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http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1BMAX_2013_v50n3_811	GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA Title & Authors GLOBAL SOLUTIONS OF THE EXPONENTIAL WAVE EQUATION WITH SMALL INITIAL DATA Huh, Hyungjin; Abstract We study the initial value problem of the exponential wave equation in $\small{\math{R}^{n+1}}$ for small initial data. We shows, in the case of \$n Keywords quasilinear wave;weakly linearly degenerate;double null form; Language English Cited by 1. Global existence of smooth solutions to exponential wave maps in FLRW spacetimes, Pacific Journal of Mathematics, 2017, 289, 2, 489 References 1. S. Alinhac, Hyperbolic Partial Differential Equations, Universitext, Springer, Dordrecht, 2009. 2. Y.-J. Chiang and Y.-H. Yang, Exponential wave maps, J. Geom. Phys. 57, (2007) no. 12, 2521-2532. 3. J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), no. 5, 385-524. 4. J. Eells and L. Lemaire, Some properties of exponentially harmonic maps, Partial differential equations, Part 1, 2 (Warsaw, 1990), 129-136, Banach Center Publ., 27, Part 1, 2, Polish Acad. Sci., Warsaw, 1992. 5. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, 1977. 6. L. Hormander, Lectures on Nonlinear Hyperbolic Differential Equations, Springer Verlag, 1997. 7. F. John, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math. 27 (1974), 377-405. 8. A. D. Kanfon, A. Fuzfa, and D. Lambert, Some examples of exponentially harmonic maps, J. Phys. A 35 (2002), no. 35, 7629-7639. 9. S. Klainerman, The null condition and global existence to nonlinear wave equations, Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 293-326, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986. 10. D. Kong, Cauchy Problem for Quasilinear Hyperbolic Systems, MSJ Memoirs, 6. Mathematical Society of Japan, Tokyo, 2000. 11. T.-T. Li, Y. Zhou, and D. Kong, Global classical solutions for general quasilinear hyperbolic systems with decay initial data, Nonlinear Anal. 28 (1997), no. 8, 1299-1332. 12. H. Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data, Comm. Pure Appl. Math. 43 (1990), no. 4, 445-472. 13. H. Lindblad, A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1095-1102. 14. M. C. Hong, Liouville theorems for exponentially harmonic functions on Riemannian manifolds, Manuscripta Math. 77 (1992), no. 1, 41-46. 15. J. M. Overduin and P. S. Wesson, Kaluza-Klein gravity, Phys. Rep. 283 (1997), no. 5-6, 303-378. 16. C. D. Sogge, Lectures on Nonlinear Wave Equations, International Press Incorporated, Boston, 1995.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 1, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7350216507911682, "perplexity": 1107.7226533844425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746171.27/warc/CC-MAIN-20181119233342-20181120015342-00305.warc.gz"}
https://sierrahash.com/don-t-tell-me-what-to-do-meme-2/	# Don T Tell Me What To Do Meme Hola If you are looking for don t tell me what to do meme ? Then, this is the place where you can find some sources that provide detailed information. ## don t tell me what to do meme I hope the above sources help you with the information related to don t tell me what to do meme . If not, reach through the comment section. what #### What Is The Lcm Of 3 And 8 Hello If you are looking for ? Then, this is the place where you can find some sources that provide detailed information. I hope the above sources help you with what #### What Is The Physics Primer? Hello If you are looking for ? Then, this is the place where you can find some sources that provide detailed information. I hope the above sources help you with what #### What Is The Lcm Of 3 And 8 Hi If you are looking for ? Then, this is the place where you can find some sources that provide detailed information. I hope the above sources help you with	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9387785196304321, "perplexity": 295.7101451855789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00777.warc.gz"}
http://www.ams.org/joursearch/servlet/PubSearch?f1=msc&pubname=all&v1=14L05&startRec=1	# American Mathematical Society My Account · My Cart · Customer Services · FAQ Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS You are here: Home > Publications AMS eContent Search Results Matches for: msc=(14L05) AND publication=(all) Sort order: Date Format: Standard display Results: 1 to 30 of 66 found Go to page: 1 2 3 [1] S. Vostokov and V. Volkov. Explicit form of the Hilbert symbol for polynomial formal groups. St. Petersburg Math. J. 26 (2015) 785-796. Abstract, references, and article information View Article: PDF [2] Nathaniel Stapleton. Subgroups of $p$-divisible groups and centralizers in symmetric groups. Trans. Amer. Math. Soc. 367 (2015) 3733-3757. Abstract, references, and article information View Article: PDF [3] Jeffrey D. Achter. Irreducibility of Newton strata in ${GU}(1,n-1)$ Shimura varieties. Proc. Amer. Math. Soc. Ser. B 1 (2014) 79-88. Abstract, references, and article information View Article: PDF [4] Ching-Li Chai, Brian Conrad and Frans Oort. Complex Multiplication and Lifting Problems. Math. Surveys Monogr. 195 (2013) MR 3137398. Book volume table of contents [5] Haruzo Hida. Local indecomposability of Tate modules of non-CM abelian varieties with real multiplication. J. Amer. Math. Soc. 26 (2013) 853-877. Abstract, references, and article information View Article: PDF [6] Oleg Demchenko and Alexander Gurevich. Reciprocity laws through formal groups. Proc. Amer. Math. Soc. 141 (2013) 1591-1596. Abstract, references, and article information View Article: PDF [7] Peter Scholze. The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups. J. Amer. Math. Soc. 26 (2013) 227-259. Abstract, references, and article information View Article: PDF [8] Eike Lau. Smoothness of the truncated display functor. J. Amer. Math. Soc. 26 (2013) 129-165. Abstract, references, and article information View Article: PDF [9] N. P. Strickland. Multicurves and equivariant cohomology. Memoirs of the AMS 213 (2011) MR 2856125. Book volume table of contents [10] Takeshi Torii. HKR characters, $p$-divisible groups and the generalized Chern character. Trans. Amer. Math. Soc. 362 (2010) 6159-6181. MR 2661512. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Jeffrey D. Achter and Peter Norman. Local monodromy of $p$-divisible groups. Trans. Amer. Math. Soc. 362 (2010) 985-1007. MR 2551513. Abstract, references, and article information View Article: PDF This article is available free of charge [12] M. V. Bondarko. Classification of finite commutative group schemes over complete discrete valuation rings; the tangent space and semistable reduction of Abelian varieties. St. Petersburg Math. J. 18 (2007) 737-755. MR 2301041. Abstract, references, and article information View Article: PDF This article is available free of charge [13] M. V. Bondarko. Isogeny classes of formal groups over complete discrete valuation fields with arbitrary residue fields. St. Petersburg Math. J. 17 (2006) 975-988. MR 2202046. Abstract, references, and article information View Article: PDF This article is available free of charge [14] Tyler Lawson. Realizability of the Adams-Novikov spectral sequence for formal $A$-modules. Proc. Amer. Math. Soc. 135 (2007) 883-890. MR 2262886. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Alexandru Buium. Arithmetic Differential Equations. Math. Surveys Monogr. 118 (2005) MR MR2166202. Book volume table of contents [16] Alexandru Buium. Flat correspondences. Math. Surveys Monogr. 118 (2005) 185-225. Book volume table of contents View Article: PDF [17] Alexandru Buium. Global theory. Math. Surveys Monogr. 118 (2005) 71-105. Book volume table of contents View Article: PDF [18] Alexandru Buium. Preliminaries from algebraic geometry. Math. Surveys Monogr. 118 (2005) 3-30. Book volume table of contents View Article: PDF [19] Alexandru Buium. Outline of $\delta$--geometry. Math. Surveys Monogr. 118 (2005) 31-67. Book volume table of contents View Article: PDF [20] Alexandru Buium. Birational theory. Math. Surveys Monogr. 118 (2005) 141-158. Book volume table of contents View Article: PDF [21] Alexandru Buium. Local theory. Math. Surveys Monogr. 118 (2005) 107-140. Book volume table of contents View Article: PDF [22] Alexandru Buium. Spherical correspondences. Math. Surveys Monogr. 118 (2005) 161-183. Book volume table of contents View Article: PDF [23] Alexandru Buium. Hyperbolic correspondences. Math. Surveys Monogr. 118 (2005) 227-297. Book volume table of contents View Article: PDF [24] Robert G. Underwood and Lindsay N. Childs. Duality for Hopf orders. Trans. Amer. Math. Soc. 358 (2006) 1117-1163. MR 2187648. Abstract, references, and article information View Article: PDF This article is available free of charge [25] Frans Oort. Foliations in moduli spaces of abelian varieties. J. Amer. Math. Soc. 17 (2004) 267-296. MR 2051612. Abstract, references, and article information View Article: PDF This article is available free of charge [26] Hirofumi Nakai and Douglas C. Ravenel. The first cohomology group of the generalized Morava stabilizer algebra. Proc. Amer. Math. Soc. 131 (2003) 1629-1639. MR 1950296. Abstract, references, and article information View Article: PDF This article is available free of charge [27] Lindsay N. Childs. Principal homogeneous spaces and formal groups. Math. Surveys Monogr. 80 (2000) 191-204. Book volume table of contents View Article: PDF [28] Lindsay N. Childs. Hopf algebras of rank $p^2$. Math. Surveys Monogr. 80 (2000) 149-159. Book volume table of contents View Article: PDF [29] Lindsay N. Childs. Formal groups. Math. Surveys Monogr. 80 (2000) 171-190. Book volume table of contents View Article: PDF [30] Lindsay N. Childs. Cyclic extensions of degree $p$. Math. Surveys Monogr. 80 (2000) 113-128. Book volume table of contents View Article: PDF Results: 1 to 30 of 66 found Go to page: 1 2 3	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9450991153717041, "perplexity": 4853.8511415992625}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396949.33/warc/CC-MAIN-20160624154956-00194-ip-10-164-35-72.ec2.internal.warc.gz"}
http://arxiv.org/abs/1207.4201	cond-mat.str-el (what is this?) # Title: Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function Abstract: We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the non-existence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter. Comments: Published version with supplemental material rebutting the recent criticism that our theorem fails if the ground-state degeneracy is lifted Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th) Journal reference: Phys. Rev. Lett. vol. 110, 090403 (2013) DOI: 10.1103/PhysRevLett.110.090403 Cite as: arXiv:1207.4201 [cond-mat.str-el] (or arXiv:1207.4201v3 [cond-mat.str-el] for this version) ## Submission history From: Philip Phillips [view email] [v1] Tue, 17 Jul 2012 20:00:56 GMT (9kb) [v2] Fri, 28 Sep 2012 14:24:43 GMT (11kb) [v3] Tue, 5 Mar 2013 16:48:01 GMT (103kb)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7518194913864136, "perplexity": 2076.2177290254235}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396887.54/warc/CC-MAIN-20160624154956-00070-ip-10-164-35-72.ec2.internal.warc.gz"}
http://www.gradesaver.com/textbooks/science/physics/physics-principles-with-applications-7th-edition/chapter-3-kinematics-in-two-dimensions-vectors-problems-page-71/51	## Physics: Principles with Applications (7th Edition) 65km/h, 58$^o$ west of north. 65km/h, 32$^o$ south of east. Call east the positive x direction and north the positive y direction. Let 1 denote Car 1, 2 denote Car 2, and s the street. The pair “12”, for example, represents Car 1’s motion relative to Car 2, i.e., as seen by Car 2. $$\vec{v_{1s}} = \vec{v_{12}} + \vec{v_{2s}}$$ $$(0, 35 km/h) = \vec{v_{12}} + (55 km/h, 0)$$ Evidently, $\vec{v_{12}} = (-55 km/h, 35 km/h)$. As expected, this is north and west (58$^o$). $\vec{v_{12}} = \sqrt {(-55 km/h)^2 + (35 km/h)^2} = 65.2km/h \approx65km/h.$ The velocity of car 2 relative to car 1 is exactly the opposite of this. $\vec{v_{21}} = (55 km/h, -35 km/h)$ $\vec{v_{21}} = \sqrt {(55 km/h)^2 + (-35 km/h)^2} = 65.2km/h \approx65km/h$ $and$ $32^o south of east$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7578852772712708, "perplexity": 1600.0878136188537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122996.52/warc/CC-MAIN-20170423031202-00255-ip-10-145-167-34.ec2.internal.warc.gz"}
http://wikien3.appspot.com/wiki/Probability_amplitude	# Probability amplitude A wave function for a single electron on 5d atomic orbital of a hydrogen atom. The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm−3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function. In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density. Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see References), and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today. ## Overview ### Physical Neglecting some technical complexities, the problem of quantum measurement is the behaviour of a quantum state, for which the value of the observable Q to be measured is uncertain. Such a state is thought to be a coherent superposition of the observable's eigenstates, states on which the value of the observable is uniquely defined, for different possible values of the observable. When a measurement of Q is made, the system (under the Copenhagen interpretation) jumps to one of the eigenstates, returning the eigenvalue to which the state belongs. The superposition of states can give them unequal "weights". Intuitively it is clear that eigenstates with heavier "weights" are more "likely" to be produced. Indeed, which of the above eigenstates the system jumps to is given by a probabilistic law: the probability of the system jumping to the state is proportional to the absolute value of the corresponding numerical factor squared. These numerical factors are called probability amplitudes, and this relationship used to calculate probabilities from given pure quantum states (such as wave functions) is called the Born rule. Different observables may define incompatible decompositions of states.[clarification needed] Observables that do not commute define probability amplitudes on different sets. ### Mathematical In a formal setup, any system in quantum mechanics is described by a state, which is a vector \|Ψ⟩, residing in an abstract complex vector space, called a Hilbert space. It may be either infinite- or finite-dimensional. A usual presentation of that Hilbert space is a special function space, called L2(X), on certain set X, that is either some configuration space or a discrete set. For a measurable function ${\displaystyle \psi }$, the condition ${\displaystyle \psi \in L^{2}(X)}$ specifies that a finitely bounded integral must apply: ${\displaystyle \int \limits _{X}\|\psi (x)\|^{2}\,\mathrm {d} \mu (x)<\infty ;}$ this integral defines the square of the norm of ψ. If that norm is equal to 1, then ${\displaystyle \int \limits _{X}\|\psi (x)\|^{2}\,\mathrm {d} \mu (x)=1.}$ It actually means that any element of L2(X) of the norm 1 defines a probability measure on X and a non-negative real expression \|ψ(x)\|2 defines its Radon–Nikodym derivative with respect to the standard measure μ. If the standard measure μ on X is non-atomic, such as the Lebesgue measure on the real line, or on three-dimensional space, or similar measures on manifolds, then a real-valued function \|ψ(x)\|2 is called a probability density; see details below. If the standard measure on X consists of atoms only (we shall call such sets X discrete), and specifies the measure of any xX equal to 1,[1] then an integral over X is simply a sum[2] and \|ψ(x)\|2 defines the value of the probability measure on the set {x}, in other words, the probability that the quantum system is in the state x. How amplitudes and the vector are related can be understood with the standard basis of L2(X), elements of which will be denoted by \|x or x\| (see bra–ket notation for the angle bracket notation). In this basis ${\displaystyle \psi (x)=\langle x\|\Psi \rangle }$ specifies the coordinate presentation of an abstract vector \|Ψ⟩. Mathematically, many L2 presentations of the system's Hilbert space can exist. We shall consider not an arbitrary one, but a convenient one for the observable Q in question. A convenient configuration space X is such that each point x produces some unique value of Q. For discrete X it means that all elements of the standard basis are eigenvectors of Q. In other words, Q shall be diagonal in that basis. Then ${\displaystyle \psi (x)}$ is the "probability amplitude" for the eigenstate x\|. If it corresponds to a non-degenerate eigenvalue of Q, then ${\displaystyle \|\psi (x)\|^{2}}$ gives the probability of the corresponding value of Q for the initial state \|Ψ⟩. For non-discrete X there may not be such states as x\| in L2(X), but the decomposition is in some sense possible; see spectral theory and Spectral theorem for accurate explanation. ## Wave functions and probabilities If the configuration space X is continuous (something like the real line or Euclidean space, see above), then there are no valid quantum states corresponding to particular xX, and the probability that the system is "in the state x" will always be zero. An archetypical example of this is the L2(R) space constructed with 1-dimensional Lebesgue measure; it is used to study a motion in one dimension. This presentation of the infinite-dimensional Hilbert space corresponds to the spectral decomposition of the coordinate operator: x\| Q \| Ψ⟩ = xx \| Ψ⟩, xR in this example. Although there are no such vectors as x \|, strictly speaking, the expression x \| Ψ⟩ can be made meaningful, for instance, with spectral theory. Generally, it is the case when the motion of a particle is described in the position space, where the corresponding probability amplitude function ψ is the wave function. If the function ψL2(X), ‖ψ‖ = 1 represents the quantum state vector \|Ψ⟩, then the real expression \|ψ(x)\|2, that depends on x, forms a probability density function of the given state. The difference of a density function from simply a numerical probability means that one should integrate this modulus-squared function over some (small) domains in X to obtain probability values – as was stated above, the system can't be in some state x with a positive probability. It gives to both amplitude and density function a physical dimension, unlike a dimensionless probability. For example, for a 3-dimensional wave function, the amplitude has the dimension [L−3/2], where L is length. Note that for both continuous and infinite discrete cases not every measurable, or even smooth function (i.e. a possible wave function) defines an element of L2(X); see #Normalisation below. ## Discrete amplitudes When the set X is discrete (see above), vectors \|Ψ⟩ represented with the Hilbert space L2(X) are just column vectors composed of "amplitudes" and indexed by X. These are sometimes referred to as wave functions of a discrete variable xX. Discrete dynamical variables are used in such problems as a particle in an idealized reflective box and quantum harmonic oscillator. Components of the vector will be denoted by ψ(x) for uniformity with the previous case; there may be either finite of infinite number of components depending on the Hilbert space. In this case, if the vector \|Ψ⟩ has the norm 1, then \|ψ(x)\|2 is just the probability that the quantum system resides in the state x. It defines a discrete probability distribution on X. \|ψ(x)\| = 1 if and only if \|x is the same quantum state as \|Ψ⟩. ψ(x) = 0 if and only if \|x and \|Ψ⟩ are orthogonal (see inner product space). Otherwise the modulus of ψ(x) is between 0 and 1. A discrete probability amplitude may be considered as a fundamental frequency[citation needed] in the Probability Frequency domain (spherical harmonics) for the purposes of simplifying M-theory transformation calculations. ## A basic example Take the simplest meaningful example of the discrete case: a quantum system that can be in two possible states: for example, the polarization of a photon. When the polarization is measured, it could be the horizontal state \| H ⟩, or the vertical state \| V ⟩. Until its polarization is measured the photon can be in a superposition of both these states, so its state \|ψ could be written as: ${\displaystyle \|\psi \rangle =\alpha \|H\rangle +\beta \|V\rangle ,\,}$ The probability amplitudes of \|ψ for the states \| H ⟩ and \| V ⟩ are α and β respectively. When the photon's polarization is measured, the resulting state is either horizontal or vertical. But in a random experiment, the probability of being horizontally polarized is α2, and the probability of being vertically polarized is β2. Therefore, a photon in a state ${\displaystyle \|\psi \rangle ={\sqrt {1 \over 3}}\|H\rangle -i{\sqrt {2 \over 3}}\|V\rangle }$ would have a probability of 1/3 to come out horizontally polarized, and a probability of 2/3 to come out vertically polarized when an ensemble of measurements are made. The order of such results, is, however, completely random. ## Normalization In the example above, the measurement must give either \| H ⟩ or \| V ⟩, so the total probability of measuring \| H ⟩ or \| V ⟩ must be 1. This leads to a constraint that α2 + β2 = 1; more generally the sum of the squared moduli of the probability amplitudes of all the possible states is equal to one. If to understand "all the possible states" as an orthonormal basis, that makes sense in the discrete case, then this condition is the same as the norm-1 condition explained above. One can always divide any non-zero element of a Hilbert space by its norm and obtain a normalized state vector. Not every wave function belongs to the Hilbert space L2(X), though. Wave functions that fulfill this constraint are called normalizable. The Schrödinger wave equation, describing states of quantum particles, has solutions that describe a system and determine precisely how the state changes with time. Suppose a wavefunction ψ0(x, t) is a solution of the wave equation, giving a description of the particle (position x, for time t). If the wavefunction is square integrable, i.e. ${\displaystyle \int _{\mathbf {R} ^{n}}\|\psi _{0}(\mathbf {x} ,t_{0})\|^{2}\,\mathrm {d\mathbf {x} } =a^{2}<\infty }$ for some t0, then ψ = ψ0/a is called the normalized wavefunction. Under the standard Copenhagen interpretation, the normalized wavefunction gives probability amplitudes for the position of the particle. Hence, at a given time t0, ρ(x) = \|ψ(x, t0)\|2 is the probability density function of the particle's position. Thus the probability that the particle is in the volume V at t0 is ${\displaystyle \mathbf {P} (V)=\int _{V}\rho (\mathbf {x} )\,\mathrm {d\mathbf {x} } =\int _{V}\|\psi (\mathbf {x} ,t_{0})\|^{2}\,\mathrm {d\mathbf {x} } .}$ Note that if any solution ψ0 to the wave equation is normalisable at some time t0, then the ψ defined above is always normalised, so that ${\displaystyle \rho _{t}(\mathbf {x} )=\left\|\psi (\mathbf {x} ,t)\right\|^{2}=\left\|{\frac {\psi _{0}(\mathbf {x} ,t)}{a}}\right\|^{2}}$ is always a probability density function for all t. This is key to understanding the importance of this interpretation, because for a given the particle's constant mass, initial ψ(x, 0) and the potential, the Schrödinger equation fully determines subsequent wavefunction, and the above then gives probabilities of locations of the particle at all subsequent times. ## The laws of calculating probabilities of events A. Provided a system evolves naturally (which under the Copenhagen interpretation means that the system is not subjected to measurement), the following laws apply: 1. The probability (or the density of probability in position/momentum space) of an event to occur is the square of the absolute value of the probability amplitude for the event: ${\displaystyle P=\|\phi \|^{2}}$. 2. If there are several mutually exclusive, indistinguishable alternatives in which an event might occur (or, in realistic interpretations of wavefunction, several wavefunctions exist for a space-time event), the probability amplitudes of all these possibilities add to give the probability amplitude for that event: ${\displaystyle \phi =\sum _{i}\phi _{i};P=\|\phi \|^{2}=\left\|\sum _{i}\phi _{i}\right\|^{2}}$. 3. If, for any alternative, there is a succession of sub-events, then the probability amplitude for that alternative is the product of the probability amplitude for each sub-event: ${\displaystyle \phi _{APB}=\phi _{AP}\phi _{PB}}$. 4. Non-entangled states of a composite quantum system have amplitudes equal to the product of the amplitudes of the states of constituent systems: ${\displaystyle \phi _{\rm {system}}(\alpha ,\beta ,\gamma ,\delta ,\ldots )=\phi _{1}(\alpha )\phi _{2}(\beta )\phi _{3}(\gamma )\phi _{4}(\delta )\ldots }$. See the #Composite systems section for more information. Law 2 is analogous to the addition law of probability, only the probability being substituted by the probability amplitude. Similarly, Law 4 is analogous to the multiplication law of probability for independent events; note that it fails for entangled states. B. When an experiment is performed to decide between the several alternatives, the same laws hold true for the corresponding probabilities: ${\displaystyle P=\sum _{i}\|\phi _{i}\|^{2}}$. Provided one knows the probability amplitudes for events associated with an experiment, the above laws provide a complete description of quantum systems in terms of probabilities. The above laws give way to the path integral formulation of quantum mechanics, in the formalism developed by the celebrated theoretical physicist Richard Feynman. This approach to quantum mechanics forms the stepping-stone to the path integral approach to quantum field theory. ## In the context of the double-slit experiment Probability amplitudes have special significance because they act in quantum mechanics as the equivalent of conventional probabilities, with many analogous laws, as described above. For example, in the classic double-slit experiment, electrons are fired randomly at two slits, and the probability distribution of detecting electrons at all parts on a large screen placed behind the slits, is questioned. An intuitive answer is that P(through either slit) = P(through first slit) + P(through second slit), where P(event) is the probability of that event. This is obvious if one assumes that an electron passes through either slit. When nature does not have a way to distinguish which slit the electron has gone through (a much more stringent condition than simply "it is not observed"), the observed probability distribution on the screen reflects the interference pattern that is common with light waves. If one assumes the above law to be true, then this pattern cannot be explained. The particles cannot be said to go through either slit and the simple explanation does not work. The correct explanation is, however, by the association of probability amplitudes to each event. This is an example of the case A as described in the previous article. The complex amplitudes which represent the electron passing each slit (ψfirst and ψsecond) follow the law of precisely the form expected: ψtotal = ψfirst + ψsecond. This is the principle of quantum superposition. The probability, which is the modulus squared of the probability amplitude, then, follows the interference pattern under the requirement that amplitudes are complex: ${\displaystyle P=\|\psi _{\rm {first}}+\psi _{\rm {second}}\|^{2}=\|\psi _{\rm {first}}\|^{2}+\|\psi _{\rm {second}}\|^{2}+2\|\psi _{\rm {first}}\|\|\psi _{\rm {second}}\|\cos(\varphi _{1}-\varphi _{2}).}$ Here, ${\displaystyle \varphi _{1}}$ and${\displaystyle \varphi _{2}}$ are the arguments of ψfirst and ψsecond respectively. A purely real formulation has too few dimensions to describe the system's state when superposition is taken into account. That is, without the arguments of the amplitudes, we cannot describe the phase-dependent interference. The crucial term ${\displaystyle 2\|\psi _{\rm {first}}\|\|\psi _{\rm {second}}\|\cos(\varphi _{1}-\varphi _{2})}$ is called the "interference term", and this would be missing if we had added the probabilities. However, one may choose to devise an experiment in which the experimenter observes which slit each electron goes through. Then case B of the above article applies, and the interference pattern is not observed on the screen. One may go further in devising an experiment in which the experimenter gets rid of this "which-path information" by a "quantum eraser". Then, according to the Copenhagen interpretation, the case A applies again and the interference pattern is restored.[3] ## Conservation of probabilities and the continuity equation Intuitively, since a normalised wave function stays normalised while evolving according to the wave equation, there will be a relationship between the change in the probability density of the particle's position and the change in the amplitude at these positions. Define the probability current (or flux) j as ${\displaystyle \mathbf {j} ={\hbar \over m}{1 \over {2i}}\left(\psi ^{}\nabla \psi -\psi \nabla \psi ^{}\right)={\hbar \over m}\operatorname {Im} \left(\psi ^{*}\nabla \psi \right),}$ measured in units of (probability)/(area × time). Then the current satisfies the equation ${\displaystyle \nabla \cdot \mathbf {j} +{\partial \over \partial t}\|\psi \|^{2}=0.}$ The probability density is ${\displaystyle \rho =\|\psi \|^{2}}$, this equation is exactly the continuity equation, appearing in many situations in physics where we need to describe the local conservation of quantities. The best example is in classical electrodynamics, where j corresponds to current density corresponding to electric charge, and the density is the charge-density. The corresponding continuity equation describes the local conservation of charges.[clarification needed] ## Composite systems For two quantum systems with spaces L2(X1) and L2(X2) and given states 1 and 2 respectively, their combined state 12 can be expressed as ψ1(x1) ψ2(x2) a function on X1×X2, that gives the product of respective probability measures. In other words, amplitudes of a non-entangled composite state are products of original amplitudes, and respective observables on the systems 1 and 2 behave on these states as independent random variables. This strengthens the probabilistic interpretation explicated above. ## Amplitudes in operators The concept of amplitudes described above is relevant to quantum state vectors. It is also used in the context of unitary operators that are important in the scattering theory, notably in the form of S-matrices. Whereas moduli of vector components squared, for a given vector, give a fixed probability distribution, moduli of matrix elements squared are interpreted as transition probabilities just as in a random process. Like a finite-dimensional unit vector specifies a finite probability distribution, a finite-dimensional unitary matrix specifies transition probabilities between a finite number of states. Note that columns of a unitary matrix, as vectors, have the norm 1. The "transitional" interpretation may be applied to L2s on non-discrete spaces as well.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 24, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9855579733848572, "perplexity": 407.4474812789907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540528490.48/warc/CC-MAIN-20191210180555-20191210204555-00472.warc.gz"}
http://www.ams.org/joursearch/servlet/DoSearch?f1=msc&v1=13C05&jrnl=one&onejrnl=tran	# American Mathematical Society My Account · My Cart · Customer Services · FAQ Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS You are here: Home > Publications AMS eContent Search Results Matches for: msc=(13C05) AND publication=(tran) Sort order: Date Format: Standard display Results: 1 to 23 of 23 found Go to page: 1 [1] Jan Šťovíček and David Pospíšil. On compactly generated torsion pairs and the classification of co-$t$-structures for commutative noetherian rings. Trans. Amer. Math. Soc. 368 (2016) 6325-6361. Abstract, references, and article information View Article: PDF [2] Steven V Sam and Andrew Snowden. GL-equivariant modules over polynomial rings in infinitely many variables. Trans. Amer. Math. Soc. 368 (2016) 1097-1158. Abstract, references, and article information View Article: PDF [3] Lidia Angeleri Hügel, David Pospíšil, Jan Šťovíček and Jan Trlifaj. Tilting, cotilting, and spectra of commutative noetherian rings. Trans. Amer. Math. Soc. 366 (2014) 3487-3517. Abstract, references, and article information View Article: PDF [4] Peter Vámos and Sylvia Wiegand. Block diagonalization and $2$-unit sums of matrices over Prüfer domains. Trans. Amer. Math. Soc. 363 (2011) 4997-5020. MR 2806699. Abstract, references, and article information View Article: PDF [5] Mark Hovey. Erratum to Classifying subcategories of modules''. Trans. Amer. Math. Soc. 360 (2008) 2809-2809. MR 2373334. Abstract, references, and article information View Article: PDF This article is available free of charge [6] Lidia Angeleri Hügel, Silvana Bazzoni and Dolors Herbera. A solution to the Baer splitting problem. Trans. Amer. Math. Soc. 360 (2008) 2409-2421. MR 2373319. Abstract, references, and article information View Article: PDF This article is available free of charge [7] Wolfgang Hassler, Ryan Karr, Lee Klingler and Roger Wiegand. Indecomposable modules of large rank over Cohen-Macaulay local rings. Trans. Amer. Math. Soc. 360 (2008) 1391-1406. MR 2357700. Abstract, references, and article information View Article: PDF This article is available free of charge [8] Hung Le Pham. The kernels of radical homomorphisms and intersections of prime ideals. Trans. Amer. Math. Soc. 360 (2008) 1057-1088. MR 2346483. Abstract, references, and article information View Article: PDF This article is available free of charge [9] Robert G. Underwood and Lindsay N. Childs. Duality for Hopf orders. Trans. Amer. Math. Soc. 358 (2006) 1117-1163. MR 2187648. Abstract, references, and article information View Article: PDF This article is available free of charge [10] David Eisenbud and Jerzy Weyman. Fitting's Lemma for $\mathbb{Z}/2$-graded modules. Trans. Amer. Math. Soc. 355 (2003) 4451-4473. MR 1990758. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Mark Hovey. Classifying subcategories of modules. Trans. Amer. Math. Soc. 353 (2001) 3181-3191. MR 1828603. Abstract, references, and article information View Article: PDF This article is available free of charge [12] Steve Files and Rüdiger Göbel. Representations over PID's with three distinguished submodules. Trans. Amer. Math. Soc. 352 (2000) 2407-2427. MR 1491863. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Mihai Cipu, Jürgen Herzog and Dorin Popescu. Indecomposable generalized Cohen-Macaulay modules . Trans. Amer. Math. Soc. 342 (1994) 107-136. MR 1104198. Abstract, references, and article information View Article: PDF This article is available free of charge [14] Andrew R. Kustin. Classification of the Tor-algebras of codimension four almost complete intersections . Trans. Amer. Math. Soc. 339 (1993) 61-85. MR 1132435. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Winfried Bruns, Aron Simis and Ngô Viêt Trung. Blow-up of straightening-closed ideals in ordinal Hodge algebras . Trans. Amer. Math. Soc. 326 (1991) 507-528. MR 1005076. Abstract, references, and article information View Article: PDF This article is available free of charge [16] Dorin Popescu. Indecomposable Cohen-Macaulay modules and their multiplicities . Trans. Amer. Math. Soc. 323 (1991) 369-387. MR 979959. Abstract, references, and article information View Article: PDF This article is available free of charge [17] J. P. Brennan, M. V. Pinto and W. V. Vasconcelos. The Jacobian module of a Lie algebra . Trans. Amer. Math. Soc. 321 (1990) 183-196. MR 958883. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Bernd Ulrich. Sums of linked ideals . Trans. Amer. Math. Soc. 318 (1990) 1-42. MR 964902. Abstract, references, and article information View Article: PDF This article is available free of charge [19] Mutsumi Amasaki. Application of the generalized Weierstrass preparation theorem to the study of homogeneous ideals . Trans. Amer. Math. Soc. 317 (1990) 1-43. MR 992603. Abstract, references, and article information View Article: PDF This article is available free of charge [20] Ernst Dieterich and Alfred Wiedemann. The Auslander-Reiten quiver of a simple curve singularity . Trans. Amer. Math. Soc. 294 (1986) 455-475. MR 825715. Abstract, references, and article information View Article: PDF This article is available free of charge [21] E. Graham Evans and Phillip Griffith. Filtering cohomology and lifting vector bundles . Trans. Amer. Math. Soc. 289 (1985) 321-332. MR 779066. Abstract, references, and article information View Article: PDF This article is available free of charge [22] R. Douglas Williams. Primary ideals in rings of analytic functions . Trans. Amer. Math. Soc. 177 (1973) 37-49. MR 0320760. Abstract, references, and article information View Article: PDF This article is available free of charge [23] Jack Ohm and David E. Rush. The finiteness of $I$ when ${\it R}[{\it X}]/{\it I}$ is flat . Trans. Amer. Math. Soc. 171 (1972) 377-408. MR 0306176. Abstract, references, and article information View Article: PDF This article is available free of charge Results: 1 to 23 of 23 found Go to page: 1	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8647622466087341, "perplexity": 2465.1678682645643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660864.21/warc/CC-MAIN-20160924173740-00264-ip-10-143-35-109.ec2.internal.warc.gz"}
https://brilliant.org/problems/is-it-straight-forward/	Is it straight forward? Algebra Level 5 Given complex numbers $$z_1,z_2$$ satisfying: • $$\|z_1\|=5,\|z_2\|=13$$ • $$39z_1-15z_2=7(4+7i)$$, If $$z_1z_2=a+bi$$ with real numbers $$a,b$$, find $$2a+b$$ Notation: $$\|z\|$$ denotes the absolute value of complex number $$z$$. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9500218033790588, "perplexity": 2676.2739151796422}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549428325.70/warc/CC-MAIN-20170727162531-20170727182531-00149.warc.gz"}
https://www.research.ed.ac.uk/portal/en/publications/measurements-of-bjet-tagging-efficiency-with-the-atlas-detector-using--toverlinet--events-at--sqrts13--tev(3c17b38e-7eca-42df-8475-533d5a6c6ffe).html	Measurements of b-jet tagging efficiency with the ATLAS detector using $t\overline{t}$ events at $\sqrt{s}=13$ TeV Research output: Contribution to journalArticle Open Documents Original language English 089 Journal of High Energy Physics 1808 https://doi.org/10.1007/JHEP08(2018)089 Published - 16 Aug 2018 Abstract The efficiency to identify jets containing $b$-hadrons ($b$-jets) is measured using a high purity sample of dileptonic top quark-antiquark pairs ($t\bar{t}$) selected from the 36.1 fb$^{-1}$ of data collected by the ATLAS detector in 2015 and 2016 from proton-proton collisions produced by the Large Hadron Collider at a centre-of-mass energy $\sqrt{s}=13$ TeV. Two methods are used to extract the efficiency from $t\bar{t}$ events, a combinatorial likelihood approach and a tag-and-probe method. A boosted decision tree, not using $b$-tagging information, is used to select events in which two $b$-jets are present, which reduces the dominant uncertainty in the modelling of the flavour of the jets. The efficiency is extracted for jets in a transverse momentum range from 20 to 300 GeV, with data-to-simulation scale factors calculated by comparing the efficiency measured using collision data to that predicted by the simulation. The two methods give compatible results, and achieve a similar level of precision, measuring data-to-simulation scale factors close to unity with uncertainties ranging from 2% to 12% depending on the jet transverse momentum. • hep-ex	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9475839734077454, "perplexity": 1599.958335674406}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669967.80/warc/CC-MAIN-20191119015704-20191119043704-00373.warc.gz"}
http://mathforum.org/mathimages/index.php?title=Fibonacci_Numbers&oldid=14709	# Fibonacci Numbers Fibonacci Spiral The spiral curve of the Nautilus sea shell follows the pattern of a spiral drawn in a Fibonacci rectangle, a collection of squares with sides that have the length of Fibonacci numbers. # Basic Description The Fibonacci sequence is the sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \ldots,$ where the first two numbers are 1s and every later number is the sum of the two previous numbers. So, given two $1$'s as the first two terms, the next terms of the sequence follows as : $1+1=2, 1+2=3, 2+3=5, 3+5=8, \dots$ Image 1 The Fibonacci numbers can be discovered in nature, such as the spiral of the Nautilus sea shell, the petals of the flowers, the seed head of a sunflower, and many other parts. The seeds at the head of the sunflower, for instance, are arranged so that one can find a collection of spirals in both clockwise and counterclockwise ways. Different patterns of spirals are formed depending on whether one is looking at a clockwise or counterclockwise way; thus, the number of spirals also differ depending on the counting direction, as shown by Image 1. The two numbers of spirals are always consecutive numbers in the Fibonacci sequence. Nature prefers this way of arranging seeds because it seems to allow the seeds to be uniformly distributed. For more information about Fibonacci patterns in nature, see Fibonacci Numbers in Nature ## Origin The Fibonacci sequence was studied by Leonardo of Pisa, or Fibonacci (1770-1240). In his work Liber Abacci, he introduced a problem involving the growth of the rabbit population. The assumptions were • there is one pair of baby rabbits placed in an enclosed place on the first day of January • this pair will grow for one month before reproducing and produce a new pair of baby rabbits on the first day of March • each new pair will mature for one month and produce a new pair of rabbits on the first day of their third month • the rabbits never die, so after they mature, the rabbits produce a new pair of baby rabbits every month. The problem was to find out how many pairs of rabbits there will be after one year. Image 2 On January 1st, there is only 1 pair. On February 1st, this baby rabbits matured to be grown up rabbits, but they have not reproduced, so there will only be the original pair present. Now look at any later month. June is a good example. As you can see in Image 2, all 5 pairs of rabbits that were alive in May continue to be alive in June. Furthermore, there are 3 new pairs of rabbits born in June, one for each pair that was alive in April (and are therefore old enough to reproduce in June). This means that on June 1st, there are 5 + 3 = 8 pairs of rabbits. This same reasoning can be applied to any month, March or later, so the number of rabbits pairs in any month is the same as the sum of the number of rabbit pairs in the two previous months. This is exactly the rule that defines the Fibonacci sequence. As you can see in the image, the population by month begins: 1, 1, 2, 3, 5, 8, ..., which is the same as the beginning of the Fibonacci sequence. The population continues to match the Fibonacci sequence no matter how many months out you go. An interesting fact is that this problem of rabbit population was not intended to explain the Fibonacci numbers. This problem was originally intended to introduce the Hindu-Arabic numerals to Western Europe, where people were still using Roman numerals, and to help people practice addition. It was coincidence that the number of rabbits followed a certain pattern which people later named as the Fibonacci sequence. # Fibonacci Numbers in Nature ### Leaf Arrangement Fibonacci numbers appear in the arrangement of leaves in certain plants. Take a plant, locate the lowest leaf and number that leaf as 0. Number the leaves by order of creation starting from 0, as shown in Image 3. Then, count the number of leaves you encounter until you reach the next leaf that is directly above and pointing in the same direction as the lowest leaf, which is the leaf with number 8 in this image. The number of leaves you pass, in this case, 8, will be a Fibonacci number. Image 3 Moreover, the number of rotations you make around the stem until you reach that leaf will also be a Fibonacci number. You make rotations up the stem by following ascending order of the leaf's number. In the image, if you follow the red arrows, the number of rotations you make until you reach 8 will be 5, which is a Fibonacci number. In Image 4, the leaf that is pointing in the same direction as the lowest leaf 0 is the leaf number 13. The number of leaves in between these two leaves is 13, which is a Fibonacci number. Moreover, going up the stem in a clockwise direction, such that we follow leaves 0, 1, 2, ..., 13, we make 8 rotations, and going up the stem in a counterclockwise direction, we make 5 rotations. The number of clockwise rotations and the number of counterclockwise rotations are always consecutive Fibonacci numbers. Image 4 ### Spirals Image 5 Fibonacci numbers can be seen in nature through spiral forms that can be constructed by Fibonacci rectangles as shown in Image 5. Fibonacci rectangles are rectangles that are built so that the ratio of the length to the width is the proportion of two consecutive Fibonacci numbers. We can build Fibonacci rectangles first by drawing two squares with length 1 next to each other. Then, we draw a new square with length 2 that is touching the sides of the original two squares. We draw another square with length 3 that is touching one unit square and the latest square with length 2. We can build Fibonacci rectangles by continuing to draw new squares that have the same length as the sum of the length of the latest two squares. After building Fibonacci rectangles, we can draw a spiral in the squares, each square containing a quarter of a circle. Such spiral is called the Fibonacci spiral, and it can be seen in sea shells, snails, the spirals of the galaxy, and other parts of nature, as shown in Image 6 and Image 7. Image 6 Image 7 ### Ancestry of Bees Fibonacci numbers also appear when studying the ancestry of bees. Bees reproduce according to the following rules: • male bees hatch from an unfertilized egg, and have only a mother and no father, • female bees hatch from a fertilized egg, and require both a mother and a father. The table below starts with a male bee, and tracks the ancestors of the male bee. Only one female was needed to produce the male bee. This female bee, on the other hand, must have had both a mother and a father to be hatched; thus, the third row of the bee family tree has one male and a female. For each male and female, such pattern repeats. When we count the number of bees for each generation, we get a Fibonacci sequence as we go up the generations, similar to the way we got Fibonacci numbers in the rabbit population problem. Image 8 # A More Mathematical Explanation ## Symbolic Definition of Fibonacci Sequence The Fibonacci sequence is the sequence UNIQ1f30f6d873 [...] ## Symbolic Definition of Fibonacci Sequence The Fibonacci sequence is the sequence $F_1, F_2, F_3, \ldots, F_n, \ldots$ where $F_n = F_{n-1} + F_{n-2} \quad \hbox{ for } n>2$, and $F_1 = 1,\ F_2 = 1$. The Fibonacci sequence is recursively defined because each term is defined in terms of its two immediately preceding terms. ## Identities and Properties ### Idenitities There are some interesting identities, including formula for the sum of first $n$ Fibonacci numbers, the sum of Fibonacci numbers with odd indices and sum of Fibonacci number with even indices. Note that all the identities and properties in this section can be proven in a more rigorous way through mathematical induction. #### Sum of first $n$ Fibonacci numbers The sum of first$n$ Fibonacci numbers is one less than the value of the ${(n+2)}^{\rm th}$ Fibonacci number: Eq. (1) $F_1+F_2+\dots+F_n=F_{n+2}-1$ For example, the sum of first $5$ Fibonacci numbers is : $F_1+F_2+F_3+F_4+F_5= 1 + 1 + 2 + 3 +5=F_7-1=12$ The example is demonstrated below. The total length of red bars that each correspond to $F_1, F_2, F_3, F_4, F_5$ is one unit less than the length of $F_7$. Image 9 $F_1=F_3-F_2$ $F_2=F_4-F_3$ $F_3=F_5-F_4$ $\dots$ $F_{n-1}=F_{n+1}-F_n$ $F_n=F_{n+2}-F_{n+1}$ Adding up all the equations, we get : $F_1+F_2+\dots+F_n=-F_2+(F_3-F_3)+(F_4-F_4)+ \dots +(F_{n+1}-F_{n+1})+F_{n+2}$ $=F_{n+2}-F_2$ Except for $F_{n+2}$ and $-F_2$, all terms on the right side of the equation is canceled out by another term that has the opposite sign and the same magnitude. Because $F_2=1$, we get : $F_1+F_2+\dots+F_n=F_{n+2}-1$ #### Sum of Fibonacci numbers with odd indices The sum of first $n$ Fibonacci numbers with odd indices is equal to the ${(2n)}^{\rm th}$ Fibonacci number: Eq. (2) $F_1+F_3+F_5+\dots+F_{2n-1}=F_{2n}$ For instance, the sum of first $4$ Fibonacci numbers with odd indices is: $F_1+F_3+F_5+F_7=1+2+5+13=21=F_8$ This example is shown below. Image 10 $F_1=F_2$ $F_3=F_4-F_2$ $F_5=F_6-F_4$ $\dots$ $F_{2n-1}=F_{2n}-F_{2n-2}$ Adding all the equations, we get : $F_1+F_3+F_5+\dots+F_{2n-1}=(F_2-F_2)+(F_4-F_4)+(F_6-F_6)+\dots+(F_{2n-2}-F_{2n-2})+F_{2n}$ $=F_{2n}$ Except for $F_{2n}$, all the terms on the right side of the equation disappear because each term is canceled out by another term that has the opposite sign and the same magnitude. #### Sum of Fibonacci numbers with even indices The sum of first $n$ Fibonacci numbers with even indices is one less than the ${(2n+1)}^{\rm th}$ Fibonacci number: $F_2+F_4+\dots+F_{2n}=F_{2n+1}-1$ For example, the sum of first $4$ Fibonacci numbers with even indices is : $F_2+F_4+F_6= 1+3+8=F_7-1=13-1=12$ This example is shown below. Image 11 To see the proof, click below. Subtracting Eq. (2), the sum of Fibonacci numbers with odd indices, from the sum of the first $2n$ Fibonacci numbers, we get the identity of the sum of Fibonacci numbers with even indices. First, when we find the sum of first $2n$ Fibonacci numbers through Eq. (1), we get: $F_1+F_2+\dots+F_{2n}=F_{2n+2}-1$ Now, subtract Eq. (2) from the above equation, and we get: $F_2+F_4+F_6+\dots+F_{2n}=F_{2n+2}-F_{2n}-1$ By definition of Fibonacci numbers, $F_{2n+2}-F_{2n}=F_{2n+1}$. Thus, $F_2+F_4+F_6+\dots+F_{2n}=F_{2n+1}-1$ #### Sum of the squares of Fibonacci numbers The sum of the squares of the first $n$ Fibonacci numbers is the product of the $n^{\rm th}$ and the ${(n+1)}^{\rm th}$ Fibonacci numbers. Image 12 $\sum_{i=1}^n {F_i}^2=F_n F_{n+1}$ This identity can be proved by studying the area of the rectangles in Image 12. The rectangle is called a Fibonacci rectangle, which is further described in Fibonacci Numbers in Nature. The numbers inside each square indicate the length of one side of the square. Notice that the lengths of the squares are all Fibonacci numbers. Any rectangle in the picture is composed of squares with lengths that are Fibonacci numbers. In fact, any rectangle is composed of every square with side lengths $F_1$ through $F_n$, with the value of $n$ depending on the rectangle. Moreover, the dimension of this rectangle is $F_n$ by $F_{n+1}$. With this information in mind, we can prove the identity $\sum_{i=1}^n {F_i}^2=F_n F_{n+1}$ by computing the area of the rectangle in two different ways. The first way of finding the area is to add the area of each squares. That is, the area of the rectangle will be : ${F_1}^2+{F_2}^2+{F_3}^2+\dots+{F_n}^2$. Another way of computing the area is by multiplying the width by the height. Using this method, the area will be : $F_n F_{n+1}$. Because we are computing the area of the same rectangle, the two methods should give the same results. Thus, ${F_1}^2+{F_2}^2+{F_3}^2+\dots+{F_n}^2=F_n F_{n+1}$. For example, for the red rectangle, the width is $5$ and the height is $8$. Since $5$ is the $5^{\rm th}$ Fibonacci number and $8$ is the $6^{\rm th}$ Fibonacci number, let $n=5$. The area of the rectangle is : $1^2+1^2+2^2+3^2+5^2={F_1}^2+{F_2}^2+{F_3}^2+{F_4}^2+{F_5}^2=\sum_{i=1}^5 {F_i}^2=40$, or $5 * 8 = F_5 F_{5+1} = F_5 F_6 = 40$. Thus, $\sum_{i=1}^5 {F_i}^2=F_5 F_{5+1}$. ### Properties #### Greatest Common Divisor The greatest common divisor of two Fibonacci numbers is the Fibonacci number whose index is the greatest common divisor of the indices of the original two Fibonacci numbers. In other words, $\gcd(F_n,F_m) = F_{\gcd(n,m)}$. For instance, $\gcd(F_9,F_6)=\gcd(34,8)=2=F_3=F_{\gcd(9,6)}$. In a special case where $F_n$ and $F_m$ are consecutive Fibonacci numbers, this property says that $\gcd(F_n, F_{n+1})=F_{\gcd(n,n+1)}=F_1=1$. That is, $F_n$ and $F_{n+1}$, or two consecutive Fibonacci numbersare always relatively prime. To see the proof for this special case, click below. Assume that $F_n$ and $F_{n+1}$ have some integer $k$ as their common divisor. Then, both $F_{n+1}$ and $F_n$ are each multiples of $k$: Eq. (3) $F_{n+1}=ka$ Eq. (4) $F_n=kb$ Subtracting Eq. (4) from Eq. (3), we get : $F_{n-1}=k(a-b)$, which means that if two consecutive Fibonacci numbers, $F_n$ and $F_{n+1}$, have $k$ as their common divisor, then the previous Fibonacci number, $F_{n-1}$ must also be a multiple of $k$. In that case, $F_{n-1}$ and $F_n$, which are also two consecutive Fibonacci numbers, will have $k$ as a common divisor. Then, it follows that $F_{n-2}$ must also be a multiple of $k$. Repeating the subtraction of consecutive Fibonacci numbers, we can conclude that the very first Fibonacci number, $F_1 = 1$ must also be a multiple of $k$. So $k=1$, and the only common divisor between two consecutive Fibonacci numbers is 1. Thus, two consecutive Fibonacci numbers are relatively prime. #### Finite Difference of Fibonacci Numbers One of the interesting properties of Fibonacci numbers is that the sequence of differences between consecutive Fibonacci numbers also forms a Fibonacci sequence, as shown in the table below. For more information about the difference table, click Difference Tables. Because the first sequence of differences of the Fibonacci sequence also includes a Fibonacci sequence, the second difference also includes a Fibonacci sequence. The Fibonacci sequence is thus reproduced in every sequence of differences. We can see that the sequence of differences is composed of Fibonacci numbers by looking at the definition of Fibonacci numbers : $F_n = F_{n-1} + F_{n-2}$. The difference between two consecutive Fibonacci numbers is : $F_n - F_{n-1} = F_{n-2}$. Thus, the difference between two consecutive Fibonacci numbers, $F_n$ and $F_{n-1}$, is equal to the value of the previous Fibonacci number, $F_{n-2}$. ## Golden Ratio Image 13 The golden ratio appears in paintings, architecture, and in various forms of nature. Two numbers are said to be in the golden ratio if the ratio of the smaller number to the larger number is equal to the ratio of the larger number to the sum of the two numbers. In Image 13, the width of A and B are in the golden ratio if$a : b = (a+b) : a$. The golden ratio is represented by the Greek lowercase phi ,$\varphi$, and the exact value is $\varphi=\frac{1 + \sqrt{5}}{2} \approx 1.61803\,39887\dots\,$ This value can be found from the definition of the golden ratio. To see an algebraic derivation of the exact value of the golden ratio, go to Golden Ratio : An Algebraic Representation. An interesting fact about golden ratio is that the ratio of two consecutive Fibonacci numbers approaches the golden ratio as the numbers get larger, as shown by the table below. $\frac{F_{n+1}}{F_n}$ $\frac{1}{1}$=1 $\frac{2}{1}$=2 $\frac{3}{2}$=1.5 $\frac{5}{3}$=1.66667 $\frac{8}{5}$=1.6 $\frac{13}{8}$=1.625 $\frac{21}{13}$=1.61538 $\frac{34}{21}$=1.61904 $\frac{55}{34}$=1.61765 $\frac{89}{55}$=1.61818 Lets assume that the ratio of two consecutive Fibonacci numbers have a limit and verify that this limit is, in fact, the golden ratio. Let $r_n$ denote the ratio of two consecutive Fibonacci numbers, that is, $r_n=\frac{F_{n+1}}{F_n}$. Then, $r_{n-1}=\frac{F_n}{F_{n-1}}$. $r_n$ and $r_{n-1}$ are related by : $r_n=\frac{F_{n+1}}{F_n}=\frac{F_n+F_{n-1}}{F_n}=1+\frac{F_{n-1}}{F_n}=1+\cfrac{1}{{F_n}/{F_{n-1}}}=1+\frac{1}{r_{n-1}}$. Assuming that the ratio $r_n$ has a limit, let $r$ be that limit: $\lim_{n \to \infty} r_n=\lim_{n \to \infty}\frac{F_{n+1}}{F_n}=r$. Then, $\lim_{n \to \infty} r_n = \lim_{n \to \infty} r_{n-1} = r$. Taking the limit of $r_n=1+\frac{1}{r_{n-1}}$ we get : $r=1+\frac{1}{r}$ Multiplying both sides by $r$, we get Eq. (5) ${r}^2=r+1$ which can be written as: $r^2 - r - 1 = 0$. Applying the quadratic formula , we get $r = \frac{1 \pm \sqrt{5}} {2}$. Because the ratio has to be a positive value, $r=\frac{1 + \sqrt{5}}{2}$ which is the golden ratio. Thus, if $r_n$ has a limit, then this limit is the golden ratio. That is, as we go farther out in the sequence, the ratio of two consecutive Fibonacci numbers approaches the golden ratio. In fact, it can be proved that $r_n$ does have a limit; one way is to use Binet's formula in the next section. For a different proof using infinite continued fraction go to Continued Fraction Representation and Fibonacci Sequences Image 14 Many people find the golden ratio in various parts of nature, art, architecture, and even music. However, there are some people who criticize this viewpoint. They claim that many mathematicians are wishfully trying to make a connection between the golden ratio and other parts of the world even though there is no real connection. One example of the golden ratio that mathematicians found in nature is the human body. According to many, an ideal human body have proportions that show the golden ratio, such as: • distance between the foot and navel : distance between the navel and the head • distance between the finger tip and the elbow : distance between the wrist and the elbow • distance between the shoulder line and top of the head : length of the head. Leonardo da Vinci's drawing Vitruvian man shown in Image 14 emphasizes the proportion of human body. This drawing shows the proportions of an ideal human body that was studied by a Roman architect Vitruvius in his book De Architectura. In the drawing, a man is simultaneously inscribed in a circle and a square. The ratio of the square side to the radius of the circle in the drawing reflects the golden ratio, although the drawing deviates from the real value of the golden ratio by 1.7 percent. The proportions of the body of the man is also known to show the golden ratio. Although people later found the golden ratio in the painting, there is no evidence whether Leonardo da Vinci was trying to show the golden ratio in his painting or not. For more information about the golden ratio, go to Golden Ratio ## Binet's Formula for Fibonacci Numbers Binet's Formula gives a formula for the $n^{\rm th}$ Fibonacci number as : $F_n=\frac{{\varphi}^n-{\bar{\varphi}}^n}{\sqrt5}$, where $\varphi$ and $\bar{\varphi}$ are the two roots of Eq. (5), that is, $\varphi=\frac{1 + \sqrt{5}}{2},\quad \bar{\varphi}=\frac{1-\sqrt{5}}{2}$. Here is one way of verifying Binet's formula through mathematical induction, but it gives no clue about how to discover the formula. Let $F_n=\frac{{\varphi}^n-{\bar{\varphi}}^n}{\sqrt5}$ as defined above. We want to verify Binet's formula by showing that the definition of Fibonacci numbers holds true even when we use Binet's formula. First, we will show through inductive step that: $F_n=F_{n-1}+F_{n-2}\quad\hbox{ for } n>2$ and then we will show the base case that: $F_1=1,\quad F_2=1$. First, according to Binet's fromula, $F_{n-1}+F_{n-2} = \frac{{\varphi}^{n-1}-{\bar{\varphi}}^{n-1}}{\sqrt5}+ \frac{{\varphi}^{n-2}-{\bar{\varphi}}^{n-2}}{\sqrt5}$ $=\frac{({\varphi}^{n-1}+{\varphi}^{n-2})-({\bar{\varphi}}^{n-1}+{\bar{\varphi}}^{n-2})}{\sqrt5}$ $=\frac{({\varphi}+1){\varphi}^{n-2}-(\bar{\varphi}+1){\bar{\varphi}}^{n-2}}{\sqrt5}$. Because $\varphi$ and $\bar{\varphi}$ are the two roots of Eq. (5), the above equation becomes : $F_{n-1}+F_{n-2}=\frac{{{\varphi}^2}{\varphi}^{n-2}-{{\bar{\varphi}}^2}{\bar{\varphi}}^{n-2}}{\sqrt5}$ $=\frac{{\varphi}^n-{\bar{\varphi}}^n}{\sqrt5}$ $=F_n$, as desired. Now, because $\varphi=\frac{1 + \sqrt{5}}{2},\quad \bar{\varphi}=\frac{1-\sqrt{5}}{2}$, $F_1=\frac{\varphi-\bar{\varphi}}{\sqrt5}=\frac{1}{\sqrt5}\left (\frac{1 + \sqrt{5}}{2}-\frac{1-\sqrt{5}}{2}\right)=\frac{1}{\sqrt5} {\sqrt5} = 1$ $F_2=\frac{{\varphi}^2-{\bar{\varphi}}^2}{\sqrt5}=\frac{(\varphi+\bar{\varphi})(\varphi-\bar{\varphi})}{\sqrt5}=\frac{1*{\sqrt5}}{\sqrt5}=1$. Binet's formula thus is a correct formula of Fibonacci numbers. ## Fibonacci Numbers and Fractals ### Fibonacci Numbers and the Mandelbrot Set Image 15 The Mandelbrot set is a set of points in which the boundary forms a fractal. It is a set of all complex numbers $c$ for which the sequence Eq. (6) $z_{n+1}=(z_n)^2+c \quad \hbox{ for } n=0,1,2,\dots$ does not go to infinity, starting with $z_0=0$. For instance, $c=0$ is included in the Mandelbrot set because $z_1=(z_0)^2+c=0^2+0 = 0$ $z_2=(z_0)^2+c=0^2+0=0$ $\dots$ $z_n=0^2+0=0$ for any $n$. Thus, the sequence defined by $c=0$ is bounded and $0$ is included in the Mandelbrot set. On the other hand, when we test$c=1$, Image 16 $z_1=(z_0)^2+c=1$ $z_2=(z_1)^2+c=2$ $z_3=(z_2)^2+c=5$ $\dots$ The terms of this sequence will increase to infinity. Thus, $c=1$ is not included in the Mandelbrot set. Image 17 People have been drawn to study the Mandelbrot set because of its aesthetic beauty. The Mandelbrot set is known to be one of the most beautiful and complicated illustration of fractal. It is surprising to many people how a simple formula like Eq. (6) can generate a complex structure of the Mandelbrot set. The Fibonacci sequence is related to the Mandelbrot set through the period of the main cardioid and some large primary bulbs. For each bulb, there are many antennas, and the largest antenna is called the main antenna. The number of spokes in the main antenna is the period of the bulb. The period of the main cardioid is considered to be 1. In Image 17, the main antenna has five spokes, including the one connecting the primary bulb and the junction point of the antenna. The period of this bulb is five. Now, we will consider the period of the largest primary bulbs that are attached to the main cardioid and are in between two larger bulbs. In Image 18, the largest bulb between the bulb of period 1 and the bulb of period 2 is the bulb of period 3, and this bulb was found by looking for the largest bulb on the periphery of the main cardioid. The largest bulb between the bulb of period 2 and period 3 is the bulb of period 5, and the one between bulb of period 3 and period 5 is the bulb of period 8. The sequence generated in this way proceeds as 1, 2, 3, 5, 8, 13, ..., following the pattern of Fibonacci sequence. Image 18 # References Maurer, Stephen B & Ralston, Anthony. (2004) Discrete Algorithmic Mathematics. Massachusetts : A K Peters. Posamentier, Alfred S & Lehmann Ingmar. (2007) The Fabulous Fibonacci Numbers. New York : Prometheus Books. Vorb'ev, N. N. (1961) Fibonacci Numbers. New York : Blaisdell Publishing Company. Hoggatt, Verner E., Jr. (1969) Fibonacci and Lucas Numbers. Boston : Houghton Mifflin Company. Knott, Ron. (n.d.). The Fibonacci Numbers and Golden Section in Nature. Retrieved from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html Fibonacci Numbers in Nature & the Golden Ratio. (n.d.). In World-Mysteries.com. Retrieved from http://www.world-mysteries.com/sci_17.htm ## Things to add(possible ideas for future) • Fibonacci numbers and Pascal's triangle • A helper page for recursively defined sequence • A section describing the Fibonacci numbers with negative subscripts. this appears in Finite Difference of Fibonacci Numbers section • A derivation of the exact value of the golden ratio. The derivation is redundant with the information in the golden ratio page. 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http://www.ck12.org/workbook/Biology-Workbook/r1/section/15.3/	<meta http-equiv="refresh" content="1; url=/nojavascript/"> Plant Evolution and Classification \| CK-12 Foundation You are reading an older version of this FlexBook® textbook: CK-12 Biology Workbook Go to the latest version. 15.3: Plant Evolution and Classification Created by: CK-12 Chapter 15 Review Worksheet Name___________________ Class______________ Date________ Multiple Choice Circle the letter of the correct choice. 1. Skunk cabbage has evolved stinky flowers because 1. the smell prevents other plants from growing nearby all year long. 2. all yellow flowers smell bad. 3. the odor attracts pollinators. 4. the odor repels pollinators. 2. Which of the following is not a characteristic of most plants? 1. carries out photosynthesis 2. has cell walls made of cellulose 3. has yellow flowers 4. has specialized reproductive organs 3. Much of the oxygen in the earth's atmosphere 1. is produced as a waste product of cellular respiration in plants. 2. is released as a byproduct of photosynthesis. 3. is produced as a waste product of cellular respiration in animals. 4. is produced by tree frogs. 4. The mature sporophyte of a fern 1. produces haploid spores by meiosis. 2. produces diploid spores by meiosis. 3. produces diploid spores by mitosis. 4. produces haploid spores by mitosis. 5. Fusion of male and female gametes in plants produces 1. a eudicot stamen. 2. a style. 3. a haploid spore. 4. a diploid embyro. 6. Marine plants 1. have always been the dominant organisms of the oceans. 2. evolved after land plants. 3. are restricted to the water closer to the air, so they can get sufficient light for photosynthesis. 4. do not need to photosynthesize. 7. The vascular tissue that transports water and minerals from the soil to the rest of the plant is the 1. phloem. 2. phlegm. 3. leaf. 4. xylem. 8. The vascular tissue that transports sugars from photosynthetic tissues to the rest of the plant is 1. phloem. 2. phlegm. 3. leaf. 4. xylem. 9. In most land plants, the ________ generation is the dominant one. 1. diploid sporophyte 2. diploid gametophyte 3. haploid sporophyte 4. haploid gametophyte 10. In seed plants, the ________ helps transfer of sperm from the pollen grain to the egg. 1. sepal 2. petal 3. tuberous ovule 4. pollen tube 11. The scales of pine cones are 1. always green. 2. modified roots. 3. modified leaves. 4. modified stems. 12. Plants that make flowers are called 1. gymnosperms. 2. byrophytes. 3. gametophytes. 4. angiosperms. 13. The class of plants that has vascular tissue and reproduces with spores is the 1. clubmosses. 2. liverworts. 3. flowering plants. 4. conifers. 14. The embryonic stem in a seed is called the 2. hypocotyl. 3. seed coat. 4. endosperm. 15. Pollen contains 1. male gametes. 2. female gametes. 3. fruits. 4. a stigma. True or False Write true if the statement is true or false if the statement is false. _______ 16. Plants are a direct or indirect source of food for most organisms living on earth. _______ 17. A ripened ovary becomes a pollen grain. _______ 18. Cross-pollination decreases genetic diversity. _______ 19. Monocot embryos have one cotyledon. _______ 20. Currently on earth, there are many more gymnosperm species than angiosperm species. Fill in the Blanks Fill in the blank with the term that best completes the sentence. 21. Switching between a haploid gametophyte stage and a diploid sporophyte stage is called ____________. 22. ____________ gives plant stems stiffness and helps protect plants against predators. 23. Nonvascular plants use ____________ for absorbing water. 24. Asexual reproduction from stems, leaves, or roots is called ____________. 25. ____________ occurs when a growing plant embryo bursts through the seed coat. 26. Liverworts, hornworts, and mosses are all ____________ plants. 27. Another name for vascular plants is ____________. 28. ____________ stores food in seed plants. 29. In a flower the ____________ contains the stigma, style, and ovary. 30. The ____________ protects the seed. Answer each question in the space provided. Refer to the figure below to answer questions 31 and 32. (Xylem and phloem image is courtesy of Jesse Landy and under the Creative Commons license CC-BY-SA 3.0.) 31. What is the function of xylem vessels? How does their structure support their function? $\\\\\\\\\\$ 32. What is the function of phloem vessels? How does their structure support their function? $\\\\\\\\\\$ 33. How did plants and pollinators co-evolve? 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https://worldwidescience.org/topicpages/b/break+repair+pathways.html	#### Sample records for break repair pathways 1. Important DNA repair proteins in DNA double-strand break repair pathways International Nuclear Information System (INIS) DNA double-strand break repair pathway is one of DNA damage repair pathways. DNA repair genes can repair DNA damage, maintain the integrity of the genetic information and inhibit the formation of tumors. There are two mechanisms-non-homologous end joining and homologous recombination to repair DNA double-strand break. In this review, an overview of important repair proteins of non--homologous end joining and homologous recombination pathways was introduced. (authors) 2. DNA double strand break repair pathway choice following ionizing radiation International Nuclear Information System (INIS) A DNA double strand break (DSB) is one of the critical DNA lesions leading to cell death if unrepaired. DSB is repaired by two distinct repair pathways, i.e. non-homologous end-joining (NHEJ) or homologous recombination (HR). NHEJ contributes to DSB repair throughout the cell cycle, while HR is active during S/G2 phase following DNA replication. We aim to elucidate the molecular mechanisms underlying DSB repair pathway choice at two ended DSBs in G2 phase following ionizing radiation (IR). Here, we discuss recent work that provides new insights into DSB repair pathways choice including our study. (author) 3. Regulation of DNA double-strand break repair pathway choice Institute of Scientific and Technical Information of China (English) Meena Shrivastav; Leyma P De Haro; Jac A Nickoloff 2008-01-01 DNA double-strand breaks (DSBs) are critical lesions that can result in cell death or a wide variety of genetic alterations including large- or small-scale deletions, loss of heterozygosity, translocations, and chromosome loss. DSBs are repaired by non-homologous end-joining (NHEJ) and homologous recombination (HR), and defects in these pathways cause genome instability and promote tumorigenesis. DSBs arise from endogenous sources includ-ing reactive oxygen species generated during cellular metabolism, collapsed replication forks, and nucleases, and from exogenous sources including ionizing radiation and chemicals that directly or indirectly damage DNA and are commonly used in cancer therapy. The DSB repair pathways appear to compete for DSBs, but the balance between them differs widely among species, between different cell types of a single species, and during different cell cycle phases of a single cell type. Here we review the regulatory factors that regulate DSB repair by NHEJ and HR in yeast and higher eukaryotes. These factors include regulated expression and phosphorylation of repair proteins, chromatin modulation of repair factor accessibility, and the availability of homologous repair templates. While most DSB repair proteins appear to function exclusively in NHEJ or HR, a number of proteins influence both pathways, including the MRE11/RAD50/NBS1 (XRS2) complex, BRCA1, histone H2AX, PARP-1, RAD18, DNA-dependent protein kinase catalytic subunit (DNA-PKcs), and ATM. DNA-PKcs plays a role in mammalian NHEJ, but it also influences HR through a complex regulatory network that may involve crosstalk with ATM, and the regulation of at least 12 proteins involved in HR that are phosphorylated by DNA-PKcs and/or ATM. 4. New tools to study DNA double-strand break repair pathway choice. Directory of Open Access Journals (Sweden) Daniel Gomez-Cabello Full Text Available A broken DNA molecule is difficult to repair, highly mutagenic, and extremely cytotoxic. Such breaks can be repaired by homology-independent or homology-directed mechanisms. Little is known about the network that controls the repair pathway choice except that a licensing step for homology-mediated repair exists, called DNA-end resection. The choice between these two repair pathways is a key event for genomic stability maintenance, and an imbalance of the ratio is directly linked with human diseases, including cancer. Here we present novel reporters to study the balance between both repair options in human cells. In these systems, a double-strand break can be alternatively repaired by homology-independent or -dependent mechanisms, leading to the accumulation of distinct fluorescent proteins. These reporters thus allow the balance between both repair pathways to be analyzed in different experimental setups. We validated the reporters by analyzing the effect of protein downregulation of the DNA end resection and non-homologous end-joining pathways. Finally, we analyzed the role of the DNA damage response on double-strand break (DSB repair mechanism selection. Our reporters could be used in the future to understand the roles of specific factors, whole pathways, or drugs in DSB repair pathway choice, or for genome-wide screening. Moreover, our findings can be applied to increase gene-targeting efficiency, making it a beneficial tool for a broad audience in the biological sciences. 5. Pathway choice in DNA double strand break repair: Observations of a balancing act NARCIS (Netherlands) I. Brandsma (Inger); D.C. van Gent (Dik) 2012-01-01 textabstractProper repair of DNA double strand breaks (DSBs) is vital for the preservation of genomic integrity. There are two main pathways that repair DSBs, Homologous recombination (HR) and Non-homologous end-joining (NHEJ). HR is restricted to the S and G2 phases of the cell cycle due to the req 6. Repair Pathway Choices and Consequences at the Double-Strand Break. Science.gov (United States) Ceccaldi, Raphael; Rondinelli, Beatrice; D'Andrea, Alan D 2016-01-01 DNA double-strand breaks (DSBs) are cytotoxic lesions that threaten genomic integrity. Failure to repair a DSB has deleterious consequences, including genomic instability and cell death. Indeed, misrepair of DSBs can lead to inappropriate end-joining events, which commonly underlie oncogenic transformation due to chromosomal translocations. Typically, cells employ two main mechanisms to repair DSBs: homologous recombination (HR) and classical nonhomologous end joining (C-NHEJ). In addition, alternative error-prone DSB repair pathways, namely alternative end joining (alt-EJ) and single-strand annealing (SSA), have been recently shown to operate in many different conditions and to contribute to genome rearrangements and oncogenic transformation. Here, we review the mechanisms regulating DSB repair pathway choice, together with the potential interconnections between HR and the annealing-dependent error-prone DSB repair pathways. 7. PARP-1 and Ku compete for repair of DNA double strand breaks by distinct NHEJ pathways Science.gov (United States) Wang, Minli; Wu, Weizhong; Wu, Wenqi; Rosidi, Bustanur; Zhang, Lihua; Wang, Huichen; Iliakis, George 2006-01-01 Poly(ADP-ribose)polymerase 1 (PARP-1) recognizes DNA strand interruptions in vivo and triggers its own modification as well as that of other proteins by the sequential addition of ADP-ribose to form polymers. This modification causes a release of PARP-1 from DNA ends and initiates a variety of responses including DNA repair. While PARP-1 has been firmly implicated in base excision and single strand break repair, its role in the repair of DNA double strand breaks (DSBs) remains unclear. Here, we show that PARP-1, probably together with DNA ligase III, operates in an alternative pathway of non-homologous end joining (NHEJ) that functions as backup to the classical pathway of NHEJ that utilizes DNA-PKcs, Ku, DNA ligase IV, XRCC4, XLF/Cernunnos and Artemis. PARP-1 binds to DNA ends in direct competition with Ku. However, in irradiated cells the higher affinity of Ku for DSBs and an excessive number of other forms of competing DNA lesions limit its contribution to DSB repair. When essential components of the classical pathway of NHEJ are absent, PARP-1 is recruited for DSB repair, particularly in the absence of Ku and non-DSB lesions. This form of DSB repair is sensitive to PARP-1 inhibitors. The results define the function of PARP-1 in DSB repair and characterize a candidate pathway responsible for joining errors causing genomic instability and cancer. PMID:17088286 8. Multiple-pathway analysis of double-strand break repair mutations in Drosophila. Directory of Open Access Journals (Sweden) Dena M Johnson-Schlitz 2007-04-01 Full Text Available The analysis of double-strand break (DSB repair is complicated by the existence of several pathways utilizing a large number of genes. Moreover, many of these genes have been shown to have multiple roles in DSB repair. To address this complexity we used a repair reporter construct designed to measure multiple repair outcomes simultaneously. This approach provides estimates of the relative usage of several DSB repair pathways in the premeiotic male germline of Drosophila. We applied this system to mutations at each of 11 repair loci plus various double mutants and altered dosage genotypes. Most of the mutants were found to suppress one of the pathways with a compensating increase in one or more of the others. Perhaps surprisingly, none of the single mutants suppressed more than one pathway, but they varied widely in how the suppression was compensated. We found several cases in which two or more loci were similar in which pathway was suppressed while differing in how this suppression was compensated. Taken as a whole, the data suggest that the choice of which repair pathway is used for a given DSB occurs by a two-stage "decision circuit" in which the DSB is first placed into one of two pools from which a specific pathway is then selected. 9. Analysis of DNA double-strand break repair pathways in mice International Nuclear Information System (INIS) During the last years significant new insights have been gained into the mechanism and biological relevance of DNA double-strand break (DSB) repair in relation to genome stability. DSBs are a highly toxic DNA lesion, because they can lead to chromosome fragmentation, loss and translocations, eventually resulting in cancer. DSBs can be induced by cellular processes such as V(D)J recombination or DNA replication. They can also be introduced by exogenous agents DNA damaging agents such as ionizing radiation or mitomycin C. During evolution several pathways have evolved for the repair of these DSBs. The most important DSB repair mechanisms in mammalian cells are nonhomologous end-joining and homologous recombination. By using an undamaged repair template, homologous recombination ensures accurate DSB repair, whereas the untemplated nonhomologous end-joining pathway does not. Although both pathways are active in mammals, the relative contribution of the two repair pathways to genome stability differs in the different cell types. Given the potential differences in repair fidelity, it is of interest to determine the relative contribution of homologous recombination and nonhomologous end-joining to DSB repair. In this review, we focus on the biological relevance of DSB repair in mammalian cells and the potential overlap between nonhomologous end-joining and homologous recombination in different tissues 10. Pathway choice in DNA double strand break repair: observations of a balancing act Directory of Open Access Journals (Sweden) Brandsma Inger 2012-11-01 Full Text Available Abstract Proper repair of DNA double strand breaks (DSBs is vital for the preservation of genomic integrity. There are two main pathways that repair DSBs, Homologous recombination (HR and Non-homologous end-joining (NHEJ. HR is restricted to the S and G2 phases of the cell cycle due to the requirement for the sister chromatid as a template, while NHEJ is active throughout the cell cycle and does not rely on a template. The balance between both pathways is essential for genome stability and numerous assays have been developed to measure the efficiency of the two pathways. Several proteins are known to affect the balance between HR and NHEJ and the complexity of the break also plays a role. In this review we describe several repair assays to determine the efficiencies of both pathways. We discuss how disturbance of the balance between HR and NHEJ can lead to disease, but also how it can be exploited for cancer treatment. 11. DNA double-strand break repair: a tale of pathway choices. Science.gov (United States) Li, Jing; Xu, Xingzhi 2016-07-01 Deoxyribonucleic acid double-strand breaks (DSBs) are cytotoxic lesions that must be repaired either through homologous recombination (HR) or non-homologous end-joining (NHEJ) pathways. DSB repair is critical for genome integrity, cellular homeostasis and also constitutes the biological foundation for radiotherapy and the majority of chemotherapy. The choice between HR and NHEJ is a complex yet not completely understood process that will entail more future efforts. Herein we review our current understandings about how the choice is made over an antagonizing balance between p53-binding protein 1 and breast cancer 1 in the context of cell cycle stages, downstream effects, and distinct chromosomal histone marks. These exciting areas of research will surely bring more mechanistic insights about DSB repair and be utilized in the clinical settings. PMID:27217474 12. MOF Phosphorylation by ATM Regulates 53BP1-Mediated Double-Strand Break Repair Pathway Choice Directory of Open Access Journals (Sweden) Arun Gupta 2014-07-01 Full Text Available Cell-cycle phase is a critical determinant of the choice between DNA damage repair by nonhomologous end-joining (NHEJ or homologous recombination (HR. Here, we report that double-strand breaks (DSBs induce ATM-dependent MOF (a histone H4 acetyl-transferase phosphorylation (p-T392-MOF and that phosphorylated MOF colocalizes with γ-H2AX, ATM, and 53BP1 foci. Mutation of the phosphorylation site (MOF-T392A impedes DNA repair in S and G2 phase but not G1 phase cells. Expression of MOF-T392A also blocks the reduction in DSB-associated 53BP1 seen in wild-type S/G2 phase cells, resulting in enhanced 53BP1 and reduced BRCA1 association. Decreased BRCA1 levels at DSB sites correlates with defective repairosome formation, reduced HR repair, and decreased cell survival following irradiation. These data support a model whereby ATM-mediated MOF-T392 phosphorylation modulates 53BP1 function to facilitate the subsequent recruitment of HR repair proteins, uncovering a regulatory role for MOF in DSB repair pathway choice during S/G2 phase. 13. Genetic polymorphisms of DNA double-strand break repair pathway genes and glioma susceptibility International Nuclear Information System (INIS) Genetic variations in DNA double-strand break repair genes can influence the ability of a cell to repair damaged DNA and alter an individual’s susceptibility to cancer. We studied whether polymorphisms in DNA double-strand break repair genes are associated with an increased risk of glioma development. We genotyped 10 potentially functional single nucleotide polymorphisms (SNPs) in 7 DNA double-strand break repair pathway genes (XRCC3, BRCA2, RAG1, XRCC5, LIG4, XRCC4 and ATM) in a case–control study including 384 glioma patients and 384 cancer-free controls in a Chinese Han population. Genotypes were determined using the OpenArray platform. In the single-locus analysis there was a significant association between gliomas and the LIG4 rs1805388 (Ex2 +54C>T, Thr9Ile) TT genotype (adjusted OR, 3.27; 95% CI, 1.87-5.71), as well as the TC genotype (adjusted OR, 1.62; 95% CI, 1.20-2.18). We also found that the homozygous variant genotype (GG) of XRCC4 rs1805377 (IVS7-1A>G, splice-site) was associated with a significantly increased risk of gliomas (OR, 1.77; 95% CI, 1.12-2.80). Interestingly, we detected a significant additive and multiplicative interaction effect between the LIG4 rs1805388 and XRCC4 rs1805377 polymorphisms with an increasing risk of gliomas. When we stratified our analysis by smoking status, LIG4 rs1805388 was associated with an increased glioma risk among smokers. These results indicate for the first time that LIG4 rs1805388 and XRCC4 rs1805377, alone or in combination, are associated with a risk of gliomas 14. PARP-1 and Ku compete for repair of DNA double strand breaks by distinct NHEJ pathways OpenAIRE Wang, Minli; Wu, Weizhong; Wu, Wenqi; Rosidi, Bustanur; Zhang, Lihua; Wang, Huichen; Iliakis, George 2006-01-01 Poly(ADP-ribose)polymerase 1 (PARP-1) recognizes DNA strand interruptions in vivo and triggers its own modification as well as that of other proteins by the sequential addition of ADP-ribose to form polymers. This modification causes a release of PARP-1 from DNA ends and initiates a variety of responses including DNA repair. While PARP-1 has been firmly implicated in base excision and single strand break repair, its role in the repair of DNA double strand breaks (DSBs) remains unclear. Here, ... 15. Reconstitution of initial steps of dsDNA break repair by the RecF pathway of E. coli. Science.gov (United States) Handa, Naofumi; Morimatsu, Katsumi; Lovett, Susan T; Kowalczykowski, Stephen C 2009-05-15 The RecF pathway of Escherichia coli is important for recombinational repair of DNA breaks and gaps. Here ;we reconstitute in vitro a seven-protein reaction that recapitulates early steps of dsDNA break repair using purified RecA, RecF, RecO, RecR, RecQ, RecJ, and SSB proteins, components of the RecF system. Their combined action results in processing of linear dsDNA and its homologous pairing with supercoiled DNA. RecA, RecO, RecR, and RecJ are essential for joint molecule formation, whereas SSB and RecF are stimulatory. This reconstituted system reveals an unexpected essential function for RecJ exonuclease: the capability to resect duplex DNA. RecQ helicase stimulates this processing, but also disrupts joint molecules. RecO and RecR have two indispensable functions: They mediate exchange of RecA for SSB to form the RecA nucleoprotein filament, and act with RecF to load RecA onto the SSB-ssDNA complex at processed ssDNA-dsDNA junctions. The RecF pathway has many parallels with recombinational repair in eukaryotes. PMID:19451222 16. A histone H3K36 chromatin switch coordinates DNA double-strand break repair pathway choice. Science.gov (United States) Pai, Chen-Chun; Deegan, Rachel S; Subramanian, Lakxmi; Gal, Csenge; Sarkar, Sovan; Blaikley, Elizabeth J; Walker, Carol; Hulme, Lydia; Bernhard, Eric; Codlin, Sandra; Bähler, Jürg; Allshire, Robin; Whitehall, Simon; Humphrey, Timothy C 2014-01-01 DNA double-strand break (DSB) repair is a highly regulated process performed predominantly by non-homologous end joining (NHEJ) or homologous recombination (HR) pathways. How these pathways are coordinated in the context of chromatin is unclear. Here we uncover a role for histone H3K36 modification in regulating DSB repair pathway choice in fission yeast. We find Set2-dependent H3K36 methylation reduces chromatin accessibility, reduces resection and promotes NHEJ, while antagonistic Gcn5-dependent H3K36 acetylation increases chromatin accessibility, increases resection and promotes HR. Accordingly, loss of Set2 increases H3K36Ac, chromatin accessibility and resection, while Gcn5 loss results in the opposite phenotypes following DSB induction. Further, H3K36 modification is cell cycle regulated with Set2-dependent H3K36 methylation peaking in G1 when NHEJ occurs, while Gcn5-dependent H3K36 acetylation peaks in S/G2 when HR prevails. These findings support an H3K36 chromatin switch in regulating DSB repair pathway choice. PMID:24909977 17. The opportunistic pathogen Pseudomonas aeruginosa activates the DNA double-strand break signaling and repair pathway in infected cells International Nuclear Information System (INIS) Highly hazardous DNA double-strand breaks can be induced in eukaryotic cells by a number of agents including pathogenic bacterial strains. We have investigated the genotoxic potential of Pseudomonas aeruginosa, an opportunistic pathogen causing devastating nosocomial infections in cystic fibrosis or immunocompromised patients. Our data revealed that infection of immune or epithelial cells by P. aeruginosa triggered DNA strand breaks and phosphorylation of histone H2AX (γH2AX), a marker of DNA double-strand breaks. Moreover, it induced formation of discrete nuclear repair foci similar to gamma-irradiation-induced foci, and containing γH2AX and 53BP1, an adaptor protein mediating the DNA-damage response pathway. Gene deletion, mutagenesis, and complementation in P. aeruginosa identified ExoS bacterial toxin as the major factor involved in γH2AX induction. Chemical inhibition of several kinases known to phosphorylate H2AX demonstrated that Ataxia Telangiectasia Mutated (ATM) was the principal kinase in P. aeruginosa-induced H2AX phosphorylation. Finally, infection led to ATM kinase activation by an auto-phosphorylation mechanism. Together, these data show for the first time that infection by P. aeruginosa activates the DNA double-strand break repair machinery of the host cells. This novel information sheds new light on the consequences of P. aeruginosa infection in mammalian cells. As pathogenic Escherichia coli or carcinogenic Helicobacter pylori can alter genome integrity through DNA double-strand breaks, leading to chromosomal instability and eventually cancer, our findings highlight possible new routes for further investigations of P. aeruginosa in cancer biology and they identify ATM as a potential target molecule for drug design. (authors) 18. The structure of ends determines the pathway choice and Mre11 nuclease dependency of DNA double-strand break repair Science.gov (United States) Liao, Shuren; Tammaro, Margaret; Yan, Hong 2016-01-01 The key event in the choice of repair pathways for DNA double-strand breaks (DSBs) is the initial processing of ends. Non-homologous end joining (NHEJ) involves limited processing, but homology-dependent repair (HDR) requires extensive resection of the 5′ strand. How cells decide if an end is channeled to resection or NHEJ is not well understood. We hypothesize that the structure of ends is a major determinant and tested this hypothesis with model DNA substrates in Xenopus egg extracts. While ends with normal nucleotides are efficiently channeled to NHEJ, ends with damaged nucleotides or bulky adducts are channeled to resection. Resection is dependent on Mre11, but its nuclease activity is critical only for ends with 5′ bulky adducts. CtIP is absolutely required for activating the nuclease-dependent mechanism of Mre11 but not the nuclease-independent mechanism. Together, these findings suggest that the structure of ends is a major determinant for the pathway choice of DSB repair and the Mre11 nuclease dependency of resection. PMID:27084932 19. A robust network of double-strand break repair pathways governs genome integrity during C. elegans development. NARCIS (Netherlands) Pontier, D.B.; Tijsterman, M. 2009-01-01 To preserve genomic integrity, various mechanisms have evolved to repair DNA double-strand breaks (DSBs). Depending on cell type or cell cycle phase, DSBs can be repaired error-free, by homologous recombination, or with concomitant loss of sequence information, via nonhomologous end-joining (NHEJ) o 20. Opposing roles of RNF8/RNF168 and deubiquitinating enzymes in ubiquitination-dependent DNA double-strand break response signaling and DNA-repair pathway choice Science.gov (United States) 2016-01-01 The E3 ubiquitin ligases ring finger protein (RNF) 8 and RNF168 transduce the DNA double-strand break (DSB) response (DDR) signal by ubiquitinating DSB sites. The depletion of RNF8 or RNF168 suppresses the accumulation of DNA-repair regulating factors such as 53BP1 and RAP80 at DSB sites, suggesting roles for RNF8- and RNF168-mediated ubiquitination in DSB repair. This mini-review provides a brief overview of the RNF8- and RNF168-dependent DDR-signaling and DNA-repair pathways. The choice of DNA-repair pathway when RNF8- and RNF168-mediated ubiquitination-dependent DDR signaling is negatively regulated by deubiquitinating enzymes (DUBs) is reviewed to clarify how the opposing roles of RNF8/RNF168 and DUBs regulate ubiquitination-dependent DDR signaling and the choice of DNA-repair pathway. PMID:26983989 1. Phosphorylation: The Molecular Switch of Double-Strand Break Repair Directory of Open Access Journals (Sweden) K. C. Summers 2011-01-01 Full Text Available Repair of double-stranded breaks (DSBs is vital to maintaining genomic stability. In mammalian cells, DSBs are resolved in one of the following complex repair pathways: nonhomologous end-joining (NHEJ, homologous recombination (HR, or the inclusive DNA damage response (DDR. These repair pathways rely on factors that utilize reversible phosphorylation of proteins as molecular switches to regulate DNA repair. Many of these molecular switches overlap and play key roles in multiple pathways. For example, the NHEJ pathway and the DDR both utilize DNA-PK phosphorylation, whereas the HR pathway mediates repair with phosphorylation of RPA2, BRCA1, and BRCA2. Also, the DDR pathway utilizes the kinases ATM and ATR, as well as the phosphorylation of H2AX and MDC1. Together, these molecular switches regulate repair of DSBs by aiding in DSB recognition, pathway initiation, recruitment of repair factors, and the maintenance of repair mechanisms. 2. Role of 53BP1 in the regulation of DNA double-strand break repair pathway choice. Science.gov (United States) Gupta, Arun; Hunt, Clayton R; Chakraborty, Sharmistha; Pandita, Raj K; Yordy, John; Ramnarain, Deepti B; Horikoshi, Nobuo; Pandita, Tej K 2014-01-01 The p53-binding protein 1 (53BP1) is a well-known DNA damage response (DDR) factor, which is recruited to nuclear structures at the site of DNA damage and forms readily visualized ionizing radiation (IR) induced foci. Depletion of 53BP1 results in cell cycle arrest in G2/M phase as well as genomic instability in human as well as mouse cells. Within the DNA damage response mechanism, 53BP1 is classified as an adaptor/mediator, required for processing of the DNA damage response signal and as a platform for recruitment of other repair factors. More recently, specific 53BP1 contributions to DSB repair pathway choice have been recognized and are being characterized. In this review, we have summarized recent advances in understanding the role of 53BP1 in regulating DNA DSBs repair pathway choice, variable diversity joining [V(D)J] recombination and class-switch recombination (CSR). PMID:24320053 3. MCM8 is required for a pathway of meiotic double-strand break repair independent of DMC1 in Arabidopsis thaliana. Directory of Open Access Journals (Sweden) Wayne Crismani Full Text Available Mini-chromosome maintenance (MCM 2-9 proteins are related helicases. The first six, MCM2-7, are essential for DNA replication in all eukaryotes. In contrast, MCM8 is not always conserved in eukaryotes but is present in Arabidopsis thaliana. MCM8 is required for 95% of meiotic crossovers (COs in Drosophila and is essential for meiosis completion in mouse, prompting us to study this gene in Arabidopsis meiosis. Three allelic Atmcm8 mutants showed a limited level of chromosome fragmentation at meiosis. This defect was dependent on programmed meiotic double-strand break (DSB formation, revealing a role for AtMCM8 in meiotic DSB repair. In contrast, CO formation was not affected, as shown both genetically and cytologically. The Atmcm8 DSB repair defect was greatly amplified in the absence of the DMC1 recombinase or in mutants affected in DMC1 dynamics (sds, asy1. The Atmcm8 fragmentation defect was also amplified in plants heterozygous for a mutation in either recombinase, DMC1 or RAD51. Finally, in the context of absence of homologous chromosomes (i.e. haploid, mutation of AtMCM8 also provoked a low level of chromosome fragmentation. This fragmentation was amplified by the absence of DMC1 showing that both MCM8 and DMC1 can promote repair on the sister chromatid in Arabidopsis haploids. Altogether, this establishes a role for AtMCM8 in meiotic DSB repair, in parallel to DMC1. We propose that MCM8 is involved with RAD51 in a backup pathway that repairs meiotic DSB without giving CO when the major pathway, which relies on DMC1, fails. 4. Role of XRCC4 phosphorylation by DNA-PK in the regulation of NHEJ repair pathway of DNA double strand break International Nuclear Information System (INIS) Non-homologous end-joining (NHEJ) is the predominant pathway of DNA double strand breaks in higher eukaryotes and is active throughout the cell cycle. NHEJ repair includes many factors as Ku70/86, DNA-PKcs, XRCC4-Ligase IV complex and XLF (also known as Cernunnos). In these factors, DNA-PKcs acts as central regulator in NHEJ repair. It recruited at the DNA damages site after DNA damage and after association with Ku its kinase activity is activated. It phosphorylates many of important NHEJ proteins in vitro including XRCC4, Ku 70/86, Artemis, and even DNA-PKcs but till now, very less studies have been done to know the role and significance of phosphorylation in the NHEJ repair. Studies by other researchers identified various phosphorylation sites in XRCC4 by DNA-PK using mass spectrometry but these phosphorylation sites were shown to be dispensable for DSB repair. In the present investigation, we identified 3 serine and one new threonine phosphorylation sites in XRCC4 protein by DNA-PK. In vivo phosphorylation at these sites was verified by generating phosphorylation specific antibodies and the requirement for DNA-PK therein was verified by using DNA-PK inhibitor and DNA-PK proficient and deficient cell lines in response to radiation and zeocin treatment. We have also found that phosphorylation at these sites showed dose dependency in response to radiation treatment. The two serine and one threonine phosphorylation site is also biological important as their mutation into alanine significantly elevated radiosensitivity as measured by colony formation assay. Neutral comet assay showed delayed kinetics in DSB repair of these mutants. Furthermore, we have found a protein, with putative DSB repair function, which interacts with domain including the phosphorylation sites.These results indicate that these phosphorylation sites would mediate functional link between XRCC4 and DNA-PK. (author) 5. Non-homologous end joining is the responsible pathway for the repair of fludarabine-induced DNA double strand breaks in mammalian cells International Nuclear Information System (INIS) Fludarabine (FLU), an analogue of adenosine, interferes with DNA synthesis and inhibits the chain elongation leading to replication arrest and DNA double strand break (DSB) formation. Mammalian cells use two main pathways of DSB repair to maintain genomic stability: homologous recombination (HR) and non-homologous end joining (NHEJ). The aim of the present work was to evaluate the repair pathways employed in the restoration of DSB formed following replication arrest induced by FLU in mammalian cells. Replication inhibition was induced in human lymphocytes and fibroblasts by FLU. DSB occurred in a dose-dependent manner on early/middle S-phase cells, as detected by γH2AX foci formation. To test whether conservative HR participates in FLU-induced DSB repair, we measured the kinetics of Rad51 nuclear foci formation in human fibroblasts. There was no significant induction of Rad51 foci after FLU treatment. To further confirm these results, we analyzed the frequency of sister chromatid exchanges (SCE) in both human cells. We did not find increased frequencies of SCE after FLU treatment. To assess the participation of NHEJ pathway in the repair of FLU-induced damage, we used two chemical inhibitors of the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), vanillin and wortmannin. Human fibroblasts pretreated with DNA-PKcs inhibitors showed increased levels of chromosome breakages and became more sensitive to cell death. An active role of NHEJ pathway was also suggested from the analysis of Chinese hamster cell lines. XR-C1 (DNA-PKcs-deficient) and XR-V15B (Ku80-deficient) cells showed hypersensitivity to FLU as evidenced by the increased frequency of chromosome aberrations, decreased mitotic index and impaired survival rates. In contrast, CL-V4B (Rad51C-deficient) and V-C8 (Brca2-deficient) cell lines displayed a FLU-resistant phenotype. Together, our results suggest a major role for NHEJ repair in the preservation of genome integrity against FLU-induced DSB 6. Non-homologous end joining is the responsible pathway for the repair of fludarabine-induced DNA double strand breaks in mammalian cells Energy Technology Data Exchange (ETDEWEB) Campos-Nebel, Marcelo de [Departamento de Genetica, Instituto de Investigaciones Hematologicas Mariano R. Castex, Academia Nacional de Medicina, Buenos Aires (Argentina)], E-mail: [email protected]; Larripa, Irene; Gonzalez-Cid, Marcela [Departamento de Genetica, Instituto de Investigaciones Hematologicas Mariano R. Castex, Academia Nacional de Medicina, Buenos Aires (Argentina) 2008-11-10 Fludarabine (FLU), an analogue of adenosine, interferes with DNA synthesis and inhibits the chain elongation leading to replication arrest and DNA double strand break (DSB) formation. Mammalian cells use two main pathways of DSB repair to maintain genomic stability: homologous recombination (HR) and non-homologous end joining (NHEJ). The aim of the present work was to evaluate the repair pathways employed in the restoration of DSB formed following replication arrest induced by FLU in mammalian cells. Replication inhibition was induced in human lymphocytes and fibroblasts by FLU. DSB occurred in a dose-dependent manner on early/middle S-phase cells, as detected by {gamma}H2AX foci formation. To test whether conservative HR participates in FLU-induced DSB repair, we measured the kinetics of Rad51 nuclear foci formation in human fibroblasts. There was no significant induction of Rad51 foci after FLU treatment. To further confirm these results, we analyzed the frequency of sister chromatid exchanges (SCE) in both human cells. We did not find increased frequencies of SCE after FLU treatment. To assess the participation of NHEJ pathway in the repair of FLU-induced damage, we used two chemical inhibitors of the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), vanillin and wortmannin. Human fibroblasts pretreated with DNA-PKcs inhibitors showed increased levels of chromosome breakages and became more sensitive to cell death. An active role of NHEJ pathway was also suggested from the analysis of Chinese hamster cell lines. XR-C1 (DNA-PKcs-deficient) and XR-V15B (Ku80-deficient) cells showed hypersensitivity to FLU as evidenced by the increased frequency of chromosome aberrations, decreased mitotic index and impaired survival rates. In contrast, CL-V4B (Rad51C-deficient) and V-C8 (Brca2-deficient) cell lines displayed a FLU-resistant phenotype. Together, our results suggest a major role for NHEJ repair in the preservation of genome integrity against FLU 7. DNA double strand break repair pathway plays a significant role in determining the radiotherapy induced normal tissue toxicity among head-and-neck and breast cancer International Nuclear Information System (INIS) The ability to predict individual risk of radiotherapy induced normal tissue complications prior to the therapy may give an opportunity to personalize the treatment aiming improved therapeutic effect and quality of life. Therefore, predicting the risk of developing acute reactions before the initiation of radiation therapy may serve as a potential biomarker. DNA double-strand break (DSB) induction and its repair kinetics in lymphocytes of Head-and-Neck (n = 183) and Breast cancer (n = 132) patients undergoing chemoradiation or radiation therapy alone were analyzed by performing γ-H2AX foci, neutral comet and a modified neutral filter elution assay. Candidate radioresponsive genes like DNA repair, antioxidant pathway, profibrotic cytokine genes were screened for the common variants for their association with normal tissue toxicity outcome. Patients were stratified as non-over responders (NOR) and over responders (OR) based on their Radiation Therapy Oncology Group grading for normal tissue adverse reactions. Our results suggest that DSB repair plays a major role in the development of normal tissue adverse reactions in H and N and Breast cancer patients. The cellular (γ-H2AX analysis) and SNP analysis may have the potential to be developed into a clinically useful predictive assay for identifying the normal tissue over reactors 8. Comet assay analysis of repair of DNA strand breaks in normal and deficient human cells exposed to radiations and chemicals. Evidence for a repair pathway specificity of DNA ligation International Nuclear Information System (INIS) The induction and resealing of DNA strand breaks in a cell line with a proven defect in DNA ligase I, 46BR, and in two Bloom's syndrome cell lines. YBL6 and GM 1492, were compared to those observed in normal human 1BR/3 fibroblasts after treatment with a variety of genotoxic agents whose lesions are processed by different repair pathways. This analysis was performed using the single-cell gel electrophoresis assay. The three types of cells were found to have similar capabilities to recognize and incise ultraviolet photoproducts and also demonstrated similar amounts of DNA breaks immediately after γ irradiation. During post-treatment incubation, 46BR cells showed a marked DNA re-ligation defect after ultraviolet radiation damage, GM 1492 cells demonstrated a highly reduced DNA joining ability after relatively high doses of ultraviolet radiation, and YBL6 cells were particularly affected in DNA re-ligation after damage by 4-nitroquinoline-1-oxide. The two Bloom's syndrome cell lines and 46BR cells had a nearly normal ability to reseal breaks resulting from γ irradiation or treatment with xanthine plus xanthine oxidase. These findings suggest that different DNA ligases may be involved in different DNA repair pathways in human cells. 60 refs., 7 figs 9. A Role for BLM in Double-Strand Break Repair Pathway Choice: Prevention of CtIP/Mre11-Mediated Alternative Nonhomologous End-Joining Directory of Open Access Journals (Sweden) Anastazja Grabarz 2013-10-01 Full Text Available The choice of the appropriate double-strand break (DSB repair pathway is essential for the maintenance of genomic stability. Here, we show that the Bloom syndrome gene product, BLM, counteracts CtIP/MRE11-dependent long-range deletions (>200 bp generated by alternative end-joining (A-EJ. BLM represses A-EJ in an epistatic manner with 53BP1 and RIF1 and is required for ionizing-radiation-induced 53BP1 focus assembly. Conversely, in the absence of 53BP1 or RIF1, BLM promotes formation of A-EJ long deletions, consistent with a role for BLM in DSB end resection. These data highlight a dual role for BLM that influences the DSB repair pathway choice: (1 protection against CtIP/MRE11 long-range deletions associated with A-EJ and (2 promotion of DNA resection. These antagonist roles can be regulated, according to cell-cycle stage, by interacting partners such as 53BP1 and TopIII, to avoid unscheduled resection that might jeopardize genome integrity. 10. Heterozygous PALB2 c.1592delT mutation channels DNA double-strand break repair into error-prone pathways in breast cancer patients. Science.gov (United States) Obermeier, K; Sachsenweger, J; Friedl, T W P; Pospiech, H; Winqvist, R; Wiesmüller, L 2016-07-21 Hereditary heterozygous mutations in a variety of DNA double-strand break (DSB) repair genes have been associated with increased breast cancer risk. In the Finnish population, PALB2 (partner and localizer of BRCA2) represents a major susceptibility gene for female breast cancer, and so far, only one mutation has been described, c.1592delT, which leads to a sixfold increased disease risk. PALB2 is thought to participate in homologous recombination (HR). However, the effect of the Finnish founder mutation on DSB repair has not been investigated. In the current study, we used a panel of lymphoblastoid cell lines (LCLs) derived from seven heterozygous female PALB2 c.1592delT mutation carriers with variable health status and six wild-type matched controls. The results of our DSB repair analysis showed that the PALB2 mutation causes specific changes in pathway usage, namely increases in error-prone single-strand annealing (SSA) and microhomology-mediated end-joining (MMEJ) compared with wild-type LCLs. These data indicated haploinsufficiency regarding the suppression of error-prone DSB repair in PALB2 mutation carriers. To the contrary, neither reduced HR activities, nor impaired RAD51 filament assembly, nor sensitization to PARP inhibition were consistently observed. Expression of truncated mutant versus wild-type PALB2 verified a causal role of PALB2 c.1592delT in the shift to error-prone repair. Discrimination between healthy and malignancy-presenting PALB2 mutation carriers revealed a pathway shift particularly in the breast cancer patients, suggesting interaction of PALB2 c.1592delT with additional genomic lesions. Interestingly, the studied PALB2 mutation was associated with 53BP1 accumulation in the healthy mutation carriers but not the patients, and 53BP1 was limiting for error-prone MMEJ in patients but not in healthy carriers. Our study identified a rise in error-prone DSB repair as a potential threat to genomic integrity in heterozygous PALB2 mutation carriers 11. A major role of the RecFOR pathway in DNA double-strand-break repair through ESDSA in Deinococcus radiodurans. Science.gov (United States) Bentchikou, Esma; Servant, Pascale; Coste, Geneviève; Sommer, Suzanne 2010-01-01 In Deinococcus radiodurans, the extreme resistance to DNA-shattering treatments such as ionizing radiation or desiccation is correlated with its ability to reconstruct a functional genome from hundreds of chromosomal fragments. The rapid reconstitution of an intact genome is thought to occur through an extended synthesis-dependent strand annealing process (ESDSA) followed by DNA recombination. Here, we investigated the role of key components of the RecF pathway in ESDSA in this organism naturally devoid of RecB and RecC proteins. We demonstrate that inactivation of RecJ exonuclease results in cell lethality, indicating that this protein plays a key role in genome maintenance. Cells devoid of RecF, RecO, or RecR proteins also display greatly impaired growth and an important lethal sectoring as bacteria devoid of RecA protein. Other aspects of the phenotype of recFOR knock-out mutants paralleled that of a DeltarecA mutant: DeltarecFOR mutants are extremely radiosensitive and show a slow assembly of radiation-induced chromosomal fragments, not accompanied by DNA synthesis, and reduced DNA degradation. Cells devoid of RecQ, the major helicase implicated in repair through the RecF pathway in E. coli, are resistant to gamma-irradiation and have a wild-type DNA repair capacity as also shown for cells devoid of the RecD helicase; in contrast, DeltauvrD mutants show a markedly decreased radioresistance, an increased latent period in the kinetics of DNA double-strand-break repair, and a slow rate of fragment assembly correlated with a slow rate of DNA synthesis. Combining RecQ or RecD deficiency with UvrD deficiency did not significantly accentuate the phenotype of DeltauvrD mutants. In conclusion, RecFOR proteins are essential for DNA double-strand-break repair through ESDSA whereas RecJ protein is essential for cell viability and UvrD helicase might be involved in the processing of double stranded DNA ends and/or in the DNA synthesis step of ESDSA. PMID:20090937 12. A major role of the RecFOR pathway in DNA double-strand-break repair through ESDSA in Deinococcus radiodurans. Directory of Open Access Journals (Sweden) Esma Bentchikou 2010-01-01 Full Text Available In Deinococcus radiodurans, the extreme resistance to DNA-shattering treatments such as ionizing radiation or desiccation is correlated with its ability to reconstruct a functional genome from hundreds of chromosomal fragments. The rapid reconstitution of an intact genome is thought to occur through an extended synthesis-dependent strand annealing process (ESDSA followed by DNA recombination. Here, we investigated the role of key components of the RecF pathway in ESDSA in this organism naturally devoid of RecB and RecC proteins. We demonstrate that inactivation of RecJ exonuclease results in cell lethality, indicating that this protein plays a key role in genome maintenance. Cells devoid of RecF, RecO, or RecR proteins also display greatly impaired growth and an important lethal sectoring as bacteria devoid of RecA protein. Other aspects of the phenotype of recFOR knock-out mutants paralleled that of a DeltarecA mutant: DeltarecFOR mutants are extremely radiosensitive and show a slow assembly of radiation-induced chromosomal fragments, not accompanied by DNA synthesis, and reduced DNA degradation. Cells devoid of RecQ, the major helicase implicated in repair through the RecF pathway in E. coli, are resistant to gamma-irradiation and have a wild-type DNA repair capacity as also shown for cells devoid of the RecD helicase; in contrast, DeltauvrD mutants show a markedly decreased radioresistance, an increased latent period in the kinetics of DNA double-strand-break repair, and a slow rate of fragment assembly correlated with a slow rate of DNA synthesis. Combining RecQ or RecD deficiency with UvrD deficiency did not significantly accentuate the phenotype of DeltauvrD mutants. In conclusion, RecFOR proteins are essential for DNA double-strand-break repair through ESDSA whereas RecJ protein is essential for cell viability and UvrD helicase might be involved in the processing of double stranded DNA ends and/or in the DNA synthesis step of ESDSA. 