitney , b. a. , & sasselov , d. d. 2000 , , 540 , 504 seaton , m.j . , mihalas , d. , & pradhan , a.k .
1994 , , 266 , 805 sestito , p. , & randich , s. 2005 , , 442 , 615 shkolnik , e. , walker , g. a. h. , & bohlender , d. a. 2003 , , 597 , 1092 shkolnik , e. , walker , g. a. h. , bohlender , d. a. , gu , p .-
g . , & krster , m. 2005 , , 622 , 1075 shkolnik , e. , bohlender , d. a. , walker , g. a. h. , & collier cameron , a. 2008 , , 676 , 628 shulyak , d. , tsymbal , v. , ryabchikova , t. , sttz ch . , & weiss , w. w. 2004 , , 428 , 993 smith , g. , & oneil , j.a .
1975 , , 38 , 1 smith , g. , & raggett , d.st.j . 1981 , j. phys .
b , 14 , 4015 smith , v. v. , lambert , d. l. , & nissen , p. e. 1998 , , 506 , 405 smith , g. 1988 , j. phys .
phys . , 21 , 2827 soubiran , c. , & girard , p. 2005
, , 438 , 139 southworth , j. 2009 , , 394 , 272 sozzetti , a. , et al .
2006 , , 131 , 2274 takeda , y. , kato , k .-
i . , watanabe , y. , & sadakane , k. 1996 , , 48 , 511 takeda , y. , et al .
2002 , , 53 , 1211 tsymbal , v. v. 1996 , in asp conf .
108 , model atmospheres and spectral synthesis , ed .
s. j. , adelman , f. , kupka , & w. w. , weiss , 198 valenti , j. a. , & fisher , d. a. 2005 , , 159 , 141 wade , g. a. , donati , j .- f .
, landstreet , j. d. , & shorlin , s. l. s. 2000 , , 313 , 823 warner , b. 1968 , , 139 , 115 wickliffe , m.e . , & lawler , j.e .
1997 , , 110 , 163 wiese , w.l . ,
fuhr , j.r . , & deters , t.m .
1996 , aip press , a critical data compilation , j. phys .
chem . ref .
data , monograph no .
7 , melville , ny , pp . 532 wiese , w.l . ,
smith , m.w .
, & miles , b.m .
1969 , nsrds - nbs , 22 wiese , w.l . , smith , m.w . , & miles , b.m .
1969 , nsrds - wsg , 22 zhao , g. , & gehren , t. 2000 , , 362 , 1077[/INST] the knowledge of accurate stellar parameters is paramount in several fields of stellar astrophysics , particularly in the study of extrasolar planets , where often the star is the only visible component and therefore used to infer the planet s fundamental parameters .
another important aspect of the analysis of planetary systems is the stellar activity and the possible star - planet interaction . here
we present a self - consistent abundance analysis of the planet hosting star wasp-12 and a high - precision search for a structured stellar magnetic field on the basis of spectropolarimetric observations obtained with the spectropolarimeter .
our results show that the star does not have a structured magnetic field , and that the obtained fundamental parameters are in good agreement with what was previously published .
in addition we derive improved constraints on the stellar age ( 1.02.65gyr ) , mass ( 1.231.49 ) , and distance ( 295465pc ) .
wasp-12 is an ideal object to look for pollution signatures in the stellar atmosphere .
we analyse the wasp-12 abundances as a function of the condensation temperature and compare them with those published by several other authors on planet hosting and non - planet hosting stars .
we find hints of atmospheric pollution in wasp-12 s photosphere , but are unable to reach firm conclusions with our present data .
we conclude that a differential analysis based on wasp-12 twins will probably clarify if an atmospheric pollution is present , the nature of this pollution and its implications in the planet formation and evolution .
we attempt also the direct detection of the circumstellar disk through infrared excess , but without success . </s> |
Subsets and Splits