13. Double-strand break repair and G4 DNA stability in Caenorhabditis elegans NARCIS (Netherlands) Pontier, D.B. 2010-01-01 DNA double-strand breaks (DSBs) can be repaired by three canonical repair pathways. Homologous recombination (HR) uses the sister chromatid or homologous chromosome as a template to repair the DSB in an error-free manner. In non-homologous end-joining (NHEJ), the broken ends are ligated with little 14. Genetics of x-ray induced double strand break repair in saccharomyces cerevisiae Energy Technology Data Exchange (ETDEWEB) Budd, M.E. 1982-07-01 15. Genetics of x-ray induced double strand break repair in saccharomyces cerevisiae International Nuclear Information System (INIS) 16. Common and unique genetic interactions of the poly(ADP-ribose) polymerases PARP1 and PARP2 with DNA double-strand break repair pathways. Science.gov (United States) Ghosh, Rajib; Roy, Sanchita; Kamyab, Johan; Dantzer, Francoise; Franco, Sonia 2016-09-01 In mammalian cells, chromatin poly(ADP-ribos)ylation (PARylation) at sites of DNA Double-Strand Breaks (DSBs) is mediated by two highly related enzymes, PARP1 and PARP2. However, enzyme-specific genetic interactions with other DSB repair factors remain largely undefined. In this context, it was previously shown that mice lacking PARP1 and H2AX, a histone variant that promotes DSB repair throughout the cell cycle, or the core nonhomologous end-joining (NHEJ) factor Ku80 are not viable, while mice lacking PARP1 and the noncore NHEJ factor DNA-PKcs are severely growth retarded and markedly lymphoma-prone. Here, we have examined the requirement for PARP2 in these backgrounds. We find that, like PARP1, PARP2 is essential for viability in mice lacking H2AX. Moreover, treatment of H2AX-deficient primary fibroblasts or B lymphocytes with PARP inhibitors leads to activation of the G2/M checkpoint and accumulation of chromatid-type breaks in a lineage- and gene-dose dependent manner. In marked contrast to PARP1, loss of PARP2 does not result in additional phenotypes in growth, development or tumorigenesis in mice lacking either Ku80 or DNA-PKcs. Altogether these findings highlight specific nonoverlapping functions of PARP1 and PARP2 at H2AX-deficient chromatin during replicative phases of the cell cycle and uncover a unique requirement for PARP1 in NHEJ-deficient cells. PMID:27373144 17. The role of homologous recombination in radiation-induced double-strand break repair International Nuclear Information System (INIS) DNA double-strand breaks (DSBs) represent the most biologically significant lesions induced by ionizing radiation (IR). HR is the predominant pathway for repairing one-ended DSBs arising in S-phase when the replication fork encounters single-stranded breaks or base damages. Here, we discuss recent findings that two-ended DSBs directly induced by X- or γ-rays in late S- or G2-phase are repaired predominantly by NHEJ, with HR only repairing a sub-fraction of such DSBs. This sub-fraction represents DSBs which localize to heterochromatic DNA regions and, which in control cells, are repaired with slow kinetics over many hours post irradiation. The observation that defined DSB populations are repaired by either NHEJ or HR suggests an assignment of specific tasks for each of the two processes. Furthermore, heavy ion induced complex DSBs, which are in general more slowly repaired than X- or γ-ray induced breaks, are nearly always repaired by HR independent of chromatin localization suggesting that the speed of repair is an important factor determining the DSB repair pathway usage. Finally, NHEJ and HR can, under certain conditions, also compensate for each other such that DSBs normally repaired by one pathway can undergo repair by the other if genetic failures necessitate the pathway switch. 18. The RSC and INO80 chromatin-remodeling complexes in DNA double-strand break repair. Science.gov (United States) Chambers, Anna L; Downs, Jessica A 2012-01-01 In eukaryotes, DNA is packaged into chromatin and is therefore relatively inaccessible to DNA repair enzymes. In order to perform efficient DNA repair, ATP-dependent chromatin-remodeling enzymes are required to alter the chromatin structure near the site of damage to facilitate processing and allow access to repair enzymes. Two of the best-studied remodeling complexes involved in repair are RSC (Remodels the Structure of Chromatin) and INO80 from Saccharomyces cerevisiae, which are both conserved in higher eukaryotes. RSC is very rapidly recruited to breaks and mobilizes nucleosomes to promote phosphorylation of H2A S129 and resection. INO80 enrichment at a break occurs later and is dependent on phospho-S129 H2A. INO80 activity at the break site also facilitates resection. Consequently, both homologous recombination and nonhomologous end-joining are defective in rsc mutants, while subsets of these repair pathways are affected in ino80 mutants. 19. Double strand break repair: two mechanisms in competition but tightly linked to cell cycle International Nuclear Information System (INIS) DNA double strand breaks (DSB) are highly toxic damage although they can be induced to create genetic diversity. Two distinct pathways can repair DSB: Homologous Recombination (HR) and Non Homologous End Joining (NHEJ). If un- or mis-repaired, this damage can lead to cancer. Thus, it is essential to investigate how these two pathways are regulated for DSB repair. NHEJ inhibition leads to HR DSB repair stimulation. However, this channeling to HR is tightly linked to cell cycle since NHEJ and HR are active in G1/early S and late S/G2, respectively. Our results suggest that G1-unrepaired DSB go through S phase to be repaired by HR in G2. Those results allow a better understanding of DSB repair mechanisms regulation. (author) 20. Making ends meet: repairing breaks in bacterial DNA by non-homologous end-joining. Directory of Open Access Journals (Sweden) Richard Bowater 2006-02-01 Full Text Available DNA double-strand breaks (DSBs are one of the most dangerous forms of DNA lesion that can result in genomic instability and cell death. Therefore cells have developed elaborate DSB-repair pathways to maintain the integrity of genomic DNA. There are two major pathways for the repair of DSBs in eukaryotes: homologous recombination and non-homologous end-joining (NHEJ. Until very recently, the NHEJ pathway had been thought to be restricted to the eukarya. However, an evolutionarily related NHEJ apparatus has now been identified and characterized in the prokarya. Here we review the recent discoveries concerning bacterial NHEJ and discuss the possible origins of this repair system. We also examine the insights gained from the recent cellular and biochemical studies of this DSB-repair process and discuss the possible cellular roles of an NHEJ pathway in the life-cycle of prokaryotes and phages. 1. Break-induced replication repair of damaged forks induces genomic duplications in human cells OpenAIRE Costantino, L.; Sotiriou, S. K.; Rantala, J. K.; Magin, S.; Mladenov, E.; Helleday, T.; Haber, J E; Iliakis, G.; Kallioniemi, O P; Halazonetis, T D 2013-01-01 In budding yeast, one-ended DNA double-strand breaks (DSBs) and damaged replication forks are repaired by break-induced replication (BIR), a homologous recombination pathway that requires the Pol32 subunit of DNA polymerase delta. DNA replication stress is prevalent in cancer, but BIR has not been characterized in mammals. In a cyclin E overexpression model of DNA replication stress, POLD3, the human ortholog of POL32, was required for cell cycle progression and processive DNA synthesis. Segm... 2. Life forms employ different repair strategies of repair single- and double strand DNA breaks caused by different qualities of radiation: criticality of RecA mediated repair system International Nuclear Information System (INIS) Different qualities of radiation, either through direct or indirect pathway, induce qualitative different spectrum of damages in DNA, which are also different in in vitro and in vivo systems. The single- and double strand breaks of DNA are of special interest as they lead to serious biological consequences. The implications of such damage to DNA and their processing by various inherent repair pathways together decide the fate of the living form 3. Genetic and environmental influence on DNA strand break repair: a twin study DEFF Research Database (Denmark) Garm, Christian; Moreno-Villanueva, Maria; Bürkle, Alexander; 2013-01-01 Accumulation of DNA damage deriving from exogenous and endogenous sources has significant consequences for cellular survival, and is implicated in aging, cancer, and neurological diseases. Different DNA repair pathways have evolved in order to maintain genomic stability. Genetic and environmental...... factors are likely to influence DNA repair capacity. In order to gain more insight into the genetic and environmental contribution to the molecular basis of DNA repair, we have performed a human twin study, where we focused on the consequences of some of the most abundant types of DNA damage (single...... dizygotic). We did not detect genetic effects on the DNA-strand break variables in our study.... 4. DNA breaks and repair in interstitial telomere sequences: Influence of chromatin structure International Nuclear Information System (INIS) Interstitial Telomeric Sequences (ITS) are over-involved in spontaneous and radiationinduced chromosome aberrations in chinese hamster cells. We have performed a study to investigate the origin of their instability, spontaneously or after low doses irradiation. Our results demonstrate that ITS have a particular chromatin structure: short nucleotide repeat length, less compaction of the 30 nm chromatin fiber, presence of G-quadruplex structures. These features would modulate breaks production and would favour the recruitment of alternative DNA repair mechanisms, which are prone to produce chromosome aberrations. These pathways could be at the origin of chromosome aberrations in ITS whereas NHEJ and HR Double Strand Break repair pathways are rather required for a correct repair in these regions. (author) 5. Distinct spatiotemporal patterns and PARP dependence of XRCC1 recruitment to single-strand break and base excision repair NARCIS (Netherlands) A. Campalans (Anna); R. Amouroux (Rachel); H. Menoni (Hervé); W. Vermeulen (Wim); J.P. Radicella (Pablo) 2013-01-01 textabstractSingle-strand break repair (SSBR) and base excision repair (BER) of modified bases and abasic sites share several players. Among them is XRCC1, an essential scaffold protein with no enzymatic activity, required for the coordination of both pathways. XRCC1 is recruited to SSBR by PARP-1, 6. Essential Roles for Polymerase θ-Mediated End Joining in the Repair of Chromosome Breaks. Science.gov (United States) Wyatt, David W; Feng, Wanjuan; Conlin, Michael P; Yousefzadeh, Matthew J; Roberts, Steven A; Mieczkowski, Piotr; Wood, Richard D; Gupta, Gaorav P; Ramsden, Dale A 2016-08-18 DNA polymerase theta (Pol θ)-mediated end joining (TMEJ) has been implicated in the repair of chromosome breaks, but its cellular mechanism and role relative to canonical repair pathways are poorly understood. We show that it accounts for most repairs associated with microhomologies and is made efficient by coupling a microhomology search to removal of non-homologous tails and microhomology-primed synthesis across broken ends. In contrast to non-homologous end joining (NHEJ), TMEJ efficiently repairs end structures expected after aborted homology-directed repair (5' to 3' resected ends) or replication fork collapse. It typically does not compete with canonical repair pathways but, in NHEJ-deficient cells, is engaged more frequently and protects against translocation. Cell viability is also severely impaired upon combined deficiency in Pol θ and a factor that antagonizes end resection (Ku or 53BP1). TMEJ thus helps to sustain cell viability and genome stability by rescuing chromosome break repair when resection is misregulated or NHEJ is compromised. PMID:27453047 7. A single double-strand break system reveals repair dynamics and mechanisms in heterochromatin and euchromatin. Science.gov (United States) Janssen, Aniek; Breuer, Gregory A; Brinkman, Eva K; van der Meulen, Annelot I; Borden, Sean V; van Steensel, Bas; Bindra, Ranjit S; LaRocque, Jeannine R; Karpen, Gary H 2016-07-15 Repair of DNA double-strand breaks (DSBs) must be properly orchestrated in diverse chromatin regions to maintain genome stability. The choice between two main DSB repair pathways, nonhomologous end-joining (NHEJ) and homologous recombination (HR), is regulated by the cell cycle as well as chromatin context.Pericentromeric heterochromatin forms a distinct nuclear domain that is enriched for repetitive DNA sequences that pose significant challenges for genome stability. Heterochromatic DSBs display specialized temporal and spatial dynamics that differ from euchromatic DSBs. Although HR is thought to be the main pathway used to repair heterochromatic DSBs, direct tests of this hypothesis are lacking. Here, we developed an in vivo single DSB system for both heterochromatic and euchromatic loci in Drosophila melanogaster Live imaging of single DSBs in larval imaginal discs recapitulates the spatio-temporal dynamics observed for irradiation (IR)-induced breaks in cell culture. Importantly, live imaging and sequence analysis of repair products reveal that DSBs in euchromatin and heterochromatin are repaired with similar kinetics, employ both NHEJ and HR, and can use homologous chromosomes as an HR template. This direct analysis reveals important insights into heterochromatin DSB repair in animal tissues and provides a foundation for further explorations of repair mechanisms in different chromatin domains. PMID:27474442 8. Single-strand gap repair involves both RecF and RecBCD pathways. Science.gov (United States) Pagès, Vincent 2016-08-01 Homologous recombination repairs discontinuities in DNA including single-strand gaps (SSGs) and double-strand breaks (DSBs). This commentary describes how the RecBCD and RecF pathways might be exchangeable for the repair of their respective DSB and SSG canonical substrates. In particular, I will discuss how the RecBCD pathway could engage in the repair of an SSG even when the latter is not associated with a DSB. PMID:26874520 9. The Heterochromatic Barrier to DNA Double Strand Break Repair: How to Get the Entry Visa Directory of Open Access Journals (Sweden) Aaron A. Goodarzi 2012-09-01 Full Text Available Over recent decades, a deep understanding of pathways that repair DNA double strand breaks (DSB has been gained from biochemical, structural, biophysical and cellular studies. DNA non-homologous end-joining (NHEJ and homologous recombination (HR represent the two major DSB repair pathways, and both processes are now well understood. Recent work has demonstrated that the chromatin environment at a DSB significantly impacts upon DSB repair and that, moreover, dramatic modifications arise in the chromatin surrounding a DSB. Chromatin is broadly divided into open, transcriptionally active, euchromatin (EC and highly compacted, transcriptionally inert, heterochromatin (HC, although these represent extremes of a spectrum. The HC superstructure restricts both DSB repair and damage response signaling. Moreover, DSBs within HC (HC-DSBs are rapidly relocalized to the EC-HC interface. The damage response protein kinase, ataxia telangiectasia mutated (ATM, is required for HC-DSB repair but is dispensable for the relocalization of HC-DSBs. It has been proposed that ATM signaling enhances HC relaxation in the DSB vicinity and that this is a prerequisite for HC-DSB repair. Hence, ATM is essential for repair of HC-DSBs. Here, we discuss how HC impacts upon the response to DSBs and how ATM overcomes the barrier that HC poses to repair. 10. Parp1-XRCC1 and the repair of DNA double strand breaks in mouse round spermatids Energy Technology Data Exchange (ETDEWEB) Ahmed, Emad A. [Department of Endocrinology and Metabolism, Faculty of Science, Utrecht University, Padualaan 8, 3584 CH Utrecht (Netherlands); Boer, Peter de [Department of Obstetrics and Gynaecology, Radboud University Nijmegen Medical Centre, 6500 HB Nijmegen (Netherlands); Philippens, Marielle E.P.; Kal, Henk B. [Department of Radiotherapy, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX Utrecht (Netherlands); Rooij, Dirk G. de, E-mail: [email protected] [Department of Endocrinology and Metabolism, Faculty of Science, Utrecht University, Padualaan 8, 3584 CH Utrecht (Netherlands); Center for Reproductive Medicine, Academic Medical Center, University of Amsterdam, 1105 AZ Amsterdam (Netherlands) 2010-01-05 The repair of DNA double strand breaks (DSBs) in male germ cells is slower and differently regulated compared to that in somatic cells. Round spermatids show DSB repair and are radioresistant to apoptosis induction. Mutation induction studies using ionizing irradiation, indicated a high frequency of chromosome aberrations (CA) in the next generation. Since they are in a G1 comparable stage of the cell cycle, haploid spermatids are expected to repair DSBs by the non-homologous end-joining pathway (NHEJ). However, immunohistochemical evidence indicates that not all components of the classical NHEJ pathway are available since the presence of DNA-PKcs cannot be shown. Here, we demonstrate that round spermatids, as well as most other types of male germ cells express both Parp1 and XRCC1. Therefore, we have determined whether the alternative Parp1/XRCC1 dependent NHEJ pathway is active in these nuclei and also have tested for classical NHEJ activity by a genetic method. To evaluate DSB repair in SCID mice, deficient for DNA-PKcs, and to study the involvement of the Parp1/XRCC1 dependent NHEJ pathway in round spermatids, the loss of {gamma}-H2AX foci after irradiation has been determined in nucleus spreads of round spermatids of SCID mice and in nucleus spreads and histological sections of Parp1-inhibited mice and their respective controls. Results show that around half of the breaks in randomly selected round spermatids are repaired between 1 and 8 h after irradiation. The repair of 16% of the induced DSBs requires DNA-PKcs and 21% Parp1. Foci numbers in the Parp1-inhibited testes tend to be higher in spermatids of all epithelial stages reaching significance in stages I-III which indicates an active Parp1/XRCC1 pathway in round spermatids and a decreased repair capacity in later round spermatid stages. In Parp1-inhibited SCID mice only 14.5% of the breaks were repaired 8 h after irradiation indicating additivity of the two NHEJ pathways in round spermatids. 11. Complex DNA repair pathways as possible therapeutic targets to overcome temozolomide resistance in glioblastoma Directory of Open Access Journals (Sweden) Koji eYoshimoto 2012-12-01 Full Text Available Many conventional chemotherapeutic drugs exert their cytotoxic function by inducing DNA damage in the tumor cell. Therefore, a cell-inherent DNA repair pathway, which reverses the DNA-damaging effect of the cytotoxic drugs, can mediate therapeutic resistance to chemotherapy. The monofunctional DNA-alkylating agent temozolomide (TMZ is a commonly used chemotherapeutic drug and the gold standard treatment for glioblastoma. Although the activity of DNA repair protein O6-methylguanine-DNA methyltransferase (MGMT has been described as the main modulator to determine the sensitivity of glioblastoma to TMZ, a subset of glioblastoma does not respond despite MGMT inactivation, suggesting that another DNA repair mechanism may also modulate the tolerance to TMZ. Considerable interest has focused on MGMT, mismatch repair (MMR, and the base-excision repair (BER pathway in the mechanism of mediating TMZ resistance, but emerging roles for the DNA strand-break repair pathway have been demonstrated. In the first part of this review article, we briefly review the significant role of MGMT, MMR, and the BER pathway in the tolerance to TMZ; in the last part, we review the recent publications that demonstrate possible roles of DNA strand-break repair pathways, such as single-strand break (SSB repair and double-strand break (DSB repair, as well as the Fanconi anemia pathway in the repair process after alkylating agent-based therapy. It is possible that all of these repair pathways have a potential to modulate the sensitivity to TMZ and aid in overcoming the therapeutic resistance in the clinic. 12. Double-strand break repair-adox: Restoration of suppressed double-strand break repair during mitosis induces genomic instability. Science.gov (United States) Terasawa, Masahiro; Shinohara, Akira; Shinohara, Miki 2014-12-01 Double-strand breaks (DSBs) are one of the severest types of DNA damage. Unrepaired DSBs easily induce cell death and chromosome aberrations. To maintain genomic stability, cells have checkpoint and DSB repair systems to respond to DNA damage throughout most of the cell cycle. The failure of this process often results in apoptosis or genomic instability, such as aneuploidy, deletion, or translocation. Therefore, DSB repair is essential for maintenance of genomic stability. During mitosis, however, cells seem to suppress the DNA damage response and proceed to the next G1 phase, even if there are unrepaired DSBs. The biological significance of this suppression is not known. In this review, we summarize recent studies of mitotic DSB repair and discuss the mechanisms of suppression of DSB repair during mitosis. DSB repair, which maintains genomic integrity in other phases of the cell cycle, is rather toxic to cells during mitosis, often resulting in chromosome missegregation and aberration. Cells have multiple safeguards to prevent genomic instability during mitosis: inhibition of 53BP1 or BRCA1 localization to DSB sites, which is important to promote non-homologous end joining or homologous recombination, respectively, and also modulation of the non-homologous end joining core complex to inhibit DSB repair. We discuss how DSBs during mitosis are toxic and the multiple safeguard systems that suppress genomic instability. 13. Nampt is involved in DNA double-strand break repair Institute of Scientific and Technical Information of China (English) Bingtao Zhu; Xiaoli Deng; Yifan Sun; Lin Bai; Zhikai Xiahou; Yusheng Cong; Xingzhi Xu 2012-01-01 DNA double-strand break (DSB) is the most severe form of DNA damage,which is repaired mainly through high-fidelity homologous recombination (HR) or error-prone non-homologous end joining (NHEJ).Defects in the DNA damage response lead to genomic instability and ultimately predispose organs to cancer.Nicotinamide phosphoribosyltransferase (Nampt),which is involved in nicotinamide adenine dinucleotide metabolism,is overexpressed in a variety of tumors.In this report,we found that Nampt physically associated with CtlP and DNA-PKcs/Ku80,which are key factors in HR and NHEJ,respectively.Depletion of Nampt by small interfering RNA (siRNA) led to defective NHEJ-mediated DSB repair and enhanced HR-mediated repair.Furthermore,the inhibition of Nampt expression promoted proliferation of cancer cells and normal human fibroblasts and decreased β-galactosidase staining,indicating a delay in the onset of cellular senescence in normal human fibroblasts.Taken together,our results suggest that Nampt is a suppressor of HR-mediated DSB repair and an enhancer of NHEJ-mediated DSB repair,contributing to the acceleration of cellular senescence. 14. Molecular Pathways: Targeting DNA Repair Pathway Defects Enriched in Metastasis. Science.gov (United States) Corcoran, Niall M; Clarkson, Michael J; Stuchbery, Ryan; Hovens, Christopher M 2016-07-01 The maintenance of a pristine genome, free from errors, is necessary to prevent cellular transformation and degeneration. When errors in DNA are detected, DNA damage repair (DDR) genes and their regulators are activated to effect repair. When these DDR pathways are themselves mutated or aberrantly downregulated, cancer and neurodegenerative disorders can ensue. Multiple lines of evidence now indicate, however, that defects in key regulators of DNA repair pathways are highly enriched in human metastasis specimens and hence may be a key step in the acquisition of metastasis and the ability of localized disease to disseminate. Some of the key regulators of checkpoints in the DNA damage response are the TP53 protein and the PARP enzyme family. Targeting of these pathways, especially through PARP inhibition, is now being exploited therapeutically to effect significant clinical responses in subsets of individuals, particularly in patients with ovarian cancer or prostate cancer, including cancers with a marked metastatic burden. Targeting DNA repair-deficient tumors with drugs that take advantage of the fundamental differences between normal repair-proficient cells and repair-deficient tumors offers new avenues for treating advanced disease in the future. Clin Cancer Res; 22(13); 3132-7. ©2016 AACR. PMID:27169997 15. Alternative end-joining pathway(s): bricolage at DNA breaks. Science.gov (United States) Frit, Philippe; Barboule, Nadia; Yuan, Ying; Gomez, Dennis; Calsou, Patrick 2014-05-01 To cope with DNA double strand break (DSB) genotoxicity, cells have evolved two main repair pathways: homologous recombination which uses homologous DNA sequences as repair templates, and non-homologous Ku-dependent end-joining involving direct sealing of DSB ends by DNA ligase IV (Lig4). During the last two decades a third player most commonly named alternative end-joining (A-EJ) has emerged, which is defined as any Ku- or Lig4-independent end-joining process. A-EJ increasingly appears as a highly error-prone bricolage on DSBs and despite expanding exploration, it still escapes full characterization. In the present review, we discuss the mechanism and regulation of A-EJ as well as its biological relevance under physiological and pathological situations, with a particular emphasis on chromosomal instability and cancer. Whether or not it is a genuine DSB repair pathway, A-EJ is emerging as an important cellular process and understanding A-EJ will certainly be a major challenge for the coming years. PMID:24613763 16. DNA Double Strand Break Response and Limited Repair Capacity in Mouse Elongated Spermatids Directory of Open Access Journals (Sweden) 2015-12-01 Full Text Available Spermatids are extremely sensitive to genotoxic exposures since during spermiogenesis only error-prone non homologous end joining (NHEJ repair pathways are available. Hence, genomic damage may accumulate in sperm and be transmitted to the zygote. Indirect, delayed DNA fragmentation and lesions associated with apoptotic-like processes have been observed during spermatid elongation, 27 days after irradiation. The proliferating spermatogonia and early meiotic prophase cells have been suggested to retain a memory of a radiation insult leading later to this delayed fragmentation. Here, we used meiotic spread preparations to localize phosphorylate histone H2 variant (γ-H2AX foci marking DNA double strand breaks (DSBs in elongated spermatids. This technique enabled us to determine the background level of DSB foci in elongated spermatids of RAD54/RAD54B double knockout (dko mice, severe combined immunodeficiency SCID mice, and poly adenosine diphosphate (ADP-ribose polymerase 1 (PARP1 inhibitor (DPQ-treated mice to compare them with the appropriate wild type controls. The repair kinetics data and the protein expression patterns observed indicate that the conventional NHEJ repair pathway is not available for elongated spermatids to repair the programmed and the IR-induced DSBs, reflecting the limited repair capacity of these cells. However, although elongated spermatids express the proteins of the alternative NHEJ, PARP1-inhibition had no effect on the repair kinetics after IR, suggesting that DNA damage may be passed onto sperm. Finally, our genetic mutant analysis suggests that an incomplete or defective meiotic recombinational repair of Spo11-induced DSBs may lead to a carry-over of the DSB damage or induce a delayed nuclear fragmentation during the sensitive programmed chromatin remodeling occurring in elongated spermatids. 17. The Impact of Hedgehog Signaling Pathway on DNA Repair Mechanisms in Human Cancer Directory of Open Access Journals (Sweden) Erhong Meng 2015-07-01 Full Text Available Defined cellular mechanisms have evolved that recognize and repair DNA to protect the integrity of its structure and sequence when encountering assaults from endogenous and exogenous sources. There are five major DNA repair pathways: mismatch repair, nucleotide excision repair, direct repair, base excision repair and DNA double strand break repair (including non-homologous end joining and homologous recombination repair. Aberrant activation of the Hedgehog (Hh signaling pathway is a feature of many cancer types. The Hh pathway has been documented to be indispensable for epithelial-mesenchymal transition, invasion and metastasis, cancer stemness, and chemoresistance. The functional transcription activators of the Hh pathway include the GLI proteins. Inhibition of the activity of GLI can interfere with almost all DNA repair types in human cancer, indicating that Hh/GLI functions may play an important role in enabling tumor cells to survive lethal types of DNA damage induced by chemotherapy and radiotherapy. Thus, Hh signaling presents an important therapeutic target to overcome DNA repair-enabled multi-drug resistance and consequently increase chemotherapeutic response in the treatment of cancer. 18. The Impact of Hedgehog Signaling Pathway on DNA Repair Mechanisms in Human Cancer Energy Technology Data Exchange (ETDEWEB) Meng, Erhong; Hanna, Ann; Samant, Rajeev S.; Shevde, Lalita A., E-mail: [email protected] [Department of Pathology, Comprehensive Cancer Center, University of Alabama at Birmingham, WTI320D, 1824 6th Avenue South, Birmingham, AL 35233 (United States) 2015-07-21 Defined cellular mechanisms have evolved that recognize and repair DNA to protect the integrity of its structure and sequence when encountering assaults from endogenous and exogenous sources. There are five major DNA repair pathways: mismatch repair, nucleotide excision repair, direct repair, base excision repair and DNA double strand break repair (including non-homologous end joining and homologous recombination repair). Aberrant activation of the Hedgehog (Hh) signaling pathway is a feature of many cancer types. The Hh pathway has been documented to be indispensable for epithelial-mesenchymal transition, invasion and metastasis, cancer stemness, and chemoresistance. The functional transcription activators of the Hh pathway include the GLI proteins. Inhibition of the activity of GLI can interfere with almost all DNA repair types in human cancer, indicating that Hh/GLI functions may play an important role in enabling tumor cells to survive lethal types of DNA damage induced by chemotherapy and radiotherapy. Thus, Hh signaling presents an important therapeutic target to overcome DNA repair-enabled multi-drug resistance and consequently increase chemotherapeutic response in the treatment of cancer. 19. The Impact of Hedgehog Signaling Pathway on DNA Repair Mechanisms in Human Cancer International Nuclear Information System (INIS) Defined cellular mechanisms have evolved that recognize and repair DNA to protect the integrity of its structure and sequence when encountering assaults from endogenous and exogenous sources. There are five major DNA repair pathways: mismatch repair, nucleotide excision repair, direct repair, base excision repair and DNA double strand break repair (including non-homologous end joining and homologous recombination repair). Aberrant activation of the Hedgehog (Hh) signaling pathway is a feature of many cancer types. The Hh pathway has been documented to be indispensable for epithelial-mesenchymal transition, invasion and metastasis, cancer stemness, and chemoresistance. The functional transcription activators of the Hh pathway include the GLI proteins. Inhibition of the activity of GLI can interfere with almost all DNA repair types in human cancer, indicating that Hh/GLI functions may play an important role in enabling tumor cells to survive lethal types of DNA damage induced by chemotherapy and radiotherapy. Thus, Hh signaling presents an important therapeutic target to overcome DNA repair-enabled multi-drug resistance and consequently increase chemotherapeutic response in the treatment of cancer 20. Lack of dependence on p53 for DNA double strand break repair of episomal vectors in human lymphoblasts Science.gov (United States) Kohli, M.; Jorgensen, T. J. 1999-01-01 The p53 tumor suppressor gene has been shown to be involved in a variety of repair processes, and recent findings have suggested that p53 may be involved in DNA double strand break repair in irradiated cells. The role of p53 in DNA double strand break repair, however, has not been fully investigated. In this study, we have constructed a novel Epstein-Barr virus (EBV)-based shuttle vector, designated as pZEBNA, to explore the influence of p53 on DNA strand break repair in human lymphoblasts, since EBV-based vectors do not inactivate the p53 pathway. We have compared plasmid survival of irradiated, restriction enzyme linearized, and calf intestinal alkaline phosphatase (CIP)-treated pZEBNA with a Simian virus 40 (SV40)-based shuttle vector, pZ189, in TK6 (wild-type p53) and WTK1 (mutant p53) lymphoblasts and determined that p53 does not modulate DNA double strand break repair in these cell lines. Copyright 1999 Academic Press. 1. A new powerful method for site-specific transgene stabilization based on chromosomal double-strand break repair. Directory of Open Access Journals (Sweden) Artem Tkachuk Full Text Available Transgenic insects are a promising tool in sterile insect techniques and population replacement strategies. Such transgenic insects can be created using nonautonomous transposons, which cannot be transferred without a transposase source. In biocontrol procedures where large numbers of insects are released, there is increased risk of transgene remobilization caused by external transposase sources that can alter the characteristics of the transgenic organisms lead horizontal transgene transfer to other species. Here we describe a novel, effective method for transgene stabilization based on the introduction of directed double-strand breaks (DSB into a genome-integrated sequence and their subsequent repair by the single-strand annealing (SSA pathway. Due to the construct's organization, the repair pathway is predictable, such that all transposon and marker sequences can be deleted, while preserving integration of exogenous DNA in the genome. The exceptional conservation of DNA repair pathways makes this method suitable for a broad range of organisms. 2. A New Powerful Method for Site-Specific Transgene Stabilization Based on Chromosomal Double-Strand Break Repair Science.gov (United States) Kravchuk, Oksana; Savitsky, Mikhail 2011-01-01 Transgenic insects are a promising tool in sterile insect techniques and population replacement strategies. Such transgenic insects can be created using nonautonomous transposons, which cannot be transferred without a transposase source. In biocontrol procedures where large numbers of insects are released, there is increased risk of transgene remobilization caused by external transposase sources that can alter the characteristics of the transgenic organisms lead horizontal transgene transfer to other species. Here we describe a novel, effective method for transgene stabilization based on the introduction of directed double-strand breaks (DSB) into a genome-integrated sequence and their subsequent repair by the single-strand annealing (SSA) pathway. Due to the construct's organization, the repair pathway is predictable, such that all transposon and marker sequences can be deleted, while preserving integration of exogenous DNA in the genome. The exceptional conservation of DNA repair pathways makes this method suitable for a broad range of organisms. PMID:22022613 3. Sibling rivalry: competition between Pol X family members in V(D)J recombination and general double strand break repair. Science.gov (United States) Nick McElhinny, Stephanie A; Ramsden, Dale A 2004-08-01 The nonhomologous end-joining pathway is a major means for repairing double-strand breaks (DSBs) in all mitotic cell types. This repair pathway is also the only efficient means for resolving DSB intermediates in V(D)J recombination, a lymphocyte-specific genome rearrangement required for assembly of antigen receptors. A role for polymerases in end-joining has been well established. They are a major factor in determining the character of repair junctions but, in contrast to 'core' end-joining factors, typically appear to have a subtle impact on the efficiency of end-joining. Recent work implicates several members of the Pol X family in end-joining and suggests surprising complexity in the control of how these different polymerases are employed in this pathway. PMID:15242403 4. Split-dose recovery is due to the repair of DNA double-strand breaks International Nuclear Information System (INIS) DNA double-strand breaks are the molecular lesions the repair of which leads to the reappearance of the shoulder observed in split-dose experiments. This conclusion is based on results obtained with the help of a diploid yeast mutant rad54-3 which is temperature-conditional for the repair of DNA double-strand breaks. Two repair steps must be met to yield the reappearance of the shoulder on a split-dose survival curve: the repair of double-strand breaks during the interval between two doses and on the nutrient agar plate after the second dose. In yeast lethality may be attributable to either an unrepaired double-strand break (i.e. a double-strand break is a potentially lethal lesion) or to the interaction of two double-strand breaks (misrepair of double-strand breaks). Evidence is presented that the two cellular phenomena of liquid holding recovery (repair of potentially lethal damage) and of split-dose recovery (repair of sublethal damage) are based on the repair of the same molecular lesion, the DNA double-strand break. (author) 5. Rtt107 phosphorylation promotes localisation to DNA double-stranded breaks (DSBs and recombinational repair between sister chromatids. Directory of Open Access Journals (Sweden) Pranav Ullal Full Text Available Efficient repair of DNA double-stranded breaks (DSB requires a coordinated response at the site of lesion. Nucleolytic resection commits repair towards homologous recombination, which preferentially occurs between sister chromatids. DSB resection promotes recruitment of the Mec1 checkpoint kinase to the break. Rtt107 is a target of Mec1 and serves as a scaffold during repair. Rtt107 plays an important role during rescue of damaged replication forks, however whether Rtt107 contributes to the repair of DSBs is unknown. Here we show that Rtt107 is recruited to DSBs induced by the HO endonuclease. Rtt107 phosphorylation by Mec1 and its interaction with the Smc5-Smc6 complex are both required for Rtt107 loading to breaks, while Rtt107 regulators Slx4 and Rtt101 are not. We demonstrate that Rtt107 has an effect on the efficiency of sister chromatid recombination (SCR and propose that its recruitment to DSBs, together with the Smc5-Smc6 complex is important for repair through the SCR pathway. 6. Detection and Repair of Ionizing Radiation-Induced DNA Double Strand Breaks: New Developments in Nonhomologous End Joining International Nuclear Information System (INIS) DNA damage can occur as a result of endogenous metabolic reactions and replication stress or from exogenous sources such as radiation therapy and chemotherapy. DNA double strand breaks are the most cytotoxic form of DNA damage, and defects in their repair can result in genome instability, a hallmark of cancer. The major pathway for the repair of ionizing radiation-induced DSBs in human cells is nonhomologous end joining. Here we review recent advances on the mechanism of nonhomologous end joining, as well as new findings on its component proteins and regulation 7. Induction and repair of DNA strand breaks in human tumor cells International Nuclear Information System (INIS) The presence of radioresistant or repair-proficient cells in a tumor is often associated with radiotherapy failure. The authors have begun to study the mechanisms of resistance in these tumor cells. Their initial studies focused on the induction and repair of DNA strand breaks as measured by DNA elution. Eight human tumor (5 squamous cell carcinomas, 2 melanomas, and 1 adenocarcinoma) and 2 nonmalignant cell lines have been examined. Their D/sub O/s range from 1.07 Gy to 2.81 Gy while their extrapolation numbers (n) range from 1.2 to 24.8. Three parameters are being investigated for X-ray-induced DNA single and double-strand breaks; 1) the initial number of breaks induced, 2) the residual DNA strand break frequency and 3) the time to repair 50% of the lesions. The kinetics of repair of DNA single-strand breaks were similar for all the lines studied. In 2 cases, radiosensitivity was associated with either a high residual DNA strand break frequency or a slower rate of repair. No single parameter or combination of parameters, however, consistently correlated with radiosensitivity or n. Thus, while differences in the induction and repair of DNA single-strand breaks might explain some of the observed differences in radiation responses, they are in general a poor predictor radiation sensitivity 8. Development of Novel Visual-Plus Quantitative Analysis Systems for Studying DNA Double-Strand Break Repairs in Zebrafish Institute of Scientific and Technical Information of China (English) Jingang Liu; Lu Gong; Changqing Chang; Cong Liu; Jinrong Peng; Jun Chen 2012-01-01 The use of reporter systems to analyze DNA double-strand break (DSB) repairs,based on the enhanced green fluorescent protein (EGFP) and meganuclease such as I-Sce Ⅰ,is usually carried out with cell lines.In this study,we developed three visual-plus quantitative assay systems for homologous recombination (HR),non-homologous end joining (NHEJ) and single-strand annealing (SSA) DSB repair pathways at the organismal level in zebrafish embryos.To initiate DNA DSB repair,we used two I-Sce Ⅰ recognition sites in opposite orientation rather than the usual single site.The NHEJ,HR and SSA repair pathways were separately triggered by the injection of three corresponding I-Sce I-cut constructions,and the repair of DNA lesion caused by I-Sce Ⅰ could be tracked by EGFP expression in the embryos.Apart from monitoring the intensity of green fluorescence,the repair frequencies could also be precisely measured by quantitative real-time polymerase chain reaction (qPCR).Analysis of DNA sequences at the DSB sites showed that NHEJ was predominant among these three repair pathways in zebrafish embryos.Furthermore,while HR and SSA reporter systems could be effectively decreased by the knockdown of rad51 and rad52,respectively,NHEJ could only be impaired by the knockdown of ligaseⅣ (lig4) when the NHEJ construct was cut by I-Sce Ⅰ in vivo.More interestingly,blocking NHEJ with lig4-MO increased the frequency of HR,but decreased the frequency of SSA.Our studies demonstrate that the major mechanisms used to repair DNA DSBs are conserved from zebrafish to mammal,and zebrafish provides an excellent model for studying and manipulating DNA DSB repair at the organismal level. 9. JNK Phosphorylates SIRT6 to Stimulate DNA Double-Strand Break Repair in Response to Oxidative Stress by Recruiting PARP1 to DNA Breaks. Science.gov (United States) Van Meter, Michael; Simon, Matthew; Tombline, Gregory; May, Alfred; Morello, Timothy D; Hubbard, Basil P; Bredbenner, Katie; Park, Rosa; Sinclair, David A; Bohr, Vilhelm A; Gorbunova, Vera; Seluanov, Andrei 2016-09-01 The accumulation of damage caused by oxidative stress has been linked to aging and to the etiology of numerous age-related diseases. The longevity gene, sirtuin 6 (SIRT6), promotes genome stability by facilitating DNA repair, especially under oxidative stress conditions. Here we uncover the mechanism by which SIRT6 is activated by oxidative stress to promote DNA double-strand break (DSB) repair. We show that the stress-activated protein kinase, c-Jun N-terminal kinase (JNK), phosphorylates SIRT6 on serine 10 in response to oxidative stress. This post-translational modification facilitates the mobilization of SIRT6 to DNA damage sites and is required for efficient recruitment of poly (ADP-ribose) polymerase 1 (PARP1) to DNA break sites and for efficient repair of DSBs. Our results demonstrate a post-translational mechanism regulating SIRT6, and they provide the link between oxidative stress signaling and DNA repair pathways that may be critical for hormetic response and longevity assurance. PMID:27568560 10. JNK Phosphorylates SIRT6 to Stimulate DNA Double-Strand Break Repair in Response to Oxidative Stress by Recruiting PARP1 to DNA Breaks Directory of Open Access Journals (Sweden) Michael Van Meter 2016-09-01 Full Text Available The accumulation of damage caused by oxidative stress has been linked to aging and to the etiology of numerous age-related diseases. The longevity gene, sirtuin 6 (SIRT6, promotes genome stability by facilitating DNA repair, especially under oxidative stress conditions. Here we uncover the mechanism by which SIRT6 is activated by oxidative stress to promote DNA double-strand break (DSB repair. We show that the stress-activated protein kinase, c-Jun N-terminal kinase (JNK, phosphorylates SIRT6 on serine 10 in response to oxidative stress. This post-translational modification facilitates the mobilization of SIRT6 to DNA damage sites and is required for efficient recruitment of poly (ADP-ribose polymerase 1 (PARP1 to DNA break sites and for efficient repair of DSBs. Our results demonstrate a post-translational mechanism regulating SIRT6, and they provide the link between oxidative stress signaling and DNA repair pathways that may be critical for hormetic response and longevity assurance. 11. Ultrafast chemical repair of DNA single and double strand break precursors in irradiated V79 cells International Nuclear Information System (INIS) The fast kinetics of reactions of free radical precursors of DNA single strand breaks (ssb) and double strand breaks (dsb) have been determined in Chinese hamster V79 cells by fast mixing and irradiation methods using the alkaline unwinding technique to assay breaks. Fast chemical repair of oxygen-dependent ssb and dsb precursors was observed and approached completion within 10 to 20 ms of irradiation. Treatment of cells with the glutathione synthesis blocking agent, buthionine sulphoximine, showed that approximately half of the chemical repair was attributable to intracellular non-protein thiols. The nature of the residual repair is obscure, but it is apparently not attributable to non-protein thiols. Similar repair rates and thiol dependences were also found for cell kill. With all three endpoints, oxygen competes with and blocks the chemical repair. 36 refs., 6 figs., 1 tab 12. c-Myc Suppression of DNA Double-strand Break Repair Directory of Open Access Journals (Sweden) Zhaozhong Li 2012-12-01 Full Text Available c-Myc is a transcriptional factor that functions as a central regulator of cell growth, proliferation, and apoptosis. Overexpression of c-Myc also enhances DNA double-strand breaks (DSBs, genetic instability, and tumorigenesis. However, the mechanism(s involved remains elusive. Here, we discovered that γ-ray ionizing radiation-induced DSBs promote c-Myc to form foci and to co-localize with γ-H2AX. Conditional expression of c-Myc in HO15.19 c-Myc null cells using the Tet-Off/Tet-On inducible system results in down-regulation of Ku DNA binding and suppressed activities of DNA-dependent protein kinase catalytic subunit (DNA-PKcs and DNA end-joining, leading to inhibition of DSB repair and enhanced chromosomal and chromatid breaks. Expression of c-Myc reduces both signal and coding joins with decreased fidelity during V(DJ recombination. Mechanistically, c-Myc directly interacts with Ku70 protein through its Myc box II (MBII domain. Removal of the MBII domain from c-Myc abrogates its inhibitory effects on Ku DNA binding, DNA-PKcs, and DNA end-joining activities, which results in loss of c-Myc's ability to block DSB repair and V(DJ recombination. Interestingly, c-Myc directly disrupts the Ku/DNA-PKcs complex in vitro and in vivo. Thus, c-Myc suppression of DSB repair and V(DJ recombination may occur through inhibition of the nonhomologous end-joining pathway, which provides insight into the mechanism of c-Myc in the development of tumors through promotion of genomic instability. 13. Repair of near-UV (365nm or 313 nm) induced DNA strand breaks International Nuclear Information System (INIS) The action of near-UV (365 nm or 313 nm) radiation in cellular inactivaton (biological measurements) and induction and repair of breaks (physical measurements) is studied in repair proficient strain and in pol A, rec A and uvr A deficient strains of Escherichia coli K-12. (M.A.C.) 14. A role for small RNAs in DNA double-strand break repair DEFF Research Database (Denmark) Wei, W.; Ba, Z.; Wu, Y.; 2012-01-01 Eukaryotes have evolved complex mechanisms to repair DNA double-strand breaks (DSBs) through coordinated actions of protein sensors, transducers, and effectors. Here we show that ∼21-nucleotide small RNAs are produced from the sequences in the vicinity of DSB sites in Arabidopsis and in human cel...... of protein complexes to DSB sites to facilitate repair. © 2012 Elsevier Inc.... 15. Colocalization of multiple DNA double-strand breaks at a single Rad52 repair centre DEFF Research Database (Denmark) Lisby, M.; Mortensen, Uffe Hasbro; Rothstein, R. 2003-01-01 DNA double-strand break repair (DSBR) is an essential process for preserving genomic integrity in all organisms. To investigate this process at the cellular level, we engineered a system of fluorescently marked DNA double-strand breaks (DSBs) in the yeast Saccharomyces cerevisiae to visualize in... 16. DNA Ligase IV and Artemis Act Cooperatively to Suppress Homologous Recombination in Human Cells: Implications for DNA Double-Strand Break Repair OpenAIRE Aya Kurosawa; Shinta Saito; Sairei So; Mitsumasa Hashimoto; Kuniyoshi Iwabuchi; Haruka Watabe; Noritaka Adachi 2013-01-01 Nonhomologous end-joining (NHEJ) and homologous recombination (HR) are two major pathways for repairing DNA double-strand breaks (DSBs); however, their respective roles in human somatic cells remain to be elucidated. Here we show using a series of human gene-knockout cell lines that NHEJ repairs nearly all of the topoisomerase II- and low-dose radiation-induced DNA damage, while it negatively affects survival of cells harbouring replication-associated DSBs. Intriguingly, we find that loss of ... 17. Repair and gamma radiation-induced single- and double-strand breaks in DNA of Escherichia coli International Nuclear Information System (INIS) Studies in the kinetics of repair of γ-radiation-induced single- and double-strand breaks in DNA of E. coli cells showed that double-strand DNA breaks are rejoined by the following two ways. The first way is conditioned by repair of single-strand breaks and represents the repair of ''oblique'' double-strand breaks in DNA, whereas the second way is conditioned by functioning of the recombination mechanisms and, to all appearance, represents the repair of ''direct'' double-strand breaks in DNA 18. Numt-mediated double-strand break repair mitigates deletions during primate genome evolution. Directory of Open Access Journals (Sweden) Einat Hazkani-Covo 2008-10-01 Full Text Available Non-homologous end joining (NHEJ is the major mechanism of double-strand break repair (DSBR in mammalian cells. NHEJ has traditionally been inferred from experimental systems involving induced double strand breaks (DSBs. Whether or not the spectrum of repair events observed in experimental NHEJ reflects the repair of natural breaks by NHEJ during chromosomal evolution is an unresolved issue. In primate phylogeny, nuclear DNA sequences of mitochondrial origin, numts, are inserted into naturally occurring chromosomal breaks via NHEJ. Thus, numt integration sites harbor evidence for the mechanisms that act on the genome over evolutionary timescales. We have identified 35 and 55 lineage-specific numts in the human and chimpanzee genomes, respectively, using the rhesus monkey genome as an outgroup. One hundred and fifty two numt-chromosome fusion points were classified based on their repair patterns. Repair involving microhomology and repair leading to nucleotide additions were detected. These repair patterns are within the experimentally determined spectrum of classical NHEJ, suggesting that information from experimental systems is representative of broader genetic loci and end configurations. However, in incompatible DSBR events, small deletions always occur, whereas in 54% of numt integration events examined, no deletions were detected. Numts show a statistically significant reduction in deletion frequency, even in comparison to DSBR involving filler DNA. Therefore, numts show a unique mechanism of integration via NHEJ. Since the deletion frequency during numt insertion is low, native overhangs of chromosome breaks are preserved, allowing us to determine that 24% of the analyzed breaks are cohesive with overhangs of up to 11 bases. These data represent, to the best of our knowledge, the most comprehensive description of the structure of naturally occurring DSBs. We suggest a model in which the sealing of DSBs by numts, and probably by other filler 19. Reduced Activity of Double-Strand Break Repair Genes in Prostate Cancer Patients With Late Normal Tissue Radiation Toxicity Energy Technology Data Exchange (ETDEWEB) 2014-03-01 20. Chromosomal Integrity after UV Irradiation Requires FANCD2-Mediated Repair of Double Strand Breaks Science.gov (United States) Federico, María Belén; Vallerga, María Belén; Radl, Analía; Paviolo, Natalia Soledad; Bocco, José Luis; Di Giorgio, Marina; Soria, Gastón; Gottifredi, Vanesa 2016-01-01 Fanconi Anemia (FA) is a rare autosomal recessive disorder characterized by hypersensitivity to inter-strand crosslinks (ICLs). FANCD2, a central factor of the FA pathway, is essential for the repair of double strand breaks (DSBs) generated during fork collapse at ICLs. While lesions different from ICLs can also trigger fork collapse, the contribution of FANCD2 to the resolution of replication-coupled DSBs generated independently from ICLs is unknown. Intriguingly, FANCD2 is readily activated after UV irradiation, a DNA-damaging agent that generates predominantly intra-strand crosslinks but not ICLs. Hence, UV irradiation is an ideal tool to explore the contribution of FANCD2 to the DNA damage response triggered by DNA lesions other than ICL repair. Here we show that, in contrast to ICL-causing agents, UV radiation compromises cell survival independently from FANCD2. In agreement, FANCD2 depletion does not increase the amount of DSBs generated during the replication of UV-damaged DNA and is dispensable for UV-induced checkpoint activation. Remarkably however, FANCD2 protects UV-dependent, replication-coupled DSBs from aberrant processing by non-homologous end joining, preventing the accumulation of micronuclei and chromatid aberrations including non-homologous chromatid exchanges. Hence, while dispensable for cell survival, FANCD2 selectively safeguards chromosomal stability after UV-triggered replication stress. PMID:26765540 1. Writers, Readers, and Erasers of Histone Ubiquitylation in DNA Double-Strand Break Repair DEFF Research Database (Denmark) Smeenk, Godelieve; Mailand, Niels 2016-01-01 DNA double-strand breaks (DSBs) are highly cytotoxic DNA lesions, whose faulty repair may alter the content and organization of cellular genomes. To counteract this threat, numerous signaling and repair proteins are recruited hierarchically to the chromatin areas surrounding DSBs to facilitate...... accurate lesion repair and restoration of genome integrity. In vertebrate cells, ubiquitin-dependent modifications of histones adjacent to DSBs by RNF8, RNF168, and other ubiquitin ligases have a key role in promoting the assembly of repair protein complexes, serving as direct recruitment platforms for a...... integrity, as well as cell and organismal fitness.... 2. Differential requirement for SUB1 in chromosomal and plasmid double-strand DNA break repair. Directory of Open Access Journals (Sweden) Lijian Yu Full Text Available Non homologous end joining (NHEJ is an important process that repairs double strand DNA breaks (DSBs in eukaryotic cells. Cells defective in NHEJ are unable to join chromosomal breaks. Two different NHEJ assays are typically used to determine the efficiency of NHEJ. One requires NHEJ of linearized plasmid DNA transformed into the test organism; the other requires NHEJ of a single chromosomal break induced either by HO endonuclease or the I-SceI restriction enzyme. These two assays are generally considered equivalent and rely on the same set of NHEJ genes. PC4 is an abundant DNA binding protein that has been suggested to stimulate NHEJ. Here we tested the role of PC4's yeast homolog SUB1 in repair of DNA double strand breaks using different assays. We found SUB1 is required for NHEJ repair of DSBs in plasmid DNA, but not in chromosomal DNA. Our results suggest that these two assays, while similar are not equivalent and that repair of plasmid DNA requires additional factor(s that are not required for NHEJ repair of chromosomal double-strand DNA breaks. Possible roles for Sub1 proteins in NHEJ of plasmid DNA are discussed. 3. How to Relate Complex DNA Repair Genotypes to Pathway Function and, Ultimately, Health Risk Energy Technology Data Exchange (ETDEWEB) Jones, IM 2002-01-09 Exposure to ionizing radiation increases the incidence of cancer. However, predicting which individuals are at most risk from radiation exposure is a distant goal. Predictive ability is needed to guide policies that regulate radiation exposure and ensure that medical treatments have maximum benefit and minimum risk. Differences between people in susceptibility to radiation are largely based on their genotype, the genes inherited from their parents. Among the important genes are those that produce proteins that repair DNA damaged by radiation. Base Excision Repair (BER) proteins repair single strand breaks and oxidized bases in DNA. Double Strand Break Repair proteins repair broken chromosomes. Using technologies and information from the Human Genome Project, we have previously determined that the DNA sequence of DNA repair genes varies within the human population. An average of 3-4 different variants were found that affect the protein for each of 37 genes studied. The average frequency of these variants is 5%. Given the many genes in each DNA repair pathway and their many variants, technical ability to determine an individual's repair genotype greatly exceeds ability to interpret the information. A long-term goal is to relate DNA repair genotypes to health risk from radiation. This study focused on the BER pathway. The BER genes are known, variants of the genes have been identified at LLNL, and LLNL had recently developed an assay for BER function using white blood cells. The goal of this initial effort was to begin developing data that could be used to test the hypothesis that many different genotypes have similar DNA repair capacity phenotypes (function). Relationships between genotype and phenotype could then be used to group genotypes with similar function and ultimately test the association of groups of genotypes with health risk from radiation. Genotypes with reduced repair function are expected to increase risk of radiation-induced health effects. The 4. An inverse switch in DNA base excision and strand break repair contributes to melphalan resistance in multiple myeloma cells. Directory of Open Access Journals (Sweden) Mirta M L Sousa Full Text Available Alterations in checkpoint and DNA repair pathways may provide adaptive mechanisms contributing to acquired drug resistance. Here, we investigated the levels of proteins mediating DNA damage signaling and -repair in RPMI8226 multiple myeloma cells and its Melphalan-resistant derivative 8226-LR5. We observed markedly reduced steady-state levels of DNA glycosylases UNG2, NEIL1 and MPG in the resistant cells and cross-resistance to agents inducing their respective DNA base lesions. Conversely, repair of alkali-labile sites was apparently enhanced in the resistant cells, as substantiated by alkaline comet assay, autoribosylation of PARP-1, and increased sensitivity to PARP-1 inhibition by 4-AN or KU58684. Reduced base-excision and enhanced single-strand break repair would both contribute to the observed reduction in genomic alkali-labile sites, which could jeopardize productive processing of the more cytotoxic Melphalan-induced interstrand DNA crosslinks (ICLs. Furthermore, we found a marked upregulation of proteins in the non-homologous end-joining (NHEJ pathway of double-strand break (DSB repair, likely contributing to the observed increase in DSB repair kinetics in the resistant cells. Finally, we observed apparent upregulation of ATR-signaling and downregulation of ATM-signaling in the resistant cells. This was accompanied by markedly increased sensitivity towards Melphalan in the presence of ATR-, DNA-PK, or CHK1/2 inhibitors whereas no sensitizing effect was observed subsequent to ATM inhibition, suggesting that replication blocking lesions are primary triggers of the DNA damage response in the Melphalan resistant cells. In conclusion, Melphalan resistance is apparently contributed by modulation of the DNA damage response at multiple levels, including downregulation of specific repair pathways to avoid repair intermediates that could impair efficient processing of cytotoxic ICLs and ICL-induced DSBs. This study has revealed several novel 5. Repair of X-ray-induced single-strand breaks by a cell-free system International Nuclear Information System (INIS) Repair of X-ray-induced single-strand breaks of DNA was studied in vitro using an exonuclease purified from mouse ascites sarcoma (SR-C3H/He) cells. X-ray-dose-dependent unscheduled DNA synthesis was primed by the exonuclease. Repair of X-ray-induced single-strand breaks in pUC19 plasmid DNA was demonstrated by agarose gel electrophoresis after incubating the damaged DNA with the exonuclease, DNA polymerase (Klenow fragment of DNA polymerase I or DNA polymerase β purified from SR-C3H/He cells), four deoxynucleoside triphosphates, ATP and DNA ligase (T4 DNA ligase or DNA ligase I purified from calf thymus). The present results suggested that the exonuclease is involved in the initiation of repair of X-ray-induced single-strand breaks in removing 3' ends of X-ray-damaged DNA. (author) 6. The Caenorhabditis elegans homolog of Gen1/Yen1 resolvases links DNA damage signaling to DNA double-strand break repair. Directory of Open Access Journals (Sweden) Aymeric P Bailly 2010-07-01 Full Text Available DNA double-strand breaks (DSBs can be repaired by homologous recombination (HR, which can involve Holliday junction (HJ intermediates that are ultimately resolved by nucleolytic enzymes. An N-terminal fragment of human GEN1 has recently been shown to act as a Holliday junction resolvase, but little is known about the role of GEN-1 in vivo. Holliday junction resolution signifies the completion of DNA repair, a step that may be coupled to signaling proteins that regulate cell cycle progression in response to DNA damage. Using forward genetic approaches, we identified a Caenorhabditis elegans dual function DNA double-strand break repair and DNA damage signaling protein orthologous to the human GEN1 Holliday junction resolving enzyme. GEN-1 has biochemical activities related to the human enzyme and facilitates repair of DNA double-strand breaks, but is not essential for DNA double-strand break repair during meiotic recombination. Mutational analysis reveals that the DNA damage-signaling function of GEN-1 is separable from its role in DNA repair. GEN-1 promotes germ cell cycle arrest and apoptosis via a pathway that acts in parallel to the canonical DNA damage response pathway mediated by RPA loading, CHK1 activation, and CEP-1/p53-mediated apoptosis induction. Furthermore, GEN-1 acts redundantly with the 9-1-1 complex to ensure genome stability. Our study suggests that GEN-1 might act as a dual function Holliday junction resolvase that may coordinate DNA damage signaling with a late step in DNA double-strand break repair. 7. XLS (c9orf142) is a new component of mammalian DNA double-stranded break repair OpenAIRE Craxton, A; J. Somers; Munnur, D; Jukes-Jones, R; Cain, K.; Malewicz, M 2015-01-01 Repair of double-stranded DNA breaks (DSBs) in mammalian cells primarily occurs by the non-homologous end-joining (NHEJ) pathway, which requires seven core proteins (Ku70/Ku86, DNA-PKcs (DNA-dependent protein kinase catalytic subunit), Artemis, XRCC4-like factor (XLF), XRCC4 and DNA ligase IV). Here we show using combined affinity purification and mass spectrometry that DNA-PKcs co-purifies with all known core NHEJ factors. Furthermore, we have identified a novel evolutionary conserved protei... 8. A comparative analysis of the DNA recombination repair pathway in mycobacterial genomes. Science.gov (United States) Singh, Amandeep; Bhagavat, Raghu; Vijayan, M; Chandra, Nagasuma 2016-07-01 In prokaryotes, repair by homologous recombination provides a major means to reinstate the genetic information lost in DNA damage. Recombination repair pathway in mycobacteria has multiple differences as compared to that in Escherichia coli. Of about 20 proteins known to be involved in the pathway, a set of 9 proteins, namely, RecF, RecO, RecR, RecA, SSBa, RuvA, RuvB and RuvC was found to be indispensable among the 43 mycobacterial strains. A domain level analysis indicated that most domains involved in recombination repair are unique to these proteins and are present as single copies in the genomes. Synteny analysis reveals that the gene order of proteins involved in the pathway is not conserved, suggesting that they may be regulated differently in different species. Sequence conservation among the same protein from different strains suggests the importance of RecO-RecA and RecFOR-RecA presynaptic pathways in the repair of double strand-breaks and single strand-breaks respectively. New annotations obtained from the analysis, include identification of a protein with a probable Holliday junction binding role present in 41 mycobacterial genomes and that of a RecB-like nuclease, containing a cas4 domain, present in 42 genomes. New insights into the binding of small molecules to the relevant proteins are provided by binding pocket analysis using three dimensional structural models. Analysis of the various features of the recombination repair pathway, presented here, is likely to provide a framework for further exploring stress response and emergence of drug resistance in mycobacteria. PMID:27450012 9. Modeling the repair of DNA strand breaks caused by γ-radiation in a minichromosome International Nuclear Information System (INIS) The objective of the studies described here was the development of a mathematical model which would fit experimental data for the repair of single and double strand breaks induced in DNA in living cells by exposure to ionizing radiation, and which would allow to better understand the processes of DNA repair. DNA breaks are believed to play the major role in radiation-induced lethality and formation of chromosome deletions, and are therefore crucial to the response of cells to radiotherapy. In an initial model which we reported on the basis of data for the repair of Epstein–Barr minichromosomes in irradiated Raji cells, we assumed that DNA breaks are induced only at the moment of irradiation and are later removed by repair systems. This work gives a development of that mathematical model which fits the experimental results more precisely and suggests strongly that DNA breaks are generated not only by direct irradiation but also later, probably by systems engaged in repair of oxidative damage. (paper) 10. The role of homologous recombination in mitotic and meiotic double-strand break repair OpenAIRE 2007-01-01 All organisms are composed of cells and the cell’s nucleus contains DNA. The induction of DNA damage is a threat to organisms. Signalling of DNA damage and subsequent repair is of substantial importance. Double-strand breaks (DSBs) in DNA can be induced by ionising radiation and DNA damaging agents but also arise as intermediates in several cellular processes (e.g. meiosis). DSBs are among the most genotoxic DNA lesions and their accurate repair is crucial. Genetic instability resulting from ... 11. RecA bundles mediate homology pairing between distant sisters during DNA break repair OpenAIRE Lesterlin, Christian; Ball, Graeme; Schermelleh, Lothar; Sherratt, David J. 2013-01-01 DNA double-strand break (DSB) repair by homologous recombination (HR) has evolved to maintain genetic integrity in all organisms 1 . Although many reactions that occur during HR are known 1-3 , it is unclear where, when and how they occur in cells is lacking. Here, by using conventional and super-resolution microscopy we describe the progression of DSB repair in live Escherichia coli. Specifically, we investigate whether HR can occur efficiently between distant sister loci that have segregate... 12. FEN1 participates in repair of the 5'-phosphotyrosyl terminus of DNA single-strand breaks. Science.gov (United States) Kametani, Yukiko; Takahata, Chiaki; Narita, Takashi; Tanaka, Kiyoji; Iwai, Shigenori; Kuraoka, Isao 2016-01-01 Etoposide is a widely used anticancer drug and a DNA topoisomerase II (Top2) inhibitor. Etoposide produces Top2-attached single-strand breaks (Top2-SSB complex) and double-strand breaks (Top2-DSB complex) that are thought to induce cell death in tumor cells. The Top2-SSB complex is more abundant than the Top2-DSB complex. Human tyrosyl-DNA phosphodiesterase 2 (TDP2) is required for efficient repair of Top2-DSB complexes. However, the identities of the proteins involved in the repair of Top2-SSB complexes are unknown, although yeast genetic data indicate that 5' to 3' structure-specific DNA endonuclease activity is required for alternative repair of Top2 DNA damage. In this study, we purified a flap endonuclease 1 (FEN1) and xeroderma pigmentosum group G protein (XPG) in the 5' to 3' structure-specific DNA endonuclease family and synthesized single-strand break DNA substrates containing a 5'-phoshotyrosyl bond, mimicking the Top2-SSB complex. We found that FEN1 and XPG did not remove the 5'-phoshotyrosyl bond-containing DSB substrates but removed the 5'-phoshotyrosyl bond-containing SSB substrates. Under DNA repair conditions, FEN1 efficiently repaired the 5'-phoshotyrosyl bond-containing SSB substrates in the presence of DNA ligase and DNA polymerase. Therefore, FEN1 may play an important role in the repair of Top2-SSB complexes in etoposide-treated cells. PMID:26581212 13. DNA polymerases δ and λ cooperate in repairing double-strand breaks by microhomology-mediated end-joining in Saccharomyces cerevisiae. Science.gov (United States) Meyer, Damon; Fu, Becky Xu Hua; Heyer, Wolf-Dietrich 2015-12-15 Maintenance of genome stability is carried out by a suite of DNA repair pathways that ensure the repair of damaged DNA and faithful replication of the genome. Of particular importance are the repair pathways, which respond to DNA double-strand breaks (DSBs), and how the efficiency of repair is influenced by sequence homology. In this study, we developed a genetic assay in diploid Saccharomyces cerevisiae cells to analyze DSBs requiring microhomologies for repair, known as microhomology-mediated end-joining (MMEJ). MMEJ repair efficiency increased concomitant with microhomology length and decreased upon introduction of mismatches. The central proteins in homologous recombination (HR), Rad52 and Rad51, suppressed MMEJ in this system, suggesting a competition between HR and MMEJ for the repair of a DSB. Importantly, we found that DNA polymerase delta (Pol δ) is critical for MMEJ, independent of microhomology length and base-pairing continuity. MMEJ recombinants showed evidence that Pol δ proofreading function is active during MMEJ-mediated DSB repair. Furthermore, mutations in Pol δ and DNA polymerase 4 (Pol λ), the DNA polymerase previously implicated in MMEJ, cause a synergistic decrease in MMEJ repair. Pol λ showed faster kinetics associating with MMEJ substrates following DSB induction than Pol δ. The association of Pol δ depended on RAD1, which encodes the flap endonuclease needed to cleave MMEJ intermediates before DNA synthesis. Moreover, Pol δ recruitment was diminished in cells lacking Pol λ. These data suggest cooperative involvement of both polymerases in MMEJ. PMID:26607450 14. RAD1 and RAD10, but not other excision repair genes, are required for double-strand break-induced recombination in Saccharomyces cerevisiae. Science.gov (United States) Ivanov, E L; Haber, J E 1995-04-01 15. The role of homologous recombination in mitotic and meiotic double-strand break repair NARCIS (Netherlands) 2007-01-01 All organisms are composed of cells and the cell’s nucleus contains DNA. The induction of DNA damage is a threat to organisms. Signalling of DNA damage and subsequent repair is of substantial importance. Double-strand breaks (DSBs) in DNA can be induced by ionising radiation and DNA damaging agents 16. Regulation of DNA double-strand break repair by ubiquitin and ubiquitin-like modifiers DEFF Research Database (Denmark) Schwertman, Petra; Bekker-Jensen, Simon; Mailand, Niels 2016-01-01 DNA double-strand breaks (DSBs) are highly cytotoxic DNA lesions. The swift recognition and faithful repair of such damage is crucial for the maintenance of genomic stability, as well as for cell and organismal fitness. Signalling by ubiquitin, SUMO and other ubiquitin-like modifiers (UBLs... 17. Repair and genetic consequences of DNA double strand breaks during animal development NARCIS (Netherlands) Lemmens, Bennie Benjamin Lodewijk Gerardus 2014-01-01 The genetic code of life is stored in DNA molecules that consist of two parallel strands of coupled nucleotides that form a DNA double helix. One of the most deleterious forms of DNA damage is a DNA double-strand break (DSB) in which both strands of the helix are broken. When not repaired adequately 18. The yeast Saccharomyces cerevisiae DNA polymerase IV: possible involvement in double strand break DNA repair. Science.gov (United States) Leem, S H; Ropp, P A; Sugino, A 1994-08-11 We identified and purified a new DNA polymerase (DNA polymerase IV), which is similar to mammalian DNA polymerase beta, from Saccharomyces cerevisiae and suggested that it is encoded by YCR14C (POLX) on chromosome III. Here, we provided a direct evidence that the purified DNA polymerase IV is indeed encoded by POLX. Strains harboring a pol4 deletion mutation exhibit neither mitotic growth defect nor a meiosis defect, suggesting that DNA polymerase IV participates in nonessential functions in DNA metabolism. The deletion strains did not exhibit UV-sensitivity. However, they did show weak sensitivity to MMS-treatment and exhibited a hyper-recombination phenotype when intragenic recombination was measured during meiosis. Furthermore, MAT alpha pol4 delta segregants had a higher frequency of illegitimate mating with a MAT alpha tester strain than that of wild-type cells. These results suggest that DNA polymerase IV participates in a double-strand break repair pathway. A 3.2kb of the POL4 transcript was weakly expressed in mitotically growing cells. During meiosis, a 2.2 kb POL4 transcript was greatly induced, while the 3.2 kb transcript stayed at constant levels. This induction was delayed in a swi4 delta strain during meiosis, while no effect was observed in a swi6 delta strain. 19. Beyond repair foci: DNA double-strand break repair in euchromatic and heterochromatic compartments analyzed by transmission electron microscopy. Directory of Open Access Journals (Sweden) Yvonne Lorat Full Text Available PURPOSE: DNA double-strand breaks (DSBs generated by ionizing radiation pose a serious threat to the preservation of genetic and epigenetic information. The known importance of local chromatin configuration in DSB repair raises the question of whether breaks in different chromatin environments are recognized and repaired by the same repair machinery and with similar efficiency. An essential step in DSB processing by non-homologous end joining is the high-affinity binding of Ku70-Ku80 and DNA-PKcs to double-stranded DNA ends that holds the ends in physical proximity for subsequent repair. METHODS AND MATERIALS: Using transmission electron microscopy to localize gold-labeled pKu70 and pDNA-PKcs within nuclear ultrastructure, we monitored the formation and repair of actual DSBs within euchromatin (electron-lucent and heterochromatin (electron-dense in cortical neurons of irradiated mouse brain. RESULTS: While DNA lesions in euchromatin (characterized by two pKu70-gold beads, reflecting the Ku70-Ku80 heterodimer are promptly sensed and rejoined, DNA packaging in heterochromatin appears to retard DSB processing, due to the time needed to unravel higher-order chromatin structures. Complex pKu70-clusters formed in heterochromatin (consisting of 4 or ≥ 6 gold beads may represent multiple breaks in close proximity caused by ionizing radiation of highly-compacted DNA. All pKu70-clusters disappeared within 72 hours post-irradiation, indicating efficient DSB rejoining. However, persistent 53BP1 clusters in heterochromatin (comprising ≥ 10 gold beads, occasionally co-localizing with γH2AX, but not pKu70 or pDNA-PKcs, may reflect incomplete or incorrect restoration of chromatin structure rather than persistently unrepaired DNA damage. DISCUSSION: Higher-order organization of chromatin determines the accessibility of DNA lesions to repair complexes, defining how readily DSBs are detected and processed. DNA lesions in heterochromatin appear to be more 20. Postreplication repair in ultraviolet-irradiated human fibroblasts: formation and repair of DNA double-strand breaks International Nuclear Information System (INIS) A neutral filter elution assay was used to determine if the post-replicational formation and repair of DNA double-strand breaks (DSB) occurs in u.v.-irradiated human cells. Excision-deficient XP12 cells were pulse-labeled with [3H]thymidine after u.v. irradiation (1.5-3J/m2), and the nascent DNA was followed during repair incubation. With increasing u.v. radiation fluences, an increasing fraction of DNA was eluted at a fast rate, indicating that DSB were produced. The maximum yield DSB was observed after about 24 h of post-irradiation incubation at 370C. Similar results were also obtained with repair-proficient VA13 cells when irradiated at much higher fluences (7.5-15J/m2). It is concluded that, at the u.v. radiation fluences used, the DSB produced in u.v.-irradiated human cells are the result of post-replication repair events, and at incubation times >24 h some of these DSB are repaired. (author) 1. Induction and repair of DNA strand breaks in bovine lens epithelial cells after high LET irradiation Science.gov (United States) Baumstark-Khan, C.; Heilmann, J.; Rink, H. The lens epithelium is the initiation site for the development of radiation induced cataracts. Radiation in the cortex and nucleus interacts with proteins, while in the epithelium, experimental results reveal mutagenic and cytotoxic effects. It is suggested that incorrectly repaired DNA damage may be lethal in terms of cellular reproduction and also may initiate the development of mutations or transformations in surviving cells. The occurrence of such genetically modified cells may lead to lens opacification. For a quantitative risk estimation for astronauts and space travelers it is necessary to know the relative biological effectiveness (RBE), because the spacial and temporal distribution of initial physical damage induced by cosmic radiation differ significantly from that of X-rays. RBEs for the induction of DNA strand breaks and the efficiency of repair of these breaks were measured in cultured diploid bovine lens epithelial cells exposed to different LET irradiation to either 300 kV X-rays or to heavy ions at the UNILAC accelerator at GSI. Accelerated ions from Z=8 (O) to Z=92 (U) were used. Strand breaks were measured by hydroxyapatite chromatography of alkaline unwound DNA (overall strand breaks). Results showed that DNA damage occurs as a function of dose, of kinetic energy and of LET. For particles having the same LET the severity of the DNA damage increases with dose. For a given particle dose, as the LET rises, the numbers of DNA strand breaks increase to a maximum and then reach a plateau or decrease. Repair kinetics depend on the fluence (irradiation dose). At any LET value, repair is much slower after heavy ion exposure than after X-irradiation. For ions with an LET of less than 10,000 keV μ -1 more than 90 percent of the strand breaks induced are repaired within 24 hours. At higher particle fluences, especially for low energetic particles with a very high local density of energy deposition within the particle track, a higher proportion of non 2. XLS (c9orf142) is a new component of mammalian DNA double-stranded break repair. Science.gov (United States) Craxton, A; Somers, J; Munnur, D; Jukes-Jones, R; Cain, K; Malewicz, M 2015-06-01 Repair of double-stranded DNA breaks (DSBs) in mammalian cells primarily occurs by the non-homologous end-joining (NHEJ) pathway, which requires seven core proteins (Ku70/Ku86, DNA-PKcs (DNA-dependent protein kinase catalytic subunit), Artemis, XRCC4-like factor (XLF), XRCC4 and DNA ligase IV). Here we show using combined affinity purification and mass spectrometry that DNA-PKcs co-purifies with all known core NHEJ factors. Furthermore, we have identified a novel evolutionary conserved protein associated with DNA-PKcs-c9orf142. Computer-based modelling of c9orf142 predicted a structure very similar to XRCC4, hence we have named c9orf142-XLS (XRCC4-like small protein). Depletion of c9orf142/XLS in cells impaired DSB repair consistent with a defect in NHEJ. Furthermore, c9orf142/XLS interacted with other core NHEJ factors. These results demonstrate the existence of a new component of the NHEJ DNA repair pathway in mammalian cells. PMID:25941166 3. Repair of DNA strand breaks in progeric fibroblasts and aging human diploid cells International Nuclear Information System (INIS) The rate of rejoining of DNA strand breaks induced by 10 krad of γ-irradiation has been studied in normal human diploid skin fibroblasts and skin fibroblasts from six patients with symptoms of progeria. Although slightly more rapid in very early passage, the repair rate in normal cells was similar throughout most of their life span in vitro. The appearance of cells with reduced repair capacity was evident as the cultures became senescent. The progeric fibroblasts varied greatly in their response to irradiation. The rate of repair was greatly reduced in two strains, whereas in two others extensive DNA degradation was consistently observed in unirradiated cells. Degradation was apparently related to the radiation received from the incorporated radiolabel. Normal repair was seen in progeric fibroblasts transformed by SV40 virus 4. Double-strand break repair by interchromosomal recombination: an in vivo repair mechanism utilized by multiple somatic tissues in mammals. Directory of Open Access Journals (Sweden) Ryan R White Full Text Available Homologous recombination (HR is essential for accurate genome duplication and maintenance of genome stability. In eukaryotes, chromosomal double strand breaks (DSBs are central to HR during specialized developmental programs of meiosis and antigen receptor gene rearrangements, and form at unusual DNA structures and stalled replication forks. DSBs also result from exposure to ionizing radiation, reactive oxygen species, some anti-cancer agents, or inhibitors of topoisomerase II. Literature predicts that repair of such breaks normally will occur by non-homologous end-joining (in G1, intrachromosomal HR (all phases, or sister chromatid HR (in S/G(2. However, no in vivo model is in place to directly determine the potential for DSB repair in somatic cells of mammals to occur by HR between repeated sequences on heterologs (i.e., interchromosomal HR. To test this, we developed a mouse model with three transgenes-two nonfunctional green fluorescent protein (GFP transgenes each containing a recognition site for the I-SceI endonuclease, and a tetracycline-inducible I-SceI endonuclease transgene. If interchromosomal HR can be utilized for DSB repair in somatic cells, then I-SceI expression and induction of DSBs within the GFP reporters may result in a functional GFP+ gene. Strikingly, GFP+ recombinant cells were observed in multiple organs with highest numbers in thymus, kidney, and lung. Additionally, bone marrow cultures demonstrated interchromosomal HR within multiple hematopoietic subpopulations including multi-lineage colony forming unit-granulocyte-erythrocyte-monocyte-megakaryocte (CFU-GEMM colonies. This is a direct demonstration that somatic cells in vivo search genome-wide for homologous sequences suitable for DSB repair, and this type of repair can occur within early developmental populations capable of multi-lineage differentiation. 5. Effects of chemopreventive natural products on non-homologous end-joining DNA double-strand break repair. Science.gov (United States) Charles, Catherine; Nachtergael, Amandine; Ouedraogo, Moustapha; Belayew, Alexandra; Duez, Pierre 2014-07-01 Double-strand breaks (DSBs) may result from endogenous (e.g., reactive oxygen species, variable (diversity) joining, meiotic exchanges, collapsed replication forks, nucleases) or exogenous (e.g., ionizing radiation, chemotherapeutic agents, radiomimetic compounds) events. DSBs disrupt the integrity of DNA and failed or improper DSBs repair may lead to genomic instability and, eventually, mutations, cancer, or cell death. Non-homologous end-joining (NHEJ) is the major pathway used by higher eukaryotic cells to repair these lesions. Given the complexity of NHEJ and the number of proteins and cofactors involved, secondary metabolites from medicinal or food plants might interfere with the process, activating or inhibiting repair. Twelve natural products, arbutin, curcumin, indole-3-carbinol, and nine flavonoids (apigenin, baicalein, chalcone, epicatechin, genistein, myricetin, naringenin, quercetin, sakuranetin) were chosen for their postulated roles in cancer chemoprevention and/or treatment. The effects of these compounds on NHEJ were investigated with an in vitro protocol based on plasmid substrates. Plasmids were linearized by a restriction enzyme, generating cohesive ends, or by a combination of enzymes, generating incompatible ends; plasmids were then incubated with a nuclear extract prepared from normal human small-intestinal cells (FHS 74 Int), either treated with these natural products or untreated (controls). The NHEJ repair complex from nuclear extracts ligates linearized plasmids, resulting in plasmid oligomers that can be separated and quantified by on-chip microelectrophoresis. Some compounds (chalcone, epicatechin, myricetin, sakuranetin and arbutin) clearly activated NHEJ, whereas others (apigenin, baicalein and curcumin) significantly reduced the repair rate of both types of plasmid substrates. Although this in vitro protocol is only partly representative of the in vivo situation, the natural products appear to interfere with NHEJ repair and warrant 6. Homologous recombination repairs secondary replication induced DNA double-strand breaks after ionizing radiation OpenAIRE Groth, Petra; Orta, Manuel Luís; Elvers, Ingegerd; Majumder, Muntasir Mamun; Lagerqvist, Anne; Helleday, Thomas 2012-01-01 Ionizing radiation (IR) produces direct two-ended DNA double-strand breaks (DSBs) primarily repaired by non-homologous end joining (NHEJ). It is, however, well established that homologous recombination (HR) is induced and required for repair of a subset of DSBs formed following IR. Here, we find that HR induced by IR is drastically reduced when post-DNA damage replication is inhibited in mammalian cells. Both IR-induced RAD51 foci and HR events in the hprt gene are reduced in the presence of ... 7. An exonuclease I-sensitive DNA repair pathway in Deinococcus radiodurans: a major determinant of radiation resistance. Science.gov (United States) Misra, Hari S; Khairnar, Nivedita P; Kota, Swathi; Shrivastava, Smriti; Joshi, Vasudha P; Apte, Shree K 2006-02-01 Deinococcus radiodurans R1 recovering from acute dose of gamma radiation shows a biphasic mechanism of DNA double-strand break repair. The possible involvement of microsequence homology-dependent, or non-homologous end joining type mechanisms during initial period followed by RecA-dependent homologous recombination pathways has been suggested for the reconstruction of complete genomes in this microbe. We have exploited the known roles of exonuclease I in DNA recombination to elucidate the nature of recombination involved in DNA double-strand break repair during post-irradiation recovery of D. radiodurans. Transgenic Deinococcus cells expressing exonuclease I functions of Escherichia coli showed significant reduction in gamma radiation radioresistance, while the resistance to far-UV and hydrogen peroxide remained unaffected. The overexpression of E. coli exonuclease I in Deinococcus inhibited DNA double-strand break repair. Such cells exhibited normal post-irradiation expression kinetics of RecA, PprA and single-stranded DNA-binding proteins but lacked the divalent cation manganese [(Mn(II)]-dependent protection from gamma radiation. The results strongly suggest that 3' (rho) 5' single-stranded DNA ends constitute an important component in recombination pathway involved in DNA double-strand break repair and that absence of sbcB from deinococcal genome may significantly aid its extreme radioresistance phenotype. PMID:16430702 8. Modulation of DNA double-strand break repair activity in cell-free extracts of gamma-irradiated mouse testicular cells International Nuclear Information System (INIS) DNA double-strand breaks (DSBs) are potentially mutagenic lesions demanding effective damage recognition and repair. Even a single DSB can be detrimental if left unrepaired or misrepaired, and if present in gamete, it can cause foetal wastage or malformations/congenital defects in the offspring. The threats posed by DSBs have triggered the evolution of two major pathways of DSB repair, homologous recombination-mediated repair (HRR) and non-homologous end-joining (NHEJ), conserved from bacteria to mammals. Though HRR is more predominant in bacteria and yeast, NHEJ is more efficient in mammalian somatic cells. Studies in our laboratory have shown that both the pathways are equally efficient in mammalian male germ cells 9. Identification of Saccharomyces cerevisiae DNA ligase IV: involvement in DNA double-strand break repair. OpenAIRE Teo, S H; Jackson, S P 1997-01-01 DNA ligases catalyse the joining of single and double-strand DNA breaks, which is an essential final step in DNA replication, recombination and repair. Mammalian cells have four DNA ligases, termed ligases I-IV. In contrast, other than a DNA ligase I homologue (encoded by CDC9), no other DNA ligases have hitherto been identified in Saccharomyces cerevisiae. Here, we report the identification and characterization of a novel gene, LIG4, which encodes a protein with strong homology to mammalian ... 10. Evaluation of DNA Double Strand Breaks Repair Efficiency in Head and Neck Cancer OpenAIRE Walczak, Anna; Rusin, Pawel; Dziki, Lukasz; Zielinska-Blizniewska, Hanna; Olszewski, Jurek; Majsterek, Ireneusz 2012-01-01 Head and neck cancers (head and neck squamous cell carcinomas [HNSCC]) are a heterogeneous group of neoplasms with varying presenting symptoms, treatment, and expected outcome. There is a need to find an effective way of its treatment at the molecular level. Thus, we should identify the mechanism of cancer cell response to damaging agents' activity, especially at DNA level. Our major goal was to evaluate the efficacy of DNA double strand breaks (DSBs) repair in HTB-43 and SCC-25 cancer cell l... 11. Atypical Role for PhoU in Mutagenic Break Repair under Stress in Escherichia coli. Directory of Open Access Journals (Sweden) Janet L Gibson Full Text Available Mechanisms of mutagenesis activated by stress responses drive pathogen/host adaptation, antibiotic and anti-fungal-drug resistance, and perhaps much of evolution generally. In Escherichia coli, repair of double-strand breaks (DSBs by homologous recombination is high fidelity in unstressed cells, but switches to a mutagenic mode using error-prone DNA polymerases when the both the SOS and general (σS stress responses are activated. Additionally, the σE response promotes spontaneous DNA breakage that leads to mutagenic break repair (MBR. We identified the regulatory protein PhoU in a genetic screen for functions required for MBR. PhoU negatively regulates the phosphate-transport and utilization (Pho regulon when phosphate is in excess, including the PstB and PstC subunits of the phosphate-specific ABC transporter PstSCAB. Here, we characterize the PhoU mutation-promoting role. First, some mutations that affect phosphate transport and Pho transcriptional regulation decrease mutagenesis. Second, the mutagenesis and regulon-expression phenotypes do not correspond, revealing an apparent new function(s for PhoU. Third, the PhoU mutagenic role is not via activation of the σS, SOS or σE responses, because mutations (or DSBs that restore mutagenesis to cells defective in these stress responses do not restore mutagenesis to phoU cells. Fourth, the mutagenesis defect in phoU-mutant cells is partially restored by deletion of arcA, a gene normally repressed by PhoU, implying that a gene(s repressed by ArcA promotes mutagenic break repair. The data show a new role for PhoU in regulation, and a new regulatory branch of the stress-response signaling web that activates mutagenic break repair in E. coli. 12. Regulation of ATM in DNA double strand break repair accounts for the radiosensitivity in human cells exposed to high linear energy transfer ionizing radiation Energy Technology Data Exchange (ETDEWEB) Xue Lian, E-mail: [email protected] [School of Radiation Medicine and Public Health, Medical College of Soochow University, No. 199, Ren' ai Road, Suzhou 215123 (China); Yu Dong, E-mail: [email protected] [Tumor Endocrinology Project, National Cancer Center Research Institute, 5-1-1 Tsukiji, Chuo-ku, Tokyo 104-0045 (Japan); Furusawa, Yoshiya; Okayasu, Ryuichi [Heavy-Ion Radiobiology Research Group, Research Center for Charged Particle Therapy, National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba-shi 263-8555 (Japan); Tong Jian; Cao Jianping; Fan Saijun [School of Radiation Medicine and Public Health, Medical College of Soochow University, No. 199, Ren' ai Road, Suzhou 215123 (China) 2009-11-02 13. Feedback inhibition of L1 and alu retrotransposition through altered double strand break repair kinetics Directory of Open Access Journals (Sweden) Wallace Nicholas A 2010-10-01 Full Text Available Abstract Background Cells adapt to various chronic toxic exposures in a multitude of ways to minimize further damage and maximize their growth potential. Expression of L1 elements in the human genome can be greatly deleterious to cells, generating numerous double strand breaks (DSBs. Cells have been reported to respond to chronic DSBs by altering the repair of these breaks, including increasing the rate of homology independent DSB repair. Retrotransposition is strongly affected by proteins involved in DSB repair. Therefore, L1 expression has the potential to be a source of chronic DSBs and thus bring about the changes in cellular environment that could ultimately restrict its own retrotransposition. Results We demonstrate that constitutive L1 expression leads to quicker DSB repair and decreases in the retrotransposition potential of L1 and other retrotransposons dependent on L1 expression for their mobility. This cellular adaptation results in reduced sensitivity to L1 induced toxicity. These effects can be induced by constitutive expression of the functional L1 ORF2 alone, but not by the constitutive expression of an L1 open reading frame 2 with mutations to its endonuclease and reverse transcriptase domains. This adaptation correlates with the relative activity of the L1 introduced into the cells. Conclusions The increased number of DSBs resulting from constitutive expression of L1 results in a more rapid rate of repair. The cellular response to this L1 expression also results in attenuation of retrotransposition and reduced sensitivity of the cells to negative consequences of L1 ORF2 expression. The influence does not appear to be through RNA interference. We believe that the increased rate of DSB repair is the most likely cause of the attenuation of retrotransposition. These alterations act as a fail safe mechanism that allows cells to escape the toxicity associated with the unchecked L1 expression. This gives cells that overexpress L1, such 14. RNF4 is required for DNA double-strand break repair in vivo DEFF Research Database (Denmark) Vyas, R; Kumar, R; Clermont, F; 2013-01-01 Unrepaired DNA double-strand breaks (DSBs) cause genetic instability that leads to malignant transformation or cell death. Cells respond to DSBs with the ordered recruitment of signaling and repair proteins to the sites of DNA lesions. Coordinated protein SUMOylation and ubiquitylation have crucial...... in other key regulators of HR repair, Rnf4 deficiency leads to age-dependent impairment in spermatogenesis. These findings identify Rnf4 as a critical component of the DDR in vivo and support the possibility that Rnf4 controls protein localization at DNA damage sites by integrating SUMOylation...... roles in regulating the dynamic assembly of protein complexes at these sites. However, how SUMOylation influences protein ubiquitylation at DSBs is poorly understood. We show herein that Rnf4, an E3 ubiquitin ligase that targets SUMO-modified proteins, accumulates in DSB repair foci and is required... 15. DNA double-strand break repair: a theoretical framework and its application. Science.gov (United States) Murray, Philip J; Cornelissen, Bart; Vallis, Katherine A; Chapman, S Jon 2016-01-01 DNA double-strand breaks (DSBs) are formed as a result of genotoxic insults, such as exogenous ionizing radiation, and are among the most serious types of DNA damage. One of the earliest molecular responses following DSB formation is the phosphorylation of the histone H2AX, giving rise to γH2AX. Many copies of γH2AX are generated at DSBs and can be detected in vitro as foci using well-established immuno-histochemical methods. It has previously been shown that anti-γH2AX antibodies, modified by the addition of the cell-penetrating peptide TAT and a fluorescent or radionuclide label, can be used to visualize and quantify DSBs in vivo. Moreover, when labelled with a high amount of the short-range, Auger electron-emitting radioisotope, (111)In, the amount of DNA damage within a cell can be increased, leading to cell death. In this report, we develop a mathematical model that describes how molecular processes at individual sites of DNA damage give rise to quantifiable foci. Equations that describe stochastic mean behaviours at individual DSB sites are derived and parametrized using population-scale, time-series measurements from two different cancer cell lines. The model is used to examine two case studies in which the introduction of an antibody (anti-γH2AX-TAT) that targets a key component in the DSB repair pathway influences system behaviour. We investigate: (i) how the interaction between anti-γH2AX-TAT and γH2AX effects the kinetics of H2AX phosphorylation and DSB repair and (ii) model behaviour when the anti-γH2AX antibody is labelled with Auger electron-emitting (111)In and can thus instigate additional DNA damage. This work supports the conclusion that DSB kinetics are largely unaffected by the introduction of the anti-γH2AX antibody, a result that has been validated experimentally, and hence the hypothesis that the use of anti-γH2AX antibody to quantify DSBs does not violate the image tracer principle. Moreover, it provides a novel model of DNA damage 16. Xbp1-mediated histone H4 deacetylation contributes to DNA double-strand break repair in yeast Institute of Scientific and Technical Information of China (English) Ran Tao; Hua Chen; Chan Gao; Pcng Xue; Fuquan Yang; Jing-Dong J Han; Bing Zhou; Ye-Guang Chen 2011-01-01 Xbp1 has been shown to regulate the cell cycle as a transcriptional repressor in budding yeast Saccharomyces cerevisiae.In this study,we demonstrated that Xbp1 regulates DNA double-strand break (DSB) repair in S.cerevisiae.Xbp1 physically and genetically interacts with the histone deacetylase Rpd3 complex.Chromatin immunoprecipitation revealed that Xbp1 is required for efficient deacetylation of histone H4 flanking DSBs by the Rpd3 complex.Deletion of XBP1 leads to the delayed deacetylation of histone H4,which is coupled with increased nucleosome displacement,increased DNA end resection and decreased non-homologous end-joining (NHEJ).In response to DNA damage,Xbp1 is upregulated in a Mec1-Rad9-Rad53 checkpoint pathway-dependent manner and undergoes dephosphorylation.Cdk1,a central regulator of S.cerevisiae cell cycle,is responsible for Xbp1 phosphorylation at residues Ser146,Ser271 and Ser551.Substitution of these serine residues with alanine not only increases the association of Xbp1 with the Rpd3 complex and its recruitment to a DSB,but also promotes DSB repair.Together,our findings reveal a role for Xbp1 in DSB repair via NHEJ through regulation of histone H4 acetylation and nucleosome displacement in a positive feedback manner. 17. Positive regulation of DNA double strand break repair activity during differentiation of long life span cells: the example of adipogenesis. Directory of Open Access Journals (Sweden) Aline Meulle 18. Effects of camptothecin on double-strand break repair by non-homologous end-joining in DNA mismatch repair-deficient human colorectal cancer cell lines OpenAIRE Jacob, Sandrine; Miquel, Catherine; Sarasin, Alain; Praz, Françoise 2005-01-01 Loss of a functional mismatch repair (MMR) system in colorectal cancer (CRC) cells is associated with microsatellite instability and increased sensitivity to topoisomerase inhibitors. In this study, we have investigated whether a defect in double-strand break (DSB) repair by non-homologous end-joining (NHEJ) could explain why MMR-deficient CRC cells are hypersensitive to camptothecin (CPT), a topoisomerase I inhibitor. To evaluate the efficiency and the fidelity of DSB repair, we have transie... 19. Melatonin enhances DNA repair capacity possibly by affecting genes involved in DNA damage responsive pathways Directory of Open Access Journals (Sweden) Liu Ran 2013-01-01 Full Text Available Abstract Background Melatonin, a hormone-like substance involved in the regulation of the circadian rhythm, has been demonstrated to protect cells against oxidative DNA damage and to inhibit tumorigenesis. Results In the current study, we investigated the effect of melatonin on DNA strand breaks using the alkaline DNA comet assay in breast cancer (MCF-7 and colon cancer (HCT-15 cell lines. Our results demonstrated that cells pretreated with melatonin had significantly shorter Olive tail moments compared to non-melatonin treated cells upon mutagen (methyl methanesulfonate, MMS exposure, indicating an increased DNA repair capacity after melatonin treatment. We further examined the genome-wide gene expression in melatonin pretreated MCF-7 cells upon carcinogen exposure and detected altered expression of many genes involved in multiple DNA damage responsive pathways. Genes exhibiting altered expression were further analyzed for functional interrelatedness using network- and pathway-based bioinformatics analysis. The top functional network was defined as having relevance for “DNA Replication, Recombination, and Repair, Gene Expression, [and] Cancer”. Conclusions These findings suggest that melatonin may enhance DNA repair capacity by affecting several key genes involved in DNA damage responsive pathways. 20. The production and repair of double strand breaks in cells from normal humans and patients with ataxia telangiectasia International Nuclear Information System (INIS) The production and repair of double strand breaks induced by γ-rays in the DNA of human fibroblasts have been measured by sedimentation in sucrose gradients under non-denaturing conditions. Unirradiated DNA formed a rapidly sedimenting gel. Low doses of radiation released freely sedimenting DNA molecules from this gel. Higher doses reduced the rate of sedimentation of the free DNA due to the introduction of double strand breaks. The breakage efficiency was 1 break/1.3x1010 daltons of DNA/krad. Postirradiation incubation after a high dose of radiation resulted in an increase in molecular weight of the free DNA molecules, and after a low dose the rapidly-sedimenting gel was reformed. These data suggest that double strand breaks are repaired in human fibroblasts. No significant differences were found between fibroblasts from two normal donors and four patients with the radiosensitive disorder, ataxia telangiectasia, in either the production or repair of double strand breaks 1. DNA polymerase θ (POLQ), double-strand break repair, and cancer. Science.gov (United States) Wood, Richard D; Doublié, Sylvie 2016-08-01 DNA polymerase theta (pol θ) is encoded in the genomes of many eukaryotes, though not in fungi. Pol θ is encoded by the POLQ gene in mammalian cells. The C-terminal third of the protein is a family A DNA polymerase with additional insertion elements relative to prokaryotic homologs. The N-terminal third is a helicase-like domain with DNA-dependent ATPase activity. Pol θ is important in the repair of genomic double-strand breaks (DSBs) from many sources. These include breaks formed by ionizing radiation and topoisomerase inhibitors, breaks arising at stalled DNA replication forks, breaks introduced during diversification steps of the mammalian immune system, and DSB induced by CRISPR-Cas9. Pol θ participates in a route of DSB repair termed "alternative end-joining" (altEJ). AltEJ is independent of the DNA binding Ku protein complex and requires DNA end resection. Pol θ is able to mediate joining of two resected 3' ends harboring DNA sequence microhomology. "Signatures" of Pol θ action during altEJ are the frequent utilization of longer microhomologies, and the insertion of additional sequences at joining sites. The mechanism of end-joining employs the ability of Pol θ to tightly grasp a 3' terminus through unique contacts in the active site, allowing extension from minimally paired primers. Pol θ is involved in controlling the frequency of chromosome translocations and preserves genome integrity by limiting large deletions. It may also play a backup role in DNA base excision repair. POLQ is a member of a cluster of similarly upregulated genes that are strongly correlated with poor clinical outcome for breast cancer, ovarian cancer and other cancer types. Inhibition of pol θ is a compelling approach for combination therapy of radiosensitization. PMID:27264557 2. γ-ray dose rate effect in DNA double-strand break repair deficient murine cells International Nuclear Information System (INIS) Objective: To analyze the dose rate effect and potentially lethal damage repair in DNA double-strand break repair deficient murine cells (SCID) irradiated by γ-ray. Methods: The wild type (CB.17+/+) and SCID cells were exposed to γ-ray at high and low dose rates. The high dose rate exposure was fractionated into two equal doses at 24 h intervals. The survival rates of irradiated cells were calculated by clone-forming analysis. Results: When γ-ray was given to wild type (CB.17+/+) cells in two fractions at 24 h intervals, the survival rate was significantly higher than that when the same total dose was given singly. In contrast, there was no difference in the survival rates between the single and fractionated exposure in SCID cells. SCID cells were more sensitive than CB.17+/+ cells to both low and high dose rates γ-ray exposure for cell killing. The survival rate by low dose rate exposure was significantly higher than that by high dose rate exposure, not only in CB.17+/+ cells but also in SCID cells. Conclusions: SCID cells are deficient in repairing γ-ray induced double-strand breaks. There is dose rate effect in both SCID and CB.17+/+ cells 3. The repair of environmentally relevant DNA double strand breaks caused by high linear energy transfer irradiation--no simple task. Science.gov (United States) Moore, Shaun; Stanley, Fintan K T; Goodarzi, Aaron A 2014-05-01 High linear energy transfer (LET) ionising radiation (IR) such as radon-derived alpha particles and high mass, high energy (HZE) particles of cosmic radiation are the predominant forms of IR to which humanity is exposed throughout life. High-LET forms of IR are established carcinogens relevant to human cancer, and their potent mutagenicity is believed, in part, to be due to a greater incidence of clustered DNA double strand breaks (DSBs) and associated lesions, as ionization events occur within a more confined genomic space. The repair of such DNA damage is now well-documented to occur with slower kinetics relative to that induced by low-LET IR, and to be more reliant upon homology-directed repair pathways. Underlying these phenomena is the relative inability of non-homologous end-joining (NHEJ) to adequately resolve high-LET IR-induced DSBs. Current findings suggest that the functionality of the DNA-dependent protein kinase (DNA-PK), comprised of the Ku70-Ku80 heterodimer and the DNA-PK catalytic subunit (DNA-PKcs), is particularly perturbed by high-LET IR-induced clustered DSBs, rendering DNA-PK dependent NHEJ less relevant to resolving these lesions. By contrast, the NHEJ-associated DNA processing endonuclease Artemis shows a greater relevance to high-LET IR-induced DSB repair. Here, we will review the cellular response to high-LET irradiation, the implications of the chronic, low-dose modality of this exposure and molecular pathways that respond to high-LET irradiation induced DSBs, with particular emphasis on NHEJ factors. PMID:24565812 4. Maintenance of genome stability in plants: repairing DNA double strand breaks and chromatin structure stability Directory of Open Access Journals (Sweden) Sujit eRoy 2014-09-01 Full Text Available Plant cells are subject to high levels of DNA damage resulting from plant’s obligatory dependence on sunlight and the associated exposure to environmental stresses like solar UV radiation, high soil salinity, drought, chilling injury and other air and soil pollutants including heavy metals and metabolic byproducts from endogenous processes. The irreversible DNA damages, generated by the environmental and genotoxic stresses affect plant growth and development, reproduction and crop productivity. Thus, for maintaining genome stability, plants have developed an extensive array of mechanisms for the detection and repair of DNA damages. This review will focus recent advances in our understanding of mechanisms regulating plant genome stability in the context of repairing of double stand breaks and chromatin structure maintenance. 5. The liver DNA breaks and repair of the fish (carassius auratus) induced by the sublethal metal mixture International Nuclear Information System (INIS) The breaks and repair of the carassius auratus's liver DNA induced by the metal mixture were studied by using the gel electrophoresis technique and 3H-TdR incorporation experiment. The results demonstrated that DNA breaks were detected after treated by zine, lead and metal mixture, and the RNSB order was the metal mixture >Pb>Zn. The DNA repair was found among the zinc treatment, cadmium treatment, lead treatment as well as metal mixture treatment, and the order of the repair ability was the metal mixture >Pb>Zn>Cd. The mixture of the metals increased the damage to the DNA. The results also showed that the result of the DNA breaks was not conformed completely to that of the DNA repair 6. DNA double strand break damage by radiation and behavioral imaging of DNA repair enzymes International Nuclear Information System (INIS) The theme in the title is described mainly on authors' studies. Finding of a jellyfish GFP (green fluorescent protein) and its genomic recombination technique with a target protein have made it possible to investigate the behavior of the protein (the repair enzymes in this review) within a cell by fluorescent microscopy. Double strand breaks (DSBs), the most severe damage of DNA leading to cell death and carcinogenesis, are induced by irradiation of ionizing radiation and/or ultraviolet light, and repair mechanisms of non homologous end-joining and homologous recombinant repair are known major in mammalian cells and in lower eukaryotes, respectively. Authors used UVA for inducing DSBs under the presence of benzo[a]pyrene in mammalian cells like Chinese hamster ovary (CHO)-K1 and xrs-5, the behaviors of Ku70/80 repair molecules tagged by GFP were imaged by confocal laser microscopy, and one of findings was that Ku80 moved to the level most intensely irradiated. Fluorescent molecular imaging technique will be employed widely in clinical diagnosis and new drug development as well as in basic bioscience. (S.I.) 7. Rapid pairing and resegregation of distant homologous loci enables double-strand break repair in bacteria. Science.gov (United States) Badrinarayanan, Anjana; Le, Tung B K; Laub, Michael T 2015-08-01 Double-strand breaks (DSBs) can lead to the loss of genetic information and cell death. Although DSB repair via homologous recombination has been well characterized, the spatial organization of this process inside cells remains poorly understood, and the mechanisms used for chromosome resegregation after repair are unclear. In this paper, we introduced site-specific DSBs in Caulobacter crescentus and then used time-lapse microscopy to visualize the ensuing chromosome dynamics. Damaged loci rapidly mobilized after a DSB, pairing with their homologous partner to enable repair, before being resegregated to their original cellular locations, independent of DNA replication. Origin-proximal regions were resegregated by the ParABS system with the ParA structure needed for resegregation assembling dynamically in response to the DSB-induced movement of an origin-associated ParB away from one cell pole. Origin-distal regions were resegregated in a ParABS-independent manner and instead likely rely on a physical, spring-like force to segregate repaired loci. Collectively, our results provide a mechanistic basis for the resegregation of chromosomes after a DSB. PMID:26240183 8. Constitutional Chromothripsis Rearrangements Involve Clustered Double-Stranded DNA Breaks and Nonhomologous Repair Mechanisms Directory of Open Access Journals (Sweden) Wigard P. Kloosterman 2012-06-01 Full Text Available Chromothripsis represents a novel phenomenon in the structural variation landscape of cancer genomes. Here, we analyze the genomes of ten patients with congenital disease who were preselected to carry complex chromosomal rearrangements with more than two breakpoints. The rearrangements displayed unanticipated complexity resembling chromothripsis. We find that eight of them contain hallmarks of multiple clustered double-stranded DNA breaks (DSBs on one or more chromosomes. In addition, nucleotide resolution analysis of 98 breakpoint junctions indicates that break repair involves nonhomologous or microhomology-mediated end joining. We observed that these eight rearrangements are balanced or contain sporadic deletions ranging in size between a few hundred base pairs and several megabases. The two remaining complex rearrangements did not display signs of DSBs and contain duplications, indicative of rearrangement processes involving template switching. Our work provides detailed insight into the characteristics of chromothripsis and supports a role for clustered DSBs driving some constitutional chromothripsis rearrangements. 9. RecBCD Enzyme and the Repair of Double-Stranded DNA Breaks OpenAIRE Dillingham, Mark S.; Kowalczykowski, Stephen C. 2008-01-01 Summary: The RecBCD enzyme of Escherichia coli is a helicase-nuclease that initiates the repair of double-stranded DNA breaks by homologous recombination. It also degrades linear double-stranded DNA, protecting the bacteria from phages and extraneous chromosomal DNA. The RecBCD enzyme is, however, regulated by a cis-acting DNA sequence known as Chi (crossover hotspot instigator) that activates its recombination-promoting functions. Interaction with Chi causes an attenuation of the RecBCD enzy... 10. Poly(ADP-Ribose) Polymerase-1 and DNA-Dependent Protein Kinase Have Equivalent Roles in Double Strand Break Repair Following Ionizing Radiation International Nuclear Information System (INIS) Purpose: Radiation-induced DNA double strand breaks (DSBs) are predominantly repaired by nonhomologous end joining (NHEJ), involving DNA-dependent protein kinase (DNA-PK). Poly(ADP-ribose) polymerase-1 (PARP-1), well characterized for its role in single strand break repair, may also facilitate DSB repair. We investigated the activation of these enzymes by differing DNA ends and their interaction in the cellular response to ionizing radiation (IR). Methods and Materials: The effect of PARP and DNA-PK inhibitors (KU-0058684 and NU7441) on repair of IR-induced DSBs was investigated in DNA-PK and PARP-1 proficient and deficient cells by measuring γH2AX foci and neutral comets. Complementary in vitro enzyme kinetics assays demonstrated the affinities of DNA-PK and PARP-1 for DSBs with varying DNA termini. Results: DNA-PK and PARP-1 both promoted the fast phase of resolution of IR-induced DSBs in cells. Inactivation of both enzymes was not additive, suggesting that PARP-1 and DNA-PK cooperate within the same pathway to promote DSB repair. The affinities of the two enzymes for oligonucleotides with blunt, 3' GGG or 5' GGG overhanging termini were similar and overlapping (Kdapp = 2.6-6.4nM for DNA-PK; 1.7-4.5nM for PARP-1). DNA-PK showed a slightly greater affinity for overhanging DNA and was significantly more efficient when activated by a 5' GGG overhang. PARP-1 had a preference for blunt-ended DNA and required a separate factor for efficient stimulation by a 5' GGG overhang. Conclusion: DNA-PK and PARP-1 are both required in a pathway facilitating the fast phase of DNA DSB repair. 11. The radioresistance kinase TLK1B protects the cells by promoting repair of double strand breaks Directory of Open Access Journals (Sweden) De Benedetti Arrigo 2005-09-01 Full Text Available Abstract Background The mammalian protein kinase TLK1 is a homologue of Tousled, a gene involved in flower development in Arabidopsis thaliana. The function of TLK1 is not well known, although knockout of the gene in Drosophila or expression of a dominant negative mutant in mouse cells causes loss of nuclear divisions and missegregation of chromosomes probably, due to alterations in chromatin remodeling capacity. Overexpression of TLK1B, a spliced variant of the TLK1 mRNA, in a model mouse cell line increases it's resistance to ionizing radiation (IR or the radiomimetic drug doxorubicin, also likely due to changes in chromatin remodeling. TLK1B is translationally regulated by the availability of the translation factor eIF4E, and its synthesis is activated by IR. The reason for this mechanism of regulation is likely to provide a rapid means of promoting repair of DSBs. TLK1B specifically phosphorylates histone H3 and Asf1, likely resulting in changes in chromatin structure, particularly at double strand breaks (DSB sites. Results In this work, we provide several lines of evidence that TLK1B protects the cells from IR by facilitating the repair of DSBs. First, the pattern of phosphorylation and dephosphorylation of H2AX and H3 indicated that cells overexpressing TLK1B return to pre-IR steady state much more rapidly than controls. Second, the repair of episomes damaged with DSBs was much more rapid in cells overexpressing TLK1B. This was also true for repair of genomic damage. Lastly, we demonstrate with an in vitro repair system that the addition of recombinant TLK1B promotes repair of a linearized plasmid incubated with nuclear extract. In addition, TLK1B in this in vitro system promotes the assembly of chromatin as shown by the formation of more highly supercoiled topomers of the plasmid. Conclusion In this work, we provide evidence that TLK1B promotes the repair of DSBs, likely as a consequence of a change in chromatin remodeling capacity that 12. Double-strand break repair processes drive evolution of the mitochondrial genome in Arabidopsis Directory of Open Access Journals (Sweden) Shedge Vikas 2011-09-01 Full Text Available Abstract Background The mitochondrial genome of higher plants is unusually dynamic, with recombination and nonhomologous end-joining (NHEJ activities producing variability in size and organization. Plant mitochondrial DNA also generally displays much lower nucleotide substitution rates than mammalian or yeast systems. Arabidopsis displays these features and expedites characterization of the mitochondrial recombination surveillance gene MSH1 (MutS 1 homolog, lending itself to detailed study of de novo mitochondrial genome activity. In the present study, we investigated the underlying basis for unusual plant features as they contribute to rapid mitochondrial genome evolution. Results We obtained evidence of double-strand break (DSB repair, including NHEJ, sequence deletions and mitochondrial asymmetric recombination activity in Arabidopsis wild-type and msh1 mutants on the basis of data generated by Illumina deep sequencing and confirmed by DNA gel blot analysis. On a larger scale, with mitochondrial comparisons across 72 Arabidopsis ecotypes, similar evidence of DSB repair activity differentiated ecotypes. Forty-seven repeat pairs were active in DNA exchange in the msh1 mutant. Recombination sites showed asymmetrical DNA exchange within lengths of 50- to 556-bp sharing sequence identity as low as 85%. De novo asymmetrical recombination involved heteroduplex formation, gene conversion and mismatch repair activities. Substoichiometric shifting by asymmetrical exchange created the appearance of rapid sequence gain and loss in association with particular repeat classes. Conclusions Extensive mitochondrial genomic variation within a single plant species derives largely from DSB activity and its repair. Observed gene conversion and mismatch repair activity contribute to the low nucleotide substitution rates seen in these genomes. On a phenotypic level, these patterns of rearrangement likely contribute to the reproductive versatility of higher plants. 13. Assembly and function of DNA double-strand break repair foci in mammalian cells DEFF Research Database (Denmark) Bekker-Jensen, Simon; Mailand, Niels 2010-01-01 DNA double-strand breaks (DSBs) are among the most cytotoxic types of DNA damage, which if left unrepaired can lead to mutations or gross chromosomal aberrations, and promote the onset of diseases associated with genomic instability such as cancer. One of the most discernible hallmarks of the cel...... of such DNA repair foci still remains limited. In this review, we focus on recent discoveries on the mechanisms that govern the formation of IRIF, and discuss the implications of such findings in light of our understanding of the physiological importance of these structures.......DNA double-strand breaks (DSBs) are among the most cytotoxic types of DNA damage, which if left unrepaired can lead to mutations or gross chromosomal aberrations, and promote the onset of diseases associated with genomic instability such as cancer. One of the most discernible hallmarks...... of the cellular response to DSBs is the accumulation and local concentration of a plethora of DNA damage signaling and repair proteins in the vicinity of the lesion, initiated by ATM-mediated phosphorylation of H2AX (¿-H2AX) and culminating in the generation of distinct nuclear compartments, so-called Ionizing... 14. Alterations in the nuclear matrix protein mass correlate with heat-induced inhibition of DNA single-strand-break repair International Nuclear Information System (INIS) The total protein mass co-isolating with the nuclear matrix or nucleoid from Chinese hamster ovary (CHO) cells was observed to increase in heated cells as a function of increasing exposure temperature between 430C and 450C or of exposure time at any temperature. The sedimentation distance of the CHO cell nucleoid in sucrose gradients increased with increasing exposure time at 450C. Both these nuclear alterations correlated in a log-linear manner with heat-induced inhibition of DNA strand break repair. A two-fold threshold increase in nuclear matrix protein mass preceded any substantial inhibition of repair of DNA single-strand breaks. When preheated cells were incubated at 370C the nuclear matrix protein mass and nucleoid sedimentation recovered with a half-time of about 5 h, while DNA single-strand-break repair recovered with a half-time of about 2 h. When preheated cells were placed at 410C a further increase was observed in the nuclear matrix protein mass and the half-time of DNA strand break repair, while nucleoid sedimentation recovered toward control values. These results implicate alterations in the protein mass of the nuclear matrix in heat-induced inhibition of repair of DNA single-strand breaks. (author) 15. RecA bundles mediate homology pairing between distant sisters during DNA break repair Science.gov (United States) Lesterlin, Christian; Ball, Graeme; Schermelleh, Lothar; Sherratt, David J. 2014-02-01 DNA double-strand break (DSB) repair by homologous recombination has evolved to maintain genetic integrity in all organisms. Although many reactions that occur during homologous recombination are known, it is unclear where, when and how they occur in cells. Here, by using conventional and super-resolution microscopy, we describe the progression of DSB repair in live Escherichia coli. Specifically, we investigate whether homologous recombination can occur efficiently between distant sister loci that have segregated to opposite halves of an E. coli cell. We show that a site-specific DSB in one sister can be repaired efficiently using distant sister homology. After RecBCD processing of the DSB, RecA is recruited to the cut locus, where it nucleates into a bundle that contains many more RecA molecules than can associate with the two single-stranded DNA regions that form at the DSB. Mature bundles extend along the long axis of the cell, in the space between the bulk nucleoid and the inner membrane. Bundle formation is followed by pairing, in which the two ends of the cut locus relocate at the periphery of the nucleoid and together move rapidly towards the homology of the uncut sister. After sister locus pairing, RecA bundles disassemble and proteins that act late in homologous recombination are recruited to give viable recombinants 1-2-generation-time equivalents after formation of the initial DSB. Mutated RecA proteins that do not form bundles are defective in sister pairing and in DSB-induced repair. This work reveals an unanticipated role of RecA bundles in channelling the movement of the DNA DSB ends, thereby facilitating the long-range homology search that occurs before the strand invasion and transfer reactions. 16. Enhancing repair of radiation-induced strand breaks in cellular DNA as a radiotherapeutic potential International Nuclear Information System (INIS) 17. DNA breaks and repair in interstitial telomere sequences: Influence of chromatin structure; Etude des cassures de l'ADN et des mecanismes de reparation dans les sequences telomeriques interstitielles: Influence de la structure chromatinienne Energy Technology Data Exchange (ETDEWEB) Revaud, D. 2009-06-15 Interstitial Telomeric Sequences (ITS) are over-involved in spontaneous and radiationinduced chromosome aberrations in chinese hamster cells. We have performed a study to investigate the origin of their instability, spontaneously or after low doses irradiation. Our results demonstrate that ITS have a particular chromatin structure: short nucleotide repeat length, less compaction of the 30 nm chromatin fiber, presence of G-quadruplex structures. These features would modulate breaks production and would favour the recruitment of alternative DNA repair mechanisms, which are prone to produce chromosome aberrations. These pathways could be at the origin of chromosome aberrations in ITS whereas NHEJ and HR Double Strand Break repair pathways are rather required for a correct repair in these regions. (author) 18. Microhomology-mediated end joining is the principal mediator of double-strand break repair during mitochondrial DNA lesions OpenAIRE Tadi, Satish Kumar; Sebastian, Robin; Dahal, Sumedha; Babu, Ravi K.; Choudhary, Bibha; Raghavan, Sathees C. 2016-01-01 Mitochondrial DNA (mtDNA) deletions are associated with various mitochondrial disorders. The deletions identified in humans are flanked by short, directly repeated mitochondrial DNA sequences; however, the mechanism of such DNA rearrangements has yet to be elucidated. In contrast to nuclear DNA (nDNA), mtDNA is more exposed to oxidative damage, which may result in double-strand breaks (DSBs). Although DSB repair in nDNA is well studied, repair mechanisms in mitochondria are not characterized.... 19. Repair of DNA double-strand breaks in Escherichia coli cells requires synthesis of proteins that can be induced by UV light International Nuclear Information System (INIS) The repair of DNA double-strand breaks in Escherichia coli cells irradiated with γ rays occurs only after new proteins are synthesized in response to damage introduced in the genome DNA. One protein whose synthesis is thus induced is the recA protein, and previous work has shown that recA- cells do not repair double-strand breaks. However, inducing recA protein by treating cells with nalidixic acid does not induce repair of double-strand breaks, so this repair requires more than the presence of the recA protein. When repair of double-strand breaks is blocked, the genome DNA is degraded by an endonuclease-like action. Evidence is presented to show that the inducible inhibition of DNA degradation after x-irradiation [Pollard, E.C. and Randall, E.P. (1973) Radiat. Res. 55, 265] is probably caused by the inducible repair of DNA double-strand breaks 20. DNA repair pathways in radiation induced cellular damage: a molecular approach NARCIS (Netherlands) L.R. van Veelen (Lieneke) 2005-01-01 markdownabstract__Abstract__ DNA damage, especially double-strand breaks, can be induced by endogenous or exogenous darnaging agents, such as ionizing radiation. Repair of DNA damage is very important in maintaining genomic stability. Incorrect repair may lead to chromosomal aberrations, translocat 1. DNA double strand break repair enzymes function at multiple steps in retroviral infection Directory of Open Access Journals (Sweden) Agematsu Kazunaga 2009-12-01 Full Text Available Abstract Background DNA double strand break (DSB repair enzymes are thought to be necessary for retroviral infection, especially for the post-integration repair and circularization of viral cDNA. However, the detailed roles of DSB repair enzymes in retroviral infection remain to be elucidated. Results A GFP reporter assay showed that the infectivity of an HIV-based vector decreased in ATM- and DNA-PKcs-deficient cells when compared with their complemented cells, while that of an MLV-based vector was diminished in Mre11- and DNA-PKcs-deficient cells. By using a method based on inverse- and Alu-PCR, we analyzed sequences around 3' HIV-1 integration sites in ATM-, Mre11- and NBS1- deficient cells. Increased abnormal junctions between the HIV-1 provirus and the host DNA were found in these mutant cell lines compared to the complemented cell lines and control MRC5SV cells. The abnormal junctions contained two types of insertions: 1 GT dinucleotides, which are normally removed by integrase during integration, and 2 inserted nucleotides of unknown origin. Artemis-deficient cells also showed such abnormalities. In Mre11-deficient cells, part of a primer binding site sequence was also detected. The 5' host-virus junctions in the mutant cells also contained these types of abnormal nucleotides. Moreover, the host-virus junctions of the MLV provirus showed similar abnormalities. These findings suggest that DSB repair enzymes play roles in the 3'-processing reaction and protection of the ends of viral DNA after reverse transcription. We also identified both 5' and 3' junctional sequences of the same provirus by inverse PCR and found that only the 3' junctions were abnormal with aberrant short repeats, indicating that the integration step was partially impaired in these cells. Furthermore, the conserved base preferences around HIV-1 integration sites were partially altered in ATM-deficient cells. Conclusions These results suggest that DSB repair enzymes are 2. Analysis of gene repair tracts from Cas9/gRNA double-stranded breaks in the human CFTR gene. Science.gov (United States) Hollywood, Jennifer A; Lee, Ciaran M; Scallan, Martina F; Harrison, Patrick T 2016-01-01 To maximise the efficiency of template-dependent gene editing, most studies describe programmable and/or RNA-guided endonucleases that make a double-stranded break at, or close to, the target sequence to be modified. The rationale for this design strategy is that most gene repair tracts will be very short. Here, we describe a CRISPR Cas9/gRNA selection-free strategy which uses deep sequencing to characterise repair tracts from a donor plasmid containing seven nucleotide differences across a 216 bp target region in the human CFTR gene. We found that 90% of the template-dependent repair tracts were >100 bp in length with equal numbers of uni-directional and bi-directional repair tracts. The occurrence of long repair tracts suggests that a single gRNA could be used with variants of the same template to create or correct specific mutations within a 200 bp range, the size of ~80% of human exons. The selection-free strategy used here also allowed detection of non-homologous end joining events in many of the homology-directed repair tracts. This indicates a need to modify the donor, possibly by silent changes in the PAM sequence, to prevent creation of a second double-stranded break in an allele that has already been correctly edited by homology-directed repair. PMID:27557525 3. Understanding the role of RecN in DSB repair pathway in Deinococcus radiodurans International Nuclear Information System (INIS) Deinococcus radiodurans is a Gram-positive bacterium known for its extreme resistance to a broad variety of DNA damaging agents. Among these, Ionizing Radiations and desiccation are the most harmful for the cell, since they introduce breaks in the genome. Double Strand Breaks (DSB) are particularly hazardous for the cell and they need to be repaired very efficiently, in order to avoid mutations leading to altered, if not lethal, phenotypes. Homologous Recombination (HR) is the most efficient mechanism by which DSBs are repaired. D. radiodurans is able to completely restore its genome in only 3 hours, and it accomplishes the entire process through the RecFOR pathway. In order to be repaired, DSBs first need to be recognized. The protein believed to be responsible for this important step that takes place soon after the damage occurs in the cell, is RecN. RecN is recruited at the early stages of DNA repair and in vivo studies have demonstrated its propensity to localize to discrete foci. In vitro studies also suggest that RecN possesses a DNA end-joining activity previously observed for SMC proteins (such as cohesin), which are structurally related to RecN. Several structural studies have been carried out on the SMC-like protein, Rad50, but so far no structural information is available for RecN. The work presented here focused on the structural characterization of RecN and its constitutive domains. We obtained crystal structures of three partially overlapping constructs of RecN and Small Angle X-ray Scattering was performed on the individual domains and the full-length protein. The study of RecN in solution complemented our crystallographic study and enabled us to build a reliable, atomic model of the full-length protein. Mutations were designed and the mutant RecN proteins were produced in order to characterize the ATP hydrolysis activity of RecN, which is a conserved feature of this family of proteins. Extensive biochemical studies were carried out on wild-type and 4. RECQL4 Promotes DNA End Resection in Repair of DNA Double-Strand Breaks. Science.gov (United States) Lu, Huiming; Shamanna, Raghavendra A; Keijzers, Guido; Anand, Roopesh; Rasmussen, Lene Juel; Cejka, Petr; Croteau, Deborah L; Bohr, Vilhelm A 2016-06-28 The RecQ helicase RECQL4, mutated in Rothmund-Thomson syndrome, regulates genome stability, aging, and cancer. Here, we identify a crucial role for RECQL4 in DNA end resection, which is the initial and an essential step of homologous recombination (HR)-dependent DNA double-strand break repair (DSBR). Depletion of RECQL4 severely reduces HR-mediated repair and 5' end resection in vivo. RECQL4 physically interacts with MRE11-RAD50-NBS1 (MRN), which senses DSBs and initiates DNA end resection with CtIP. The MRE11 exonuclease regulates the retention of RECQL4 at laser-induced DSBs. RECQL4 also directly interacts with CtIP via its N-terminal domain and promotes CtIP recruitment to the MRN complex at DSBs. Moreover, inactivation of RECQL4's helicase activity impairs DNA end processing and HR-dependent DSBR without affecting its interaction with MRE11 and CtIP, suggesting an important role for RECQL4's unwinding activity in the process. Thus, we report that RECQL4 is an important participant in HR-dependent DSBR. 5. Deficiency of DNA double-strand break repair and enhanced radiosensitivity in Tip60 silenced cells International Nuclear Information System (INIS) Objective: To investigate the effect of Tip60 on the cellular radiosensitivity,and to explore the related mechanism. Methods: siRNA and anacardic acid (AA, an inhibitor of Tip60 acetyltransferase) were used to inhibit Tip60 expression and its acetyltransferase activity, respectively. Radiosensitivity was analyzed by colony-forming ability assay. γ-H2AX foci were detected to analyze the DNA double-strand break (DSB). Immunoprecipitation was used to determine the interaction of proteins. Results: siRNA-mediated silencing of Tip60 led to enhanced sensitivity of U2OS cells at 1, 2 Gy after γ-ray irradiation, but had no significant effect at 4 Gy post-irradiation (t=3.364, 3.979, P<0.05).γ-H2AX foci detection indicated that Tip60 silencing resulted in a decreased capability of DNA double-strand break repair at 1, 4 and 8 h after irradiation (t=3.875, 3.183 and 3.175, respectively, P<0.05). The interaction of Tip60 and DNA-PKcs was prompted by ionizing radiation. Anacardic acid largely abrogated the phosphorylation of DNA-PKcs at T2609 site induced by irradiation. Conclusions: Tip60 plays a role in the cellular response to ionizing radiation-induced DNA damage through, at least in part, interacting with DNA-PKcs and regulating its phosphorylation. (authors) 6. Repair pathways independent of the Fanconi anemia nuclear core complex play a predominant role in mitigating formaldehyde-induced DNA damage Energy Technology Data Exchange (ETDEWEB) Noda, Taichi [Department of Biology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Department of Dermatology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Takahashi, Akihisa [Department of Biology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Kondo, Natsuko [Particle Radiation Oncology Research Center, Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 590-0494 (Japan); Mori, Eiichiro [Department of Biology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Okamoto, Noritomo [Department of Otorhinolaryngology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Nakagawa, Yosuke [Department of Oral and Maxillofacial Surgery, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); Ohnishi, Ken [Department of Biology, Ibaraki Prefectual University of Health Sciences, 4669-2 Ami, Ami-mati, Inasiki-gun, Ibaraki 300-0394 (Japan); Zdzienicka, Malgorzata Z. [Department of Molecular Cell Genetics, Collegium Medicum in Bydgoszcz, Nicolaus-Copernicus-University in Torun, ul. Sklodowskiej-Curie 9, 85-094 Bydgoszcz (Poland); Thompson, Larry H. [Biosciences and Biotechnology Division, L452, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-0808 (United States); Helleday, Thomas [Gray Institute for Radiation Oncology and Biology, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford, OX3 7DQ (United Kingdom); Department of Genetics, Microbiology and Toxicology Stockholm University, SE-106 91 Stockholm (Sweden); Asada, Hideo [Department of Dermatology, School of Medicine, Nara Medical University, 840 Shijo-cho, Kashihara, Nara 634-8521 (Japan); and others 2011-01-07 The role of the Fanconi anemia (FA) repair pathway for DNA damage induced by formaldehyde was examined in the work described here. The following cell types were used: mouse embryonic fibroblast cell lines FANCA{sup -/-}, FANCC{sup -/-}, FANCA{sup -/-}C{sup -/-}, FANCD2{sup -/-} and their parental cells, the Chinese hamster cell lines FANCD1 mutant (mt), FANCGmt, their revertant cells, and the corresponding wild-type (wt) cells. Cell survival rates were determined with colony formation assays after formaldehyde treatment. DNA double strand breaks (DSBs) were detected with an immunocytochemical {gamma}H2AX-staining assay. Although the sensitivity of FANCA{sup -/-}, FANCC{sup -/-} and FANCA{sup -/-}C{sup -/-} cells to formaldehyde was comparable to that of proficient cells, FANCD1mt, FANCGmt and FANCD2{sup -/-} cells were more sensitive to formaldehyde than the corresponding proficient cells. It was found that homologous recombination (HR) repair was induced by formaldehyde. In addition, {gamma}H2AX foci in FANCD1mt cells persisted for longer times than in FANCD1wt cells. These findings suggest that formaldehyde-induced DSBs are repaired by HR through the FA repair pathway which is independent of the FA nuclear core complex. -- Research highlights: {yields} We examined to clarify the repair pathways of formaldehyde-induced DNA damage. Formaldehyde induces DNA double strand breaks (DSBs). {yields} DSBs are repaired through the Fanconi anemia (FA) repair pathway. {yields} This pathway is independent of the FA nuclear core complex. {yields} We also found that homologous recombination repair was induced by formaldehyde. 7. Mre11 ATLD17/18 mutation retains Tel1/ATM activity but blocks DNA double-strand break repair NARCIS (Netherlands) O. Limbo (Oliver); D. Moiani (Davide); A. Kertokalio (Aryandi); C. Wyman (Claire); J.A. Tainer (John); P. Russell (Paul) 2012-01-01 textabstractThe Mre11 complex (Mre11-Rad50-Nbs1 or MRN) binds double-strand breaks where it interacts with CtIP/Ctp1/Sae2 and ATM/Tel1 to preserve genome stability through its functions in homology-directed repair, checkpoint signaling and telomere maintenance. Here, we combine biochemical, structur 8. Increased DNA double-strand break was associated with downregulation of repair and upregulation of apoptotic factors in rat hippocampus after alcohol exposure. Science.gov (United States) Suman, Shubhankar; Kumar, Santosh; N'Gouemo, Prosper; Datta, Kamal 2016-08-01 Binge drinking is known to cause damage in critical areas of the brain, including the hippocampus, which is important for relational memory and is reported to be sensitive to alcohol toxicity. However, the roles of DNA double-strand break (DSB) and its repair pathways, homologous recombination (HR), and non-homologous end joining (NHEJ) in alcohol-induced hippocampal injury remain to be elucidated. The purpose of this first study was to assess alcohol-induced DNA DSB and the mechanism by which alcohol affects DSB repair pathways in rat hippocampus. Male Sprague-Dawley rats (8-10 weeks old) were put on a 4-day binge ethanol treatment regimen. Control animals were maintained under similar conditions but were given the vehicle without ethanol. All animals were humanely euthanized 24 h after the last dose of ethanol administration and the hippocampi were dissected for immunoblot and immunohistochemistry analysis. Ethanol exposure caused increased 4-hydroxynonenal (4-HNE) staining as well as elevated γH2AX and 53BP1 foci in hippocampal cells. Immunoblot analysis showed decreased Mre11, Rad51, Rad50, and Ku86 as well as increased Bax and p21 in samples from ethanol-treated rats. Additionally, we also observed increased activated caspase3 staining in hippocampal cells 24 h after ethanol withdrawal. Taken together, our data demonstrated that ethanol concurrently induced DNA DSB, downregulated DSB repair pathway proteins, and increased apoptotic factors in hippocampal cells. We believe these findings will provide the impetus for further research on DNA DSB and its repair pathways in relation to alcohol toxicity in brain. PMID:27565756 9. Targeting the DNA Repair Pathway in Ewing Sarcoma Directory of Open Access Journals (Sweden) Elizabeth Stewart 2014-11-01 Full Text Available Ewing sarcoma (EWS is a tumor of the bone and soft tissue that primarily affects adolescents and young adults. With current therapies, 70% of patients with localized disease survive, but patients with metastatic or recurrent disease have a poor outcome. We found that EWS cell lines are defective in DNA break repair and are sensitive to PARP inhibitors (PARPis. PARPi-induced cytotoxicity in EWS cells was 10- to 1,000-fold higher after administration of the DNA-damaging agents irinotecan or temozolomide. We developed an orthotopic EWS mouse model and performed pharmacokinetic and pharmacodynamic studies using three different PARPis that are in clinical development for pediatric cancer. Irinotecan administered on a low-dose, protracted schedule previously optimized for pediatric patients was an effective DNA-damaging agent when combined with PARPis; it was also better tolerated than combinations with temozolomide. Combining PARPis with irinotecan and temozolomide gave complete and durable responses in more than 80% of the mice. 10. Molecular Process Producing Oncogene Fusion in Lung Cancer Cells by Illegitimate Repair of DNA Double-Strand Breaks Directory of Open Access Journals (Sweden) Yoshitaka Seki 2015-09-01 Full Text Available Constitutive activation of oncogenes by fusion to partner genes, caused by chromosome translocation and inversion, is a critical genetic event driving lung carcinogenesis. Fusions of the tyrosine kinase genes ALK (anaplastic lymphoma kinase, ROS1 (c-ros oncogene 1, or RET (rearranged during transfection occur in 1%–5% of lung adenocarcinomas (LADCs and their products constitute therapeutic targets for kinase inhibitory drugs. Interestingly, ALK, RET, and ROS1 fusions occur preferentially in LADCs of never- and light-smokers, suggesting that the molecular mechanisms that cause these rearrangements are smoking-independent. In this study, using previously reported next generation LADC genome sequencing data of the breakpoint junction structures of chromosome rearrangements that cause oncogenic fusions in human cancer cells, we employed the structures of breakpoint junctions of ALK, RET, and ROS1 fusions in 41 LADC cases as “traces” to deduce the molecular processes of chromosome rearrangements caused by DNA double-strand breaks (DSBs and illegitimate joining. We found that gene fusion was produced by illegitimate repair of DSBs at unspecified sites in genomic regions of a few kb through DNA synthesis-dependent or -independent end-joining pathways, according to DSB type. This information will assist in the understanding of how oncogene fusions are generated and which etiological factors trigger them. 11. How SUMOylation Fine-Tunes the Fanconi Anemia DNA Repair Pathway. Science.gov (United States) Coleman, Kate E; Huang, Tony T 2016-01-01 Fanconi anemia (FA) is a rare human genetic disorder characterized by developmental defects, bone marrow failure and cancer predisposition, primarily due to a deficiency in the repair of DNA interstrand crosslinks (ICLs). ICL repair through the FA DNA repair pathway is a complicated multi-step process, involving at least 19 FANC proteins and coordination of multiple DNA repair activities, including homologous recombination, nucleotide excision repair and translesion synthesis (TLS). SUMOylation is a critical regulator of several DNA repair pathways, however, the role of this modification in controlling the FA pathway is poorly understood. Here, we summarize recent advances in the fine-tuning of the FA pathway by small ubiquitin-like modifier (SUMO)-targeted ubiquitin ligases (STUbLs) and other SUMO-related interactions, and discuss the implications of these findings in the design of novel therapeutics for alleviating FA-associated condition, including cancer. PMID:27148358 12. Homologous recombination and non-homologous end-joining repair pathways in bovine embryos with different developmental competence International Nuclear Information System (INIS) This study investigated the expression of genes controlling homologous recombination (HR), and non-homologous end-joining (NHEJ) DNA-repair pathways in bovine embryos of different developmental potential. It also evaluated whether bovine embryos can respond to DNA double-strand breaks (DSBs) induced with ultraviolet irradiation by regulating expression of genes involved in HR and NHEJ repair pathways. Embryos with high, intermediate or low developmental competence were selected based on the cleavage time after in vitro insemination and were removed from in vitro culture before (36 h), during (72 h) and after (96 h) the expected period of embryonic genome activation. All studied genes were expressed before, during and after the genome activation period regardless the developmental competence of the embryos. Higher mRNA expression of 53BP1 and RAD52 was found before genome activation in embryos with low developmental competence. Expression of 53BP1, RAD51 and KU70 was downregulated at 72 h and upregulated at 168 h post-insemination in response to DSBs induced by ultraviolet irradiation. In conclusion, important genes controlling HR and NHEJ DNA-repair pathways are expressed in bovine embryos, however genes participating in these pathways are only regulated after the period of embryo genome activation in response to ultraviolet-induced DSBs. 13. Homologous recombination and non-homologous end-joining repair pathways in bovine embryos with different developmental competence Energy Technology Data Exchange (ETDEWEB) Henrique Barreta, Marcos [Universidade Federal de Santa Catarina, Campus Universitario de Curitibanos, Curitibanos, SC (Brazil); Laboratorio de Biotecnologia e Reproducao Animal-BioRep, Universidade Federal de Santa Maria, Santa Maria, RS (Brazil); Garziera Gasperin, Bernardo; Braga Rissi, Vitor; Cesaro, Matheus Pedrotti de [Laboratorio de Biotecnologia e Reproducao Animal-BioRep, Universidade Federal de Santa Maria, Santa Maria, RS (Brazil); Ferreira, Rogerio [Centro de Educacao Superior do Oeste-Universidade do Estado de Santa Catarina, Chapeco, SC (Brazil); Oliveira, Joao Francisco de; Goncalves, Paulo Bayard Dias [Laboratorio de Biotecnologia e Reproducao Animal-BioRep, Universidade Federal de Santa Maria, Santa Maria, RS (Brazil); Bordignon, Vilceu, E-mail: [email protected] [Department of Animal Science, McGill University, Ste-Anne-De-Bellevue, QC (Canada) 2012-10-01 This study investigated the expression of genes controlling homologous recombination (HR), and non-homologous end-joining (NHEJ) DNA-repair pathways in bovine embryos of different developmental potential. It also evaluated whether bovine embryos can respond to DNA double-strand breaks (DSBs) induced with ultraviolet irradiation by regulating expression of genes involved in HR and NHEJ repair pathways. Embryos with high, intermediate or low developmental competence were selected based on the cleavage time after in vitro insemination and were removed from in vitro culture before (36 h), during (72 h) and after (96 h) the expected period of embryonic genome activation. All studied genes were expressed before, during and after the genome activation period regardless the developmental competence of the embryos. Higher mRNA expression of 53BP1 and RAD52 was found before genome activation in embryos with low developmental competence. Expression of 53BP1, RAD51 and KU70 was downregulated at 72 h and upregulated at 168 h post-insemination in response to DSBs induced by ultraviolet irradiation. In conclusion, important genes controlling HR and NHEJ DNA-repair pathways are expressed in bovine embryos, however genes participating in these pathways are only regulated after the period of embryo genome activation in response to ultraviolet-induced DSBs. 14. Recombinational repair of radiation-induced double-strand breaks occurs in the absence of extensive resection Science.gov (United States) Westmoreland, James W.; Resnick, Michael A. 2016-01-01 Recombinational repair provides accurate chromosomal restitution after double-strand break (DSB) induction. While all DSB recombination repair models include 5′-3′ resection, there are no studies that directly assess the resection needed for repair between sister chromatids in G-2 arrested cells of random, radiation-induced ‘dirty’ DSBs. Using our Pulse Field Gel Electrophoresis-shift approach, we determined resection at IR-DSBs in WT and mutants lacking exonuclease1 or Sgs1 helicase. Lack of either reduced resection length by half, without decreased DSB repair or survival. In the exo1Δ sgs1Δ double mutant, resection was barely detectable, yet it only took an additional hour to achieve a level of repair comparable to WT and there was only a 2-fold dose-modifying effect on survival. Results with a Dnl4 deletion strain showed that remaining repair was not due to endjoining. Thus, similar to what has been shown for a single, clean HO-induced DSB, a severe reduction in resection tract length has only a modest effect on repair of multiple, dirty DSBs in G2-arrested cells. Significantly, this study provides the first opportunity to directly relate resection length at DSBs to the capability for global recombination repair between sister chromatids. PMID:26503252 15. The Vitamin A Derivative All-Trans Retinoic Acid Repairs Amyloid-β-Induced Double-Strand Breaks in Neural Cells and in the Murine Neocortex Directory of Open Access Journals (Sweden) Emmanuelle Gruz-Gibelli 2016-01-01 Full Text Available The amyloid-β peptide or Aβ is the key player in the amyloid-cascade hypothesis of Alzheimer’s disease. Aβ appears to trigger cell death but also production of double-strand breaks (DSBs in aging and Alzheimer’s disease. All-trans retinoic acid (RA, a derivative of vitamin A, was already known for its neuroprotective effects against the amyloid cascade. It diminishes, for instance, the production of Aβ peptides and their oligomerisation. In the present work we investigated the possible implication of RA receptor (RAR in repair of Aβ-induced DSBs. We demonstrated that RA, as well as RAR agonist Am80, but not AGN 193109 antagonist, repair Aβ-induced DSBs in SH-SY5Y cells and an astrocytic cell line as well as in the murine cortical tissue of young and aged mice. The nonhomologous end joining pathway and the Ataxia Telangiectasia Mutated kinase were shown to be involved in RA-mediated DSBs repair in the SH-SY5Y cells. Our data suggest that RA, besides increasing cell viability in the cortex of young and even of aged mice, might also result in targeted DNA repair of genes important for cell or synaptic maintenance. This phenomenon would remain functional up to a point when Aβ increase and RA decrease probably lead to a pathological state. 16. Histone deacetylase inhibitors decrease NHEJ both by acetylation of repair factors and trapping of PARP1 at DNA double-strand breaks in chromatin Science.gov (United States) Robert, Carine; Nagaria, Pratik K.; Pawar, Nisha; Adewuyi, Adeoluwa; Gojo, Ivana; Meyers, David J.; Cole, Philip A.; Rassool, Feyruz V. 2016-01-01 Histone deacetylase inhibitors (HDACi) induce acetylation of histone and non-histone proteins, and modulate the acetylation of proteins involved in DNA double-strand break (DSB) repair. Non-homologous end-joining (NHEJ) is one of the main pathways for repairing DSBs. Decreased NHEJ activity has been reported with HDACi treatment. However, mechanisms through which these effects are regulated in the context of chromatin are unclear. We show that pan-HDACi, trichostatin A (TSA), causes differential acetylation of DNA repair factors Ku70/Ku80 and poly ADP-ribose polymerase-1 (PARP1), and impairs NHEJ. Repair effects are reversed by treatments with p300/CBP inhibitor C646, with significantly decreased acetylation of PARP1. In keeping with these findings, TSA treatment significantly increases PARP1 binding to DSBs in chromatin. Notably, AML patients treated with HDACi entinostat (MS275) in vivo also show increased formation of poly ADP-ribose (PAR) that co-localizes with DSBs. Further, we demonstrate that PARP1 bound to chromatin increases with duration of TSA exposure, resembling PARP “trapping”. Knockdown of PARP1 inhibits trapping and mitigates HDACi effects on NHEJ. Finally, combination of HDACi with potent PARP inhibitor talazoparib (BMN673) shows a dose-dependent increase in PARP “trapping”, which correlates with increased apoptosis. These results provide a mechanism through which HDACi inhibits deacetylation and increases binding of PARP1 to DSBs, leading to decreased NHEJ and cytotoxicity of leukemia cells. PMID:27064363 17. Identification of defective illegitimate recombinational repair of oxidatively-induced DNA double-strand breaks in ataxia-telangiectasia cells Science.gov (United States) Dar, M. E.; Winters, T. A.; Jorgensen, T. J. 1997-01-01 Ataxia-telangiectasia (A-T) is an autosomal-recessive lethal human disease. Homozygotes suffer from a number of neurological disorders, as well as very high cancer incidence. Heterozygotes may also have a higher than normal risk of cancer, particularly for the breast. The gene responsible for the disease (ATM) has been cloned, but its role in mechanisms of the disease remain unknown. Cellular A-T phenotypes, such as radiosensitivity and genomic instability, suggest that a deficiency in the repair of DNA double-strand breaks (DSBs) may be the primary defect; however, overall levels of DSB rejoining appear normal. We used the shuttle vector, pZ189, containing an oxidatively-induced DSB, to compare the integrity of DSB rejoining in one normal and two A-T fibroblast cells lines. Mutation frequencies were two-fold higher in A-T cells, and the mutational spectrum was different. The majority of the mutations found in all three cell lines were deletions (44-63%). The DNA sequence analysis indicated that 17 of the 17 plasmids with deletion mutations in normal cells occurred between short direct-repeat sequences (removing one of the repeats plus the intervening sequences), implicating illegitimate recombination in DSB rejoining. The combined data from both A-T cell lines showed that 21 of 24 deletions did not involve direct-repeats sequences, implicating a defect in the illegitimate recombination pathway. These findings suggest that the A-T gene product may either directly participate in illegitimate recombination or modulate the pathway. Regardless, this defect is likely to be important to a mechanistic understanding of this lethal disease. 18. DNA single-strand breaks, double-strand breaks, and crosslinks in rat testicular germ cells: Measurements of their formation and repair by alkaline and neutral filter elution International Nuclear Information System (INIS) This work describes a neutral and alkaline elution method for measuring DNA single-strand breaks (SSBs), DNA double-strand breaks (DSBs), and DNA-DNA crosslinks in rat testicular germ cells after treatments in vivo or in vitro with both chemical mutagens and gamma-irradiation. The methods depend upon the isolation of testicular germ cells by collagenase and trypsin digestion, followed by filtration and centrifugation. 137Cs irradiation induced both DNA SSBs and DSBs in germ cells held on ice in vitro. Irradiation of the whole animal indicated that both types of DNA breaks are induced in vivo and can be repaired. A number of germ cell mutagens induced either DNA SSBs, DSBs, or cross-links after in vivo and in vitro dosing. These chemicals included methyl methanesulfonate, ethyl methanesulfonate, ethyl nitrosourea, dibromochlorpropane, ethylene dibromide, triethylene melamine, and mitomycin C. These results suggest that the blood-testes barrier is relatively ineffective for these mutagens, which may explain in part their in vivo mutagenic potency. This assay should be a useful screen for detecting chemical attack upon male germ-cell DNA and thus, it should help in the assessment of the mutagenic risk of chemicals. In addition, this approach can be used to study the processes of SSB, DSB, and crosslink repair in DNA of male germ cells, either from all stages or specific stages of development 19. Ago2 facilitates Rad51 recruitment and DNA double-strand break repair by homologous recombination DEFF Research Database (Denmark) Gao, Min; Wei, Wei; Li, Ming Hua; 2014-01-01 (Ago) proteins and play an important role in DSB repair, though the mechanism through which they act remains unclear. Here, we report that the role of diRNAs in DSB repair is restricted to repair by homologous recombination (HR) and that it specifically relies on the effector protein Ago2 in mammalian...... to facilitate repair by HR.... 20. Experimental investigation of two oil dispersion pathways by breaking waves Science.gov (United States) Li, Cheng; Katz, Joseph 2014-11-01 This experimental study focuses on generation and size distribution of airborne and subsurface oil droplets as breaking surface waves interact with a crude oil slick (MC252 surrogate). Experiments in a specialized wave tank investigate the effects of wave height and wave properties (e.g. spilling vs. plunging), as well as drastically reducing the oil-water interfacial tension by orders of magnitude by introducing dispersant (Coexist 9500-A). This dispersant is applied at varying dispersant-to-oil ratios either by premixing or surface spraying, the latter consistent with typical application. The data include high-speed visualizations of processes affecting the entrainment of subsurface oil and bubbles as well as airborne aerosols. High-speed digital holographic cinematography is employed to track the droplet trajectories, and quantify the droplet size distributions above and below the surface. Introduction of dispersants drastically reduces the size of subsurface droplets to micron and even submicron levels. Ahead of the wave, the 25 μm (our present resolution limit) to 2 mm airborne droplet trajectories are aligned with the wave direction. Behind the wave, these droplets reverse their direction, presumably due to the airflow above the wave. Supported by Gulf of Mexico Research Initiative (GoMRI). 1. Approach to the classical radiation biology. Ionizing radiation effects and repair mechanism of DNA double strand breaks International Nuclear Information System (INIS) Split-dose recovery has been observed under a variety of experimental conditions in many cell systems and believed to be the recovery of sublethal damage (SLD). It is considered to be one of the most widespread and important cellular responses in clinical radiotherapy. To study the molecular mechanism of this recovery, we analyzed the knockout mutants KU70-/-, RAD54-/-, and KU70-/-/ RAD54-/- of the chicken B-cell line, DT40. Rad54 participates in the homologous recombinational (HR) repair of DNA double-strand breaks (DSB), while Ku proteins are involved in non-homologous end-joining (NHEJ). Split-dose recovery was observed in the parent DT40 and KU70-/- cells. Moreover the split-dose survival enhancement had all of the characteristics of SLD recovery that had been demonstrated earlier: e.g., the reappearance of the shoulder of the survival curve with dose fractionation; repair at 25degC; and inhibition by the antibiotic actinomycin D. These results strongly suggest that SLD recovery is due to DSB repair via or mediated by HR, and that these breaks constitute SLD. The tonicity-sensitive potentially lethal damage (PLD) recovery was also found only in DT40 and KU70 -/- cells. Delayed-plating PLD recovery may be controlled by NHEJ repair that works through the cell cycle. These results lead to the conclusion that the repair of DSBs could explain the classical operational recovery phenomena. We have also investigated RBE/LET using those mutants. (author) 2. PML nuclear body disruption impairs DNA double-strand break sensing and repair in APL Science.gov (United States) di Masi, A; Cilli, D; Berardinelli, F; Talarico, A; Pallavicini, I; Pennisi, R; Leone, S; Antoccia, A; Noguera, N I; Lo-Coco, F; Ascenzi, P; Minucci, S; Nervi, C 2016-01-01 Proteins involved in DNA double-strand break (DSB) repair localize within the promyelocytic leukemia nuclear bodies (PML-NBs), whose disruption is at the root of the acute promyelocytic leukemia (APL) pathogenesis. All-trans-retinoic acid (RA) treatment induces PML-RARα degradation, restores PML-NB functions, and causes terminal cell differentiation of APL blasts. However, the precise role of the APL-associated PML-RARα oncoprotein and PML-NB integrity in the DSB response in APL leukemogenesis and tumor suppression is still lacking. Primary leukemia blasts isolated from APL patients showed high phosphorylation levels of H2AX (γ-H2AX), an initial DSBs sensor. By addressing the consequences of ionizing radiation (IR)-induced DSB response in primary APL blasts and RA-responsive and -resistant myeloid cell lines carrying endogenous or ectopically expressed PML-RARα, before and after treatment with RA, we found that the disruption of PML-NBs is associated with delayed DSB response, as revealed by the impaired kinetic of disappearance of γ-H2AX and 53BP1 foci and activation of ATM and of its substrates H2AX, NBN, and CHK2. The disruption of PML-NB integrity by PML-RARα also affects the IR-induced DSB response in a preleukemic mouse model of APL in vivo. We propose the oncoprotein-dependent PML-NB disruption and DDR impairment as relevant early events in APL tumorigenesis. PMID:27468685 3. DNA Double Strand Break Repair and its Association with Inherited Predispositions to Breast Cancer Directory of Open Access Journals (Sweden) Scott Rodney J 2004-02-01 Full Text Available Abstract Mutations in BRCA1 account for the majority of familial aggregations of early onset breast and ovarian cancer (~70% and about 1/5 of all early onset breast cancer families; in contrast, mutations in BRCA2 account for a smaller proportion of breast/ovarian cancer families and a similar proportion of early onset breast cancer families. BRCA2 has also been shown to be associated with a much more pleiotropic disease spectrum compared to BRCA1. Since the identification of both BRCA1 and BRCA2 investigations into the functions of these genes have revealed that both are associated with the maintenance of genomic integrity via their apparent roles in cellular response to DNA damage, especially their involvement in the process of double strand DNA break repair. This review will focus on the specific roles of both genes and how functional differences may account for the diverse clinical findings observed between families that harbour BRCA1 or BRCA2 mutations. 4. The DNA damage checkpoint pathway promotes extensive resection and nucleotide synthesis to facilitate homologous recombination repair and genome stability in fission yeast. Science.gov (United States) Blaikley, Elizabeth J; Tinline-Purvis, Helen; Kasparek, Torben R; Marguerat, Samuel; Sarkar, Sovan; Hulme, Lydia; Hussey, Sharon; Wee, Boon-Yu; Deegan, Rachel S; Walker, Carol A; Pai, Chen-Chun; Bähler, Jürg; Nakagawa, Takuro; Humphrey, Timothy C 2014-05-01 DNA double-strand breaks (DSBs) can cause chromosomal rearrangements and extensive loss of heterozygosity (LOH), hallmarks of cancer cells. Yet, how such events are normally suppressed is unclear. Here we identify roles for the DNA damage checkpoint pathway in facilitating homologous recombination (HR) repair and suppressing extensive LOH and chromosomal rearrangements in response to a DSB. Accordingly, deletion of Rad3(ATR), Rad26ATRIP, Crb2(53BP1) or Cdc25 overexpression leads to reduced HR and increased break-induced chromosome loss and rearrangements. We find the DNA damage checkpoint pathway facilitates HR, in part, by promoting break-induced Cdt2-dependent nucleotide synthesis. We also identify additional roles for Rad17, the 9-1-1 complex and Chk1 activation in facilitating break-induced extensive resection and chromosome loss, thereby suppressing extensive LOH. Loss of Rad17 or the 9-1-1 complex results in a striking increase in break-induced isochromosome formation and very low levels of chromosome loss, suggesting the 9-1-1 complex acts as a nuclease processivity factor to facilitate extensive resection. Further, our data suggest redundant roles for Rad3ATR and Exo1 in facilitating extensive resection. We propose that the DNA damage checkpoint pathway coordinates resection and nucleotide synthesis, thereby promoting efficient HR repair and genome stability. PMID:24623809 5. TIGAR regulates DNA damage and repair through pentosephosphate pathway and Cdk5-ATM pathway. Science.gov (United States) Yu, Hong-Pei; Xie, Jia-Ming; Li, Bin; Sun, Yi-Hui; Gao, Quan-Geng; Ding, Zhi-Hui; Wu, Hao-Rong; Qin, Zheng-Hong 2015-01-01 Previous study revealed that the protective effect of TIGAR in cell survival is mediated through the increase in PPP (pentose phosphate pathway) flux. However, it remains unexplored if TIGAR plays an important role in DNA damage and repair. This study investigated the role of TIGAR in DNA damage response (DDR) induced by genotoxic drugs and hypoxia in tumor cells. Results showed that TIGAR was increased and relocated to the nucleus after epirubicin or hypoxia treatment in cancer cells. Knockdown of TIGAR exacerbated DNA damage and the effects were partly reversed by the supplementation of PPP products NADPH, ribose, or the ROS scavenger NAC. Further studies with pharmacological and genetic approaches revealed that TIGAR regulated the phosphorylation of ATM, a key protein in DDR, through Cdk5. The Cdk5-AMT signal pathway involved in regulation of DDR by TIGAR defines a new role of TIGAR in cancer cell survival and it suggests that TIGAR may be a therapeutic target for cancers. PMID:25928429 6. Either non-homologous ends joining or homologous recombination is required to repair double-strand breaks in the genome of macrophage-internalized Mycobacterium tuberculosis. Directory of Open Access Journals (Sweden) Anna Brzostek Full Text Available The intracellular pathogen Mycobacterium tuberculosis (Mtb is constantly exposed to a multitude of hostile conditions and is confronted by a variety of potentially DNA-damaging assaults in vivo, primarily from host-generated antimicrobial toxic radicals. Exposure to reactive nitrogen species and/or reactive oxygen species causes different types of DNA damage, including oxidation, depurination, methylation and deamination, that can result in single- or double-strand breaks (DSBs. These breaks affect the integrity of the whole genome and, when left unrepaired, can lead to cell death. Here, we investigated the role of the DSB repair pathways, homologous recombination (HR and non-homologous ends joining (NHEJ, in the survival of Mtb inside macrophages. To this end, we constructed Mtb strains defective for HR (ΔrecA, NHEJ [Δ(ku,ligD], or both DSB repair systems [Δ(ku,ligD,recA]. Experiments using these strains revealed that either HR or NHEJ is sufficient for the survival and propagation of tubercle bacilli inside macrophages. Inhibition of nitric oxide or superoxide anion production with L-NIL or apocynin, respectively, enabled the Δ(ku,ligD,recA mutant strain lacking both systems to survive intracellularly. Complementation of the Δ(ku,ligD,recA mutant with an intact recA or ku-ligD rescued the ability of Mtb to propagate inside macrophages. 7. Effects of hyperthermia on DNA repair pathways: one treatment to inhibit them all. Science.gov (United States) Oei, Arlene L; Vriend, Lianne E M; Crezee, Johannes; Franken, Nicolaas A P; Krawczyk, Przemek M 2015-01-01 The currently available arsenal of anticancer modalities includes many DNA damaging agents that can kill malignant cells. However, efficient DNA repair mechanisms protect both healthy and cancer cells against the effects of treatment and contribute to the development of drug resistance. Therefore, anti-cancer treatments based on inflicting DNA damage can benefit from inhibition of DNA repair. Hyperthermia - treatment at elevated temperature - considerably affects DNA repair, among other cellular processes, and can thus sensitize (cancer) cells to DNA damaging agents. This effect has been known and clinically applied for many decades, but how heat inhibits DNA repair and which pathways are targeted has not been fully elucidated. In this review we attempt to summarize the known effects of hyperthermia on DNA repair pathways relevant in clinical treatment of cancer. Furthermore, we outline the relationships between the effects of heat on DNA repair and sensitization of cells to various DNA damaging agents. PMID:26245485 8. More efficient repair of DNA double-strand breaks in skeletal muscle stem cells compared to their committed progeny Directory of Open Access Journals (Sweden) Leyla Vahidi Ferdousi 2014-11-01 Full Text Available The loss of genome integrity in adult stem cells results in accelerated tissue aging and is possibly cancerogenic. Adult stem cells in different tissues appear to react robustly to DNA damage. We report that adult skeletal stem (satellite cells do not primarily respond to radiation-induced DNA double-strand breaks (DSBs via differentiation and exhibit less apoptosis compared to other myogenic cells. Satellite cells repair these DNA lesions more efficiently than their committed progeny. Importantly, non-proliferating satellite cells and post-mitotic nuclei in the fiber exhibit dramatically distinct repair efficiencies. Altogether, reduction of the repair capacity appears to be more a function of differentiation than of the proliferation status of the muscle cell. Notably, satellite cells retain a high efficiency of DSB repair also when isolated from the natural niche. Finally, we show that repair of DSB substrates is not only very efficient but, surprisingly, also very accurate in satellite cells and that accurate repair depends on the key non-homologous end-joining factor DNA-PKcs. 9. Double-strand break repair and colorectal cancer: gene variants within 3′ UTRs and microRNAs binding as modulators of cancer risk and clinical outcome Science.gov (United States) Naccarati, Alessio; Rosa, Fabio; Vymetalkova, Veronika; Barone, Elisa; Jiraskova, Katerina; Di Gaetano, Cornelia; Novotny, Jan; Levy, Miroslav; Vodickova, Ludmila; Gemignani, Federica; Buchler, Tomas; Landi, Stefano 2016-01-01 Genetic variations in 3′ untranslated regions of target genes may affect microRNA binding, resulting in differential protein expression. microRNAs regulate DNA repair, and single-nucleotide polymorphisms in miRNA binding sites (miRSNPs) may account for interindividual differences in the DNA repair capacity. Our hypothesis is that miRSNPs in relevant DNA repair genes may ultimately affect cancer susceptibility and impact prognosis. In the present study, we analysed the association of polymorphisms in predicted microRNA target sites of double-strand breaks (DSBs) repair genes with colorectal cancer (CRC) risk and clinical outcome. Twenty-one miRSNPs in non-homologous end-joining and homologous recombination pathways were assessed in 1111 cases and 1469 controls. The variant CC genotype of rs2155209 in MRE11A was strongly associated with decreased cancer risk when compared with the other genotypes (OR 0.54, 95% CI 0.38–0.76, p = 0.0004). A reduced expression of the reporter gene was observed for the C allele of this polymorphism by in vitro assay, suggesting a more efficient interaction with potentially binding miRNAs. In colon cancer patients, the rs2155209 CC genotype was associated with shorter survival while the TT genotype of RAD52 rs11226 with longer survival when both compared with their respective more frequent genotypes (HR 1.63, 95% CI 1.06-2.51, p = 0.03 HR 0.60, 95% CI 0.41–0.89, p = 0.01, respectively). miRSNPs in DSB repair genes involved in the maintenance of genomic stability may have a role on CRC susceptibility and clinical outcome. PMID:26735576 10. Detection of DNA single-strand breaks during the repair of UV damage in xeroderma pigmentosum cells International Nuclear Information System (INIS) In this investigation, xeroderma pigmentosum (XP) fibroblasts, XP12BE, were uv-irradiated and then incubated with cytosine arabinoside and hydroxyurea for 4 hr to inhibit the polymerase step of DNA excision repair. By alkaline elution, DNA single-strand breaks (SSB) were detected in XP cells with this regimen with an efficiency of 0.1-0.2 SSB per 109 daltons of DNA per J m-2. There was an approximately linear relation between the SSB frequency and uv dose over a range of 0.2 to 25 J m-2. This effect was approximately two orders of magnitude greater in excision-proficient normal human fibroblasts than in XP cells. These results support the conclusion that a low residual level of DNA excision repair occurs in XP group A cells and that the SSB generated during this repair can be accumulated with this polymerase inhibitor 11. Contribution of DNA double-strand break repair gene XRCC3 genotypes to oral cancer susceptibility in Taiwan. Science.gov (United States) Tsai, Chia-Wen; Chang, Wen-Shin; Liu, Juhn-Cherng; Tsai, Ming-Hsui; Lin, Cheng-Chieh; Bau, Da-Tian 2014-06-01 The DNA repair gene X-ray repair cross complementing protein 3 (XRCC3) is thought to play a major role in double-strand break repair and in maintaining genomic stability. Very possibly, defective double-strand break repair of cells can lead to carcinogenesis. Therefore, a case-control study was performed to reveal the contribution of XRCC3 genotypes to individual oral cancer susceptibility. In this hospital-based research, the association of XRCC3 rs1799794, rs45603942, rs861530, rs3212057, rs1799796, rs861539, rs28903081 genotypes with oral cancer risk in a Taiwanese population was investigated. In total, 788 patients with oral cancer and 956 age- and gender-matched healthy controls were genotyped. The results showed that there was significant differential distribution among oral cancer and controls in the genotypic (p=0.001428) and allelic (p=0.0013) frequencies of XRCC3 rs861539. As for the other polymorphisms, there was no difference between case and control groups. In gene-lifestyle interaction analysis, we have provided the first evidence showing that there is an obvious joint effect of XRCC3 rs861539 genotype with individual areca chewing habits on oral cancer risk. In conclusion, the T allele of XRCC3 rs861539, which has an interaction with areca chewing habit in oral carcinogenesis, may be an early marker for oral cancer in Taiwanese. 12. Involvement of a periplasmic protein kinase in DNA strand break repair and homologous recombination in Escherichia coli. Science.gov (United States) Khairnar, Nivedita P; Kamble, Vidya A; Mangoli, Suhas H; Apte, Shree K; Misra, Hari S 2007-07-01 The involvement of signal transduction in the repair of radiation-induced damage to DNA has been known in eukaryotes but remains understudied in bacteria. This article for the first time demonstrates a role for the periplasmic lipoprotein (YfgL) with protein kinase activity transducing a signal for DNA strand break repair in Escherichia coli. Purified YfgL protein showed physical as well as functional interaction with pyrroloquinoline-quinone in solution and the protein kinase activity of YfgL was strongly stimulated in the presence of pyrroloquinoline-quinone. Transgenic E. coli cells producing Deinococcus radiodurans pyrroloquinoline-quinone synthase showed nearly four log cycle improvement in UVC dark survival and 10-fold increases in gamma radiation resistance as compared with untransformed cells. Pyrroloquinoline-quinone enhanced the UV resistance of E. coli through the YfgL protein and required the active recombination repair proteins. The yfgL mutant showed higher sensitivity to UVC, mitomycin C and gamma radiation as compared with wild-type cells and showed a strong impairment in homologous DNA recombination. The mutant expressing an active YfgL in trans recovered the lost phenotypes to nearly wild-type levels. The results strongly suggest that the periplasmic phosphoquinolipoprotein kinase YfgL plays an important role in radiation-induced DNA strand break repair and homologous recombination in E. coli. PMID:17630970 13. Novel Smad proteins localize to IR-induced double-strand breaks: interplay between TGFβ and ATM pathways Science.gov (United States) Wang, Minli; Saha, Janapriya; Hada, Megumi; Anderson, Jennifer A.; Pluth, Janice M.; O’Neill, Peter; Cucinotta, Francis A. 2013-01-01 14. An alternative mechanism for radioprotection by dimethyl sulfoxide. Possible facilitation of DNA double-strand break repair International Nuclear Information System (INIS) 15. Nonhomologous end joining of complex DNA double-strand breaks with proximal thymine glycol and interplay with base excision repair. Science.gov (United States) Almohaini, Mohammed; Chalasani, Sri Lakshmi; Bafail, Duaa; Akopiants, Konstantin; Zhou, Tong; Yannone, Steven M; Ramsden, Dale A; Hartman, Matthew C T; Povirk, Lawrence F 2016-05-01 DNA double-strand breaks induced by ionizing radiation are often accompanied by ancillary oxidative base damage that may prevent or delay their repair. In order to better define the features that make some DSBs repair-resistant, XLF-dependent nonhomologous end joining of blunt-ended DSB substrates having the oxidatively modified nonplanar base thymine glycol at the first (Tg1), second (Tg2), third (Tg3) or fifth (Tg5) positions from one 3' terminus, was examined in human whole-cell extracts. Tg at the third position had little effect on end-joining even when present on both ends of the break. However, Tg as the terminal or penultimate base was a major barrier to end joining (>10-fold reduction in ligated products) and an absolute barrier when present at both ends. Dideoxy trapping of base excision repair intermediates indicated that Tg was excised from Tg1, Tg2 and Tg3 largely if not exclusively after DSB ligation. However, Tg was rapidly excised from the Tg5 substrate, resulting in a reduced level of DSB ligation, as well as slow concomitant resection of the opposite strand. Ligase reactions containing only purified Ku, XRCC4, ligase IV and XLF showed that ligation of Tg3 and Tg5 was efficient and only partially XLF-dependent, whereas ligation of Tg1 and Tg2 was inefficient and only detectable in the presence of XLF. Overall, the results suggest that promoting ligation of DSBs with proximal base damage may be an important function of XLF, but that Tg can still be a major impediment to repair, being relatively resistant to both trimming and ligation. Moreover, it appears that base excision repair of Tg can sometimes interfere with repair of DSBs that would otherwise be readily rejoined. PMID:27049455 16. DNA ligase IV and artemis act cooperatively to suppress homologous recombination in human cells: implications for DNA double-strand break repair. Directory of Open Access Journals (Sweden) Aya Kurosawa Full Text Available Nonhomologous end-joining (NHEJ and homologous recombination (HR are two major pathways for repairing DNA double-strand breaks (DSBs; however, their respective roles in human somatic cells remain to be elucidated. Here we show using a series of human gene-knockout cell lines that NHEJ repairs nearly all of the topoisomerase II- and low-dose radiation-induced DNA damage, while it negatively affects survival of cells harbouring replication-associated DSBs. Intriguingly, we find that loss of DNA ligase IV, a critical NHEJ ligase, and Artemis, an NHEJ factor with endonuclease activity, independently contribute to increased resistance to replication-associated DSBs. We also show that loss of Artemis alleviates hypersensitivity of DNA ligase IV-null cells to low-dose radiation- and topoisomerase II-induced DSBs. Finally, we demonstrate that Artemis-null human cells display increased gene-targeting efficiencies, particularly in the absence of DNA ligase IV. Collectively, these data suggest that DNA ligase IV and Artemis act cooperatively to promote NHEJ, thereby suppressing HR. Our results point to the possibility that HR can only operate on accidental DSBs when NHEJ is missing or abortive, and Artemis may be involved in pathway switching from incomplete NHEJ to HR. 17. Repair of adjacent single-strand breaks is often accompanied by the formation of tandem sequence duplications in plant genomes. Science.gov (United States) Schiml, Simon; Fauser, Friedrich; Puchta, Holger 2016-06-28 Duplication of existing sequences is a major mechanism of genome evolution. It has been previously shown that duplications can occur by replication slippage, unequal sister chromatid exchange, homologous recombination, and aberrant double-strand break-induced synthesis-dependent strand annealing reactions. In a recent study, the abundant presence of short direct repeats was documented by comparative bioinformatics analysis of different rice genomes, and the hypothesis was put forward that such duplications might arise due to the concerted repair of adjacent single-strand breaks (SSBs). Applying the CRISPR/Cas9 technology, we were able to test this hypothesis experimentally in the model plant Arabidopsis thaliana Using a Cas9 nickase to induce adjacent genomic SSBs in different regions of the genome (genic, intergenic, and heterochromatic) and at different distances (∼20, 50, and 100 bps), we analyzed the repair outcomes by deep sequencing. In addition to deletions, we regularly detected the formation of direct repeats close to the break sites, independent of the genomic context. The formation of these duplications as well as deletions may be associated with the presence of microhomologies. Most interestingly, we found that even the induction of two SSBs on the same DNA strand can cause genome alterations, albeit at a much lower level. Because such a scenario reflects a natural step during nucleotide excision repair, and given that the germline is set aside only late during development in plants, the repair of adjacent SSBs indeed seems to have an important influence on the shaping of plant genomes during evolution. PMID:27307441 18. Impact of DNA repair pathways on the cytotoxicity of piperlongumine in chicken DT40 cell-lines. Science.gov (United States) Okamoto, Saki; Narita, Takeo; Sasanuma, Hiroyuki; Takeda, Shunichi; Masunaga, Shin-Ichiro; Bessho, Tadayoshi; Tano, Keizo 2014-07-01 Piperlongumine is a naturally-occurring small molecule with various biological activities. Recent studies demonstrate that piperlongumine selectively kills various types of transformed cells with minimal toxicity to non-transformed cells by inducing a high level of reactive oxygen species (ROS). ROS generates various types of DNA lesions, including base modifications and single strand breaks. In order to examine the contribution of ROS-induced DNA damage to the cytotoxicity by piperlongumine, various DNA repair-deficient chicken DT40 cell-lines with a single DNA repair gene deletion were tested for cellular sensitivity to piperlongumine. The results showed that cell lines defective in homologous recombination (HR) display hyper-sensitivity to piperlongumine, while other cell lines with a deficiency in non-homologous end joining (NHEJ), base excision repair (BER), nucleotide excision repair (NER), Fanconi anemia (FA) pathway, or translesion DNA synthesis (TLS) polymerases, show no sensitivity to piperlongumine. The results strongly implicate that double strand breaks (DSBs) generated by piperlongumine are major cytotoxic DNA lesions. Furthermore, a deletion of 53BP1 or Ku70 in the BRCA1-deficient cell line restored cellular resistance to piperlongumine. This strongly supports the idea that piperlongumine induces DSB- mediated cell death. Interestingly, piperlongumine makes the wild type DT40 cell line hypersensitive to a PARP-inhibitor, Olaparib. The results implicate that piperlongumine inhibits HR. Further analysis with cell-based HR assay and the kinetic study of Rad51 foci formation confirmed that piperlongumine suppresses HR activity. Altogether, we revealed novel mechanisms of piperlongumine-induced cytotoxicity. PMID:25221646 19. Targeting base excision repair as a sensitization strategy in radiotherapy. NARCIS (Netherlands) Vens, C.; Begg, A.C. 2010-01-01 Cellular DNA repair determines survival after ionizing radiation. Human tumors commonly exhibit aberrant DNA repair since they drive mutagenesis and chromosomal instability. Recent reports have shown alterations in the base excision repair (BER) and single strand break repair (SSBR) pathways in huma 20. Approach to the classical radiation biology. Ionizing radiation effects and repair mechanism of DNA double strand breaks Energy Technology Data Exchange (ETDEWEB) Utsumi, Hiroshi [Kyoto Univ., Kumatori, Osaka (Japan). Research Reactor Inst 2000-09-01 Split-dose recovery has been observed under a variety of experimental conditions in many cell systems and believed to be the recovery of sublethal damage (SLD). It is considered to be one of the most widespread and important cellular responses in clinical radiotherapy. To study the molecular mechanism of this recovery, we analyzed the knockout mutants KU70{sup -/-}, RAD54{sup -/-}, and KU70{sup -/-}/ RAD54{sup -/-} of the chicken B-cell line, DT40. Rad54 participates in the homologous recombinational (HR) repair of DNA double-strand breaks (DSB), while Ku proteins are involved in non-homologous end-joining (NHEJ). Split-dose recovery was observed in the parent DT40 and KU70{sup -/-} cells. Moreover the split-dose survival enhancement had all of the characteristics of SLD recovery that had been demonstrated earlier: e.g., the reappearance of the shoulder of the survival curve with dose fractionation; repair at 25degC; and inhibition by the antibiotic actinomycin D. These results strongly suggest that SLD recovery is due to DSB repair via or mediated by HR, and that these breaks constitute SLD. The tonicity-sensitive potentially lethal damage (PLD) recovery was also found only in DT40 and KU70 {sup -/-} cells. Delayed-plating PLD recovery may be controlled by NHEJ repair that works through the cell cycle. These results lead to the conclusion that the repair of DSBs could explain the classical operational recovery phenomena. We have also investigated RBE/LET using those mutants. (author) 1. QUANTITATION OF INTRACELLULAR NAD(P)H IN LIVING CELLS CAN MONITOR AN IMBALANCE OF DNA SINGLE STRAND BREAK REPAIR IN REAL TIME Science.gov (United States) Quantitation of intracellular NAD(P)H in living cells can monitor an imbalance of DNA single strand break repair in real time.ABSTRACTDNA single strand breaks (SSBs) are one of the most frequent DNA lesions in genomic DNA generated either by oxidative stress or du... 2. Conservation of the rad21 Schizosaccharomyces pombe DNA double-strand break repair gene in mammals International Nuclear Information System (INIS) Purpose/Objective: Genetic factors are likely to be major determinants of human cellular ionizing radiation sensitivity. DNA double strand breaks (dsbs) are significant ionizing radiation-induced lesions; cellular DNA dsb processing is also important in a number of other contexts. To further the understanding of DNA dsb processing in mammalian cells, we cloned and sequenced mammalian homologs of the rad21 Schizosaccharomyces pombe DNA dsb repair gene. Materials and Methods: The genes were cloned by evolutionary walking, exploiting sequence homology between the yeast and mammalian genes. Results: No major motifs indicative of a particular function were present in the predicted amino acid sequences of the mammalian genes. Alignment of the Rad21 amino acid sequence with its putative homologs showed that similarity was distributed across the length of the proteins, with more highly conserved regions at both termini. The mHR21sp (mouse homolog ofR ad21, S. pombe) and hHR21sp (humanh omolog of Rad21, S. pombe) predicted proteins were 96% identical, whereas the human and S. pombe proteins were 25% identical and 47% similar. RNA blot analysis showed that mHR21sp mRNA was abundant in all adult mouse tissues examined, with highest expression in testis and thymus. In addition to a 3.1kb mRNA transcript in all tissues, an additional 2.2kb transcript was present at a high level in post-meiotic spermatids, white expression of the 3.1kb mRNA in testis was confined to the meiotic compartment. hHR21sp mRNA was cell cycle regulated in human cells, increasing in late S phase to a peak in G2 phase. The level of hHR21sp transcripts was not altered by exposure of normal diploid fibroblasts to 10 Gy ionizing radiation. In situ hybridization showed mHR21sp resided on chromosome 15D3, whereashHR21sp localized to the syntenic 8q24 region. Conclusion: Cloning these novel mammalian genes and characterization of their protein products should contribute to the understanding of cellular DNA dsb 3. Histone chaperone Anp32e removes H2A.Z from DNA double-strand breaks and promotes nucleosome reorganization and DNA repair. Science.gov (United States) Gursoy-Yuzugullu, Ozge; Ayrapetov, Marina K; Price, Brendan D 2015-06-16 The repair of DNA double-strand breaks (DSBs) requires open, flexible chromatin domains. The NuA4-Tip60 complex creates these flexible chromatin structures by exchanging histone H2A.Z onto nucleosomes and promoting acetylation of histone H4. Here, we demonstrate that the accumulation of H2A.Z on nucleosomes at DSBs is transient, and that rapid eviction of H2A.Z is required for DSB repair. Anp32e, an H2A.Z chaperone that interacts with the C-terminal docking domain of H2A.Z, is rapidly recruited to DSBs. Anp32e functions to remove H2A.Z from nucleosomes, so that H2A.Z levels return to basal within 10 min of DNA damage. Further, H2A.Z removal by Anp32e disrupts inhibitory interactions between the histone H4 tail and the nucleosome surface, facilitating increased acetylation of histone H4 following DNA damage. When H2A.Z removal by Anp32e is blocked, nucleosomes at DSBs retain elevated levels of H2A.Z, and assume a more stable, hypoacetylated conformation. Further, loss of Anp32e leads to increased CtIP-dependent end resection, accumulation of single-stranded DNA, and an increase in repair by the alternative nonhomologous end joining pathway. Exchange of H2A.Z onto the chromatin and subsequent rapid removal by Anp32e are therefore critical for creating open, acetylated nucleosome structures and for controlling end resection by CtIP. Dynamic modulation of H2A.Z exchange and removal by Anp32e reveals the importance of the nucleosome surface and nucleosome dynamics in processing the damaged chromatin template during DSB repair. 4. Double-Strand Break Repair by Interchromosomal Recombination: An In Vivo Repair Mechanism Utilized by Multiple Somatic Tissues in Mammals OpenAIRE White, Ryan R; Sung, Patricia; Vestal, C. Greer; Benedetto, Gregory; Cornelio, Noelle; Richardson, Christine 2013-01-01 Homologous recombination (HR) is essential for accurate genome duplication and maintenance of genome stability. In eukaryotes, chromosomal double strand breaks (DSBs) are central to HR during specialized developmental programs of meiosis and antigen receptor gene rearrangements, and form at unusual DNA structures and stalled replication forks. DSBs also result from exposure to ionizing radiation, reactive oxygen species, some anti-cancer agents, or inhibitors of topoisomerase II. Literature p... 5. Fanconi DNA repair pathway is required for survival and long-term maintenance of neural progenitors NARCIS (Netherlands) Sii-Felice, Karine; Etienne, Olivier; Hoffschir, Francoise; Mathieu, Celine; Riou, Lydia; Barroca, Vilma; Haton, Celine; Arwert, Fre; Fouchet, Pierre; Boussin, Francois D.; Mouthon, Marc-Andre 2008-01-01 Although brain development abnormalities and brain cancer predisposition have been reported in some Fanconi patients, the possible role of Fanconi DNA repair pathway during neurogenesis is unclear. We thus addressed the role of fanca and fancg, which are involved in the activation of Fanconi pathway 6. PI3K/Akt/mTOR pathway inhibitors enhance radiosensitivity in radioresistant prostate cancer cells through inducing apoptosis, reducing autophagy, suppressing NHEJ and HR repair pathways. Science.gov (United States) Chang, L; Graham, P H; Hao, J; Ni, J; Bucci, J; Cozzi, P J; Kearsley, J H; Li, Y 2014-01-01 7. The influence of bromodeoxyuridine on the induction and repair of DNA double-strand breaks in glioblastoma cells International Nuclear Information System (INIS) Aims: To examine the dose response of DNA damage and its modification by the radiosensitizer, 5-bromo-2'-deoxyuridine (BrdU). The sensitizing mechanism is analyzed with regard to its influence on the induction and repair of DNA double-strand breaks (DSBs). Material and Methods: Cells from three different human glioblastoma lines, A7, LH and U87MG, were X-irradiated with and without exposure to BrdU. DNA fragments were separated by field-inversion gel electrophoresis (FIGE) and quantified by fluorometry immediately and 24 h after irradiation. Results: In all cell lines, the dose response followed a linear-quadratic rather than a purely linear function. BrdU-treated cells exhibited a significantly higher amount of mobile DNA. In repair experiments with and without BrdU, the amount of mobile DNA fell close to control values within 24 h. Conclusions: The linear-quadratic model appropriately describes the X-ray induced fragmentation of DNA. BrdU sensitizing acts predominantly by increasing DNA fragility, and not by impairing damage repair. The amount of DSBs persistent after 24 h of repair is minimal, even after highly cytotoxic doses. However, it appears to depend on the extent of initial damage, causing sensitized cells to retain more DSBs than unsensitized cells. (orig.) 8. Nonrecurrent MECP2 duplications mediated by genomic architecture-driven DNA breaks and break-induced replication repair. Science.gov (United States) Bauters, Marijke; Van Esch, Hilde; Friez, Michael J; Boespflug-Tanguy, Odile; Zenker, Martin; Vianna-Morgante, Angela M; Rosenberg, Carla; Ignatius, Jaakko; Raynaud, Martine; Hollanders, Karen; Govaerts, Karen; Vandenreijt, Kris; Niel, Florence; Blanc, Pierre; Stevenson, Roger E; Fryns, Jean-Pierre; Marynen, Peter; Schwartz, Charles E; Froyen, Guy 2008-06-01 Recurrent submicroscopic genomic copy number changes are the result of nonallelic homologous recombination (NAHR). Nonrecurrent aberrations, however, can result from different nonexclusive recombination-repair mechanisms. We previously described small microduplications at Xq28 containing MECP2 in four male patients with a severe neurological phenotype. Here, we report on the fine-mapping and breakpoint analysis of 16 unique microduplications. The size of the overlapping copy number changes varies between 0.3 and 2.3 Mb, and FISH analysis on three patients demonstrated a tandem orientation. Although eight of the 32 breakpoint regions coincide with low-copy repeats, none of the duplications are the result of NAHR. Bioinformatics analysis of the breakpoint regions demonstrated a 2.5-fold higher frequency of Alu interspersed repeats as compared with control regions, as well as a very high GC content (53%). Unexpectedly, we obtained the junction in only one patient by long-range PCR, which revealed nonhomologous end joining as the mechanism. Breakpoint analysis in two other patients by inverse PCR and subsequent array comparative genomic hybridization analysis demonstrated the presence of a second duplicated region more telomeric at Xq28, of which one copy was inserted in between the duplicated MECP2 regions. These data suggest a two-step mechanism in which part of Xq28 is first inserted near the MECP2 locus, followed by breakage-induced replication with strand invasion of the normal sister chromatid. Our results indicate that the mechanism by which copy number changes occur in regions with a complex genomic architecture can yield complex rearrangements. 9. Stripped-down DNA repair in a highly reduced parasite Directory of Open Access Journals (Sweden) Fast Naomi M 2007-03-01 Full Text Available Abstract Background Encephalitozoon cuniculi is a member of a distinctive group of single-celled parasitic eukaryotes called microsporidia, which are closely related to fungi. Some of these organisms, including E. cuniculi, also have uniquely small genomes that are within the prokaryotic range. Thus, E. cuniculi has undergone a massive genome reduction which has resulted in a loss of genes from diverse biological pathways, including those that act in DNA repair. DNA repair is essential to any living cell. A loss of these mechanisms invariably results in accumulation of mutations and/or cell death. Six major pathways of DNA repair in eukaryotes include: non-homologous end joining (NHEJ, homologous recombination repair (HRR, mismatch repair (MMR, nucleotide excision repair (NER, base excision repair (BER and methyltransferase repair. DNA polymerases are also critical players in DNA repair processes. Given the close relationship between microsporidia and fungi, the repair mechanisms present in E. cuniculi were compared to those of the yeast Saccharomyces cerevisiae to ascertain how the process of genome reduction has affected the DNA repair pathways. Results E. cuniculi lacks 16 (plus another 6 potential absences of the 56 DNA repair genes sought via BLASTP and PSI-BLAST searches. Six of 14 DNA polymerases or polymerase subunits are also absent in E. cuniculi. All of these genes are relatively well conserved within eukaryotes. The absence of genes is not distributed equally among the different repair pathways; some pathways lack only one protein, while there is a striking absence of many proteins that are components of both double strand break repair pathways. All specialized repair polymerases are also absent. Conclusion Given the large number of DNA repair genes that are absent from the double strand break repair pathways, E. cuniculi is a prime candidate for the study of double strand break repair with minimal machinery. Strikingly, all of the 10. X-ray repair cross complementing protein 1 in base excision repair DEFF Research Database (Denmark) Hanssen-Bauer, Audun; Solvang-Garten, Karin; Akbari, Mansour; 2012-01-01 X-ray Repair Cross Complementing protein 1 (XRCC1) acts as a scaffolding protein in the converging base excision repair (BER) and single strand break repair (SSBR) pathways. XRCC1 also interacts with itself and rapidly accumulates at sites of DNA damage. XRCC1 can thus mediate the assembly of large... 11. A model of oncogenic rearrangements: differences between chromosomal translocation mechanisms and simple double-strand break repair OpenAIRE Weinstock, David M.; Elliott, Beth; Jasin, Maria 2006-01-01 Recurrent reciprocal translocations are present in many hematologic and mesenchymal malignancies. Because significant sequence homology is absent from translocation breakpoint junctions, non-homologous end-joining (NHEJ) pathways of DNA repair are presumed to catalyze their formation. We developed translocation reporters for use in mammalian cells from which NHEJ events can be selected after precise chromosomal breakage. Translocations were efficiently recovered with these reporters using mou... 12. Long-range heterochromatin association is mediated by silencing and double-strand DNA break repair proteins OpenAIRE Jacob G Kirkland; Kamakaka, Rohinton T. 2013-01-01 The eukaryotic genome is highly organized in the nucleus, and this organization affects various nuclear processes. However, the molecular details of higher-order organization of chromatin remain obscure. In the present study, we show that the Saccharomyces cerevisiae silenced loci HML and HMR cluster in three-dimensional space throughout the cell cycle and independently of the telomeres. Long-range HML–HMR interactions require the homologous recombination (HR) repair pathway and phosphorylate... 13. Multiple gene sequence analysis using genes of the bacterial DNA repair pathway OpenAIRE Miguel Rotelok Neto; Carolina Weigert Galvão; Leonardo Magalhães Cruz; Dieval Guizelini; Leilane Caline Silva; Jarem Raul Garcia; Rafael Mazer Etto 2015-01-01 The ability to recognize and repair abnormal DNA structures is common to all forms of life. Physiological studies and genomic sequencing of a variety of bacterial species have identified an incredible diversity of DNA repair pathways. Despite the amount of available genes in public database, the usual method to place genomes in a taxonomic context is based mainly on the 16S rRNA or housekeeping genes. Thus, the relationships among genomes remain poorly understood. In this work, an approach of... 14. Formaldehyde catabolism is essential in cells deficient for the Fanconi anemia DNA-repair pathway. Science.gov (United States) Rosado, Ivan V; Langevin, Frédéric; Crossan, Gerry P; Takata, Minoru; Patel, Ketan J 2011-11-13 Metabolism is predicted to generate formaldehyde, a toxic, simple, reactive aldehyde that can damage DNA. Here we report a synthetic lethal interaction in avian cells between ADH5, encoding the main formaldehyde-detoxifying enzyme, and the Fanconi anemia (FA) DNA-repair pathway. These results define a fundamental role for the combined action of formaldehyde catabolism and DNA cross-link repair in vertebrate cell survival. 15. Genistein sensitizes sarcoma cells in vitro and in vivo by enhancing apoptosis and by inhibiting DSB repair pathways. Science.gov (United States) Liu, X X; Sun, C; Jin, X D; Li, P; Zheng, X G; Zhao, T; Li, Q 2016-06-01 The aim of this work was to investigate the radiosensitization effects of genistein on mice sarcoma cells and the corresponding biological mechanisms in vitro and in vivo Using the non-toxic dosage of 10 μM genistein, the sensitizer enhancement ratios after exposure to X-rays at 50% cell survival (IC50) was 1.45 for S180 cells. For mice cotreated with genistein and X-rays, the excised tumor tissues had reduced blood vessels and decreased size and volume compared with the control and irradiation-only groups. Moreover, a significant increase in apoptosis was accompanied by upregulation of Bax and downregulation of Bcl-2 in the mitochondria, and lots of cytochrome c being transferred to the cytoplasm. Furthermore, X-rays combined with genistein inhibited the activity of DNA-PKcs, so DNA-injured sites were dominated by Ku70/80, leading to incompleteness of homologous recombination (HR) and non-homologous end-joining (NHEJ) repairs and the eventual occurrence of cell apoptosis. Our study, for the first time, demonstrated that genistein sensitized sarcoma cells to X-rays and that this radiosensitizing effect depended on induction of the mitochondrial apoptosis pathway and inhibition of the double-strand break (DSB) repair pathways. PMID:26922091 16. Resection is a major repair pathway of heavy ion-induced DNA lesions Science.gov (United States) Durante, Marco; Averbeck, Nicole; Taucher-Scholz, Gisela Space radiation include densely ionizing heavy ions, which can produce clustered DNA damage with high frequency in human cells. Repair of these complex lesions is generally assumed to be more difficult than for simple double-strand breaks. We show here that human cells use break resection with increasing frequency after exposure to heavy ions. Resection can lead to misrepair of the DNA lesion, via microhomology mediated end-joining. Resection can therefore be responsible for the increased effectiveness of heavy ions in the induction of mutations and genetic late effects. 17. Nontoxic concentration of DNA-PK inhibitor NU7441 radio-sensitizes lung tumor cells with little effect on double strand break repair. Science.gov (United States) Sunada, Shigeaki; Kanai, Hideki; Lee, Younghyun; Yasuda, Takeshi; Hirakawa, Hirokazu; Liu, Cuihua; Fujimori, Akira; Uesaka, Mitsuru; Okayasu, Ryuichi 2016-09-01 High-linear energy transfer (LET) heavy ions have been increasingly employed as a useful alternative to conventional photon radiotherapy. As recent studies suggested that high LET radiation mainly affects the nonhomologous end-joining (NHEJ) pathway of DNA double strand break (DSB) repair, we further investigated this concept by evaluating the combined effect of an NHEJ inhibitor (NU7441) at a non-toxic concentration and carbon ions. NU7441-treated non-small cell lung cancer (NSCLC) A549 and H1299 cells were irradiated with X-rays and carbon ions (290 MeV/n, 50 keV/μm). Cell survival was measured by clonogenic assay. DNA DSB repair, cell cycle distribution, DNA fragmentation and cellular senescence induction were studied using a flow cytometer. Senescence-associated protein p21 was detected by western blotting. In the present study, 0.3 μM of NU7441, nontoxic to both normal and tumor cells, caused a significant radio-sensitization in tumor cells exposed to X-rays and carbon ions. This concentration did not seem to cause inhibition of DNA DSB repair but induced a significant G2/M arrest, which was particularly emphasized in p53-null H1299 cells treated with NU7441 and carbon ions. In addition, the combined treatment induced more DNA fragmentation and a higher degree of senescence in H1299 cells than in A549 cells, indicating that DNA-PK inhibitor contributes to various modes of cell death in a p53-dependent manner. In summary, NSCLC cells irradiated with carbon ions were radio-sensitized by a low concentration of DNA-PK inhibitor NU7441 through a strong G2/M cell cycle arrest. Our findings may contribute to further effective radiotherapy using heavy ions. PMID:27341700 18. DNA double strand break repair in mammalian cells: role of MRE11 and BLM proteins at the initiation of Non Homologous End Joining (NHEJ) International Nuclear Information System (INIS) DNA double strand breaks (DSBs) are highly cytotoxic lesions, which can lead to genetic rearrangements. Two pathways are responsible for repairing these lesions: homologous recombination (HR) and non homologous end joining (NHEJ). In our laboratory, an intrachromosomal substrate has been established in order to measure the efficiency and the fidelity of NHEJ in living cells (Guirouilh-Barbat 2004). This approach led us to identify a KU-independent alternative pathway, which uses micro homologies in the proximity of the junction to accomplish repair - the alternative NHEJ (Guirouilh-Barbat 2004, Guirouilh-Barbat et Rass 2007). The goal of my thesis consisted in identifying and characterising major actors of this pathway. In the absence of KU, alternative NHEJ would be initiated by ssDNA resection of damaged ends. We showed that the nuclease activity of MRE11 is necessary for this mechanism. MRE11 overexpression leads to a two fold stimulation of NHEJ efficiency, while the extinction of MRE11 by siRNA results in a two fold decrease. Our results demonstrate that the proteins RAD50 and CtIP act in the same pathway as MRE11. Moreover, in cells deficient for XRCC4, MIRIN - an inhibitor of the MRN complex - leads to a decrease in repair efficiency, implicating MRE11 in alternative NHEJ. We also showed that MRE11 can act in an ATM-dependent and independent manner (Rass et Grabarz Nat Struct Mol Biol 2009). The initiation of break resection needs to be pursued by a more extensive degradation of DNA, which is accomplished in yeast by the proteins Exo1 and Sgs1/Dna2. In human cells, in vitro studies have recently proposed a similar model of a two-step break resection. We chose to elucidate the role of one of the human homologs of Sgs1 - the RecQ helicase BLM - in the resection process. Our experiments show, that he absence of BLM decreases the efficiency of end joining by NHEJ, accompanied by an increase in error-prone events, especially long-range deletions (≥200 nt). This 19. Increased repair of {gamma}-induced DNA double-strand breaks at lower dose-rate in CHO cells Energy Technology Data Exchange (ETDEWEB) Boucher, D.; Hindo, J.; Averbeck, D. [Centre Universitaire d' Orsay, Inst. Curie-Section de Recherche, Orsay CEDEX (France)]. E-mail: [email protected] 2004-02-01 DNA double-strand breaks (DSBs) are highly cell damaging. We asked whether for a given dose a longer irradiation time would be advantageous for the repair of DSBs. Varying the {gamma}-irradiation dose and its delivery time (0.05 Gy/min low dose-rate (LDR) compared with 3.5 Gy/min high dose-rate), confluent Chinese hamster ovary cells (CHO-K1) and Ku80 mutant cells (xrs-6) deficient in nonhomologous end-joining (NHEJ) were irradiated in agarose plugs at room temperature using a cesium-137 {gamma}-ray source. We used pulsed-field gel electrophoresis (PFGE) to measure DSBs in terms of the fraction of activity released (FAR). At LDR, one third of DSBs were repaired in CHO-K1 but not in xrs-6 cells, indicating the involvement of NHEJ in the repair of {gamma}-induced DSBs at a prolonged irradiation incubation time. To improve DSB measurements, we introduced in our PFGE protocol an antioxidant at the cell lysis step, thus avoiding free-radical side reactions on DNA and spurious DSBs. Addition of the metal chelator deferoxamine (DFO) decreased more efficiently the basal DSB level than did reduced glutathione (GSH), showing that measuring DSBs in the absence of DFO reduces precision and underestimates the role of NHEJ in the dose-rate effect on DSB yield. (author) 20. Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways. Directory of Open Access Journals (Sweden) Emmanuelle Martini 2011-09-01 Full Text Available Meiotic DNA double-strand breaks (DSBs initiate crossover (CO recombination, which is necessary for accurate chromosome segregation, but DSBs may also repair as non-crossovers (NCOs. Multiple recombination pathways with specific intermediates are expected to lead to COs and NCOs. We revisited the mechanisms of meiotic DSB repair and the regulation of CO formation, by conducting a genome-wide analysis of strand-transfer intermediates associated with recombination events. We performed this analysis in a SK1 × S288C Saccharomyces cerevisiae hybrid lacking the mismatch repair (MMR protein Msh2, to allow efficient detection of heteroduplex DNAs (hDNAs. First, we observed that the anti-recombinogenic activity of MMR is responsible for a 20% drop in CO number, suggesting that in MMR-proficient cells some DSBs are repaired using the sister chromatid as a template when polymorphisms are present. Second, we observed that a large fraction of NCOs were associated with trans-hDNA tracts constrained to a single chromatid. This unexpected finding is compatible with dissolution of double Holliday junctions (dHJs during repair, and it suggests the existence of a novel control point for CO formation at the level of the dHJ intermediate, in addition to the previously described control point before the dHJ formation step. Finally, we observed that COs are associated with complex hDNA patterns, confirming that the canonical double-strand break repair model is not sufficient to explain the formation of most COs. We propose that multiple factors contribute to the complexity of recombination intermediates. These factors include repair of nicks and double-stranded gaps, template switches between non-sister and sister chromatids, and HJ branch migration. Finally, the good correlation between the strand transfer properties observed in the absence of and in the presence of Msh2 suggests that the intermediates detected in the absence of Msh2 reflect normal intermediates. 1. Nucleolin participates in DNA double-strand break-induced damage response through MDC1-dependent pathway. Directory of Open Access Journals (Sweden) Junya Kobayashi Full Text Available H2AX is an important factor for chromatin remodeling to facilitate accumulation of DNA damage-related proteins at DNA double-strand break (DSB sites. In order to further understand the role of H2AX in the DNA damage response (DDR, we attempted to identify H2AX-interacting proteins by proteomics analysis. As a result, we identified nucleolin as one of candidates. Here, we show a novel role of a major nucleolar protein, nucleolin, in DDR. Nucleolin interacted with γ-H2AX and accumulated to laser micro-irradiated DSB damage sites. Chromatin Immunoprecipitation assay also displayed the accumulation of nucleolin around DSB sites. Nucleolin-depleted cells exhibited repression of both ATM-dependent phosphorylation following exposure to γ-ray and subsequent cell cycle checkpoint activation. Furthermore, nucleolin-knockdown reduced HR and NHEJ activity and showed decrease in IR-induced chromatin accumulation of HR/NHEJ factors, agreeing with the delayed kinetics of γ-H2AX focus. Moreover, nucleolin-knockdown decreased MDC1-related events such as focus formation of 53 BP1, RNF168, phosphorylated ATM, and H2A ubiquitination. Nucleolin also showed FACT-like activity for DSB damage-induced histone eviction from chromatin. Taken together, nucleolin could promote both ATM-dependent cell cycle checkpoint and DSB repair by functioning in an MDC1-related pathway through its FACT-like function. 2. Homologous recombination contributes to the repair of DNA double-strand breaks induced by high-energy iron ions Energy Technology Data Exchange (ETDEWEB) Zafar, Faria; Seidler, Sara B.; Kronenberg, Amy; Schild, David; Wiese, Claudia 2010-06-29 3. Homologous recombination contributes to the repair of DNA double-strand breaks induced by high-energy iron ions International Nuclear Information System (INIS) 4. Break-induced ATR and Ddb1-Cul4(Cdt)² ubiquitin ligase-dependent nucleotide synthesis promotes homologous recombination repair in fission yeast DEFF Research Database (Denmark) Moss, Jennifer; Tinline-Purvis, Helen; Walker, Carol A; 2010-01-01 the Ddb1-Cul4(Cdt)² ubiquitin ligase complex and ribonucleotide reductase (RNR) to be required for HR repair of a DNA double-strand break (DSB). The Ddb1-Cul4(Cdt)² ubiquitin ligase complex is required for degradation of Spd1, an inhibitor of RNR in fission yeast. Accordingly, deleting spd1(+) suppressed...... through increasing Cdt2 nuclear levels in response to DNA damage. Our findings support a model in which break-induced Rad3 and Ddb1-Cul4(Cdt)² ubiquitin ligase-dependent Spd1 degradation and RNR activation promotes postsynaptic ssDNA gap filling during HR repair.... 5. Repair responses to DNA damage: enzymatic pathways in E coli and human cells International Nuclear Information System (INIS) Bacteria and eukaryotic cells employ a variety of enzymatic pathways to remove damage from DNA or to lessen its impact upon cellular functions. Most of these processes were discovered in Escherichia coli and have been most extensively analyzed in this organism because suitable mutants have been isolated and characterized. Analogous pathways have been inferred to exist in mammalian cells from the presence of enzyme activities similar to those known to be involved in repair in bacteria, from the analysis of events in cells treated with DNA damaging agents, and from the analysis of the few naturally occurring mutant cell types. Mammalian cells possess an excision repair pathway similar to the constitutive pathway in E coli. Although not as well understood, the incision event is at least as complex, and repair resynthesis produces patches of about the same size as the constitutive short patches. In mammalian cells, no patches comparable in size to those produced by the inducible pathway of E coli are observed. Endonuclease V of bacteriophage T4 incises DNA at pyrimidine dimers by cleaving first the glycosylic bond between deoxyribose and the 5'pyrimidine of the dimer and then the phosphodiester bond between the two pyrimidines. We have cloned the gene (den V) that codes for this enzyme and have demonstrated its expression in uvrA recA and uvrB recA cells of E coli. Because T4 endonuclease V can alleviate the excission repair deficiency of xeroderma pigmentosum when added to permeabilized cells or to isolated nuclei after UV irradiation, the cloned denV gene may ultimately be of value for analyzing DNA repair pathways in cultured human cells 6. Nrf2 facilitates repair of radiation induced DNA damage through homologous recombination repair pathway in a ROS independent manner in cancer cells Energy Technology Data Exchange (ETDEWEB) Jayakumar, Sundarraj; Pal, Debojyoti; Sandur, Santosh K., E-mail: [email protected] 2015-09-15 Highlights: • Nrf2 inhibition in A549 cells led to attenuated DNA repair and radiosensitization. • Influence of Nrf2 on DNA repair is not linked to its antioxidant function. • Nrf2 influences DNA repair through homologous recombination (HR) repair pathway. • Many genes involved in HR pathway show ARE sequences in their upstream region. - Abstract: Nrf2 is a redox sensitive transcription factor that is involved in the co-ordinated transcription of genes involved in redox homeostasis. But the role of Nrf2 in DNA repair is not investigated in detail. We have employed A549 and MCF7 cells to study the role of Nrf2 on DNA repair by inhibiting Nrf2 using all-trans retinoic acid (ATRA) or by knock down approach prior to radiation exposure (4 Gy). DNA damage and repair analysis was studied by γH2AX foci formation and comet assay. Results suggested that the inhibition of Nrf2 in A549 or MCF7 cells led to significant slowdown in DNA repair as compared to respective radiation controls. The persistence of residual DNA damage even in the presence of free radical scavenger N-acetyl cysteine, suggested that the influence of Nrf2 on DNA repair was not linked to its antioxidant functions. Further, its influence on non-homologous end joining repair pathway was studied by inhibiting both Nrf2 and DNA-PK together. This led to synergistic reduction of survival fraction, indicating that Nrf2 may not be influencing the NHEJ pathway. To investigate the role of homologous recombination repair (HR) pathway, RAD51 foci formation was monitored. There was a significant reduction in the foci formation in cells treated with ATRA or shRNA against Nrf2 as compared to their respective radiation controls. Further, Nrf2 inhibition led to significant reduction in mRNA levels of RAD51. BLAST analysis was also performed on upstream regions of DNA repair genes to identify antioxidant response element and found that many repair genes that are involved in HR pathway may be regulated by Nrf2 7. Genetic polymorphisms in the nucleotide excision repair pathway and lung cancer risk: A meta-analysis Directory of Open Access Journals (Sweden) Chikako Kiyohara, Kouichi Yoshimasu 2007-01-01 Full Text Available Various DNA alterations can be caused by exposure to environmental and endogenous carcinogens. Most of these alterations, if not repaired, can result in genetic instability, mutagenesis and cell death. DNA repair mechanisms are important for maintaining DNA integrity and preventing carcinogenesis. Recent lung cancer studies have focused on identifying the effects of single nucleotide polymorphisms (SNPs in candidate genes, among which DNA repair genes are increasingly being studied. Genetic variations in DNA repair genes are thought to modulate DNA repair capacity and are suggested to be related to lung cancer risk. We identified a sufficient number of epidemiologic studies on lung cancer to conduct a meta-analysis for genetic polymorphisms in nucleotide excision repair pathway genes, focusing on xeroderma pigmentosum group A (XPA, excision repair cross complementing group 1 (ERCC1, ERCC2/XPD, ERCC4/XPF and ERCC5/XPG. We found an increased risk of lung cancer among subjects carrying the ERCC2 751Gln/Gln genotype (odds ratio (OR = 1.30, 95% confidence interval (CI = 1.14 - 1.49. We found a protective effect of the XPA 23G/G genotype (OR = 0.75, 95% CI = 0.59 - 0.95. Considering the data available, it can be conjectured that if there is any risk association between a single SNP and lung cancer, the risk fluctuation will probably be minimal. Advances in the identification of new polymorphisms and in high-throughput genotyping techniques will facilitate the analysis of multiple genes in multiple DNA repair pathways. Therefore, it is likely that the defining feature of future epidemiologic studies will be the simultaneous analysis of large samples. 8. Effects of expression level of DNA repair-related genes involved in the NHEJ pathway on radiation-induced cognitive impairment International Nuclear Information System (INIS) Cranial radiation therapy can induce cognitive decline. Impairments of hippocampal neurogenesis are thought to be a paramountly important mechanism underlying radiation-induced cognitive dysfunction. In the mature nervous system, DNA double-strand breaks (DSBs) are mainly repaired by non-homologous end-joining (NHEJ) pathways. It has been demonstrated that NHEJ deficiencies are associated with impaired neurogenesis. In our study, rats were randomly divided into five groups to be irradiated by single doses of 0 (control), 0 (anesthesia control), 2, 10, and 20 Gy, respectively. The cognitive function of the irradiated rats was measured by open field, Morris water maze and passive avoidance tests. Real-time PCR was also used to detect the expression level of DNA DSB repair-related genes involved in the NHEJ pathway, such as XRCC4, XRCC5 and XRCC6, in the hippocampus. The influence of different radiation doses on cognitive function in rats was investigated. From the results of the behavior tests, we found that rats receiving 20 Gy irradiation revealed poorer learning and memory, while no significant loss of learning and memory existed in rats receiving irradiation from 0-10 Gy. The real-time PCR and Western blot results showed no significant difference in the expression level of DNA repair-related genes between the 10 and 20 Gy groups, which may help to explain the behavioral results, id est (i.e.) DNA damage caused by 0-10 Gy exposure was appropriately repaired, however, damage induced by 20 Gy exceeded the body's maximum DSB repair ability. Ionizing radiation-induced cognitive impairments depend on the radiation dose, and more directly on the body's own ability to repair DNA DSBs via the NHEJ pathway. (author) 9. The repair fidelity of restriction enzyme-induced double strand breaks in plasmid DNA correlates with radioresistance in human tumor cell lines International Nuclear Information System (INIS) 10. Interplay between Target Sequences and Repair Pathways Determines Distinct Outcomes of AID-Initiated Lesions. Science.gov (United States) Chen, Zhangguo; Eder, Maxwell D; Elos, Mihret T; Viboolsittiseri, Sawanee S; Chen, Xiaomi; Wang, Jing H 2016-03-01 Activation-induced deaminase (AID) functions by deaminating cytosines and causing U:G mismatches, a rate-limiting step of Ab gene diversification. However, precise mechanisms regulating AID deamination frequency remain incompletely understood. Moreover, it is not known whether different sequence contexts influence the preferential access of mismatch repair or uracil glycosylase (UNG) to AID-initiated U:G mismatches. In this study, we employed two knock-in models to directly compare the mutability of core Sμ and VDJ exon sequences and their ability to regulate AID deamination and subsequent repair process. We find that the switch (S) region is a much more efficient AID deamination target than the V region. Igh locus AID-initiated lesions are processed by error-free and error-prone repair. S region U:G mismatches are preferentially accessed by UNG, leading to more UNG-dependent deletions, enhanced by mismatch repair deficiency. V region mutation hotspots are largely determined by AID deamination. Recurrent and conserved S region motifs potentially function as spacers between AID deamination hotspots. We conclude that the pattern of mutation hotspots and DNA break generation is influenced by sequence-intrinsic properties, which regulate AID deamination and affect the preferential access of downstream repair. Our studies reveal an evolutionarily conserved role for substrate sequences in regulating Ab gene diversity and AID targeting specificity. 11. DNA-PK. The major target for wortmannin-mediated radiosensitization by the inhibition of DSB repair via NHEJ pathway International Nuclear Information System (INIS) The effect of wortmannin posttreatment was studied in cells derived from different species (hamster, mouse, chicken, and human) with normal and defective DNA-dependent protein kinase (DNA-PK) activity, cells with and without the ataxia telangiectasia mutated (ATM) gene, and cells lacking other regulatory proteins involved in the DNA double-strand break (DSB) repair pathways. Clonogenic assays were used to obtain all results. Wortmannin radiosensitization was observed in Chinese hamster cells (V79-B310H, CHO-K1), mouse mammary carcinoma cells (SR-1), transformed human fibroblast (N2KYSV), chicken B lymphocyte wild-type cells (DT40), and chicken Rad54 knockout cells (Rad54-/-). However, mouse mammary carcinoma cells (SX9) with defects in the DNA-PK and chicken DNA-PK catalytic subunit (DNA-PKcs) knockout cells (DNA-PKcs-/-/-) failed to exhibit wortmannin radiosensitization. On the other hand, severe combined immunodeficiency (SCID) mouse cells (SC3VA2) exposed to wortmannin exhibited significant increases in radiosensitivity, possibly because of some residual function of DNA-PKcs. Moreover, the transformed human cells derived from AT patients (AT2KYSV) and chicken ATM knockout cells (ATM-/-) showed pronounced wortmannin radiosensitization. These studies demonstrate confirm that the mechanism underlying wortmannin radiosensitization is the inhibition of DNA-PK, but not of ATM, thereby resulting in the inhibition of DSB repair via nonhomologous endjoining (NHEJ). (author) 12. Roles of Nucleoid-Associated Proteins in Stress-Induced Mutagenic Break Repair in Starving Escherichia coli. Science.gov (United States) Moore, Jessica M; Magnan, David; Mojica, Ana K; Núñez, María Angélica Bravo; Bates, David; Rosenberg, Susan M; Hastings, P J 2015-12-01 The mutagenicity of DNA double-strand break repair in Escherichia coli is controlled by DNA-damage (SOS) and general (RpoS) stress responses, which let error-prone DNA polymerases participate, potentially accelerating evolution during stress. Either base substitutions and indels or genome rearrangements result. Here we discovered that most small basic proteins that compact the genome, nucleoid-associated proteins (NAPs), promote or inhibit mutagenic break repair (MBR) via different routes. Of 15 NAPs, H-NS, Fis, CspE, and CbpA were required for MBR; Dps inhibited MBR; StpA and Hha did neither; and five others were characterized previously. Three essential genes were not tested. Using multiple tests, we found the following: First, Dps, which reduces reactive oxygen species (ROS), inhibited MBR, implicating ROS in MBR. Second, CbpA promoted F' plasmid maintenance, allowing MBR to be measured in an F'-based assay. Third, Fis was required for activation of the SOS DNA-damage response and could be substituted in MBR by SOS-induced levels of DinB error-prone DNA polymerase. Thus, Fis promoted MBR by allowing SOS activation. Fourth, H-NS represses ROS detoxifier sodB and was substituted in MBR by deletion of sodB, which was not otherwise mutagenic. We conclude that normal ROS levels promote MBR and that H-NS promotes MBR by maintaining ROS. CspE positively regulates RpoS, which is required for MBR. Four of five previously characterized NAPs promoted stress responses that enhance MBR. Hence, most NAPs affect MBR, the majority via regulatory functions. The data show that a total of six NAPs promote MBR by regulating stress responses, indicating the importance of nucleoid structure and function to the regulation of MBR and of coupling mutagenesis to stress, creating genetic diversity responsively. PMID:26500258 13. Melatonin sensitizes human breast cancer cells to ionizing radiation by downregulating proteins involved in double-strand DNA break repair. Science.gov (United States) Alonso-González, Carolina; González, Alicia; Martínez-Campa, Carlos; Gómez-Arozamena, José; Cos, Samuel 2015-03-01 14. RAD50 is required for efficient initiation of resection and recombinational repair at random, gamma-induced double-strand break ends. Directory of Open Access Journals (Sweden) Jim Westmoreland 2009-09-01 15. ATM protein is indispensable to repair complex-type DNA double strand breaks induced by high LET heavy ion irradiation. Science.gov (United States) Sekine, Emiko; Yu, Dong; Fujimori, Akira; Anzai, Kazunori; Okayasu, Ryuichi 16. Mitosis, double strand break repair, and telomeres: a view from the end: how telomeres and the DNA damage response cooperate during mitosis to maintain genome stability. Science.gov (United States) Cesare, Anthony J 2014-11-01 Double strand break (DSB) repair is suppressed during mitosis because RNF8 and downstream DNA damage response (DDR) factors, including 53BP1, do not localize to mitotic chromatin. Discovery of the mitotic kinase-dependent mechanism that inhibits DSB repair during cell division was recently reported. It was shown that restoring mitotic DSB repair was detrimental, resulting in repair dependent genome instability and covalent telomere fusions. The telomere DDR that occurs naturally during cellular aging and in cancer is known to be refractory to G2/M checkpoint activation. Such DDR-positive telomeres, and those that occur as part of the telomere-dependent prolonged mitotic arrest checkpoint, normally pass through mitosis without covalent ligation, but result in cell growth arrest in G1 phase. The discovery that suppressing DSB repair during mitosis may function primarily to protect DDR-positive telomeres from fusing during cell division reinforces the unique cooperation between telomeres and the DDR to mediate tumor suppression. 17. The nucleotide excision repair pathway is required for UV-C-induced apoptosis in Caenorhabditis elegans. Science.gov (United States) Stergiou, L; Doukoumetzidis, K; Sendoel, A; Hengartner, M O 2007-06-01 Ultraviolet (UV) radiation is a mutagen of major clinical importance in humans. UV-induced damage activates multiple signaling pathways, which initiate DNA repair, cell cycle arrest and apoptosis. To better understand these pathways, we studied the responses to UV-C light (254 nm) of germ cells in Caenorhabditis elegans. We found that UV activates the same cellular responses in worms as in mammalian cells. Both UV-induced apoptosis and cell cycle arrest were completely dependent on the p53 homolog CEP-1, the checkpoint proteins HUS-1 and CLK-2, and the checkpoint kinases CHK-2 and ATL-1 (the C. elegans homolog of ataxia telangiectasia and Rad3-related); ATM-1 (ataxia telangiectasia mutated-1) was also required, but only at low irradiation doses. Importantly, mutation of genes encoding nucleotide excision repair pathway components severely disrupted both apoptosis and cell cycle arrest, suggesting that these genes not only participate in repair, but also signal the presence of damage to downstream components of the UV response pathway that we delineate here. Our study suggests that whereas DNA damage response pathways are conserved in metazoans in their general outline, there is significant evolution in the relative importance of individual checkpoint genes in the response to specific types of DNA damage. 18. Ser1778 of 53BP1 Plays a Role in DNA Double-strand Break Repairs OpenAIRE Lee, Jung-Hee; Cheong, Hyang-Min; Kang, Mi-Young; Kim, Sang-Young; Kang, Yoonsung 2009-01-01 53BP1 is an important genome stability regulator, which protects cells against double-strand breaks. Following DNA damage, 53BP1 is rapidly recruited to sites of DNA breakage, along with other DNA damage response proteins, including γ-H2AX, MDC1, and BRCA1. The recruitment of 53BP1 requires a tandem Tudor fold which associates with methylated histones H3 and H4. It has already been determined that the majority of DNA damage response proteins are phosphorylated by ATM and/or ATR after DNA dama... 19. The Fanconi anemia DNA damage repair pathway in the spotlight for germline predisposition to colorectal cancer Science.gov (United States) Esteban-Jurado, Clara; Franch-Expósito, Sebastià; Muñoz, Jenifer; Ocaña, Teresa; Carballal, Sabela; López-Cerón, Maria; Cuatrecasas, Miriam; Vila-Casadesús, Maria; Lozano, Juan José; Serra, Enric; Beltran, Sergi; Brea-Fernández, Alejandro; Ruiz-Ponte, Clara; Castells, Antoni; Bujanda, Luis; Garre, Pilar; Caldés, Trinidad; Cubiella, Joaquín; Balaguer, Francesc; Castellví-Bel, Sergi 2016-01-01 Colorectal cancer (CRC) is one of the most common neoplasms in the world. Fanconi anemia (FA) is a very rare genetic disease causing bone marrow failure, congenital growth abnormalities and cancer predisposition. The comprehensive FA DNA damage repair pathway requires the collaboration of 53 proteins and it is necessary to restore genome integrity by efficiently repairing damaged DNA. A link between FA genes in breast and ovarian cancer germline predisposition has been previously suggested. We selected 74 CRC patients from 40 unrelated Spanish families with strong CRC aggregation compatible with an autosomal dominant pattern of inheritance and without mutations in known hereditary CRC genes and performed germline DNA whole-exome sequencing with the aim of finding new candidate germline predisposition variants. After sequencing and data analysis, variant prioritization selected only those very rare alterations, producing a putative loss of function and located in genes with a role compatible with cancer. We detected an enrichment for variants in FA DNA damage repair pathway genes in our familial CRC cohort as 6 families carried heterozygous, rare, potentially pathogenic variants located in BRCA2/FANCD1, BRIP1/FANCJ, FANCC, FANCE and REV3L/POLZ. In conclusion, the FA DNA damage repair pathway may play an important role in the inherited predisposition to CRC. PMID:27165003 20. Effect of Wortmannin on the repair profiles of DNA double-strand breaks in the whole genome and in interstitial telomeric sequences of Chinese hamster cells International Nuclear Information System (INIS) The DNA breakage detection-fluorescence in situ hybridization (DBD-FISH) procedure was applied to analyze the effect of Wortmannin (WM) in the rejoining kinetics of ionizing radiation-induced DNA double-strand breaks (DSBs) in the whole genome and in the long interstitial telomeric repeat sequence (ITRS) blocks from Chinese hamster cell lines. The results indicate that the ITRS blocks from wild-type Chinese hamster cell lines, CHO9 and V79B, exhibit a slower initial rejoining rate of ionizing radiation-induced DSBs than the genome overall. Neither Rad51C nor the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs) activities, involved in homologous recombination (HR) and in non-homologous end-joining (NHEJ) pathways of DSB repair respectively, influenced the rejoining kinetics within ITRS in contrast to DNA sequences in the whole genome. Nevertheless, DSB removal rate within ITRS was decreased in the absence of Ku86 activity, though at a lower affectation level than in the whole genome, thus homogenizing both rejoining kinetics rates. WM treatment slowed down the DSB rejoining kinetics rate in ITRS, this effect being more pronounced in the whole genome, resulting in a similar pattern to that of the Ku86 deficient cells. In fact, no WM effect was detected in the Ku86 deficient Chinese hamster cells, so probably WM does not add further impairment in DSB rejoining than that resulted as a consequence of absence of Ku activity. The same slowing effect was also observed after treatment of Rad51C and DNA-PKcs defective hamster cells by WM, suggesting that: (1) there is no potentiation of the HR when the NHEJ is impaired by WM, either in the whole genome or in the ITRS, and (2) that this impairment may probably involve more targets than DNA-PKcs. These results suggest that there is an intragenomic heterogeneity in DSB repair, as well as in the effect of WM on this process 1. PAXX and XLF DNA repair factors are functionally redundant in joining DNA breaks in a G1-arrested progenitor B-cell line. Science.gov (United States) Kumar, Vipul; Alt, Frederick W; Frock, Richard L 2016-09-20 Classical nonhomologous end joining (C-NHEJ) is a major mammalian DNA double-strand break (DSB) repair pathway. Core C-NHEJ factors, such as XRCC4, are required for joining DSB intermediates of the G1 phase-specific V(D)J recombination reaction in progenitor lymphocytes. Core factors also contribute to joining DSBs in cycling mature B-lineage cells, including DSBs generated during antibody class switch recombination (CSR) and DSBs generated by ionizing radiation. The XRCC4-like-factor (XLF) C-NHEJ protein is dispensable for V(D)J recombination in normal cells, but because of functional redundancy, it is absolutely required for this process in cells deficient for the ataxia telangiectasia-mutated (ATM) DSB response factor. The recently identified paralogue of XRCC4 and XLF (PAXX) factor has homology to these two proteins and variably contributes to ionizing radiation-induced DSB repair in human and chicken cells. We now report that PAXX is dispensable for joining V(D)J recombination DSBs in G1-arrested mouse pro-B-cell lines, dispensable for joining CSR-associated DSBs in a cycling mouse B-cell line, and dispensable for normal ionizing radiation resistance in both G1-arrested and cycling pro-B lines. However, we find that combined deficiency for PAXX and XLF in G1-arrested pro-B lines abrogates DSB joining during V(D)J recombination and sensitizes the cells to ionizing radiation exposure. Thus, PAXX provides core C-NHEJ factor-associated functions in the absence of XLF and vice versa in G1-arrested pro-B-cell lines. Finally, we also find that PAXX deficiency has no impact on V(D)J recombination DSB joining in ATM-deficient pro-B lines. We discuss implications of these findings with respect to potential PAXX and XLF functions in C-NHEJ. PMID:27601633 2. Feasibility of measuring radiation-induced DNA double strand breaks and their repair by pulsed field gel electrophoresis in freshly isolated cells from the mouse RIF-1 tumor NARCIS (Netherlands) vanWaarde, MAWH; vanAssen, AJ; Konings, AWT; Kampinga, HH 1996-01-01 Purpose: To examine the technical feasibility of pulsed field gel electrophoresis (PFGE) as a predictive assay for the radioresponsiveness of tumors. Induction and repair of DNA double strand breaks (DSBs) in a freshly prepared cell suspension from a RIF-1 tumor (irradiated ex vivo) was compared wit 3. DNA apoptosis and stability in B-cell chronic lymphoid leukaemia: implication of the DNA double-strand breaks repair system by non homologous recombination International Nuclear Information System (INIS) After an introduction presenting the diagnosis and treatment of chronic lymphoid leukaemia, its molecular and genetic characteristics, and its cellular origin and clonal evolution, this research thesis describes the apoptosis (definition and characteristics, cancer and chemotherapy, apoptotic ways induced by gamma irradiation), the genotoxic stresses, the different repair mechanisms for different damages, and the DNA repair processes. It reports how human chronic lymphocytic leukaemia B cells can escape DNA damage-induced apoptosis through the non-homologous end-joining DNA repair pathway, and presents non-homologous end-joining DNA repair as a potent mutagenic process in human chronic lymphocytic leukaemia B cells 4. Comparison of transformation, DNA single strand breaks and its repair in human blood lymphocytes stimulated with PHA, ConA and PWM following exposure to γ-rays International Nuclear Information System (INIS) The transformation, DNA single strand breaks and its repair in human peripheral blood lymphocytes stimulated with PHA, ConA and PWM respectively following exposure to 60Co γ-rays were analyzed by 3H-thymidine incorporation and hydroxylapatite chromatography. The transformation of lymphocytes stimulated with PHA, ConA and PWM were suppressed by γ-rays and the dose-effect curves were biphasic within the range of 0-8 Gy. The lymphocytes stimulated with PWM were the most resistant to γ-rays. The extent of DNA single strand breaks in lymphocytes induced by γ-rays was linearly related to the dose within the range of 0-30 Gy and there was no marked difference in the three kinds of lymphocytes. After a period of post-irradiation (15 Gy) incubation at 37 deg C, the DNA single strand breaks could be rejoined but incompletely. The rejoined strands broke again if the cells were incubated longer. The repair ratio of single strand breaks in the lymphocytes stimulated with PWM was the highest among the cells with three mitogens. The results suggest that the difference of the radiation effect on transformation in different lytphocytes is probably related to the repair ability of DNA single strand breaks 5. Frequent and efficient use of the sister chromatid for DNA double-strand break repair during budding yeast meiosis. Directory of Open Access Journals (Sweden) Tamara Goldfarb Full Text Available Recombination between homologous chromosomes of different parental origin (homologs is necessary for their accurate segregation during meiosis. It has been suggested that meiotic inter-homolog recombination is promoted by a barrier to inter-sister-chromatid recombination, imposed by meiosis-specific components of the chromosome axis. Consistent with this, measures of Holliday junction-containing recombination intermediates (joint molecules [JMs] show a strong bias towards inter-homolog and against inter-sister JMs. However, recombination between sister chromatids also has an important role in meiosis. The genomes of diploid organisms in natural populations are highly polymorphic for insertions and deletions, and meiotic double-strand breaks (DSBs that form within such polymorphic regions must be repaired by inter-sister recombination. Efforts to study inter-sister recombination during meiosis, in particular to determine recombination frequencies and mechanisms, have been constrained by the inability to monitor the products of inter-sister recombination. We present here molecular-level studies of inter-sister recombination during budding yeast meiosis. We examined events initiated by DSBs in regions that lack corresponding sequences on the homolog, and show that these DSBs are efficiently repaired by inter-sister recombination. This occurs with the same timing as inter-homolog recombination, but with reduced (2- to 3-fold yields of JMs. Loss of the meiotic-chromosome-axis-associated kinase Mek1 accelerates inter-sister DSB repair and markedly increases inter-sister JM frequencies. Furthermore, inter-sister JMs formed in mek1Δ mutants are preferentially lost, while inter-homolog JMs are maintained. These findings indicate that inter-sister recombination occurs frequently during budding yeast meiosis, with the possibility that up to one-third of all recombination events occur between sister chromatids. We suggest that a Mek1-dependent reduction in 6. Chemical repair of base lesions, AP-sites, and strand breaks on plasmid DNA in dilute aqueous solution by ascorbic acid Energy Technology Data Exchange (ETDEWEB) Hata, Kuniki [Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakatashirane, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Urushibara, Ayumi; Yamashita, Shinichi; Shikazono, Naoya; Yokoya, Akinari [Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakatashirane, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Katsumura, Yosuke, E-mail: [email protected] [Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Nuclear Professional School, School of Engineering, The University of Tokyo, 2-22 Shirakatashirane, Tokai-mura, Naka-gun, Ibaraki 319-1188 (Japan) 2013-05-03 Highlights: •We report a novel mechanism of radiation protection of DNA by chemical activity of ascorbic acid. •The “chemical repair” of DNA damage was revealed using biochemical assay and chemical kinetics analysis. •We found that ascorbic acid significantly repairs precursors of nucleobase lesions and abasic sites. •However, ascorbic acid seldom repairs precursors of DNA-strand breaks. -- Abstract: We quantified the damage yields produced in plasmid DNA by γ-irradiation in the presence of low concentrations (10–100 μM) of ascorbic acid, which is a major antioxidant in living systems, to clarify whether it chemically repairs radiation damage in DNA. The yield of DNA single strand breaks induced by irradiation was analyzed with agarose gel electrophoresis as conformational changes in closed circular plasmids. Base lesions and abasic sites were also observed as additional conformational changes by treating irradiated samples with glycosylase proteins. By comparing the suppression efficiencies to the induction of each DNA lesion, in addition to scavenging of the OH radicals derived from water radiolysis, it was found that ascorbic acid promotes the chemical repair of precursors of AP-sites and base lesions more effectively than those of single strand breaks. We estimated the efficiency of the chemical repair of each lesion using a kinetic model. Approximately 50–60% of base lesions and AP-sites were repaired by 10 μM ascorbic acid, although strand breaks were largely unrepaired by ascorbic acid at low concentrations. The methods in this study will provide a route to understanding the mechanistic aspects of antioxidant activity in living systems. 7. Chemical repair of base lesions, AP-sites, and strand breaks on plasmid DNA in dilute aqueous solution by ascorbic acid International Nuclear Information System (INIS) Highlights: •We report a novel mechanism of radiation protection of DNA by chemical activity of ascorbic acid. •The “chemical repair” of DNA damage was revealed using biochemical assay and chemical kinetics analysis. •We found that ascorbic acid significantly repairs precursors of nucleobase lesions and abasic sites. •However, ascorbic acid seldom repairs precursors of DNA-strand breaks. -- Abstract: We quantified the damage yields produced in plasmid DNA by γ-irradiation in the presence of low concentrations (10–100 μM) of ascorbic acid, which is a major antioxidant in living systems, to clarify whether it chemically repairs radiation damage in DNA. The yield of DNA single strand breaks induced by irradiation was analyzed with agarose gel electrophoresis as conformational changes in closed circular plasmids. Base lesions and abasic sites were also observed as additional conformational changes by treating irradiated samples with glycosylase proteins. By comparing the suppression efficiencies to the induction of each DNA lesion, in addition to scavenging of the OH radicals derived from water radiolysis, it was found that ascorbic acid promotes the chemical repair of precursors of AP-sites and base lesions more effectively than those of single strand breaks. We estimated the efficiency of the chemical repair of each lesion using a kinetic model. Approximately 50–60% of base lesions and AP-sites were repaired by 10 μM ascorbic acid, although strand breaks were largely unrepaired by ascorbic acid at low concentrations. The methods in this study will provide a route to understanding the mechanistic aspects of antioxidant activity in living systems 8. Members of the RAD52 Epistasis Group Contribute to Mitochondrial Homologous Recombination and Double-Strand Break Repair in Saccharomyces cerevisiae. Science.gov (United States) Stein, Alexis; Kalifa, Lidza; Sia, Elaine A 2015-11-01 Mitochondria contain an independently maintained genome that encodes several proteins required for cellular respiration. Deletions in the mitochondrial genome have been identified that cause several maternally inherited diseases and are associated with certain cancers and neurological disorders. The majority of these deletions in human cells are flanked by short, repetitive sequences, suggesting that these deletions may result from recombination events. Our current understanding of the maintenance and repair of mtDNA is quite limited compared to our understanding of similar events in the nucleus. Many nuclear DNA repair proteins are now known to also localize to mitochondria, but their function and the mechanism of their action remain largely unknown. This study investigated the contribution of the nuclear double-strand break repair (DSBR) proteins Rad51p, Rad52p and Rad59p in mtDNA repair. We have determined that both Rad51p and Rad59p are localized to the matrix of the mitochondria and that Rad51p binds directly to mitochondrial DNA. In addition, a mitochondrially-targeted restriction endonuclease (mtLS-KpnI) was used to produce a unique double-strand break (DSB) in the mitochondrial genome, which allowed direct analysis of DSB repair in vivo in Saccharomyces cerevisiae. We find that loss of these three proteins significantly decreases the rate of spontaneous deletion events and the loss of Rad51p and Rad59p impairs the repair of induced mtDNA DSBs. 9. The nucleotide excision repair system of Borrelia burgdorferi is the sole pathway involved in repair of DNA damage by UV light. Science.gov (United States) Hardy, Pierre-Olivier; Chaconas, George 2013-05-01 To survive and avoid accumulation of mutations caused by DNA damage, the genomes of prokaryotes encode a variety of DNA repair pathways most well characterized in Escherichia coli. Some of these are required for the infectivity of various pathogens. In this study, the importance of 25 DNA repair/recombination genes for Borrelia burgdorferi survival to UV-induced DNA damage was assessed. In contrast to E. coli, where 15 of these genes have an effect on survival of UV irradiation, disruption of recombinational repair, transcription-coupled repair, methyl-directed mismatch correction, and repair of arrested replication fork pathways did not decrease survival of B. burgdorferi exposed to UV light. However, the disruption of the B. burgdorferi nucleotide excision repair (NER) pathway (uvrA, uvrB, uvrC, and uvrD) resulted in a 10- to 1,000-fold increase in sensitivity to UV light. A functional NER pathway was also shown to be required for B. burgdorferi resistance to nitrosative damage. Finally, disruption of uvrA, uvrC, and uvrD had only a minor effect upon murine infection by increasing the time required for dissemination. PMID:23475971 10. The RecRO pathway of DNA recombinational repair in Helicobacter pylori and its role in bacterial survival in the host. Science.gov (United States) Wang, Ge; Lo, Leja F; Maier, Robert J 2011-04-01 Two pathways for DNA recombination, AddAB (RecBCD-like) and RecRO, were identified in Helicobacter pylori, a pathogenic bacterium that colonizes human stomachs resulting in a series of gastric diseases. In this study, we examined the physiological roles of H. pylori RecRO pathway in DNA recombinational repair. We characterized H. pylori single mutants in recR and in recO, genes in the putative gap repair recombination pathway, and an addA recO double mutant that is thus deficient in both pathways that initiate DNA recombinational repair. The recR or recO single mutants showed the same level of sensitivity to mitomycin C as the parent strain, suggesting that the RecRO pathway is not responsible for the repair of DNA double strand breaks. However, H. pylori recR and recO mutants are highly sensitive to oxidative stress and separately to acid stress, two major stress conditions that H. pylori encounters in its physiological niche. The complementation of the recR mutant restored the sensitivity to oxidative and acid stress to the wild type level. By measuring DNA transformation frequencies, the recR and recO single mutants were shown to have no effect on inter-genomic recombination, whereas the addA recO double mutant had a greatly (∼12-fold) reduced transformation frequency. On the other hand, the RecRO pathway was shown to play a significant role in intra-genomic recombination with direct repeat sequences. Whereas the recA strain had a deletion frequency 35-fold lower than that of background level, inactivation of recR resulted in a 4-fold decrease in deletion frequency. In a mouse infection model, the three mutant strains displayed a greatly reduced ability to colonize the host stomachs. The geometric means of colonization number for the wild type, recR, recO, and addA recO strains were 6 x 10⁵, 1.6 x 10⁴, 1.4 x 10⁴ and 4 x 10³ CFU/g stomach, respectively. H. pylori RecRO-mediated DNA recombinational repair (intra-genomic recombination) is thus involved in 11. MOF phosphorylation by ATM regulates 53BP1-mediated DSB repair pathway choice Science.gov (United States) Gupta, Arun; Hunt, Clayton R.; Hegdec, Muralidhar L.; Chakraborty, Sharmistha; Udayakumar, Durga; Horikoshi, Nobuo; Singh1, Mayank; Ramnarain, Deepti B.; Hittelman, Walter N.; Namjoshi, Sarita; Asaithamby, Aroumougame; Hazra, Tapas K.; Ludwig, Thomas; Pandita, Raj K.; Tyler, Jessica K.; Pandita, Tej K. 2014-01-01 Cell cycle phase is a critical determinant of the choice between DNA damage repair by non-homologous end joining (NHEJ) or homologous recombination (HR). Here we report that DSBs induce ATM-dependent MOF (a histone H4 acetyl-transferase) phosphorylation (p-T392-MOF) and that phosphorylated MOF co-localizes with γ-H2AX, ATM, and 53BP1 foci. Mutation of the phosphorylation site (MOF-T392A) impedes DNA repair in S- and G2-phase but not G1-phase cells. Expression of MOF-T392A also reverses the reduction in DSB associated 53BP1 seen in wild type S/G2-phase cells, resulting in enhanced 53BP1 and reduced BRCA1 association. Decreased BRCA1 levels at DSB sites correlates with defective repairosome formation, reduced HR repair and decreased cell survival following irradiation. These data support a model whereby ATM mediated MOF-T392 phosphorylation modulates 53BP1 function to facilitate the subsequent recruitment of HR repair proteins, uncovering a regulatory role for MOF in DSB repair pathway choice during S/G2-phase. PMID:24953651 12. Genomically amplified Akt3 activates DNA repair pathway and promotes glioma progression. Science.gov (United States) Turner, Kristen M; Sun, Youting; Ji, Ping; Granberg, Kirsi J; Bernard, Brady; Hu, Limei; Cogdell, David E; Zhou, Xinhui; Yli-Harja, Olli; Nykter, Matti; Shmulevich, Ilya; Yung, W K Alfred; Fuller, Gregory N; Zhang, Wei 2015-03-17 Akt is a robust oncogene that plays key roles in the development and progression of many cancers, including glioma. We evaluated the differential propensities of the Akt isoforms toward progression in the well-characterized RCAS/Ntv-a mouse model of PDGFB-driven low grade glioma. A constitutively active myristoylated form of Akt1 did not induce high-grade glioma (HGG). In stark contrast, Akt2 and Akt3 showed strong progression potential with 78% and 97% of tumors diagnosed as HGG, respectively. We further revealed that significant variations in polarity and hydropathy values among the Akt isoforms in both the pleckstrin homology domain (P domain) and regulatory domain (R domain) were critical in mediating glioma progression. Gene expression profiles from representative Akt-derived tumors indicated dominant and distinct roles for Akt3, consisting primarily of DNA repair pathways. TCGA data from human GBM closely reflected the DNA repair function, as Akt3 was significantly correlated with a 76-gene signature DNA repair panel. Consistently, compared with Akt1 and Akt2 overexpression models, Akt3-expressing human GBM cells had enhanced activation of DNA repair proteins, leading to increased DNA repair and subsequent resistance to radiation and temozolomide. Given the wide range of Akt3-amplified cancers, Akt3 may represent a key resistance factor. 13. Determination of human DNA polymerase utilization for the repair of a model ionizing radiation-induced DNA strand break lesion in a defined vector substrate Science.gov (United States) Winters, T. A.; Russell, P. S.; Kohli, M.; Dar, M. E.; Neumann, R. D.; Jorgensen, T. J. 1999-01-01 Human DNA polymerase and DNA ligase utilization for the repair of a major class of ionizing radiation-induced DNA lesion [DNA single-strand breaks containing 3'-phosphoglycolate (3'-PG)] was examined using a novel, chemically defined vector substrate containing a single, site-specific 3'-PG single-strand break lesion. In addition, the major human AP endonuclease, HAP1 (also known as APE1, APEX, Ref-1), was tested to determine if it was involved in initiating repair of 3'-PG-containing single-strand break lesions. DNA polymerase beta was found to be the primary polymerase responsible for nucleotide incorporation at the lesion site following excision of the 3'-PG blocking group. However, DNA polymerase delta/straightepsilon was also capable of nucleotide incorporation at the lesion site following 3'-PG excision. In addition, repair reactions catalyzed by DNA polymerase beta were found to be most effective in the presence of DNA ligase III, while those catalyzed by DNA polymerase delta/straightepsilon appeared to be more effective in the presence of DNA ligase I. Also, it was demonstrated that the repair initiating 3'-PG excision reaction was not dependent upon HAP1 activity, as judged by inhibition of HAP1 with neutralizing HAP1-specific polyclonal antibody. 14. Mathematical modelling of the automated FADU assay for the quantification of DNA strand breaks and their repair in human peripheral mononuclear blood cells International Nuclear Information System (INIS) Cells continuously undergo DNA damage from exogenous agents like irradiation or genotoxic chemicals or from endogenous radicals produced by normal cellular metabolic activities. DNA strand breaks are one of the most common genotoxic lesions and they can also arise as intermediates of DNA repair activity. Unrepaired DNA damage can lead to genomic instability, which can massively compromise the health status of organisms. Therefore it is important to measure and quantify DNA damage and its repair. We have previously published an automated method for measuring DNA strand breaks based on fluorimetric detection of alkaline DNA unwinding [1], and here we present a mathematical model of the FADU assay, which enables to an analytic expression for the relation between measured fluorescence and the number of strand breaks. Assessment of the formation and also the repair of DNA strand breaks is a crucial functional parameter to investigate genotoxicity in living cells. A reliable and convenient method to quantify DNA strand breakage is therefore of significant importance for a wide variety of scientific fields, e.g. toxicology, pharmacology, epidemiology and medical sciences 15. Signalization and repair of the DNA double-strand breaks of in the cerebral tumors: modulation of the radiation response with the chemotherapy treatments International Nuclear Information System (INIS) 16. The Nucleotide Excision Repair System of Borrelia burgdorferi Is the Sole Pathway Involved in Repair of DNA Damage by UV Light OpenAIRE Hardy, Pierre-Olivier; Chaconas, George 2013-01-01 To survive and avoid accumulation of mutations caused by DNA damage, the genomes of prokaryotes encode a variety of DNA repair pathways most well characterized in Escherichia coli. Some of these are required for the infectivity of various pathogens. In this study, the importance of 25 DNA repair/recombination genes for Borrelia burgdorferi survival to UV-induced DNA damage was assessed. In contrast to E. coli, where 15 of these genes have an effect on survival of UV irradiation, disruption of... 17. MEIOTIC F-BOX Is Essential for Male Meiotic DNA Double-Strand Break Repair in Rice[OPEN Science.gov (United States) Wang, Chong; Yu, Junping; Zong, Jie; Lu, Pingli 2016-01-01 F-box proteins constitute a large superfamily in plants and play important roles in controlling many biological processes, but the roles of F-box proteins in male meiosis in plants remain unclear. Here, we identify the rice (Oryza sativa) F-box gene MEIOTIC F-BOX (MOF), which is essential for male meiotic progression. MOF belongs to the FBX subfamily and is predominantly active during leptotene to pachytene of prophase I. mof meiocytes display disrupted telomere bouquet formation, impaired pairing and synapsis of homologous chromosomes, and arrested meiocytes at late prophase I, followed by apoptosis. Although normal, programmed double-stranded DNA breaks (DSBs) form in mof mutants, foci of the phosphorylated histone variant γH2AX, a marker for DSBs, persist in the mutant, indicating that many of the DSBs remained unrepaired. The recruitment of Completion of meiosis I (COM1) and Radiation sensitive51C (RAD51C) to DSBs is severely compromised in mutant meiocytes, indicating that MOF is crucial for DSB end-processing and repair. Further analyses showed that MOF could physically interact with the rice SKP1-like Protein1 (OSK1), indicating that MOF functions as a component of the SCF E3 ligase to regulate meiotic progression in rice. Thus, this study reveals the essential role of an F-box protein in plant meiosis and provides helpful information for elucidating the roles of the ubiquitin proteasome system in plant meiotic progression. PMID:27436711 18. Correlativity study between expression of DNA double-strand break repair protein and radiosensitivity of tumor cells Institute of Scientific and Technical Information of China (English) Liang ZHUANG; Shiying YU; Xiaoyuan HUANG; Yang CAO; Huihua XIONG 2009-01-01 DNA double-strand break (DSB) is generally regarded as the most lethal of all DNA lesions after radiation. KuS0, DNA-PK catalytic subunit (DNA-PKcs) and ataxia telangiectasia mutated (ATM) proteins are major DSB repair proteins. In this study, survival fraction at 2Gy (SF2) values of eight human tumor cell lines (including four human cervical carcinoma cell lines HeLa, SiHa, C33A, Caski, three human breast carcinoma cell lines MCF-7, MDA-MB-231, MDA-MB-453, and one human lung carcinoma cell line A549) were acquired by clone formation assay, and western blot was applied to detect the expressions of Ku80, DNA-PKcs and ATM protein. The correlativity of protein expression with SF2 value was analyzed by Pearson linear correlation analysis. We found that the expression of the same protein in different cell lines and the expression of three proteins in the same cell line had a significant difference. The SF2 values were also different in eight tumor cell lines and there was a positive correlativity between the expression of DNA-PKcs and SF2 (r=0.723, P =0.043), but Ku80 and ATM expression had no correlation with SF2 (P>0.05). These findings suggest that the expression level of DNA-PKcs protein can be an indicator for predicting the radiosensitivity of tumor cells. 19. Haploid meiosis in Arabidopsis: double-strand breaks are formed and repaired but without synapsis and crossovers. Directory of Open Access Journals (Sweden) Marta Cifuentes Full Text Available Two hallmark features of meiosis are i the formation of crossovers (COs between homologs and ii the production of genetically-unique haploid spores that will fuse to restore the somatic ploidy level upon fertilization. In this study we analysed meiosis in haploid Arabidopsis thaliana plants and a range of haploid mutants to understand how meiosis progresses without a homolog. Extremely low chiasma frequency and very limited synapsis occurred in wild-type haploids. The resulting univalents segregated in two uneven groups at the first division, and sister chromatids segregated to opposite poles at the second division, leading to the production of unbalanced spores. DNA double-strand breaks that initiate meiotic recombination were formed, but in half the number compared to diploid meiosis. They were repaired in a RAD51- and REC8-dependent manner, but independently of DMC1, presumably using the sister chromatid as a template. Additionally, turning meiosis into mitosis (MiMe genotype in haploids resulted in the production of balanced haploid gametes and restoration of fertility. The variability of the effect on meiosis of the absence of homologous chromosomes in different organisms is then discussed. 20. Post-irradiation chemical processing of DNA damage generates double-strand breaks in cells already engaged in repair Science.gov (United States) Singh, Satyendra K.; Wang, Minli; Staudt, Christian; Iliakis, George 2011-01-01 In cells exposed to ionizing radiation (IR), double-strand breaks (DSBs) form within clustered-damage sites from lesions disrupting the DNA sugar–phosphate backbone. It is commonly assumed that these DSBs form promptly and are immediately detected and processed by the cellular DNA damage response (DDR) apparatus. This assumption is questioned by the observation that after irradiation of naked DNA, a fraction of DSBs forms minutes to hours after exposure as a result of temperature dependent, chemical processing of labile sugar lesions. Excess DSBs also form when IR-exposed cells are processed at 50°C, but have been hitherto considered method-related artifact. Thus, it remains unknown whether DSBs actually develop in cells after IR exposure from chemically labile damage. Here, we show that irradiation of ‘naked’ or chromatin-organized mammalian DNA produces lesions, which evolve to DSBs and add to those promptly induced, after 8–24 h in vitro incubation at 37°C or 50°C. The conversion is more efficient in chromatin-associated DNA, completed within 1 h in cells and delayed in a reducing environment. We conclude that IR generates sugar lesions within clustered-damage sites contributing to DSB formation only after chemical processing, which occurs efficiently at 37°C. This subset of delayed DSBs may challenge DDR, may affect the perceived repair kinetics and requires further characterization. PMID:21745815 1. Replication Protein A (RPA) deficiency activates the Fanconi anemia DNA repair pathway. Science.gov (United States) Jang, Seok-Won; Jung, Jin Ki; Kim, Jung Min 2016-09-01 The Fanconi anemia (FA) pathway regulates DNA inter-strand crosslink (ICL) repair. Despite our greater understanding of the role of FA in ICL repair, its function in the preventing spontaneous genome instability is not well understood. Here, we show that depletion of replication protein A (RPA) activates the FA pathway. RPA1 deficiency increases chromatin recruitment of FA core complex, leading to FANCD2 monoubiquitination (FANCD2-Ub) and foci formation in the absence of DNA damaging agents. Importantly, ATR depletion, but not ATM, abolished RPA1 depletion-induced FANCD2-Ub, suggesting that ATR activation mediated FANCD2-Ub. Interestingly, we found that depletion of hSSB1/2-INTS3, a single-stranded DNA-binding protein complex, induces FANCD2-Ub, like RPA1 depletion. More interestingly, depletion of either RPA1 or INTS3 caused increased accumulation of DNA damage in FA pathway deficient cell lines. Taken together, these results indicate that RPA deficiency induces activation of the FA pathway in an ATR-dependent manner, which may play a role in the genome maintenance. PMID:27398742 2. Nucleotide Excision Repair Pathway Polymorphisms and Pancreatic Cancer Risk: Evidence for role of MMS19L Science.gov (United States) McWilliams, Robert R.; Bamlet, William R.; de Andrade, Mariza; Rider, David N.; Cunningham, Julie M.; Petersen, Gloria M. 2009-01-01 Background Nucleotide excision repair (NER) is a vital response to DNA damage, including damage from tobacco exposure. Single nucleotide polymorphisms (SNPs) in the NER pathway may encode alterations that affect DNA repair function and therefore influence risk for pancreatic cancer development. Methods A clinic based case-control study in non-Hispanic white persons compared 1,143 patients with pancreatic adenocarcinoma with 1,097 healthy controls. Twenty-seven genes directly and indirectly involved in the NER pathway were identified and 236 tag-SNPs were selected from 26 of these (one had no SNPs identified). Association studies were performed at the gene level by principal components analysis, while recursive partitioning analysis was utilized to identify potential gene-gene and gene-environment interactions within the pathway. At the individual SNP level, adjusted additive, dominant, and recessive models were investigated, and gene-environment interactions were also assessed. Results Gene level analyses showed an association of MMS19L genotype (chromosome 10q24.1) with altered pancreatic cancer risk (p=0.023). Haplotype analysis of MMS19L also showed a significant association (p=0.0132). Analyses of 7 individual SNPs in this gene showed both protective and risk associations for minor alleles, broadly distributed across patient subgroups defined by smoking status, sex, and age. Conclusion In a candidate pathway SNP association study analysis, common variation in a NER gene, MMS19L, was associated with risk for pancreatic cancer. PMID:19318433 3. Novel Smad proteins localize to IR-induced double-strand breaks: interplay between TGFβ and ATM pathways OpenAIRE Wang, Minli; Saha, Janapriya; Hada, Megumi; Anderson, Jennifer A.; Pluth, Janice M.; O’Neill, Peter; Cucinotta, Francis A. 2012-01-01 Cellular damage from ionizing radiation (IR) is in part due to DNA damage and reactive oxygen species, which activate DNA damage response (DDR) and cytokine signaling pathways, including the ataxia telangiectasia mutated (ATM) and transforming growth factor (TGF)β/Smad pathways. Using classic double-strand breaks (DSBs) markers, we studied the roles of Smad proteins in DDR and the crosstalk between TGFβ and ATM pathways. We observed co-localization of phospho-Smad2 (pSmad2) and Smad7 with DSB... 4. Alkylation base damage is converted into repairable double-strand breaks and complex intermediates in G2 cells lacking AP endonuclease. Directory of Open Access Journals (Sweden) Wenjian Ma 2011-04-01 Full Text Available DNA double-strand breaks (DSBs are potent sources of genome instability. While there is considerable genetic and molecular information about the disposition of direct DSBs and breaks that arise during replication, relatively little is known about DSBs derived during processing of single-strand lesions, especially for the case of single-strand breaks (SSBs with 3'-blocked termini generated in vivo. Using our recently developed assay for detecting end-processing at random DSBs in budding yeast, we show that single-strand lesions produced by the alkylating agent methyl methanesulfonate (MMS can generate DSBs in G2-arrested cells, i.e., S-phase independent. These derived DSBs were observed in apn1/2 endonuclease mutants and resulted from aborted base excision repair leading to 3' blocked single-strand breaks following the creation of abasic (AP sites. DSB formation was reduced by additional mutations that affect processing of AP sites including ntg1, ntg2, and, unexpectedly, ogg1, or by a lack of AP sites due to deletion of the MAG1 glycosylase gene. Similar to direct DSBs, the derived DSBs were subject to MRX (Mre11, Rad50, Xrs2-determined resection and relied upon the recombinational repair genes RAD51, RAD52, as well as on the MCD1 cohesin gene, for repair. In addition, we identified a novel DNA intermediate, detected as slow-moving chromosomal DNA (SMD in pulsed field electrophoresis gels shortly after MMS exposure in apn1/2 cells. The SMD requires nicked AP sites, but is independent of resection/recombination processes, suggesting that it is a novel structure generated during processing of 3'-blocked SSBs. Collectively, this study provides new insights into the potential consequences of alkylation base damage in vivo, including creation of novel structures as well as generation and repair of DSBs in nonreplicating cells. 5. Identification of Pathways in Liver Repair Potentially Targeted by Secretory Proteins from Human Mesenchymal Stem Cells Directory of Open Access Journals (Sweden) Sandra Winkler 2016-07-01 Full Text Available Background: The beneficial impact of mesenchymal stem cells (MSC on both acute and chronic liver diseases has been confirmed, although the molecular mechanisms behind it remain elusive. We aim to identify factors secreted by undifferentiated and hepatocytic differentiated MSC in vitro in order to delineate liver repair pathways potentially targeted by MSC. Methods: Secreted factors were determined by protein arrays and related pathways identified by biomathematical analyses. Results: MSC from adipose tissue and bone marrow expressed a similar pattern of surface markers. After hepatocytic differentiation, CD54 (intercellular adhesion molecule 1, ICAM-1 increased and CD166 (activated leukocyte cell adhesion molecule, ALCAM decreased. MSC secreted different factors before and after differentiation. These comprised cytokines involved in innate immunity and growth factors regulating liver regeneration. Pathway analysis revealed cytokine-cytokine receptor interactions, chemokine signalling pathways, the complement and coagulation cascades as well as the Januskinase-signal transducers and activators of transcription (JAK-STAT and nucleotide-binding oligomerization domain-like receptor (NOD-like receptor signalling pathways as relevant networks. Relationships to transforming growth factor β (TGF-β and hypoxia-inducible factor 1-α (HIF1-α signalling seemed also relevant. Conclusion: MSC secreted proteins, which differed depending on cell source and degree of differentiation. The factors might address inflammatory and growth factor pathways as well as chemo-attraction and innate immunity. Since these are prone to dysregulation in most liver diseases, MSC release hepatotropic factors, potentially supporting liver regeneration. 6. DNA repair pathways underlie a common genetic mechanism modulating onset in polyglutamine diseases Science.gov (United States) Bettencourt, Conceição; Hensman‐Moss, Davina; Flower, Michael; Wiethoff, Sarah; Brice, Alexis; Goizet, Cyril; Stevanin, Giovanni; Koutsis, Georgios; Karadima, Georgia; Panas, Marios; Yescas‐Gómez, Petra; García‐Velázquez, Lizbeth Esmeralda; Alonso‐Vilatela, María Elisa; Lima, Manuela; Raposo, Mafalda; Traynor, Bryan; Sweeney, Mary; Wood, Nicholas; Giunti, Paola; Durr, Alexandra; Holmans, Peter; Houlden, Henry; Tabrizi, Sarah J. 2016-01-01 Objective The polyglutamine diseases, including Huntington's disease (HD) and multiple spinocerebellar ataxias (SCAs), are among the commonest hereditary neurodegenerative diseases. They are caused by expanded CAG tracts, encoding glutamine, in different genes. Longer CAG repeat tracts are associated with earlier ages at onset, but this does not account for all of the difference, and the existence of additional genetic modifying factors has been suggested in these diseases. A recent genome‐wide association study (GWAS) in HD found association between age at onset and genetic variants in DNA repair pathways, and we therefore tested whether the modifying effects of variants in DNA repair genes have wider effects in the polyglutamine diseases. Methods We assembled an independent cohort of 1,462 subjects with HD and polyglutamine SCAs, and genotyped single‐nucleotide polymorphisms (SNPs) selected from the most significant hits in the HD study. Results In the analysis of DNA repair genes as a group, we found the most significant association with age at onset when grouping all polyglutamine diseases (HD+SCAs; p = 1.43 × 10–5). In individual SNP analysis, we found significant associations for rs3512 in FAN1 with HD+SCAs (p = 1.52 × 10–5) and all SCAs (p = 2.22 × 10–4) and rs1805323 in PMS2 with HD+SCAs (p = 3.14 × 10–5), all in the same direction as in the HD GWAS. Interpretation We show that DNA repair genes significantly modify age at onset in HD and SCAs, suggesting a common pathogenic mechanism, which could operate through the observed somatic expansion of repeats that can be modulated by genetic manipulation of DNA repair in disease models. This offers novel therapeutic opportunities in multiple diseases. Ann Neurol 2016;79:983–990 PMID:27044000 7. A role for the malignant brain tumour (MBT domain protein LIN-61 in DNA double-strand break repair by homologous recombination. Directory of Open Access Journals (Sweden) Nicholas M Johnson Full Text Available Malignant brain tumour (MBT domain proteins are transcriptional repressors that function within Polycomb complexes. Some MBT genes are tumour suppressors, but how they prevent tumourigenesis is unknown. The Caenorhabditis elegans MBT protein LIN-61 is a member of the synMuvB chromatin-remodelling proteins that control vulval development. Here we report a new role for LIN-61: it protects the genome by promoting homologous recombination (HR for the repair of DNA double-strand breaks (DSBs. lin-61 mutants manifest numerous problems associated with defective HR in germ and somatic cells but remain proficient in meiotic recombination. They are hypersensitive to ionizing radiation and interstrand crosslinks but not UV light. Using a novel reporter system that monitors repair of a defined DSB in C. elegans somatic cells, we show that LIN-61 contributes to HR. The involvement of this MBT protein in HR raises the possibility that MBT-deficient tumours may also have defective DSB repair. 8. Dynamics and Cell-Type Specificity of the DNA Double-Strand Break Repair Protein RecN in the Developmental Cyanobacterium Anabaena sp. Strain PCC 7120. Directory of Open Access Journals (Sweden) Sheng Hu Full Text Available DNA replication and repair are two fundamental processes required in life proliferation and cellular defense and some common proteins are involved in both processes. The filamentous cyanobacterium Anabaena sp. strain PCC 7120 is capable of forming heterocysts for N2 fixation in the absence of a combined-nitrogen source. This developmental process is intimately linked to cell cycle control. In this study, we investigated the localization of the DNA double-strand break repair protein RecN during key cellular events, such as chromosome damaging, cell division, and heterocyst differentiation. Treatment by a drug causing DNA double-strand breaks (DSBs induced reorganization of the RecN focus preferentially towards the mid-cell position. RecN-GFP was absent in most mature heterocysts. Furthermore, our results showed that HetR, a central player in heterocyst development, was involved in the proper positioning and distribution of RecN-GFP. These results showed the dynamics of RecN in DSB repair and suggested a differential regulation of DNA DSB repair in vegetative cell and heterocysts. The absence of RecN in mature heterocysts is compatible with the terminal nature of these cells. 9. Dynamics and Cell-Type Specificity of the DNA Double-Strand Break Repair Protein RecN in the Developmental Cyanobacterium Anabaena sp. Strain PCC 7120. Science.gov (United States) Hu, Sheng; Wang, Jinglan; Wang, Li; Zhang, Cheng-Cai; Chen, Wen-Li 2015-01-01 DNA replication and repair are two fundamental processes required in life proliferation and cellular defense and some common proteins are involved in both processes. The filamentous cyanobacterium Anabaena sp. strain PCC 7120 is capable of forming heterocysts for N2 fixation in the absence of a combined-nitrogen source. This developmental process is intimately linked to cell cycle control. In this study, we investigated the localization of the DNA double-strand break repair protein RecN during key cellular events, such as chromosome damaging, cell division, and heterocyst differentiation. Treatment by a drug causing DNA double-strand breaks (DSBs) induced reorganization of the RecN focus preferentially towards the mid-cell position. RecN-GFP was absent in most mature heterocysts. Furthermore, our results showed that HetR, a central player in heterocyst development, was involved in the proper positioning and distribution of RecN-GFP. These results showed the dynamics of RecN in DSB repair and suggested a differential regulation of DNA DSB repair in vegetative cell and heterocysts. The absence of RecN in mature heterocysts is compatible with the terminal nature of these cells. 10. The Fanconi anemia pathway and DNA interstrand cross-link repair Institute of Scientific and Technical Information of China (English) Xiaoyu Su; Jun Huang 2011-01-01 Fanconi anemia (FA) is an autosomal or X-linked recessive disorder characterized by chromosomal instability,bone marrow failure,cancer susceptibility,and a profound sensitivity to agents that produce DNA interstrand cross-link (ICL).To date,15 genes have been identified that,when mutated,result in FA or an FA-like syndrome.It is believed that cellular resistance to DNA interstrand cross-linking agents requires all 15 FA or FA-like proteins.Here,we review our current understanding of how these FA proteins participate in ICL repair and discuss the molecular mechanisms that regulate the FA pathway to maintain genome stability. 11. Polymorphisms in DNA Repair Genes, Recreational Physical Activity and Breast Cancer Risk OpenAIRE McCullough, Lauren E.; Santella, Regina M.; Cleveland, Rebecca J.; Millikan, Robert C.; Olshan, Andrew F.; North, Kari E; Bradshaw, Patrick T.; Eng, Sybil M.; Terry, Mary Beth; Shen, Jing; Crew, Katherine D.; Rossner, Pavel; Teitelbaum, Susan L.; Neugut, Alfred I.; Gammon, Marilie D. 2013-01-01 The mechanisms driving the inverse association between recreational physical activity (RPA) and breast cancer risk are complex. While exercise is associated with increased reactive oxygen species production it may also improve damage repair systems, particularly those that operate on single-strand breaks including base excision repair (BER), nucleotide excision repair (NER) and mismatch repair (MMR). Of these repair pathways, the role of MMR in breast carcinogenesis is least investigated. Pol... 12. DNA double strand break repair is enhanced by P53 following induction by DNA damage and is dependent on the C-terminal domain of P53 International Nuclear Information System (INIS) Purpose: The tumor suppressor gene p53 can mediate cell cycle arrest or apoptosis in response to DNA damage. Accumulating evidence suggests that it may also directly or indirectly influence the DNA repair machinery. In the present study, we investigated whether p53, induced by DNA damage, could enhance the rejoining of double-strand DNA breaks. Materials and Methods: DNA double-strand breaks (dsb) were made by restriction enzyme digestion of a plasmid, between a promoter and a 'reporter' gene: luciferase (LUC) or chloramphenicol acetyl-transferase (CAT). Linear or circular plasmid DNA (LUC or CAT) was co-transfected with circular β-Gal plasmid (to normalize for uptake) into mouse embryonic fibroblasts genetically matched to be (+/+) or (-/-) for p53. Their ability to rejoin linearized plasmid was measured by the luciferase or CAT activity detected in rescued plasmids. The activity detected in cells transfected with linear plasmid was scored relative to the activity detected in cells transfected with circular plasmid. Results: Ionizing radiation (IR, 2 Gy) enhanced the dsb repair activity in wild type p53 cells; however, p53 null cells lose this effect, indicating that the enhancement of dsb repair was p53-dependent. REF cells with dominant-negative mutant p53 showed a similar induction compared with the parental REF cells with wild-type p53. This ala-143 mutant p53 prevents cell cycle arrest and transactivation of p21WAF1/cip1) following IR, indicating that the p53-dependent enhancement of DNA repair is distinct from transactivation. Immortalized murine embryonic fibroblasts, 10(1)VasK1 cells, which express p53 cDNA encoding a temperature-sensitive mutant in the DNA sequence specific binding domain (ala135 to val135) with an alternatively spliced C-terminal domain (ASp53: amino-acids 360-381) and, 10(1)Val5 cells, which express the normal spliced p53 (NSp53) with the same temperature-sensitive mutant were compared. It was found that 10(1)VasK1 cells showed no DNA 13. Significant accumulation of persistent organic pollutants and dysregulation in multiple DNA damage repair pathways in the electronic-waste-exposed populations International Nuclear Information System (INIS) Electronic waste (e-waste) has created a worldwide environmental and health problem, by generating a diverse group of hazardous compounds such as persistent organic pollutants (POPs). Our previous studies demonstrated that populations from e-waste exposed region have a significantly higher level of chromosomal aberrancy and incidence of DNA damage. In this study, we further demonstrated that various POPs persisted at a significantly higher concentration in the exposed group than those in the unexposed group. The level of reactive oxygen species and micronucleus rate were also significantly elevated in the exposed group. RNA sequencing analysis revealed 31 genes in DNA damage responses and repair pathways that were differentially expressed between the two groups (Log 2 ratio >1 or <−1). Our data demonstrated that both females and males of the exposed group have activated a series of DNA damage response genes; however many important DNA repair pathways have been dysregulated. Expressions of NEIL1/3 and RPA3, which are critical in initiating base pair and nucleotide excision repairs respectively, have been downregulated in both females and males of the exposed group. In contrast, expression of RNF8, an E3 ligase involved in an error prone non-homologous end joining repair for DNA double strand break, was upregulated in both genders of the exposed group. The other genes appeared to be differentially expressed only when the males or females of the two groups were compared respectively. Importantly, the expression of cell cycle regulatory gene CDC25A that has been implicated in multiple kinds of malignant transformation was significantly upregulated among the exposed males while downregulated among the exposed females. In conclusion, our studies have demonstrated significant correlations between e-waste disposing and POPs accumulation, DNA lesions and dysregulation of multiple DNA damage repair mechanisms in the residents of the e-waste exposed region. - Highlights: 14. Significant accumulation of persistent organic pollutants and dysregulation in multiple DNA damage repair pathways in the electronic-waste-exposed populations Energy Technology Data Exchange (ETDEWEB) He, Xiaobo; Jing, Yaqing; Wang, Jianhai; Li, Keqiu [Basic Medical College, Tianjin Medical University, Tianjin 300070 (China); Yang, Qiaoyun [Department of Occupational and Environmental Health, School of Public Health, Tianjin Medical University, Tianjin 300070 (China); Zhao, Yuxia [Basic Medical College, Tianjin Medical University, Tianjin 300070 (China); Li, Ran [State Key Joint Laboratory for Environmental Simulation and Pollution Control, College of Environmental Sciences and Engineering and Center for Environment and Health, Peking University, Beijing 100871 (China); Ge, Jie [Department of Breast Surgery, Tianjin Medical University Cancer Institute and Hospital, Tianjin 300060 (China); Key Laboratory of Breast Cancer Prevention and Treatment of the Ministry of Education, Tianjin Medical University Cancer Institute and Hospital, Tianjin 300060 (China); Qiu, Xinghua, E-mail: [email protected] [State Key Joint Laboratory for Environmental Simulation and Pollution Control, College of Environmental Sciences and Engineering and Center for Environment and Health, Peking University, Beijing 100871 (China); Li, Guang, E-mail: [email protected] [Basic Medical College, Tianjin Medical University, Tianjin 300070 (China) 2015-02-15 Electronic waste (e-waste) has created a worldwide environmental and health problem, by generating a diverse group of hazardous compounds such as persistent organic pollutants (POPs). Our previous studies demonstrated that populations from e-waste exposed region have a significantly higher level of chromosomal aberrancy and incidence of DNA damage. In this study, we further demonstrated that various POPs persisted at a significantly higher concentration in the exposed group than those in the unexposed group. The level of reactive oxygen species and micronucleus rate were also significantly elevated in the exposed group. RNA sequencing analysis revealed 31 genes in DNA damage responses and repair pathways that were differentially expressed between the two groups (Log 2 ratio >1 or <−1). Our data demonstrated that both females and males of the exposed group have activated a series of DNA damage response genes; however many important DNA repair pathways have been dysregulated. Expressions of NEIL1/3 and RPA3, which are critical in initiating base pair and nucleotide excision repairs respectively, have been downregulated in both females and males of the exposed group. In contrast, expression of RNF8, an E3 ligase involved in an error prone non-homologous end joining repair for DNA double strand break, was upregulated in both genders of the exposed group. The other genes appeared to be differentially expressed only when the males or females of the two groups were compared respectively. Importantly, the expression of cell cycle regulatory gene CDC25A that has been implicated in multiple kinds of malignant transformation was significantly upregulated among the exposed males while downregulated among the exposed females. In conclusion, our studies have demonstrated significant correlations between e-waste disposing and POPs accumulation, DNA lesions and dysregulation of multiple DNA damage repair mechanisms in the residents of the e-waste exposed region. - Highlights: 15. Developmental pathways from childhood aggression-disruptiveness, chronic peer rejection, and deviant friendships to early-adolescent rule breaking. Science.gov (United States) 2015-01-01 Childhood aggression-disruptiveness (AD), chronic peer rejection, and deviant friendships were examined as predictors of early-adolescent rule-breaking behaviors. Using a sample of 383 children (193 girls and 190 boys) who were followed from ages 6 to 14, peer rejection trajectories were identified and incorporated into a series of alternative models to assess how chronic peer rejection and deviant friendships mediate the association between stable childhood AD and early-adolescent rule breaking. There were multiple mediated pathways to rule breaking that included both behavioral and relational risk factors, and findings were consistent for boys and girls. Results have implications for better understanding the influence of multiple social processes in the continuity of antisocial behaviors from middle childhood to early adolescence. PMID:25403544 16. Impaired nucleotide excision repair pathway as a possible factor in pathogenesis of head and neck cancer Energy Technology Data Exchange (ETDEWEB) Sliwinski, T. [Department of Molecular Genetics, University of Lodz, Lodz (Poland); Markiewicz, L. [Department of Clinical Chemistry and Biochemistry, Medical University of Lodz, Lodz (Poland); Rusin, P. [Department of Molecular Genetics, University of Lodz, Lodz (Poland); Department of Clinical Chemistry and Biochemistry, Medical University of Lodz, Lodz (Poland); Kabzinski, J. [Department of Clinical Chemistry and Biochemistry, Medical University of Lodz, Lodz (Poland); Dziki, L. [Department of General and Colorectal Surgery, Medical University of Lodz, Lodz (Poland); Milonski, J.; Olszewski, J. [Department of Otolaryngology and Oncology, Medical University of Lodz, Lodz (Poland); Blaszczyk, J. [Department of Human Physiology, Medical University of Lodz, Lodz (Poland); Szemraj, J. [Department of Medical Biochemistry, Medical University of Lodz, Lodz (Poland); Majsterek, I., E-mail: [email protected] [Department of Clinical Chemistry and Biochemistry, Medical University of Lodz, Lodz (Poland) 2011-11-01 17. In Vitro Expansion of Bone Marrow Derived Mesenchymal Stem Cells Alters DNA Double Strand Break Repair of Etoposide Induced DNA Damage Directory of Open Access Journals (Sweden) Ian Hare 2016-01-01 Full Text Available Mesenchymal stem cells (MSCs are of interest for use in diverse cellular therapies. Ex vivo expansion of MSCs intended for transplantation must result in generation of cells that maintain fidelity of critical functions. Previous investigations have identified genetic and phenotypic alterations of MSCs with in vitro passage, but little is known regarding how culturing influences the ability of MSCs to repair double strand DNA breaks (DSBs, the most severe of DNA lesions. To investigate the response to DSB stress with passage in vitro, primary human MSCs were exposed to etoposide (VP16 at various passages with subsequent evaluation of cellular damage responses and DNA repair. Passage number did not affect susceptibility to VP16 or the incidence and repair kinetics of DSBs. Nonhomologous end joining (NHEJ transcripts showed little alteration with VP16 exposure or passage; however, homologous recombination (HR transcripts were reduced following VP16 exposure with this decrease amplified as MSCs were passaged in vitro. Functional evaluations of NHEJ and HR showed that MSCs were unable to activate NHEJ repair following VP16 stress in cells after successive passage. These results indicate that ex vivo expansion of MSCs alters their ability to perform DSB repair, a necessary function for cells intended for transplantation. 18. Initial steps of the base excision repair pathway within the nuclear architecture International Nuclear Information System (INIS) Oxidative stress induced lesions threaten aerobic organisms by representing a major cause of genomic instability. A common product of guanine oxidation, 8-oxo-guanine (8- oxoG) is particularly mutagenic by provoking G to T transversions. Removal of oxidised bases from DNA is initiated by the recognition and excision of the damaged base by a DNA glycosylase, initiating the base excision repair (BER) pathway. In mammals, 8-oxoG is processed by the 8-oxoG-DNA-glycosylase I (OGG1), which biochemical mechanisms has been well characterised in vitro. However how and where this enzyme finds the modified base within the complex chromatin architecture is not yet understood. We show that upon induction of 8-oxoG, OGG1, together with at least two other proteins involved in BER, is recruited from a soluble fraction to chromatin. Formation kinetics of this patches correlates with 8-oxoG excision, suggesting a direct link between presence of this chromatin-associated complexes and 8-oxoG repair. More precisely, these repair patches are specifically directed to euchromatin regions, and completely excluded from heterochromatin regions. Inducing of artificial chromatin compaction results in a complete inhibition of the in vivo repair of 8-oxoG, probably by impeding the access of OGG1 to the lesion. Using OGG1 mutants, we show that OGG1 direct recognition of 8-oxoG did not trigger its re-localisation to the chromatin. We conclude that in response to the induction of oxidative DNA damage, the DNA glycosylase is actively recruited to regions of open chromatin allowing the access of the BER machinery to the lesions. (author) 19. The Impact of Individual In Vivo Repair of DNA Double-Strand Breaks on Oral Mucositis in Adjuvant Radiotherapy of Head-and-Neck Cancer International Nuclear Information System (INIS) 20. Feasibility of measuring radiation-induced DNA double strand breaks and their repair by pulsed field gel electrophoresis in freshly isolated cells from the mouse RIF-1 tumor International Nuclear Information System (INIS) Purpose: To examine the technical feasibility of pulsed field gel electrophoresis (PFGE) as a predictive assay for the radio responsiveness of tumors. Induction and repair of DNA double strand breaks (DSBs) in a freshly prepared cell suspension from a RIF-1 tumor (irradiated ex vivo) was compared with DSB induction and repair in exponentially growing RIF-1 cells in culture (irradiated in vitro). Methods and Materials: A murine RIF-1 tumor grown in vivo was digested, and cells were exposed to x-rays (ex vivo) at doses of 1 to 75 Gy. DNA damage was measured using CHEF (clamped homogeneous electric fields) electrophoresis. Repair kinetics were studied at 37 deg. C for 4 h after irradiation. Radiosensitivity was determined by clonogenic assay, and cell cycle distributions by flow cytometry. For comparison, a trypsinized suspension of exponentially growing RIF-1 cells in vitro was run parallel with each ex vivo experiment. Results: Induction of DSBs, expressed as % DNA extracted from the plug, was similar in the in vitro and ex vivo irradiated cells. Compared to repair rates in in vitro cultured RIF-1 cells, repair kinetics in a freshly prepared cell suspension from the tumor were decreased, unrelated to differences in radiosensitivity. Differences in repair could not be explained by endogenous DNA degradation, nor by influences of enzymes used for digestion of the tumor. A lower plating efficiency and differences in ploidy (as revealed by flow cytometry) were the only reproducible differences between in vivo and in vitro grown cells that may explain the differences in repair kinetics. Conclusions: The current results do not support the idea that PFGE is a technique robust enough to be a predictive assay for the radiosensitivity of tumor cells 1. Single-stranded DNA oligomers stimulate error-prone alternative repair of DNA double-strand breaks through hijacking Ku protein. Science.gov (United States) Yuan, Ying; Britton, Sébastien; Delteil, Christine; Coates, Julia; Jackson, Stephen P; Barboule, Nadia; Frit, Philippe; Calsou, Patrick 2015-12-01 In humans, DNA double-strand breaks (DSBs) are repaired by two mutually-exclusive mechanisms, homologous recombination or end-joining. Among end-joining mechanisms, the main process is classical non-homologous end-joining (C-NHEJ) which relies on Ku binding to DNA ends and DNA Ligase IV (Lig4)-mediated ligation. Mostly under Ku- or Lig4-defective conditions, an alternative end-joining process (A-EJ) can operate and exhibits a trend toward microhomology usage at the break junction. Homologous recombination relies on an initial MRN-dependent nucleolytic degradation of one strand at DNA ends. This process, named DNA resection generates 3' single-stranded tails necessary for homologous pairing with the sister chromatid. While it is believed from the current literature that the balance between joining and recombination processes at DSBs ends is mainly dependent on the initiation of resection, it has also been shown that MRN activity can generate short single-stranded DNA oligonucleotides (ssO) that may also be implicated in repair regulation. Here, we evaluate the effect of ssO on end-joining at DSB sites both in vitro and in cells. We report that under both conditions, ssO inhibit C-NHEJ through binding to Ku and favor repair by the Lig4-independent microhomology-mediated A-EJ process. PMID:26350212 2. RAD24 (=R1/sup S/) gene product of Saccharomyces cerevisiae participates in two different pathways of DNA repair International Nuclear Information System (INIS) The moderately UV- and X-ray-sensitive mutant of Saccharomyces cerevisiae originally designated r1/sup s/ complements all rad and mms mutants available. Therefore, the new nomination rad24-1 according to the RAD nomenclature is suggested. RAD24 maps on chromosome V, close to RAD3 (1.3 cM). In order to associate the RAD24 gene with one of the three repair pathways, double mutants of rad24 and various representative genes of each pathway were constructed. The UV and X-ray sensitivities of the double mutants compared to the single mutants indicate that RAD24 is involved in excision repair of UV damage (RAD3 epistasis group), as well as in recombination repair of UV and X-ray damage (RAD52 epistasis group). Properties of the mutant are discussed which hint at the control of late steps in the pathways 3. The Fanconi anemia pathway: Repairing the link between DNA damage and squamous cell carcinoma Energy Technology Data Exchange (ETDEWEB) Romick-Rosendale, Lindsey E. [Division of Oncology, Cancer and Blood Diseases Institute, Cincinnati Children' s Hospital Medical Center, Department of Pediatrics, University of Cincinnati College of Medicine, Cincinnati, OH 45229 (United States); Lui, Vivian W.Y.; Grandis, Jennifer R. [Department of Otolaryngology, University of Pittsburgh School of Medicine, University of Pittsburgh, Pittsburgh, PA 15213 (United States); Wells, Susanne I., E-mail: [email protected] [Division of Oncology, Cancer and Blood Diseases Institute, Cincinnati Children' s Hospital Medical Center, Department of Pediatrics, University of Cincinnati College of Medicine, Cincinnati, OH 45229 (United States) 2013-03-15 Fanconi anemia (FA) is a rare inherited recessive disease caused by mutations in one of fifteen genes known to encode FA pathway components. In response to DNA damage, nuclear FA proteins associate into high molecular weight complexes through a cascade of post-translational modifications and physical interactions, followed by the repair of damaged DNA. Hematopoietic cells are particularly sensitive to the loss of these interactions, and bone marrow failure occurs almost universally in FA patients. FA as a disease is further characterized by cancer susceptibility, which highlights the importance of the FA pathway in tumor suppression, and will be the focus of this review. Acute myeloid leukemia is the most common cancer type, often subsequent to bone marrow failure. However, FA patients are also at an extreme risk of squamous cell carcinoma (SCC) of the head and neck and gynecological tract, with an even greater incidence in those individuals who have received a bone marrow transplant and recovered from hematopoietic disease. FA tumor suppression in hematopoietic versus epithelial compartments could be mechanistically similar or distinct. Definition of compartment specific FA activities is now critical to assess the effects of today's bone marrow failure treatments on tomorrow's solid tumor development. It is our hope that current therapies can then be optimized to decrease the risk of malignant transformation in both hematopoietic and epithelial cells. Here we review our current understanding of the mechanisms of action of the Fanconi anemia pathway as it contributes to stress responses, DNA repair and squamous cell carcinoma susceptibility. 4. Inter-individual variation in DNA double-strand break repair in human fibroblasts before and after exposure to low doses of ionizing radiation International Nuclear Information System (INIS) DNA double-strand breaks (DSB) are generally considered the most critical lesion induced by ionizing radiation (IR) and may initiate carcinogenesis and other disease. Using an immunofluorescence assay to simultaneously detect nuclear foci of the phosphorylated forms of histone H2AX and ATM kinase at sites of DSBs, we examined the response of 25 apparently normal and 10 DNA repair-deficient (ATM, ATR, NBN, LIG1, LIG4, and FANCG) primary fibroblast strains irradiated with low doses of 137Cs γ-rays. Quiescent G0/G1-phase cultures were exposed to 5, 10, and 25 cGy and allowed to repair for 24 h. The maximum level of IR-induced foci (0.15 foci per cGy, at 10 or 30 min) in the normal strains showed much less inter-individual variation (CV ∼ 0.2) than the level of spontaneous foci, which ranged from 0.2-2.6 foci/cell (CV ∼ 0.6; mean ± SD of 1.00 ± 0.57). Significantly slower focus formation post-irradiation was observed in seven normal strains, similar to most mutant strains examined. There was variation in repair efficiency measured by the fraction of IR-induced foci remaining 24 h post-irradiation, curiously with the strains having slower focus formation showing more efficient repair after 25 cGy. Interestingly, the ranges of spontaneous and residual induced foci levels at 24 h in the normal strains were as least as large as those observed for the repair-defective mutant strains. The inter-individual variation in DSB foci parameters observed in cells exposed to low doses of ionizing radiation in this small survey of apparently normal people suggests that hypomorphic genetic variants in genomic maintenance and/or DNA damage signaling and repair genes may contribute to differential susceptibility to cancer induced by environmental mutagens. 5. Studies on the repair of double strand break of DNA and cellular carcinogenesis, and consideration on the concept of extinction of nuclear power International Nuclear Information System (INIS) This paper describes the relationship between the repair of double strand break (DSB) of DNA and cellular carcinogenesis mainly on author's investigations, and his recent thought aiming at the extinction of nuclear power. The molecular repairing system is explained about DNA DSB induced by radiation and chemicals. When DSB occurs, nucleosome consisting from 4 core-histones participates to link the broken ends and then repair mechanisms of homologous recombination (HRR) and non-homologous end joining (NHEJ) begin to work. The latter is dominant in mammalians. Thus the genetic defect in these systems of DSB response and repair is a course of disorders such as ataxia telangiectasia (AT) (DSB sensor defect), genetic breast cancer (HRR defect), and radiosensitive-severe combined immunodeficiency (RS-SCID) (NHEJ defect), all of which result in cancer formation. NHEJ repair is known to be error-prone. Against multi-step carcinogenesis where accumulated gene mutations lead to the cancer formation, the author thinks chromosomal instability is one of important carcinogenic causes: the instability can be a trigger of producing cancer stem cells because the cells can be yielded from mouse embryonic stem cells where DSB is shown to participate in the process. Low dose radiation produces a small amount of DSB, to which the repair response is less sensitive at G2/M checkpoint, ultimately leading to genomic instability. Considering effects of the low dose radiation exposure above, and of the internal exposure to 3H-thymidine beta ray in cells, of indoor Rn participating 16% of lung cancer incidence (Canadian epidemiological data) and so on, together with moral and social responsibility of scientist and technologist, the author says to have attained to the concept of the ''Extinction of Nuclear Power''. (T.T) 6. Reduced DNA double-strand break repair capacity and risk of squamous cell carcinoma of the head and neck-A case-control study. Science.gov (United States) Liu, Zhensheng; Liu, Hongliang; Gao, Fengqin; Dahlstrom, Kristina R; Sturgis, Erich M; Wei, Qingyi 2016-04-01 Tobacco smoke and alcohol use play important roles in the etiology of squamous cell carcinoma of the head and neck (SCCHN). Smoking causes DNA damage, including double-strand DNA breaks (DSBs), that leads to carcinogenesis. To test the hypothesis that suboptimal DSB repair capacity is associated with risk of SCCHN, we applied a flow cytometry-based method to detect the DSB repair phenotype first in four EBV-immortalized human lymphoblastoid cell lines and then in human peripheral blood T-lymphocytes (PBTLs). With this blood-based laboratory assay, we conducted a pilot case-control study of 100 patients with newly diagnosed, previously untreated SCCHN and 124 cancer-free controls of non-Hispanic whites. We found that the mean DSB repair capacity level was significantly lower in cases (42.1%) than that in controls (54.4%) (P<0.001). When we used the median DSB repair capacity level in the controls as the cutoff value for calculating the odds ratios (ORs) with adjustment for age, sex, smoking and drinking status, the cases were more likely than the controls to have a reduced DSB repair capacity (adjusted OR=1.93; 95% confidence interval, CI=1.04-3.56, P=0.037), especially for those subjects who were ever drinkers (adjusted OR=2.73; 95% CI=1.17-6.35, P=0.020) and had oropharyngeal tumors (adjusted OR=2.17; 95% CI=1.06-4.45, P=0.035). In conclusion, these findings suggest that individuals with a reduced DSB repair capacity may be at an increased risk of developing SCCHN. Larger studies are warranted to confirm these preliminary findings. PMID:26963119 7. DNA breaks caused by monochromatic 365 nm ultraviolet-A radiation or hydrogen peroxide and their repair in human epithelioid and xeroderma pigmentosum cells International Nuclear Information System (INIS) The induction and repair of DNA single-strand breaks (SSB) assayed by alkaline filter elution was compared in human epithelioid P3 and xeroderma pigmentosum (XP) cells exposed to monochromatic 365-nm UV-A radiation and H2O2. Initial yields of SSB were measured with the cells held at 0.5oC during exposure. The yield from exposure to 365-nm radiation was slightly greater in XP than in P3 cells, whereas H2O2 produced more than three times as many SSB in P3 compared with XP cells. o-Phenanthroline (50 mM) markedly inhibited the yields of SSB induced in XP cells by H2O2, but had no effect on those produced by 365-nm UV-A. These results are consistent with the fact that P3 cells, unlike XP cells, have undetectable levels of catalase. The measured production of trace amounts of H2O2 by the actual 365-nm UV0A exposures was not sufficient to account for the numbers of breaks that were observed. Single-strand breaks produced by both agents were completely repaired after 50 min in P3 cells, as were H2O2-induced SSB in XP cells. However, 25% of the 365-nm UV-A-induced SSB in XP cells remained refractory to repair after 60 min. The results show that SSB produced by these two agents are different and that 365 nm radiation produces most SSB in cells by mechanisms other than by production of H2O2. (author) 8. DNA breaks caused by monochromatic 365 nm ultraviolet-A radiation or hydrogen peroxide and their repair in human epithelioid and xeroderma pigmentosum cells. Science.gov (United States) Peak, J G; Pilas, B; Dudek, E J; Peak, M J 1991-08-01 The induction and repair of DNA single-strand breaks (SSB) assayed by alkaline filter elution was compared in human epithelioid P3 and xeroderma pigmentosum (XP) cells exposed to monochromatic 365-nm UV-A radiation and H2O2. Initial yields of SSB were measured with the cells held at 0.5 degrees C during exposure. The yield from exposure to 365-nm radiation was slightly greater in XP than in P3 cells, whereas H2O2 produced more than three times as many SSB in P3 compared with XP cells. o-Phenanthroline (50 mM) markedly inhibited the yields of SSB induced in XP cells by H2O2, but had no effect on those produced by 365-nm UV-A. These results are consistent with the fact that P3 cells, unlike XP cells, have undetectable levels of catalase. The measured production of trace amounts of H2O2 by the actual 365-nm UV-A exposures was not sufficient to account for the numbers of breaks that were observed. Single-strand breaks produced by both agents were completely repaired after 50 min in P3 cells, as were H2O2-induced SSB in XP cells. However, 25% of the 365-nm UV-A-induced SSB in XP cells remained refractory to repair after 60 min. The results show that SSB produced by these two agents are different and that 365 nm radiation produces most SSB in cells by mechanisms other than by production of H2O2. PMID:1780357 9. The role of the Mre11-Rad50-Nbs1 complex in double-strand break repair-facts and myths. Science.gov (United States) Takeda, Shunichi; Hoa, Nguyen Ngoc; Sasanuma, Hiroyuki 2016-08-01 Homologous recombination (HR) initiates double-strand break (DSB) repair by digesting 5'-termini at DSBs, the biochemical reaction called DSB resection, during which DSBs are processed by nucleases to generate 3' single-strand DNA. Rad51 recombinase polymerizes along resected DNA, and the resulting Rad51-DNA complex undergoes homology search. Although DSB resection by the Mre11 nuclease plays a critical role in HR in Saccharomyces cerevisiae, it remains elusive whether DSB resection by Mre11 significantly contributes to HR-dependent DSB repair in mammalian cells. Depletion of Mre11 decreases the efficiency of DSB resection only by 2- to 3-fold in mammalian cells. We show that although Mre11 is required for efficient HR-dependent repair of ionizing-radiation-induced DSBs, Mre11 is largely dispensable for DSB resection in both chicken DT40 and human TK6 B cell lines. Moreover, a 2- to 3-fold decrease in DSB resection has virtually no impact on the efficiency of HR. Thus, although a large number of researchers have reported the vital role of Mre11-mediated DSB resection in HR, the role may not explain the very severe defect in HR in Mre11-deficient cells, including their lethality. We here show experimental evidence for the additional roles of Mre11 in (i) elimination of chemical adducts from DSB ends for subsequent DSB repair, and (ii) maintaining HR intermediates for their proper resolution. 10. Ghrelin Prevents Cisplatin-Induced Testicular Damage by Facilitating Repair of DNA Double Strand Breaks Through Activation of p53 in Mice. Science.gov (United States) Garcia, Jose M; Chen, Ji-an; Guillory, Bobby; Donehower, Lawrence A; Smith, Roy G; Lamb, Dolores J 2015-07-01 Cisplatin administration induces DNA damage resulting in germ cell apoptosis and subsequent testicular atrophy. Although 50 percent of male cancer patients receiving cisplatin-based chemotherapy develop long-term secondary infertility, medical treatment to prevent spermatogenic failure after chemotherapy is not available. Under normal conditions, testicular p53 promotes cell cycle arrest, which allows time for DNA repair and reshuffling during meiosis. However, its role in the setting of cisplatin-induced infertility has not been studied. Ghrelin administration ameliorates the spermatogenic failure that follows cisplatin administration in mice, but the mechanisms mediating these effects have not been well established. The aim of the current study was to characterize the mechanisms of ghrelin and p53 action in the testis after cisplatin-induced testicular damage. Here we show that cisplatin induces germ cell damage through inhibition of p53-dependent DNA repair mechanisms involving gamma-H2AX and ataxia telangiectasia mutated protein kinase. As a result, testicular weight and sperm count and motility were decreased with an associated increase in sperm DNA damage. Ghrelin administration prevented these sequelae by restoring the normal expression of gamma-H2AX, ataxia telangiectasia mutated, and p53, which in turn allows repair of DNA double stranded breaks. In conclusion, these findings indicate that ghrelin has the potential to prevent or diminish infertility caused by cisplatin and other chemotherapeutic agents by restoring p53-dependent DNA repair mechanisms. PMID:26019260 11. The role of the Mre11-Rad50-Nbs1 complex in double-strand break repair-facts and myths. Science.gov (United States) Takeda, Shunichi; Hoa, Nguyen Ngoc; Sasanuma, Hiroyuki 2016-08-01 Homologous recombination (HR) initiates double-strand break (DSB) repair by digesting 5'-termini at DSBs, the biochemical reaction called DSB resection, during which DSBs are processed by nucleases to generate 3' single-strand DNA. Rad51 recombinase polymerizes along resected DNA, and the resulting Rad51-DNA complex undergoes homology search. Although DSB resection by the Mre11 nuclease plays a critical role in HR in Saccharomyces cerevisiae, it remains elusive whether DSB resection by Mre11 significantly contributes to HR-dependent DSB repair in mammalian cells. Depletion of Mre11 decreases the efficiency of DSB resection only by 2- to 3-fold in mammalian cells. We show that although Mre11 is required for efficient HR-dependent repair of ionizing-radiation-induced DSBs, Mre11 is largely dispensable for DSB resection in both chicken DT40 and human TK6 B cell lines. Moreover, a 2- to 3-fold decrease in DSB resection has virtually no impact on the efficiency of HR. Thus, although a large number of researchers have reported the vital role of Mre11-mediated DSB resection in HR, the role may not explain the very severe defect in HR in Mre11-deficient cells, including their lethality. We here show experimental evidence for the additional roles of Mre11 in (i) elimination of chemical adducts from DSB ends for subsequent DSB repair, and (ii) maintaining HR intermediates for their proper resolution. PMID:27311583 12. G9a inhibition potentiates the anti-tumour activity of DNA double-strand break inducing agents by impairing DNA repair independent of p53 status. Science.gov (United States) Agarwal, Pallavi; Jackson, Stephen P 2016-10-01 Cancer cells often exhibit altered epigenetic signatures that can misregulate genes involved in processes such as transcription, proliferation, apoptosis and DNA repair. As regulation of chromatin structure is crucial for DNA repair processes, and both DNA repair and epigenetic controls are deregulated in many cancers, we speculated that simultaneously targeting both might provide new opportunities for cancer therapy. Here, we describe a focused screen that profiled small-molecule inhibitors targeting epigenetic regulators in combination with DNA double-strand break (DSB) inducing agents. We identify UNC0638, a catalytic inhibitor of histone lysine N-methyl-transferase G9a, as hypersensitising tumour cells to low doses of DSB-inducing agents without affecting the growth of the non-tumorigenic cells tested. Similar effects are also observed with another, structurally distinct, G9a inhibitor A-366. We also show that small-molecule inhibition of G9a or siRNA-mediated G9a depletion induces tumour cell death under low DNA damage conditions by impairing DSB repair in a p53 independent manner. Furthermore, we establish that G9a promotes DNA non-homologous end-joining in response to DSB-inducing genotoxic stress. This study thus highlights the potential for using G9a inhibitors as anti-cancer therapeutic agents in combination with DSB-inducing chemotherapeutic drugs such as etoposide. PMID:27431310 OpenAIRE Hays, S L; Firmenich, A A; Berg, P 1995-01-01 The repair of DNA double-strand breaks in Saccharomyces cerevisiae requires genes of the RAD52 epistasis group, of which RAD55 and RAD57 are members. Here, we show that the x-ray sensitivity of rad55 and rad57 mutant strains is suppressible by overexpression of RAD51 or RAD52. Virtually complete suppression is provided by the simultaneous overexpression of RAD51 and RAD52. This suppression occurs at 23 degrees C, where these mutants are more sensitive to x-rays, as well as at 30 degrees C and... 14. Structure of the FANCI-FANCD2 Complex: Insights into the Fanconi Anemia DNA Repair Pathway Energy Technology Data Exchange (ETDEWEB) Joo, Woo; Xu, Guozhou; Persky, Nicole S.; Smogorzewska, Agata; Rudge, Derek G.; Buzovetsky, Olga; Elledge, Stephen J.; Pavletich, Nikola P. (Harvard-Med); (Cornell); (MSKCC) 2011-08-29 Fanconi anemia is a cancer predisposition syndrome caused by defects in the repair of DNA interstrand cross-links (ICLs). Central to this pathway is the Fanconi anemia I-Fanconi anemia D2 (FANCI-FANCD2) (ID) complex, which is activated by DNA damage-induced phosphorylation and monoubiquitination. The 3.4 angstrom crystal structure of the {approx}300 kilodalton ID complex reveals that monoubiquitination and regulatory phosphorylation sites map to the I-D interface, suggesting that they occur on monomeric proteins or an opened-up complex and that they may serve to stabilize I-D heterodimerization. The 7.8 angstrom electron-density map of FANCI-DNA crystals and in vitro data show that each protein has binding sites for both single- and double-stranded DNA, suggesting that the ID complex recognizes DNA structures that result from the encounter of replication forks with an ICL. 15. Structure of the FANCI-FANCD2 Complex: Insights into the Fanconi Anemia DNA Repair Pathway Energy Technology Data Exchange (ETDEWEB) W Joo; G Xu; n Persky; A Smogorzewska; D Rudge; O Buzovetsky; S Elledge; N Pavletich 2011-12-31 Fanconi anemia is a cancer predisposition syndrome caused by defects in the repair of DNA interstrand cross-links (ICLs). Central to this pathway is the Fanconi anemia I-Fanconi anemia D2 (FANCI-FANCD2) (ID) complex, which is activated by DNA damage-induced phosphorylation and monoubiquitination. The 3.4 angstrom crystal structure of the {approx}300 kilodalton ID complex reveals that monoubiquitination and regulatory phosphorylation sites map to the I-D interface, suggesting that they occur on monomeric proteins or an opened-up complex and that they may serve to stabilize I-D heterodimerization. The 7.8 angstrom electron-density map of FANCI-DNA crystals and in vitro data show that each protein has binding sites for both single- and double-stranded DNA, suggesting that the ID complex recognizes DNA structures that result from the encounter of replication forks with an ICL. 16. DNA Strand Breaks, Photoproducts, and Repair in Analog Space and Mars Environments: Implications for Microbial Interplanetary Transfer Science.gov (United States) Nicholson, W. L.; Möller, R.; Douki, T.; Robles, J.; Bruno, G.; Fajardo-Cavazos, P.; Schuerger, A. C. 2008-03-01 Bacterial spores are considered good candidates for interplanetary transport by natural impacts or human spaceflight. In this work we consider the mechanisms of DNA damage and repair in spores subjected to a hypothetical Earth-to-Mars transfer. 17. Conservation of the nucleotide excision repair pathway: characterization of hydra Xeroderma Pigmentosum group F homolog. Directory of Open Access Journals (Sweden) Apurva Barve Full Text Available Hydra, one of the earliest metazoans with tissue grade organization and nervous system, is an animal with a remarkable regeneration capacity and shows no signs of organismal aging. We have for the first time identified genes of the nucleotide excision repair (NER pathway from hydra. Here we report cloning and characterization of hydra homolog of xeroderma pigmentosum group F (XPF gene that encodes a structure-specific 5' endonuclease which is a crucial component of NER. In silico analysis shows that hydra XPF amino acid sequence is very similar to its counterparts from other animals, especially vertebrates, and shows all features essential for its function. By in situ hybridization, we show that hydra XPF is expressed prominently in the multipotent stem cell niche in the central region of the body column. Ectoderm of the diploblastic hydra was shown to express higher levels of XPF as compared to the endoderm by semi-quantitative RT-PCR. Semi-quantitative RT-PCR analysis also demonstrated that interstitial cells, a multipotent and rapidly cycling stem cell lineage of hydra, express higher levels of XPF mRNA than other cell types. Our data show that XPF and by extension, the NER pathway is highly conserved during evolution. The prominent expression of an NER gene in interstitial cells may have implications for the lack of senescence in hydra. 18. Non-repair pathways for minimizing protein isoaspartyl damage in the yeast Saccharomyces cerevisiae. Science.gov (United States) Patananan, Alexander N; Capri, Joseph; Whitelegge, Julian P; Clarke, Steven G 2014-06-13 The spontaneous degradation of asparaginyl and aspartyl residues to isoaspartyl residues is a common type of protein damage in aging organisms. Although the protein-l-isoaspartyl (d-aspartyl) O-methyltransferase (EC 2.1.1.77) can initiate the repair of l-isoaspartyl residues to l-aspartyl residues in most organisms, no gene homolog or enzymatic activity is present in the budding yeast Saccharomyces cerevisiae. Therefore, we used biochemical approaches to elucidate how proteins containing isoaspartyl residues are metabolized in this organism. Surprisingly, the level of isoaspartyl residues in yeast proteins (50-300 pmol of isoaspartyl residues/mg of protein extract) is comparable with organisms with protein-l-isoaspartyl (d-aspartyl) O-methyltransferase, suggesting a novel regulatory pathway. Interfering with common protein quality control mechanisms by mutating and inhibiting the proteasomal and autophagic pathways in vivo did not increase isoaspartyl residue levels compared with wild type or uninhibited cells. However, the inhibition of metalloproteases in in vitro aging experiments by EDTA resulted in an ∼3-fold increase in the level of isoaspartyl-containing peptides. Characterization by mass spectrometry of these peptides identified several proteins involved in metabolism as targets of isoaspartyl damage. Further analysis of these peptides revealed that many have an N-terminal isoaspartyl site and originate from proteins with short half-lives. These results suggest that one or more metalloproteases participate in limiting isoaspartyl formation by robust proteolysis. 19. Nucleotide excision repair pathway assessment in DNA exposed to low-intensity red and infrared lasers Energy Technology Data Exchange (ETDEWEB) Fonseca, A.S.; Campos, V.M.A.; Magalhaes, L.A.G., E-mail: [email protected] [Instituto de Biologia Roberto Alcantara Gomes, Rio de Janeiro, RJ (Brazil). Departamento de Biofisica e Biometria. Lab. de Ciencias Radiologicas; Paoli, F. [Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, MG (Brazil). Instituto de Ciencias Biologicas. Departamento de Morfologia 2015-10-15 Low-intensity lasers are used for prevention and management of oral mucositis induced by anticancer therapy, but the effectiveness of treatment depends on the genetic characteristics of affected cells. This study evaluated the survival and induction of filamentation of Escherichia coli cells deficient in the nucleotide excision repair pathway, and the action of T{sub 4} endonuclease V on plasmid DNA exposed to low-intensity red and near-infrared laser light. Cultures of wild-type (strain AB1157) E. coli and strain AB1886 (deficient in uvrA protein) were exposed to red (660 nm) and infrared (808 nm) lasers at various fluences, powers and emission modes to study bacterial survival and filamentation. Also, plasmid DNA was exposed to laser light to study DNA lesions produced in vitro by T{sub 4} endonuclease V. Low-intensity lasers: i) had no effect on survival of wild-type E. coli but decreased the survival of uvrA protein-deficient cells, ii) induced bacterial filamentation, iii) did not alter the electrophoretic profile of plasmids in agarose gels, and iv) did not alter the electrophoretic profile of plasmids incubated with T{sub 4} endonuclease V. These results increase our understanding of the effects of laser light on cells with various genetic characteristics, such as xeroderma pigmentosum cells deficient in nucleotide excision pathway activity in patients with mucositis treated by low-intensity lasers. (author) 20. Nucleotide excision repair pathway assessment in DNA exposed to low-intensity red and infrared lasers Directory of Open Access Journals (Sweden) A.S. Fonseca 2015-01-01 Full Text Available Low-intensity lasers are used for prevention and management of oral mucositis induced by anticancer therapy, but the effectiveness of treatment depends on the genetic characteristics of affected cells. This study evaluated the survival and induction of filamentation of Escherichia coli cells deficient in the nucleotide excision repair pathway, and the action of T4 endonuclease V on plasmid DNA exposed to low-intensity red and near-infrared laser light. Cultures of wild-type (strain AB1157 E. coli and strain AB1886 (deficient in uvrA protein were exposed to red (660 nm and infrared (808 nm lasers at various fluences, powers and emission modes to study bacterial survival and filamentation. Also, plasmid DNA was exposed to laser light to study DNA lesions produced in vitro by T4 endonuclease V. Low-intensity lasers: i had no effect on survival of wild-type E. coli but decreased the survival of uvrA protein-deficient cells, ii induced bacterial filamentation, iii did not alter the electrophoretic profile of plasmids in agarose gels, and iv did not alter the electrophoretic profile of plasmids incubated with T4 endonuclease V. These results increase our understanding of the effects of laser light on cells with various genetic characteristics, such as xeroderma pigmentosum cells deficient in nucleotide excision pathway activity in patients with mucositis treated by low-intensity lasers. 1. DSB修复过程中的组蛋白修饰作用%Histone Modifications in DNA Double-Strand Breaks Damage Repair Institute of Scientific and Technical Information of China (English) 贾兆君; 伍会健 2013-01-01 DNA doubled-strand breaks (DSBs) which is the most serious species in DNA damage can lead to the loss of genetic message or even cell death.To resist DSB damage,the organism has developed a DNA-damage response (DDR) mechanism for DNA damage repair to avoid the transfer of inaccurate genetic message.In this process,histone which is the main structural protein of chromatin is regulated by multi-modifications,such as phosphorylation,methylation,acetylation,ubiquitination and so on.These modifications of histones promote the recruitment of DDR-related protein to the site of DNA damage in the process of DNA damage repair,and change chromatin structure to facilitate repair progress in DDR.%DNA双键断裂(DNA doubled-strand breaks,DSBs)是目前已知DNA损伤中最为严重的一种,会造成遗传信息丢失,甚至细胞死亡.为了应对DSB损伤,生命体进化出DNA损伤应答(DNA-damage response,DDR)机制,进行损伤修复以防止错误遗传信息的传递.在这一过程中,作为染色质主要结构蛋白的组蛋白发生多种修饰,包括磷酸化、甲基化、乙酰化、泛素化等.这些组蛋白修饰促进DDR相关蛋白在DNA损伤处的招募,并改变染色质结构,以促进修复过程顺利进行. 2. Coordination and processing of DNA ends during double-strand break repair: the role of the bacteriophage T4 Mre11/Rad50 (MR) complex. Science.gov (United States) Almond, Joshua R; Stohr, Bradley A; Panigrahi, Anil K; Albrecht, Dustin W; Nelson, Scott W; Kreuzer, Kenneth N 2013-11-01 The in vivo functions of the bacteriophage T4 Mre11/Rad50 (MR) complex (gp46/47) in double-strand-end processing, double-strand break repair, and recombination-dependent replication were investigated. The complex is essential for T4 growth, but we wanted to investigate the in vivo function during productive infections. We therefore generated a suppressed triple amber mutant in the Rad50 subunit to substantially reduce the level of complex and thereby reduce phage growth. Growth-limiting amounts of the complex caused a concordant decrease in phage genomic recombination-dependent replication. However, the efficiencies of double-strand break repair and of plasmid-based recombination-dependent replication remained relatively normal. Genetic analyses of linked markers indicated that double-strand ends were less protected from nuclease erosion in the depleted infection and also that end coordination during repair was compromised. We discuss models for why phage genomic recombination-dependent replication is more dependent on Mre11/Rad50 levels when compared to plasmid recombination-dependent replication. We also tested the importance of the conserved histidine residue in nuclease motif I of the T4 Mre11 protein. Substitution with multiple different amino acids (including serine) failed to support phage growth, completely blocked plasmid recombination-dependent replication, and led to the stabilization of double-strand ends. We also constructed and expressed an Mre11 mutant protein with the conserved histidine changed to serine. The mutant protein was found to be completely defective for nuclease activities, but retained the ability to bind the Rad50 subunit and double-stranded DNA. These results indicate that the nuclease activity of Mre11 is critical for phage growth and recombination-dependent replication during T4 infections. 3. β-HPV 5 and 8 E6 disrupt homology dependent double strand break repair by attenuating BRCA1 and BRCA2 expression and foci formation. Directory of Open Access Journals (Sweden) Nicholas A Wallace 2015-03-01 Full Text Available Recent work has explored a putative role for the E6 protein from some β-human papillomavirus genus (β-HPVs in the development of non-melanoma skin cancers, specifically β-HPV 5 and 8 E6. Because these viruses are not required for tumor maintenance, they are hypothesized to act as co-factors that enhance the mutagenic capacity of UV-exposure by disrupting the repair of the resulting DNA damage. Supporting this proposal, we have previously demonstrated that UV damage signaling is hindered by β-HPV 5 and 8 E6 resulting in an increase in both thymine dimers and UV-induced double strand breaks (DSBs. Here we show that β-HPV 5 and 8 E6 further disrupt the repair of these DSBs and provide a mechanism for this attenuation. By binding and destabilizing a histone acetyltransferase, p300, β-HPV 5 and 8 E6 reduce the enrichment of the transcription factor at the promoter of two genes critical to the homology dependent repair of DSBs (BRCA1 and BRCA2. The resulting diminished BRCA1/2 transcription not only leads to lower protein levels but also curtails the ability of these proteins to form repair foci at DSBs. Using a GFP-based reporter, we confirm that this reduced foci formation leads to significantly diminished homology dependent repair of DSBs. By deleting the p300 binding domain of β-HPV 8 E6, we demonstrate that the loss of robust repair is dependent on viral-mediated degradation of p300 and confirm this observation using a combination of p300 mutants that are β-HPV 8 E6 destabilization resistant and p300 knock-out cells. In conclusion, this work establishes an expanded ability of β-HPV 5 and 8 E6 to attenuate UV damage repair, thus adding further support to the hypothesis that β-HPV infections play a role in skin cancer development by increasing the oncogenic potential of UV exposure. 4. H. pylori-Induced DNA Strand Breaks Are Introduced by Nucleotide Excision Repair Endonucleases and Promote NF-κB Target Gene Expression Directory of Open Access Journals (Sweden) Mara L. Hartung 2015-10-01 Full Text Available The human bacterial pathogen Helicobacter pylori exhibits genotoxic properties that promote gastric carcinogenesis. H. pylori introduces DNA double strand breaks (DSBs in epithelial cells that trigger host cell DNA repair efforts. Here, we show that H. pylori-induced DSBs are repaired via error-prone, potentially mutagenic non-homologous end-joining. A genome-wide screen for factors contributing to DSB induction revealed a critical role for the H. pylori type IV secretion system (T4SS. Inhibition of transcription, as well as NF-κB/RelA-specific RNAi, abrogates DSB formation. DSB induction further requires β1-integrin signaling. DSBs are introduced by the nucleotide excision repair endonucleases XPF and XPG, which, together with RelA, are recruited to chromatin in a highly coordinated, T4SS-dependent manner. Interestingly, XPF/XPG-mediated DNA DSBs promote NF-κB target gene transactivation and host cell survival. In summary, H. pylori induces XPF/XPG-mediated DNA damage through activation of the T4SS/β1-integrin signaling axis, which promotes NF-κB target gene expression and host cell survival. 5. Androgen receptor in Sertoli cells regulates DNA double-strand break repair and chromosomal synapsis of spermatocytes partially through intercellular EGF-EGFR signaling. Science.gov (United States) Chen, Su-Ren; Hao, Xiao-Xia; Zhang, Yan; Deng, Shou-Long; Wang, Zhi-Peng; Wang, Yu-Qian; Wang, Xiu-Xia; Liu, Yi-Xun 2016-04-01 Spermatogenesis does not progress beyond the pachytene stages of meiosis in Sertoli cell-specific AR knockout (SCARKO) mice. However, further evidence of meiotic arrest and underlying paracrine signals in SCARKO testes is still lacking. We utilized co-immunostaining of meiotic surface spreads to examine the key events during meiotic prophase I. SCARKO spermatocytes exhibited a failure in chromosomal synapsis observed by SCP1/SCP3 double-staining and CREST foci quantification. In addition, DNA double-strand breaks (DSBs) were formed but were not repaired in the mutant spermatocytes, as revealed by γ-H2AX staining and DNA-dependent protein kinase (DNA-PK) activity examination. The later stages of DSB repair, such as the accumulation of the RAD51 strand exchange protein and the localization of mismatch repair protein MLH1, were correspondingly altered in SCARKO spermatocytes. Notably, the expression of factors that guide RAD51 loading onto sites of DSBs, including TEX15, BRCA1/2 and PALB2, was severely impaired when either AR was down-regulated or EGF was up-regulated. We observed that some ligands in the epidermal growth factor (EGF) family were over-expressed in SCARKO Sertoli cells and that some receptors in the EGF receptor (EGFR) family were ectopically activated in the mutant spermatocytes. When EGF-EGFR signaling was repressed to approximately normal by the specific inhibitor AG1478 in the cultured SCARKO testis tissues, the arrested meiosis was partially rescued, and functional haploid cells were generated. Based on these data, we propose that AR in Sertoli cells regulates DSB repair and chromosomal synapsis of spermatocytes partially through proper intercellular EGF-EGFR signaling. 6. Molecular basis for DNA strand displacement by NHEJ repair polymerases OpenAIRE Bartlett, Edward J.; Brissett, Nigel C.; Plocinski, Przemyslaw; Carlberg, Tom; Doherty, Aidan J. 2015-01-01 The non-homologous end-joining (NHEJ) pathway repairs DNA double-strand breaks (DSBs) in all domains of life. Archaea and bacteria utilize a conserved set of multifunctional proteins in a pathway termed Archaeo-Prokaryotic (AP) NHEJ that facilitates DSB repair. Archaeal NHEJ polymerases (Pol) are capable of strand displacement synthesis, whilst filling DNA gaps or partially annealed DNA ends, which can give rise to unligatable intermediates. However, an associated NHEJ phosphoesterase (PE) re... 7. Modulation of DNA Damage and Repair Pathways by Human Tumour Viruses Directory of Open Access Journals (Sweden) Robert Hollingworth 2015-05-01 Full Text Available With between 10% and 15% of human cancers attributable to viral infection, there is great interest, from both a scientific and clinical viewpoint, as to how these pathogens modulate host cell functions. Seven human tumour viruses have been identified as being involved in the development of specific malignancies. It has long been known that the introduction of chromosomal aberrations is a common feature of viral infections. Intensive research over the past two decades has subsequently revealed that viruses specifically interact with cellular mechanisms responsible for the recognition and repair of DNA lesions, collectively known as the DNA damage response (DDR. These interactions can involve activation and deactivation of individual DDR pathways as well as the recruitment of specific proteins to sites of viral replication. Since the DDR has evolved to protect the genome from the accumulation of deleterious mutations, deregulation is inevitably associated with an increased risk of tumour formation. This review summarises the current literature regarding the complex relationship between known human tumour viruses and the DDR and aims to shed light on how these interactions can contribute to genomic instability and ultimately the development of human cancers. 8. Post-irradiation chemical processing of DNA damage generates double-strand breaks in cells already engaged in repair OpenAIRE Satyendra K Singh; Wang, Minli; Staudt, Christian; Iliakis, George 2011-01-01 In cells exposed to ionizing radiation (IR), double-strand breaks (DSBs) form within clustered-damage sites from lesions disrupting the DNA sugar–phosphate backbone. It is commonly assumed that these DSBs form promptly and are immediately detected and processed by the cellular DNA damage response (DDR) apparatus. This assumption is questioned by the observation that after irradiation of naked DNA, a fraction of DSBs forms minutes to hours after exposure as a result of temperature dependent, c... 9. Heavy ion induced DNA strand breaks and their repair in diploid cells of the epithelium of the lens International Nuclear Information System (INIS) This diploma thesis investigates by means of alkaline unwinding and neutral elution the induction of DNA strand breaks and of rejoining processes as an effect of irradiation with very heavy, accelerated ions. It is found that: The effectiveness of very heavy ions (Z > 18) increases per particle with higher ordinal number, and with increasing velocities. The relative biological effectiveness increases with higher particle masses and lower velocities. The effects of very heavy ions are determined both by the LET and by the particle track extension (specific energy) of the various particles. Heavy ions are much more effective than X-rays with regard to inducing double strand breaks, as compared to DNA single strand breaks induced. Rejoining processes induced by heavy ions have been found to be delayed and incomplete, as compared to the X-ray effects. The number of rejoining processes decreases with rising ordinal number. The experiments indicate that the irradiation with lead or uranium ions most probably makes rejoining impossible. (orig./MG) 10. The Hypoxia-Inducible Factor Pathway, Prolyl Hydroxylase Domain Protein Inhibitors, and Their Roles in Bone Repair and Regeneration Directory of Open Access Journals (Sweden) Lihong Fan 2014-01-01 Full Text Available Hypoxia-inducible factors (HIFs are oxygen-dependent transcriptional activators that play crucial roles in angiogenesis, erythropoiesis, energy metabolism, and cell fate decisions. The group of enzymes that can catalyse the hydroxylation reaction of HIF-1 is prolyl hydroxylase domain proteins (PHDs. PHD inhibitors (PHIs activate the HIF pathway by preventing degradation of HIF-α via inhibiting PHDs. Osteogenesis and angiogenesis are tightly coupled during bone repair and regeneration. Numerous studies suggest that HIFs and their target gene, vascular endothelial growth factor (VEGF, are critical regulators of angiogenic-osteogenic coupling. In this brief perspective, we review current studies about the HIF pathway and its role in bone repair and regeneration, as well as the cellular and molecular mechanisms involved. Additionally, we briefly discuss the therapeutic manipulation of HIFs and VEGF in bone repair and bone tumours. This review will expand our knowledge of biology of HIFs, PHDs, PHD inhibitors, and bone regeneration, and it may also aid the design of novel therapies for accelerating bone repair and regeneration or inhibiting bone tumours. 11. Analysis of Repair Mechanisms following an Induced Double-Strand Break Uncovers Recessive Deleterious Alleles in the Candida albicans Diploid Genome Science.gov (United States) Feri, Adeline; Loll-Krippleber, Raphaël; Commere, Pierre-Henri; Maufrais, Corinne; Sertour, Natacha; Schwartz, Katja; Sherlock, Gavin; Bougnoux, Marie-Elisabeth 2016-01-01 ABSTRACT The diploid genome of the yeast Candida albicans is highly plastic, exhibiting frequent loss-of-heterozygosity (LOH) events. To provide a deeper understanding of the mechanisms leading to LOH, we investigated the repair of a unique DNA double-strand break (DSB) in the laboratory C. albicans SC5314 strain using the I-SceI meganuclease. Upon I-SceI induction, we detected a strong increase in the frequency of LOH events at an I-SceI target locus positioned on chromosome 4 (Chr4), including events spreading from this locus to the proximal telomere. Characterization of the repair events by single nucleotide polymorphism (SNP) typing and whole-genome sequencing revealed a predominance of gene conversions, but we also observed mitotic crossover or break-induced replication events, as well as combinations of independent events. Importantly, progeny that had undergone homozygosis of part or all of Chr4 haplotype B (Chr4B) were inviable. Mining of genome sequencing data for 155 C. albicans isolates allowed the identification of a recessive lethal allele in the GPI16 gene on Chr4B unique to C. albicans strain SC5314 which is responsible for this inviability. Additional recessive lethal or deleterious alleles were identified in the genomes of strain SC5314 and two clinical isolates. Our results demonstrate that recessive lethal alleles in the genomes of C. albicans isolates prevent the occurrence of specific extended LOH events. While these and other recessive lethal and deleterious alleles are likely to accumulate in C. albicans due to clonal reproduction, their occurrence may in turn promote the maintenance of corresponding nondeleterious alleles and, consequently, heterozygosity in the C. albicans species. PMID:27729506 12. Rad52 promotes second-end DNA capture in double-stranded break repair to form complement-stabilized joint molecules. Science.gov (United States) Nimonkar, Amitabh V; Sica, R Alejandro; Kowalczykowski, Stephen C 2009-03-01 Saccharomyces cerevisiae Rad52 performs multiple functions during the recombinational repair of double-stranded DNA (dsDNA) breaks (DSBs). It mediates assembly of Rad51 onto single-stranded DNA (ssDNA) that is complexed with replication protein A (RPA); the resulting nucleoprotein filament pairs with homologous dsDNA to form joint molecules. Rad52 also catalyzes the annealing of complementary strands of ssDNA, even when they are complexed with RPA. Both Rad51 and Rad52 can be envisioned to promote "second-end capture," a step that pairs the ssDNA generated by processing of the second end of a DSB to the joint molecule formed by invasion of the target dsDNA by the first processed end. Here, we show that Rad52 promotes annealing of complementary ssDNA that is complexed with RPA to the displaced strand of a joint molecule, to form a complement-stabilized joint molecule. RecO, a prokaryotic homolog of Rad52, cannot form complement-stabilized joint molecules with RPA-ssDNA complexes, nor can Rad52 promote second-end capture when the ssDNA is bound with either human RPA or the prokaryotic ssDNA-binding protein, SSB, indicating a species-specific process. We conclude that Rad52 participates in second-end capture by annealing a resected DNA break, complexed with RPA, to the joint molecule product of single-end invasion event. These studies support a role for Rad52-promoted annealing in the formation of Holliday junctions in DSB repair. PMID:19204284 13. Genetic control of multiple pathways of post-replicational repair in uvrB strains of Escherichia coli K-12 International Nuclear Information System (INIS) The effect of the recA, uvrD, exrA, and recB mutations and of post-irradiation treatment with chloramphenicol on the survival and post-replicational repair after ultraviolet irradiation of uvrB strains of Escherichia coli K-12 was examined. Each of these mutations or treatments was found to decrease survival and the extent of repair. The interactions of the inhibitory effects of the uvrD, exrA, and recB mutations and chloramphenicol treatment were determined by examining the survival and repair characteristics of the several multiple mutants. The survival results suggest that the post-replication repair process in uvrB strains may be subdivided into at least five different branches. These include three branches that are blocked by the exrA, recB, or uvrD mutation, a fourth branch that is blocked by any one of these mutations and is also sensitive to chloramphenicol treatment, and at least one additional branch that is not sensitive to either of these mutations or to chloramphenicol treatment. The extent of post-replicational repair observed with each of the strains is in general agreement with the pathways postulated on the basis of the survival data, although there are several apparent exceptions to this correlation 14. The Over-expression of the β2 Catalytic Subunit of the Proteasome Decreases Homologous Recombination and Impairs DNA Double-Strand Break Repair in Human Cells Directory of Open Access Journals (Sweden) Anita Collavoli 2011-01-01 Full Text Available By a human cDNA library screening, we have previously identified two sequences coding two different catalytic subunits of the proteasome which increase homologous recombination (HR when overexpressed in the yeast Saccharomyces cerevisiae. Here, we investigated the effect of proteasome on spontaneous HR and DNA repair in human cells. To determine if the proteasome has a role in the occurrence of spontaneous HR in human cells, we overexpressed the β2 subunit of the proteasome in HeLa cells and determined the effect on intrachromosomal HR. Results showed that the overexpression of β2 subunit decreased HR in human cells without altering the cell proteasome activity and the Rad51p level. Moreover, exposure to MG132 that inhibits the proteasome activity reduced HR in human cells. We also found that the expression of the β2 subunit increases the sensitivity to the camptothecin that induces DNA double-strand break (DSB. This suggests that the β2 subunit has an active role in HR and DSB repair but does not alter the intracellular level of the Rad51p. 15. Collision of Trapped Topoisomerase 2 with Transcription and Replication: Generation and Repair of DNA Double-Strand Breaks with 5′ Adducts Directory of Open Access Journals (Sweden) Hong Yan 2016-07-01 Full Text Available Topoisomerase 2 (Top2 is an essential enzyme responsible for manipulating DNA topology during replication, transcription, chromosome organization and chromosome segregation. It acts by nicking both strands of DNA and then passes another DNA molecule through the break. The 5′ end of each nick is covalently linked to the tyrosine in the active center of each of the two subunits of Top2 (Top2cc. In this configuration, the two sides of the nicked DNA are held together by the strong protein-protein interactions between the two subunits of Top2, allowing the nicks to be faithfully resealed in situ. Top2ccs are normally transient, but can be trapped by cancer drugs, such as etoposide, and subsequently processed into DSBs in cells. If not properly repaired, these DSBs would lead to genome instability and cell death. Here, I review the current understanding of the mechanisms by which DSBs are induced by etoposide, the unique features of such DSBs and how they are repaired. Implications for the improvement of cancer therapy will be discussed. 16. Collision of Trapped Topoisomerase 2 with Transcription and Replication: Generation and Repair of DNA Double-Strand Breaks with 5' Adducts. Science.gov (United States) Yan, Hong; Tammaro, Margaret; Liao, Shuren 2016-01-01 Topoisomerase 2 (Top2) is an essential enzyme responsible for manipulating DNA topology during replication, transcription, chromosome organization and chromosome segregation. It acts by nicking both strands of DNA and then passes another DNA molecule through the break. The 5' end of each nick is covalently linked to the tyrosine in the active center of each of the two subunits of Top2 (Top2cc). In this configuration, the two sides of the nicked DNA are held together by the strong protein-protein interactions between the two subunits of Top2, allowing the nicks to be faithfully resealed in situ. Top2ccs are normally transient, but can be trapped by cancer drugs, such as etoposide, and subsequently processed into DSBs in cells. If not properly repaired, these DSBs would lead to genome instability and cell death. Here, I review the current understanding of the mechanisms by which DSBs are induced by etoposide, the unique features of such DSBs and how they are repaired. Implications for the improvement of cancer therapy will be discussed. PMID:27376333 17. The proteomic investigation reveals interaction of mdig protein with the machinery of DNA double-strand break repair. Science.gov (United States) Wang, Wei; Lu, Yongju; Stemmer, Paul M; Zhang, Xiangmin; Bi, Yongyi; Yi, Zhengping; Chen, Fei 2015-09-29 To investigate how mineral dust-induced gene (mdig, also named as mina53, MINA, or NO52) promotes carcinogenesis through inducing active chromatin, we performed proteomics analyses for the interacting proteins that were co-immunoprecipitated by anti-mdig antibody from either the lung cancer cell line A549 cells or the human bronchial epithelial cell line BEAS-2B cells. On SDS-PAGE gels, three to five unique protein bands were consistently observed in the complexes pulled-down by mdig antibody, but not the control IgG. In addition to the mdig protein, several DNA repair or chromatin binding proteins, including XRCC5, XRCC6, RBBP4, CBX8, PRMT5, and TDRD, were identified in the complexes by the proteomics analyses using both Orbitrap Fusion and Orbitrap XL nanoESI-MS/MS in four independent experiments. The interaction of mdig with some of these proteins was further validated by co-immunoprecipitation using antibodies against mdig and its partner proteins, respectively. These data, thus, provide evidence suggesting that mdig accomplishes its functions on chromatin, DNA repair and cell growth through interacting with the partner proteins. PMID:26293673 18. Differential modes of DNA binding by mismatch uracil DNA glycosylase from Escherichia coli: implications for abasic lesion processing and enzyme communication in the base excision repair pathway OpenAIRE Grippon, Seden; Zhao, Qiyuan; Robinson, Tom; Marshall, Jacqueline J. T.; O’Neill, Rory J.; Manning, Hugh; Kennedy, Gordon; Dunsby, Christopher; Neil, Mark; Halford, Stephen E.; French, Paul M. W.; Baldwin, Geoff S. 2010-01-01 Mismatch uracil DNA glycosylase (Mug) from Escherichia coli is an initiating enzyme in the base-excision repair pathway. As with other DNA glycosylases, the abasic product is potentially more harmful than the initial lesion. Since Mug is known to bind its product tightly, inhibiting enzyme turnover, understanding how Mug binds DNA is of significance when considering how Mug interacts with downstream enzymes in the base-excision repair pathway. We have demonstrated differential binding modes o... 19. Electronic structure of (6-4) DNA photoproduct repair involving a non-oxetane pathway. Science.gov (United States) Domratcheva, Tatiana; Schlichting, Ilme 2009-12-16 Mutagenic pyrimidine-pyrimidone (6-4) photoproducts are one of the main DNA lesions induced by solar UV radiation. These lesions can be photoreversed by (6-4) photolyases. The originally published repair mechanism involves rearrangement of the lesion into an oxetane intermediate upon binding to the (6-4) photolyase, followed by light-induced electron transfer from the reduced flavin cofactor. In a recent crystallographic study on a (6-4) photoproduct complexed with (6-4) photolyase from Drosophila melanogaster no oxetane was observed, raising the possibility of a non-oxetane repair mechanism. Using quantum-chemical calculations we find that in addition to repair via an oxetane, a direct transfer of the hydroxyl group results in reversal of the radical anion (6-4) photoproduct. In both mechanisms, the transition states have high energies and correspond to avoided crossings of the ground and excited electronic states. To study whether the repair can proceed via these state crossings, the excited-state potential energy curves were computed. The radical excitation energies and accessibility of the nonadiabatic repair path were found to depend on hydrogen bonds and the protonation state of the lesion. On the basis of the energy calculations, a nonadiabatic repair of the excited (6-4) lesion radical anion via hydroxyl transfer is probable. This repair mechanism is in line with the recent structural data on the (6-4) photolyase from D. melanogaster . PMID:19921821 20. Individual repair of radiation-induced DNA double-strand breaks in lymphocytes. Implications for radiation-induced dermatitis in breast cancer International Nuclear Information System (INIS) 1. DNA双链断裂NHEJ修复及其与肿瘤的研究%Non-homologous end joining pathway of DSB repair and cancer Institute of Scientific and Technical Information of China (English) 张耀伟 2010-01-01 非同源末端连接是哺乳动物最主要的DNA双链断裂(DSB)连接方式.肿瘤细胞非同源末端连接能力的提高与其放化疗抵抗有关,抑制肿瘤细胞非同源末端连接能力,可能增加其对放化疗的敏感性.因此,参与非同源末端连接的修复因子可能成为肿瘤分子靶向治疗及放化疗增敏的新治疗点.%Non-homologous end joining (NHEJ) is the major pathway for repairing DNA doublestrand break (DSB) in mammalian species. The capacity of NHEJ increases in tumor cell,which plays a role in radiation/chemotherapy-resistant agent Inhibiting DSB rejoining may play a crucial role in the enhancement of cellular radiation/chemotherapy-sensitizing. Thus, the protein molecule enrolled in NHEJ may be new potential targets for radiation/chemotherapy -sensitizing. 2. Repair of x-ray-induced DNA double-strand breaks in specific Not I restriction fragments in human fibroblasts: joining of correct and incorrect ends Science.gov (United States) Lobrich, M.; Rydberg, B.; Cooper, P. K.; Chatterjee, A. (Principal Investigator) 1995-01-01 An assay that allows measurement of absolute induction frequencies for DNA double-strand breaks (dsbs) in defined regions of the genome and that quantitates rejoining of correct DNA ends has been used to study repair of dsbs in normal human fibroblasts after x-irradiation. The approach involves hybridization of single-copy DNA probes to Not I restriction fragments separated according to size by pulsed-field gel electrophoresis. Induction of dsbs is quantitated from the decrease in the intensity of the hybridizing restriction fragment and an accumulation of a smear below the band. Rejoining of dsbs results in reconstitution of the intact restriction fragment only if correct DNA ends are joined. By comparing results from this technique with results from a conventional electrophoresis assay that detects all rejoining events, it is possible to quantitate the misrejoining frequency. Three Not I fragments on the long arm of chromosome 21 were investigated with regard to dsb induction, yielding an identical induction rate of 5.8 X 10(-3) break per megabase pair per Gy. Correct dsb rejoining was measured for two of these Not I fragments after initial doses of 80 and 160 Gy. The misrejoining frequency was about 25% for both fragments and was independent of dose. This result appears to be representative for the whole genome as shown by analysis of the entire Not I fragment distribution. The correct rejoining events primarily occurred within the first 2 h, while the misrejoining kinetics included a much slower component, with about half of the events occurring between 2 and 24 h. These misrejoining kinetics are similar to those previously reported for production of exchange aberrations in interphase chromosomes. 3. DNA 双链断裂损伤修复的随机模型研究%A Stochastic Model on DNA Double Strand Breaks Repair Institute of Scientific and Technical Information of China (English) 孙廷哲; 崔隽 2015-01-01 DNA double strand breaks (DSBs)pose serious threat to life.Efficient repair of DSBs is cru-cial for maintaining genomic integrity.Dynamic investigations of DSB repair have received intensive at-tention.However,previous models do not take into account the relation between extrinsic and intrinsic DNA damage.Therefore,a refined Monte Carlo model was constructed by considering spontaneous DNA damage and setting a threshold for cell cycle reentry.The refined model can better describe the dynamic DSB repair under stressed conditions.Extrinsic DSBs induced by irradiation were first fixed.When the level of damage falls below the threshold,intrinsic DNA damage will then emerge and both the extrinsic and intrinsic DSBs will possibly be simultaneously repaired during a specific period.The current model integrates both extrinsic and intrinsic DNA damage and sets a fertile ground for other models with DNA damage repair process.%DNA 双链断裂是一种非常严重的 DNA 损伤。对 DNA 双链断裂有效的修复对于维持基因组的稳定至关重要。对 DNA 双链断裂修复的动力学研究一直得到了广泛的关注。然而，以往的模型研究都没有充分考虑外源性和内源性 DNA 损伤修复之间的关联。因此，通过在细胞周期重启后引入自发生成的随机 DNA 双键断裂损伤，并设定触发细胞周期阻滞的阈值，一个精细化的 Monte Carlo 模型被构建并可以更好的模拟受迫状态下的损伤修复过程。细胞首先修复辐射刺激造成的 DNA 损伤，接着在总损伤水平低于特定阈值后产生内源性的 DNA 损伤并可能在某特定时间段内对两种来源损伤同时进行修复。本模型综合考虑了外源性和内源性 DNA 损伤修复的整合效应，为其它涵盖 DNA 损伤修复模块的模型研究提供了基础。 4. A cell-cycle-stage-related chromosomal X-ray hypersensitivity in larval neuroblasts of Drosophila mei-9 and mei 41 mutants suggesting defective DNA double-strand break repair International Nuclear Information System (INIS) The authors have examined the chromosomal X-ray hypersensitivity in relation to the cell cycle in larval neuroblasts of the mutagen-sensitive and excision repair-defective mutant mei-9 and of the mutagen-sensitive and post-replication repair-defective mutant mei-41 of Drosophila melanogaster. When compared to wild-type cells, cells bearing the mei-9L1 allele produced unusually high levels in particular of chromatid deletions and to a lesser extent also of isochromatid deletions, but virtually no exchange aberrations. The chromosomal hypersensitivity is apparent at M1 when cells are irradiated in S or G2 but not when irradiated in G1. On the other hand, following irradiation cells bearing the mei-41D5 allele predominantly produce chromosome deletions. The phases of major sensitivity are the S and G1. Mei-9 and mei-41 mutants have been classified to date as proficient in DNA double-strand break repair. The data presented in this paper revealed an S-independent clastogenic hypersensitivity of mei-9 and mei-41 cells. They are interpreted as indicative evidence for the presence of impaired DNA double-strand break repair. The cell-cycle-related difference in the ratio of chromatid- versus chromosome-type deletions in both mutants suggests repair defects at partially different phases of the cell cycle in mei-9 and mei-41 mutant cells. (author). 47 refs.; 2 figs.; 5 tabs 5. MMS2, Encoding a ubiquitin-conjugating-enzyme-like protein, is a member of the yeast error-free postreplication repair pathway International Nuclear Information System (INIS) Among the three Saccharomyces cerevisiae DNA repair epistasis groups, the RAD6 group is the most complicated and least characterized, primarily because it consists of two separate repair pathways: an error-free postreplication repair pathway, and a mutagenesis pathway. The rad6 and rad18 mutants are defective in both pathways, and the rev3 mutant affects only the mutagenesis pathway, but a yeast gene that is involved only in error-free postreplication repair has not been reported. We cloned the MMS2 gene from a yeast genomic library by functional complementation of the mms2-1 mutant [Prakash, L. and Prakash, S. (1977) Genetics 86, 33-55]. MMS2 encodes a 137-amino acid, 15.2-kDa protein with significant sequence homology to a conserved family of ubiquitin-conjugating (Ubc) proteins. However, Mms2 does not appear to possess Ubc activity. Genetic analyses indicate that the mms2 mutation is hypostatic to rad6 and rad18 but is synergistic with the rev3 mutation, and the mms2 mutant is proficient in UV-induced mutagenesis. These phenotypes are reminiscent of a pol30-46 mutant known to be impaired in postreplication repair. The mms2 mutant also displayed a REV3-dependent mutator phenotype, strongly suggesting that the MMS2 gene functions in the error-free postreplication repair pathway, parallel to the REV3 mutagenesis pathway. Furthermore, with respect to UV sensitivity, mms2 was found to be hypostatic to the rad6 delta 1-9 mutation, which results in the absence of the first nine amino acids of Rad6. On the basis of these collective results, we propose that the mms2 null mutation and two other allele-specific mutations, rad6 delta 1-9 and pol30-46, define the error-free mode of DNA postreplication repair, and that these mutations may enhance both spontaneous and DNA damage-induced mutagenesis 6. ATM and Artemis promote homologous recombination of radiation-induced DNA double-strand breaks in G2 OpenAIRE Beucher, Andrea; Birraux, Julie; Tchouandong, Leopoldine; Barton, Olivia; Shibata, Atsushi; Conrad, Sandro; Goodarzi, Aaron A.; KREMPLER, ANDREA; Jeggo, Penny; Lo¨brich, Markus 2009-01-01 Homologous recombination (HR) and non-homologous end joining (NHEJ) represent distinct pathways for repairing DNA double-strand breaks (DSBs). Previous work implicated Artemis and ATM in an NHEJ-dependent process, which repairs a defined subset of radiation-induced DSBs in G1-phase. Here, we show that in G2, as in G1, NHEJ represents the major DSB-repair pathway whereas HR is only essential for repair of ∼15% of X- or γ-ray-induced DSBs. In addition to requiring the known HR proteins, Brca2, ... 7. The RecRO pathway of DNA recombinational repair in Helicobacter pylori and its role in bacterial survival in the host OpenAIRE Wang, Ge; Lo, Leja F.; Maier, Robert J. 2011-01-01 Two pathways for DNA recombination, AddAB (RecBCD-like) and RecRO, were identified in Helicobacter pylori, a pathogenic bacterium that colonizes human stomachs resulting in a series of gastric diseases. In this study, we examined the physiological roles of H. pylori RecRO pathway in DNA recombinational repair. We characterized H. pylori single mutants in recR and in recO, genes in the putative gap repair recombination pathway, and an addA recO double mutant that is thus deficient in both path... 8. Electroacupuncture in the repair of spinal cord injury: inhibiting the Notch signaling pathway and promoting neural stem cell proliferation Directory of Open Access Journals (Sweden) Xin Geng 2015-01-01 Full Text Available Electroacupuncture for the treatment of spinal cord injury has a good clinical curative effect, but the underlying mechanism is unclear. In our experiments, the spinal cord of adult Sprague-Dawley rats was clamped for 60 seconds. Dazhui (GV14 and Mingmen (GV4 acupoints of rats were subjected to electroacupuncture. Enzyme-linked immunosorbent assay revealed that the expression of serum inflammatory factors was apparently downregulated in rat models of spinal cord injury after electroacupuncture. Hematoxylin-eosin staining and immunohistochemistry results demonstrated that electroacupuncture contributed to the proliferation of neural stem cells in rat injured spinal cord, and suppressed their differentiation into astrocytes. Real-time quantitative PCR and western blot assays showed that electroacupuncture inhibited activation of the Notch signaling pathway induced by spinal cord injury. These findings indicate that electroacupuncture repaired the injured spinal cord by suppressing the Notch signaling pathway and promoting the proliferation of endogenous neural stem cells. 9. Electroacupuncture in the repair of spinal cord injury：inhibiting the Notch signaling pathway and promoting neural stem cell proliferation Institute of Scientific and Technical Information of China (English) Xin Geng; Tao Sun; Jing-hui Li; Ning Zhao; Yong Wang; Hua-lin Yu 2015-01-01 Electroacupuncture for the treatment of spinal cord injury has a good clinical curative effect, but the underlying mechanism is unclear. In our experiments, the spinal cord of adult Sprague-Daw-ley rats was clamped for 60 seconds.Dazhui (GV14) andMingmen (GV4) acupoints of rats were subjected to electroacupuncture. Enzyme-linked immunosorbent assay revealed that the expres-sion of serum inlfammatory factors was apparently downregulated in rat models of spinal cord injury after electroacupuncture. Hematoxylin-eosin staining and immunohistochemistry results demonstrated that electroacupuncture contributed to the proliferation of neural stem cells in rat injured spinal cord, and suppressed their differentiation into astrocytes. Real-time quantitative PCR and western blot assays showed that electroacupuncture inhibited activation of the Notch signaling pathway induced by spinal cord injury. These ifndings indicate that electroacupuncture repaired the injured spinal cord by suppressing the Notch signaling pathway and promoting the proliferation of endogenous neural stem cells. 10. New discoveries linking transcription to DNA repair and damage tolerance pathways. Science.gov (United States) Cohen, Susan E; Walker, Graham C 2011-01-01 In Escherichia coli, the transcription elongation factor NusA is associated with all elongating RNA polymerases where it functions in transcription termination and antitermination. Here, we review our recent results implicating NusA in the recruitment of DNA repair and damage tolerance mechanisms to sites of stalled transcription complexes. 11. TODRA, a lncRNA at the RAD51 Locus, Is Oppositely Regulated to RAD51, and Enhances RAD51-Dependent DSB (Double Strand Break) Repair Science.gov (United States) Renbaum, Paul; Zeligson, Sharon; Eini, Lital; Bashari, Dana; Smith, Yoav; Lahad, Amnon; Goldberg, Michal; Ginsberg, Doron; Levy-Lahad, Ephrat 2015-01-01 12. The Rate and Spectrum of Spontaneous Mutations in Mycobacterium smegmatis, a Bacterium Naturally Devoid of the Postreplicative Mismatch Repair Pathway. Science.gov (United States) Kucukyildirim, Sibel; Long, Hongan; Sung, Way; Miller, Samuel F; Doak, Thomas G; Lynch, Michael 2016-01-01 Mycobacterium smegmatis is a bacterium that is naturally devoid of known postreplicative DNA mismatch repair (MMR) homologs, mutS and mutL, providing an opportunity to investigate how the mutation rate and spectrum has evolved in the absence of a highly conserved primary repair pathway. Mutation accumulation experiments of M. smegmatis yielded a base-substitution mutation rate of 5.27 × 10(-10) per site per generation, or 0.0036 per genome per generation, which is surprisingly similar to the mutation rate in MMR-functional unicellular organisms. Transitions were found more frequently than transversions, with the A:T→G:C transition rate significantly higher than the G:C→A:T transition rate, opposite to what is observed in most studied bacteria. We also found that the transition-mutation rate of M. smegmatis is significantly lower than that of other naturally MMR-devoid or MMR-knockout organisms. Two possible candidates that could be responsible for maintaining high DNA fidelity in this MMR-deficient organism are the ancestral-like DNA polymerase DnaE1, which contains a highly efficient DNA proofreading histidinol phosphatase (PHP) domain, and/or the existence of a uracil-DNA glycosylase B (UdgB) homolog that might protect the GC-rich M. smegmatis genome against DNA damage arising from oxidation or deamination. Our results suggest that M. smegmatis has a noncanonical Dam (DNA adenine methylase) methylation system, with target motifs differing from those previously reported. The mutation features of M. smegmatis provide further evidence that genomes harbor alternative routes for improving replication fidelity, even in the absence of major repair pathways. PMID:27194804 13. Crystal Structures of DNA-Whirly Complexes and Their Role in Arabidopsis Organelle Genome Repair Energy Technology Data Exchange (ETDEWEB) Cappadocia, Laurent; Maréchal, Alexandre; Parent, Jean-Sébastien; Lepage, Étienne; Sygusch, Jurgen; Brisson, Normand (Montreal) 2010-09-07 DNA double-strand breaks are highly detrimental to all organisms and need to be quickly and accurately repaired. Although several proteins are known to maintain plastid and mitochondrial genome stability in plants, little is known about the mechanisms of DNA repair in these organelles and the roles of specific proteins. Here, using ciprofloxacin as a DNA damaging agent specific to the organelles, we show that plastids and mitochondria can repair DNA double-strand breaks through an error-prone pathway similar to the microhomology-mediated break-induced replication observed in humans, yeast, and bacteria. This pathway is negatively regulated by the single-stranded DNA (ssDNA) binding proteins from the Whirly family, thus indicating that these proteins could contribute to the accurate repair of plant organelle genomes. To understand the role of Whirly proteins in this process, we solved the crystal structures of several Whirly-DNA complexes. These reveal a nonsequence-specific ssDNA binding mechanism in which DNA is stabilized between domains of adjacent subunits and rendered unavailable for duplex formation and/or protein interactions. Our results suggest a model in which the binding of Whirly proteins to ssDNA would favor accurate repair of DNA double-strand breaks over an error-prone microhomology-mediated break-induced replication repair pathway. 14. Rad52 forms DMA repair and recombination centers during S phase DEFF Research Database (Denmark) Lisby, M.; Rothstein, R.; Mortensen, Uffe Hasbro 2001-01-01 cerevisiae, homologous recombination is the major pathway for repairing DNA double-strand breaks. The key role played by Rad52 in this pathway has been attributed to its ability to seek out and mediate annealing of homologous DNA strands. In this study, we find that S. cerevisiae Rad52 fused to green... 15. Gefitinib Radiosensitizes Stem-Like Glioma Cells: Inhibition of Epidermal Growth Factor Receptor-Akt-DNA-PK Signaling, Accompanied by Inhibition of DNA Double-Strand Break Repair Energy Technology Data Exchange (ETDEWEB) Kang, Khong Bee, E-mail: [email protected] [Brain Tumour Research Laboratory, Division of Medical Sciences, National Cancer Centre Singapore (Singapore); Zhu Congju; Wong Yinling; Gao Qiuhan; Ty, Albert; Wong, Meng Cheong [Brain Tumour Research Laboratory, Division of Medical Sciences, National Cancer Centre Singapore (Singapore) 2012-05-01 16. Gefitinib Radiosensitizes Stem-Like Glioma Cells: Inhibition of Epidermal Growth Factor Receptor-Akt-DNA-PK Signaling, Accompanied by Inhibition of DNA Double-Strand Break Repair International Nuclear Information System (INIS) 17. DNA repair and damage pathway related cancer suppressor genes in low-dose-rate irradiated AKR/J an IR mice Energy Technology Data Exchange (ETDEWEB) Bang, Hyun Soon; Bong, Jin Jong; Kang, Yumi; Choi, Moo Hyun; Lee, Hae Un; Yoo, Jae Young; Choi, Seung Jin; Kim, Hee Sun [Radiation Health Research Institute, Korea Hydro and Nuclear Power Co., Ltd, Gyeongju (Korea, Republic of); Lee, Kyung Mi [Global Research Lab, BAERI Institute, Dept. of Biochemistry and Molecular Biology, Korea University College of Medicine, Seoul (Korea, Republic of) 2012-11-15 It has been reported that low-dose-rate radiation stimulates the immune response, prolongs life span and inhibits carcinogenesis. The high dose-rate radiation influences the expression of DNA repair and damage-related genes. In contrast, DNA repair and damage signaling triggered by low-dose-rate irradiation remain unclear. In the present study, we investigated the differential expression of DNA repair and damage pathway related genes in the thymus of AKR/J and ICR mice after 100th day low-dose-rate irradiation. Our findings demonstrated that low-dose-rate γ -radiation suppressed tumorigenesis. 18. Ku80-Deleted Cells are Defective at Base Excision Repair OpenAIRE Li, Han; Marple, Teresa; Hasty, Paul 2013-01-01 Ku80 forms a heterodimer with Ku70, called Ku, that repairs DNA double-strand breaks (DSBs) via the nonhomologous end joining (NHEJ) pathway. As a consequence of deleting NHEJ, Ku80-mutant cells are hypersensitive to agents that cause DNA DSBs like ionizing radiation. Here we show that Ku80 deletion also decreased resistance to ROS and alkylating agents that typically cause base lesions and single-strand breaks (SSBs). This is unusual since base excision repair (BER), not NHEJ, typically repa... 19. Genetic variation in DNA-repair pathways and response to radiochemotherapy in esophageal adenocarcinoma: a retrospective cohort study of the Eastern Cooperative Oncology Group International Nuclear Information System (INIS) Recent data in esophageal cancer suggests the variant allele of a single-nucleotide polymorphism (SNP) in XRCC1 may be associated with resistance to radiochemotherapy. However, this SNP has not been assessed in a histologically homogeneous clinical trial cohort that has been treated with a uniform approach. In addition, whether germline DNA may serve as a surrogate for tumor genotype at this locus is unknown in this disease. Our objective was to assess this SNP in relation to the pathologic complete response (pCR) rate in subjects with esophageal adenocarcinoma who received cisplatin-based preoperative radiochemotherapy in a multicenter clinical trial (Eastern Cooperative Oncology Group 1201). As a secondary aim, we investigated the rate of allelic imbalance between germline and tumor DNA. Eighty-one eligible treatment-naïve subjects with newly diagnosed resectable esophageal adenocarcinoma received radiotherapy (45 Gy) concurrent with cisplatin-based chemotherapy, with planned subsequent surgical resection. The primary endpoint was pCR, defined as complete absence of tumor in the surgical specimen after radiochemotherapy. Using germline DNA from 60 subjects, we examined the base-excision repair SNP, XRCC1 Arg399Gln, and 4 other SNPs in nucleotide excision (XPD Lys751Gln and Asp312Asn, ERCC1 3' flank) and double-stranded break (XRCC2 5' flank) repair pathways, and correlated genotype with pCR rate. Paired tumor tissue was used to estimate the frequency of allelic imbalance at the XRCC1 SNP. The variant allele of the XRCC1 SNP (399Gln) was detected in 52% of subjects. Only 6% of subjects with the variant allele experienced a pCR, compared to 28% of subjects without the variant allele (odds ratio 5.37 for failing to achieve pCR, p = 0.062). Allelic imbalance at this locus was found in only 10% of informative subjects, suggesting that germline genotype may reflect tumor genotype at this locus. No significant association with pCR was noted for other SNPs 20. Genetic variation in DNA-repair pathways and response to radiochemotherapy in esophageal adenocarcinoma: a retrospective cohort study of the Eastern Cooperative Oncology Group Directory of Open Access Journals (Sweden) Wu Xifeng 2011-05-01 Full Text Available Abstract Background Recent data in esophageal cancer suggests the variant allele of a single-nucleotide polymorphism (SNP in XRCC1 may be associated with resistance to radiochemotherapy. However, this SNP has not been assessed in a histologically homogeneous clinical trial cohort that has been treated with a uniform approach. In addition, whether germline DNA may serve as a surrogate for tumor genotype at this locus is unknown in this disease. Our objective was to assess this SNP in relation to the pathologic complete response (pCR rate in subjects with esophageal adenocarcinoma who received cisplatin-based preoperative radiochemotherapy in a multicenter clinical trial (Eastern Cooperative Oncology Group 1201. As a secondary aim, we investigated the rate of allelic imbalance between germline and tumor DNA. Methods Eighty-one eligible treatment-naïve subjects with newly diagnosed resectable esophageal adenocarcinoma received radiotherapy (45 Gy concurrent with cisplatin-based chemotherapy, with planned subsequent surgical resection. The primary endpoint was pCR, defined as complete absence of tumor in the surgical specimen after radiochemotherapy. Using germline DNA from 60 subjects, we examined the base-excision repair SNP, XRCC1 Arg399Gln, and 4 other SNPs in nucleotide excision (XPD Lys751Gln and Asp312Asn, ERCC1 3' flank and double-stranded break (XRCC2 5' flank repair pathways, and correlated genotype with pCR rate. Paired tumor tissue was used to estimate the frequency of allelic imbalance at the XRCC1 SNP. Results The variant allele of the XRCC1 SNP (399Gln was detected in 52% of subjects. Only 6% of subjects with the variant allele experienced a pCR, compared to 28% of subjects without the variant allele (odds ratio 5.37 for failing to achieve pCR, p = 0.062. Allelic imbalance at this locus was found in only 10% of informative subjects, suggesting that germline genotype may reflect tumor genotype at this locus. No significant association 1. Fixation stability dictates the differentiation pathway of periosteal progenitor cells in fracture repair. Science.gov (United States) Hagiwara, Yusuke; Dyment, Nathaniel A; Jiang, Xi; Jiang Ping, Huang; Ackert-Bicknell, Cheryl; Adams, Douglas J; Rowe, David W 2015-07-01 This study compared fracture repair stabilized by intramedullary pin (IMP) or external fixation (EF) in GFP reporter mice. A modified IMP was used as control while EF utilized six needles inserted transversely through the tibia and into a segment of a syringe barrel. X-rays taken at days 0, 14, and 35 showed that IMP resulted in significant three-dimensional deformity with a large callus while EF showed minimal deformity and callus formation. Cryohistological analysis of IMP at day 14 confirmed a large ColX-RFPchry+ callus surrounded by woven bone (Col3.6-GFPcyan) and TRAP+ osteoclasts with mature bone (hOC-GFPtpz) at the base. By day 35, cartilaginous components had been resorbed and an outer cortical shell (OCS) showed evidence of inward modeling. In contrast, the EF at day 14 showed no evidence of cartilage formation. Instead, periosteal-derived osteoblasts (Col3.6-GFPcyan) entered the fracture cleft and formed woven bone that spanned the marrow space. By day 35, mature bone had formed that was contiguous with the opposing cortical bone. Fracture site stability greatly affects the cellular response during repair and must be considered in the preclinical models that test therapies for improving fracture healing. PMID:25639792 2. Repair of γ-irradiation-induced DNA single-strand breaks in human bone marrow cells. Analysis of unfractionated and CD34+ cells using single-cell gel electrophoresis International Nuclear Information System (INIS) Human bone marrow mononuclear cells (BMMNCs) were separated by density gradient centrifugation, and a subpopulation of progenitor cells was further isolated using anti-CD34-coated magnetic beads. The cells were irradiated with γ-rays (0.93-5.43 Gy) from a 137Cs source. The extent of DNA damage, i.e., single-strand breaks (SSBs) and alkali-labile lesions of individual cells, was investigated using the alkaline single-cell gel electrophoresis technique. The irradiation resulted in a dose-dependent increase in DNA migration, reflecting the number of detectable DNA lesions. An approximately similar extent of SSB formation was observed in BMMNCs and CD34+ cells. Damage was repaired when the cells were incubated at 37C: a fast initial repair phase was followed by a slower rejoining of SSBs in both BMMNC and CD34+ cell populations. A significantly longer time was required to repair the lesions caused by 5.43 Gy than those caused by 0.93 Gy. In the present work we report, for the first time, the induction and repair of DNA SSBs at the level of single human bone marrow cells when exposed to ionizing radiation at clinically relevant doses. These data, together with our previous results with human blood granulocytes and lymphocytes, indicate an approximately similar extent of formation and repair of γ-irradiation-induced DNA SSBs in immature and mature human hematopoietic cells 3. RIP4 is a target of multiple signal transduction pathways in keratinocytes: Implications for epidermal differentiation and cutaneous wound repair Energy Technology Data Exchange (ETDEWEB) Adams, Stephanie [Charite, University Medicine Berlin, Institute of Physiology, Arnimallee 22, D-14195 Berlin (Germany); Munz, Barbara, E-mail: [email protected] [Charite, University Medicine Berlin, Institute of Physiology, Arnimallee 22, D-14195 Berlin (Germany) 2010-01-01 Receptor interacting protein 4 (RIP4) is an important regulator of epidermal morphogenesis during embryonic development. We could previously show that expression of the rip4 gene is strongly downregulated in cutaneous wound repair, which might be initiated by a broad variety of growth factors and cytokines. Here, we demonstrate that in keratinocytes, rip4 expression is controlled by a multitude of different signal transduction pathways, such as the p38 mitogen-activated protein kinase (MAPK) and the nuclear factor kappa B (NF-{kappa}B) cascade, in a unique and specific manner. Furthermore, we show that the steroid dexamethasone abolishes the physiological rip4 downregulation after injury and might thus contribute to the phenotype of reduced and delayed wound reepithelialization seen in glucocorticoid-treated patients. As a whole, our data indicate that rip4 expression is regulated in a complex manner, which might have therapeutic implications. 4. SELECTIVE-INHIBITION OF REPAIR OF ACTIVE GENES BY HYPERTHERMIA IS DUE TO INHIBITION OF GLOBAL AND TRANSCRIPTION COUPLED REPAIR PATHWAYS NARCIS (Netherlands) SAKKERS, RJ; FILON, AR; BRUNSTING, JF; KAMPINGA, HH; KONINGS, AWT; MULLENDERS, LHF 1995-01-01 Hyperthermia specifically inhibits the repair of UV-induced DNA photolesions in transcriptionally active genes, To define more precisely which mechanisms underlie the heat-induced inhibition of repair of active genes, removal of cyclobutane pyrimidine dimers (CPDs) was studied in human fibroblasts w 5. Metformin enhances radiosensitivity via inhibition of DNA repair pathway in colorectal cancer Energy Technology Data Exchange (ETDEWEB) Jeong, Youn Kyoung; Kim, Mi Sook; Lee, Ji Young; Song, Kyung Hee; Choi, Kyul; Kim, Eun Ho; Ha, Hun Joo [Ewha Womans University, Seoul (Korea, Republic of) 2014-04-15 In this study, we provide a scientific rationale for the clinical application of metformin as a radiosensitizer in colorectal cancer. Colorectal cancer (CRC) is the third most common cancer in men and the second most common cancer in women worldwide. Currently, it is one of the commonest chemoradiotherapy worked better than the radiotherapy or chemotherapy in colorectal cancer. To enhance radiosensitivity of tumor cells for chemoradiotherapy, it is to use potential anticancer agents that act as radiosensitizers. Metformin, one of the most widely used antidiabetic drugs, has recently been associated with potential antitumorigenic effects. Our data shows that metformin combined with radiation enhances the efficacy of radiotherapy and down-regulates DNA repair proteins. Therefore, we provides a scientific rationale for the clinical application of metformin as a radiosensitizer in colorectal cancer. 6. D-ribose inhibits DNA repair synthesis in human lymphocytes Energy Technology Data Exchange (ETDEWEB) Zunica, G.; Marini, M.; Brunelli, M.A.; Chiricolo, M.; Franceschi, C. 1986-07-31 D-ribose is cytotoxic for quiescent human lymphocytes and severely inhibits their PHA-induced proliferation at concentrations (25-50 mM) at which other simple sugars are ineffective. In order to explain these effects, DNA repair synthesis was evaluated in PHA-stimulated human lymphocytes treated with hydroxyurea and irradiated. D-ribose, in contrast to other reducing sugars, did not induce repair synthesis and therefore did not apparently damage DNA in a direct way, although it markedly inhibited gamma ray-induced repair. Taking into account that lymphocytes must rejoin physiologically-formed DNA strand breaks in order to enter the cell cycle, we suggest that D-ribose exerts its cytotoxic activity by interfering with metabolic pathways critical for the repair of DNA breaks. 7. Role of polynucleotide kinase/phosphatase in mitochondrial DNA repair OpenAIRE Tahbaz, Nasser; Subedi, Sudip; Weinfeld, Michael 2011-01-01 Mutations in mitochondrial DNA (mtDNA) are implicated in a broad range of human diseases and in aging. Compared to nuclear DNA, mtDNA is more highly exposed to oxidative damage due to its proximity to the respiratory chain and the lack of protection afforded by chromatin-associated proteins. While repair of oxidative damage to the bases in mtDNA through the base excision repair pathway has been well studied, the repair of oxidatively induced strand breaks in mtDNA has been less thoroughly exa... 8. DNA double-strand break repair, DNA-PK, and DNA ligases in two human squamous carcinoma cell lines with different radiosensitivity International Nuclear Information System (INIS) Purpose: Variation in sensitivity to radiotherapy among tumors has been related to the capacity of cells to repair radiation-induced DNA double-strand breaks (DSBs). DNA-dependent protein kinase (DNA-PK) and DNA ligases may affect DNA dsb rejoining. This study was performed to compare rate of rejoining of radiation-induced DSBs, DNA-PK, and DNA ligase activities in two human squamous carcinoma cell lines with different sensitivity to ionizing radiation. Methods and Materials: Cell survival of two human squamous carcinoma cell lines, UM-SCC-1 and UM-SCC-14A, was determined by an in vitro clonogenic assay. DSB rejoining was studied using pulsed field gel electrophoresis (PFGE). DNA-PK activity was determined using BIOTRAK DNA-PK enzyme assay system (Amersham). DNA ligase activity in crude cell extracts was measured using [5'-33P] Poly (dA)·(oligo (dT) as a substrate. Proteolytic degradation of proteins was analyzed by means of Western blotting. Results: Applying the commonly used linear-quadratic equation to describe cell survival, S = e-αD-βD2, the two cell lines roughly have the same α value (∼0.40 Gy-1) whereas the β value was considerably higher in UM-SCC-14A (0.067 Gy-2 ± 0.007 Gy-2 [SEM]) as compared to UM-SCC-1 (0.013 Gy-2 ± 0.004 Gy-2 [SEM]). Furthermore, UM-SCC-1 was more proficient in rejoining of X-ray-induced DSBs as compared to UM-SCC-14A as quantified by PFGE. The constitutive level of DNA-PK activity was 1.6 times higher in UM-SCC-1 as compared to UM-SCC-14A (p < 0.05). The constitutive level of DNA ligase activity was similar in the two cell lines. Conclusions: The results suggest that the proficiency in rejoining of DSBs is associated with DNA-PK activity but not with total DNA ligase activity 9. Human DNA repair and recombination genes International Nuclear Information System (INIS) Several genes involved in mammalian DNA repair pathways were identified by complementation analysis and chromosomal mapping based on hybrid cells. Eight complementation groups of rodent mutants defective in the repair of uv radiation damage are now identified. At least seven of these genes are probably essential for repair and at least six of them control the incision step. The many genes required for repair of DNA cross-linking damage show overlap with those involved in the repair of uv damage, but some of these genes appear to be unique for cross-link repair. Two genes residing on human chromosome 19 were cloned from genomic transformants using a cosmid vector, and near full-length cDNA clones of each gene were isolated and sequenced. Gene ERCC2 efficiently corrects the defect in CHO UV5, a nucleotide excision repair mutant. Gene XRCC1 normalizes repair of strand breaks and the excessive sister chromatid exchange in CHO mutant EM9. ERCC2 shows a remarkable /approximately/52% overall homology at both the amino acid and nucleotide levels with the yeast RAD3 gene. Evidence based on mutation induction frequencies suggests that ERCC2, like RAD3, might also be an essential gene for viability. 100 refs., 4 tabs 10. Role of Double-Strand Break End-Tethering during Gene Conversion in Saccharomyces cerevisiae. Directory of Open Access Journals (Sweden) Suvi Jain 2016-04-01 Full Text Available Correct repair of DNA double-strand breaks (DSBs is critical for maintaining genome stability. Whereas gene conversion (GC-mediated repair is mostly error-free, repair by break-induced replication (BIR is associated with non-reciprocal translocations and loss of heterozygosity. We have previously shown that a Recombination Execution Checkpoint (REC mediates this competition by preventing the BIR pathway from acting on DSBs that can be repaired by GC. Here, we asked if the REC can also determine whether the ends that are engaged in a GC-compatible configuration belong to the same break, since repair involving ends from different breaks will produce potentially deleterious translocations. We report that the kinetics of repair are markedly delayed when the two DSB ends that participate in GC belong to different DSBs (termed Trans compared to the case when both DSB ends come from the same break (Cis. However, repair in Trans still occurs by GC rather than BIR, and the overall efficiency of repair is comparable. Hence, the REC is not sensitive to the "origin" of the DSB ends. When the homologous ends for GC are in Trans, the delay in repair appears to reflect their tethering to sequences on the other side of the DSB that themselves recombine with other genomic locations with which they share sequence homology. These data support previous observations that the two ends of a DSB are usually tethered to each other and that this tethering facilitates both ends encountering the same donor sequence. We also found that the presence of homeologous/repetitive sequences in the vicinity of a DSB can distract the DSB end from finding its bona fide homologous donor, and that inhibition of GC by such homeologous sequences is markedly increased upon deleting Sgs1 but not Msh6. 11. Disruption of Maternal DNA Repair Increases Sperm-DerivedChromosomal Aberrations Energy Technology Data Exchange (ETDEWEB) Marchetti, Francesco; Essers, Jeroun; Kanaar, Roland; Wyrobek,Andrew J. 2007-02-07 The final weeks of male germ cell differentiation occur in aDNA repair-deficient environment and normal development depends on theability of the egg to repair DNA damage in the fertilizing sperm. Geneticdisruption of maternal DNA double-strand break repair pathways in micesignificantly increased the frequency of zygotes with chromosomalstructural aberrations after paternal exposure to ionizing radiation.These findings demonstrate that radiation-induced DNA sperm lesions arerepaired after fertilization by maternal factors and suggest that geneticvariation in maternal DNA repair can modulate the risk of early pregnancylosses and of children with chromosomal aberrations of paternalorigin. 12. Developmental Pathways from Childhood Aggression-Disruptiveness, Chronic Peer Rejection and Deviant Friendships to Early-Adolescent Rule Breaking OpenAIRE 2014-01-01 Childhood aggression-disruptiveness, chronic peer rejection, and deviant friendships were examined as predictors of early-adolescent rule breaking behaviors. Using a sample of 383 children (193 girls and 190 boys) who were followed from ages 6 to 14, peer rejection trajectories were identified and incorporated into a series of alternative models to assess how chronic peer rejection and deviant friendships mediate the association between stable childhood aggression-disruptiveness and early-ado... 13. Calmodulin Mediates DNA Repair Pathways Involving H2AX in Response to Low-Dose Radiation Exposure of RAW 264.7 Macrophages Energy Technology Data Exchange (ETDEWEB) Smallwood, Heather S.; Lopez Ferrer, Daniel; Eberlein, P. Elis; Watson, David J.; Squier, Thomas C. 2009-02-05 Understanding the molecular mechanisms that modulate macrophage radioresistance is necessary for the development of effective radiation therapies, as tumor-associated macrophages promote both angiogenesis and matrix remodeling that, in turn, enhance metastasis. In this respect, we have identified a dose-dependent increase in the abundance of the calcium regulatory protein calmodulin (CaM) in RAW 264.7 macrophages upon irradiation. CaM overexpression results in increased macrophage survival following radiation exposure, acting to diminish the sensitivity to low-dose exposures. Increases in CaM abundance also result in an increase in the number of phosphorylated histone H2AX protein complexes associated with DNA repair following macrophage irradiation, with no change in the extent of double-stranded DNA damage. In comparison, when NFκB-dependent pathways are inhibited, through the expression of a dominant-negative IκB construct, there is no significant increase in phosphorylated H2AX upon irradiation. These results indicate that the molecular basis for the up-regulation of histone H2AX mediated DNA-repair pathways is not the result of nonspecific NFκB-dependent pathways or a specific threshold of DNA damage. Rather, increases in CaM abundance act to minimize the low-dose hypersensitivity to radiation to enhance macrophage radioresistance through processes that include the upregulation of DNA repair pathways involving histone protein H2AX phosphorylation. 14. The roles of APE1, APE2, DNA polymerase β and mismatch repair in creating S region DNA breaks during antibody class switch OpenAIRE Schrader, Carol E.; Guikema, Jeroen E.J.; Wu, Xiaoming; Stavnezer, Janet 2008-01-01 Immunoglobulin class switch recombination (CSR) occurs by an intrachromosomal deletion requiring generation of double-stranded DNA breaks (DSBs) in immunoglobulin switch region DNA. The initial steps of DSB formation have been elucidated: cytosine deamination by activation-induced cytidine deaminase (AID) and the generation of abasic sites by uracil-DNA glycosylase (UNG). We show that abasic sites are converted into single-strand breaks (SSBs) by apurinic/apyrimidinic endonucleases (APE1 and ... 15. Cell resistance to the Cytolethal Distending Toxin involves an association of DNA repair mechanisms Science.gov (United States) Bezine, Elisabeth; Malaisé, Yann; Loeuillet, Aurore; Chevalier, Marianne; Boutet-Robinet, Elisa; Salles, Bernard; Mirey, Gladys; Vignard, Julien 2016-01-01 The Cytolethal Distending Toxin (CDT), produced by many bacteria, has been associated with various diseases including cancer. CDT induces DNA double-strand breaks (DSBs), leading to cell death or mutagenesis if misrepaired. At low doses of CDT, other DNA lesions precede replication-dependent DSB formation, implying that non-DSB repair mechanisms may contribute to CDT cell resistance. To address this question, we developed a proliferation assay using human cell lines specifically depleted in each of the main DNA repair pathways. Here, we validate the involvement of the two major DSB repair mechanisms, Homologous Recombination and Non Homologous End Joining, in the management of CDT-induced lesions. We show that impairment of single-strand break repair (SSBR), but not nucleotide excision repair, sensitizes cells to CDT, and we explore the interplay of SSBR with the DSB repair mechanisms. Finally, we document the role of the replicative stress response and demonstrate the involvement of the Fanconi Anemia repair pathway in response to CDT. In conclusion, our work indicates that cellular survival to CDT-induced DNA damage involves different repair pathways, in particular SSBR. This reinforces a model where CDT-related genotoxicity primarily involves SSBs rather than DSBs, underlining the importance of cell proliferation during CDT intoxication and pathogenicity. PMID:27775089 16. Mitochondrial base excision repair assays DEFF Research Database (Denmark) Maynard, Scott; de Souza-Pinto, Nadja C; Scheibye-Knudsen, Morten; 2010-01-01 glycosylases, AP endonuclease, DNA polymerase (POLgamma in mitochondria) and DNA ligase. This article outlines procedures for measuring oxidative damage formation and BER in mitochondria, including isolation of mitochondria from tissues and cells, protocols for measuring BER enzyme activities, gene......The main source of mitochondrial DNA (mtDNA) damage is reactive oxygen species (ROS) generated during normal cellular metabolism. The main mtDNA lesions generated by ROS are base modifications, such as the ubiquitous 8-oxoguanine (8-oxoG) lesion; however, base loss and strand breaks may also occur....... Many human diseases are associated with mtDNA mutations and thus maintaining mtDNA integrity is critical. All of these lesions are repaired primarily by the base excision repair (BER) pathway. It is now known that mammalian mitochondria have BER, which, similarly to nuclear BER, is catalyzed by DNA... 17. Effects of ara A and fresh medium on chromosome damage and DNA double-strand break repair in X-irradiated stationary cells Energy Technology Data Exchange (ETDEWEB) Bryant, P.E. (GSF-Abteilung fuer Biophysikalische Strahlenforschung, Frankfurt am Main (Germany, F.R.)) 1984-01-01 The detailed kinetics of repair of dsb in Ehrlich ascites tumour cells over long repair intervals have been studied and compared under conditions simulating procedures known to cause large changes in cell survival, i.e. holding cells in stationary phase for 7 h after x-radiation, transference of cells to fresh growth medium immediately after x-radiation, and treatment with the DNA synthesis inhibitor 9-..beta..-D-arabinofuranosyladenine (ara A) for 30 min before, during and for 7 h after x-irradiation. These conditions have also been investigated for their effects on frequencies of chromosome abnormalities (anaphase bridges and fragments). Conditions leading to both an inhibition of dsb repair (in the presence of ara A) as well as an acceleration of dsb repair (by fresh growth medium) led to higher frequencies of chromosome abnormalities compared with those for cells under stationary conditions for 7 h after irradiation. Holding dsb open for long periods with ara A may maximize the probability of formation of aberrations, however, the data for fresh medium treatment showed it is not merely the rate at which dsb repair which determines the aberration frequency, and indicated the presence of other biochemical mechanisms in the cell determining the frequency of conversion of dsb into chromosome aberrations. 18. JMJD1C demethylates MDC1 to regulate the RNF8 and BRCA1-mediated chromatin response to DNA breaks DEFF Research Database (Denmark) Watanabe, Sugiko; Watanabe, Kenji; Akimov, Vyacheslav; 2013-01-01 Chromatin ubiquitylation flanking DNA double-strand breaks (DSBs), mediated by RNF8 and RNF168 ubiquitin ligases, orchestrates a two-branch pathway, recruiting repair factors 53BP1 or the RAP80-BRCA1 complex. We report that human demethylase JMJD1C regulates the RAP80-BRCA1 branch of this DNA... 19. Functional analysis of the RAD50/MRE11 protein complex through targeted disruption of the murine RAD50 genomic locus: implications for DNA double strand break repair. An astro research fellowship presentation International Nuclear Information System (INIS) Purpose/Objective: The products of the S. cerevisiae genes ScRAD50 and ScMRE11 act in a protein complex and are required for non-homologous end-joining, the predominant mechanism of DNA double strand break (dsb) repair in mammalian cells. Mutation of these genes results in sensitivity to ionizing radiation (IR), a defect in initiation of meiosis, increased and error-prone recombination during mitosis, and overall genomic instability. This resultant phenotype is reminiscent of that seen in mammalian syndromes of genomic instability such as ataxia-telangiectasia and Bloom syndrome, hallmarks of which are radiation sensitivity and predisposition to malignancy. The murine homologues to ScRAD50 and ScMRE11 have recently been identified; both demonstrate impressive primary sequence conservation with their yeast counterparts, and are expected to mediate conserved functions. The roles of muRAD50 in genomic maintenance and in dsb repair will be examined in two parts. The first will include a determination of normal muRAD50 expression patterns. Second, the effects of disruption of the muRAD50 gene will be assessed. A specific targeting event has introduced a conditional murad50 null mutation into the genome of murine embryonic stem (ES) cells. These mutant ES cells are being used to create mutant mice, thus allowing functional characterization of muRAD50 on both the cellular and organismic levels. Such analyses will contribute to the delineation of the mammalian dsb repair pathway and to the cellular response to IR, and will serve as a mammalian model system for genomic instability. Materials and Methods: Wild-type tissue expression patterns and protein-protein interactions were determined by standard biochemical techniques, including immunoprecipitation, polyacrylamide gel electrophoresis, and Western blotting. Molecular cloning techniques were used to create the gene targeting vectors, which were designed to result in either a deletion of exon 1 (equivalent to a null 20. Comparison of repair of DNA double-strand breaks in identical sequences in primary human fibroblast and immortal hamster-human hybrid cells harboring a single copy of human chromosome 11 Science.gov (United States) Fouladi, B.; Waldren, C. A.; Rydberg, B.; Cooper, P. K.; Chatterjee, A. (Principal Investigator) 2000-01-01 We have optimized a pulsed-field gel electrophoresis assay that measures induction and repair of double-strand breaks (DSBs) in specific regions of the genome (Lobrich et al., Proc. Natl. Acad. Sci. USA 92, 12050-12054, 1995). The increased sensitivity resulting from these improvements makes it possible to analyze the size distribution of broken DNA molecules immediately after the introduction of DSBs and after repair incubation. This analysis shows that the distribution of broken DNA pieces after exposure to sparsely ionizing radiation is consistent with the distribution expected from randomly induced DSBs. It is apparent from the distribution of rejoined DNA pieces after repair incubation that DNA ends continue to rejoin between 3 and 24 h postirradiation and that some of these rejoining events are in fact misrejoining events, since novel restriction fragments both larger and smaller than the original fragment are generated after repair. This improved assay was also used to study the kinetics of DSB rejoining and the extent of misrejoining in identical DNA sequences in human GM38 cells and human-hamster hybrid A(L) cells containing a single human chromosome 11. Despite the numerous differences between these cells, which include species and tissue of origin, levels of TP53, expression of telomerase, and the presence or absence of a homologous chromosome for the restriction fragments examined, the kinetics of rejoining of radiation-induced DSBs and the extent of misrejoining were similar in the two cell lines when studied in the G(1) phase of the cell cycle. Furthermore, DSBs were removed from the single-copy human chromosome in the hamster A(L) cells with similar kinetics and misrejoining frequency as at a locus on this hybrid's CHO chromosomes. 1. Efficacy of DNA double-strand breaks repair in breast cancer is decreased in carriers of the variant allele of the UBC9 gene c.73G>A polymorphism Energy Technology Data Exchange (ETDEWEB) Synowiec, Ewelina [Department of Molecular Genetics, University of Lodz, Lodz (Poland); Krupa, Renata [Laboratory of DNA Repair, Department of Molecular Genetics, University of Lodz, Banacha 12/16, Lodz (Poland); Morawiec, Zbigniew; Wasylecka, Maja [Department of Surgical Oncology, N. Copernicus Hospital, Lodz (Poland); Dziki, Lukasz; Morawiec, Jan [Department of General and Colorectal Surgery, Medical University of Lodz, Lodz (Poland); Blasiak, Janusz [Department of Molecular Genetics, University of Lodz, Lodz (Poland); Wozniak, Katarzyna, E-mail: [email protected] [Laboratory of DNA Repair, Department of Molecular Genetics, University of Lodz, Banacha 12/16, Lodz (Poland) 2010-12-10 UBC9 (E2) SUMO conjugating enzyme plays an important role in the maintenance of genome stability and integrity. In the present work we examined the association between the c.73G>A (Val25Met) polymorphism of the UBC9 gene (rs11553473) and efficacy of DNA double-strand breaks (DSBs) repair (DRE) in breast cancer patients. We determined the level of endogenous (basal) and exogenous (induced by {gamma}-irradiation) DSBs and efficacy of their repair in peripheral blood lymphocytes of 57 breast cancer patients and 70 healthy individuals. DNA damage and repair were studied by neutral comet assay. Genotypes were determined in DNA from peripheral blood lymphocytes by allele-specific PCR (ASO-PCR). We also correlated genotypes with the clinical characteristics of breast cancer patients. We observed a strong association between breast cancer occurrence and the variant allele carried genotypes in patients with elevated level of basal as well as induced DNA damage (OR 6.74, 95% CI 2.27-20.0 and OR 5.33, 95% CI 1.81-15.7, respectively). We also found statistically significant (p < 0.05) difference in DRE related to the c.73G>A polymorphism of the UBC9 gene in breast cancer patients. Carriers of variant allele have decreased DNA DRE as compared to wild type genotype carriers. We did not find any association with the UBC9 gene polymorphism and estrogen and progesterone receptor status. The variant allele of the UBC9 gene polymorphism was strongly inversely related to HER negative breast cancer patients (OR 0.03, 95% CI 0.00-0.23). Our results suggest that the c.73G>A polymorphism of the UBC9 gene may affect DNA DSBs repair efficacy in breast cancer patients. 2. The role of polymorphisms of genes repair pathway to the radiotoxicity in patients with cancer of the cervix International Nuclear Information System (INIS) 3. Assessing SNP-SNP interactions among DNA repair, modification and metabolism related pathway genes in breast cancer susceptibility. Directory of Open Access Journals (Sweden) Full Text Available Genome-wide association studies (GWASs have identified low-penetrance common variants (i.e., single nucleotide polymorphisms, SNPs associated with breast cancer susceptibility. Although GWASs are primarily focused on single-locus effects, gene-gene interactions (i.e., epistasis are also assumed to contribute to the genetic risks for complex diseases including breast cancer. While it has been hypothesized that moderately ranked (P value based weak single-locus effects in GWASs could potentially harbor valuable information for evaluating epistasis, we lack systematic efforts to investigate SNPs showing consistent associations with weak statistical significance across independent discovery and replication stages. The objectives of this study were i to select SNPs showing single-locus effects with weak statistical significance for breast cancer in a GWAS and/or candidate-gene studies; ii to replicate these SNPs in an independent set of breast cancer cases and controls; and iii to explore their potential SNP-SNP interactions contributing to breast cancer susceptibility. A total of 17 SNPs related to DNA repair, modification and metabolism pathway genes were selected since these pathways offer a priori knowledge for potential epistatic interactions and an overall role in breast carcinogenesis. The study design included predominantly Caucasian women (2,795 cases and 4,505 controls from Alberta, Canada. We observed two two-way SNP-SNP interactions (APEX1-rs1130409 and RPAP1-rs2297381; MLH1-rs1799977 and MDM2-rs769412 in logistic regression that conferred elevated risks for breast cancer (P(interaction<7.3 × 10(-3. Logic regression identified an interaction involving four SNPs (MBD2-rs4041245, MLH1-rs1799977, MDM2-rs769412, BRCA2-rs1799943 (P(permutation = 2.4 × 10(-3. SNPs involved in SNP-SNP interactions also showed single-locus effects with weak statistical significance, while BRCA2-rs1799943 showed stronger statistical significance (P 4. DNA repair in neurons: So if they don't divide what's to repair? Energy Technology Data Exchange (ETDEWEB) Fishel, Melissa L. [Department of Pediatrics (Section of Hematology/Oncology), Herman B Wells Center for Pediatric Research, Indiana University School of Medicine, 1044 W. Walnut, Room 302C, Indianapolis, IN 46202 (United States); Vasko, Michael R. [Department of Pharmacology and Toxicology, Indiana University School of Medicine, 1044 W. Walnut St., Indianapolis, IN 46202 (United States); Kelley, Mark R. [Department of Pediatrics (Section of Hematology/Oncology), Herman B Wells Center for Pediatric Research, Indiana University School of Medicine, 1044 W. Walnut, Room 302C, Indianapolis, IN 46202 (United States) and Department of Pharmacology and Toxicology, Indiana University School of Medicine, 1044 W. Walnut St., Indianapolis, IN 46202 (United States) and Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, 1044 W. Walnut, Room 302C, Indianapolis, IN 46202 (United States)]. E-mail: [email protected] 2007-01-03 Neuronal DNA repair remains one of the most exciting areas for investigation, particularly as a means to compare the DNA repair response in mitotic (cancer) vs. post-mitotic (neuronal) cells. In addition, the role of DNA repair in neuronal cell survival and response to aging and environmental insults is of particular interest. DNA damage caused by reactive oxygen species (ROS) such as generated by mitochondrial respiration includes altered bases, abasic sites, and single- and double-strand breaks which can be prevented by the DNA base excision repair (BER) pathway. Oxidative stress accumulates in the DNA of the human brain over time especially in the mitochondrial DNA (mtDNA) and is proposed to play a critical role in aging and in the pathogenesis of several neurological disorders including Parkinson's disease, ALS, and Alzheimer's diseases. Because DNA damage accumulates in the mtDNA more than nuclear DNA, there is increased interest in DNA repair pathways and the consequence of DNA damage in the mitochondria of neurons. The type of damage that is most likely to occur in neuronal cells is oxidative DNA damage which is primarily removed by the BER pathway. Following the notion that the bulk of neuronal DNA damage is acquired by oxidative DNA damage and ROS, the BER pathway is a likely area of focus for neuronal studies of DNA repair. BER variations in brain aging and pathology in various brain regions and tissues are presented. Therefore, the BER pathway is discussed in greater detail in this review than other repair pathways. Other repair pathways including direct reversal, nucleotide excision repair (NER), mismatch repair (MMR), homologous recombination and non-homologous end joining are also discussed. Finally, there is a growing interest in the role that DNA repair pathways play in the clinical arena as they relate to the neurotoxicity and neuropathy associated with cancer treatments. Among the numerous side effects of cancer treatments, major 5. Oxidative stress alters base excision repair pathway and increases apoptotic response in apurinic/apyrimidinic endonuclease 1/redox factor-1 haploinsufficient mice. Science.gov (United States) Unnikrishnan, Archana; Raffoul, Julian J; Patel, Hiral V; Prychitko, Thomas M; Anyangwe, Njwen; Meira, Lisiane B; Friedberg, Errol C; Cabelof, Diane C; Heydari, Ahmad R 2009-06-01 Apurinic/apyrimidinic endonuclease 1/redox factor-1 (APE1/Ref-1) is the redox regulator of multiple stress-inducible transcription factors, such as NF-kappaB, and the major 5'-endonuclease in base excision repair (BER). We utilized mice containing a heterozygous gene-targeted deletion of APE1/Ref-1 (Apex(+/-)) to determine the impact of APE1/Ref-1 haploinsufficiency on the processing of oxidative DNA damage induced by 2-nitropropane (2-NP) in the liver tissue of mice. APE1/Ref-1 haploinsufficiency results in a significant decline in NF-kappaB DNA-binding activity in response to oxidative stress in liver. In addition, loss of APE1/Ref-1 increases the apoptotic response to oxidative stress, in which significant increases in GADD45g expression, p53 protein stability, and caspase activity are observed. Oxidative stress displays a differential impact on monofunctional (UNG) and bifunctional (OGG1) DNA glycosylase-initiated BER in the liver of Apex(+/-) mice. APE1/Ref-1 haploinsufficiency results in a significant decline in the repair of oxidized bases (e.g., 8-OHdG), whereas removal of uracil is increased in liver nuclear extracts of mice using an in vitro BER assay. Apex(+/-) mice exposed to 2-NP displayed a significant decline in 3'-OH-containing single-strand breaks and an increase in aldehydic lesions in their liver DNA, suggesting an accumulation of repair intermediates of failed bifunctional DNA glycosylase-initiated BER. PMID:19268524 6. Role of polynucleotide kinase/phosphatase in mitochondrial DNA repair Science.gov (United States) Tahbaz, Nasser; Subedi, Sudip; Weinfeld, Michael 2012-01-01 Mutations in mitochondrial DNA (mtDNA) are implicated in a broad range of human diseases and in aging. Compared to nuclear DNA, mtDNA is more highly exposed to oxidative damage due to its proximity to the respiratory chain and the lack of protection afforded by chromatin-associated proteins. While repair of oxidative damage to the bases in mtDNA through the base excision repair pathway has been well studied, the repair of oxidatively induced strand breaks in mtDNA has been less thoroughly examined. Polynucleotide kinase/phosphatase (PNKP) processes strand-break termini to render them chemically compatible for the subsequent action of DNA polymerases and ligases. Here, we demonstrate that functionally active full-length PNKP is present in mitochondria as well as nuclei. Downregulation of PNKP results in an accumulation of strand breaks in mtDNA of hydrogen peroxide-treated cells. Full restoration of repair of the H2O2-induced strand breaks in mitochondria requires both the kinase and phosphatase activities of PNKP. We also demonstrate that PNKP contains a mitochondrial-targeting signal close to the C-terminus of the protein. We further show that PNKP associates with the mitochondrial protein mitofilin. Interaction with mitofilin may serve to translocate PNKP into mitochondria. PMID:22210862 7. The Vitamin A Derivative All-Trans Retinoic Acid Repairs Amyloid-β-Induced Double-Strand Breaks in Neural Cells and in the Murine Neocortex OpenAIRE Emmanuelle Gruz-Gibelli; Natacha Chessel; Clélia Allioux; Pascale Marin; Françoise Piotton; Geneviève Leuba; Herrmann, François R.; Armand Savioz 2016-01-01 The amyloid-β peptide or Aβ is the key player in the amyloid-cascade hypothesis of Alzheimer's disease. Aβ appears to trigger cell death but also production of double-strand breaks (DSBs) in aging and Alzheimer's disease. All-trans retinoic acid (RA), a derivative of vitamin A, was already known for its neuroprotective effects against the amyloid cascade. It diminishes, for instance, the production of Aβ peptides and their oligomerisation. In the present work we investigat... 8. Targeting DNA repair pathways: a new episode in targeted cancer therapeutics%基于DNA损伤修复的分子靶向治疗:肿瘤靶向治疗的新篇章 Institute of Scientific and Technical Information of China (English) 王东 2014-01-01 DNA,as the fundamental material carrying genetics information,is consistently challengedby endogenous and exogenous stimuli,including oxidative stress,ionizing irradiation,and chemotherapeuticagents,just to name a few.DNA repair mechanisms are then essential for cell survival under stress.Altered DNA repair networks is one of the most important features of cancer cells,which makes targeting DNA repair pathways an emerging strategy in cancer therapeutics.We reviewed the evolving variety of strategies and current potent clinical drug candidates in DNA repair targeting therapeutics. 9. Repair processes in diverse systems: overview International Nuclear Information System (INIS) Studies on DNA repair in several bacterial systems as well as in eukaryotes are reviewed. Some topics discussed are: excision repair of uv damage in Mycoplasma; repair replication in uv-irradiated Tetrahymena; repair of double-strand breaks in DNA of Micrococcus radiodurans; DNA repair in Neurospora; lack of dimer excision in x-irradiated Vicia faba; and DNA repair in Nicotiana, Haplopappus, and Chlamydomonas 10. Pars plana vitrectomy for the repair of primary, inferior rhegmatogenous retinal detachment associated to inferior breaks. A comparison of a 25-gauge versus a 20-gauge system OpenAIRE dell’Omo, Roberto; Barca, Francesco; Tan, H. Stevie; Bijl, Heico M.; Oberstein, Sarit Y Lesnik; Mura, Marco 2012-01-01 Background To compare anatomical, functional outcomes and complications of high-speed 25-gauge (G) pars plana vitrectomy (PPV) versus 20-G PPV for the management of primary inferior rhegmatogenous retinal detachment (RRD) associated to inferior breaks/holes. Methods Eighty-five eyes from 85 patients with a minimum follow-up of 3 months were retrospectively evaluated. Forty-one patients underwent 25-G and 44 patients underwent 20-G PPV. All patients underwent PPV with fluid-air exchange, sulfu... 11. Collision of Trapped Topoisomerase 2 with Transcription and Replication: Generation and Repair of DNA Double-Strand Breaks with 5′ Adducts OpenAIRE Hong Yan; Margaret Tammaro; Shuren Liao 2016-01-01 Topoisomerase 2 (Top2) is an essential enzyme responsible for manipulating DNA topology during replication, transcription, chromosome organization and chromosome segregation. It acts by nicking both strands of DNA and then passes another DNA molecule through the break. The 5′ end of each nick is covalently linked to the tyrosine in the active center of each of the two subunits of Top2 (Top2cc). In this configuration, the two sides of the nicked DNA are held together by the strong protein-prot... 12. Molecular basis for DNA strand displacement by NHEJ repair polymerases. Science.gov (United States) Bartlett, Edward J; Brissett, Nigel C; Plocinski, Przemyslaw; Carlberg, Tom; Doherty, Aidan J 2016-03-18 The non-homologous end-joining (NHEJ) pathway repairs DNA double-strand breaks (DSBs) in all domains of life. Archaea and bacteria utilize a conserved set of multifunctional proteins in a pathway termed Archaeo-Prokaryotic (AP) NHEJ that facilitates DSB repair. Archaeal NHEJ polymerases (Pol) are capable of strand displacement synthesis, whilst filling DNA gaps or partially annealed DNA ends, which can give rise to unligatable intermediates. However, an associated NHEJ phosphoesterase (PE) resects these products to ensure that efficient ligation occurs. Here, we describe the crystal structures of these archaeal (Methanocella paludicola) NHEJ nuclease and polymerase enzymes, demonstrating their strict structural conservation with their bacterial NHEJ counterparts. Structural analysis, in conjunction with biochemical studies, has uncovered the molecular basis for DNA strand displacement synthesis in AP-NHEJ, revealing the mechanisms that enable Pol and PE to displace annealed bases to facilitate their respective roles in DSB repair. PMID:26405198 13. Breaking Bat Science.gov (United States) Aguilar, Isaac-Cesar; Kagan, David 2013-01-01 The sight of a broken bat in Major League Baseball can produce anything from a humorous dribbler in the infield to a frightening pointed projectile headed for the stands. Bats usually break at the weakest point, typically in the handle. Breaking happens because the wood gets bent beyond the breaking point due to the wave sent down the bat created… 14. Electron Transfer Mechanisms of DNA Repair by Photolyase Science.gov (United States) Zhong, Dongping 2015-04-01 Photolyase is a flavin photoenzyme that repairs two DNA base damage products induced by ultraviolet (UV) light: cyclobutane pyrimidine dimers and 6-4 photoproducts. With femtosecond spectroscopy and site-directed mutagenesis, investigators have recently made significant advances in our understanding of UV-damaged DNA repair, and the entire enzymatic dynamics can now be mapped out in real time. For dimer repair, six elementary steps have been characterized, including three electron transfer reactions and two bond-breaking processes, and their reaction times have been determined. A unique electron-tunneling pathway was identified, and the critical residues in modulating the repair function at the active site were determined. The dynamic synergy between the elementary reactions for maintaining high repair efficiency was elucidated, and the biological nature of the flavin active state was uncovered. For 6-4 photoproduct repair, a proton-coupled electron transfer repair mechanism has been revealed. The elucidation of electron transfer mechanisms and two repair photocycles is significant and provides a molecular basis for future practical applications, such as in rational drug design for curing skin cancer. 15. Single-nucleotide polymorphisms in base excision repair, nucleotide excision repair, and double strand break genes as markers for response to radiotherapy in patients with Stage I to II head-and-neck cancer International Nuclear Information System (INIS) Purpose: Polymorphisms in DNA repair genes can influence response to radiotherapy. We analyzed single-nucleotide polymorphisms (SNP) in nine DNA repair genes in 108 patients with head-and-neck cancer (HNSCC) who had received radiotherapy only. Methods and Materials: From May 1993 to December 2004, patients with Stage I and II histopathologically confirmed HNSCC underwent radiotherapy. DNA was obtained from paraffin-embedded tissue, and SNP analysis was performed using a real-time polymerase chain reaction allelic discrimination TaqMan assay with minor modifications. Results: Patients were 101 men (93.5%) and 7 (6.5%) women, with a median age of 64 years (range, 40 to 89 years). Of the patients, 76 (70.4%) patients were Stage I and 32 (29.6%) were Stage II. The XPF/ERCC1 SNP at codon 259 and XPG/ERCC5 at codon 46 emerged as significant predictors of progression (p 0.00005 and 0.049, respectively) and survival (p = 0.0089 and 0.0066, respectively). Similarly, when variant alleles of XPF/ERCC1, XPG/ERCC5 and XPA were examined in combination, a greater number of variant alleles was associated with shorter time to progression (p = 0.0003) and survival (p 0.0002). Conclusions: Genetic polymorphisms in XPF/ERCC1, XPG/ERCC5, and XPA may significantly influence response to radiotherapy; large studies are warranted to confirm their role in HNSCC 16. Inter-individual variation in nucleotide excision repair pathway is modulated by non-synonymous polymorphisms in ERCC4 and MBD4 genes Energy Technology Data Exchange (ETDEWEB) Allione, Alessandra, E-mail: [email protected] [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Guarrera, Simonetta; Russo, Alessia [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Ricceri, Fulvio [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Department of Medical Sciences, University of Turin, Via Santena 19, 10126 Turin (Italy); Purohit, Rituraj [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Bioinformatics Division, School of Bio Sciences and Technology, Vellore Institute of Technology University, Vellore 632014, Tamil Nadu (India); Pagnani, Andrea; Rosa, Fabio; Polidoro, Silvia; Voglino, Floriana [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Matullo, Giuseppe [Human Genetics Foundation (HuGeF), Via Nizza 52, 10126 Turin (Italy); Department of Medical Sciences, University of Turin, Via Santena 19, 10126 Turin (Italy) 2013-11-15 Highlights: • We reported a large inter-individual variability of NER capacity. • ERCC4 rs1800124 and MBD4 rs10342 nsSNP variants were associated with DNA repair capacity. • DNA–protein interaction analyses showed alteration of binding for ERCC4 and MBD4 variants. • A new possible cross-talk between NER and BER pathways has been reported. - Abstract: Inter-individual differences in DNA repair capacity (DRC) may lead to genome instability and, consequently, modulate individual cancer risk. Among the different DNA repair pathways, nucleotide excision repair (NER) is one of the most versatile, as it can eliminate a wide range of helix-distorting DNA lesions caused by ultraviolet light irradiation and chemical mutagens. We performed a genotype–phenotype correlation study in 122 healthy subjects in order to assess if any associations exist between phenotypic profiles of NER and DNA repair gene single nucleotide polymorphisms (SNPs). Individuals were genotyped for 768 SNPs with a custom Illumina Golden Gate Assay, and peripheral blood mononuclear cells (PBMCs) of the same subjects were tested for a NER comet assay to measure DRC after challenging cells by benzo(a)pyrene diolepoxide (BPDE). We observed a large inter-individual variability of NER capacity, with women showing a statistically significant lower DRC (mean ± SD: 6.68 ± 4.76; p = 0.004) than men (mean ± SD: 8.89 ± 5.20). Moreover, DRC was significantly lower in individuals carrying a variant allele for the ERCC4 rs1800124 non-synonymous SNP (nsSNP) (p = 0.006) and significantly higher in subjects with the variant allele of MBD4 rs2005618 SNP (p = 0.008), in linkage disequilibrium (r{sup 2} = 0.908) with rs10342 nsSNP. Traditional in silico docking approaches on protein–DNA and protein–protein interaction showed that Gly875 variant in ERCC4 (rs1800124) decreases the DNA–protein interaction and that Ser273 and Thr273 variants in MBD4 (rs10342) indicate complete loss of protein 17. Pathways of homologous recombinantion and DNA interstrand cross-link repair : roles of mammalian RAD54 and SNMI NARCIS (Netherlands) M.L.G. Dronkert (Mies) 2002-01-01 textabstractThe aim of this thesis is to investigate mammalian DNA interstrand cross-link (ICL) repair. ICLs are formed by a number of agents used in tumor therapy, like mitomycin C and cisplatin. They constitute one of the most toxic damages to DNA, as they inhibit DNA strand separation. However, l 18. Optimality in DNA repair. Science.gov (United States) Richard, Morgiane; Fryett, Matthew; Miller, Samantha; Booth, Ian; Grebogi, Celso; Moura, Alessandro 2012-01-01 DNA within cells is subject to damage from various sources. Organisms have evolved a number of mechanisms to repair DNA damage. The activity of repair enzymes carries its own risk, however, because the repair of two nearby lesions may lead to the breakup of DNA and result in cell death. We propose a mathematical theory of the damage and repair process in the important scenario where lesions are caused in bursts. We use this model to show that there is an optimum level of repair enzymes within cells which optimises the cell's response to damage. This optimal level is explained as the best trade-off between fast repair and a low probability of causing double-stranded breaks. We derive our results analytically and test them using stochastic simulations, and compare our predictions with current biological knowledge. PMID:21945337 19. Nucleotide excision repair in the test tube. NARCIS (Netherlands) N.G.J. Jaspers (Nicolaas); J.H.J. Hoeijmakers (Jan) 1995-01-01 textabstractThe eukaryotic nucleotide excision-repair pathway has been reconstituted in vitro, an achievement that should hasten the full enzymological characterization of this highly complex DNA-repair pathway. 20. Extracts of proliferating and non-proliferating human cells display different base excision pathways and repair fidelity DEFF Research Database (Denmark) Akbari, Mansour; Pena Diaz, Javier; Andersen, Sonja; 2009-01-01 cells both had capacity for single- and two-nucleotide insertion BER activity. However, patch size longer than two nucleotides was only detected in extracts from proliferating cells. Relative to extracts from proliferating cells, extracts from non-proliferating cells had approximately two-fold higher...... concentration of POLbeta, which contributed to most of two-nucleotide insertion BER. In contrast, two-nucleotide insertion in extracts from proliferating cells was not dependent on POLbeta. BER fidelity was two- to three-fold lower in extracts from the non-proliferating compared with extracts of proliferating...... cells. Furthermore, although one-nucleotide deletion was the predominant type of repair error in both extracts, the pattern of repair errors was somewhat different. These results establish two-nucleotide patch BER as a distinct POLbeta-dependent mechanism in non-proliferating cells and demonstrate that... 1. Prolonged Particulate Hexavalent Chromium Exposure Suppresses Homologous Recombination Repair in Human Lung Cells. Science.gov (United States) Browning, Cynthia L; Qin, Qin; Kelly, Deborah F; Prakash, Rohit; Vanoli, Fabio; Jasin, Maria; Wise, John Pierce 2016-09-01 Genomic instability is one of the primary models of carcinogenesis and a feature of almost all cancers. Homologous recombination (HR) repair protects against genomic instability by maintaining high genomic fidelity during the repair of DNA double strand breaks. The defining step of HR repair is the formation of the Rad51 nucleofilament, which facilitates the search for a homologous sequence and invasion of the template DNA strand. Particulate hexavalent chromium (Cr(VI)), a human lung carcinogen, induces DNA double strand breaks and chromosome instability. Since the loss of HR repair increases Cr(VI)-induced chromosome instability, we investigated the effect of extended Cr(VI) exposure on HR repair. We show acute (24 h) Cr(VI) exposure induces a normal HR repair response. In contrast, prolonged (120 h) exposure to particulate Cr(VI) inhibited HR repair and Rad51 nucleofilament formation. Prolonged Cr(VI) exposure had a profound effect on Rad51, evidenced by reduced protein levels and Rad51 mislocalization to the cytoplasm. The response of proteins involved in Rad51 nuclear import and nucleofilament formation displayed varying responses to prolonged Cr(VI) exposure. BRCA2 formed nuclear foci after prolonged Cr(VI) exposure, while Rad51C foci formation was suppressed. These results suggest that particulate Cr(VI), a major chemical carcinogen, inhibits HR repair by targeting Rad51, causing DNA double strand breaks to be repaired by a low fidelity, Rad51-independent repair pathway. These results further enhance our understanding of the underlying mechanism of Cr(VI)-induced chromosome instability and thus, carcinogenesis. PMID:27449664 2. Induction and repair of DNA double-strand breaks in blood lymphocytes of patients undergoing 18F-FDG PET/CT examinations International Nuclear Information System (INIS) The purpose of this study was to evaluate DNA double-strand breaks (DSBs) in blood lymphocytes of patients undergoing positron emission tomography (PET)/CT using γ-H2AX immunofluorescence microscopy and to differentiate between 18F-fluorodeoxyglucose (FDG) and CT-induced DNA lesions. This study was approved by the local Ethics Committee and complies with Health Insurance Portability and Accountability Act (HIPAA) requirements. After written informed consent was obtained, 33 patients underwent whole-body 18F-FDG PET/CT (3 MBq/kg body weight, 170/100 reference mAs at 120 kV). The FDG PET and CT portions were performed as an initial CT immediately followed by the PET. Blood samples were obtained before, at various time points following 18F-FDG application and up to 24 h after the CT scan. Distinct foci representing DSBs were quantified in isolated lymphocytes using fluorescence microscopy after staining against the phosphorylated histone variant γ-H2AX. The DSB values at the various time points were significantly different (p 18F-FDG administration (median excess foci 0.11/cell, range 0.06-0.27/cell) and 5 min after CT (median excess foci 0.17/cell, range 0.05-0.54/cell). A significant correlation between CT-induced DSBs and dose length product was obtained (ρ = 0.898, p 18F-FDG injection and 5 min after CT. The radionuclide contributes considerably to the total DSB induction in this setting. (orig.) 3. Signalization and repair of the DNA double-strand breaks of in the cerebral tumors: modulation of the radiation response with the chemotherapy treatments; Signalization et reparation des cassures double-brin de l'ADN dans les gliomes: modulation de la reponse aux traitements chimio-radiotherapeutiques Energy Technology Data Exchange (ETDEWEB) Marcinkova-Bencokova, Z 2007-07-15 4. Impact of DNA repair pathways on the cytotoxicity of piperlongumine in chicken DT40 cell-lines OpenAIRE Okamoto, Saki; Narita, Takeo; Sasanuma, Hiroyuki; Takeda, Shunichi; Masunaga, Shin-Ichiro; Bessho, Tadayoshi; Tano, Keizo 2014-01-01 Piperlongumine is a naturally-occurring small molecule with various biological activities. Recent studies demonstrate that piperlongumine selectively kills various types of transformed cells with minimal toxicity to non-transformed cells by inducing a high level of reactive oxygen species (ROS). ROS generates various types of DNA lesions, including base modifications and single strand breaks. In order to examine the contribution of ROS-induced DNA damage to the cytotoxicity by piperlongumine,... 5. Signalling of double strand breaks and deprotected telomeres in Arabidopsis. Directory of Open Access Journals (Sweden) Simon eAmiard 2013-10-01 Full Text Available Failure to repair DNA double strand breaks (DSB can lead to chromosomal rearrangements and eventually to cancer or cell death. Radiation and environmental pollutants induce DSB and this is of particular relevance to plants due to their sessile life style. DSB also occur naturally in cells during DNA replication and programmed induction of DSB initiates the meiotic recombination essential for gametogenesis in most eukaryotes. The linear nature of most eukaryotic chromosomes means that each chromosome has two "broken" ends. Chromosome ends, or telomeres, are protected by nucleoprotein caps which avoid their recognition as DSB by the cellular DNA repair machinery. Deprotected telomeres are recognized as DSB and become substrates for recombination leading to chromosome fusions, the "bridge-breakage-fusion" cycle, genome rearrangements and cell death. The importance of repair of DSB and the severity of the consequences of their misrepair have led to the presence of multiple, robust mechanisms for their detection and repair. After a brief overview of DSB repair pathways to set the context, we present here an update of current understanding of the detection and signalling of DSB in the plant, Arabidopsis thaliana. 6. Esc2 and Sgs1 act in functionally distinct branches of the homologous recombination repair pathway in Saccharomyces cerevisiae DEFF Research Database (Denmark) Mankouri, Hocine W; Ngo, Hien-Ping; Hickson, Ian D 2009-01-01 Esc2 is a member of the RENi family of SUMO-like domain proteins and is implicated in gene silencing in Saccharomyces cerevisiae. Here, we identify a dual role for Esc2 during S-phase in mediating both intra-S-phase DNA damage checkpoint signaling and preventing the accumulation of Rad51-dependen......, and sgs1esc2 cells attempt to undergo mitosis with unprocessed HRR intermediates. We propose a model whereby Esc2 acts in an Mph1-dependent process, separately from Sgs1, to influence the repair/tolerance of MMS-induced lesions during S-phase.... 7. Conserved XPB Core Structure and Motifs for DNA Unwinding:Implications for Pathway Selection of Transcription or ExcisionRepair Energy Technology Data Exchange (ETDEWEB) Fan, Li; Arval, Andrew S.; Cooper, Priscilla K.; Iwai, Shigenori; Hanaoka, Fumio; Tainer, John A. 2005-04-01 The human xeroderma pigmentosum group B (XPB) helicase is essential for transcription, nucleotide excision repair, and TFIIH functional assembly. Here, we determined crystal structures of an Archaeoglobus fulgidus XPB homolog (AfXPB) that characterize two RecA-like XPB helicase domains and discover a DNA damage recognition domain (DRD), a unique RED motif, a flexible thumb motif (ThM), and implied conformational changes within a conserved functional core. RED motif mutations dramatically reduce helicase activity, and the DRD and ThM, which flank the RED motif, appear structurally as well as functionally analogous to the MutS mismatch recognition and DNA polymerase thumb domains. Substrate specificity is altered by DNA damage, such that AfXPB unwinds dsDNA with 3' extensions, but not blunt-ended dsDNA, unless it contains a lesion, as shown for CPD or (6-4) photoproducts. Together, these results provide an unexpected mechanism of DNA unwinding with Implications for XPB damage verification in nucleotide excision repair. 8. Aberrant expression of proteins involved in signal transduction and DNA repair pathways in lung cancer and their association with clinical parameters. Directory of Open Access Journals (Sweden) Yong He Full Text Available BACKGROUND: Because cell signaling and cell metabolic pathways are executed through proteins, protein signatures in primary tumors are useful for identifying key nodes in signaling networks whose alteration is associated with malignancy and/or clinical outcomes. This study aimed to determine protein signatures in primary lung cancer tissues. METHODOLOGY/ PRINCIPAL FINDINGS: We analyzed 126 proteins and/or protein phosphorylation sites in case-matched normal and tumor samples from 101 lung cancer patients with reverse-phase protein array (RPPA assay. The results showed that 18 molecules were significantly different (p<0.05 by at least 30% between normal and tumor tissues. Most of those molecules play roles in cell proliferation, DNA repair, signal transduction and lipid metabolism, or function as cell surface/matrix proteins. We also validated RPPA results by Western blot and/or immunohistochemical analyses for some of those molecules. Statistical analyses showed that Ku80 levels were significantly higher in tumors of nonsmokers than in those of smokers. Cyclin B1 levels were significantly overexpressed in poorly differentiated tumors while Cox2 levels were significantly overexpressed in neuroendocrinal tumors. A high level of Stat5 is associated with favorable survival outcome for patients treated with surgery. CONCLUSIONS/ SIGNIFICANCE: Our results revealed that some molecules involved in DNA damage/repair, signal transductions, lipid metabolism, and cell proliferation were drastically aberrant in lung cancer tissues, and Stat5 may serve a molecular marker for prognosis of lung cancers. 9. Dominant mutations in S. cerevisiae PMS1 identify the Mlh1-Pms1 endonuclease active site and an exonuclease 1-independent mismatch repair pathway. Directory of Open Access Journals (Sweden) Catherine E Smith 2013-10-01 Full Text Available Lynch syndrome (hereditary nonpolypsis colorectal cancer or HNPCC is a common cancer predisposition syndrome. Predisposition to cancer in this syndrome results from increased accumulation of mutations due to defective mismatch repair (MMR caused by a mutation in one of the mismatch repair genes MLH1, MSH2, MSH6 or PMS2/scPMS1. To better understand the function of Mlh1-Pms1 in MMR, we used Saccharomyces cerevisiae to identify six pms1 mutations (pms1-G683E, pms1-C817R, pms1-C848S, pms1-H850R, pms1-H703A and pms1-E707A that were weakly dominant in wild-type cells, which surprisingly caused a strong MMR defect when present on low copy plasmids in an exo1Δ mutant. Molecular modeling showed these mutations caused amino acid substitutions in the metal coordination pocket of the Pms1 endonuclease active site and biochemical studies showed that they inactivated the endonuclease activity. This model of Mlh1-Pms1 suggested that the Mlh1-FERC motif contributes to the endonuclease active site. Consistent with this, the mlh1-E767stp mutation caused both MMR and endonuclease defects similar to those caused by the dominant pms1 mutations whereas mutations affecting the predicted metal coordinating residue Mlh1-C769 had no effect. These studies establish that the Mlh1-Pms1 endonuclease is required for MMR in a previously uncharacterized Exo1-independent MMR pathway. 10. DNA repair: Dynamic defenders against cancer and aging Energy Technology Data Exchange (ETDEWEB) Fuss, Jill O.; Cooper, Priscilla K. 2006-04-01 You probably weren't thinking about your body's cellular DNA repair systems the last time you sat on the beach in the bright sunshine. Fortunately, however, while you were subjecting your DNA to the harmful effects of ultraviolet light, your cells were busy repairing the damage. The idea that our genetic material could be damaged by the sun was not appreciated in the early days of molecular biology. When Watson and Crick discovered the structure of DNA in 1953 [1], it was assumed that DNA is fundamentally stable since it carries the blueprint of life. However, over 50 years of research have revealed that our DNA is under constant assault by sunlight, oxygen, radiation, various chemicals, and even our own cellular processes. Cleverly, evolution has provided our cells with a diverse set of tools to repair the damage that Mother Nature causes. DNA repair processes restore the normal nucleotide sequence and DNA structure of the genome after damage [2]. These responses are highly varied and exquisitely regulated. DNA repair mechanisms are traditionally characterized by the type of damage repaired. A large variety of chemical modifications can alter normal DNA bases and either lead to mutations or block transcription if not repaired, and three distinct pathways exist to remove base damage. Base excision repair (BER) corrects DNA base alterations that do not distort the overall structure of the DNA helix such as bases damaged by oxidation resulting from normal cellular metabolism. While BER removes single damaged bases, nucleotide excision repair (NER) removes short segments of nucleotides (called oligonucleotides) containing damaged bases. NER responds to any alteration that distorts the DNA helix and is the mechanism responsible for repairing bulky base damage caused by carcinogenic chemicals such as benzo [a]pyrene (found in cigarette smoke and automobile exhaust) as well as covalent linkages between adjacent pyrimidine bases resulting from the ultraviolet 11. Break It Institute of Scientific and Technical Information of China (English) MATTHEW PLOWRIGHT; GWYNN GUILFORD 2008-01-01 @@ Resolutions are not natural - otherwise you wouldn't have to "resolve" to execute them. This year, instead of planning how to commit to a slew of unattainable goals, why not prepare for breaking your resolutions the right way? 12. DNA repair deficiency in neurodegeneration DEFF Research Database (Denmark) Jeppesen, Dennis Kjølhede; Bohr, Vilhelm A; Stevnsner, Tinna V. 2011-01-01 Deficiency in repair of nuclear and mitochondrial DNA damage has been linked to several neurodegenerative disorders. Many recent experimental results indicate that the post-mitotic neurons are particularly prone to accumulation of unrepaired DNA lesions potentially leading to progressive...... neurodegeneration. Nucleotide excision repair is the cellular pathway responsible for removing helix-distorting DNA damage and deficiency in such repair is found in a number of diseases with neurodegenerative phenotypes, including Xeroderma Pigmentosum and Cockayne syndrome. The main pathway for repairing oxidative...... base lesions is base excision repair, and such repair is crucial for neurons given their high rates of oxygen metabolism. Mismatch repair corrects base mispairs generated during replication and evidence indicates that oxidative DNA damage can cause this pathway to expand trinucleotide repeats, thereby... 13. A Role for BLM in Double-Strand Break Repair Pathway Choice: Prevention of CtIP/Mre11-Mediated Alternative Nonhomologous End-Joining DEFF Research Database (Denmark) Grabarz, Anastazja; Guirouilh-Barbat, Josée; Barascu, Aurelia; 2013-01-01 represses A-EJ in an epistatic manner with 53BP1 and RIF1 and is required for ionizing-radiation-induced 53BP1 focus assembly. Conversely, in the absence of 53BP1 or RIF1, BLM promotes formation of A-EJ long deletions, consistent with a role for BLM in DSB end resection. These data highlight a dual role... 14. A High-Throughput Screening Strategy to Identify Protein-Protein Interaction Inhibitors That Block the Fanconi Anemia DNA Repair Pathway. Science.gov (United States) Voter, Andrew F; Manthei, Kelly A; Keck, James L 2016-07-01 Induction of the Fanconi anemia (FA) DNA repair pathway is a common mechanism by which tumors evolve resistance to DNA crosslinking chemotherapies. Proper execution of the FA pathway requires interaction between the FA complementation group M protein (FANCM) and the RecQ-mediated genome instability protein (RMI) complex, and mutations that disrupt FANCM/RMI interactions sensitize cells to DNA crosslinking agents. Inhibitors that block FANCM/RMI complex formation could be useful therapeutics for resensitizing tumors that have acquired chemotherapeutic resistance. To identify such inhibitors, we have developed and validated high-throughput fluorescence polarization and proximity assays that are sensitive to inhibitors that disrupt interactions between the RMI complex and its binding site on FANCM (a peptide referred to as MM2). A pilot screen of 74,807 small molecules was performed using the fluorescence polarization assay. Hits from the primary screen were further tested using the proximity assay, and an orthogonal proximity assay was used to assess inhibitor selectivity. Direct physical interaction between the RMI complex and the most selective inhibitor identified through the screening process was measured by surface plasmon resonance and isothermal titration calorimetry. Observation of direct binding by this small molecule validates the screening protocol. 15. Chapter 10 the primary cilium coordinates signaling pathways in cell cycle control and migration during development and tissue repair DEFF Research Database (Denmark) Christensen, Søren T; Pedersen, Stine F; Satir, Peter; 2008-01-01 Cell cycle control and migration are critical processes during development and maintenance of tissue functions. Recently, primary cilia were shown to take part in coordination of the signaling pathways that control these cellular processes in human health and disease. In this review, we present...... with the extracellular matrix, coordinate Wnt signaling, and modulate cytoskeletal changes that impinge on both cell cycle control and cell migration.... 16. Competitive repair by naturally dispersed repetitive DNA during non-allelic homologous recombination Energy Technology Data Exchange (ETDEWEB) Hoang, Margaret L.; Tan, Frederick J.; Lai, David C.; Celniker, Sue E.; Hoskins, Roger A.; Dunham, Maitreya J.; Zheng, Yixian; Koshland, Douglas 2010-08-27 Genome rearrangements often result from non-allelic homologous recombination (NAHR) between repetitive DNA elements dispersed throughout the genome. Here we systematically analyze NAHR between Ty retrotransposons using a genome-wide approach that exploits unique features of Saccharomyces cerevisiae purebred and Saccharomyces cerevisiae/Saccharomyces bayanus hybrid diploids. We find that DNA double-strand breaks (DSBs) induce NAHR-dependent rearrangements using Ty elements located 12 to 48 kilobases distal to the break site. This break-distal recombination (BDR) occurs frequently, even when allelic recombination can repair the break using the homolog. Robust BDR-dependent NAHR demonstrates that sequences very distal to DSBs can effectively compete with proximal sequences for repair of the break. In addition, our analysis of NAHR partner choice between Ty repeats shows that intrachromosomal Ty partners are preferred despite the abundance of potential interchromosomal Ty partners that share higher sequence identity. This competitive advantage of intrachromosomal Tys results from the relative efficiencies of different NAHR repair pathways. Finally, NAHR generates deleterious rearrangements more frequently when DSBs occur outside rather than within a Ty repeat. These findings yield insights into mechanisms of repeat-mediated genome rearrangements associated with evolution and cancer. 17. Perspectives on the combination of radiotherapy and targeted therapy with DNA repair inhibitors in the treatment of pancreatic cancer. Science.gov (United States) Yang, Shih-Hung; Kuo, Ting-Chun; Wu, Hsu; Guo, Jhe-Cyuan; Hsu, Chiun; Hsu, Chih-Hung; Tien, Yu-Wen; Yeh, Kun-Huei; Cheng, Ann-Lii; Kuo, Sung-Hsin 2016-08-28 18. The Break DEFF Research Database (Denmark) Strand, Anete Mikkala Camille 2016-01-01 storytelling to enact fruitful breakings of patterns unbecoming. The claim being, that the hamster wheel of Work-life anno 2016 needs reconfiguration and the simple yet fruitful manner by which this is done is through acknowledging the benefits of bodies, spaces and artifacts – and the benefits of actually...... taking a break, discontinuing for a moment in order to continue better, wiser and more at ease. Both within and as part of the daily routines, and – now and then – outside these routines in the majesty of nature with time to explore and redirect the course of life in companionships with fellow man... 19. String breaking CERN Document Server Bali, G S; Lippert, T; Neff, H; Prkacin, Z; Schilling, K; Bali, Gunnar S; Dussel, Thomas; Lippert, Thomas; Neff, Hartmut; Prkacin, Zdravko; Schilling, Klaus 2006-01-01 We numerically investigate the transition of the static quark-antiquark string into a static-light meson-antimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for Nf=2 lattice QCD at zero temperature. We discuss the lattice techniques used and present results on energy levels and mixing angle of the static two-state system. We visualize the action density distribution in the region of string breaking as a function of the static colour source-antisource separation. The results can be related to properties of quarkonium systems. 20. Nonhomologous Mechanisms of Repair of Chromosomal Breaks Energy Technology Data Exchange (ETDEWEB) Haber, J. E. 2001-12-19 Discovered three new proteins involved in DNA damage assessment. Interestingly they are all proteins involved in recombination, but they have very different roles in that process and other proteins that might be expected to be equivalently involved are not. This is developing into a very significant area of research. 1. Upregulated Ras/Raf/ERK1/2 signaling pathway: a new hope in the repair of spinal cord injury Directory of Open Access Journals (Sweden) Tao Liu 2015-01-01 Full Text Available An increasing number of studies report that the Ras/Raf/extracellular signal-regulated kinase 1/2 (ERK1/2 signaling pathway has a death-promoting apoptotic function in neural cells. We hypothesized that the Ras/Raf/ERK1/2 signaling pathway may be abnormally regulated in rat injured spinal cord models. The weight drop method was used to establish rat spinal cord injury at T 9 . Western blot analysis and immunohistochemical staining revealed Ras expression was dramatically elevated, and the phosphorylations of A-Raf, B-Raf and C-Raf were all upregulated in the injured spinal cord. Both mitogen-activated protein kinase kinase 1/2 and ERK1/2, which belong to the Ras/Raf signaling kinases, were upregulated. These results indicate that Ras/Raf/ERK1/2 signaling may be upregulated in injured spinal cord and are involved in recovery after spinal cord injury. 2. Influence of XRCC1 Genetic Polymorphisms on Ionizing Radiation-Induced DNA Damage and Repair Directory of Open Access Journals (Sweden) Silvia Sterpone 2010-01-01 Full Text Available It is well known that ionizing radiation (IR can damage DNA through a direct action, producing single- and double-strand breaks on DNA double helix, as well as an indirect effect by generating oxygen reactive species in the cells. Mammals have evolved several and distinct DNA repair pathways in order to maintain genomic stability and avoid tumour cell transformation. This review reports important data showing a huge interindividual variability on sensitivity to IR and in susceptibility to developing cancer; this variability is principally represented by genetic polymorphisms, that is, DNA repair gene polymorphisms. In particular we have focussed on single nucleotide polymorphisms (SNPs of XRCC1, a gene that encodes for a scaffold protein involved basically in Base Excision Repair (BER. In this paper we have reported and presented recent studies that show an influence of XRCC1 variants on DNA repair capacity and susceptibility to breast cancer. 3. Supersymmetry breaking Emilian Dudas 2009-01-01 We review the various mechanisms of supersymmetry breaking and its trans-mission to the observable sector. We argue that hybrid models where gauge dominates over gravity mediation, but gravity provides the main contributions to the Higgs sector masses and the neutralino mass, are able to combine the advantages and reduce the disadvantages of the two transmission mechanisms. 4. Recognition and repair of chemically heterogeneous structures at DNA ends. Science.gov (United States) Andres, Sara N; Schellenberg, Matthew J; Wallace, Bret D; Tumbale, Percy; Williams, R Scott 2015-01-01 Exposure to environmental toxicants and stressors, radiation, pharmaceutical drugs, inflammation, cellular respiration, and routine DNA metabolism all lead to the production of cytotoxic DNA strand breaks. Akin to splintered wood, DNA breaks are not "clean." Rather, DNA breaks typically lack DNA 5'-phosphate and 3'-hydroxyl moieties required for DNA synthesis and DNA ligation. Failure to resolve damage at DNA ends can lead to abnormal DNA replication and repair, and is associated with genomic instability, mutagenesis, neurological disease, ageing and carcinogenesis. An array of chemically heterogeneous DNA termini arises from spontaneously generated DNA single-strand and double-strand breaks (SSBs and DSBs), and also from normal and/or inappropriate DNA metabolism by DNA polymerases, DNA ligases and topoisomerases. As a front line of defense to these genotoxic insults, eukaryotic cells have accrued an arsenal of enzymatic first responders that bind and protect damaged DNA termini, and enzymatically tailor DNA ends for DNA repair synthesis and ligation. These nucleic acid transactions employ direct damage reversal enzymes including Aprataxin (APTX), Polynucleotide kinase phosphatase (PNK), the tyrosyl DNA phosphodiesterases (TDP1 and TDP2), the Ku70/80 complex and DNA polymerase β (POLβ). Nucleolytic processing enzymes such as the MRE11/RAD50/NBS1/CtIP complex, Flap endonuclease (FEN1) and the apurinic endonucleases (APE1 and APE2) also act in the chemical "cleansing" of DNA breaks to prevent genomic instability and disease, and promote progression of DNA- and RNA-DNA damage response (DDR and RDDR) pathways. Here, we provide an overview of cellular first responders dedicated to the detection and repair of abnormal DNA termini. PMID:25111769 5. XRCC1 and DNA polymerase β in cellular protection against cytotoxic DNA single-strand breaks Institute of Scientific and Technical Information of China (English) Julie K Horton; Mary Watson; Donna F Stefanick; Daniel T Shaughnessy; Jack A Taylor; Samuel H Wilson 2008-01-01 Single-strand breaks (SSBs) can occur in cells either directly, or indirectly following initiation of base excision re-pair (BER). SSBs generally have blocked termini lacking the conventional 5'-phosphate and 3'-hydroxyl groups and require further processing prior to DNA synthesis and ligation. XRCC1 is devoid of any known enzymatic activity, but it can physically interact with other proteins involved in all stages of the overlapping SSB repair and BER pathways, including those that conduct the rate-limiting end-tailoring, and in many cases can stimulate their enzymatic activities. XRCC1-/- mouse fibroblasts are most hypersensitive to agents that produce DNA lesions repaired by monofunctional glycosylase-initiated BER and that result in formation of indirect SSBs. A requirement for the deoxyribose phosphate lyase activity of DNA polymerase β (polβ) is specific to this pathway, whereas pol β is implicated in gap-filling during repair of many types of SSBs. Elevated levels of strand breaks, and diminished repair, have been demonstrated in MMS-treated XRCC1-/-, and to a lesser extent in polβ-/- cell lines, compared with wild-type cells. Thus a strong correlation is observed between cellular sensitivity to MMS and the ability of cells to repair MMS-induced damage. Exposure of wild-type andpolβ-/- cells to an inhibitor of PARP activity dramatically potentiates MMS-induccd cytotoxicity. XRCC1-/- cellsare also sensitized by PARP inhibition demonstrating that PARP-mediated poly(ADP-ribosyl)ation plays a role inmodulation of cytotoxicity beyond recruitment of XRCC1 to sites of DNA damage. 6. Comet assay to measure DNA repair: approach and applications OpenAIRE Azqueta, Amaya; SLYSKOVA, JANA; Langie, Sabine A. S.; O’Neill Gaivão, Isabel; Collins, Andrew 2014-01-01 Cellular repair enzymes remove virtually all DNA damage before it is fixed; repair therefore plays a crucial role in preventing cancer. Repair studied at the level of transcription correlates poorly with enzyme activity, and so assays of phenotype are needed. In a biochemical approach, substrate nucleoids containing specific DNA lesions are incubated with cell extract; repair enzymes in the extract induce breaks at damage sites; and the breaks are measured with the comet assay. The nature of ... 7. DNA repair in PHA stimulated human lymphocytes International Nuclear Information System (INIS) Damage an repair of radiation induced DNA strand breaks were measured by alkaline lysis and hydroxyapatite chromatography. PHA stimulated human lymphocytes show that the rejoining process is complete within the first 50 min., afterwords secondary DNA damage and chromatid aberration. DNA repair, in synchronized culture, allows to evaluate individual repair capacity and this in turn can contribute to the discovery of individual who, although they do not demonstrate apparent clinical signs, are carriers of DNA repair deficiency. Being evident that a correlation exists between DNA repair capacity and carcinogenesis, the possibility of evaluating the existent relationship between DNA repair and survival in tumor cells comes therefore into discussion 8. 1,4-Dihydropyridines Active on the SIRT1/AMPK Pathway Ameliorate Skin Repair and Mitochondrial Function and Exhibit Inhibition of Proliferation in Cancer Cells. Science.gov (United States) Valente, Sergio; Mellini, Paolo; Spallotta, Francesco; Carafa, Vincenzo; Nebbioso, Angela; Polletta, Lucia; Carnevale, Ilaria; Saladini, Serena; Trisciuoglio, Daniela; Gabellini, Chiara; Tardugno, Maria; Zwergel, Clemens; Cencioni, Chiara; Atlante, Sandra; Moniot, Sébastien; Steegborn, Clemens; Budriesi, Roberta; Tafani, Marco; Del Bufalo, Donatella; Altucci, Lucia; Gaetano, Carlo; Mai, Antonello 2016-02-25 Modulators of sirtuins are considered promising therapeutic targets for the treatment of cancer, cardiovascular, metabolic, inflammatory, and neurodegenerative diseases. Here we prepared new 1,4-dihydropyridines (DHPs) bearing changes at the C2/C6, C3/C5, C4, or N1 position. Tested with the SIRTainty procedure, some of them displayed increased SIRT1 activation with respect to the prototype 3a, high NO release in HaCat cells, and ameliorated skin repair in a mouse model of wound healing. In C2C12 myoblasts, two of them improved mitochondrial density and functions. All the effects were reverted by coadministration of compound C (9), an AMPK inhibitor, or of EX-527 (10), a SIRT1 inhibitor, highlighting the involvement of the SIRT1/AMPK pathway in the action of DHPs. Finally, tested in a panel of cancer cells, the water-soluble form of 3a, compound 8, displayed antiproliferative effects in the range of 8-35 μM and increased H4K16 deacetylation, suggesting a possible role for SIRT1 activators in cancer therapy. PMID:26689352 9. Symmetry breaking in spreading RAT2 fibroblasts requires the MAPK/ERK pathway scaffold RACK1 that integrates FAK, p190A-RhoGAP and ERK2 signaling. Science.gov (United States) Klímová, Zuzana; Bráborec, Vojtěch; Maninová, Miloslava; Čáslavský, Josef; Weber, Michael J; Vomastek, Tomáš 2016-09-01 The spreading of adhering cells is a morphogenetic process during which cells break spherical or radial symmetry and adopt migratory polarity with spatially segregated protruding cell front and non-protruding cell rear. The organization and regulation of these symmetry-breaking events, which are both complex and stochastic, are not fully understood. Here we show that in radially spreading cells, symmetry breaking commences with the development of discrete non-protruding regions characterized by large but sparse focal adhesions and long peripheral actin bundles. Establishment of this non-protruding static region specifies the distally oriented protruding cell front and thus determines the polarity axis and the direction of cell migration. The development of non-protruding regions requires ERK2 and the ERK pathway scaffold protein RACK1. RACK1 promotes adhesion-mediated activation of ERK2 that in turn inhibits p190A-RhoGAP signaling by reducing the peripheral localization of p190A-RhoGAP. We propose that sustained ERK signaling at the prospective cell rear induces p190A-RhoGAP depletion from the cell periphery resulting in peripheral actin bundles and cell rear formation. Since cell adhesion activates both ERK and p190A-RhoGAP signaling this constitutes a spatially confined incoherent feed-forward signaling circuit. PMID:27212270 10. Homologous recombination in DNA repair and DNA damage tolerance Institute of Scientific and Technical Information of China (English) Xuan Li; Wolf-Dietrich Heyer 2008-01-01 Homologous recombination (HR) comprises a series of interrelated pathways that function in the repair of DNA double-stranded breaks (DSBs) and interstrand crosslinks (ICLs). In addition, recombination provides critical sup-port for DNA replication in the recovery of stalled or broken replication forks, contributing to tolerance of DNA damage. A central core of proteins, most critically the RecA homolog Rad51, catalyzes the key reactions that typify HR: homology search and DNA strand invasion. The diverse functions of recombination are reflected in the need for context-specific factors that perform supplemental functions in conjunction with the core proteins. The inability to properly repair complex DNA damage and resolve DNA replication stress leads to genomic instability and contributes to cancer etiology. Mutations in the BRCA2 recombination gene cause predisposition to breast and ovarian cancer as well as Fanconi anemia, a cancer predisposition syndrome characterized by a defect in the repair of DNA interstrand crosslinks. The cellular functions of recombination are also germane to DNA-based treatment modaUties of cancer, which target replicating cells by the direct or indirect induction of DNA lesions that are substrates for recombination pathways. This review focuses on mechanistic aspects of HR relating to DSB and ICL repair as well as replication fork support. 11. 核苷酸切除修复通路基因多态性与肺癌易感性%Gene polymorphisms in the nucleotide excision repair pathway and lung cancer susceptibility Institute of Scientific and Technical Information of China (English) 钱莹莹; 束永前 2013-01-01 Nucleotide excision repair (NER) pathway is one of the principal ways of the repair of DNA damage.The single nucleotide polymorphisms (SNP) of its key genes such as xeroderma pigmentosum group A (XPA) gene,excision repair cross complementingl (ERCC1) gene and xeroderma pigmentosum group D (XPD) gene may be associated with differences in the DNA repair capacity and may influence an individual's risk of lung cancer,because the variant genotype in those polymorphisms might destroy or alter repair function.%核苷酸切除修复(NER)通路是修复DNA损伤的主要途径之一,其中着色性于皮病A型(XPA)基因、核苷酸切除修复交叉互补1(ERCC1)基因和着色性干皮病D型(XPD)基因的单核苷酸多态性(SNP)改变了NER通路中重要酶与蛋白的修复功能,引起DNA损伤修复能力的差异,最终导致个体肺癌易感性不同. 12. Breaking Routines DEFF Research Database (Denmark) Kesting, Peter; Jørgensen, Frances On some level, innovation begins when the current way of doing things is questioned and alternatives are sought. In cognitive terms, this can be conceptualized as the point at which an agent breaks with existing routine and returns to planning and decision-making. Thus far, however, very little...... is known about this cognitive structure or the factors that trigger the search for alternatives. In cooperation with the Danish Research Centre for Magnetic Resonance, University of Copenhagen, Denmark, we are in the process of designing an experimental study designed to gain insights into the triggers... 13. Breaking Symmetries CERN Document Server Peters, Kirstin 2010-01-01 A well-known result by Palamidessi tells us that {\\pi}mix (the {\\pi}-calculus with mixed choice) is more expressive than {\\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\\pi}mix i... 14. Sapacitabine, the prodrug of CNDAC, is a nucleoside analog with a unique action mechanism of inducing DNA strand breaks Institute of Scientific and Technical Information of China (English) Xiao-Jun Liu; Billie Nowak; Ya-Qing Wang; William Plunkett 2012-01-01 Sapacitabine is an orally bioavailable prodrug of the nucleoside analog 2'-C-cyano-2'-deoxy-1-β-D-arabino-pentofuranosylcytosine (CNDAC).Both the prodrug and active metabolite are in clinical trials for hematologic malignancies and/or solid tumors.CNDAC has a unique mechanism of action:after incorporation into DNA,it induces single-strand breaks (SSBs) that are converted into double-strand breaks (DSBs) when cells go through a second S phase.In our previous studies,we demonstrated that CNDAC-induced SSBs can be repaired by the transcription-coupled nucleotide excision repair pathway,whereas lethal DSBs are mainly repaired through homologous recombination.In the current work,we used clonogenic assays to compare the DNA damage repair mechanism of CNDAC with two other deoxycytidine analogs:cytarabine,which is used in hematologic malignacies,and gemcitabine,which shows activity in solid tumors.Deficiency in two Rad51 paralogs,Rad51D and XRCC3,greatly sensitized cells to CNDAC,but not to cytarabine or gemcitabine,indicating that homologous recombination is not a major mechanism for repairing damage caused by the latter two analogs.This study further suggests clinical activity and application of sapacitabine that is distinct from that of cytarabine or gemcitabine. 15. The Transcriptional Response to DNA-Double-Strand Breaks in Physcomitrella patens Science.gov (United States) Kamisugi, Yasuko; Whitaker, John W. 2016-01-01 The model bryophyte Physcomitrella patens is unique among plants in supporting the generation of mutant alleles by facile homologous recombination-mediated gene targeting (GT). Reasoning that targeted transgene integration occurs through the capture of transforming DNA by the homology-dependent pathway for DNA double-strand break (DNA-DSB) repair, we analysed the genome-wide transcriptomic response to bleomycin-induced DNA damage and generated mutants in candidate DNA repair genes. Massively parallel (Illumina) cDNA sequencing identified potential participants in gene targeting. Transcripts encoding DNA repair proteins active in multiple repair pathways were significantly up-regulated. These included Rad51, CtIP, DNA ligase 1, Replication protein A and ATR in homology-dependent repair, Xrcc4, DNA ligase 4, Ku70 and Ku80 in non-homologous end-joining and Rad1, Tebichi/polymerase theta, PARP in microhomology-mediated end-joining. Differentially regulated cell-cycle components included up-regulated Rad9 and Hus1 DNA-damage-related checkpoint proteins and down-regulated D-type cyclins and B-type CDKs, commensurate with the imposition of a checkpoint at G2 of the cell cycle characteristic of homology-dependent DNA-DSB repair. Candidate genes, including ATP-dependent chromatin remodelling helicases associated with repair and recombination, were knocked out and analysed for growth defects, hypersensitivity to DNA damage and reduced GT efficiency. Targeted knockout of PpCtIP, a cell-cycle activated mediator of homology-dependent DSB resection, resulted in bleomycin-hypersensitivity and greatly reduced GT efficiency. PMID:27537368 16. Equipment maintenance and repair Directory of Open Access Journals (Sweden) Walia DS 2010-10-01 Full Text Available The repair and maintenance of ophthalmic equipment, including surgical instruments and diagnostic devices, can be compared to the maintenance of a motor vehicle, something many of us understand well.If you had a car, would you drive it until the fuel runs out or until a tyre punctures, and then abandon it to buy a new car? Of course not. However, many eye care units purchase (or receive as a donation expensive and delicate equipment which, because of poor maintenance, ends up breaking down. If there is not a system in place to report breakdowns and to plan or carry out repairs, equipment can remain unusable for long periods of time. Sometimes, this equipment ends up being dumped. Good maintenance habits and an effective repair system will minimise the amount of time equipment is unusable. 17. Using the comet assay to study DNA repair: progress in the past decade. Directory of Open Access Journals (Sweden) Sabine Langie 2015-06-01 Full Text Available The comet assay is a versatile and sensitive method for measuring strand breaks in DNA. The first paper on this single-cell gel electrophoresis assay was published in 1984 by Ostling and Johanson (1984. This assay (with and without inclusion of lesion-specific enzymes is widely used as a biomarker assay in human population studies - primarily to measure DNA damage, but increasingly also to assess the capacity of cells for DNA repair. Ostling and Johanson were also the first to report experiments to measure DNA repair, by simply following the decrease of DNA damage over time after challenging cells with ionising radiation. However, this approach is time-consuming and laborious, and therefore not ideal for biomonitoring studies, which typically require high-throughput processing of many samples. As an alternative approach, the in vitro comet-based repair assay was developed: a cell extract is incubated with a DNA substrate containing specific lesions, and DNA incisions accumulate. The in vitro comet-based repair assay was first devised to measure base excision repair in lymphocytes (Collins et al., 2001. However, over the past decade it has been modified and improved to study incision of other lesions and thus other repair pathways, as well as being applied to tissue samples in addition to cell suspensions. The application of the in vitro repair assay in dietary intervention, environmental biomonitoring and animal studies will be discussed. 18. PARP-1: Friend or Foe of DNA Damage and Repair in Tumorigenesis? International Nuclear Information System (INIS) Oxidative stress induced by reactive oxygen species can result in DNA damage within cells and subsequently increase risk for carcinogenesis. This may be averted by repair of DNA damage through the base or nucleotide excision repair (BER/NER) pathways. PARP, a BER protein, is known for its role in DNA-repair. However, multiple lesions can occur within a small range of DNA, known as oxidative clustered DNA lesions (OCDLs), which are difficult to repair and may lead to the more severe DNA double-strand break (DSB). Inefficient DSB repair can then result in increased mutagenesis and neoplastic transformation. OCDLs occur more frequently within a variety of tumor tissues. Interestingly, PARP is highly expressed in several human cancers. Additionally, chronic inflammation may contribute to tumorigenesis through ROS-induced DNA damage. Furthermore, PARP can modulate inflammation through interaction with NFκB and regulating the expression of inflammatory signaling molecules. Thus, the upregulation of PARP may present a double-edged sword. PARP is needed to repair ROS-induced DNA lesions, but PARP expression may lead to increased inflammation via upregulation of NFκB signaling. Here, we discuss the role of PARP in the repair of oxidative damage versus the formation of OCDLs and speculate on the feasibility of PARP inhibition for the treatment and prevention of cancers by exploiting its role in inflammation 19. PARP-1: Friend or Foe of DNA Damage and Repair in Tumorigenesis? Energy Technology Data Exchange (ETDEWEB) Swindall, Amanda F.; Stanley, Jennifer A. [Department of Radiation Oncology Comprehensive Cancer Center, University of Alabama at Birmingham School of Medicine, 176F HSROC Suite 2232B, 1700 6th Avenue South, Birmingham, AL 35249 (United States); Yang, Eddy S., E-mail: [email protected] [Department of Radiation Oncology Comprehensive Cancer Center, University of Alabama at Birmingham School of Medicine, 176F HSROC Suite 2232B, 1700 6th Avenue South, Birmingham, AL 35249 (United States); Department of Cell, Developmental and Integrative Biology, University of Alabama at Birmingham, Birmingham, AL 35249 (United States); Department of Pharmacology and Toxicology, University of Alabama at Birmingham, Birmingham, AL 35249 (United States) 2013-07-26 Oxidative stress induced by reactive oxygen species can result in DNA damage within cells and subsequently increase risk for carcinogenesis. This may be averted by repair of DNA damage through the base or nucleotide excision repair (BER/NER) pathways. PARP, a BER protein, is known for its role in DNA-repair. However, multiple lesions can occur within a small range of DNA, known as oxidative clustered DNA lesions (OCDLs), which are difficult to repair and may lead to the more severe DNA double-strand break (DSB). Inefficient DSB repair can then result in increased mutagenesis and neoplastic transformation. OCDLs occur more frequently within a variety of tumor tissues. Interestingly, PARP is highly expressed in several human cancers. Additionally, chronic inflammation may contribute to tumorigenesis through ROS-induced DNA damage. Furthermore, PARP can modulate inflammation through interaction with NFκB and regulating the expression of inflammatory signaling molecules. Thus, the upregulation of PARP may present a double-edged sword. PARP is needed to repair ROS-induced DNA lesions, but PARP expression may lead to increased inflammation via upregulation of NFκB signaling. Here, we discuss the role of PARP in the repair of oxidative damage versus the formation of OCDLs and speculate on the feasibility of PARP inhibition for the treatment and prevention of cancers by exploiting its role in inflammation. 20. Overexpression of DNA ligase III in mitochondria protects cells against oxidative stress and improves mitochondrial DNA base excision repair DEFF Research Database (Denmark) Akbari, Mansour; Keijzers, Guido; Maynard, Scott; 2014-01-01 by rotenone. Our results suggest that the amount of DNA ligase III in mitochondria may be critical for cell survival following prolonged oxidative stress, and demonstrate a functional link between mitochondrial DNA damage and repair, cell survival upon oxidative stress, and removal of dysfunctional......Base excision repair (BER) is the most prominent DNA repair pathway in human mitochondria. BER also results in a temporary generation of AP-sites, single-strand breaks and nucleotide gaps. Thus, incomplete BER can result in the generation of DNA repair intermediates that can disrupt mitochondrial...... DNA replication and transcription and generate mutations. We carried out BER analysis in highly purified mitochondrial extracts from human cell lines U2OS and HeLa, and mouse brain using a circular DNA substrate containing a lesion at a specific position. We found that DNA ligation is significantly... 1. Nucleotide excision repair in yeast NARCIS (Netherlands) Eijk, Patrick van 2012-01-01 Nucleotide Excision Repair (NER) is a conserved DNA repair pathway capable of removing a broad spectrum of DNA damage. In human cells a defect in NER leads to the disorder Xeroderma pigmentosum (XP). The yeast Saccharomyces cerevisiae is an excellent model organism to study the mechanism of NER. The 2. Xeroderma pigmentosum, DNA repair and carcinogenesis International Nuclear Information System (INIS) The following topics are reviewed: Symptoms of xeroderma pigmentosum; xeroderma pigmentosum as a defect in the biochemistry of repair of radiation damage; major classes of DNA damage and repair mechanisms; excision repair in relation to biochemical steps and the XP defect; sensitivity of xeroderma pigmentosum cells; host-cell reactivation of UV-damaged viruses; excision of pyrimidine dimers from human cells; formation and sealing of single strand breaks during dimer excision; insertion of new bases to repair DNA; and DNA repair, carcinogens, and carcinogenesis 3. Ku80-deleted cells are defective at base excision repair Energy Technology Data Exchange (ETDEWEB) Li, Han [The University of Texas Health Science Center at San Antonio, The Institute of Biotechnology, The Department of Molecular Medicine, 15355 Lambda Drive, San Antonio, TX 78245-3207 (United States); Tumor Suppression Group, Spanish National Cancer Research Centre (CNIO), Madrid 28029 (Spain); Marple, Teresa [The University of Texas Health Science Center at San Antonio, The Institute of Biotechnology, The Department of Molecular Medicine, 15355 Lambda Drive, San Antonio, TX 78245-3207 (United States); Hasty, Paul, E-mail: [email protected] [The University of Texas Health Science Center at San Antonio, The Institute of Biotechnology, The Department of Molecular Medicine, 15355 Lambda Drive, San Antonio, TX 78245-3207 (United States); Tumor Suppression Group, Spanish National Cancer Research Centre (CNIO), Madrid 28029 (Spain) 2013-05-15 Graphical abstract: - Highlights: • Ku80-deleted cells are hypersensitive to ROS and alkylating agents. • Cells deleted for Ku80, but not Ku70 or Lig4, have reduced BER capacity. • OGG1 rescues hypersensitivity to H{sub 2}O{sub 2} and paraquat in Ku80-mutant cells. • Cells deleted for Ku80, but not Lig4, are defective at repairing AP sites. • Cells deleted for Ku80, but not Lig4 or Brca2 exon 27, exhibit increased PAR. - Abstract: Ku80 forms a heterodimer with Ku70, called Ku, that repairs DNA double-strand breaks (DSBs) via the nonhomologous end joining (NHEJ) pathway. As a consequence of deleting NHEJ, Ku80-mutant cells are hypersensitive to agents that cause DNA DSBs like ionizing radiation. Here we show that Ku80 deletion also decreased resistance to ROS and alkylating agents that typically cause base lesions and single-strand breaks (SSBs). This is unusual since base excision repair (BER), not NHEJ, typically repairs these types of lesions. However, we show that deletion of another NHEJ protein, DNA ligase IV (Lig4), did not cause hypersensitivity to these agents. In addition, the ROS and alkylating agents did not induce γ-H2AX foci that are diagnostic of DSBs. Furthermore, deletion of Ku80, but not Lig4 or Ku70, reduced BER capacity. Ku80 deletion also impaired BER at the initial lesion recognition/strand scission step; thus, involvement of a DSB is unlikely. Therefore, our data suggests that Ku80 deletion impairs BER via a mechanism that does not repair DSBs. 4. Role of ubiquitination in meiotic recombination repair Institute of Scientific and Technical Information of China (English) 2010-01-01 Programmed and unprogrammed double-strand breaks (DSBs) often arise from such physiological requirements as meiotic recombination, and exogenous insults, such as ionizing radiation (IR). Due to deleterious impacts on genome stability, DSBs must be appropriately processed and repaired in a regulatory manner. Recent investigations have indicated that ubiquitination is a critical factor in DNA damage response and meiotic recombination repair. This review summarizes the effects of proteins and complexes associated with ubiquitination with regard to homologous recombination (HR)-dependent DSB repair. 5. DNA damage response and repair data with pharmacological modulators of Tousled Directory of Open Access Journals (Sweden) Prakash Srinivasan Timiri Shanmugam 2016-06-01 Full Text Available Human Tousled kinase 1 (TLK1 plays an important role in chromatin remodeling, replication, and DNA damage response and repair. TLK1 activity is immediately, but transiently, downregulated after genotoxic insult, and its recovery is important for exit from checkpoint arrest and cell survival after radiation. The data in this article compliments research presented in the paper titled, “Tousled kinase activator, gallic acid, promotes DNA repair and suppresses radiation cytotoxicity in salivary gland cells” [1]. The identification of small molecule activators and inhibitors of TLK1 provided an opportunity to pharmacologically alter the protein׳s activity to elucidate its role in DNA damage response pathways. TLK1 effectors, gallic acid (GA and thioridazine (THD activate and inhibit the kinase, respectively, and the data report on the impact of these compounds and the significance of TLK1 to DNA break repair and the survival of human salivary acinar cells. 6. Mechanisms of DNA repair and radio-induced mutagenesis in higher eukaryotes; Mecanismes de reparation et mutagenese radio-induite chez les eucaryotes superieurs Energy Technology Data Exchange (ETDEWEB) Averbeck, D. [Centre Universitaire d' Orsay, Institut Curie, Section de Recherche, Lab. Raymond-Latarjet, UMR 2027 CNRS, 91 (France) 2000-10-01 7. Replication independent DNA double-strand break retention may prevent genomic instability Directory of Open Access Journals (Sweden) Pornthanakasem Wichai 2010-03-01 Full Text Available Abstract Background Global hypomethylation and genomic instability are cardinal features of cancers. Recently, we established a method for the detection of DNA methylation levels at sites close to endogenous DNA double strand breaks (EDSBs, and found that those sites have a higher level of methylation than the rest of the genome. Interestingly, the most significant differences between EDSBs and genomes were observed when cells were cultured in the absence of serum. DNA methylation levels on each genomic location are different. Therefore, there are more replication-independent EDSBs (RIND-EDSBs located in methylated genomic regions. Moreover, methylated and unmethylated RIND-EDSBs are differentially processed. Euchromatins respond rapidly to DSBs induced by irradiation with the phosphorylation of H2AX, γ-H2AX, and these initiate the DSB repair process. During G0, most DSBs are repaired by non-homologous end-joining repair (NHEJ, mediated by at least two distinct pathways; the Ku-mediated and the ataxia telangiectasia-mutated (ATM-mediated. The ATM-mediated pathway is more precise. Here we explored how cells process methylated RIND-EDSBs and if RIND-EDSBs play a role in global hypomethylation-induced genomic instability. Results We observed a significant number of methylated RIND-EDSBs that are retained within deacetylated chromatin and free from an immediate cellular response to DSBs, the γ-H2AX. When cells were treated with tricostatin A (TSA and the histones became hyperacetylated, the amount of γ-H2AX-bound DNA increased and the retained RIND-EDSBs were rapidly repaired. When NHEJ was simultaneously inhibited in TSA-treated cells, more EDSBs were detected. Without TSA, a sporadic increase in unmethylated RIND-EDSBs could be observed when Ku-mediated NHEJ was inhibited. Finally, a remarkable increase in RIND-EDSB methylation levels was observed when cells were depleted of ATM, but not of Ku86 and RAD51. Conclusions Methylated RIND-EDSBs are 8. Sequence Context Specific Mutagenesis and Base Excision Repair OpenAIRE Donigan, Katherine; Sweasy, Joann B. 2009-01-01 Base excision repair is critical for the maintenance of genome stability because it repairs at least 20,000 endogenously generated DNA lesions per cell per day. Several enzymes within the base excision repair pathway exhibit sequence context dependency during the excision and DNA synthesis steps of repair. New evidence is emerging that germ line and tumor-associated variants of enzymes in this repair pathway exhibit sequence context dependence that is different from their ancestral counterpar... 9. Rethinking Transcription Coupled DNA Repair OpenAIRE Kamarthapu, Venu; Nudler, Evgeny 2015-01-01 Nucleotide excision repair (NER) is an evolutionarily conserved, multistep process that can detect a wide variety of DNA lesions. Transcription coupled repair (TCR) is a sub-pathway of NER that repairs the transcribed DNA strand faster than the rest of the genome. RNA polymerase (RNAP) stalled at DNA lesions mediates the recruitment of NER enzymes to the damage site. In this review we focus on a newly identified bacterial TCR pathway in which the NER enzyme UvrD, in conjunction with NusA, pla... 10. Rethinking transcription coupled DNA repair. Science.gov (United States) Kamarthapu, Venu; Nudler, Evgeny 2015-04-01 Nucleotide excision repair (NER) is an evolutionarily conserved, multistep process that can detect a wide variety of DNA lesions. Transcription coupled repair (TCR) is a subpathway of NER that repairs the transcribed DNA strand faster than the rest of the genome. RNA polymerase (RNAP) stalled at DNA lesions mediates the recruitment of NER enzymes to the damage site. In this review we focus on a newly identified bacterial TCR pathway in which the NER enzyme UvrD, in conjunction with NusA, plays a major role in initiating the repair process. We discuss the tradeoff between the new and conventional models of TCR, how and when each pathway operates to repair DNA damage, and the necessity of pervasive transcription in maintaining genome integrity. PMID:25596348 11. DNA repair and radiation sensitivity in mammalian cells International Nuclear Information System (INIS) Ionizing radiation induces various types of damage in mammalian cells including DNA single-strand breaks, DNA double-strand breaks (DSB), DNA-protein cross links, and altered DNA bases. Although human cells can repair many of these lesions there is little detailed knowledge of the nature of the genes and the encoded enzymes that control these repair processes. We report here on the cellular and genetic analyses of DNA double-strand break repair deficient mammalian cells. It has been well established that the DNA double-strand break is one of the major lesions induced by ionizing radiation. Utilizing rodent repair-deficient mutant, we have shown that the genes responsible for DNA double-strand break repair are also responsible for the cellular expression of radiation sensitivity. The molecular genetic analysis of DSB repair in rodent/human hybrid cells indicate that at least 6 different genes in mammalian cells are responsible for the repair of radiation-induced DNA double-strand breaks. Mapping and the prospect of cloning of human radiation repair genes are reviewed. Understanding the molecular and genetic basis of radiation sensitivity and DNA repair in man will provide a rational foundation to predict the individual risk associated with radiation exposure and to prevent radiation-induced genetic damage in the human population 12. DNA Polymerases λ and β: The Double-Edged Swords of DNA Repair. Science.gov (United States) Mentegari, Elisa; Kissova, Miroslava; Bavagnoli, Laura; Maga, Giovanni; Crespan, Emmanuele 2016-01-01 DNA is constantly exposed to both endogenous and exogenous damages. More than 10,000 DNA modifications are induced every day in each cell's genome. Maintenance of the integrity of the genome is accomplished by several DNA repair systems. The core enzymes for these pathways are the DNA polymerases. Out of 17 DNA polymerases present in a mammalian cell, at least 13 are specifically devoted to DNA repair and are often acting in different pathways. DNA polymerases β and λ are involved in base excision repair of modified DNA bases and translesion synthesis past DNA lesions. Polymerase λ also participates in non-homologous end joining of DNA double-strand breaks. However, recent data have revealed that, depending on their relative levels, the cell cycle phase, the ratio between deoxy- and ribo-nucleotide pools and the interaction with particular auxiliary proteins, the repair reactions carried out by these enzymes can be an important source of genetic instability, owing to repair mistakes. This review summarizes the most recent results on the ambivalent properties of these enzymes in limiting or promoting genetic instability in mammalian cells, as well as their potential use as targets for anticancer chemotherapy. PMID:27589807 13. DNA Polymerases λ and β: The Double-Edged Swords of DNA Repair Directory of Open Access Journals (Sweden) Elisa Mentegari 2016-08-01 Full Text Available DNA is constantly exposed to both endogenous and exogenous damages. More than 10,000 DNA modifications are induced every day in each cell’s genome. Maintenance of the integrity of the genome is accomplished by several DNA repair systems. The core enzymes for these pathways are the DNA polymerases. Out of 17 DNA polymerases present in a mammalian cell, at least 13 are specifically devoted to DNA repair and are often acting in different pathways. DNA polymerases β and λ are involved in base excision repair of modified DNA bases and translesion synthesis past DNA lesions. Polymerase λ also participates in non-homologous end joining of DNA double-strand breaks. However, recent data have revealed that, depending on their relative levels, the cell cycle phase, the ratio between deoxy- and ribo-nucleotide pools and the interaction with particular auxiliary proteins, the repair reactions carried out by these enzymes can be an important source of genetic instability, owing to repair mistakes. This review summarizes the most recent results on the ambivalent properties of these enzymes in limiting or promoting genetic instability in mammalian cells, as well as their potential use as targets for anticancer chemotherapy. 14. Radiation damage and its repair in non-sporulating bacteria International Nuclear Information System (INIS) A review is given of radiation damage and its repair in non-sporulating bacteria. The identification and measurement of radiation damage in the DNA of the bacteria after exposure to ultraviolet radiation and ionizing radiation is described. Measuring the extent of DNA repair and ways of isolating repair mutants are also described. The DNA repair mechanisms for UV-induced damage are discussed including photoreactivation repair, excision repair, post-replication recombination repair and induced error-prone repair. The DNA repair mechanisms for ionizing radiation damage are also discussed including the repair of both single and double-strand breaks. Other aspects discussed include the effects of growth, irradiation medium and recovery medium on survival, DNA repair in humans, the commercial use of UV and ionizing radiations and the future of ionizing irradiation as a food treatment process. (U.K.) 15. 46 CFR 176.704 - Breaking of safety valve seals. Science.gov (United States) 2010-10-01 ... 46 Shipping 7 2010-10-01 2010-10-01 false Breaking of safety valve seals. 176.704 Section 176.704... TONS) INSPECTION AND CERTIFICATION Repairs and Alterations § 176.704 Breaking of safety valve seals... the seal on a boiler safety valve on a vessel is broken.... 16. 46 CFR 115.704 - Breaking of safety valve seals. Science.gov (United States) 2010-10-01 ... 46 Shipping 4 2010-10-01 2010-10-01 false Breaking of safety valve seals. 115.704 Section 115.704... CERTIFICATION Repairs and Alterations § 115.704 Breaking of safety valve seals. The owner, managing operator, or master shall notify the cognizant OCMI as soon as practicable after the seal on a boiler safety valve... Science.gov (United States) Bladder birth defect repair; Everted bladder repair; Exposed bladder repair; Repair of bladder exstrophy ... Bladder exstrophy repair involves two surgeries. The first surgery is to repair the bladder and the second one is to attach ... 18. Ku Regulates Signaling to DNA Damage Response Pathways through the Ku70 von Willebrand A Domain OpenAIRE Fell, Victoria L.; Schild-Poulter, Caroline 2012-01-01 The Ku heterodimer (Ku70/Ku80) is a main component of the nonhomologous end-joining (NHEJ) pathway that repairs DNA double-strand breaks (DSBs). Ku binds the broken DNA end and recruits other proteins to facilitate the processing and ligation of the broken end. While Ku interacts with many proteins involved in DNA damage/repair-related functions, few interactions have been mapped to the N-terminal von Willebrand A (vWA) domain, a predicted protein interaction domain. The mutagenesis of Ku70 v... 19. Membrane receptor signaling and control of DNA repair after exposure to ionizing radiation International Nuclear Information System (INIS) Accumulated evidence indicates that activation of erbB family of receptors, when mutated or over-expressed, mediates chemo and radiotherapy resistance. In this context signaling pathways down-stream of epidermal growth factor receptor (EGFR), when abnormally activated, invoke cell survival mechanisms, which leads to resistance against radiation. In several reports it has been demonstrated that molecular targeting of EGFR signaling enhances the cytotoxic effects of radiotherapy. The radiosensitizing effects of EGFR antagonists correlate with a suppression of the ability of tumor cells to repair radiation-induced DNA double strand breaks (DNA-DSBs) through non-homologous endjoining repair pathway (NHEJ). The purpose of this review is to highlight the function of EGFR and erbB2 receptors on signaling pathways, i.e. PI3K/Akt activated by ionizing radiation (IR) and involved in repair of DNA-DSB which can explain the radiosensitizing effects of related antagonists. Advances in understanding the mechanism of erbB-signaling in regulating DNA-DSB repair will promote translational approaches to test new strategies for clinically applicable molecular targeting. (orig.) 20. DNA repair processes and the shape of dose-response curves for induced genetic changes in yeast International Nuclear Information System (INIS) Gene conversion is a genetic change which requires a functional recombinational repair system. Dose-response curves for induced gene conversion in D7 strains of diploid S. cerevisiae appear to be one-hit (effect proportional to dose) for ionizing radiation or mitomycin C, but are closer to two-hit characteristics (effect proportional to square of dose) for 254 nm UV radiation or nitrous acid at sublethal doses of these agents. These data are suggest that recombinational repair in normal cells is stimulated by coincident or double-strand damage in the DNA: for example, a double-strand break produced by ionizing radiation, an interstrand cross-link produced by mitomycin C, or a double strand break produced by ''overlapping'' excision repair of two pyrimidine dimers located on opposite DNA strands within about 100 base pairs of each other. Other initiating mechanisms for UV-induced conversion may predominate when the excision repair pathway is not available (as in rad 3 mutants). It is of interest that the shapes of the dose-response curves for back mutations affecting the iIvl locus in repair - proficient D7 strains are similar to those observed for gene conversions induced by γ-rays, UV light and nitrous acid, even though the relative yields of convertants and back mutations vary considerably from one agent to another 1. The key residue for SSB-RecO interaction is dispensable for Deinococcus radiodurans DNA repair in vivo. Science.gov (United States) Cheng, Kaiying; Xu, Xin; Zhao, Ye; Wang, Liangyan; Xu, Guangzhi; Hua, Yuejin 2014-05-01 The RecFOR DNA repair pathway is one of the major RecA-dependent recombinatorial repair pathways in bacteria and plays an important role in double-strand breaks repair. RecO, one of the major recombination mediator proteins in the RecFOR pathway, has been shown to assist RecA loading onto single-stranded binding protein (SSB) coated single-stranded DNA (ssDNA). However, it has not been characterized whether the protein-protein interaction between RecO and SSB contributes to that process in vivo. Here, we identified the residue arginine-121 of Deinococcus radiodurans RecO (drRecO-R121) as the key residue for RecO-SSB interaction. The substitution of drRecO-R121 with alanine greatly abolished the binding of RecO to SSB but not the binding to RecR. Meanwhile, SSB-coated ssDNA annealing activity was also compromised by the mutation of the residue of drRecO. However, the drRecO-R121A strain showed only modest sensitivity to DNA damaging agents. Taking these data together, arginine-121 of drRecO is the key residue for SSB-RecO interaction, which may not play a vital role in the SSB displacement and RecA loading process of RecFOR DNA repair pathway in vivo. PMID:24681881 2. The key residue for SSB-RecO interaction is dispensable for Deinococcus radiodurans DNA repair in vivo. Science.gov (United States) Cheng, Kaiying; Xu, Xin; Zhao, Ye; Wang, Liangyan; Xu, Guangzhi; Hua, Yuejin 2014-05-01 The RecFOR DNA repair pathway is one of the major RecA-dependent recombinatorial repair pathways in bacteria and plays an important role in double-strand breaks repair. RecO, one of the major recombination mediator proteins in the RecFOR pathway, has been shown to assist RecA loading onto single-stranded binding protein (SSB) coated single-stranded DNA (ssDNA). However, it has not been characterized whether the protein-protein interaction between RecO and SSB contributes to that process in vivo. Here, we identified the residue arginine-121 of Deinococcus radiodurans RecO (drRecO-R121) as the key residue for RecO-SSB interaction. The substitution of drRecO-R121 with alanine greatly abolished the binding of RecO to SSB but not the binding to RecR. Meanwhile, SSB-coated ssDNA annealing activity was also compromised by the mutation of the residue of drRecO. However, the drRecO-R121A strain showed only modest sensitivity to DNA damaging agents. Taking these data together, arginine-121 of drRecO is the key residue for SSB-RecO interaction, which may not play a vital role in the SSB displacement and RecA loading process of RecFOR DNA repair pathway in vivo. 3. Autophosphorylation of the DNA-dependent protein kinase catalytic subunit is required for rejoining of DNA double-strand breaks OpenAIRE Chan, Doug W.; Chen, Benjamin Ping-Chi; Prithivirajsingh, Sheela; Kurimasa, Akihiro; Story, Michael D.; Qin, Jun; Chen, David J. 2002-01-01 Nonhomologous end-joining (NHEJ) is the predominant pathway that repairs DNA double-strand breaks (DSBs) in mammalian cells. The DNA-dependent protein kinase (DNA-PK), consisting of Ku and DNA-PK catalytic subunit (DNA-PKcs), is activated by DNA in vitro and is required for NHEJ. We report that DNA-PKcs is autophosphorylated at Thr2609 in vivo in a Ku-dependent manner in response to ionizing radiation. Phosphorylated DNA-PKcs colocalizes with both γ-H2AX and 53BP1 after DNA damage. Mutation o... 4. Poly(ADP-ribose polymerase (PARP-1 is not involved in DNA double-strand break recovery Directory of Open Access Journals (Sweden) Fernet Marie 2003-07-01 Full Text Available Abstract Background The cytotoxicity and the rejoining of DNA double-strand breaks induced by γ-rays, H2O2 and neocarzinostatin, were investigated in normal and PARP-1 knockout mouse 3T3 fibroblasts to determine the role of poly(ADP-ribose polymerase (PARP-1 in DNA double-strand break repair. Results PARP-1-/- were considerably more sensitive than PARP-1+/+ 3T3s to induced cell kill by γ-rays and H2O2. However, the two cell lines did not show any significant difference in the susceptibility to neocarzinostatin below 1.5 nM drug. Restoration of PARP-1 expression in PARP-1-/- 3T3s by retroviral transfection of the full PARP-1 cDNA did not induce any change in neocarzinostatin response. Moreover the incidence and the rejoining kinetics of neocarzinostatin-induced DNA double-strand breaks were identical in PARP-1+/+ and PARP-1-/- 3T3s. Poly(ADP-ribose synthesis following γ-rays and H2O2 was observed in PARP-1-proficient cells only. In contrast neocarzinostatin, even at supra-lethal concentration, was unable to initiate PARP-1 activation yet it induced H2AX histone phosphorylation in both PARP1+/+ and PARP-1-/- 3T3s as efficiently as γ-rays and H2O2. Conclusions The results show that PARP-1 is not a major determinant of DNA double-strand break recovery with either strand break rejoining or cell survival as an endpoint. Even though both PARP-1 and ATM activation are major determinants of the cell response to γ-rays and H2O2, data suggest that PARP-1-dependent poly(ADP-ribose synthesis and ATM-dependent H2AX phosphorylation, are not inter-related in the repair pathway of neocarzinostatin-induced DNA double-strand breaks. 5. An essential role for CtIP in chromosomal translocation formation through an alternative end-joining pathway OpenAIRE Zhang, Yu; Jasin, Maria 2010-01-01 Chromosomal translocations arise from the misjoining of DNA breaks, but the identity of the DNA repair factors and activities involved in their formation has been elusive. Here we show that depletion of CtIP, a DNA end-resection factor, results in a substantial decrease in chromosomal translocation frequency in mouse cells. Moreover, microhomology usage, a signature of the alternative nonhomologous end-joining pathway (alt-NHEJ), is significantly lower in translocation breakpoint junctions re... 6. DNA repair in Chromobacterium violaceum. Science.gov (United States) Duarte, Fábio Teixeira; Carvalho, Fabíola Marques de; Bezerra e Silva, Uaska; Scortecci, Kátia Castanho; Blaha, Carlos Alfredo Galindo; Agnez-Lima, Lucymara Fassarella; Batistuzzo de Medeiros, Silvia Regina 2004-03-31 Chromobacterium violaceum is a Gram-negative beta-proteobacterium that inhabits a variety of ecosystems in tropical and subtropical regions, including the water and banks of the Negro River in the Brazilian Amazon. This bacterium has been the subject of extensive study over the last three decades, due to its biotechnological properties, including the characteristic violacein pigment, which has antimicrobial and anti-tumoral activities. C. violaceum promotes the solubilization of gold in a mercury-free process, and has been used in the synthesis of homopolyesters suitable for the production of biodegradable polymers. The complete genome sequence of this organism has been completed by the Brazilian National Genome Project Consortium. The aim of our group was to study the DNA repair genes in this organism, due to their importance in the maintenance of genomic integrity. We identified DNA repair genes involved in different pathways in C. violaceum through a similarity search against known sequences deposited in databases. The phylogenetic analyses were done using programs of the PHILYP package. This analysis revealed various metabolic pathways, including photoreactivation, base excision repair, nucleotide excision repair, mismatch repair, recombinational repair, and the SOS system. The similarity between the C. violaceum sequences and those of Neisserie miningitidis and Ralstonia solanacearum was greater than that between the C. violaceum and Escherichia coli sequences. The peculiarities found in the C. violaceum genome were the absence of LexA, some horizontal transfer events and a large number of repair genes involved with alkyl and oxidative DNA damage. 7. Base excision repair in sugarcane Directory of Open Access Journals (Sweden) Agnez-Lima Lucymara F. 2001-01-01 Full Text Available DNA damage can be induced by a large number of physical and chemical agents from the environment as well as compounds produced by cellular metabolism. This type of damage can interfere with cellular processes such as replication and transcription, resulting in cell death and/or mutations. The low frequency of mutagenesis in cells is due to the presence of enzymatic pathways which repair damaged DNA. Several DNA repair genes (mainly from bacteria, yeasts and mammals have been cloned and their products characterized. The high conservation, especially in eukaryotes, of the majority of genes related to DNA repair argues for their importance in the maintenance of life on earth. In plants, our understanding of DNA repair pathways is still very poor, the first plant repair genes having only been cloned in 1997 and the mechanisms of their products have not yet been characterized. The objective of our data mining work was to identify genes related to the base excision repair (BER pathway, which are present in the database of the Sugarcane Expressed Sequence Tag (SUCEST Project. This search was performed by tblastn program. We identified sugarcane clusters homologous to the majority of BER proteins used in the analysis and a high degree of conservation was observed. The best results were obtained with BER proteins from Arabidopsis thaliana. For some sugarcane BER genes, the presence of more than one form of mRNA is possible, as shown by the occurrence of more than one homologous EST cluster. 8. Genetics of repair of radiation damage to DNA in bacteria International Nuclear Information System (INIS) 9. Craniosynostosis repair Science.gov (United States) ... will be asleep and will not feel pain. Traditional surgery is called open repair. It includes these ... helps keep the swelling down. Talking, singing, playing music, and telling stories may help soothe your child. ... 10. Mutagenicity of 2-amino-3-methylimidazo[4,5-f]quinoline in colon and liver of Big Blue rats: role of DNA adducts, strand breaks, DNA repair and oxidative stress DEFF Research Database (Denmark) Moller, P.; Wallin, H.; Vogel, U.; 2002-01-01 The contribution of oxidative stress, different types of DNA damage and expression of DNA repair enzymes in colon and liver mutagenesis induced by 2-amino-3-methylimidazo [4,5-f]quinoline (IQ) was investigated in four groups of six Big Blue rats fed diets with 0, 20, 70, and 200 mg IQ/kg for 3....... Investigations of oxidative stress biomarkers produced inconclusive results. Oxidative DNA damage detected by the endonuclease III enzyme and 7-hydro-8-oxo-2'-deoxyguanosine in colon, liver and/or urine was unaltered by IQ. However, there was increased level of gamma-glutamyl semialdehyde in liver proteins......, indicating a higher rate of protein oxidation in the liver following IQ administration. In plasma and erythrocytes there were unaltered levels of oxidized protein, malondialdehyde, and antioxidant enzyme activities (superoxide dismutase, glutathione peroxidase, catalase, glutathione reductase) indicating... 11. Mutagenicity of 2-amino-3-methylimidazo[4,5-f]quinoline in colon and liver of Big Blue Rats: role of DNA adducts, strand breaks, DNA repair and oxidative stress DEFF Research Database (Denmark) Møller, Peter; Wallin, Håkan; Vogel, Ulla; 2002-01-01 The contribution of oxidative stress, different types of DNA damage and expression of DNA repair enzymes in colon and liver mutagenesis induced by 2-amino-3-methylimidazo [4,5-f]quinoline (IQ) was investigated in four groups of six Big Blue rats fed diets with 0, 20, 70, and 200 mg IQ/kg for 3....... Investigations of oxidative stress biomarkers produced inconclusive results. Oxidative DNA damage detected by the endonuclease III enzyme and 7-hydro-8-oxo-2'-deoxyguanosine in colon, liver and/or urine was unaltered by IQ. However, there was increased level of gamma-glutamyl semialdehyde in liver proteins......, indicating a higher rate of protein oxidation in the liver following IQ administration. In plasma and erythrocytes there were unaltered levels of oxidized protein, malondialdehyde, and antioxidant enzyme activities (superoxide dismutase, glutathione peroxidase, catalase, glutathione reductase) indicating... 12. Long repair replication patches are produced by the short-patch pathway in a uvrD252 (recL152) mutant of Escherichia coli K-12. OpenAIRE Rothman, R H; Fried, B 1984-01-01 The uvrD252 mutation leads to increased UV sensitivity, diminished dimer excision and host cell reactivation capacity, and an increase in the average patch size after repair replication. A recA56 uvrD252 double mutant was far more resistant to UV than was a recA56 uvrB5 double mutant. Its host cell reactivation capacity was identical to that of uvrD252 single mutant and was far greater than that of the uvrB5 single mutant. The strain showed no Weigle reactivation. From these results, we concl... 13. Oxidative stress alters base excision repair pathway and increases apoptotic response in Apurinic/apyrimidinic endonuclease 1/Redox factor-1 haploinsufficient mice OpenAIRE Unnikrishnan, Archana; Raffoul, Julian J.; Patel, Hiral V.; Prychitko, Thomas M.; Anyangwe, Njwen; Meira, Lisiane B.; Friedberg, Errol C.; Cabelof, Diane C.; Heydari, Ahmad R. 2009-01-01 Apurinic/apyrimidinic endonuclease 1/redox factor-1 (APE1/Ref-1) is the redox regulator of multiple stress-inducible transcription factors, such as NF-κB, and the major 5’-endonuclease in base excision repair (BER). We utilized mice containing heterozygous gene-targeted deletion of APE1/Ref-1 (Apex+/-) to determine the impact of APE1/Ref-1 haploinsufficiency on the processing of oxidative DNA damage induced by 2-nitropropane (2-NP) in the liver tissue of mice. APE1/Ref-1 haploinsufficiency re... 14. A novel small molecule inhibitor of the DNA repair protein Ku70/80. Science.gov (United States) Weterings, Eric; Gallegos, Alfred C; Dominick, Lauren N; Cooke, Laurence S; Bartels, Trace N; Vagner, Josef; Matsunaga, Terry O; Mahadevan, Daruka 2016-07-01 Non-Homologous End-Joining (NHEJ) is the predominant pathway for the repair of DNA double strand breaks (DSBs) in human cells. The NHEJ pathway is frequently upregulated in several solid cancers as a compensatory mechanism for a separate DSB repair defect or for innate genomic instability, making this pathway a powerful target for synthetic lethality approaches. In addition, NHEJ reduces the efficacy of cancer treatment modalities which rely on the introduction of DSBs, like radiation therapy or genotoxic chemotherapy. Consequently, inhibition of the NHEJ pathway can modulate a radiation- or chemo-refractory disease presentation. The Ku70/80 heterodimer protein plays a pivotal role in the NHEJ process. It possesses a ring-shaped structure with high affinity for DSBs and serves as the first responder and central scaffold around which the rest of the repair complex is assembled. Because of this central position, the Ku70/80 dimer is a logical target for the disruption of the entire NHEJ pathway. Surprisingly, specific inhibitors of the Ku70/80 heterodimer are currently not available. We here describe an in silico, pocket-based drug discovery methodology utilizing the crystal structure of the Ku70/80 heterodimer. We identified a novel putative small molecule binding pocket and selected several potential inhibitors by computational screening. Subsequent biological screening resulted in the first identification of a compound with confirmed Ku-inhibitory activity in the low micro-molar range, capable of disrupting the binding of Ku70/80 to DNA substrates and impairing Ku-dependent activation of another NHEJ factor, the DNA-PKCS kinase. Importantly, this compound synergistically sensitized human cell lines to radiation treatment, indicating a clear potential to diminish DSB repair. The chemical scaffold we here describe can be utilized as a lead-generating platform for the design and development of a novel class of anti-cancer agents. PMID:27130816 15. The BRCA1/2 pathway prevents hematologic cancers in addition to breast and ovarian cancers OpenAIRE Friedenson Bernard 2007-01-01 Abstract Background The present study was designed to test the hypothesis that inactivation of virtually any component within the pathway containing the BRCA1 and BRCA2 proteins would increase the risks for lymphomas and leukemias. In people who do not have BRCA1 or BRCA2 gene mutations, the encoded proteins prevent breast/ovarian cancer. However BRCA1 and BRCA2 proteins have multiple functions including participating in a pathway that mediates repair of DNA double strand breaks by error-free... 16. Use of metabolic inhibitors to investigate the excision repair of pyrimidine dimers and non-dimer DNA damages induced in human and ICR 2A frog cells by solar ultraviolet radiation International Nuclear Information System (INIS) ICR 2A frog and normal human skin fibroblasts were exposed to either 5J/m2 of 254 nm UV or 50 kJ/m2 of the Mylar-filtered solar UV wavelengths produced by a fluorescent sunlamp. Following these approximately equitoxic treatments, cells were incubated in medium containing the DNA synthesis inhibitors hydroxyurea (HU) and 1-β-D-arabinofuranosyl cytosine (ara C0 for 0-20 min (human fibroblasts) or 0-4 h (frog cells) to accumulate DNA breaks resulting from enzymatic incision during excision repair. It was found that breaks were formed in human cells at about a 200-fold-higher rate compared with the ICR 2A cells indicating a relatively low capacity for excision repair in the frog cells. In addition, the rate of DNA break formation in solar UV-irradiated cells was only one-third of the level detected in 254 nm-irradiated cells. This result is consistent with the conclusion that the pathway(s) involved in the repair of solar UV-induced DNA damages differs from the repair of lesions produced in cells exposed to 254 nm UV. (author) 17. Formation of radiation-induced DNA breaks: the ratio of double-strand breaks to single-strand breaks International Nuclear Information System (INIS) Ionizing radiation causes the formation of strand breaks in cellular DNA, as well as other types of lesions in the chromatin of cells. Some of the earliest investigations of the molecular basis of radiation-induced damage and the implications of enzymatic repair were done by Dr. H. S. Kaplan. Because it is difficult to assay for DNA lesions in the large mammalian genome, the authors have developed a method of assaying for DNA double-strand breaks in the supercoiled nucleosome-complexed Simian virus 40 (SV40) genome, irradiated intracellularly. In this communication they present their measurements of the DNA double-strand breaks (DSBs) to single-strand breaks (SSBs) ratio obtained from the intracellularly irradiated SV40 genome. After cobalt gamma ray and X ray irradiations, this ratio is about 1/10. Their methods and results are compared with pertinent data in the literature. If the DSBs/SSBs ratio of 1/10 for cellular chromatin is correct, a substantial number of DNA double-strand breaks are formed in a mammalian cell after moderate doses (1 Gy) of radiation. The implications of different types of DNA double-strand breaks are discussed 18. Pectus excavatum repair Science.gov (United States) Funnel chest repair; Chest deformity repair; Sunken chest repair; Cobbler's chest repair; Nuss repair; Ravitch repair ... There are two types of surgery to repair this condition -- open surgery ... surgery is done while the child is in a deep sleep and pain- ... 19. DNA damage and repair in human cells exposed to sunlight International Nuclear Information System (INIS) Cultured human cells were treated with direct sunlight under conditions which minimised the hypertonic, hyperthermic and fixative effects of solar radiation. Sunlight produced similar levels of DNA strand breaks as equitoxic 254 nm UV in two fibroblast strains and a melanoma cell line, but DNA repair synthesis and inhibition of semiconservative DNA synthesis and of DNA chain elongation were significantly less for sunlight-exposed cells. DNA breaks induced by sunlight were removed more rapidly. Thus, the repair of solar damage differs considerably from 254 nm UV repair. Glass-filtered sunlight (>320 nm) was not toxic to cells and did not induce repair synthesis but gave a low level of short-lived DNA breaks and some inhibition of DNA chain elongation; thymidine uptake was enhanced. Filtered sunlight slightly enhanced UV-induced repair synthesis and UV toxicity; photoreactivation of UV damage was not found. Attempts to transform human fibroblasts using sunlight, with or without phorbol ester, were unsuccessful. (author) 20. Targeting telomerase and DNA repair in human cancers International Nuclear Information System (INIS) Telomerase reactivation is essential for telomere maintenance in human cancer cells ensuring indefinite proliferation. Targeting telomere homeostasis has become one of the promising strategies in the therapeutic management of tumours. One major potential drawback, however, is the time lag between telomerase inhibition and critically shortened telomeres triggering cell death, allowing cancer cells to acquire drug resistance. Numerous studies over the last decade have highlighted the role of DNA repair proteins such as Poly (ADP-Ribose) Polymerase-1 (PARP-1), and DNA-dependent protein kinase (DNA-PKcs) in the maintenance of telomere homoeostasis. Dysfunctional telomeres, resulting from the loss of telomeric DNA repeats or the loss of function of telomere-associated proteins trigger DNA damage responses similar to that observed for double strand breaks. We have been working on unravelling such synthetic lethality in cancer cells and this talk would be on one such recently concluded study that demonstrates that inhibition of DNA repair pathways, i.e., NHEJ pathway and that of telomerase could be an alternative strategy to enhance anti-tumour effects and circumvent the possibility of drug resistance. (author) 1. Arabidopsis DNA polymerase lambda mutant is mildly sensitive to DNA double strand breaks but defective in integration ofa transgene. Directory of Open Access Journals (Sweden) Tomoyuki eFurukawa 2015-05-01 Full Text Available The DNA double-strand break (DSB is a critical type of damage, and can be induced by both endogenous sources (e.g. errors of oxidative metabolism, transposable elements, programmed meiotic breaks, or perturbation of the DNA replication fork and exogenous sources (e.g. ionizing radiation or radiomimetic chemicals. Although higher plants, like mammals, are thought to preferentially repair DSBs via nonhomologous end joining (NHEJ, much remains unclear about plant DSB repair pathways. Our reverse genetic approach suggests that DNA polymerase λ is involved in DSB repair in Arabidopsis. The Arabidopsis T-DNA insertion mutant (atpolλ-1 displayed sensitivity to both gamma-irradiation and treatment with radiomimetic reagents, but not to other DNA damaging treatments. The atpolλ-1 mutant showed a moderate sensitivity to DSBs, while Arabidopsis Ku70 and DNA ligase 4 mutants (atku70-3 and atlig4-2, both of which play critical roles in NHEJ, exhibited a hypersensitivity to these treatments. The atpolλ-1/atlig4-2 double mutant exhibited a higher sensitivity to DSBs than each single mutant, but the atku70/atpolλ-1 showed similar sensitivity to the atku70-3 mutant. We showed that transcription of the DNA ligase 1, DNA ligase 6, and Wee1 genes was quickly induced by BLM in several NHEJ deficient mutants in contrast to wild-type. Finally, the T-DNA transformation efficiency dropped in NHEJ deficient mutants and the lowest transformation efficiency was scored in the atpolλ-1/atlig4-2 double mutant. These results imply that AtPolλ is involved in both DSB repair and DNA damage response pathway. 2. Break-induced replication requires DNA damage-induced phosphorylation of Pif1 and leads to telomere lengthening. Directory of Open Access Journals (Sweden) Yulia Vasianovich 2014-10-01 Full Text Available Broken replication forks result in DNA breaks that are normally repaired via homologous recombination or break induced replication (BIR. Mild insufficiency in the replicative ligase Cdc9 in budding yeast Saccharomyces cerevisiae resulted in a population of cells with persistent DNA damage, most likely due to broken replication forks, constitutive activation of the DNA damage checkpoint and longer telomeres. This telomere lengthening required functional telomerase, the core DNA damage signaling cascade Mec1-Rad9-Rad53, and the components of the BIR repair pathway - Rad51, Rad52, Pol32, and Pif1. The Mec1-Rad53 induced phosphorylation of Pif1, previously found necessary for inhibition of telomerase at double strand breaks, was also important for the role of Pif1 in BIR and telomere elongation in cdc9-1 cells. Two other mutants with impaired DNA replication, cdc44-5 and rrm3Δ, were similar to cdc9-1: their long telomere phenotype was dependent on the Pif1 phosphorylation locus. We propose a model whereby the passage of BIR forks through telomeres promotes telomerase activity and leads to telomere lengthening. 3. Rad18 is required for functional interactions between FANCD2, BRCA2, and Rad51 to repair DNA topoisomerase 1-poisons induced lesions and promote fork recovery Science.gov (United States) Tripathi, Kaushlendra; Mani, Chinnadurai; Clark, David W; Palle, Komaraiah 2016-01-01 Camptothecin (CPT) and its analogues are chemotherapeutic agents that covalently and reversibly link DNA Topoisomerase I to its nicked DNA intermediate eliciting the formation of DNA double strand breaks (DSB) during replication. The repair of these DSB involves multiple DNA damage response and repair proteins. Here we demonstrate that CPT-induced DNA damage promotes functional interactions between BRCA2, FANCD2, Rad18, and Rad51 to repair the replication-associated DSB through homologous recombination (HR). Loss of any of these proteins leads to equal disruption of HR repair, causes chromosomal aberrations and sensitizes cells to CPT. Rad18 appears to function upstream in this repair pathway as its downregulation prevents activation of FANCD2, diminishes BRCA2 and Rad51 protein levels, formation of nuclear foci of all three proteins and recovery of stalled or collapsed replication forks in response to CPT. Taken together this work further elucidates the complex interplay of DNA repair proteins in the repair of replication-associated DSB. PMID:26871286 4. Femoral hernia repair Science.gov (United States) Femorocele repair; Herniorrhaphy; Hernioplasty - femoral ... During surgery to repair the hernia, the bulging tissue is pushed back in. The weakened area is sewn closed or strengthened. This repair ... 5. Undescended testicle repair Science.gov (United States) Orchidopexy; Inguinal orchidopexy; Orchiopexy; Repair of undescended testicle; Cryptorchidism repair ... first year of life without treatment. Undescended testicle repair surgery is recommended for patients whose testicles do ... 6. A Stylistic Analysis of Break,Break,Break Institute of Scientific and Technical Information of China (English) 李瑶 2015-01-01 Break, Break, Break is a poem by Alfred Lord Tennyson, the Poet Laureate during the Queen Victoria's reign. This exquisite little poem is wel known for the poet's grief-stricken feelings and heart-broken emotions over the premature death of his best friend, Arthur Henry Halam. Most of the previous studies on this poem focus on the emotional level to consider it as an elegy, expressing sorrow and lamentation for the death of a particular person. However, in order to have a deep understanding in general, this paper analyzes the poem based on the stylistic theory, concerning on the lexical level and the semantic level. It aims at helping the readers to cultivate a sense of appropriateness, to sharpen the understanding and appreciation of literary works and to achieve adaptation in translation. 7. Multiple host-cell recombination pathways act in Agrobacterium-mediated transformation of plant cells. Science.gov (United States) Mestiri, Imen; Norre, Frédéric; Gallego, Maria E; White, Charles I 2014-02-01 Using floral-dip, tumorigenesis and root callus transformation assays of both germline and somatic cells, we present here results implicating the four major non-homologous and homologous recombination pathways in Agrobacterium-mediated transformation of Arabidopsis thaliana. All four single mutant lines showed similar mild reductions in transformability, but knocking out three of four pathways severely compromised Agrobacterium-mediated transformation. Although integration of T-DNA into the plant genome is severely compromised in the absence of known DNA double-strand break repair pathways, it does still occur, suggesting the existence of other pathways involved in T-DNA integration. Our results highlight the functional redundancy of the four major plant recombination pathways in transformation, and provide an explanation for the lack of strong effects observed in previous studies on the roles of plant recombination functions in transformation. 8. Polymorphisms in XRCC5, XRCC6, XRCC7 genes are involved in DNA double-strand breaks(DSBs) repair associated with the risk of acute myeloid leukemia(AML) in Chinese population Institute of Scientific and Technical Information of China (English) Guoqiang Wang; Shuyu Wang; Qun Shen; Shiwei Yin; Chunping Li; Aiping Li; Jianyong Li; Jianwei Zhou; Qizhan Liu 2009-01-01 Objective:To investigate the association between the X-ray repair cross complementing(XRCC) group 5, XRCC6 and XRCC7 polymorphisms and risk of acute myeloid leukemia(AML). Methods:This hospital-based case-control study included 120 AML patients and 210 cancer-free controls in a Chinese population. Three polymorphisms of XRCCS, XRCC6 and XRCC7 were genotyped using the polymerase chain reaction(PCR) or polymerase chain reaction-restriction fragment length polymorphism(PCR-RFLP) method. Results: We found that there was a significant decrease in risk of AML associated with the XRCC6-61 CG/GG genotype(adjusted odd ratio (OR)=0.55;95% confident interval(CI)=0.34-0.89) compared with the-61CC genotype. For the novel tandem repeat polymorphism (VNTR) in the XRCC5 promoter, we found when the XRCC5 six genotypes were dichotomized(i.e., 2R/2R, 2R/1R versus 2R/0R, 1R/1R, 1R/0R and 0R/0R), the latter group was associated with increased risk of AML(adjusted OR=1.67;95% CI=1.00-2.79) compared to 2R/ 2R+2R/1R genotype. However, the XRCC7 6721G>T polymorphism had no effect on risk of AML. Conclusion:The XRCC6-61C > G and XRCC5 2R/1R/0R polymorphisms, but not XRCC7 6721G > T polymorphism, could play an important role in the development of AML. Larger scale studies with more detailed data on environment exposure are needed to verify these findings. 9. Clustered DNA lesion repair in eukaryotes: Relevance to mutagenesis and cell survival Energy Technology Data Exchange (ETDEWEB) Sage, Evelyne [Institut Curie, Bat. 110, Centre Universitaire, 91405 Orsay (France); CNRS UMR3348, Bat. 110, Centre Universitaire, 91405 Orsay (France); Harrison, Lynn, E-mail: [email protected] [Department of Molecular and Cellular Physiology, LSUHSC-S, 1501 Kings Highway, Shreveport, LA 71130 (United States) 2011-06-03 A clustered DNA lesion, also known as a multiply damaged site, is defined as {>=}2 damages in the DNA within 1-2 helical turns. Only ionizing radiation and certain chemicals introduce DNA damage in the genome in this non-random way. What is now clear is that the lethality of a damaging agent is not just related to the types of DNA lesions introduced, but also to how the damage is distributed in the DNA. Clustered DNA lesions were first hypothesized to exist in the 1990s, and work has progressed where these complex lesions have been characterized and measured in irradiated as well as in non-irradiated cells. A clustered lesion can consist of single as well as double strand breaks, base damage and abasic sites, and the damages can be situated on the same strand or opposing strands. They include tandem lesions, double strand break (DSB) clusters and non-DSB clusters, and base excision repair as well as the DSB repair pathways can be required to remove these complex lesions. Due to the plethora of oxidative damage induced by ionizing radiation, and the repair proteins involved in their removal from the DNA, it has been necessary to study how repair systems handle these lesions using synthetic DNA damage. This review focuses on the repair process and mutagenic consequences of clustered lesions in yeast and mammalian cells. By examining the studies on synthetic clustered lesions, and the effects of low vs high LET radiation on mammalian cells or tissues, it is possible to extrapolate the potential biological relevance of these clustered lesions to the killing of tumor cells by radiotherapy and chemotherapy, and to the risk of cancer in non-tumor cells, and this will be discussed. 10. Clustered DNA lesion repair in eukaryotes: Relevance to mutagenesis and cell survival International Nuclear Information System (INIS) A clustered DNA lesion, also known as a multiply damaged site, is defined as ≥2 damages in the DNA within 1-2 helical turns. Only ionizing radiation and certain chemicals introduce DNA damage in the genome in this non-random way. What is now clear is that the lethality of a damaging agent is not just related to the types of DNA lesions introduced, but also to how the damage is distributed in the DNA. Clustered DNA lesions were first hypothesized to exist in the 1990s, and work has progressed where these complex lesions have been characterized and measured in irradiated as well as in non-irradiated cells. A clustered lesion can consist of single as well as double strand breaks, base damage and abasic sites, and the damages can be situated on the same strand or opposing strands. They include tandem lesions, double strand break (DSB) clusters and non-DSB clusters, and base excision repair as well as the DSB repair pathways can be required to remove these complex lesions. Due to the plethora of oxidative damage induced by ionizing radiation, and the repair proteins involved in their removal from the DNA, it has been necessary to study how repair systems handle these lesions using synthetic DNA damage. This review focuses on the repair process and mutagenic consequences of clustered lesions in yeast and mammalian cells. By examining the studies on synthetic clustered lesions, and the effects of low vs high LET radiation on mammalian cells or tissues, it is possible to extrapolate the potential biological relevance of these clustered lesions to the killing of tumor cells by radiotherapy and chemotherapy, and to the risk of cancer in non-tumor cells, and this will be discussed. 11. DNA damage and gene therapy of xeroderma pigmentosum, a human DNA repair-deficient disease Energy Technology Data Exchange (ETDEWEB) Dupuy, Aurélie [Laboratory of Genetic Instability and Oncogenesis UMR8200CNRS, Institut Gustave Roussy and University Paris-Sud, Villejuif (France); Sarasin, Alain, E-mail: [email protected] [Laboratory of Genetic Instability and Oncogenesis UMR8200CNRS, Institut Gustave Roussy and University Paris-Sud, Villejuif (France); Service de Génétique, Institut Gustave Roussy (France) 2015-06-15 Graphical abstract: - Highlights: • Full correction of mutation in the XPC gene by engineered nucleases. • Meganucleases and TALENs are inhibited by 5-MeC for inducing double strand breaks. • Gene therapy of XP cells is possible using homologous recombination for DSB repair. - Abstract: Xeroderma pigmentosum (XP) is a genetic disease characterized by hypersensitivity to ultra-violet and a very high risk of skin cancer induction on exposed body sites. This syndrome is caused by germinal mutations on nucleotide excision repair genes. No cure is available for these patients except a complete protection from all types of UV radiations. We reviewed the various techniques to complement or to correct the genetic defect in XP cells. We, particularly, developed the correction of XP-C skin cells using the fidelity of the homologous recombination pathway during repair of double-strand break (DSB) in the presence of XPC wild type sequences. We used engineered nucleases (meganuclease or TALE nuclease) to induce a DSB located at 90 bp of the mutation to be corrected. Expression of specific TALE nuclease in the presence of a repair matrix containing a long stretch of homologous wild type XPC sequences allowed us a successful gene correction of the original TG deletion found in numerous North African XP patients. Some engineered nucleases are sensitive to epigenetic modifications, such as cytosine methylation. In case of methylated sequences to be corrected, modified nucleases or demethylation of the whole genome should be envisaged. Overall, we showed that specifically-designed TALE-nuclease allowed us to correct a 2 bp deletion in the XPC gene leading to patient's cells proficient for DNA repair and showing normal UV-sensitivity. The corrected gene is still in the same position in the human genome and under the regulation of its physiological promoter. This result is a first step toward gene therapy in XP patients. 12. DNA damage and gene therapy of xeroderma pigmentosum, a human DNA repair-deficient disease International Nuclear Information System (INIS) Graphical abstract: - Highlights: • Full correction of mutation in the XPC gene by engineered nucleases. • Meganucleases and TALENs are inhibited by 5-MeC for inducing double strand breaks. • Gene therapy of XP cells is possible using homologous recombination for DSB repair. - Abstract: Xeroderma pigmentosum (XP) is a genetic disease characterized by hypersensitivity to ultra-violet and a very high risk of skin cancer induction on exposed body sites. This syndrome is caused by germinal mutations on nucleotide excision repair genes. No cure is available for these patients except a complete protection from all types of UV radiations. We reviewed the various techniques to complement or to correct the genetic defect in XP cells. We, particularly, developed the correction of XP-C skin cells using the fidelity of the homologous recombination pathway during repair of double-strand break (DSB) in the presence of XPC wild type sequences. We used engineered nucleases (meganuclease or TALE nuclease) to induce a DSB located at 90 bp of the mutation to be corrected. Expression of specific TALE nuclease in the presence of a repair matrix containing a long stretch of homologous wild type XPC sequences allowed us a successful gene correction of the original TG deletion found in numerous North African XP patients. Some engineered nucleases are sensitive to epigenetic modifications, such as cytosine methylation. In case of methylated sequences to be corrected, modified nucleases or demethylation of the whole genome should be envisaged. Overall, we showed that specifically-designed TALE-nuclease allowed us to correct a 2 bp deletion in the XPC gene leading to patient's cells proficient for DNA repair and showing normal UV-sensitivity. The corrected gene is still in the same position in the human genome and under the regulation of its physiological promoter. This result is a first step toward gene therapy in XP patients 13. 碱基切除修复与抗肿瘤药物耐药%Base excision repair and antineoplastic drug resistance Institute of Scientific and Technical Information of China (English) 况里杉; 王宇亮; 周向东 2013-01-01 Chemotherapy is one of the main methods to treat malignant tumors in clinical practice. Resistance to antineoplastic agents is one of the important reasons for treatment failure. The antineoplastic mechanism of various chemotherapeutic agents is to cause DNA damage, then result in apoptosis of tumor cells. It is suggested that the function of DNA repair is directly associated with the efficacy of antineoplastic agents. Current studies suggest that there are four major DNA repair pathways including BER (base excision repair), NER (nucleotide excision repair), MMR (mismatch repair) and DSBR (double strand break repair). Of these four pathways, BER is one of the main mechanisms of DNA repair and its malfunction is closely related to the resistance to antineoplastic agents. Recently, many kinds of agents and strategies targeting BER have been developed to reverse chemoresistance. This review summarizes the progress in research in this area and discusses the mechanism of resistance to antineoplastic agents and the potential preventive and therapeutic strategies.%化疗是目前临床上治疗肿瘤的主要方法之一,抗肿瘤药物耐药则是导致肿瘤治疗失败的重要原因之一.多种化疗药物抗肿瘤的主要机制是引起DNA损伤,进而导致肿瘤细胞凋亡；因此,DNA修复功能状态与抗肿瘤药物疗效有着直接的关系.目前,已知有4种主要的DNA修复途径:碱基切除修复(base excision repair,BER)、核苷酸切除修复(nucleotide excision repair,NER)、错配修复(mismatch repair,MMR)和双键断裂修复(double strand break repair,DSBR).其中,BER是主要的DNA修复机制之一,其修复功能异常与抗肿瘤药物耐药有着密切的联系.近年来,以BER为靶点开发了多种逆转耐药的药物或方法.本文将简要综述相关的研究进展,深入探讨抗肿瘤药物耐药的发生机制及防治措施. 14. Energy and Technology Review: Unlocking the mysteries of DNA repair Energy Technology Data Exchange (ETDEWEB) Quirk, W.A. 1993-04-01 DNA, the genetic blueprint, has the remarkable property of encoding its own repair following diverse types of structural damage induced by external agents or normal metabolism. We are studying the interplay of DNA damaging agents, repair genes, and their protein products to decipher the complex biochemical pathways that mediate such repair. Our research focuses on repair processes that correct DNA damage produced by chemical mutagens and radiation, both ionizing and ultraviolet. The most important type of DNA repair in human cells is called excision repair. This multistep process removes damaged or inappropriate pieces of DNA -- often as a string of 29 nucleotides containing the damage -- and replaces them with intact ones. We have isolated, cloned, and mapped several human repair genes associated with the nucleotide excision repair pathway and involved in the repair of DNA damage after exposure to ultraviolet light or mutagens in cooked food. We have shown that a defect in one of these repair genes, ERCC2, is responsible for the repair deficiency in one of the groups of patients with the recessive genetic disorder xeroderma pigmentosum (XP group D). We are exploring ways to purify sufficient quantities (milligrams) of the protein products of these and other repair genes so that we can understand their functions. Our long-term goals are to link defective repair proteins to human DNA repair disorders that predispose to cancer, and to produce DNA-repair-deficient mice that can serve as models for the human disorders. 15. Intestinal obstruction repair Science.gov (United States) Repair of volvulus; Intestinal volvulus - repair; Bowel obstruction - repair ... Intestinal obstruction repair is done while you are under general anesthesia . This means you are asleep and DO NOT feel pain. ... 16. Aortic aneurysm repair - endovascular Science.gov (United States) EVAR; Endovascular aneurysm repair - aorta; AAA repair - endovascular; Repair - aortic aneurysm - endovascular ... Endovascular aortic repair is done because your aneurysm is very large, growing quickly, or is leaking or bleeding. You may have ... 17. Motorcycle Repair. Science.gov (United States) Hein, Jim; Bundy, Mike This motorcycle repair curriculum guide contains the following ten areas of study: brake systems, clutches, constant mesh transmissions, final drives, suspension, mechanical starting mechanisms, electrical systems, fuel systems, lubrication systems, and overhead camshafts. Each area consists of one or more units of instruction. Each instructional… 18. Hydrocele repair Science.gov (United States) ... small surgical cut in the fold of the groin, and then drains the fluid. The sac (hydrocele) holding the fluid may be removed. The surgeon strengthens the muscle wall with stitches. This is called a hernia repair. Sometimes the surgeon uses a laparoscope to do ... 19. Turbine repair process, repaired coating, and repaired turbine component Energy Technology Data Exchange (ETDEWEB) Das, Rupak; Delvaux, John McConnell; Garcia-Crespo, Andres Jose 2015-11-03 A turbine repair process, a repaired coating, and a repaired turbine component are disclosed. The turbine repair process includes providing a turbine component having a higher-pressure region and a lower-pressure region, introducing particles into the higher-pressure region, and at least partially repairing an opening between the higher-pressure region and the lower-pressure region with at least one of the particles to form a repaired turbine component. The repaired coating includes a silicon material, a ceramic matrix composite material, and a repaired region having the silicon material deposited on and surrounded by the ceramic matrix composite material. The repaired turbine component a ceramic matrix composite layer and a repaired region having silicon material deposited on and surrounded by the ceramic matrix composite material. 20. Characterization of oxidative guanine damage and repair in mammalian telomeres. Directory of Open Access Journals (Sweden) Zhilong Wang 2010-05-01 Full Text Available 8-oxo-7,8-dihydroguanine (8-oxoG and 2,6-diamino-4-hydroxy-5-formamidopyrimidine (FapyG are among the most common oxidative DNA lesions and are substrates for 8-oxoguanine DNA glycosylase (OGG1-initiated DNA base excision repair (BER. Mammalian telomeres consist of triple guanine repeats and are subject to oxidative guanine damage. Here, we investigated the impact of oxidative guanine damage and its repair by OGG1 on telomere integrity in mice. The mouse cells were analyzed for telomere integrity by telomere quantitative fluorescence in situ hybridization (telomere-FISH, by chromosome orientation-FISH (CO-FISH, and by indirect immunofluorescence in combination with telomere-FISH and for oxidative base lesions by Fpg-incision/Southern blot assay. In comparison to the wild type, telomere lengthening was observed in Ogg1 null (Ogg1(-/- mouse tissues and primary embryonic fibroblasts (MEFs cultivated in hypoxia condition (3% oxygen, whereas telomere shortening was detected in Ogg1(-/- mouse hematopoietic cells and primary MEFs cultivated in normoxia condition (20% oxygen or in the presence of an oxidant. In addition, telomere length abnormalities were accompanied by altered telomere sister chromatid exchanges, increased telomere single- and double-strand breaks, and preferential telomere lagging- or G-strand losses in Ogg1(-/- mouse cells. Oxidative guanine lesions were increased in telomeres in Ogg1(-/- mice with aging and primary MEFs cultivated in 20% oxygen. Furthermore, oxidative guanine lesions persisted at high level in Ogg1(-/- MEFs after acute exposure to hydrogen peroxide, while they rapidly returned to basal level in wild-type MEFs. These findings indicate that oxidative guanine damage can arise in telomeres where it affects length homeostasis, recombination, DNA replication, and DNA breakage repair. Our studies demonstrate that BER pathway is required in repairing oxidative guanine damage in telomeres and maintaining telomere integrity 1. WHERE MULTIFUNCTIONAL DNA REPAIR PROTEINS MEET: MAPPING THE INTERACTION DOMAINS BETWEEN XPG AND WRN Energy Technology Data Exchange (ETDEWEB) Rangaraj, K.; Cooper, P.K.; Trego, K.S. 2009-01-01 The rapid recognition and repair of DNA damage is essential for the maintenance of genomic integrity and cellular survival. Multiple complex and interconnected DNA damage responses exist within cells to preserve the human genome, and these repair pathways are carried out by a specifi c interplay of protein-protein interactions. Thus a failure in the coordination of these processes, perhaps brought about by a breakdown in any one multifunctional repair protein, can lead to genomic instability, developmental and immunological abnormalities, cancer and premature aging. This study demonstrates a novel interaction between two such repair proteins, Xeroderma pigmentosum group G protein (XPG) and Werner syndrome helicase (WRN), that are both highly pleiotropic and associated with inherited genetic disorders when mutated. XPG is a structure-specifi c endonuclease required for the repair of UV-damaged DNA by nucleotide excision repair (NER), and mutations in XPG result in the diseases Xeroderma pigmentosum (XP) and Cockayne syndrome (CS). A loss of XPG incision activity results in XP, whereas a loss of non-enzymatic function(s) of XPG causes CS. WRN is a multifunctional protein involved in double-strand break repair (DSBR), and consists of 3’–5’ DNA-dependent helicase, 3’–5’ exonuclease, and single-strand DNA annealing activities. Nonfunctional WRN protein leads to Werner syndrome, a premature aging disorder with increased cancer incidence. Far Western analysis was used to map the interacting domains between XPG and WRN by denaturing gel electrophoresis, which separated purifi ed full length and recombinant XPG and WRN deletion constructs, based primarily upon the length of each polypeptide. Specifi c interacting domains were visualized when probed with the secondary protein of interest which was then detected by traditional Western analysis using the antibody of the secondary protein. The interaction between XPG and WRN was mapped to the C-terminal region of 2. Mammalian mismatch repair DEFF Research Database (Denmark) Pena Diaz, Javier; Jiricny, Josef 2012-01-01 A considerable surge of interest in the mismatch repair (MMR) system has been brought about by the discovery of a link between Lynch syndrome, an inherited predisposition to cancer of the colon and other organs, and malfunction of this key DNA metabolic pathway. This review focuses on recent...... advances in our understanding of the molecular mechanisms of canonical MMR, which improves replication fidelity by removing misincorporated nucleotides from the nascent DNA strand. We also discuss the involvement of MMR proteins in two other processes: trinucleotide repeat expansion and antibody maturation... 3. Nucleotide Excision Repair in Caenorhabditis elegans OpenAIRE Hannes Lans; Wim Vermeulen 2011-01-01 Nucleotide excision repair (NER) plays an essential role in many organisms across life domains to preserve and faithfully transmit DNA to the next generation. In humans, NER is essential to prevent DNA damage-induced mutation accumulation and cell death leading to cancer and aging. NER is a versatile DNA repair pathway that repairs many types of DNA damage which distort the DNA helix, such as those induced by solar UV light. A detailed molecular model of the NER pathway has emerged from in vi... 4. A nonsense mutation in the DNA repair factor Hebo causes mild bone marrow failure and microcephaly. Science.gov (United States) Zhang, Shu; Pondarre, Corinne; Pennarun, Gaelle; Labussiere-Wallet, Helene; Vera, Gabriella; France, Benoit; Chansel, Marie; Rouvet, Isabelle; Revy, Patrick; Lopez, Bernard; Soulier, Jean; Bertrand, Pascale; Callebaut, Isabelle; de Villartay, Jean-Pierre 2016-05-30 Inherited bone marrow failure syndromes are human conditions in which one or several cell lineages of the hemopoietic system are affected. They are present at birth or may develop progressively. They are sometimes accompanied by other developmental anomalies. Three main molecular causes have been recognized to result in bone marrow failure syndromes: (1) defects in the Fanconi anemia (FA)/BRCA DNA repair pathway, (2) defects in telomere maintenance, and (3) abnormal ribosome biogenesis. We analyzed a patient with mild bone marrow failure and microcephaly who did not present with the typical FA phenotype. Cells from this patient showed increased sensitivity to ionizing radiations and phleomycin, attesting to a probable DNA double strand break (dsb) repair defect. Linkage analysis and whole exome sequencing revealed a homozygous nonsense mutation in the ERCC6L2 gene. We identified a new ERCC6L2 alternative transcript encoding the DNA repair factor Hebo, which is critical for complementation of the patient's DNAdsb repair defect. Sequence analysis revealed three structured regions within Hebo: a TUDOR domain, an adenosine triphosphatase domain, and a new domain, HEBO, specifically present in Hebo direct orthologues. Hebo is ubiquitously expressed, localized in the nucleus, and rapidly recruited to DNAdsb's in an NBS1-dependent manner. 5. Stalled replication fork repair and misrepair during thymineless death in Escherichia coli. Science.gov (United States) Kuong, Kawai J; Kuzminov, Andrei 2010-06-01 Starvation for DNA precursor dTTP, known as 'thymineless death' (TLD), kills bacterial and eukaryotic cells alike. Despite numerous investigations, toxic mechanisms behind TLD remain unknown, although wrong nucleotide incorporation with subsequent excision dominates the explanations. We show that kinetics of TLD in Escherichia coli is not affected by mutations in DNA repair, ruling out excision after massive misincorporation as the cause of TLD. We found that the rate of DNA synthesis in thymine-starved cells decreases exponentially, indicating replication fork stalling. Processing of stalled replication forks by recombinational repair is known to fragment the chromosome, and we detect significant chromosomal fragmentation during TLD. Moreover, we report that, out of major recombinational repair functions, only inactivation of recF and recO relieves TLD, identifying the poisoning mechanism. Inactivation of recJ and rep has slight effect, while the recA, recBC, ruvABC, recG and uvrD mutations all accelerate TLD, identifying the protection mechanisms. Our epistatic analysis argues for two distinct pathways protecting against TLD: RecABCD/Ruv repairs the double-strand breaks, whereas UvrD counteracts RecAFO-catalyzed toxic single-strand gap processing. PMID:20465561 6. Inhibition of homologous recombination repair in irradiated tumor cells pretreated with Hsp90 inhibitor 17-allylamino-17-demethoxygeldanamycin International Nuclear Information System (INIS) In order to investigate the mechanism of radio-sensitization by an Hsp90 inhibitor 17-allylamino-17-demethoxygeldanamycin (17-AAG), we studied repair of DNA double strand breaks (DSBs) in irradiated human cells pre-treated with 17-AAG. DSBs are thought to be the critical target for radiation-induced cell death. Two human tumor cell lines DU145 and SQ-5 which showed clear radio-sensitization by 17-AAG revealed a significant inhibition of DSB repair, while normal human cells which did not show radio-sensitization by the drug indicated no change in the DSB repair kinetics with 17-AAG. We further demonstrated that BRCA2 was a novel client protein for Hsp90, and 17-AAG caused the degradation of BRCA2 and in turn altered the behavior of Rad51, a critical protein for homologous recombination (HR) pathway of DSB repair. Our data demonstrate for the first time that 17-AAG inhibits the HR repair process and could provide a new therapeutic strategy to selectively result in higher tumor cell killing 7. Involvement of DNA-PK(sub cs) in DSB Repair Following Fe-56 Ion Irradiation Science.gov (United States) O'Neill, Peter; Harper, Jane; Anderson, Jennifer a.; Cucinnota, Francis A. 2007-01-01 8. Non-canonical uracil processing in DNA gives rise to double-strand breaks and deletions: relevance to class switch recombination. Science.gov (United States) Bregenhorn, Stephanie; Kallenberger, Lia; Artola-Borán, Mariela; Peña-Diaz, Javier; Jiricny, Josef 2016-04-01 During class switch recombination (CSR), antigen-stimulated B-cells rearrange their immunoglobulin constant heavy chain (CH) loci to generate antibodies with different effector functions. CSR is initiated by activation-induced deaminase (AID), which converts cytosines in switch (S) regions, repetitive sequences flanking the CH loci, to uracils. Although U/G mispairs arising in this way are generally efficiently repaired to C/Gs by uracil DNA glycosylase (UNG)-initiated base excision repair (BER), uracil processing in S-regions of activated B-cells occasionally gives rise to double strand breaks (DSBs), which trigger CSR. Surprisingly, genetic experiments revealed that CSR is dependent not only on AID and UNG, but also on mismatch repair (MMR). To elucidate the role of MMR in CSR, we studied the processing of uracil-containing DNA substrates in extracts of MMR-proficient and -deficient human cells, as well as in a system reconstituted from recombinant BER and MMR proteins. Here, we show that the interplay of these repair systems gives rise to DSBs in vitro and to genomic deletions and mutations in vivo, particularly in an S-region sequence. Our findings further suggest that MMR affects pathway choice in DSB repair. Given its amenability to manipulation, our system represents a powerful tool for the molecular dissection of CSR. 9. Non-canonical uracil processing in DNA gives rise to double-strand breaks and deletions: relevance to class switch recombination. Science.gov (United States) Bregenhorn, Stephanie; Kallenberger, Lia; Artola-Borán, Mariela; Peña-Diaz, Javier; Jiricny, Josef 2016-04-01 During class switch recombination (CSR), antigen-stimulated B-cells rearrange their immunoglobulin constant heavy chain (CH) loci to generate antibodies with different effector functions. CSR is initiated by activation-induced deaminase (AID), which converts cytosines in switch (S) regions, repetitive sequences flanking the CH loci, to uracils. Although U/G mispairs arising in this way are generally efficiently repaired to C/Gs by uracil DNA glycosylase (UNG)-initiated base excision repair (BER), uracil processing in S-regions of activated B-cells occasionally gives rise to double strand breaks (DSBs), which trigger CSR. Surprisingly, genetic experiments revealed that CSR is dependent not only on AID and UNG, but also on mismatch repair (MMR). To elucidate the role of MMR in CSR, we studied the processing of uracil-containing DNA substrates in extracts of MMR-proficient and -deficient human cells, as well as in a system reconstituted from recombinant BER and MMR proteins. Here, we show that the interplay of these repair systems gives rise to DSBs in vitro and to genomic deletions and mutations in vivo, particularly in an S-region sequence. Our findings further suggest that MMR affects pathway choice in DSB repair. Given its amenability to manipulation, our system represents a powerful tool for the molecular dissection of CSR. PMID:26743004 10. Targeting the CD80/CD86 costimulatory pathway with CTLA4-Ig directs microglia toward a repair phenotype and promotes axonal outgrowth. Science.gov (United States) Louveau, Antoine; Nerrière-Daguin, Véronique; Vanhove, Bernard; Naveilhan, Philippe; Neunlist, Michel; Nicot, Arnaud; Boudin, Hélène 2015-12-01 Among the costimulatory factors widely studied in the immune system is the CD28/cytotoxic T-lymphocyte antigen-4 (CTLA4)-CD80/CD86 pathway, which critically controls the nature and duration of the T-cell response. In the brain, up-regulated expression of CD80/CD86 during inflammation has consistently been reported in microglia. However, the role of CD80/CD86 molecules has mainly been studied in a context of microglia-T cell interactions in pathological conditions, while the function of CD80/CD86 in the regulation of intrinsic brain cells remains largely unknown. In this study, we used a transgenic pig line in which neurons express releasable CTLA4-Ig, a synthetic molecule mimicking CTLA4 and binding to CD80/CD86. The effects of CTLA4-Ig on brain cells were analyzed after intracerebral transplantation of CTLA4-Ig-expressing neurons or wild-type neurons as control. This model provided in vivo evidence that CTLA4-Ig stimulated axonal outgrowth, in correlation with a shift of the nearby microglia from a compact to a ramified morphology. In a culture system, we found that the CTLA4-Ig-induced morphological change of microglia was mediated through CD86, but not CD80. This was accompanied by microglial up-regulated expression of the anti-inflammatory molecule Arginase 1 and the neurotrophic factor BDNF, in an astrocyte-dependent manner through the purinergic P2Y1 receptor pathway. Our study identifies for the first time CD86 as a key player in the modulation of microglia phenotype and suggests that CTLA4-Ig-derived compounds might represent new tools to manipulate CNS microglia. 11. Polymorphisms in DNA Repair Genes, Smoking, and Pancreatic Adenocarcinoma Risk OpenAIRE Robert R McWilliams; William R Bamlet; Cunningham, Julie M.; Goode, Ellen L.; de ANDRADE, MARIZA; Lisa A Boardman; Petersen, Gloria M. 2008-01-01 Base excision repair and nucleotide excision repair are vital responses to multiple types of DNA damage, including damage from tobacco exposure. Single-nucleotide polymorphisms (SNP) in these pathways may affect DNA repair capacity and therefore influence risk for cancer development. We performed a clinic-based, case-control study comprising 481 consecutive patients with confirmed pancreatic adenocarcinoma and 625 healthy controls. Allele and genotype frequencies for 16 SNPs in DNA repair gen... 12. No Evidence for “Break-Induced Replication” in a Higher Plant – But Break-Induced Conversion May Occur OpenAIRE Schubert, Ingo; Schubert, Veit; Fuchs, Jörg 2011-01-01 Break-induced replication” (BIR) is considered as one way to repair DNA double-strand breaks (DSBs). BIR is defined as replication of the proximal break-ends up to the end of the broken chromosome using an undamaged (homologous) double-stranded template and mimicking a non-reciprocal translocation. This phenomenon was detected by genetic experiments in yeast. BIR is assumed to occur also in mammals, but experimental evidence is not yet at hand. We have studied chromosomes of the field bean, ... 13. No evidence for 'break-induced replication' in a higher plant – but break-induced conversion may occur OpenAIRE Ingo eSchubert; Veit eSchubert; Jörg eFuchs 2011-01-01 Break-induced replication’ (BIR) is considered as one way to repair DNA double-strand breaks (DSBs). BIR is defined as replication of the proximal break-ends up to the end of the broken chromosome using an undamaged homologous double-stranded template and mimicking a non-reciprocal translocation. This phenomenon was detected by genetic experiments in yeast. BIR is assumed to occur also in mammals, but experimental evidence is not yet at hand. We have studied chromosomes of the field bean, V... 14. BRCA1 silencing is associated with failure of DNA repairing in retinal neurocytes. Directory of Open Access Journals (Sweden) Pei Chen Full Text Available Retinal post-mitotic neurocytes display genomic instability after damage induced by physiological or pathological factors. The involvement of BRCA1, an important factor in development and DNA repair in mature retinal neurocytes remains unclear. Thus, we investigated the developmental expression profile of BRCA1 in the retina and defined the role of BRCA1 in DNA repair in retinal neurocytes. Our data show the expression of BRCA1 is developmentally down-regulated in the retinas of mice after birth. Similarly, BRCA1 is down-regulated after differentiation induced by TSA in retinal precursor cells. An end-joining activity assay and DNA fragmentation analysis indicated that the DNA repair capacity is significantly reduced. Moreover, DNA damage in differentiated cells or cells in which BRCA1 is silenced by siRNA interference is more extensive than that in precursor cells subjected to ionizing radiation. To further investigate non-homologous end joining (NHEJ, the major repair pathway in non-divided neurons, we utilized an NHEJ substrate (pEPI-NHEJ in which double strand breaks are generated by I-SceI. Our data showed that differentiation and the down-regulation of BRCA1 respectively result in a 2.39-fold and 1.68-fold reduction in the total NHEJ frequency compared with that in cells with normal BRCA1. Furthermore, the analysis of NHEJ repair junctions of the plasmid substrate indicated that BRCA1 is involved in the fidelity of NHEJ. In addition, as expected, the down-regulation of BRCA1 significantly inhibits the viability of retina precursor cells. Therefore, our data suggest that BRCA1 plays a critical role in retinal development and repairs DNA damage of mature retina neurocytes. 15. Small molecules, inhibitors of DNA-PK, targeting DNA repair and beyond Directory of Open Access Journals (Sweden) David eDavidson 2013-01-01 Full Text Available Many current chemotherapies function by damaging genomic DNA in rapidly dividing cells ultimately leading to cell death. This therapeutic approach differentially targets cancer cells that generally display rapid cell division compared to normal tissue cells. However, although these treatments are initially effective in arresting tumor growth and reducing tumor burden, resistance and disease progression eventually occur. A major mechanism underlying this resistance is increased levels of cellular DNA repair. Most cells have complex mechanisms in place to repair DNA damage that occurs due to environmental exposures or normal metabolic processes. These systems, initially overwhelmed when faced with chemotherapy induced DNA damage, become more efficient under constant selective pressure and as a result chemotherapies become less effective. Thus, inhibiting DNA repair pathways using target specific small molecule inhibitors may overcome cellular resistance to DNA damaging chemotherapies. Non-homologous end joining (NHEJ a major mechanism for the repair of double strand breaks (DSB in DNA is regulated in part by the serine/threonine kinase, DNA dependent protein kinase (DNA-PK. The DNA-PK holoenzyme acts as a scaffold protein tethering broken DNA ends and recruiting other repair molecules. It also has enzymatic activity that may be involved in DNA damage signaling. Because of its’ central role in repair of DSBs, DNA-PK has been the focus of a number of small molecule studies. In these studies specific DNA-PK inhibitors have shown efficacy in synergizing chemotherapies in vitro. However, compounds currently known to specifically inhibit DNA-PK are limited by poor pharmacokinetics: these compounds have poor solubility and have high metabolic lability in vivo leading to short serum half-lives. Future improvement in DNA-PK inhibition will likely be achieved by designing new molecules based on the recently reported crystallographic structure of DNA 16. Checkpoint adaptation and recovery: back with Polo after the break NARCIS (Netherlands) Vugt, M.A.T.M. van; Medema, R.H. 2004-01-01 S. cerevisiae cells that are unable to repair a double strand break ultimately escape the DNA damage checkpoint arrest and enter mitosis. This process called 'adaptation' depends on functional Cdc5, a Polo-like kinase, and was long thought to be limited to single-cell organisms. However, the recent 17. Checkpoint adaptation and recovery : back with Polo after the break NARCIS (Netherlands) van Vugt, Marcel A T M; Medema, René H 2004-01-01 S. cerevisiae cells that are unable to repair a double strand break ultimately escape the DNA damage checkpoint arrest and enter mitosis. This process called 'adaptation' depends on functional Cdc5, a Polo-like kinase, and was long thought to be limited to single-cell organisms. However, the recent 18. Silencing of the DNA Mismatch Repair Gene MLH1 Induced by Hypoxic Stress in a Pathway Dependent on the Histone Demethylase LSD1 Directory of Open Access Journals (Sweden) Yuhong Lu 2014-07-01 Full Text Available Silencing of MLH1 is frequently seen in sporadic colorectal cancers. We show here that hypoxia causes decreased histone H3 lysine 4 (H3K4 methylation at the MLH1 promoter via the action of the H3K4 demethylases LSD1 and PLU-1 and promotes durable long-term silencing in a pathway that requires LSD1. Knockdown of LSD1 or its corepressor, CoREST, also prevents the resilencing (and associated cytosine DNA methylation of the endogenous MLH1 promoter in RKO colon cancer cells following transient reactivation by treatment with the DNA methyltransferase inhibitor 5-aza-2′-deoxycytidine (5-aza-dC. The results demonstrate that hypoxia is a driving force for silencing of MLH1 and that the LSD1/CoREST complex is necessary for this process. The results reveal a mechanism by which hypoxia promotes cancer cell evolution to drive malignant progression through epigenetic modulation. Our findings suggest that LSD1/CoREST acts as a colon cancer oncogene by epigenetically silencing MLH1 and also identify the LSD1/CoREST complex as a potential target for therapy. 19. Protein expression of DNA damage repair proteins dictates response to topoisomerase and PARP inhibitors in triple-negative breast cancer. Directory of Open Access Journals (Sweden) Julie L Boerner Full Text Available Patients with metastatic triple-negative breast cancer (TNBC have a poor prognosis. New approaches for the treatment of TNBC are needed to improve patient survival. The concept of synthetic lethality, brought about by inactivating complementary DNA repair pathways, has been proposed as a promising therapeutic option for these tumors. The TNBC tumor type has been associated with BRCA mutations, and inhibitors of Poly (ADP-ribose polymerase (PARP, a family of proteins that facilitates DNA repair, have been shown to effectively kill BRCA defective tumors by preventing cells from repairing DNA damage, leading to a loss of cell viability and clonogenic survival. Here we present preclinical efficacy results of combining the PARP inhibitor, ABT-888, with CPT-11, a topoisomerase I inhibitor. CPT-11 binds to topoisomerase I at the replication fork, creating a bulky adduct that is recognized as damaged DNA. When DNA damage was stimulated with CPT-11, protein expression of the nucleotide excision repair enzyme ERCC1 inversely correlated with cell viability, but not clonogenic survival. However, 4 out of the 6 TNBC cells were synergistically responsive by cell viability and 5 out of the 6 TNBC cells were synergistically responsive by clonogenic survival to the combination of ABT-888 and CPT-11. In vivo, the BRCA mutant cell line MX-1 treated with CPT-11 alone demonstrated significant decreased tumor growth; this decrease was enhanced further with the addition of ABT-888. Decrease in tumor growth correlated with an increase in double strand DNA breaks as measured by γ-H2AX phosphorylation. In summary, inhibiting two arms of the DNA repair pathway simultaneously in TNBC cell lines, independent of BRCA mutation status, resulted in un-repairable DNA damage and subsequent cell death. 20. Chromatin challenges during DNA replication and repair DEFF Research Database (Denmark) Groth, Anja; Rocha, Walter; Verreault, Alain; 2007-01-01 the challenge of maintenance, cells have evolved efficient nucleosome-assembly pathways and chromatin-maturation mechanisms that reproduce chromatin organization in the wake of DNA replication and repair. The aim of this Review is to describe how these pathways operate and to highlight how the epigenetic... 1. uv photobiology: excision repair International Nuclear Information System (INIS) The following topics are discussed: steps in nucleotide excision; damage to DNA by uv-endonuclease; use of complementation to study DNA repair in Escherichia coli and mammalian cells; role of BUDR photolysis in excision repair, relation between DNA repair defect and human disease; base excision repair; and excision repair by removal of damaged region of a base in DNA without excision 2. Reduced repair capacity of a DNA clustered damage site comprised of 8-oxo-7,8-dihydro-2′-deoxyguanosine and 2-deoxyribonolactone results in an increased mutagenic potential of these lesions Energy Technology Data Exchange (ETDEWEB) Cunniffe, Siobhan [CRUK-MRC Gray Institute for Radiation Oncology and Biology, Department of Oncology, University of Oxford, Old Road Campus Research Building, Roosevelt Drive, Oxford OX3 7DQ (United Kingdom); O’Neill, Peter, E-mail: [email protected] [CRUK-MRC Gray Institute for Radiation Oncology and Biology, Department of Oncology, University of Oxford, Old Road Campus Research Building, Roosevelt Drive, Oxford OX3 7DQ (United Kingdom); Greenberg, Marc M. [Johns Hopkins University, Department of Chemistry, 3400 N. Charles St. , Baltimore, MD 21218 (United States); Lomax, Martine E. [CRUK-MRC Gray Institute for Radiation Oncology and Biology, Department of Oncology, University of Oxford, Old Road Campus Research Building, Roosevelt Drive, Oxford OX3 7DQ (United Kingdom) 2014-04-15 Highlights: • A dL lesion is not repaired as effectively as an AP site. • The repair of a cluster with dL and 8-oxodGuo lesions is compromised. • Delayed repair of the cluster leads to an increase in mutation frequency. - Abstract: A signature of ionizing radiation is the induction of DNA clustered damaged sites. Non-double strand break (DSB) clustered damage has been shown to compromise the base excision repair pathway, extending the lifetimes of the lesions within the cluster, compared to isolated lesions. This increases the likelihood the lesions persist to replication and thus increasing the mutagenic potential of the lesions within the cluster. Lesions formed by ionizing radiation include 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-oxodGuo) and 2-deoxyribonolactone (dL). dL poses an additional challenge to the cell as it is not repaired by the short-patch base excision repair pathway. Here we show recalcitrant dL repair is reflected in mutations observed when DNA containing it and a proximal 8-oxodGuo is replicated in Escherichia coli. 8-oxodGuo in close proximity to dL on the opposing DNA strand results in an enhanced frequency of mutation of the lesions within the cluster and a 20 base sequence flanking the clustered damage site in an E. coli based plasmid assay. In vitro repair of a dL lesion is reduced when compared to the repair of an abasic (AP) site and a tetrahydrofuran (THF), and this is due mainly to a reduction in the activity of polymerase β, leading to retarded FEN1 and ligase 1 activities. This study has given insights in to the biological effects of clusters containing dL. 3. Reduced repair capacity of a DNA clustered damage site comprised of 8-oxo-7,8-dihydro-2′-deoxyguanosine and 2-deoxyribonolactone results in an increased mutagenic potential of these lesions International Nuclear Information System (INIS) Highlights: • A dL lesion is not repaired as effectively as an AP site. • The repair of a cluster with dL and 8-oxodGuo lesions is compromised. • Delayed repair of the cluster leads to an increase in mutation frequency. - Abstract: A signature of ionizing radiation is the induction of DNA clustered damaged sites. Non-double strand break (DSB) clustered damage has been shown to compromise the base excision repair pathway, extending the lifetimes of the lesions within the cluster, compared to isolated lesions. This increases the likelihood the lesions persist to replication and thus increasing the mutagenic potential of the lesions within the cluster. Lesions formed by ionizing radiation include 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-oxodGuo) and 2-deoxyribonolactone (dL). dL poses an additional challenge to the cell as it is not repaired by the short-patch base excision repair pathway. Here we show recalcitrant dL repair is reflected in mutations observed when DNA containing it and a proximal 8-oxodGuo is replicated in Escherichia coli. 8-oxodGuo in close proximity to dL on the opposing DNA strand results in an enhanced frequency of mutation of the lesions within the cluster and a 20 base sequence flanking the clustered damage site in an E. coli based plasmid assay. In vitro repair of a dL lesion is reduced when compared to the repair of an abasic (AP) site and a tetrahydrofuran (THF), and this is due mainly to a reduction in the activity of polymerase β, leading to retarded FEN1 and ligase 1 activities. This study has given insights in to the biological effects of clusters containing dL 4. Ku counteracts mobilization of PARP1 and MRN in chromatin damaged with DNA double-strand breaks. Science.gov (United States) Cheng, Qiao; Barboule, Nadia; Frit, Philippe; Gomez, Dennis; Bombarde, Oriane; Couderc, Bettina; Ren, Guo-Sheng; Salles, Bernard; Calsou, Patrick 2011-12-01 In mammalian cells, the main pathway for DNA double-strand breaks (DSBs) repair is classical non-homologous end joining (C-NHEJ). An alternative or back-up NHEJ (B-NHEJ) pathway has emerged which operates preferentially under C-NHEJ defective conditions. Although B-NHEJ appears particularly relevant to genomic instability associated with cancer, its components and regulation are still largely unknown. To get insights into this pathway, we have knocked-down Ku, the main contributor to C-NHEJ. Thus, models of human cell lines have been engineered in which the expression of Ku70/80 heterodimer can be significantly lowered by the conditional induction of a shRNA against Ku70. On Ku reduction in cells, resulting NHEJ competent protein extracts showed a shift from C- to B-NHEJ that could be reversed by addition of purified Ku protein. Using a cellular fractionation protocol after treatment with a strong DSBs inducer followed by western blotting or immunostaining, we established that, among C-NHEJ factors, Ku is the main counteracting factor against mobilization of PARP1 and the MRN complex to damaged chromatin. In addition, Ku limits PAR synthesis and single-stranded DNA production in response to DSBs. These data support the involvement of PARP1 and the MRN proteins in the B-NHEJ route for the repair of DNA DSBs. PMID:21880593 5. A miR-590/Acvr2a/Rad51b Axis Regulates DNA Damage Repair during mESC Proliferation Directory of Open Access Journals (Sweden) Qidong Liu 2014-12-01 Full Text Available Embryonic stem cells (ESCs enable rapid proliferation that also causes DNA damage. To maintain genomic stabilization during rapid proliferation, ESCs must have an efficient system to repress genotoxic stress. Here, we show that withdrawal of leukemia inhibitory factor (LIF, which maintains the self-renewal capability of mouse ESCs (mESCs, significantly inhibits the cell proliferation and DNA damage of mESCs and upregulates the expression of miR-590. miR-590 promotes single-strand break (SSB and double-strand break (DSB damage repair, thus slowing proliferation of mESCs without influencing stemness. miR-590 directly targets Activin receptor type 2a (Acvr2a to mediate Activin signaling. We identified the homologous recombination-mediated repair (HRR gene, Rad51b, as a downstream molecule of the miR-590/Acvr2a pathway regulating the SSB and DSB damage repair and cell cycle. Our study shows that a miR-590/Acvr2a/Rad51b signaling axis ensures the stabilization of mESCs by balancing DNA damage repair and rapid proliferation during self-renewal. 6. Break the ice Institute of Scientific and Technical Information of China (English) 2015-01-01 Jacky：My sister is mad at me.She refuses（拒绝）to talk to me.What can I do to break the ice？Ella：You can buy her a little gift.Break的意思是＂打破＂,ice是指＂冰块＂。冰是又冷又硬的东西,作为俗语break the ice是指＂打破沉默（僵局）＂。Jacky惹妹妹生气,妹妹不理他了,他能通过送小礼物break the ice吗？ 7. Extracellular matrix metalloproteinase inducer (CD147/BSG/EMMPRIN)-induced radioresistance in cervical cancer by regulating the percentage of the cells in the G2/m phase of the cell cycle and the repair of DNA Double-strand Breaks (DSBs). Science.gov (United States) Ju, Xingzhu; Liang, Shanhui; Zhu, Jun; Ke, Guihao; Wen, Hao; Wu, Xiaohua 2016-01-01 Our preliminary study found that CD147 is related to radioresistance and maybe an adverse prognostic factor in cervical cancer. To date, the mechanisms underlying CD147-induced radioresistance in cervical cancer remain unclear. In the present study, we investigated the mechanisms by which CD147 affects radiosensitivity in cervical cancer both in vitro and in vivo. In this study, the clonogenic assay showed that radiosensitivity was significantly higher in the experimental group (the CD147-negative cell lines) than in the control group (the CD147-positive cell lines). After radiotherapy, the residual tumour volume was significantly lower in the experimental group. FCM analysis showed the cells percentage in the G2/M phase of the cell cycle were significantly higher in the CD147-negative group than in the control group. However, there was no significant difference in terms of apoptosis. The expression of gamma-H2A histone family, member X (γH2AX) was dramatically elevated in the CD147-negative cell lines after irradiation, but the expression of ataxia-telangiectasia mutated (ATM) was not different between the two groups. WB analysis did not show any other proteins relating to the expression of CD147. In conclusion, it is likely that CD147 regulates radioresistance by regulating the percentage of the cells in the G2/M phase of the cell cycle and the repair of DNA double-strand breaks (DSBs). Inhibition of CD147 expression enhances the radiosensitivity of cervical cancer cell lines and promotes post-radiotherapy xenograft tumour regression in nude mice. Therefore, CD147 may be used in individualized therapy against cervical cancer and is worth further exploration. PMID:27398135 8. Involvement of DNA-PK(sub cs) in DSB Repair Following Fe-56 Ion Irradiation Science.gov (United States) O'Neill, Peter; Harper, Jane; Anderson, Jennifer a.; Cucinnota, Francis A. 2007-01-01 9. Recombinational DNA repair is regulated by compartmentalization of DNA lesions at the nuclear pore complex DEFF Research Database (Denmark) Géli, Vincent; Lisby, Michael 2015-01-01 The nuclear pore complex (NPC) is emerging as a center for recruitment of a class of "difficult to repair" lesions such as double-strand breaks without a repair template and eroded telomeres in telomerase-deficient cells. In addition to such pathological situations, a recent study by Su and colle...... lesions that relocalize to the NPC, the putative mechanisms of relocalization, and the types of recombinational repair that are stimulated by the NPC, and present a model for NPC-facilitated repair.... 10. Bax-induced apoptosis shortens the life span of DNA repair defect Ku70-knockout mice by inducing emphysema. Science.gov (United States) Matsuyama, Shigemi; Palmer, James; Bates, Adam; Poventud-Fuentes, Izmarie; Wong, Kelvin; Ngo, Justine; Matsuyama, Mieko 2016-06-01 Cells with DNA damage undergo apoptosis or cellular senescence if the damage cannot be repaired. Recent studies highlight that cellular senescence plays a major role in aging. However, age-associated diseases, including emphysema and neurodegenerative disorders, are caused by apoptosis of lung alveolar epithelial cells and neurons, respectively. Therefore, enhanced apoptosis also promotes aging and shortens the life span depending on the cell type. Recently, we reported that ku70(-) (/) (-)bax(-) (/) (-) and ku70(-) (/) (-)bax(+/) (-) mice showed significantly extended life span in comparison with ku70(-) (/) (-)bax(+/+) mice. Ku70 is essential for non-homologous end joining pathway for DNA double strand break repair, and Bax plays an important role in apoptosis. Our study suggests that Bax-induced apoptosis has a significant impact on shortening the life span of ku70(-) (/) (-) mice, which are defective in one of DNA repair pathways. The lung alveolar space gradually enlarges during aging, both in mouse and human, and this age-dependent change results in the decrease of respiration capacity during aging that can lead to emphysema in more severe cases. We found that emphysema occurred in ku70(-) (/) (-) mice at the age of three-months old, and that Bax deficiency was able to suppress it. These results suggest that Bax-mediated apoptosis induces emphysema in ku70(-) (/) (-) mice. We also found that the number of cells, including bronchiolar epithelial cells and type 2 alveolar epithelial cells, shows a higher DNA double strand break damage response in ku70 KO mouse lung than in wild type. Recent studies suggest that non-homologous end joining activity decreases with increased age in mouse and rat model. Together, we hypothesize that the decline of Ku70-dependent DNA repair activity in lung alveolar epithelial cells is one of the causes of age-dependent decline of lung function resulting from excess Bax-mediated apoptosis of lung alveolar epithelial cells (and their 11. Testing cosmological supersymmetry breaking CERN Document Server Kabat, D; Kabat, Daniel; Rajaraman, Arvind 2001-01-01 Banks has proposed a relation between the scale of supersymmetry breaking and the cosmological constant in de Sitter space. His proposal has a natural extension to a general FRW cosmology, in which the supersymmetry breaking scale is related to the Hubble parameter. We study one consequence of such a relation, namely that coupling constants change as the universe evolves. We find that the most straightforward extension of Banks' proposal is disfavored by experimental bounds on variation of the fine structure constant. 12. Self-Breaking Technicolor CERN Document Server Martin, S P 1993-01-01 We propose a scenario in which the electroweak symmetry is spontaneously broken by an $SU(4)$ technicolor gauge interaction which also manages to break itself completely. The technicolor gauge bosons and technifermions are not confined by the technicolor force, but get large masses. Starting with a single technidoublet, one emerges with a complete standard model family of technifermions after the symmetry breaking is complete. This suggests a broad new avenue for model building. A few variations on the theme are mentioned. 13. Brain aneurysm repair Science.gov (United States) ... aneurysm repair; Dissecting aneurysm repair; Endovascular aneurysm repair - brain; Subarachnoid hemorrhage - aneurysm ... Your scalp, skull, and the coverings of the brain are opened. A metal clip is placed at ... 14. The Fanconi anaemia pathway: new players and new functions. Science.gov (United States) Ceccaldi, Raphael; Sarangi, Prabha; D'Andrea, Alan D 2016-06-01 The Fanconi anaemia pathway repairs DNA interstrand crosslinks (ICLs) in the genome. Our understanding of this complex pathway is still evolving, as new components continue to be identified and new biochemical systems are used to elucidate the molecular steps of repair. The Fanconi anaemia pathway uses components of other known DNA repair processes to achieve proper repair of ICLs. Moreover, Fanconi anaemia proteins have functions in genome maintenance beyond their canonical roles of repairing ICLs. Such functions include the stabilization of replication forks and the regulation of cytokinesis. Thus, Fanconi anaemia proteins are emerging as master regulators of genomic integrity that coordinate several repair processes. Here, we summarize our current understanding of the functions of the Fanconi anaemia pathway in ICL repair, together with an overview of its connections with other repair pathways and its emerging roles in genome maintenance. PMID:27145721 15. The Fanconi anaemia pathway: new players and new functions. Science.gov (United States) Ceccaldi, Raphael; Sarangi, Prabha; D'Andrea, Alan D 2016-06-01 The Fanconi anaemia pathway repairs DNA interstrand crosslinks (ICLs) in the genome. Our understanding of this complex pathway is still evolving, as new components continue to be identified and new biochemical systems are used to elucidate the molecular steps of repair. The Fanconi anaemia pathway uses components of other known DNA repair processes to achieve proper repair of ICLs. Moreover, Fanconi anaemia proteins have functions in genome maintenance beyond their canonical roles of repairing ICLs. Such functions include the stabilization of replication forks and the regulation of cytokinesis. Thus, Fanconi anaemia proteins are emerging as master regulators of genomic integrity that coordinate several repair processes. Here, we summarize our current understanding of the functions of the Fanconi anaemia pathway in ICL repair, together with an overview of its connections with other repair pathways and its emerging roles in genome maintenance. 16. Patch repair: compatibility issues OpenAIRE Garbacz, Andrzej; Courard, Luc; Bissonnette, Benoît; Głodkowska, W. 2014-01-01 Repair of any concrete structure results in formation of complex, at least two-component repair systems. Compatibility approach is treated as a basic requirement during selection of repair material. Recently, the understanding for compatibility requirements in repair systems approach is demonstrated in many papers. The aim of this paper is analyzing the compatibility between repair materials and concrete substrate in the case of patch repair. The compatibility issues were discussed in light o...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5384766459465027, "perplexity": 16394.655131767533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463605188.47/warc/CC-MAIN-20170522151715-20170522171715-00058.warc.gz"}
https://stats.stackexchange.com/questions/74561/how-to-create-forecast-data-prediction-interval-bands	# How to create forecast data prediction interval bands I have seasonal data from which I create forecasts. The steps I perform are: deseasonalizing the data, finding the linear regression for the deseasonalized points, predicting a few points from the linear regression and adding seasonality to the predicted values to get forecast data. My input is quite sinusoidal so all works well. The problem is that the more in the future you predict, the more prediction errors increase. I'd like to show that on a chart, but I am not sure how to calculate these errors. I was thinking something like prediction interval bands for forecast data (whatever they are called). These bands would increase the further you predict in the future. Here are some images that show what I'm trying to do: sample bands image1 sample bands image2 My question is what is the name for these bands? (then I can do a google search for it) I'd also appreciate the formulas needed for the band calculations. I'm guessing there is a standard deviation in there somewhere. I've looked at confidence interval, but that seems to be for the data already present, not for the forecast data. • Are you sure that your time series is deterministic in time? I.e., $Y_t=at+\epsilon_t$ after deseasonalizing, or have you considered a random walk with fixed drift: $Y_{t+1}=Y_t+\delta+\epsilon_t$? Where $\delta$ is a fixed "drift".The differnece is that the second form has much more variance and will not fall on a neat line, but it will increase over time. Just something to consider, as that info will help us recommend prediction bands. – user31668 Nov 4 '13 at 19:25 • @Eupraxis1981 The data is from google analytics so I am guessing it is deterministic in time. BTW my stats background is minimal. – Adrian Nov 4 '13 at 21:27 • Thanks for clarifying. I was asking about the specific data you are modeling. Is there a reason to believe that the linear trend model is appropriate. I.e., would you expect "regression towards the mean" at time $t>t_0$ if you saw a large/small value at $t_0$? Or, would you expect the trend to continue from the last observed point? – user31668 Nov 4 '13 at 21:42 • @Eupraxis1981 yes the linear trend is fine. – Adrian Nov 5 '13 at 16:30 ## 1 Answer Based on OP's comment that deseasonalized time series is a linear trend (t is a true predictor), then you will either want the Prediction Interval for linear regression (if you are trying to predict 1 time period ahead), or tolerance intervals if you are trying to capture a specific proportion of future measurements. If the residuals from your linear fit to the deseasonalized data are approximately normal, then there are nice formulas for as you will see in the above links: Also, eee this other CrossValidated Post. You would then re-seasonalize these intervals/bands to get your actual forcasts. • This is a great answer. The links are very useful. – Adrian Nov 5 '13 at 19:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8201520442962646, "perplexity": 862.5337522597531}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141750841.83/warc/CC-MAIN-20201205211729-20201206001729-00393.warc.gz"}
https://www.studyadda.com/notes/6th-class/mathematics/arithmetic/arithmetic/6161	# 6th Class Mathematics Arithmetic ARITHMETIC ARITHMETIC Category : 6th Class Learning Objective • To understand the term fraction and its types (proper, improper mixed, equivalent, like and unlike fractions) • To learn how to odd. Subtract multiply and divide proper, improper and mixed factions. • To understand the term decimal and representation of decimals on number line. • To learn how to compare decimal. • To learn how to add, subtract multiply and divide decimals. • To understand the terms ratio and proportion. • To learn how to find the value of one unit by using unitary method. FRACTION Fraction is a method for representing the parts of a whole number. In the fraction, $\frac{a}{b},$ a is the numerator and b is the denominator. Example: $\frac{2}{3},\,\frac{7}{8},\,\frac{3}{7},\,\frac{4}{9}]\ etc. TYPES OF FRACTION PROPER FRACTIONS In a proper fraction, the numerator is always smaller than the denominator. For example: \[\frac{1}{4},\,\frac{3}{5}$ etc. IMPROPER FRACTIONS In an improper fraction the numerator is greater than the denominator. For example: $\frac{5}{3},\,\frac{7}{4}$ is Fractions in the form of $1\frac{1}{4}$ or $2\frac{1}{2}$ are know as mixed fractions. Let us represent mixed fraction by using figures. EQUIVALENT FRACTIONS Equivalent fractions represent same part of the whole. For example $\frac{1}{2}\,=\frac{2}{4}\,=\frac{3}{6}\,=\frac{4}{8}\,=\frac{5}{10}$ We can find more equivalent fractions by multiplying or dividing the numerator and the denominator by the same number. SIMPLEST FORM OF A FRACTION A fraction is said to be in the simplest form (or lowest form) if its numerator and denominator have no common factor except 1. The easiest way to find the simplest form of a fraction is to divide the numerator and denominator by their HCF. For example: To reduce $\frac{125}{225},$ find their HCF. HCF of 125 and 225 =25 $\therefore \,\,\,\,\,\,\frac{125}{225}\div \frac{25}{25}=\frac{5}{9}$ simplest form To reduce $\frac{36}{72}$ H.C.F of 36 and 72 = 36 $\therefore \,\,\,\,\,\frac{36}{72}\div \frac{36}{36}=\frac{1}{2}$ simplest form. LIKE FRACTIONS Fractions with the same denominator are called like fractions. $\frac{4}{13},\,\frac{3}{13},\,\frac{12}{13},\,\frac{9}{13}$ are examples of like fractions. UNLIKE FRACTIONS Fractions like $\frac{1}{5},\,\frac{2}{3},\,\frac{3}{4}$ have different denominators are called unlike fractions. Fraction on the number line Let us draw a number line and mark $\frac{3}{4}$ on it. $\frac{3}{4}$ is greater than 0 and less that 1. As $\frac{3}{4}$ means 3 part out of 4, we will divide the gap between 0 and 1 into four equal parts, and mark $\frac{1}{4},\,\frac{2}{4},\,\frac{3}{4},\,\frac{4}{4}(=1)$ as shown below. COMPARING FRACTIONS COMPARING LIKE FRACTIONS To compare like fractions like $\frac{2}{5},\,\frac{7}{5},\,\frac{1}{5},\,\frac{3}{5},\,\frac{9}{5}$ we compare the numerators only $1<2<3<7<9$ $\frac{1}{5},\,\frac{2}{5},\,\frac{3}{5},\,\frac{7}{5},\,\frac{9}{5}$ To compare unlike fractions like $\frac{2}{3},\,\frac{3}{4},\,\frac{5}{7}$. We must first convert then to like fraction as follows: (i) Find the L.C.M of denominators 3, 4 and 7 i.e., L.C.M of 3, 4 and 7 is 84. (ii) Make each denominator 84. $\frac{2\times 28}{3\times 28}=\frac{56}{84}$ $\frac{3\times 21}{4\times 21}\,=\frac{63}{84}$ $\frac{5\times 12}{7\times 12}\,=\frac{60}{84}$ (iii) Now, we compare the numerators of these like fractions $\frac{56}{84},\,\frac{63}{84},\,\frac{60}{84}$ $\Rightarrow \,\,\frac{56}{84},\,\frac{60}{84},\,\frac{63}{84}$ i.e., $\frac{2}{3},\,\frac{5}{7},\,\frac{3}{4}$ ADDITION AND SUBTRACTION OF LIKE FRACTIONS Addition and subtraction of like fraction is very simple as they have same denominator. For example: $\frac{2}{10}+\frac{9}{10}=\frac{11}{10}$ (add the numerators) $\frac{9}{11}-\frac{5}{11}=\frac{4}{11}$ (subtract the numerators) ADDITION AND SUBTRACTION OF UNLIKE FRACTIONS To add or subtract unlike fractions, we should first find their equivalent fractions with the same denominator For example: To add $\frac{3}{2}$ and $\frac{4}{3},$ we find the LCM of the denominators 2 and 3 which is 6 Thus $\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}$ (add the numerators) Similarly, to subtract $\frac{1}{3}$ from $\frac{8}{7}$ i.e., $\frac{8}{7}-\frac{1}{3}$ LCM of 7 and 3 =21 $\frac{8}{7}\times \frac{3}{3}\,=\frac{24}{21}$ and $\frac{1}{3}\,\times \frac{7}{7}=\frac{7}{21}$ Thus $\frac{24}{21}\,-\frac{7}{21}\,=\frac{17}{21}$ (subtract the numerators) ADDITION AND SUBTRACTION OF MIXED FRACTIONS Method I: Convert mixed fraction into improper fraction and add as in the case of unlike fraction. For example: Add: $3\frac{3}{5}$ and $2\frac{5}{6}$ $3\frac{3}{5}+2\frac{5}{6}=\frac{18}{5}+\frac{17}{6}=\frac{18\times 6}{5\times 6}\,+\frac{17\times 5}{6\times 5}$ $=\frac{108}{30}+\frac{85}{30}$ (L.C.M of 5, 6 is 30) $\frac{193}{30}=6\frac{13}{30}$ Subtract: $3\frac{1}{4}-1\frac{1}{6}$ $3\frac{1}{4}\,-1\frac{1}{6}\,=\frac{13}{4}-\frac{7}{6}$ $=\frac{13\times 3}{4\times 3}-\frac{7\times 2}{6\times 2}$ $=\frac{39}{12}-\frac{14}{12}$ $=\frac{25}{12}=2\,\frac{1}{12}$ Method II The other method is to add the whole parts and proper fractions separately. For example: Add: $3\frac{3}{5}+2\frac{5}{6}$ $3\frac{3}{5}+2\frac{5}{6}\,=3+2+\frac{3}{5}+\frac{5}{6}\,=5+\frac{3}{5}+\frac{5}{6}$ Now, $\frac{3}{5}+\frac{5}{6}\,=\frac{3\times 6}{5\times 6}\,+\frac{5\times 5}{\,6\times 5}\,=\frac{18}{30}+\frac{25}{30}=\frac{43}{30}\,=1\frac{13}{30}$ $\therefore \,\,3+2+\frac{3}{5}+\frac{5}{6}\,=5+1\frac{13}{30}\,=5+1+\frac{13}{30}\,=6\frac{13}{30}$ Subtract: $3\frac{1}{4}\,-1\frac{1}{6}$ $3\frac{1}{4}\,-1\frac{1}{6}=3-1+\frac{1}{4}-\frac{1}{6}$ Consider, $\frac{1}{4}-\frac{1}{6}=\frac{1\times 3}{4\times 3}-\frac{1\times 2}{6\times 2}$ $=\frac{3}{12}-\frac{2}{12}=\frac{1}{12}$ $\therefore \,\,3-1\,+\frac{1}{4}\,-\frac{1}{6}\,=2+\frac{1}{12}=2\frac{1}{12}$ DECIMALS Decimal numbers or simply decimals are the fractions with denominators 10, 100, 1000 etc. For example: $\frac{7}{10},\,\frac{15}{100},\,\frac{21}{1000}$ etc. The number before the decimal point is called the whole part or integral part, whereas the number after the decimal point is called the decimal part. For example: In 12.73 Whole part is 12 and decimal part is 73 We read 12.73 as twelve point seven three. LIKE DECIMALS Like decimals have an equal number of digits to the right of the decimal point. For example: $13.$ and $4.$ are like decimals. UNLIKE DECIMALS The decimals having the different number of decimal places are called unlike decimals. For example: $2.$ $1.$ $2.$ REPRESENTATION OF DECIMALS ON THE NUMBER LINE REPRESENTATION OF 4.2 ON THE NUMBER LINE Clearly 4.2 lies between 4 and 5 in Fig. (i). Take a magnified look of the line segment between 4 and 5 and divide it into 10 equal parts and mark each point of division between 4 and 5 as shown in the Fig. (ii). We can see in Fig. (ii), 4.2 is represented by the second mark of division after 4 in between 4 and 5. FRACTIONS AS DECIMALS To express given fraction into decimals, we follow the following steps: Case I: Fractions whose denominators are of 10, 100, 1000 etc. Step (i) Count the number of zeroes in denominator. Step (ii) Place the decimal point in numerator so that the number of digits on right of decimal point becomes equal to the number of zeroes in denominator. Step (iii) In case the number of digits in numerator is less than the number of zeroes in denominator, we place zero just right to decimal. For example: In $\frac{14}{1000},$ number of zeros in denominator is 3 So, $\frac{14}{1000}=0.014$ Case II: Fractions whose denominators are not 10, 100, 1000 etc. Divide the numerator by the denominator and write the quotient in decimal form. DECIMALS AS FRACTION (i) To express the given decimals into fraction, we follow the following steps; Step (i) Write the decimal without the decimal point as the numerator of the fraction. Step (ii) Write the denominator of the fraction by inserting as many zeros on the right of 1 as the number of decimal places in the given decimals. Step (iii) Simplify the fraction and write the fraction in the lowest form. For example: Express 0.038 as fraction $0.038\,=\frac{38}{1000}\,=\frac{19}{500}$ COMPARING DECIMALS TO COMPARE LIKE DECIMALS To compare like decimals follow these steps. 1. Compare the whole part of the decimal number. The number with greater whole part will be greater they are same, then go to the second step. 2. Compare the tenths place digits. The number with greater tenths digit will be greater. If they are also same, then go to the third step. 3. Compare the digit in the hundredths place. The number with greater hundredths digit will be greater. If they are also equal, then compare the thousandths place and so on. For example: To compare 0.275, 2.34, 4.67, 2.24,4.67 > 2.34 > 2.24 > 0.275. TO COMPARE UNLIKE DECIMALS Like decimals and follow the steps to compare like decimals. For example: To compare 4.2 and 4.27 first convert them to like decimals 4.20 and 4.27, 4.27 > 4.20 (0. 7 > 0) USES OF DECIMALS (I) IN MONEY VALUE We know that 100 paise = Rs 1 Therefore, 1 paisa $=\frac{1}{100}=\text{Rs}\,0.01$ So 45paisa $=\frac{45}{100}=\text{Rs}\,0.45$ (II) IN MEASURES OF LENGTH 1km = 1000m $1m\,=\frac{1}{1000}km$ 1m = 100 cm $1cm=\frac{1}{100}m$ 1dm =10 cm $1cm=\frac{1}{10}\,dm$ 1 cm = 10 mm $1mm=\frac{1}{10}\,cm$ For example: $7m=\frac{7}{1000}\,=0.007km$ (III) IN MEASURES OF WEIGHT Same as discussed in length (above) just use 'g' instead of 'm'. 1kg = 1000gm 1gm = 1000mg i.e., $1\,g\,=\frac{1}{1000}\,kg$ $1mg\,=\frac{1}{1000}\,gm$ For example: $7gm\,=\frac{7}{1000}\,kg\,=0.007\,gm$ OPERATIONS OF DECIMALS Step (i) Convert the given decimals to like decimals. Step (ii) Write the decimals in columns with the decimal points directly below each other so that tenths come under tenths hundredths come under hundredths and so on. Step (iv) Place the decimal point in the answer directly below the other decimal points. For Example: Add 12.73, 4.7, 1.074 12.730 + 4.700 + 1.074 _______ 18.504 _______ 9.23 + 4.75 + 8.10 ______ 22.08 ______ SUBTRACTION OF DECIMALS We may follow the following steps to subtract a decimal number from another decimal number. Step (i) Convert the given decimals to like decimals. Step (ii) Write the decimals in columns with decimal points directly below each other. Step (iii) Subtract as we subtract whole numbers starting from right. Step (iv) Place the decimal point in the difference directly below the other decimal points. For example: Subtract 10.205 from 20.05 20.050 - 10.250 _______ 9.800 _______ RATIO Ratio: If a and $b(b\ne 0)$ are two quantities of the same kind, then the fraction a- is called the ratio of a to b. • For a ratio the two quantities must be in the same unit. • Two ratios are equivalent, if the fractions corresponding to them are equivalent. • Ratio is expressed in its simplest form cannot be further simplified. COMPARISON OF RATIOS To compare two given ratios, we follow the following steps: (i) Express the given ratio in the form of a fraction. (ii) Convert the fraction in its simplest form. (iii) Find the L.C.M of the denominators of the simplest form of the fraction obtained in above step. (iv) Divide the L.C.M obtained in step (iii) by the donominator of first fraction to get a number a (say). Now, multiply the numerator and denominator of the fraction by x. Apply the same procedure for other fraction. (v) Compare the numerators of the fractions obtained in step (v). (vi) Having the same denominators. The fraction having larger numerator will be larger than the other. For example: Compare the ratios 7 : 12 and 5:8 we have, $7:12\,=\frac{7}{12}$ and $5:8=\frac{5}{8}$ (given ratios are in their simplest form) Now, L.C.M. of 12 and 8 is 24. Making the denominators equal to 24 of each fraction, we have $\frac{7\times 2}{12\times 2}\,=\frac{14}{24}\,$ and $\frac{5\times 3}{\,8\times 3}\,=\frac{15}{24}$ Clearly, 15 > 14 $\therefore \,\,\,\frac{15}{24}>\frac{14}{24}$ $\Rightarrow \,\,\,\frac{5}{8}\,>\frac{7}{12}$ EQUIVALENT RATIOS A ratio obtained by multiplying or dividing the numerator and denominator by the same number is called an equivalent ratio. For example: Consider the ratio 5 : 7 We have, $\frac{5}{7}=\frac{5\times 2}{7\times 2}\,=\frac{10}{14}$ $\frac{5}{7}\,=\frac{5\times 3}{7\times 3}\,=\frac{15}{21}$ and so on. also, $\frac{10}{14}=\frac{10\div 2}{14\div 2}=\frac{5}{7}$ $\frac{10}{14},\,\frac{15}{21},\,\frac{20}{28}$ etc. are equivalent to the ratio $\frac{5}{7}$ PROPORTION PROPORTION Proportion is defined as an equality of two ratios, Four (non-zero) quantities of the same kind a, b, c and d are said to be in proportion if the ratio of a to b is equal to the ratio of c to d i.e., if $\frac{a}{b}=\frac{c}{d}$ we can write as a : b : : c : d a, b, c, d are in proportion if ad = be The (non-zero) quantities of the same kind a, b, c, d, e, f,... are said to be in continued proportion. $\frac{a}{b}=\frac{b}{c}\,=\frac{c}{d}=\frac{d}{e}=$ If a, b, c are in continued proportion, then b is called mean proportional of a and c. If a, b, c are in continued proportion then c is called the third proportional. For example: Check if 3,4, 6 and 12 are in proportion we have, a = 3, b = 4, c = 6 and d = 12 $\frac{a}{b}=\frac{3}{4}$ and $\frac{c}{d}=\frac{6}{12}\,=\frac{1}{2}$ Clearly, $\frac{a}{b}\ne \frac{c}{d}$ $\therefore \,\,\,\,\,\,3:4\ne 6:12$ Hence, 3, 4, 6 and 12 are not in proportion. UNITARY METHOD The method in which first we find the value of one unit and then the value of required number of units by multiplying the value of one unit with the number of required units. For example: A car travels 240 km in 4 hours. How for does it travel in 7 hours? Solution We have, Distance travelled in 4 hours = 240 km \Distance travelled in 1 hour $=\left( \frac{240}{4} \right)$ km = 60 km Hence, the distance travelled in 7 hours = (60 x 7) = 420 km For example: The cost of four dozens of mangoes is Rs 150. What will be the cost of such 12 dozens of mangoes? Solution: We know cost of 1 dozen mangoes $=\frac{150}{4}$ cost of 12 dozen of mangoes $=\frac{150}{\bcancel{4}}\times {{\bcancel{12}}^{3}}$ = Rs450 #### Other Topics ##### Notes - Arithmetic You need to login to perform this action. 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https://bartoszregula.me/code/probabilistic-coherence	## Probabilistic distillation of quantum coherence arxiv:1804.09500 ### The semidefinite programs for $P_{\text{MIO}}(\rho,m,\varepsilon)$ and $P_{\text{DIO}}(\rho,m,\varepsilon)$ The semidefinite programs used to compute the maximal probability of successful distillation of a given quantum state are derived in the manuscript. The implementation below uses CVX and returns both the primal and the dual optimal solutions, following the notation used in the Supplemental Material of the manuscript. function [prob,C,G,X,Y,Z,lam] = prob_mio(rho, m, tol) % prob_mio(rho,m,tol) computes the maximal probability of distillation of an m-dimensional maximally coherent state under DIO with tolerance tol % rho: dxd density matrix or normalised state vector % m: target state dimension % tol: error tolerance 0<=tol<=1 d=size(rho,2); if d==1 rho=rhorho'; d=size(rho,1); end rho=(rho+rho')/2; cvx_begin sdp quiet variable C(d,d) hermitian semidefinite variable G(d,d) hermitian dual variable X dual variable Y dual variable Z dual variable lam maximize ( trace(Grho) ) Y : C <= G X : G <= eye(d) Z : diag(diag(G))==mdiag(diag(C)) lam : trace(Crho) >= (1-tol)trace(Grho) cvx_end prob = cvx_optval; end function [prob,C,X,Y,lam] = prob_dio(rho, m, tol) % prob_dio(rho,m,tol) computes the maximal probability of distillation of an m-dimensional maximally coherent state under DIO with tolerance tol % rho: dxd density matrix or normalised state vector % m: target state dimension % tol: error tolerance 0<=tol<=1 d=size(rho,2); if d==1 rho=rhorho'; d=size(rho,1); end rho=(rho+rho')/2; cvx_begin sdp quiet variable C(d,d) hermitian semidefinite dual variable X dual variable Y dual variable lam maximize ( mtrace(diag(diag(C))rho) ) Y : C - mdiag(diag(C)) <= 0 X : mdiag(diag(C)) <= eye(d) lam : trace(Crho) >= (1-tol)trace(mdiag(diag(C))rho) cvx_end prob = cvx_optval; end Note that we show the probability of exact ($\varepsilon=0$) distillation under DIO for pure states to be equal to the probability of distillation under SIO, which is much simpler to compute — an example implementation is given below. function [prob] = prob_sio(psi, m) % prob_sio(psi,m) computes the probability of distillation of an m-dimensional maximally coherent state from the pure state vector psi d = max(size(psi)); psi = sort(abs(psi),'descend'); minsum=sum(psi(m:d).^2); for j=2:m jsum = sum(psi(m-j+1:d).^2)/j; minsum = min([jsum, minsum]); end prob = mminsum; end	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7353127002716064, "perplexity": 14202.102013035439}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304961.89/warc/CC-MAIN-20220126192506-20220126222506-00644.warc.gz"}
https://stats.stackexchange.com/questions/259479/if-i-toss-a-biased-coin-4-times-and-i-bet-on-one-side-twice-then-the-other-side	# If I toss a biased coin 4 times, and I bet on one side twice then the other side twice, does it matter which side I start on? Steven and I have a biased coin. The coin has a 90% chance to show heads, and a 10% chance to show tails. We flip the coin in the same way 4 times. Steven picks heads for the first two rounds and I pick tails for the first two rounds. Then I choose heads for the last two rounds and Steven chooses tails for the last two rounds. In order to win, one of us must succeed 3 times. Is one of us more likely to win? My calculation shows that we each have a 0.1557 chance of winning. My friend is arguing that I am wrong based on absorbing markov chains. Here's what I've done: https://www.scribd.com/document/338158368/Swap-Side-Balance Am I crazy or is this really obvious that it doesn't matter which side you start on? • Which player does your friend claim will win more often and why? – whuber Oct 19 '17 at 14:44 Before looking at the precise numbers, this looks essentially symmetric if you toss four times and so each player has the same probability of winning. Stopping after somebody has three should not change this Now looking at the probabilities, Steven wins if: • HHH probability $0.9^3=0.081$ • HHTH probability $0.9^3\times 0.1 = 0.0729$ • HTHH probability $0.9 \times 0.1^3=0.0009$ • THHH probability $0.9 \times 0.1^3=0.0009$ which is $0.1557$ as you say You win if • TTT probability $0.9 \times 0.1^2=0.009$ • TTHT probability $0.9 \times 0.1^3=0.0009$ • THTT probability $0.9^3\times 0.1 = 0.0729$ • HTTT probability $0.9^3\times 0.1 = 0.0729$ which is also $0.1557$ You can calculate the probability of a two-two tie as $0.9^4+4\times 0.9^2\times 0.1^2+0.1^4=0.6886$, making the total probability $1$ Check out the 'Monty Hall' problem ( https://betterexplained.com/articles/understanding-the-monty-hall-problem/ ) If you assume you know, in advance, what will be the odds then you will get problematic logic. In this case, you assume both of you know this coin is biased, and what the odds are. Thus, the 'betting strategy' makes no difference: either of you can choose the first two (or last two) tosses, and things will be equal. Things come out very differently if either (1) only one of you knows the facts, or (2) neither of you knows the facts. People have written long papers on the Monty Hall problem. In the end - all math aside - it comes down to the fact he knows something you do not. A great deal of the field of Information Theory is about dealing with the balance of the known and unknown.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8802645802497864, "perplexity": 720.2200215900679}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347432521.57/warc/CC-MAIN-20200603081823-20200603111823-00558.warc.gz"}
https://registration.mcs.cmu.edu/event/1/contributions/6/	Jun 2 – 7, 2019 Carnegie Mellon University America/New_York timezone ## Properties of hadrons in medium in the context of Fermi Liquid Model and diquarks. Jun 4, 2019, 4:30 PM 30m Rangos 2 ### Speaker The Landau Fermi liquid theory is an phenomenological approach to strongly interacting normal Fermi system at small excitation energies. It is a model which suggest a point to point correspondence between low energy excitation of non interacting Fermi gas. The model has been widely used to study the properties of liquid He-3, electron in metal and nuclear matter. It gives an effective description of low energy elementary excitations like the quasi particles in crystal lattice. The model is found to be successful in describing some aspects of QCD, quark and hadronic matter also. In the current work a Fermi liquid model for hadrons has been suggested for the hadrons in medium. The hadrons are supposed to behave like quasi particle as Fermi excitation while in the medium and the effective mass of the hadrons have been estimated using Fermi liquid model. Considering a momentum dependent potential like $V(r,p^{2}) =V^{'}e^{-\gamma(\frac{p^{2}}{m}})\upsilon(r)$ inside the medium to describe the interaction, the effective masses of the hadrons are estimated.Compressibility, specific heats, density of states in medium have been studied. We have extracted the values of available well depths which give the idea about the binding energy of the particles in medium. We have also studied the masses of exotic baryons in the framework of diquark formalism. A quasi particle model of diquark has been suggested in an analogy with composite fermion and subsequently used to compute the masses of baryons like $\lambda_{b}^{0}$, $\Sigma_{b}^{0}$, $\Xi_{b}^{0}$, $\Xi_{cc}^{+}$, $\Omega_{cc}^{+}$, $\Omega_{cb}^{0}$,$\Omega_{ccc}$, $\Omega_{bbb}$. Using a density and momenum dependent potential of the form $V_p = \frac{\rho/\rho_{0}}{1+ {(\frac{p}{\lambda})}^2}$ at p= $p_{f}$, the mass of the diquark have been estimated. The results are found to be very interesting and compared with the other theoretical and experimental studies available in literature.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9507775902748108, "perplexity": 484.65560940981055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711108.34/warc/CC-MAIN-20221206124909-20221206154909-00570.warc.gz"}
http://lists.gnu.org/archive/html/texinfo-commits/2010-10/msg00122.html	texinfo-commits [Top][All Lists] ## texinfo ChangeLog doc/texinfo.txi util/htmlxref... From: Karl Berry Subject: texinfo ChangeLog doc/texinfo.txi util/htmlxref... Date: Mon, 25 Oct 2010 16:26:36 +0000 ```CVSROOT: /sources/texinfo Module name: texinfo Changes by: Karl Berry <karl> 10/10/25 16:26:36 Modified files: . : ChangeLog doc : texinfo.txi util : htmlxref.cnf Log message: (HTML Customization for {Anchors,Images}): rename+edit; alphabetization fixes in Command List CVSWeb URLs: http://cvs.savannah.gnu.org/viewcvs/texinfo/ChangeLog?cvsroot=texinfo&r1=1.1163&r2=1.1164 http://cvs.savannah.gnu.org/viewcvs/texinfo/doc/texinfo.txi?cvsroot=texinfo&r1=1.332&r2=1.333 http://cvs.savannah.gnu.org/viewcvs/texinfo/util/htmlxref.cnf?cvsroot=texinfo&r1=1.21&r2=1.22 Patches: Index: ChangeLog =================================================================== RCS file: /sources/texinfo/texinfo/ChangeLog,v retrieving revision 1.1163 retrieving revision 1.1164 diff -u -b -r1.1163 -r1.1164 --- ChangeLog 24 Oct 2010 22:52:51 -0000 1.1163 +++ ChangeLog 25 Oct 2010 16:26:35 -0000 1.1164 @@ -1,3 +1,11 @@ + + * doc/texinfo.txi (Command List): alphabetization fixes. + Report from Christophe Jarry, 23 Oct 2010 17:45:54. + + (HTML Customization for Anchors, HTML Customization for Images): + rename+edit. + * texi2html/texi2html.pl (%index_names): remove the 'prefixes' key, Index: doc/texinfo.txi =================================================================== RCS file: /sources/texinfo/texinfo/doc/texinfo.txi,v retrieving revision 1.332 retrieving revision 1.333 diff -u -b -r1.332 -r1.333 --- doc/texinfo.txi 15 Oct 2010 18:36:16 -0000 1.332 +++ doc/texinfo.txi 25 Oct 2010 16:26:35 -0000 1.333 @@ -1,5 +1,5 @@ \input texinfo.tex @c --texinfo-- address@hidden \$Id: texinfo.txi,v 1.332 2010/10/15 18:36:16 karl Exp \$ address@hidden \$Id: texinfo.txi,v 1.333 2010/10/25 16:26:35 karl Exp \$ @c Ordinarily, Texinfo files have the extension .texi. But texinfo.texi @c clashes with texinfo.tex on 8.3 filesystems, so we use texinfo.txi. @@ -5352,6 +5352,7 @@ feature, for that group of nodes. In those cases, you will need to explicitly specify all pointers. + @node anchor @section @code{@@anchor}: Defining Arbitrary Cross-reference Targets @@ -11380,23 +11381,22 @@ @table @asis @item @result{} @item @expansion{} @item @print{} @item @error{} message. @item @equiv{} @item @point{} @end table @@ -20854,19 +20854,20 @@ Texinfo commands used within the running text. -* Argless: Customizing HTML for Commands Without Arguments. -* @@-Colon: Customizing HTML After @@-Colon. -* Simple: Customizing HTML for Simple Commands. -* Formatting special simple commands:: +* Argless: HTML Customization for Commands Without Arguments. +* @@-Colon: HTML Customization After @@-Colon. +* Simple: HTML Customization for Simple Commands. +* Anchors: HTML Customization for Anchors. +* Images: HTML Customization for Images. * Formatting characters and text:: * Formatting of simple line commands:: address@hidden Customizing HTML for Commands Without Arguments address@hidden Customizing HTML for Commands Without Arguments address@hidden HTML Customization for Commands Without Arguments address@hidden HTML Customization for Commands Without Arguments address@hidden Customizing HTML for commands without arguments address@hidden HTML customization for commands without arguments @cindex Commands without arguments, customizing HTML for @cindex Insertion commands, customizing HTML for @@ -20939,10 +20940,10 @@ @end deftypefn @cindex Punctuation after @code{@@:}, customizing HTML for @cindex Sentence punctuation, customizing HTML for @@ -20965,10 +20966,10 @@ @end deftypefn address@hidden Customizing HTML for Simple Commands address@hidden Customizing HTML for Simple Commands address@hidden HTML Customization for Simple Commands address@hidden HTML Customization for Simple Commands address@hidden Customizing HTML for simple commands address@hidden HTML customization for simple commands @cindex Simple commands, customizing HTML for @cindex Style commands, customizing HTML for @cindex Accent commands, customizing HTML for @@ -21177,8 +21178,8 @@ @cindex Custom interface for simple HTML customization @cindex Interface for simple HTML customization, custom -If you don't like the hash interface described in the previous -section, it is possible to change how the ``simple'' Texinfo commands +If the hash interface described in the previous section does not +suffice, it is possible to change how the ``simple'' Texinfo commands are processed by redefining the following function reference: @deftypefn {Function Reference} \$resulting_text style \$style \$command \$text @ @@ -21216,85 +21217,129 @@ @end deftypefn address@hidden Formatting of anchors, images and spaces -The formatting of special simple commands is controlled by functions. To -customize the output, the corresponding function references should be -redefined. All these functions return a formatted text. -The formatting of anchors is controlled by @code{\$anchor_label}. +The HTML formatting of anchors (@pxref{anchor,, @code{@@anchor}}) is +controlled by functions. To customize the output, the function +reference @code{\$anchor_label} should be redefined. The function +should return the formatted text. @deftypefn {Function Reference} \$anchor_label anchor_label \$identifier \$anchor address@hidden is the anchor identifier, @var{\$anchor} is the @code{@@anchor} -argument. address@hidden is the anchor identifier, and @var{\$anchor} is the @end deftypefn -In the default case, it uses a function reference, @code{\$anchor} - that can do -a reference target or link. It is especially relevant for @acronym{HTML} -but can be used in other formats, it is a rather common element -of different formats. address@hidden {Function Reference} \$anchor anchor \$identifier \$href \$text \$attributes -If @var{\$identifier} is not empty, this value should be used to create -a target for links (typically associated with a name or id -attribute in @acronym{HTML}). -The @var{\$href} argument specifies a hpertextual reference which should be -used to link to a target. -In case both @var{\$identifier} and @var{\$href} are given the text produced -should be both a target for @var{\$identifier} and a link to @var{\$href}. address@hidden is the text to be displayed. -It should be reasonable to assume that the attributes are for a @code{<a>} +By default, this uses a function reference, @code{\$anchor}, which can +do a reference target or link. This is especially relevant for HTML +but can potentially be used in other formats, since it is a rather +common element among output formats. + address@hidden {Function Reference} \$anchor anchor @ + \$identifier \$href \$text \$attributes +If @var{\$identifier} is not empty, its value should be used to create +a target for links (typically associated with a name or id attribute +in HTML). The @var{\$href} argument specifies a hypertext reference +which should be used to link to a target. If both @var{\$identifier} +and @var{\$href} are given, the text produced should be both a target +for @var{\$identifier} and a link to @var{\$href}. @var{\$text} is the +text to be displayed. @var{\$attributes} are additional attributes for +an @code{<a>} HTML element. @end deftypefn + + + @vindex @@IMAGE_EXTENSIONS -To customize the images produced by @code{@@image}, the first possibility -is to modify the @code{@@IMAGE_EXTENSIONS} array, which holds a list of -filename extensions for image files. It is also possible to redefine -the function used to determine the filename of the image: - address@hidden {Function Reference} \$filename image_files \$basename \$extension \$texi_base \$texi_extension address@hidden is the first @code{@@image} argument, @var{\$extension} -is the corresponding @code{@@image} argument, both are formatted. -Similarly @var{\$texi_base} is the first @code{@@image} argument -without formatting, and @var{\$texi_extension} is the extension, unformatted. -This function reference -should return an array of array references, each array reference holding -a formatted and an unformatted image filenames without path that the main -program should look for. - -Last, it is possible to control -the formatting of @code{@@image} by redefining: address@hidden {Function Reference} \$image image \$file_path \$basename \$preformatted \$file_name \$alt_text \$width \$height \$raw_alt \$extension \$working_dir \$file_relative_path \$in_paragraph \@@file_locations \$base_simple_format \$extension_simple_format \$file_name_simple_format \$line_nr address@hidden is the image file name with the path from the output directory -to the source manual directory prepended, @var{\$basename} -the file name without extension (the first @code{@@image} argument). address@hidden is true if the image -appears in preformatted text. @var{\$file_name} is the file name without path -but with extension. @var{\$alt_text} is the alternate text, it may be -undefined. @var{\$width} and @var{\$height} are the corresponding arguments -of @code{@@image}, @var{\$raw_alt} is the unmodified alt argument of address@hidden@@image} and @var{\$extension} holds the corresponding address@hidden is the path to working dir relative to the output -directory. @var{\$file_relative_path} is the file name relative to the address@hidden is true if in paragraphs. address@hidden@@file_locations} is a reference on an array which itself holds a reference on an -array with 3 elements: the file name array reference as returned by @code{image_files}, -the image location if it was found, or undef, and the file name formatted using -a simple formatting in string context. address@hidden is the @var{\$basename} formatted with a simple format. address@hidden is the @var{\$extension} formatted with a simple format. address@hidden is the @var{\$file_name} formatted with a simple format. -is an opaque structure containing the information about the line number of the -@@-command. +To customize the images produced by @code{@@image} (@pxref{Images}), +the first possibility is to modify the @code{@@IMAGE_EXTENSIONS} +array, which holds a list of filename extensions for image files. + +Second, it is also possible to redefine the function used to determine +the filename of the image: + address@hidden {Function Reference} \$filename image_files @ + \$basename \$extension \$texi_base \$texi_extension address@hidden is the first @code{@@image} argument, and address@hidden is the corresponding @code{@@image} argument; both +are formatted. @var{\$texi_base} is the first @code{@@image} argument +and @var{\$texi_extension} is the extension, unformatted. This +function reference should return an array of array references, each +holding both formatted and unformatted image filenames without any path +for which the main program should look. + +Third, it is possible to control the formatting of @code{@@image} by +redefining this: + address@hidden {Function Reference} \$image image \$file_path \$basename @ + \$preformatted \$file_name \$alt_text \$width \$height \$raw_alt @ + \$extension \$working_dir \$file_relative_path \$in_paragraph @ + \@@file_locations \$base_simple_format @ + \$extension_simple_format \$file_name_simple_format \$line_nr +The image file name with the path from the output directory to the +source manual directory prepended. + +The file name without extension---the first argument to the + +True if the image appears in preformatted text. + +The file name without path but with extension. + +The alternate text, possibly undefined. + +The corresponding @code{@@image} arguments. + +The unmodified alternate-text @code{@@image} argument. + +The corresponding @code{@@image} argument. + +Path to the working directory relative to the output directory. + +The file name relative to @var{\$working_dir}. + +True if within a paragraph. + +Array reference holding another array reference with 3 elements: the +file name array reference as returned by @code{image_files}; the image +location if it was found, or undef; and the file name formatted using +simple formatting in string context. + +The corresponding arguments formatted using simple formatting in +string context. + +An opaque structure containing the information about the line number +of the @@-command. @end deftypefn + The formatting of @code{@@sp} is controlled by: @deftypefn {Function Reference} \$sp sp \$number \$preformatted @var{\$number} is the numeric argument of @code{@@sp}. @@ -21314,7 +21359,7 @@ reference on an array containing the simply fomatted explanation lines, @var{\$explanation_text} is the explanation text formatted, @var{\$explanation_simply_formatted} is the explanation formatted in -a string context, enabling in @acronym{HTML} (or @acronym{XML}) the explanation +a string context, enabling in HTML (or @acronym{XML}) the explanation to be in an attribute. @end deftypefn @@ -21346,11 +21391,11 @@ In the default case the @samp{---}, @samp{--}, @samp{``} and @samp{''} constructs are expanded if needed and the text is upper-cased if in @code{@@sc}. Special characters (@samp{&}, @samp{"}, address@hidden<} and @samp{>} in @acronym{HTML}) are protected if needed. address@hidden<} and @samp{>} in HTML) are protected if needed. @end deftypefn Some characters are special, for example we have @samp{&}, @samp{"}, address@hidden<} and @samp{>} in @acronym{HTML}. In some cases some address@hidden<} and @samp{>} in HTML. In some cases some pieces of text don't go through the above function, but still needs to be protected to appear in text. This is done by the function associated with the function reference @@ -21581,7 +21626,7 @@ The @code{end} should lead to the end of the formatted output. @item class -The @acronym{HTML} class. If not defined, the command name. +The HTML class. If not defined, the command name. @item pre_style The preformatted style. If not defined the corresponding @acronym{CSS} style is used. @@ -22380,7 +22425,7 @@ @deftypefn {Function Reference} \$target index_entry_label \$identifier \$preformatted \$entry \$index_name \$index_command \$texi_entry \$formatted_entry \$in_region_not_in_output \%index_entry @var{\$identifier} should be used to create a target for links (typically associated with a name or id -attribute in @acronym{HTML}). +attribute in HTML). @var{\$preformatted} is true if the index entry appeared in preformatted text. @var{\$entry} is the index entry with all the @@-commands removed. @var{\$index_name} is the index name, @var{\$command} is the index command which @@ -23103,6 +23148,14 @@ Highlight the name of a book or other reference that has no companion Info file. @xref{cite, , @code{@@cite}}. +Unset @var{flag}, preventing the Texinfo formatting commands from +formatting text between subsequent pairs of @code{@@ifset @var{flag}} +and @code{@@end ifset} commands, and preventing which address@hidden clear value, , @code{@@set} @code{@@clear} @code{@@value}}. + Represent a single ``click'' in a GUI. Used within @code{@@clicksequence}. @xref{Click Sequences}. @@ -23115,14 +23168,6 @@ @code{@@arrow}. The usual following empty braces on @@@var{cmd} are omitted. @xref{Click Sequences}. -Unset @var{flag}, preventing the Texinfo formatting commands from -formatting text between subsequent pairs of @code{@@ifset @var{flag}} -and @code{@@end ifset} commands, and preventing which address@hidden clear value, , @code{@@set} @code{@@clear} @code{@@value}}. - Indicate an expression, a syntactically complete token of a program, or a program name. Unquoted in Info output. @xref{code, , @@ -23364,10 +23409,6 @@ Ends @var{environment}, as in @samp{@@end example}. @xref{Formatting Commands,,@@-commands}. -Indicate an environment variable name, such as @env{PATH}. - Generate an end-of-sentence ellipsis, like this: @enddots{} @@ -23378,18 +23419,22 @@ @code{@@end enumerate}. @xref{enumerate, , @code{@@enumerate}}. +Indicate an environment variable name, such as @env{PATH}. + Indicate to the reader the exact equivalence of two forms with a -Generate the Euro currency sign. - Indicate to the reader with a glyph that the following text is an error message: @address@hidden @xref{Error Glyph}. +Generate the Euro currency sign. + Specify page footings resp.@: headings for even-numbered (left-hand) @@ -24757,7 +24802,7 @@ (@url{http://www.gnu.org/software/rcs}) version control systems, which expand it into a string such as: @example -\$Id: texinfo.txi,v 1.332 2010/10/15 18:36:16 karl Exp \$ +\$Id: texinfo.txi,v 1.333 2010/10/25 16:26:35 karl Exp \$ @end example (This is useful in all sources that use version control, not just manuals.) You may wish to include the @samp{\$Id:} comment in the @code{@@copying} @@ -24836,7 +24881,7 @@ @verbatim \input texinfo @c --texinfo-- address@hidden \$Id: texinfo.txi,v 1.332 2010/10/15 18:36:16 karl Exp \$ address@hidden \$Id: texinfo.txi,v 1.333 2010/10/25 16:26:35 karl Exp \$ @setfilename sample.info @include version.texi Index: util/htmlxref.cnf =================================================================== RCS file: /sources/texinfo/texinfo/util/htmlxref.cnf,v retrieving revision 1.21 retrieving revision 1.22 diff -u -b -r1.21 -r1.22 --- util/htmlxref.cnf 15 Oct 2010 18:36:17 -0000 1.21 +++ util/htmlxref.cnf 25 Oct 2010 16:26:36 -0000 1.22 @@ -1,6 +1,6 @@ # htmlxref.cnf - reference file for Texinfo files on the web. -htmlxrefversion=2010-10-15.17; # UTC +htmlxrefversion=2010-10-25.15; # UTC # Copyright 2010 Free Software Foundation, Inc. # @@ -194,6 +194,9 @@ global mono \${GS}/global/manual/global.html +gmp mono \${GS}/gmp/manual/html_mono/gmp.html +gmp node \${GS}/gmp/manual/html_node/ + gnu-arch node \${GS}/gnu-arch/tutorial/ gnu-crypt node \${GS}/gnu-crypto/manual/ @@ -217,9 +220,18 @@ gnuschool mono \${GS}/gnuschool/gnuschool.html +gnutls mono \${GS}/gnutls/manual/gnutls.html +gnutls node \${GS}/gnutls/manual/html_node/ + gperf mono \${GS}/gperf/manual/gperf.html gperf node \${GS}/gperf/manual/html_node/ +gsasl mono \${GS}/gsasl/manual/gsasl.html +gsasl node \${GS}/gsasl/manual/html_node/ + +gss mono \${GS}/gss/manual/gss.html +gss node \${GS}/gss/manual/html_node/ + gtypist mono \${GS}/gtypist/doc/ guile mono \${GS}/guile/manual/guile.html ```	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8350175023078918, "perplexity": 27814.223573687053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637904886.43/warc/CC-MAIN-20141030025824-00040-ip-10-16-133-185.ec2.internal.warc.gz"}
http://www.pantoday.com/page/18867-Electronics-Analog-multipliers	# Electronics Analog multipliers 24 July 02:38 An ana log multiplier is a ambit with an achievement that is proportional to the artefact of two inputs: :$v_ = K v_1 cdot v_2$ where K is a connected amount whose ambit is the changed of a voltage. In accepted we ability apprehend that the two inputs can be both absolute or negative, and so can be the output. Anyway, alotof of the implementations plan alone if both inputs are carefully positive: this is not such a absolute because we can about-face the ascribe and the achievement in adjustment to accept a amount alive alone with absolute signals but alien interfaces alive with any polarity (within assertive banned according to the accurate configuration). Two accessible implementations will be shown. Both will be using operational amplifiers, but the first one will use diodes to get the bare relationships, the additional one MOSFET transistors. As known, using operational amplifiers and diodes its absolutely simple to access the log arithm and the exponential of a assertive input. Canonizing the acreage of log arithms: :$log \left(a cdot b\right) = log a + log b$ we can accumulate two signals first artful their logarithm, then accretion them and assuredly artful the exponential of such a sum. From the point of appearance of mathematics, such an access works as continued as the two inputs are positive, because the logarithm of a abrogating amount does not is (in the absolute domain). Able-bodied see that this absolute is accurate for the absolute ambit as well, even if the cause will be added physical. The block diagram of this accomplishing is the following: If we artlessly adjoin the circuits for logarithm, sum and exponential we get the afterward configuration: for a quick overview on the behavior of the circuit, able-bodied accept that all the resistors R accept the aforementioned value. It is acutely accessible to use altered ethics to get altered results, but we will not accede it here. Let us use the afterward characters for the accord amid accepted and voltage on a diode: :$i = I_s left\left( e^ - 1\right\}$ ight) where $V_T simeq 0.6 V$ is the beginning voltage and Is is the accepted abounding through the diode if its inverse-polarized. If we assay the ambit after introducing any approximation we get: :$v_a = - left\left[ - V_T ln left\left( frac + 1$ ight) - V_T ln left( frac + 1 ight) ight] = V_T ln left[ left( frac + 1 ight) left( frac + 1 ight) ight] so the final achievement is: :$v_b = - R I_s left\left( e^ - 1\right\}$ ight) = - frac - (v_1 + v_2) as it is clear, in the achievement there is the multiplication we were searching for, but there is addition appellation we dont want. It deceit be artlessly advised an absurdity because it ability be as abundant as the multiplication element, so it has to be removed. Anyhow this is an simple task, back it is all-important alone to add addition date to sum absolutely $v_1 + v_2$, so we will accept no error. The complete multiplier ambit is the following: where the achievement voltage is accustomed :$v_ = - left\left( - frac - \left(v_1 + v_2\right) + \left(v_1 + v_2\right)$ ight) = frac thats absolutely what we wanted. The ambit works as continued as the afterward accord is verified: :$v_1 , v_2 > - R I_s$ so the inputs can be aught or admirable abrogating but, back $R I_s$ will be a baby voltage, we are accustomed to carbon the affiliation artlessly as $v_1 , v_2 geq 0$. From the algebraic point of appearance this is due to the actuality that we deceit account the logarithm of a abrogating number, from a concrete point of appearance the absolute is due to the actuality that we can access alone actual baby currents (almost zero) inverse-polarizing the diodes. In applied applications, the diodes are replaced with BJTs affiliated so to plan like a diode. Since it is accessible to use a MOSFET transistor as a voltage controlled resistor, we can use this affection to make an analog multiplier. Let us accredit to account on the right. With the letter we announce the altered pins: Drain, Antecedent and Gate. MOS are balanced devices, so we could alter the cesspool with the antecedent after affecting the behavior of the device. Anyhow able-bodied alarm antecedent the everyman voltage pin and cesspool the point with the accomplished voltage. If the voltage amid aboideau and antecedent is beneath than the voltage amid cesspool and source, i.e. $V_ < V_$, the accord amid accepted and voltage is the following: :$I_ = K \left[2 \left(V_ - V_T\right) V_ - V_^2\right] simeq 2 K \left(V_ - V_T\right) V_; qquad V_ < V_$ assuming we can consistently use this relationship, the analog multiplier agreement is the following: where antecedent and cesspool of both accessories are acicular out. If $v_2$ and $V_$ are positive, then the sources will abide there because that credibility are around affiliated to arena by the operational amplifiers. The accepted abounding through $R_1$ is defined: one ancillary of the resistor has the voltage $v_1$, the additional one is grounded. That aforementioned accepted will breeze through the MOS $M_1$, appropriately defining the voltage $V_G$. The accepted is accustomed :$frac = - I_ = - 2 K \left(V_ - V_\right) V_$ but $V_ = V_G$ and $V_ = V_$. replacing and artful we get: :$V_G = V_ - frac$ considering the additional MOS $M_2$ we have: :$; I_ = 2 K \left(V_ - V_\right) V_$ where $V_ = V_G$ and $V_ = v_2$. Replacing we get: :$I_ = - frac$ from which we assuredly get the achievement voltage: :$v_ = frac frac; qquad V_, v_1, v_2 > 0$ and this is what we wanted. The aberration amid the antecedent configurations are: In additional words, the diode accomplishing is added complicated but it works accomplished for a added ambit on inputs. Tags: point, different, works, relationship, electronics, limit, circuit, analog, positive, source voltage, frac, ight, left, following, output, inputs, source, circuit, current, drain, analog, logarithm, positive, negative, diode, diodes, point, multiplier, relationship, limit, anyway, inverse, simply, exponential, operational, calculating, works, amplifiers, configuration, different, , left frac, ln left, operational amplifiers, analog multiplier, ln left frac, current flowing through, relationship between current, electronics analog multipliers, Share Electronics Analog multipliers:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 29, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7289726138114929, "perplexity": 5279.2247093984715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00454-ip-10-147-4-33.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-applied-math/225822-archimedean-property.html	1. ## Archimedean property So there is this statement, claiming that N (Natural numbers) is not bounded above in R, which is really easy to prove, however after proving that they drew a conclusion as I saw in my lecture notes, Conclusion; For every epsilon (I will write epsilon as e because I don't know how else to write it) greater than zero there exist n in N with 0<1/n<e How did he drew this conclusion from the fact that N is not bounded above in R? From what I understand what this says , for every epsilon in R (that is greater than 0) you can find a natural number n that is bigger than him. Is this logic correct? 2. ## Re: Archimedean property Originally Posted by davidciprut Conclusion; For every epsilon (I will write epsilon as e because I don't know how else to write it) greater than zero there exist n in N with 0<1/n<e How did he drew this conclusion from the fact that N is not bounded above in R? Using LaTeX you can enter [TEX]\forall\varepsilon>0 [/TEX] gives $\displaystyle \forall\varepsilon>0$ If $\displaystyle \mathbb{N}$ is not bounded above then $\displaystyle \frac{1}{\varepsilon}$ is not an upper bound. So $\displaystyle \exists n\in\mathbb{N}$ such that $\displaystyle n>\frac{1}{\varepsilon}$. Can you see how it works?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9891591668128967, "perplexity": 305.2671156258104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646375.29/warc/CC-MAIN-20180319042634-20180319062634-00775.warc.gz"}
http://nbviewer.ipython.org/github/erichutchins/mircon2013/blob/master/MIRCon%20Yara%20Magic.ipynb	Yara Cell Magic by Eric Hutchins Yara is a powerful, flexible signature language. From the documentation (PDF), it is a tool "aimed at helping malware researchers to identify and classify malware families." Far beyond just malware, Yara provides a language to define sets of rules each with sets of complex conditions with robust regular expressions, match offset specifications, and many other features that, when combined, make Yara a swiss army knife for finding stuff. Wherever you have stuff and want to find a complex set of conditions, Yara can help with that. It also has a nice Python API. The typical way to use Yara in Python is to either read in the rules from an external file or specify the rules in a Python string. Using one language (Python) to write another language (Yara) always frustrates me. At least python's triple quote """ lets you nicely write multi-line strings. import yara yarasig = """rule helloworld { strings: $a = "hello" ascii$b = "world" nocase condition: any of them }""" myrules = yara.compile(source=yarasig) But still, I want to edit a blob of text for a language in a native editor. I want to see matching parentheses and brackets as I type them. I want to be able to bulk comment out lines. I want to see line numbers so I can debug Yara error messages. I want syntax highlighting. IPython lets us accomplish in a nice, clean fashion. I wrote a custom magic %%yara that turns a code cell into a inline Yara editor. Write rules with proper syntax highlighting (using a new CodeMirror mode for yara that I also wrote). Run the cell, and yara compiles the code and puts the compiled rule object back in your namespace. Then use it to Find Stuff. Notebook Prerequisites Modules Custom • yaramagic.py -- Custom code for %%yara cell magic • yara.js -- CodeMirror custom mode for yara syntax highlighting Data Hello World In [1]: from pprint import pprint In [2]: %%yara -n myrules /* My first rule called "helloworld" with category "testing" */ rule helloworld : testing { meta: version = "0.1" strings: $a = "hello" ascii$b = "world" nocase condition: all of them } Adding compiled rules as "myrules" to namespace In [3]: pprint( myrules.match_data(data="This is a hello WoRlD test") ) {'main': [{'matches': True, 'meta': {'version': '0.1'}, 'rule': 'helloworld', 'strings': [{'data': 'WoRlD', 'flags': 27, 'identifier': '$b', 'offset': 16L}, {'data': 'hello', 'flags': 19, 'identifier': '$a', 'offset': 10L}], 'tags': ['testing']}]} To help debug a rule, toggle the line numbers in your %%yara cell by typing Ctrl-m-l. The yara CodeMirror mode starts line numbering at 0 so Yara's offending line number error message matches the notebook display. In [4]: %%yara { strings: $a = "hello" conditio: //<-- oops all of them } Syntax error! <undef>:5: syntax error, unexpected _IDENTIFIER_, expecting _CONDITION_ ### Classic Use Case: Volatility¶ The Volatility Framework has a built-in YaraScan plugin, but this only accepts an external yara rule file or a plain string. In order to use our compiled rules, I'm hacking together pieces from the various classes under YaraScan for this demonstration. I'm using the same ds_fuzz_hidden_proc.img sample from Volatility's public memory images page. The following code will flag processes that match a specific Yara rules object. In [5]: # Base Volatility import import volatility.conf as conf import volatility.registry as registry import volatility.commands as commands import volatility.addrspace as addrspace registry.PluginImporter() config = conf.ConfObject() registry.register_global_options(config, commands.Command) registry.register_global_options(config, addrspace.BaseAddressSpace) cmds = registry.get_plugin_classes(commands.Command, lower = True) In [6]: # Use-case specific imports from volatility.plugins.filescan import PSScan import volatility.utils as utils import volatility.constants as constants In [7]: config.PROFILE = "WinXPSP2x86" config.LOCATION = "file:///c:/ds_fuzz_hidden_proc.img" In [8]: # A simplified (and surely imperfect) merging of code from YaraScan, VadYaraScanner, and BaseYaraScanner from volatility.malfind def yrscan(task, rules, contextsize=16): results = [] for vad, address_space in task.get_vads(): offset = vad.Start maxlen = vad.Length # Start scanning from offset until maxlen: i = offset while i < offset + maxlen: # Read some data and match it. to_read = min(constants.SCAN_BLOCKSIZE + 1024, offset + maxlen - i) data = address_space.zread(i, to_read) if data: for match in rules.match_data(data).get('main', []): if all([hit['offset'] < constants.SCAN_BLOCKSIZE for hit in match.get('strings', [])]): results.append((i, match)) i += constants.SCAN_BLOCKSIZE return results In [9]: %%yara -n volarules rule exe_on_desktop { // Look for files on the Desktop that end in .exe strings:$a = /\\Desktop\\[\w .-]{1,20}\.exe/ nocase condition: all of them } Adding compiled rules as "volarules" to namespace In [10]: ps = PSScan(config) In [11]: for task in ps.calculate(): # Pass the compiled rules object to our method yrscan if len(hits) > 0: print '-----------------------------------' print 'Process name: %s' % task.ImageFileName print 'Create time: %s' % (task.CreateTime or '') print 'Exit time: %s' % (task.ExitTime or '') else: next print '> Rule name: %s' % hit.get('rule') for string in hit.get('strings', []): # Modified from original print "".join( ["{0:#010x} {1:<48} {2}\n".format(string.get('offset') + addr + o, h, ''.join(c)) for o, h, c in utils.Hexdump(string.get('data', '')) ]) ----------------------------------- Process name: wuauclt.exe PID: 1372 PPID: 1064 Create time: 2008-11-26 07:39:38 Exit time: > Rule name: exe_on_desktop 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe > Rule name: exe_on_desktop 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe > Rule name: exe_on_desktop 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe ----------------------------------- Process name: explorer.exe PID: 1516 PPID: 1452 Create time: 2008-11-26 07:38:27 Exit time: > Rule name: exe_on_desktop 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe > Rule name: exe_on_desktop 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe ----------------------------------- Process name: svchost.exe PID: 844 PPID: 672 Create time: 2008-11-26 07:38:18 Exit time: > Rule name: exe_on_desktop 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe ----------------------------------- Process name: svchost.exe PID: 1064 PPID: 672 Create time: 2008-11-26 07:38:20 Exit time: > Rule name: exe_on_desktop 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x0214342f 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x0214343f 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe > Rule name: exe_on_desktop 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x022fecb7 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x022fecc7 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe > Rule name: exe_on_desktop 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe 0x023e9e87 5c 44 65 73 6b 74 6f 70 5c 6e 65 74 77 6f 72 6b \Desktop\network 0x023e9e97 5f 6c 69 73 74 65 6e 65 72 2e 65 78 65 _listener.exe ### Unorthodox Use Case: Filtering Logs in Pandas¶ As stated, Yara is great at Finding Stuff. When you have a lot of data in a Pandas DataFrame, you'll want to filter it to find important stuff. Pandas provides robust string matching/searching capabilities, but perhaps you already detections defined in yara sigs and want to apply those sigs to this data. Perhaps your analysts are more accustomed to writing Yara sigs than complex Pandas filtering conditions. For this example, we load in a handful of user-agent strings into a DataFrame and we'll use Yara to match on a set of rules. This example highlights one more feature of Yara and the %%yara magic: external variables. When the Yara engine scans data, it normally is scanning a blob of data, but it can also load in named chunks of data into a dictionary called external variables. Since a DataFrame is intuitively chunked into columns, we can specify an external variable container for each column in the DataFrame. In [12]: import pandas as pd from cStringIO import StringIO In [13]: useragentcsv = """useragent Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; WOW64; Trident/5.0) "Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.17 (KHTML, like Gecko) Chrome/24.0.1312.57 Safari/537.17" "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/27.0.1453.65 Safari/537.36" "Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/27.0.1453.110 Safari/537.36" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_4) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/29.0.1547.65 Safari/537.36" Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Win64; x64; Trident/5.0) "Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/28.0.1500.72 Safari/537.36" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_3) AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.152 Safari/537.22" Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1) "Mozilla/5.0 (iPhone; CPU iPhone OS 6_1 like Mac OS X) AppleWebKit/536.26 (KHTML, like Gecko) Version/6.0 Mobile/10B144 Safari/8536.25" "Mozilla/5.0 (iPad; CPU OS 6_0 like Mac OS X) AppleWebKit/536.26 (KHTML, like Gecko) Version/6.0 Mobile/10A403 Safari/8536.25" Mozilla/5.0 (Windows NT 5.1; rv:16.0) Gecko/20100101 Firefox/16.0 "Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/29.0.1547.66 Safari/537.36" "Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.17 (KHTML, like Gecko) Chrome/24.0.1312.57 Safari/537.17" """ In [14]: df = pd.read_csv(StringIO(useragentcsv)) Out[14]: useragent 0 Mozilla/5.0 (compatible; MSIE 9.0; Windows NT ... 1 Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKi... 2 Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/53... 3 Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.3... 4 Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_4)... In the cell below, the -e option to the %%yara magic specifies the external variable. The externals must be specified at the time of compilation, which, for the %%yara cell magic, that means at write-time. %%yara accepts multiple -e parameters as well as comma,separated,lists. External variables are referenced directly in the condition block rather than a strings statement. Ensure the external variable names match the column names. (For more details, see the docstring by running %%yara? in a cell) In [15]: %%yara -n uarules -e useragent { condition: useragent contains "iPhone;" or } rule Chrome25Plus { condition: useragent matches /Chrome\/((2[5-9])\|3[0-9])/ } Adding compiled rules as "uarules" to namespace For the next method, we have to get a little creative. DataFrame.apply provides the means to apply a function to rows or columns of the DataFrame. It does not, however, let you specify parameters to the invoked method; the only parameter will be the data from the column or row. (In our example, we use axis=1 which tells pandas to look at data row-by-row). In order to have flexibility to pass in various Yara rule files (and avoid global variables), we have a general yarafilter method that takes a compiled yara rules object as a parameter. The function generates the necessary worker function that DataFrame.apply will accept and preloads a subset of columns as external variables for the yara engine. The function returns a comma separated list of rules that matched on each row or blank string if no matches. In [16]: def yarafilter(rules): # Specify a list of the column names we used in for external variables # in the yara rules externals = ['useragent'] def worker(row): m = rules.match(data=" ", externals=row[externals].to_dict()) if m: return ','.join( [y.get('rule', '') for y in m.get('main', [])] ) else: return '' return worker In [17]: df['yarahits'] = df.apply(yarafilter(uarules), axis=1) In [18]: df Out[18]: useragent yarahits 0 Mozilla/5.0 (compatible; MSIE 9.0; Windows NT ... 1 Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKi... 2 Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/53... Chrome25Plus 3 Mozilla/5.0 (Windows NT 6.1) AppleWebKit/537.3... Chrome25Plus 4 Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_4)... Chrome25Plus 5 Mozilla/5.0 (compatible; MSIE 9.0; Windows NT ... 6 Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKi... Chrome25Plus 7 Mozilla/5.0 (Macintosh; Intel Mac OS X 10_8_3)... Chrome25Plus 8 Mozilla/4.0 (compatible; MSIE 6.0; Windows NT ... 9 Mozilla/5.0 (iPhone; CPU iPhone OS 6_1 like Ma... iPad_iPhone 10 Mozilla/5.0 (iPad; CPU OS 6_0 like Mac OS X) A... iPad_iPhone 11 Mozilla/5.0 (Windows NT 5.1; rv:16.0) Gecko/20...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8548943996429443, "perplexity": 5943.191318430535}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637900397.29/warc/CC-MAIN-20141030025820-00165-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.tiborstiluslapja.hu/profile/Delphi-2014-R3-Keygen-15-Latest-2022/profile	Csatlakozás dátuma: 2022. máj. 13. ###### Névjegy Delphi 2014 R3 Keygen 15 [Latest] 2022 new york city, delphi 2014 r3 keygen 31 suisun city,delphi 2014 r3 keygen with word pad support,delphi 2014 r3 keygen may,delphi 2014 r3 keygen bbpress city,delphi 2014 r3 keygen asus city,delphi 2014 r3 keygen for mac.August 25th Saw most of the recent SFG post on P300, so I’ll comment briefly. The points I take issue with are: First, the P300 latency is on the order of 200ms, which is a very long time. Rather than interpret a peak latency at 200ms as the result of a predictable response time (400ms in the classic experiment by Sutton et al. (1988), for example), we need to keep in mind that it is a very rare phenomenon, not to be expected at all times. People respond to stimuli in the environment with certain relative probabilities, but the response itself is only a potential of action, it is not a certainty. If we assume, in the absence of data to the contrary, that this means that the P300 is a “slow” process, it means nothing to the overall problem of driving attention. In fact, it means the opposite. All that slow latency indicates is a large need for attention. Second, the latency of the P300 is the result of a complex process, and it can vary a great deal between individuals and over the course of time, depending on how much prefrontal cortex is functioning. Although in many conditions we can predict where the P300 will be by its latency, and so we can say that it is a “pre-cognitive” attention signal, the question of whether it is cognitive, or a mere potential of action, is something that we don’t know and don’t have a way of knowing at this time. We can say that the higher the P300 latency, the lower the odds of any action taking place. We can say that the more likely it is that a stimulus will lead to an action, the lower the latency. But we cannot say that all subjects with high P300 latency will ignore the stimulus, nor that all subjects with low P300 latency will attend to the stimulus. As we just saw in the SFG post, and in the comments of Seth and Marieke, the P300 can come and go, peak and trough, without any overall change in driving attention. 44926395d7	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8848583102226257, "perplexity": 1208.799894625056}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710953.78/warc/CC-MAIN-20221204004054-20221204034054-00123.warc.gz"}
https://www.abs.gov.au/methodologies/education-and-work-australia-methodology/may-2019	This is not the latest release View the latest release # Education and Work, Australia methodology Reference period May 2019 Released 13/11/2019 ## Explanatory notes ### Overview This publication contains results from the 2019 Survey of Education and Work (SEW) conducted throughout Australia in May 2019 as a supplement to the monthly Labour Force Survey (LFS). The SEW provides annual information on a range of key indicators of educational participation and attainment of people aged 15-74 years, along with data on people's transitions between education and work. The annual time series allows for ongoing monitoring of the level of education of Australia's population including participation in: • current and previous study; • type of educational institution attended; • highest year of school completed; • level and field of highest non-school qualification; • characteristics of people's transitions between education and work; and • selected characteristics of apprentices and trainees. The publication Labour Force, Australia (cat. no. 6202.0) contains information about survey design, sample redesign, scope, coverage and population benchmarks relevant to the monthly LFS, which also apply to supplementary surveys such as the SEW. It also contains definitions of demographic and labour force characteristics. ### Concepts, sources, and methods The conceptual framework used in Australia's LFS aligns closely with the standards and guidelines set out in Resolutions of the International Conference of Labour Statisticians. Descriptions of the underlying concepts and structure of Australia's labour force statistics, and the sources and methods used in compiling these estimates, are presented in Labour Statistics: Concepts, Sources and Methods (cat. no. 6102.0.55.001). In July 2014, the LFS survey questionnaire underwent a number of developments. For further information see Information Paper: Questionnaire Used in the Labour Force Survey, July 2014. ### Scope The scope of the SEW is restricted to people aged 15-74 years who were usual residents of private dwellings and non-institutionalised special dwellings excluding: • members of the permanent defence forces; • certain diplomatic personnel of overseas governments, customarily excluded from the Census of Population and Housing and estimated resident populations; • overseas residents in Australia; • members of non-Australian defence forces (and their dependants); • institutionalised people (e.g. patients in hospitals, residents of retirement homes, residents of homes for people with disabilities, inmates of prisons); • Indigenous communities; and • boarding school pupils. Boarding school pupils have been excluded from the scope of the SEW since 2005, but were included in earlier collections. Since 2009, SEW has included people living in 'very remote' areas who are not in Indigenous Communities. Prior to SEW 2009, all people living in 'very remote' parts of Australia were excluded. Nationally, less than 1% of people in scope of SEW live in 'very remote' areas that are not Indigenous Communities. In the Northern Territory, this proportion is higher, at around 8%. In 2013, the scope of SEW was extended to include all people aged 65-74 years for the first time. From 2009 to 2012, people aged 65-74 years who were in the labour force, or were marginally attached to the labour force were included. Persons who are permanently unable to work were included in the scope of SEW for the first time in 2013. There were an estimated 456,733 people who reported being permanently unable to work in May 2019. ### Coverage In the LFS, coverage rules are applied which aim to ensure that each person is associated with only one dwelling and has only one chance of selection in the survey. See Labour Force, Australia (cat. no. 6202.0) for more details. Data from the SEW is available by State, Greater Capital City Statistical Area, Section of State, Remoteness area and Statistical Area Level 4, subject to confidentiality constraints. Geography has been classified according to the Australian Statistical Geography Standard (ASGS), July 2016. For a list of these publications see the ABS Geography Publications page. ### How the data is collected Information was collected from respondents over a two week period in May 2019. The data were collected through interviews, conducted either face-to-face or over the telephone, or respondents were able to provide their information over the internet via a self-completed form. All information in the SEW was obtained from any person in the household aged 15 years or over who was asked to respond on behalf of all people in the household in scope of the survey. If the responsible adult was unable to supply all of the details for another individual in the household, a personal interview was conducted with that particular individual. Approximately 91% of the selected households were fully responding to the Monthly Population survey in May 2019, which resulted in 38,683 completed interviews. ### Australian Standard Classification of Education (ASCED) Education data are coded to the Australian Standard Classification of Education, 2001 (cat. no. 1272.0). The ASCED is a national standard classification which can be applied to all sectors of the Australian education system, including schools, vocational education and training, and higher education. It includes: • Level of Education, defined as a function of the quality and quantity of learning involved in an educational activity. There are nine broad levels, 15 narrow levels and 64 detailed levels of education. • Field of Education, defined as the subject matter of an educational activity. Fields of education are related to each other through the similarity of subject matter, through the broad purpose for which the education is undertaken, and through the theoretical content which underpins the subject matter. There are 12 broad fields, 71 narrow fields and 356 detailed fields of education ### Level of education of current study Since 2014, people identified in the Labour Force Survey as currently studying a school level qualification have been asked in the Survey of Education and Work (SEW) whether they are currently studying for any non-school qualifications. If they are still attending school, their level of study is recorded as their current year of schooling, not their non-school qualification. ### Level of highest education attainment Level of highest educational attainment identifies the highest achievement a person has attained in any area of formal study. It is derived from highest year of school completed and level of highest non-school qualification. The derivation process determines which of the 'school' or 'non-school' attainments will be regarded as the highest. Usually the higher ranking attainment is self-evident, but in some cases some secondary education is regarded, for the purposes of obtaining a single measure, as higher than some certificate level attainments. There are two types of measures used in this publication a to determine level of highest educational attainment: 'Non-School Priority' and 'Standard Education Priority'. • 'Non-School Priority' is where all non-school qualifications are considered of higher ranking than secondary education. For example, a person whose highest year of school completed was Year 12, and whose level of highest non-school qualification was a Certificate I, would have their level of highest education attainment output as Certificate I. This concept is used in Table 10 of this publication. • 'Standard education priority' is where some school qualifications are ranked higher than some non-school qualifications. For example, years 10, 11 and 12 are ranked higher than Certificates I, II and n.f.d. The standard education priority was designed for the purpose of obtaining a single value for level of highest educational attainment and is not intended to convey any other hierarchy. The following decision table shows which responses to 'highest year of school completed' and 'level of highest non-school qualification' are regarded as the highest. For example, a person a person's level of highest educational attainment if they had a Yr 12 Certificate and a Certificate III would be 'Certificate III'. However, if the same person answered 'certificate' to the highest non-school qualification question, their level of highest educational attainment would be output as 'Level not determined'. ### Decision table - level of highest educational attainment Highest year of school completed Level of highest non-school qualification Cert IVCert IIICert III & IV n.f.d.Cert IICert ICert I & II n.f.d.Cert n.f.d.Inadequately described L.n.d.Not Stated Year 12Cert IVCert IIICert III & IV n.f.d.Year 12Year 12Year 12L.n.d.L.n.d.N.S. Year 11Cert IVCert IIICert III & IV n.f.d.Year 11Year 11Year 11L.n.d.L.n.d.N.S. Senior Sec. Education n.f.dCert IVCert IIICert III & IV n.f.d.Senior Sec. n.f.d.Senior Sec. n.f.d.Senior Sec. n.f.d.L.n.d.L.n.d.N.S. Year 10Cert IVCert IIICert III & IV n.f.d.Year 10Year 10Year 10L.n.d.L.n.d.N.S. Year 9 and belowCert IVCert IIICert III & IV n.f.d.Cert IICert ICert I & II n.f.d.Cert n.f.d.L.n.d.N.S. Sec. Education n.f.dCert IVCert IIICert III & IV n.f.d.L.n.d.L.n.d.L.n.d.L.n.d.L.n.d.N.S. Junior Sec. Education n.f.dCert IVCert IIICert III & IV n.f.d.L.n.d.L.n.d.L.n.d.L.n.d.L.n.d.N.S. Not statedCert IVCert IIICert III & IV n.f.d.N.S.N.S.N.S.N.S.N.S.N.S. Never attended schoolCert IVCert IIICert III & IV n.f.d.Cert IICert ICert I & II n.f.d.Cert n.f.d.L.n.d.N.S. Cert = Certificate L.n.d = Level not determined n.f.d = not further defined N.S. = Not Stated Sec. = Secondary For ease of interpretability, the layout of this table has been modified from Education Variables, June 2014 (cat. no. 1246.0), however the ranking of different levels of attainment has not changed. ### Engagement in employment and education The term 'engagement' is used when assessing a person's level of participation in employment and education. The following table shows the ways in which people can be 'Fully engaged', 'Partially engaged', or 'Not engaged'. Employment StatusEducation Status Full-time studyPart-time studyNot Studying Full-time employmentFully engagedFully engagedFully engaged Part-time employmentFully engagedFully engagedPartially engaged Unemployed looking for full-time workFully engagedPartially engagedNot engaged Unemployed looking for part-time workFully engagedPartially engagedNot engaged Not in the labour forceFully engagedPartially engagedNot engaged ### Weighting Weighting is the process of adjusting results from a sample survey to estimate characteristics of the total population. To do this, a 'weight' is allocated to each enumerated person. The weight is a value which indicates how many people in the population are represented by the sample person. The first step in calculating weights for each unit is to assign an initial weight, which is the inverse of the probability of the unit being selected in the survey. For example, if the probability of a person being selected in the survey was 1 in 300, then the person would have an initial weight of 300 (that is, they represent 300 people). ### Population benchmarks The initial weights are then calibrated to align with independent estimates of the population, referred to as benchmarks. The population included in the benchmarks is the survey scope. This calibration process ensures that the weighted data conform to the independently estimated distribution of the population described by the benchmarks rather than to the distribution within the sample itself. Calibration to population benchmarks helps to compensate for over or under-enumeration of particular categories which may occur due to either the random nature of sampling or non-response. The survey was benchmarked to the estimated resident population (ERP) aged 15-74 years living in private dwellings and non-institutionalised special dwellings in each state and territory. People living in remote Indigenous communities were excluded. ### Estimation Survey estimates of counts of people are obtained by summing the weights of people with the characteristics of interest. ### Confidentiality To minimise the risk of identifying individuals in aggregate statistics, a technique called perturbation is used to randomly adjust cell values. Perturbation involves small random adjustment of the statistics which have a negligible impact on the underlying pattern. This is considered the most satisfactory technique for avoiding the release of identifiable data while maximising the range of information that can be released. After perturbation, a given published cell value will be consistent across all tables. However, adding up cell values in Data Cubes to derive a total may give a slightly different result to the published totals. The introduction of perturbation in publications ensures that these statistics are consistent with statistics released via services such as TableBuilder. ### Reliability of estimates All sample surveys are subject to error which can be broadly categorised as either sampling or non-sampling error. For more information refer to the Technical Note. ### Seasonal factors The estimates are based on information collected in May 2019, and due to seasonal factors (such as school terms, semesters, or intake periods for other qualifications), they may not be representative of other months of the year. ### Comparability of time series In addition to the changes in scope listed in the 'Scope' section, there are a number of other changes to be aware of with regard to how SEW has been collected and reported over time. ### Size of the sample Supplementary surveys are not always conducted on the full LFS sample. Since August 1994 the sample for supplementary surveys has been restricted to no more than seven-eighths of the LFS sample. Since it was introduced, this survey has been conducted on various proportional samples and therefore sampling errors associated with previous supplementary surveys may vary from the sampling error for this survey. ### Classification changes Since 2007, industry data in the SEW have been classified according to the Australian and New Zealand Standard Industrial Classification, 2006 (cat. no. 1292.0). Prior to this, they were classified according to the Australian and New Zealand Standard Industrial Classification, 1993 (cat. no. 1292.0) and are therefore not directly comparable to data for 2007 and subsequent years. Since 2007, occupation data in the SEW have been classified according to the Australian and New Zealand Standard Classifications of Occupations, First Edition, Revision 1 (cat. no. 1220.0). Prior to this, they were classified according to the Australian Standard Classifications of Occupations, Second Edition, 1997 (cat. no. 1220.0) and are therefore not directly comparable to 2007 and subsequent years. ### Apprenticeship/traineeship scope Prior to 2008, only people aged 15-54 years were included in the apprenticeship/traineeship survey questions. In 2008, the age scope was extended to include people aged 55-64 years and in 2009, the scope was further extended to include people aged 65-74 years for these questions. In 2008, the definition for apprentices and trainees changed from those employed as apprentices/trainees to include only those with a formal contract under the Australian Apprenticeships scheme. Therefore data on apprentices from previous years are not directly comparable to 2008 and subsequent data. ### Other comparability issues • The May 2013 SEW was the first supplementary survey to incorporate an online data collection method, where the option was offered to just over one-quarter of the SEW sample. Since the May 2014 SEW this option has been offered to all respondents. For more information see the article Transition to Online Collection of the Labour Force Survey. • Revisions are made to population benchmarks for the LFS after each five-yearly Census of Population and Housing. The latest revision based on the 2016 Census of Population and Housing has been in use since November 2018. See Labour Force, Australia (cat. no. 6202.0) for more information. • As announced in the June 2012 issue of Australian Demographic Statistics (cat. no. 3101.0), intercensal error between the 2006 and 2011 Censuses was larger than normal due to improved methodologies used in the 2011 Census Post Enumeration Survey. The intercensal error analysis indicated that previous population estimates for the base Census years were over-counted. An indicative estimate of the size of the over-count is that there should have been 240,000 fewer people at June 2006, 130,000 fewer in 2001 and 70,000 fewer in 1996. As a result, Estimated Resident Population estimates have been revised for the last 20 years rather than the usual five. Consequently, estimates of particular populations derived since SEW 2014 may be lower than those published for previous years as the SEW estimates have not been revised. Therefore, comparisons of SEW estimates since 2014 with previous years should not be made. However, for comparable data items, comparison of rates or proportions between years is appropriate. • Since 2014, data in the SEW has been randomly adjusted to avoid the release of confidential statistics. Discrepancies may occur between sums of the component items and totals. See the Confidentiality section for more information on perturbation. ### Comparability with other ABS surveys Since the SEW is conducted as a supplement to the LFS, data items collected in the LFS are also available in SEW. However, there are some important differences between the two surveys. The SEW sample is a subset of the LFS sample (see the Overview section of these Explanatory Notes) and has a response rate which is slightly lower than the LFS response rate for the same period. Also, the scope of the SEW differs slightly to the scope of the LFS (refer to the Scope section above). Due to these differences between the samples, the SEW data are weighted as a separate process to the weighting of LFS data. Differences may therefore be found in the estimates collected in the LFS and published as part of the SEW, when compared with estimates published in the May 2019 issue of Labour Force, Australia (cat. no. 6202.0). From September 2016, the ABS has published education data from the LFS as part of the Labour Force publication Labour Force, Australia, Detailed, Quarterly (cat. no. 6291.0.55.003). For more information on the differences between SEW and LFS in relation to education data items see the Fact Sheet: Expanded education data from the Labour Force Survey (in cat. no. 6291.0.55.003). Estimates from the SEW may differ from the estimates produced from other ABS collections, for several reasons. The SEW is a sample survey and its results are subject to sampling error. Results may differ from other sample surveys, which are also subject to sampling error. Users should take account of the measures of error on all published statistics where comparisons are made. Refer to the Technical Note for more information about how error is measured for the SEW. Differences may also exist in the scope and/or coverage of the SEW compared to other surveys. Differences in estimates, when compared to the estimates of other surveys, may result from different reference periods reflecting seasonal variations, non-seasonal events that may have impacted on one period but not another, or because of underlying trends in the phenomena being measured. Finally, differences can occur as a result of using different collection methodologies. This is often evident in comparisons of similar data items reported from different ABS collections where, after taking account of definition and scope differences and sampling error, residual differences remain. These differences are often the result of the mode of the collections, such as whether data are collected by an interviewer or self-enumerated by the respondent and whether the data are collected from the person themselves or from a proxy respondent. Differences may also result from the context in which questions are asked, i.e. where in the interview the questions are asked and the nature of preceding questions. The impacts on data of different collection methodologies are difficult to quantify. Every effort is made to minimise such differences. ### How the data is released A number of data cubes (spreadsheets) containing all tables produced for this publication are available from the Data downloads section of the Education and work topic page. The data cubes present tables of estimates and proportions, and their associated measures of error. ### TableBuilder For users who wish to undertake more detailed analysis of the data, the survey microdata will be released through the TableBuilder product (see Microdata: Education and Work, Australia (cat. no. 6227.0.30.001) for more detail). Microdata can be used by approved users to produce customised tables and analysis from the survey data. Microdata products are designed to ensure the integrity of the data whilst maintaining the confidentiality of the respondents to the survey. More information can be found at How to Apply for Microdata. ### DataLab Detailed microdata may also be available on DataLab for users who want to undertake interactive (real time) complex analysis of microdata in the secure ABS environment. For more details, refer to About the DataLab. ### Custom tables Customised statistical tables to meet individual requirements can be produced on request. These are subject to confidentiality and sampling variability constraints which may limit what can be provided. Enquiries on the information available and the cost of these services should be made to the National Information and Referral Service on 1300 135 070. ### History of changes Results of similar surveys have been published in previous issues. These surveys were conducted annually from February 1964 to February 1974, in May 1975 and 1976, in August 1977 and 1978, and annually in May since 1979. Results of previous surveys were published in Transition from Education to Work, Australia (cat. no. 6227.0) from 1964 to 2000. Since May 2001, the results of the survey have been published in Education and Work, Australia (cat. no. 6227.0). The ABS intends to conduct this survey again in May 2020. ## Technical note ### Reliability of estimates Two types of error are possible in estimates based on a sample survey: • non-sampling error • sampling error ### Non-sampling error Non-sampling error is caused by factors other than those related to sample selection. It is any factor that results in the data values not accurately reflecting the true value of the population. It can occur at any stage throughout the survey process. Examples include: • selected people that do not respond (e.g. refusals, non-contact) • questions being misunderstood • responses being incorrectly recorded • errors in coding or processing the survey data ### Sampling error Sampling error is the expected difference that can occur between the published estimates and the value that would have been produced if the whole population had been surveyed. Sampling error is the result of random variation and can be estimated using measures of variance in the data. ### Standard error One measure of sampling error is the standard error (SE). There are about two chances in three that an estimate will differ by less than one SE from the figure that would have been obtained if the whole population had been included. There are about 19 chances in 20 that an estimate will differ by less than two SEs. ### Relative standard error The relative standard error (RSE) is a useful measure of sampling error. It is the SE expressed as a percentage of the estimate: $$R S E \%=\Large{\left(\frac{S E}{\text {estimate}}\right) }\normalsize{\times 100}$$ The smaller the estimate, the higher the RSE. Very small estimates are subject to high SEs (relative to the size of the estimate) which reduces their value for most uses. Only estimates with RSEs less than 25% are considered reliable for most purposes. Estimates with larger RSEs, between 25% and less than 50% have been included in the publication, but are flagged to indicate they are subject to high SEs. These should be used with caution. Estimates with RSEs of 50% or more have also been flagged and are considered unreliable for most purposes. RSEs for these estimates are not published. ### Margin of error for proportions Another useful measure is the margin of error (MOE), which shows the largest possible difference (due to sampling error) that could exist between the estimate and what would have been produced had all people been included in the survey, at a given level of confidence. It is useful for understanding and comparing the accuracy of proportion estimates. Confidence levels can vary (e.g. typically 90%, 95% or 99%), but in this publication, all MOEs are provided for estimates at the 95% confidence level. At this level, there are 19 chances in 20 that the estimate will differ from the population value by less than the provided MOE. The 95% MOE is obtained by multiplying the SE by 1.96. $$M O E=S E \times 1.96$$ Depending on how the estimate is to be used, an MOE of greater than 10% may be considered too large to inform decisions. For example, a proportion of 15% with an MOE of plus or minus 11% would mean the estimate could be anything from 4% to 26%. ### Confidence intervals The estimate combined with the MOE defines a range, known as a confidence interval. This range is likely to include the true population value with a given level of confidence. A confidence interval is calculated by taking the estimate plus or minus the MOE of that estimate. It is important to consider this range when using the estimates to make assertions about the population or to inform decisions. Because MOEs in this publication are provided at the 95% confidence level, a 95% confidence interval can be calculated around the estimate, as follows: $$95 \% \text { Confidence Interval }=(\text {estimate}-M O E, \text { estimate }+M O E)$$ ### Measures of error in this publication This publication reports the relative standard error (RSE) for estimates of counts ('000) and the margin of error (MOE) for estimates of proportions (%). These measures are included in the datacubes available under the Data downloads section on the education and work topic page. In the first datacube (Tables 1-20: Education and Work), time series tables include both RSE of proportion and MOE of proportion, as do tables 21- 34. For years prior to 2018, MOE of proportion has been calculated using rounded figures and the result may have slightly less precision than the MOE of proportion calculated for years after 2017. In the first datacube (Tables 1-20: Education and Work), estimates of proportions with a MOE greater than 10% are annotated to indicate they are subject to high sample variability and particular consideration should be given to the MOE when using these estimates. In addition, estimates with a corresponding standard 95% confidence interval that includes 0% or 100% are annotated to indicate they are usually considered unreliable for most purposes. ### Calculating measures of error Proportions or percentages formed from the ratio of two count estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when the numerator (x) is a subset of the denominator (y): $$\operatorname{RSE}\left(\Large\frac{x}{y}\right) \approx\sqrt{[R S E(x)]^{2}-[R S E(y)]^{2}}$$ When calculating measures of error, it may be useful to convert RSE or MOE to SE. This allows the use of standard formulas involving the SE. The SE can be obtained from RSE or MOE using the following formulas: $$S E=\Large\frac{R S E \% \times \text { estimate }}{100}$$ $$S E=\Large\frac{M O E}{1.96}$$ The RSE can also be used to directly calculate a MOE with a 95% confidence level: $$M O E=\Large\frac{R S E \% \times e s t i m a t e \times 1.96}{100}$$ ### Calculating differences The difference between two survey estimates (counts or percentages) can also be calculated from published estimates. Such an estimate is also subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x - y) may be calculated by the following formula: $$S E(x-y) \approx \sqrt{[S E(x)]^{2}+[S E(y)]^{2}}$$ While this formula will only be exact for differences between separate and uncorrelated characteristics or sub populations, it provides a good approximation for the differences likely to be of interest in this publication. ### Significance testing When comparing estimates between surveys or between populations within a survey, it is useful to determine whether apparent differences are 'real' differences or simply the product of differences between the survey samples. One way to examine this is to determine whether the difference between the estimates is statistically significant. This is done by calculating the standard error of the difference between two estimates (x and y) and using that to calculate the test statistic using the formula below: $$\Large\frac{\|x-y\|}{\operatorname{SE}(x-y)}$$ where $$S E(y) \approx \Large\frac {R S E(y) \times y}{100}$$ If the value of the statistic is greater than 1.96, we can say there is good evidence of a statistically significant difference at 95% confidence levels between the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations. ## Glossary ### Show all #### Apprentice An apprentice is a person who has entered into a legal contract (called a training agreement or contract of training) with an employer, to serve a period of training for the purpose of attaining tradesperson status in a recognised trade. In this survey, persons who are apprentices and trainees are identified by their answer to a question specifically pertaining to a contract under the Australian Apprenticeships scheme. Students undertaking school based apprenticeships are not included. #### Balance of state/territory Comprises the balance of each state/territory not included in Capital City. See Australian Statistical Geography Standard (ASGS): Volume 1 - Main Structure and Greater Capital City Statistical Areas, July 2016 (cat. no. 1270.0.55.001). #### Capital city Refers to Greater Capital City Statistical Areas (GCCSA) as defined by the ASGS. The GCCSAs represent the socio-economic extent of each of the eight State and Territory capital cities. The whole of the ACT is included in the GCCSA. #### Certificate n.f.d. (Certificate not further defined) Survey responses are coded to Certificate not further defined (n.f.d.) when there is not enough information to code them to Certificate I, II, III or IV in the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0), Level of education classification. #### Completed a qualification A person having 'completed' a qualification means they have successfully passed all of the requirements for the qualification and excludes people who have stopped studying without gaining the qualification. #### Country of birth Country of birth has been classified according to the Standard Australian Classification of Countries (SACC), Second Edition (cat. no. 1269.0). 'Born in Australia' refers to all persons born in Australia or any of its external territories. 'Born overseas' refers to all persons not 'born in Australia', including those born at sea and persons whose country of birth is unknown. #### Currently enrolled in study Enrolled in a course of formal study for a trade certificate, diploma, degree or any other educational qualification, in May of the survey year. #### Dependent child Persons aged less than 15 years who have a parent/guardian in the household. #### Educational institution Any institution whose primary role is education. Included are schools, higher education establishments, colleges of technical and further education and public and private colleges. #### Employed Persons who, during the reference week: • worked for one hour or more for pay, profit, commission or payment in kind in a job or business, or on a farm (comprising employees, employers and own account workers); or • worked for one hour or more without pay in a family business or on a farm (i.e. contributing family workers); or • were employees who had a job but were not at work and were: • away from work for less than four weeks up to the end of the reference week; or • away from work for more than four weeks up to the end of the reference week and received pay for some or all of the four week period to the end of the reference week; or • away from work as a standard work or shift arrangement; or • on strike or locked out; or • on workers' compensation and expected to return to their job; or • were employers or own account workers who had a job, business or farm, but were not at work. #### Employed full-time Employed persons who usually worked 35 hours or more a week (in all jobs) and those who, although usually working less than 35 hours a week, worked 35 hours or more during the reference week. #### Employed part-time Employed persons who usually worked less than 35 hours a week (in all jobs) and either did so during the reference week, or were not at work in the reference week. #### Engagement The term engagement is used when assessing a persons level of participation in employment and education. People can be Fully engaged, Partially engaged, or Not engaged. For more information, see the explanatory notes. #### Enrolled Refers to persons registered for a course of formal study in the particular reference period (e.g. survey month, or previous calendar year). This includes online or distance education and excludes any course of study that doesn't result in a formal educational qualification. #### Enrolled full-time Includes anyone enrolled in a course of study that is considered full-time by their institution. #### Enrolled part-time Includes anyone enrolled in a course of study that is not considered full-time by their institution. All apprentices and trainees are considered to be enrolled in part-time study. #### Field not determined Field not determined includes inadequately described responses or where no responses were given. #### Field of highest educational attainment The subject matter of the educational activity for the highest achievement a person has attained in any area of formal study. Refers to the occupation of an apprentice or trainee and is classified according to the Australian and New Zealand Standard Classification of Occupations (ANZSCO), First Edition, Revision 1 (cat. no. 1220.0) Unit Group. #### Formal study Any study being undertaken that will lead to a recognised qualification, issued by a relevant approved body, in recognition that a person has achieved learning outcomes or competencies relevant to identified individual, professional, industry or community needs. This includes study for a school qualification. In this survey, if the respondent was still attending school their level of study was recorded as their current year of schooling. If the respondent had left school and was enrolled in formal study they were asked the level of the qualification. #### Fully engaged People who were employed full-time and/or in full-time study, or employed part-time combined with part-time study. #### Higher education institution or organisation An Australian institution providing higher education courses, e.g. universities; colleges of advanced education; institutes of advanced education; institutes of higher education; institutes of tertiary education; agricultural colleges; and some institutes of technology, and the equivalent institutions overseas. #### Industry Industry data is classified according to the Australian and New Zealand Standard Industrial Classification (ANZSIC), 2006 (cat. no. 1292.0). #### Level of highest educational attainment Level of highest educational attainment identifies the highest achievement a person has attained in any area of formal study. It is not a measurement of the relative importance of different fields of study, but a ranking of qualifications and other educational attainments regardless of the particular area of study or the type of institution in which the study was undertaken. For more information regarding how this is derived see the explanatory notes. It is categorised according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0) Level of education classification. Level of education is also classified according to the International Standard Classification of Education (ISCED), 2011. #### Level of highest educational attainment (non-school priority) A person's level of highest educational attainment (non-school priority) is their highest non-school qualification where they have completed one. For persons who have not completed a non-school qualification their level of highest educational attainment (non-school priority) is the highest year of school they have completed. It is categorised according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0) Level of education classification. #### Level of highest non-school qualification A person's level of highest non-school qualification is the highest qualification a person has attained in any area of formal study other than school study. It is categorised according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0) Level of education classification. #### Level not determined Level not determined includes inadequately described responses or where no responses were given. #### Main field of education The main subject matter of the study undertaken by a person in completing an educational activity. Where a qualification covered multiple fields (e.g. a double degree) the 'main' field is the one considered most important. It is categorised according to the Australian Standard Classification of Education (ASCED), 2001 (cat. no. 1272.0) Field of education classification. Main field of education is also classified according the International Standard Classification of Education (ISCED), 2011. #### Non-school qualification Non-school qualifications are awarded for educational attainments other than those of pre-primary, primary or secondary education. They include qualifications at the Postgraduate Degree level, Master Degree level, Graduate Diploma and Graduate Certificate level, Bachelor Degree level, Advanced Diploma and Diploma level, and Certificates I, II, III and IV levels. School level qualifications obtained through institutions other than primary and secondary schools (such as TAFE) are not included. Non-school qualifications may be attained concurrently with school qualifications. #### Not in labour force Persons who were not in the categories ‘employed’ or ‘unemployed’. #### Not engaged People who were not employed and not studying. #### Partially engaged People who were employed part-time and not studying, or in part-time study and not employed. #### Qualification Formal certification, issued by a relevant approved body, in recognition that a person has achieved an appropriate level of learning outcomes or competencies relevant to identified individual, professional, industry or community needs. Statements of attainment awarded for partial completion of a course of study at a particular level are excluded. #### Remoteness The Australian Statistical Geography Standard (ASGS) was used to define remoteness. The Remoteness Structure is described in detail in the publication Australian Statistical Geography Standard (ASGS): Volume 5 - Remoteness Structure, July 2016 (cat. no. 1270.0.55.005). #### Reference week The week preceding the week in which the interview was conducted. #### School-based apprenticeship or traineeship School-based apprenticeships or traineeships are undertaken part-time while at school and combine paid employment as an apprentice or trainee, vocational training and senior secondary school studies. This is a different population to those people who are undertaking apprenticeships or traineeships through the Australian Apprenticeships scheme which are considered separately. #### School leavers People aged 15-24 years who attended school in the previous year, but were not attending school in May of the survey year. Note that these people may have been studying a school year level at a non-school institution (e.g. studying Year 12 at TAFE). In this survey, school leavers are grouped by the highest level of school completed: year 12 or equivalent, and year 11 or below. #### School study School study is participation in primary or secondary level education, regardless of the institution or location where the study is or was undertaken. It therefore includes such study undertaken in a Technical and Further Education (TAFE) or other institution. #### Science, Technology, Engineering and Mathematics (STEM) In this publication, the ABS has described STEM fields of education according to the definition in the Report on Australia's STEM Workforce by the Office of the Chief Scientist. This includes the Australian Standard Classification of Education (ASCED) fields of education: 01. Natural and Physical Sciences (excluding 0101. Mathematical Sciences) 02. Information Technology 03. Engineering and Related Technologies 05. Agriculture, Environment and Related Studies 0101. Mathematical Sciences (listed separately to other Natural and Physical Sciences). This publication also compares these fields with the fields 04. Architecture and Building and 06. Health; which are described as STEM-related fields and are sometimes included in broader definitions of STEM. #### Socio-Economic Status (SEIFA-IRSD) This is one of four Socio-Economic Indexes for Areas (SEIFAs) compiled by the ABS following each Census of Population and Housing, from various characteristics of persons resident in particular areas. The Index of Relative Socio-Economic Disadvantage summarises attributes such as income, educational attainment, unemployment, and occupation skill levels. The index refers to the area (the Statistical Area Level 1) in which a person lives, not to the socio-economic situation of the particular individual. The index ranks areas on a continuum from most disadvantaged to least disadvantaged. A low score on the index (i.e. lowest quintile or decile) indicates a high proportion of relatively disadvantaged people in an area. Such areas include many households with low income, people with no qualifications and many people in low skill occupations. It should be noted that it cannot be concluded that an area with a very high score has a large proportion of relatively advantaged ('well off') people, as there are no variables in the index to indicate this. It can only be concluded that such an area has a relatively low incidence of disadvantage. The indexes used in this publication were those compiled following the 2016 Census. For further information about the indexes, see Census of Population and Housing: Socio-Economic Indexes for Areas (SEIFA), Australia, 2016 (cat. no. 2033.0.55.001). #### TAFE A Technical and Further Education institution. In Victoria this may also be interpreted as Training and Further Education. #### Trainee A trainee is a person who has entered into a legal contract (called a training agreement or contract of training) with an employer, to serve a period of training in a vocational area (e.g. office administration, information technology, hospitality). In this survey, persons who are apprentices and trainees are identified by their answer to a question specifically pertaining to a contract under the Australian Apprenticeships scheme. #### Underemployed workers Employed persons aged 15 years and over who want, and are available for, more hours of work than they currently have. They comprise: • persons employed part-time who want to work more hours and are available to start work with more hours, either in the reference week or in the four weeks subsequent to the survey; or • persons employed full-time who worked part-time hours in the reference week for economic reasons (such as being stood down or insufficient work being available). It is assumed that these people wanted to work full-time in the reference week and would have been available to do so. #### Unemployed Persons who were not employed during the reference week, and: • had actively looked for full-time or part-time work at any time in the four weeks up to the end of the reference week and were available for work in the reference week; or • were waiting to start a new job within four weeks from the end of the reference week and could have started in the reference week if the job had been available then. #### Vocational Education and Training (VET) VET relates to education and training that aims to equip people with knowledge, skills and/or competences required in particular occupations or, more broadly, on the labour market. VET is a component of apprenticeships or traineeships, including those that are school-based. However, VET can be undertaken without also undertaking an apprenticeship or traineeship. ## Quality declaration - summary ### Institutional environment For information on the institutional environment of the Australian Bureau of Statistics (ABS), including the legislative obligations of the ABS, financing and governance arrangements, and mechanisms for scrutiny of ABS operations, please see ABS Institutional Environment. ### Relevance The Survey of Education and Work (SEW) provides information for a range of key indicators relating to the educational participation and attainment of persons aged 15 to 74 years, along with data on their transition between education and work. The type of information collected includes: • general demographic and labour force characteristics; • participation in education in the survey month and in the year prior to the survey; • type of educational institution attended; • level of education of current and previous study; • level and main field of highest non-school qualification; • transition from education to work; unmet demand for education; and • selected characteristics of apprentices, including unmet demand for apprenticeships and traineeships. The Australian Standard Classification of Education (ASCED) is used to classify the Level and Field of education. The ASCED is a national standard classification which can be applied to all sectors of the Australian education system including schools, vocational education and training and higher education. As SEW is collected as a supplement to the Labour Force Survey (LFS), persons excluded from the LFS are also excluded from this survey (see Explanatory Notes in Labour Force, Australia for standard LFS exclusions). Additional exclusions from SEW are persons aged 75 years or older, institutionalised persons, boarding school pupils and persons in Indigenous Communities. Persons permanently unable to work and persons aged 65 to 74 years who are not intending to work, or not in the labour force, or not marginally attached to the labour force, were included for the first time in 2013. ### Timeliness Data from the survey are released approximately six months after they have been collected. The ABS has been conducting similar education and work surveys annually since 1964. These surveys were conducted in February from 1964 to 1974, in May 1975 and 1976, in August 1977 and 1978, and in May since 1979. ### Accuracy The LFS is primarily designed to provide estimates for the whole of Australia and, secondly, for each state and territory. The LFS is based on a sample of private dwellings and non-private dwellings, such as hotels and motels. The number of completed interviews for the 2019 Survey of Education and Work (after taking into account scope and coverage exclusions) was 38,683. The sample size was achieved by obtaining a response rate of 91% from the Monthly Population Survey. Two types of error are possible in an estimate based on a sample survey: non-sampling error and sampling error. Non-sampling error arises from inaccuracies in collecting, recording and processing the data. Every effort is made to minimise reporting error by the careful design of questionnaires, intensive training and supervision of interviewers, and efficient data processing procedures. Sampling error occurs because a sample, rather than the entire population, is surveyed. Sampling error can be estimated by measuring variability within a sample. In this publication sample error is reported using relative standard error and margins of error at the 95% confidence interval. For more information about error in SEW data see the technical note on data quality. ### Coherence The ABS seeks to maximise consistency and comparability over time by minimising changes to its surveys. However, sound survey practice requires ongoing development and maintenance to maintain the integrity of the data and the efficiency of collection. Information about comparability of SEW data to other ABS publications is available in the Explanatory Notes. For information on comparability of the SEW data over time see 'History of changes' in the Explanatory Notes. For a full list of changes made to the LFS, see the Labour force comparability over time chapter of Labour Statistics: Concepts, Sources and Methods, Feb 2018 (cat. no. 6102.0.55.001) and Information Paper: Forthcoming Changes to Labour Force Statistics, Aug 2015 (cat. no. 6292.0). ### Interpretability Detailed information on the terminology, classifications and other technical aspects associated with the SEW can be found in the associated methodology and relevant web pages provided with this release. ### Accessibility Tabulated data and associated measures of error are available in spreadsheet format and can be accessed from the Data downloads section. Data from this survey will also be accessible in the TableBuilder environment, enabling users to create their own customised output as required. For further details, refer to the Microdata Entry Page on the ABS website. Customised data are also available on request. Note that detailed data can be subject to high measures of error which in some cases may result in data being confidentialised. For further information about these or related statistics, contact the National Information and Referral Service on 1300 135 070, or email [email protected]. The ABS Privacy Policy outlines how the ABS will handle any personal information that you provide to us. ## Abbreviations ### Show all ABS Australian Bureau of Statistics ABSCQ Australian Bureau of Statistics Classification of Qualifications ANZSCO Australian and New Zealand Standard Classification of Occupations ANZSIC Australian and New Zealand Standard Industrial Classification ASCED Australian Standard Classification of Education ASGS Australian Statistical Geography Standard CURF Confidentialised Unit Record File GCCSA Greater Capital City Statistical Areas IRSD Index of Relative Socio-Economic Disadvantage ISCED International Standard Classification of Education ISCO International Standard Classification of Occupations ISIC International Standard Industrial Classification of All Economic Activities LFS Labour Force Survey MOE Margin of Error n.f.d. not further defined RSE relative standard error SA4 Statistical Area Level 4 SACC Standard Australian Classification of Countries SE standard error SEIFA Socio-Economic Indexes for Areas SEW Survey of Education and Work TAFE Technical and Further Education VET Vocational Education and Training	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39920416474342346, "perplexity": 2825.9731436974266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358953.29/warc/CC-MAIN-20211130050047-20211130080047-00514.warc.gz"}
https://getrevising.co.uk/revision-tests/physics_ac_circuits	Physics- Ac circuits HideShow resource information • Created by: FireDwarf • Created on: 23-11-13 12:09 What is a ac current? An ac current is when a current repeatly reverses its direction. In one cycle, the carrier moves one way in the circuit and then reverse direction then re-reverse direction. 1 of 11 What is the freqency? The number of complete cycles it passes through each second (hz) 2 of 11 Peak value? Maximum current/pd which is the same in either direction. 3 of 11 What does time period mean? Time for one complete cycle. 4 of 11 Why do we use ac? Because a larger V is more efficent then larger current because less power is dissipated. 5 of 11 What is the freqency and mean voltage of the UK? 50hz and 230V 6 of 11 What does RMS mean? It is the root mean square value and is the value of DC current that would give the same heating effect as the AC in the same resistor. 7 of 11 What are the formulas for RMS? Prms= Po (Peak Power)/ square root of 2 (same for Irms) Power = Irms(^2)R, Vrms = Irms x R 8 of 11 heating effect of an AC current? an electric heater at a very low frequency would be going cold then hot then cold then hot due to the alternating current (switching directions). 9 of 11 How does an ossiliscope work? Electron gun emits an electron at a flurescent screen. Posistion of the spot of light is effected by the P.D across either of the deflecting plates. With no pd, the spot remains in the same space. Displacement is proportional to the applied p.d 10 of 11 Therefore how can it be used as a volt meter? As the displacement of the beam is proprotional to the p.d applied. 11 of 11 Other cards in this set Card 2 Front What is the freqency? Back The number of complete cycles it passes through each second (hz) Peak value? Card 4 Front What does time period mean? Card 5 Front Why do we use ac?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8782323598861694, "perplexity": 3789.618537746322}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542686.84/warc/CC-MAIN-20161202170902-00057-ip-10-31-129-80.ec2.internal.warc.gz"}
http://lambda-the-ultimate.org/node/690	## Best route for new language to be self-hosting Does any particular language stand out above the crowd to be a host in which to develop general purpose languages? I am interested because of the development of Perl6 using Haskell as a host by Autrijus (See pugs.) I expect that any of OCaml, Haskell, Scheme or Lisp would be better than using C <grin> to develop a host, but is one of those (or something else entirely) likely to be significantly better than anything else? I expect that a good host language: • Has an active, friendly community. • Is super productive (for a skilled developer who has experience in host language). • Has good libraries. Especially language related libraries for say parser generators. Possibly part of language. • Is fast enough. Self-hosting may come after the initial childhood and growing pains of new language, so nice if the host language can be used for some time. • Is relatively stable. (Not hot off the press, not one-man-band, time spent learning it is usable in future, unlikely to be a pure research language) • Is mostly learnable in a few months by a bright developer (Hopefully that is me! My work has always been with imperative languages, but I am certain I can be quickly seduced by functional programming...). • Is open source (No vendor lock-in, ability to share with other developers). I hope this is the perfect forum to get an answer to this personally vexing question! Morris PS: For those that wonder at the need for self-hosting (rather than just keep another language under the hood): • I think that to build a community of developers for any new language wants ownership of â€˜their languageâ€™ that is â€˜better than other languagesâ€™. You canâ€™t have that without self-hosting (note: C is great as a host, but not great for prototyping!). • Reduce dependencies PPS: I do think the world needs another language! Of course I am preaching to the converted here. ## Comment viewing options I should add that the question relates to developing a mostly imperative language. This simplifies the question because there is no advantage to choosing a hosting language that is similar to the desired language (I would like to ignore that issue for the discussion). I also would like not to initiate a functional vs. imperative debate - although I am not sure if that is possible! ;-P No, no language stands out for GPL compiler development; any GPL will do. Actually, my thought given your statement is that most - if not all - GPLs seem to meet your requirements. So my guess is that you are stating the wrong requirements? This simplifies the question because there is no advantage to choosing a hosting language that is similar to the desired language(I would like to ignore that issue for the discussion). Yeah well, I wouldn't like to ignore that issue and I strongly suggest you don't too. There are tons of reasons to choose a hosting language similar to the desired language; there are also tons of reasons not to. I also would like not to initiate a functional vs. imperative debate - although I am not sure if that is possible! ;-P I don't think anyone is interested in that debate anyway. I really suggest that you define your language features and some roadmap first. ### Pick a language with macros Choose a language that can be bent into behaving the same way as the language to be implemented. Embed the new language in the host language: implement the new language's dataypes and operations in the host language using normal techniques, and use macros to implement the control structures. You can now write programs in you new language (using the syntax of the host language). Now implement the compiler in the embedded language. Finally, you need to convert the compiler source from the host syntax to the new syntax. Do this by redefining the macros implementing the embedded language to emit code in stead performing the construct in question. My personal choice would be PLT Scheme since the combination of its modules and macros allow the creation of embedded languages. As you can see, I am ignorant of most of the issues. I have only had a small involvement with language design in the past. As an aside I am really looking forward to seeing how much the Haskell language influences Larry and the design of Perl (There is plenty of opportunity to improve Perl... but there is some really ugly stuff planned for Perl6!) ### Use whatever you're best at I think the best route to self-hosted programming is to get off the host language as fast as you can. Your new language is much better for development, isn't it? Assuming your new language is simple enough, it shouldn't take too long to make a simplified subset of your language in a host language. This would be easiest done in whatever language you feel most comfortable in. The sooner you're done with this, the sooner you can throw out the better. You shouldn't worry about speed. If you have to use the host language implementation for a long period of time, you might be focusing your efforts in the wrong place (though I'm not sure of the purpose of this language, so I may be wrong). If you don't already have a favorite language that has a parsing library (or already have a favorite language and are good at writing your own parsers), then I'm not sure which language is best. This commment is probably completely useless because of that. I personally like Factor, which has a friendly but extremely small community. Right now, it doesn't really have a mature parsing library, and the language isn't very stable, so it's probably a bad choice. If your language is s-expression based, I think Common Lisp would be a great choice, because there's read and it's just a very productive language. If not, OCaml and Haskell both have good parsing libraries and IMHO are ok languages. OCaml in particular is very fast, but as I said, I'm not sure that matters. Haskell might make it awkward to implement an imperative language, and if you like imperative languages, you probably won't like Haskell anyway. But OCaml and Common Lisp can be as imperative as you want ### Get a good stable base, first. Before trying to self-host a language; it is important that the language design itself be reasonably stable. Not perfect, mind you; but stable enough so that you won't be breaking yourself. The decision to go and self-host (or when to do so) is complicated by several other factors. In the following discussion, the language being developed is known as L, and the bootstrapping language is B: * The goodness of the tool-set. Even if L is far more expressive than B; chances are that B has a more mature tool-set available for it. Better libraries, robust compilers, IDEs, debuggers (please no "debuggers are for morons" rants), etc. None of these will exist for L until you (or someone) writes them. A good REPL will make a basic development environment, but using B's tools may be more productive. * That said, if L is to become a useful language, at some point somebody will have to write the aforementioned tools; so doing so isn't at all wasted effort. The key question is not if, but when. * If you are writing a HLL, chances are that at least part of the runtime infrastructure will need to be written in a systems' language such as C/C++. Java, for example, is not a suitable language for implementing a JVM. * If you are writing a domain-specific language; you'd be better off not trying to self-host (unless the problem domain being addressed is compilers and such). * When self-hosting, be wary of the hornets nest of paradoxes and infinite recursions that comes with self-hosting. Read Art of the Meta-Object Protocol, which discusses such issues in depth. Also read Ken Thompson's famous Turing Award lecture Reflections on Trusting Trust. * Eating your own dog-food is a time-honored engineering principle; and there is a longstanding bias in the CS world that a (general purpose) programming language must be self-hosting in order to be worth anything. Many developers of high-level languages express a desire to free themselves from the "shackles" of low-level-language B, as if having a compiler written in B somehow limits the capability of L. It doesn't. The migration to self-hosting, if done at all, should be done for sound ease-of-development principles. (That said, starting a self-hosting implementation in L might be a good test case for L, so it has those advantages). Quite a few production-grade compilers and such are not written in the target language--GCC, for example, is written (mostly) in C despite supporting translation of numerous other languages. Don't let pride lead you to self-host prematurely. * The transition to self-hosting should be incremental. A good technique is to replace one section at a time, until the whole implementation is self-hosting, possibly excluding the low-level bits that require C or some other systems language. * Don't throw away the bootstrap compiler! (Or interpeter--see next point). The next user will need it to bring L up on his system. * Regardless of self-hosting or not; write an interpreter first. Only when the language definition is stable, and the interpreter fully working, should you attempt to compile to assembly language and/or bytecode. The interpreter will give you a reference implementation to compare your compiler against. * At all times: Don't bite off more than you can chew. ### Wanted: Stable base with many careful owners. Scott has stated much more insightfully than I the issues associated with looking for a bootstrapping language B. I disagree with the grandparent that I should use what I know. Note that I am avoiding saying anything specific about the language L, because it would only lead to people commenting on L, when for this discussion I am interested in comments on B. However imagine L is a descendent of popular recent scripting languages with a C flavour syntax, and you would have a good idea of L! My premise is that there are better languages for B that I have no experience with, which would be more productive to use as a bootstrapping language (including time to learn the language.) Is my premise correct? For example, last week I started learning Visual Basic 6 to use for a project and it would be execrable to use as B (or for that matter virtually anything :-). Most other languages I know would be 10x more productive for me than VB. I believe that a more suitable language for B could be 10x more productive again. However my experience is in imperative and scripting languages, and I have no experience in the languages usually recommended for B. Lisp descendents are often cited for B, but I have yet to be convinced they would be resoundingly better than say Haskell or ocaml (I admit I know neither) for my needs. ### For translation or slow interpetration, any of Lisp/ML/Haskell would work fine. Haskell might be the hardest to learn, if you aren't already familiar with it, because it's lazy evaluation is quite different from what programmers used to eager evaluation semantics might come to expect. I'm tempted to recommend ML over Common Lisp, if for no other reason than the existence of MLKit and similar tools. (What sort of typing system are you employing, BTW)? The above assumes you are implementing a reference or prototype interpeter (and not too concerned with performance); until your language is up and running you ought not be in the business of cycle counting. Alternatively, both are good at implementing compilers (which is just rather complex symbolic processing). When it comes to higher-performance implementations, I would recommend first that you target an existing VM or abstract machine (JVM, ParrotCode, .NET) rather than re-inventing this particular wheel. What of C++, Java, C, C#, etc? I wouldn't use plain C; as it has a primitive type system and is rather poor at symbolic manipulation compared to other languages. C++ is better (especially augmented with the numerous high-quality libraries from boost.org and others), but it's lack of garbage collection will be a problem for any interpeter. Some consider it's manifest typing a problem (others don't mind). You can get a GC for C++, but it's one thing that other languages don't make you worry about. Java and C# are often both used successfully for this sort of project (and make it easier to target the JVM and or .NET platforms respectively), but both are less "expressive" than ML. O'Caml (an object-oriented ML dialect) can be made rather fast if you like. A lot also depends on your goals. Are you trying to get a system working as fast as possible, or is your goal more to learn something new? If the latter, you might be better off sticking with a familiar language. If the latter, consider acquiring a new language part of the learning experience. ### Parsers not included Lisp beats Haskell/Ocaml only if L is parenthesized-prefix syntax. In that case, you avoid writing a lexer/parser, instead using the Lisp reader to transform program text into data structures your interpreter can understand. You can often implement the whole language as macros, cutting down significantly on developer time. If you have a moderately-complicated syntax, you're probably better off with Ocaml. Between ocamllex, ocamlyacc, and caml4p, you've got a really good set of parsing tools, and then algebraic data types and pattern matching often help you destructure the syntax trees for interpretation/compilation. I know Lisp has similar tools, but I don't think they're as mature (does anyone in the Lisp world ever use syntax?) and then your type system isn't as rich once you've got the actual syntax tree. Then again, it's so easy to destructure lists (destructuring-bind anyone?) that perhaps you don't need it. One interesting bootstrap possibility might be to use Lisp as B, create L as a prefix-syntaxed language, and then write a parser-generator in prefix-L that parses full-L. This way, you decouple the syntax from the compiler, so you automatically have the ability to create multiple syntaxes, and macros are a simple library away. I've thought some about implementing a language this way, but never got around to it. ### My favorite toy languge there is a longstanding bias in the CS world that a (general purpose) programming language must be self-hosting in order to be worth anything And there is the canonical reaction to this: â€œHas it been used for anything besides its own compiler?â€ Fortunately self-hosting is academic to me at present! On reflection, I now think the topic title should be something like "What are the most productive host languages to use for developing a new imperative language?" ### Ceterum censeo Carthaginem delendam esse I say "underspecified" or "if you abstract away from everything, then everybody is right." Java, Javascript, Pyhton, Lua, Php, C++, D, Perl, Icon, Ruby, Nice, F#, Dylan, ML, OCaml... Think about this for a while: Lua in Haskell? Dylan in Python? Ocaml in Java? ML in Perl? I can give arguments and counterarguments for any combination. Each of the mentioned languages have/had their own specific requirements, they all have/had their own manner of getting there. What do you mean with productive? I assume you want the shortest route to your goal. Almost no requirements, no goal, therefor any well-known language fits. ### Java not suitable for self-hosting Java, for example, is not a suitable language for implementing a JVM. Really? What about Jikes? I'd also note that the most widely used Java compilers are written in Java. This discussion makes me realize that my traditional understanding of the term "self-hosting" (is the compiler/interpreter written in its source language) is somewhat naive, considering both the compiler/interpreter and runtimes for a language may be implemented in any mixture of languages. I don't think I know of any strictly self-hosting implementations, considering even C compilers have parts of the runtime library implemented in assembly. -- Java.Next	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21774984896183014, "perplexity": 1578.6903651943933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806844.51/warc/CC-MAIN-20171123161612-20171123181612-00535.warc.gz"}
http://peeterjoot.com/tag/electromagnetic-field-strength/	## Potential solutions to the static Maxwell’s equation using geometric algebra When neither the electromagnetic field strength $$F = \BE + I \eta \BH$$, nor current $$J = \eta (c \rho – \BJ) + I(c\rho_m – \BM)$$ is a function of time, then the geometric algebra form of Maxwell’s equations is the first order multivector (gradient) equation \label{eqn:staticPotentials:20} While direct solutions to this equations are possible with the multivector Green’s function for the gradient \label{eqn:staticPotentials:40} G(\Bx, \Bx’) = \inv{4\pi} \frac{\Bx – \Bx’}{\Norm{\Bx – \Bx’}^3 }, the aim in this post is to explore second order (potential) solutions in a geometric algebra context. Can we assume that it is possible to find a multivector potential $$A$$ for which \label{eqn:staticPotentials:60} is a solution to the Maxwell statics equation? If such a solution exists, then Maxwell’s equation is simply \label{eqn:staticPotentials:80} which can be easily solved using the scalar Green’s function for the Laplacian \label{eqn:staticPotentials:240} G(\Bx, \Bx’) = -\inv{\Norm{\Bx – \Bx’} }, a beastie that may be easier to convolve than the vector valued Green’s function for the gradient. It is immediately clear that some restrictions must be imposed on the multivector potential $$A$$. In particular, since the field $$F$$ has only vector and bivector grades, this gradient must have no scalar, nor pseudoscalar grades. That is \label{eqn:staticPotentials:100} This constraint on the potential can be avoided if a grade selection operation is built directly into the assumed potential solution, requiring that the field is given by \label{eqn:staticPotentials:120} However, after imposing such a constraint, Maxwell’s equation has a much less friendly form \label{eqn:staticPotentials:140} Luckily, it is possible to introduce a transformation of potentials, called a gauge transformation, that eliminates the ugly grade selection term, and allows the potential equation to be expressed as a plain old Laplacian. We do so by assuming first that it is possible to find a solution of the Laplacian equation that has the desired grade restrictions. That is \label{eqn:staticPotentials:160} \begin{aligned} \end{aligned} for which $$F = \spacegrad A’$$ is a grade 1,2 solution to $$\spacegrad F = J$$. Suppose that $$A$$ is any formal solution, free of any grade restrictions, to $$\spacegrad^2 A = J$$, and $$F = \gpgrade{\spacegrad A}{1,2}$$. Can we find a function $$\tilde{A}$$ for which $$A = A’ + \tilde{A}$$? Maxwell’s equation in terms of $$A$$ is \label{eqn:staticPotentials:180} \begin{aligned} J \end{aligned} or \label{eqn:staticPotentials:200} This non-homogeneous Laplacian equation that can be solved as is for $$\tilde{A}$$ using the Green’s function for the Laplacian. Alternatively, we may also solve the equivalent first order system using the Green’s function for the gradient. \label{eqn:staticPotentials:220} Clearly $$\tilde{A}$$ is not unique, as we can add any function $$\psi$$ satisfying the homogeneous Laplacian equation $$\spacegrad^2 \psi = 0$$. In summary, if $$A$$ is any multivector solution to $$\spacegrad^2 A = J$$, that is \label{eqn:staticPotentials:260} A(\Bx) = \int dV’ G(\Bx, \Bx’) J(\Bx’) = -\int dV’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} }, then $$F = \spacegrad A’$$ is a solution to Maxwell’s equation, where $$A’ = A – \tilde{A}$$, and $$\tilde{A}$$ is a solution to the non-homogeneous Laplacian equation or the non-homogeneous gradient equation above. ### Integral form of the gauge transformation. Additional insight is possible by considering the gauge transformation in integral form. Suppose that \label{eqn:staticPotentials:280} A(\Bx) = -\int_V dV’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \tilde{A}(\Bx), is a solution of $$\spacegrad^2 A = J$$, where $$\tilde{A}$$ is a multivector solution to the homogeneous Laplacian equation $$\spacegrad^2 \tilde{A} = 0$$. Let’s look at the constraints on $$\tilde{A}$$ that must be imposed for $$F = \spacegrad A$$ to be a valid (i.e. grade 1,2) solution of Maxwell’s equation. \label{eqn:staticPotentials:300} \begin{aligned} F &= -\int_V dV’ \lr{ \spacegrad \inv{\Norm{\Bx – \Bx’} } } J(\Bx’) &= \int_V dV’ \lr{ \spacegrad’ \inv{\Norm{\Bx – \Bx’} } } J(\Bx’) &= \int_V dV’ \spacegrad’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \int_V dV’ \frac{\spacegrad’ J(\Bx’)}{\Norm{\Bx – \Bx’} } &= \int_{\partial V} dA’ \ncap’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \int_V \frac{\spacegrad’ J(\Bx’)}{\Norm{\Bx – \Bx’} } \end{aligned} Where $$\ncap’ = (\Bx’ – \Bx)/\Norm{\Bx’ – \Bx}$$, and the fundamental theorem of geometric calculus has been used to transform the gradient volume integral into an integral over the bounding surface. Operating on Maxwell’s equation with the gradient gives $$\spacegrad^2 F = \spacegrad J$$, which has only grades 1,2 on the left hand side, meaning that $$J$$ is constrained in a way that requires $$\spacegrad J$$ to have only grades 1,2. This means that $$F$$ has grades 1,2 if \label{eqn:staticPotentials:320} = \int_{\partial V} dA’ \frac{ \gpgrade{\ncap’ J(\Bx’)}{0,3} }{\Norm{\Bx – \Bx’} }. The product $$\ncap J$$ expands to \label{eqn:staticPotentials:340} \begin{aligned} \ncap J &= &= \ncap \cdot (-\eta \BJ) + \gpgradethree{\ncap (-I \BM)} \\ &=- \eta \ncap \cdot \BJ -I \ncap \cdot \BM, \end{aligned} so \label{eqn:staticPotentials:360} = -\int_{\partial V} dA’ \frac{ \eta \ncap’ \cdot \BJ(\Bx’) + I \ncap’ \cdot \BM(\Bx’)}{\Norm{\Bx – \Bx’} }. Observe that if there is no flux of current density $$\BJ$$ and (fictitious) magnetic current density $$\BM$$ through the surface, then $$F = \spacegrad A$$ is a solution to Maxwell’s equation without any gauge transformation. Alternatively $$F = \spacegrad A$$ is also a solution if $$\lim_{\Bx’ \rightarrow \infty} \BJ(\Bx’)/\Norm{\Bx – \Bx’} = \lim_{\Bx’ \rightarrow \infty} \BM(\Bx’)/\Norm{\Bx – \Bx’} = 0$$ and the bounding volume is taken to infinity. # References ## Generalizing Ampere’s law using geometric algebra. The question I’d like to explore in this post is how Ampere’s law, the relationship between the line integral of the magnetic field to current (i.e. the enclosed current) \label{eqn:flux:20} \oint_{\partial A} d\Bx \cdot \BH = -\int_A \ncap \cdot \BJ, generalizes to geometric algebra where Maxwell’s equations for a statics configuration (all time derivatives zero) is \label{eqn:flux:40} where the multivector fields and currents are \label{eqn:flux:60} \begin{aligned} F &= \BE + I \eta \BH \\ J &= \eta \lr{ c \rho – \BJ } + I \lr{ c \rho_\txtm – \BM }. \end{aligned} Here (fictitious) the magnetic charge and current densities that can be useful in antenna theory have been included in the multivector current for generality. My presumption is that it should be possible to utilize the fundamental theorem of geometric calculus for expressing the integral over an oriented surface to its boundary, but applied directly to Maxwell’s equation. That integral theorem has the form \label{eqn:flux:80} \int_A d^2 \Bx \boldpartial F = \oint_{\partial A} d\Bx F, where $$d^2 \Bx = d\Ba \wedge d\Bb$$ is a two parameter bivector valued surface, and $$\boldpartial$$ is vector derivative, the projection of the gradient onto the tangent space. I won’t try to explain all of geometric calculus here, and refer the interested reader to [1], which is an excellent reference on geometric calculus and integration theory. The gotcha is that we actually want a surface integral with $$\spacegrad F$$. We can split the gradient into the vector derivative a normal component \label{eqn:flux:160} so \label{eqn:flux:100} = \int_A d^2 \Bx \boldpartial F + \int_A d^2 \Bx \ncap \lr{ \ncap \cdot \spacegrad } F, so \label{eqn:flux:120} \begin{aligned} \oint_{\partial A} d\Bx F &= \int_A d^2 \Bx \lr{ J – \ncap \lr{ \ncap \cdot \spacegrad } F } \\ &= \int_A dA \lr{ I \ncap J – \lr{ \ncap \cdot \spacegrad } I F } \end{aligned} This is not nearly as nice as the magnetic flux relationship which was nicely split with the current and fields nicely separated. The $$d\Bx F$$ product has all possible grades, as does the $$d^2 \Bx J$$ product (in general). Observe however, that the normal term on the right has only grades 1,2, so we can split our line integral relations into pairs with and without grade 1,2 components \label{eqn:flux:140} \begin{aligned} &= \int_A dA \gpgrade{ I \ncap J }{0,3} \\ &= \int_A dA \lr{ \gpgrade{ I \ncap J }{1,2} – \lr{ \ncap \cdot \spacegrad } I F }. \end{aligned} Let’s expand these explicitly in terms of the component fields and densities to check against the conventional relationships, and see if things look right. The line integrand expands to \label{eqn:flux:180} \begin{aligned} d\Bx F &= d\Bx \lr{ \BE + I \eta \BH } = d\Bx \cdot \BE + I \eta d\Bx \cdot \BH + d\Bx \wedge \BE + I \eta d\Bx \wedge \BH \\ &= d\Bx \cdot \BE – \eta (d\Bx \cross \BH) + I (d\Bx \cross \BE ) + I \eta (d\Bx \cdot \BH), \end{aligned} the current integrand expands to \label{eqn:flux:200} \begin{aligned} I \ncap J &= I \ncap \lr{ \frac{\rho}{\epsilon} – \eta \BJ + I \lr{ c \rho_\txtm – \BM } } \\ &= \ncap I \frac{\rho}{\epsilon} – \eta \ncap I \BJ – \ncap c \rho_\txtm + \ncap \BM \\ &= \ncap \cdot \BM + \eta (\ncap \cross \BJ) – \ncap c \rho_\txtm + I (\ncap \cross \BM) + \ncap I \frac{\rho}{\epsilon} – \eta I (\ncap \cdot \BJ). \end{aligned} We are left with \label{eqn:flux:220} \begin{aligned} \oint_{\partial A} \lr{ d\Bx \cdot \BE + I \eta (d\Bx \cdot \BH) } &= \int_A dA \lr{ \ncap \cdot \BM – \eta I (\ncap \cdot \BJ) } \\ \oint_{\partial A} \lr{ – \eta (d\Bx \cross \BH) + I (d\Bx \cross \BE ) } &= \int_A dA \lr{ \eta (\ncap \cross \BJ) – \ncap c \rho_\txtm + I (\ncap \cross \BM) + \ncap I \frac{\rho}{\epsilon} -\PD{n}{} \lr{ I \BE – \eta \BH } }. \end{aligned} This is a crazy mess of dots, crosses, fields and sources. We can split it into one equation for each grade, which will probably look a little more regular. That is \label{eqn:flux:240} \begin{aligned} \oint_{\partial A} d\Bx \cdot \BE &= \int_A dA \ncap \cdot \BM \\ \oint_{\partial A} d\Bx \cross \BH &= \int_A dA \lr{ – \ncap \cross \BJ + \frac{ \ncap \rho_\txtm }{\mu} – \PD{n}{\BH} } \\ \oint_{\partial A} d\Bx \cross \BE &= \int_A dA \lr{ \ncap \cross \BM + \frac{\ncap \rho}{\epsilon} – \PD{n}{\BE} } \\ \oint_{\partial A} d\Bx \cdot \BH &= -\int_A dA \ncap \cdot \BJ \\ \end{aligned} The first and last equations could have been obtained much more easily from Maxwell’s equations in their conventional form more easily. The two cross product equations with the normal derivatives are not familiar to me, even without the fictitious magnetic sources. It is somewhat remarkable that so much can be packed into one multivector equation: \label{eqn:flux:260} \oint_{\partial A} d\Bx F = I \int_A dA \lr{ \ncap J – \PD{n}{F} }. # References [1] A. Macdonald. Vector and Geometric Calculus. CreateSpace Independent Publishing Platform, 2012.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967906475067139, "perplexity": 3152.3234565702055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671363.79/warc/CC-MAIN-20191122143547-20191122172547-00073.warc.gz"}
https://ec.gateoverflow.in/1522/gate2020-ec-1	If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$? 1. It is not necessary that these vectors span $\mathbb{R}^{4}$. 3. Any four of these vectors form a basis for $\mathbb{R}^{4}$. 4. If $\left \{ v_{1},v_{3},v_{5},v_{6} \right\}$ spans $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9738558530807495, "perplexity": 391.35277514013103}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874026.22/warc/CC-MAIN-20201020162922-20201020192922-00662.warc.gz"}
http://www.maths.ox.ac.uk/events/past/627/1990--now?field_seminar_date_value_op=%3C&field_seminar_date_value%5Bvalue%5D=&field_seminar_date_value%5Bmin%5D=&field_seminar_date_value%5Bmax%5D=&page=9	# Past Applied Analysis and Mechanics Seminar 2 February 2004 17:00 Daniel Faraco Abstract Recently Friesecke, James and Muller established the following quantitative version of the rigidity of SO(n) the group of special orthogonal matrices. Let U be a bounded Lipschitz domain. Then there exists a constant C(U) such that for any mapping v in the L2-Sobelev space the L^2-distance of the gradient controlls the distance of v a a single roation. This interesting inequality is fundamental in several problems concerning dimension reduction in nonlinear elasticity. In this talk, we will present a joint work with Muller and Zhong where we investigate an analagous quantitative estimate where we replace SO(n) by an arbitrary smooth, compact and SO(n) invariant subset of the conformal matrices E. The main novelty is that exact solutions to the differential inclusion Df(x) in E a.e.x in U are not necessarily affine mappings. • Applied Analysis and Mechanics Seminar 26 January 2004 17:00 Jonathan Bevan Abstract Using a technique explored in unpublished work of Ball and Mizel I shall show that already in 2 and 3 dimensions there are vectorfields which are singular minimizers of integral functionals whose integrand is strictly polyconvex and depends on the gradient of the map only. The analysis behind these results gives rise to an interesting question about the relationship between the regularity of a polyconvex function and that of its possible convex representatives. I shall indicate why this question is interesting in the context of the regularity results above and I shall answer it in certain cases. • Applied Analysis and Mechanics Seminar 7 January 2004 16:00 N Kikuchi Abstract • Applied Analysis and Mechanics Seminar 1 December 2003 17:00 Jan Maly Abstract • Applied Analysis and Mechanics Seminar 17 November 2003 17:00 Dr Andrew Lorent Abstract Take any region omega and let function u defined inside omega be the distance from the boundary, u solves the iconal equation \lt\|Du\rt\|=1 with boundary condition zero. Functional u is also conjectured (in some cases proved) to be the "limiting minimiser" of various functionals that arise models of blistering and micro magnetics. The precise formulation of these problems involves the notion of gamma convergence. The Aviles Giga functional is a natural "second order" generalisation of the Cahn Hilliard model which was one of the early success of the theory of gamma convergence. These problems turn out to be surprisingly rich with connections to a number of areas of pdes. We will survey some of the more elementary results, describe in detail of one main problems in field and state some partial results. • Applied Analysis and Mechanics Seminar 10 November 2003 17:00 Viet Ha Hoang Abstract • Applied Analysis and Mechanics Seminar 3 November 2003 17:00 Carlos Mora-Corral Abstract • Applied Analysis and Mechanics Seminar 13 October 2003 17:00 David Schaeffer Abstract • Applied Analysis and Mechanics Seminar	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9337983131408691, "perplexity": 1346.9350865969798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156192.24/warc/CC-MAIN-20180919102700-20180919122700-00297.warc.gz"}
https://www.physicsforums.com/threads/potential-energy-of-an-arrangement-of-point-charges.796375/	# Potential energy of an arrangement of point charges 1. Feb 6, 2015 ### acdurbin953 1. The problem statement, all variables and given/known data What is the potential energy of the system composed of the three charges q1, q3, and q4, when q1 is at point R? Define the potential energy to be zero at infinity. Charges are arranged in a triangle, with q3 and q4 located up and down 2.2 cm from the origin, and q1 on the x axis at a distance R = 3.5 cm from the origin. q1 = 1.9uC q3 = q4 = -1.8 uC distance from q1 to each of the other 2 charges is 4.1 cm 2. Relevant equations U-kqq/r 3. The attempt at a solution U1 = [(9E9)(-1.8E-6)(1.9E6)]/0.041 = -0.751 Since there is symmetry I doubled U1 to find U = -1.501, however that answer is wrong. Where am I messing up? 2. Feb 6, 2015 ### acdurbin953 I just figured out that you have to also considered the two point charges potential energy on each other. Case closed! Sorry for the (unnecessary) post.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.880260169506073, "perplexity": 770.8304214851963}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648431.63/warc/CC-MAIN-20180323180932-20180323200932-00227.warc.gz"}
https://wiki.polkadot.network/docs/maintain-guides-democracy	# Participate in Democracy The public referenda chamber is one of the three bodies of on-chain governance as it's instantiated in Polkadot and Kusama. The other two bodies are the council and the technical committee. Public referenda can be proposed and voted on by any token holder in the system as long as they provide a bond. After a proposal is made, others can agree with it by seconding it and putting up tokens equal to the original bond. Every launch period, the most seconded proposal will be moved to the public referenda table where it can be voted upon. Voters who are willing to lock up their tokens for a greater duration of time can do so and get their vote amplified. For more details on the governance system please see here. This guide will instruct token holders how to propose and vote on public referenda using the Democracy module. Below are a few links to stay informed and directly engage with the community. • Polkadot Direction - a place to discuss governance and the future of Polkadot. • Kusama Direction - a place to discuss governance and the future of Kusama. • Polkadot and Kusama Polkassembly - for current referenda, latest proposals, motions, treasury proposals, tips, bounties, and more. • Polkadot Daily Digest - News about what is happening in the Polkadot ecosystem, published every weekday except holidays. ## Important Parameters The important parameters to be aware of when voting using the Democracy module are as follow: Launch Period - How often new public referenda are launched. Voting Period - How often votes for referenda are tallied. Emergency Voting Period - The minimum voting period for a fast-tracked emergency referendum. Minimum Deposit - The minimum amount to be used as a deposit for a public referendum proposal. Enactment Period - The minimum period for locking funds and the period between a proposal being approved and enacted. Cooloff Period - The period in blocks where a proposal may not be re-submitted after being vetoed. ## Proposing an Action Proposing an action to be taken requires you to bond some tokens. In order to ensure you have enough tokens to make the minimum deposit you can check the parameter in the chain state. The bonded tokens will only be released once the proposal is tabled (that is, brought to a vote); there is no way for the user to "revoke" their proposal and get the bond back before it has become a referendum. Since it is essentially impossible to predict definitely when a proposal may become a referendum (if ever), this means that any tokens bonded will be locked for an indeterminate amount of time. Proposals cannot be revoked by the proposer, even if they never turn into a referendum. It is important to realize that there is no guarantee that DOT you use for proposing or seconding a proposal will be returned to that account in any given timeframe. On Polkadot Apps you can use the "Democracy" tab to make a new proposal. In order to submit a proposal, you will need to submit what's called the preimage hash. The preimage hash is simply the hash of the proposal to be enacted. The easiest way to get the preimage hash is by clicking on the "Submit preimage" button and configuring the action that you are proposing. For example, if you wanted to propose that the account "Dave" would have a balance of 10 tokens your proposal may look something like the below image. The preimage hash would be 0xa50af1fadfca818feea213762d14cd198404d5496bca691294ec724be9d2a4c0. You can copy this preimage hash and save it for the next step. There is no need to click Submit Preimage at this point, though you could. We'll go over that in the next section. Now you will click on the "Submit proposal" button and enter the preimage hash in the input titled "preimage hash" and at least the minimum deposit into the "locked balance" field. Click on the blue "Submit proposal" button and confirm the transaction. You should now see your proposal appear in the "proposals" column on the page. Now your proposal is visible by anyone who accesses the chain and others can second it or submit a preimage. However, it's hard to tell what exactly this proposal does since it shows the hash of the action. Other holders will not be able to make a judgement for whether they second it or not until someone submits the actual preimage for this proposal. In the next step you will submit the preimage. ## Submitting a Preimage The act of making a proposal is split from submitting the preimage for the proposal since the storage cost of submitting a large preimage could be pretty expensive. Allowing for the preimage submission to come as a separate transaction means that another account could submit the preimage for you if you don't have the funds to do so. It also means that you don't have to pay so many funds right away as you can prove the preimage hash out-of-band. However, at some point before the proposal passes you will need to submit the preimage or else the proposal cannot be enacted. The guide will now show you how to do this. Click on the blue "Submit preimage" button and configure it to be the same as what you did before to acquire the preimage hash. This time, instead of copying the hash to another tab, you will follow through and click "Submit preimage" and confirm the transaction. Once the transaction is included you should see the UI update with the information for your already submitted proposal. ## Seconding a Proposal Seconding a proposal means that you are agreeing with the proposal and backing it with an equal amount of deposit as was originally locked. The bonded tokens will be released once the proposal is tabled (that is, brought to a vote), just like the original proposer's bond. By seconding a proposal you will move it higher up the rank of proposals. The most seconded proposal in value, not number of supporters will be brought to a referendum every launch period. It is important to note that there is no way to stop or cancel seconding a proposal once it has been done. Therefore, the DOT that was seconded will be reserved until the proposal is tabled as a referendum. This is an indeterminate amount of time, since there is no guarantee that a proposal will become a referendum for a given period, as other proposals may be proposed and tabled before it. Note that it is possible for a single account to second a proposal multiple times. This is by design; it is the value, not the number of seconds per se, that counts in terms of weighting. If there were a limit of one second per account, it would be trivial for a user with, for example, 1000 DOT to create ten accounts with 100 DOT instead of a single account with 1000 DOT. Thus, no restrictions are made on the number of times a single account can second a proposal. To second a proposal, navigate to the proposal you want to second and click on the "Second" button. You will be prompted with the full details of the proposal (if the preimage has been submitted!) and can then broadcast the transaction by clicking the blue "Second" button. Once successful you will see your second appear in the dropdown in the proposal details. ## Voting on a Proposal At the end of each launch period, the most seconded proposal will move to referendum. During this time you can cast a vote for or against the proposal. You may also lock up your tokens for a greater length of time to weigh your vote more strongly. During the time your tokens are locked, you are unable to transfer them, however they can still be used for further votes. Locks are layered on top of each other, so an eight week lock does not become a 15 week lock if you vote again a week later, rather another eight week lock is placed to extend the lock just one extra week. To vote on a referendum, navigate to the "Democracy" tab of Polkadot Apps. Any active referendum will show in the "referenda" column. Click the blue button "Vote" to cast a vote for the referendum. If you would like to cast your vote for the proposal select the "Aye, I approve" option. If you would like to cast your vote against the proposal in referendum you will select "Nay, I do not approve" option. The second option is to select your conviction for this vote. The longer you are willing to lock your tokens, the stronger your vote will be weighted. The timeline for the conviction starts after the voting period ends; tokens used for voting will always be locked until the end of the voting period, no matter what conviction you vote with. Unwillingness to lock your tokens means that your vote only counts for 10% of the tokens that you hold, while the maximum lock up of 896 days means you can make your vote count for 600% of the tokens that you hold. When you are comfortable with the decision you have made, click the blue "Vote" button to submit your transaction and wait for it to be included in a block. ## Unlocking Locked Tokens Like vesting, the tokens that are locked in democracy are unlocked lazily. This means that you, the user, must explicitly call an unlock extrinsic to make your funds available again after the lock expires. Unbonding is another term you hear a lot in Polkadot, it means withdrawing your DOT that was used in staking. To know more about it, please see here. You can do this from the "Accounts" page in Polkadot-JS Apps, unless you use Ledger (see below). First check that your account has a "democracy" lock by opening the details on your balance. In the example below the account has 150 KSM locked in democracy. Now you can click the menu button on Apps and find the option that says "Clear expired democracy locks". After selecting this option you may confirm the transaction and your locks will be cleared when successful. #### With a Ledger hardware wallet or Unlocking Very Old Locks If you do not see an option to clear expired democracy votes, it may be that the lock is very old. Or, if you are using the Ledger hardware wallet, you will not be able to issue the batch Unlock action from the UI. Instead, you must clear the lock by directly issuing the correct extrinsics. Navigate to the Extrinsics page and submit the following extrinsic: democracy.removeVote(index) using the account that you voted with. For the index number (ReferendumIndex), enter the number of the referendum for which you voted ("12" in the image below). The number of the referendum for which you voted is visible in an explorer such as Polkascan. You need to press the "Submit Transaction" button to submit the extrinsic. Now submit the following extrinsic: democracy.unlock(target), where target is your your account address. If you return to the Accounts page, you should see that the democracy lock has been released. Note that this applies only to locked DOT that were used for voting on referenda. In order to unlock DOT locked by voting for members of the Polkadot Council, you need to go to the Council page, click "Vote", and then click on "Unvote All". ## Delegate a Vote If you are too busy to keep up and vote on upcoming referenda, there is an option to delegate your vote to another account whose opinion you trust. When you delegate to another account, that account gets the added voting power of your tokens along with the conviction that you set. The conviction for delegation works just like the conviction for regular voting, except your tokens may be locked longer than they would normally since locking resets when you undelegate your vote. The account that is being delegated to does not make any special action once the delegation is in place. They can continue to vote on referenda how they see fit. The difference is now when the Democracy system tallies votes, the delegated tokens now are added to whatever vote the delegatee has made. You can delegate your vote to another account and even attach a "Conviction" to the delegation. Navigate to the "Extrinsics" tab on Polkadot Apps and select the options "democracy" and "delegate". This means you are accessing the democracy pallet and choosing the delegate transaction type to send. Your delegation will count toward whatever the account you delegated for votes on until you explicitly undelegate your vote. In the first input select the account you want to delegate to and in the second input select the amount of your conviction. Remember, higher convictions means that your vote will be locked longer. So choose wisely! After you send the delegate transaction, you can verify it went through by navigating to the "Chain State" tab and selecting the "democracy" and "delegations" options. You will see an output similar to below, showing the addresses to which you have delegated your voting power. ## Undelegate a Vote You may decide at some point in the future to remove your delegation to a target account. In this case, your tokens will be locked for the maximum amount of time in accordance with the conviction you set at the beginning of the delegation. For example, if you chose "2x" delegation for four weeks lock up time, your tokens will be locked for 4 weeks after sending the undelegate transaction. Once your vote has been undelegated, you are in control of making votes with it once again. You can start to vote directly, or chose a different account to act as your delegate. The undelegate transaction must be sent from the account that you wish to clear of its delegation. For example, if Alice has delegated her tokens to Bob, Alice would need to be the one to call the undelegate transaction to clear her delegation. The easiest way to do this is from the "Extrinsics" tab of Polkadot Apps. Select the "democracy" pallet and the "undelegate" transaction type. Ensure that you are sending the transaction from the account you want to clear of delegations. Click "Submit transaction" and confirm. ## Voting with a Governance Proxy Making a vote on behalf of a stash requires a "proxy" transaction from the Proxy pallet. When you choose this transaction from the "Extrinsics" tab, it will let you select "vote" from the Democracy pallet, and you will specify the index of the referendum that is being voted, the judgement (i.e. "Aye" for approval or "Nay" for rejection), and the conviction, just like a normal vote. For more material on adding and removing Governance proxies, as well as other types, please see the Proxy page. ## Interpreting On-Chain Voting Data Consider the following example showcasing how votes would be displayed on a block explorer. Nay 0.1x => 0Nay 1x => 1Nay 2x => 2Nay 3x => 3Nay 4x => 4Nay 5x => 5Nay 6x => 6Aye 0.1x => 128Aye 1x => 129Aye 2x => 130Aye 3x => 131Aye 4x => 132Aye 5x => 133Aye 6x => 134 At first glance, it may be difficult to interpret what you voted on. We need to take a step back and consider the "voting data" at the binary level. The vote is stored as a byte using a bitfield data structure and displayed on the block explorer as a decimal integer. The bitfield stores both the conviction and aye/nay boolean, where the boolean is represented using the MSB of the byte. This would mean that the grouping of the 7 remaining bits is used to store the conviction.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17221666872501373, "perplexity": 2128.5318924092303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585522.78/warc/CC-MAIN-20211022212051-20211023002051-00248.warc.gz"}
https://cs.stackexchange.com/questions/101936/are-there-strings-which-get-accepted-only-by-pda-by-empty-stack-and-not-by-pda-b	# Are there strings which get accepted only by PDA by empty stack and not by PDA by final state, and vice versa? Can the same PDA accept both by final state and empty stack in the sense that there are some set of strings that are getting accepted by empty stack, while other set of string by final state and language accepted by the PDA is union of these two? For example, Consider the PDA shown below:- I was trying to figure out the language accepted by this PDA and I got confused on the point that a string w=b is given as input, that will be popped out and the stack will be empty so would b be an element of language accepted by PDA or if we consider it only as acceptance by final state (considering that acceptance by final stack requires the bottom of stack symbol to be left in the stack ) the language accepted by this PDA will be : {w\| any prefix of w has number of a's more than number of b's} However a string like "ab" can also be accepted if we allow both acceptance by empty stack and final state (The confusion here is strictly more a's or it can be equal too). • You can define whatever model of computation you want. The two standard models of computation for PDA, however, are “final state” PDAs and “empty stack” PDAs. When describing a PDA, we have to state which of these two we’re using. – Yuval Filmus Dec 22 '18 at 11:45 • @YuvalFilmus So since this PDA accepts by final state, so would the language of this PDA include "b"? – Amisha Bansal Dec 22 '18 at 14:44 • The PDA accepts all strings having a computation ending at a final state. – Yuval Filmus Dec 22 '18 at 14:52 Since it was not explicitly mentioned, I'll assume that the PDA in the question is a PDA $$P_s$$ that has been defined for acceptance by empty stack. Let the language accepted by $$P_s$$ be $$L_s = N(P_s)$$. There definitely exists another PDA $$P_f$$ which produces a language $$L_f = L_s$$ by defining acceptance on final state. This is why we say that: However, it is wrong to expect that the two PDA $$P_s$$ and $$P_f$$ are the same.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5229114294052124, "perplexity": 747.0703772008143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572289.5/warc/CC-MAIN-20190915195146-20190915221146-00356.warc.gz"}
http://mathhelpforum.com/calculus/28099-equation-motion-particle-where-s-meters-t-seconds-gi-print.html	# The equation of motion of a particle, where s is in meters and t is in seconds, is gi • Feb 12th 2008, 01:03 PM plstevens The equation of motion of a particle, where s is in meters and t is in seconds, is gi s=7t^3-3t (a)Find the velocity and acceleration as functions of t. v(t)= a(t)= (b) Find the acceleration after 7 seconds. _______m/s^2 (c) Find the acceleration when the velocity is 0. (Round the answer to one decimal place) _______m/s^2 • Feb 12th 2008, 02:11 PM CaptainBlack Quote: Originally Posted by plstevens s=7t^3-3t (a)Find the velocity and acceleration as functions of t. v(t)= a(t)= (b) Find the acceleration after 7 seconds. _______m/s^2 (c) Find the acceleration when the velocity is 0. (Round the answer to one decimal place) _______m/s^2 $v(t)=\frac{ds}{dt}(t)$ and: $a(t)=\frac{dv}{dt}(t)=\frac{d^2 s}{dt^2}(t)$ RonL • Feb 12th 2008, 06:01 PM plstevens so what do i do for b and c • Feb 12th 2008, 06:41 PM topsquark Quote: Originally Posted by plstevens so what do i do for b and c b) You have your function for a(t) so what is a(7)? c) When is v(t) = 0? Find that value of t and then find the acceleration at that time. -Dan • Feb 12th 2008, 06:50 PM plstevens i don't mean to be a dumby but i still don't get it • Feb 12th 2008, 07:45 PM topsquark Quote: Originally Posted by plstevens i don't mean to be a dumby but i still don't get it If I gave you a function, for example, a(t) = 8t + 3 what would you tell me the value of a(7) is? Part b is exactly this, but of course with the function you derived in part a). -Dan • Feb 12th 2008, 07:47 PM plstevens I'm so sorry but thats not making sense • Feb 12th 2008, 07:54 PM topsquark Quote: Originally Posted by plstevens I'm so sorry but thats not making sense In part a) your position function is given as $s(t) = 7t^3 - 3t$. From this you get that the acceleration function is $a(t) = 42t$ What is the value of a(7), the value of the function a(t) when t = 7? If you can't answer that, then I suggest you have a long talk with your instructor. -Dan	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9406499266624451, "perplexity": 895.2331551248528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814833.62/warc/CC-MAIN-20180223194145-20180223214145-00107.warc.gz"}
http://www.soulphysics.org/2009/01/two-tough-cases-of-underdetermination/	# Two Tough Cases of Underdetermination John Earman once pointed out two tough cases of underdetermination, neither of which arises in a silly algorithmic way. Today, I’d like to argue for an important difference between these two examples. Ultimately, I suspect the first is more deeply intractable than the second. Earman’s first example is this. I claim that there do exist examples of rival empirically indistinguishable theories that posit interestingly different theoretical structures. For instance, TN [Newtonian Theory] (sans absolute space) can be opposed by a theory which eschews gravitational force in favor of a non-flat affine connection and which predicts exactly the same particle orbits as TN for gravitationally interacting particles (Earman 1993, 31). In short: Newtonian gravitation can be described as particles interacting via forces on a flat spacetime — or as particles in freefall in curved spacetime, as in Cartan’s ‘geometricized’ Newtonian gravitation. (See Malament (1986) for a discussion of the latter. This underdetermination has been beautifully and rigorously argued for by Jonathan Bain — PDF.) Earman’s second example is the existence of observationally indistinguishable spacetimes: Relativity theory tells us that the data available to an observer through such interactions [as observation] are restricted to events that are swept out by the observer’s past light cone…. As a result, even idealized observers who live forever may be unable to empirically distinguish hypotheses about global topological features of some of the cosmological models allowed by Einstein’s field equations for gravitation (ibid). Indeed, my distinguished colleague John Manchak has greatly generalized this result, and shown that all spacetimes have an indistinguishable counterpart that preserves all the local properties of spacetime (Philsci-Archive). What’s the difference between Earman’s two examples? In short, it is that the first is about underdetermination of theories, while the second is about underdetermination of models of a particular theory, by available empirical evidence. What’s the significance of that? The first example strikes me as a completely convincing case of underdetermination (especially on Bain’s treatment). But note: whether or not the second kind of underdetermination obtains depends on how one formulates a theory. For that reason, this underdetermination might often be avoided by a well-motivated reformulation. For example: there is a particular class of models of Einstein’s Field Equations (EFE) that can be described. There is a smaller class of models when one also requires that the Energy Conditions (EC) be satisfied. Any causal condition (CC) will place further restrictions on the class of models. So, we have multiple formulations of general relativity: • EFE • EFE + EC • EFE + CC • EFE + EC + CC all of which correspond to different classes of models. So, when one argues, model M and model N are observationally indistinguishable models of our world, this underdetermination might be avoided by moving to a more restricted formulation of General Relativity. And, unfortunately, the issue of which formulation of general relativity is the correct one is deeply contentious. Of course, there are some cases of observational indistinguishability which are can obtain even in EFE + EC + CC — for example, David Malament (PDF) describes observationally indistinguishable counterparts to de Sitter spacetime. But one wonders if this might not lead us to a suspicous game: you show me an example of observational indistinguishability, and I try to rule it out by further restricting the class of models of General Relativity. At any rate, a claim about underdetermination at the level of theories (such as in Earman’s first example) does not seem to suffer from this kind of regress. Soul Physics is authored by Bryan W. Roberts. Thanks for subscribing. Want more Soul Physics? Try the Soul Physics Tweet. ## 3 thoughts on “Two Tough Cases of Underdetermination” 1. Gabriele Contessa Intuitively, I think I see the distinction you are trying to draw, but I’m not sure how you can draw it in a principled manner once you make clear what notion of theory you are working with. If, following the semantic view, you take a theory to be a set of models, then I don’t see how you can distinguish between the two kinds of underdetermination (what you call different formulations of GRT would simply be different theories). If you don’t and you think that theories are distinct from their models, then what is a theory? I think the most plausible answer would be a set of propositions but then again the different formulations of GRT would seem to count as different theories. However, and probably here is the difference the different formulations of GRT are such that one is a proper set of the other, while the different formulations of Newtonian Mechanics are not. Does this capture the difference between the two cases. If not, how would you characterize it? 2. Bryan That’s very interesting. You may be more of an expert on semantic accounts than I am. A semantic theorist takes a set of models stand in for a ‘theory.’ But it seems that he would still make a principled distinction between the two kinds of underdetermination like this: 1. You have two sets of models, with distinct ontologies (the models of one set might be curved spacetimes, and the models of the other set might be flat). But the two sets are pairwise-indistinguishable — that is, each model in one of the sets has an empirically indistinguishable counterpart in the other set. 2. You have just one set of models, with one ontology (say, curved spacetimes). But there are pairs of distinct models in the set that are empirically indistinguishable. Perhaps the ‘subset’ relation could also be used to make the distinction. I’m not sure, but it’s an interesting idea to try. Thanks for the thought! 3. nogre Here’s how I see the two kinds of underdetermination: For any theory, there are some parts of that theory that are considered to be the “fixed” parts of the theory, and other parts which are the “results” of that theory. Those parts that are considered to be fixed can turn into the results, and vice verso, according to our scientific whim/ experience, but at any given point these two parts always exist. Secondly, insofar as all theories have these two parts, we can have distinct underdetermination claims about both parts within a single theory.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7232427000999451, "perplexity": 719.8284681371422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658662.31/warc/CC-MAIN-20190117000104-20190117022104-00254.warc.gz"}
http://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/Lévy+hierarchy	foundations # The Lévy hierarchy ## Idea In logic, model theory, and set theory, the Lévy hierarchy is a stratification of formulas, definable sets, and (definable) classes according to the complexity of the unbounded quantifiers. ## Definition ###### Definition We define classes of formulas $\Sigma_n$, $\Pi_n$, and $\Delta_n$ by induction on $n$. • A formula is $\Sigma_0$ iff it is $\Pi_0$ iff it is $\Delta_0$, by definition if it is equivalent to a formula all of whose quantifiers are bounded, i.e. of the form $\forall x\in A$ or $\exists x\in A$. • A formula is $\Sigma_{n+1}$ if it is equivalent to one of the form $\exists \vec{x}. \phi$, where $\vec{x}$ is a list of variables and $\phi$ is $\Pi_n$. • A formula is $\Pi_{n+1}$ if it is equivalent to one of the form $\forall \vec{x}. \phi$, where $\vec{x}$ is a list of variables and $\phi$ is $\Sigma_n$. • A formula is $\Delta_n$ if it is both $\Sigma_n$ and $\Pi_n$. A class is given one of these labels if it can be defined by a formula which has that label. ###### Remark The notation “$\Sigma$” and “$\Pi$” can be explained by the fact that the existential quantifier is related to a dependent sum, while the universal quantifier is related to the dependent product. ###### Remark These definitions are most useful in classical mathematics, in which every formula is equivalent to one all of whose unbounded quantifiers are in the front, that is, a formula in prenex normal form?, so that every formula belongs to some $\Sigma_n$ or $\Pi_n$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 26, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9994100332260132, "perplexity": 167.81380824022992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301720.45/warc/CC-MAIN-20220120035934-20220120065934-00342.warc.gz"}
https://www.myopenmath.com/course/public.php?cid=8812&folder=0-10-4	## Section 4.3: Linear Equations in Standard Form Textbook Section 4.3: Linear Equations in Standard Form Textbook Section 4.3: Linear Equations in Standard Form Learning Objectives • Write equivalent equations in standard form. • Find the slope and y−intercept from an equation in standard form. • Write equations in standard form from a graph. • Solve real-world problems using linear models in standard form. Section 4.3 Videos This is the publicly accessible content from a course on MyOpenMath. There may be additional content available by logging in	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9598469138145447, "perplexity": 3553.9075807934796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891816370.72/warc/CC-MAIN-20180225110552-20180225130552-00187.warc.gz"}
http://curiouscheetah.com/BlogMath/constructing-a-tangent/	# Constructing a Tangent I was recently asked for an elegant proof of the following problem. It’s based on a construction challenge from Euclidea. Given: Circles A, B, and C, such that point C is on circle A, point B is on circles A and C, point E is on circles B and C, and point D is on all three circles. Prove: $$\overleftrightarrow{BE}$$ is tangent to circle A. In Euclidea, the challenge is to construct the tangent on circle A through point B given only those two objects. The most efficient solution is: 1. Draw a circle with center C (arbitrarily placed) on A, with B on that circle. 2. Draw a circle with center B, such that the intersection of circles A and C is on B. 3. Draw a line through the other intersection of circles B and C. This will be tangent to A at B. The challenge I was given was to create as elegant a proof as possible. I have a proof; whether it is sufficiently elegant is a matter of opinion. In addition to the circles, I have drawn three triangles. The goal is to prove that $$m\angle ABE = 90^\circ$$. Each of these triangles is isosceles; $$\Delta BCD$$ and $$\Delta BCE$$ each have two legs that are radii of circle C, while $$\Delta BAD$$ has two legs that are radii of circle A. Since they are radii of circle B, $$\overline{BE}\cong\overline{BD}$$. By SSS, $$\Delta BCD \cong \Delta BCE$$. We can now isolate the concave pentagon and examine its interior angles. I’ve labeled all congruent angles with the same Greek letters in the diagram, and will use them to complete the proof. By the Triangle Sum Theorem, we know that $$2\alpha + \beta = 2\gamma + \delta = 180^\circ$$. Inscribed angles have half the measure of central angles, and inscribed $$\angle DCB$$ corresponds to the reflex of central $$\angle DAB$$, so $$2\beta = 360^\circ – \delta$$; thus, $$\delta = 360^\circ – 2\beta$$. By substitution, $$2\gamma + 360^\circ – 2\beta = 180^\circ$$. Simplify this to $$\beta – \gamma = 90^\circ$$. Since we know $$\beta = 180^\circ – 2\alpha$$, substitute again to $$180^\circ – 2\alpha – \gamma = 90^\circ$$, that is, $$2\alpha + \gamma = 90^\circ$$. We can see that $$m\angle ABE = 2\alpha + \gamma = 90^\circ$$. Thus $$\overline{EB} \perp \overline{AB}$$, QED.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7401620149612427, "perplexity": 288.58941242369184}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572235.63/warc/CC-MAIN-20190915175150-20190915201150-00188.warc.gz"}
https://web2.0calc.com/questions/sos_12	+0 # SOS +1 135 4 int(x+4/x^2-5x+6) Guest Jun 16, 2017 Sort: #1 +4488 +2 $$\int(x+\frac4{x^2}-5x+6)\,dx \\~\\ =\int(\frac4{x^2}-4x+6)\,dx \\~\\ =\int \frac4{x^2}\,dx+\int-4x\,dx+\int6\,dx \\~\\ =4\int x^{-2}\,dx-4\int x\,dx+6\int 1\,dx$$ Combine like terms. Applying the power rule gives us... $$=4(\frac{x^{-1}}{-1})-4(\frac{x^2}{2})+6(x) +c\\~\\ =-4x^{-1}-2x^2+6x+c$$ , where c is a constant. hectictar Jun 16, 2017 #2 +18573 +1 integral( (x+4) / (x^2-5x+6) ) dx $$\begin{array}{rcl} && \int { \frac{x+4} {x^2-5x+6} \ dx} \quad & \| \quad x^2-5x+6 = (x-3)(x-2) \\ &=& \int { \frac{x+4} {(x-3)(x-2)} \ dx} \\ \end{array}$$ Partial fraction decomposition: $$\begin{array}{\|lrcll\|} \hline & \frac{x+4} {(x-3)(x-2)} &=& \frac{A}{x-3} + \frac{B}{x-2} \\ & x+4 &=& A\cdot (x-2) + B\cdot (x-3) \\ x = 2: & 2+4 &=& A\cdot (2-2) + B\cdot (2-3) \\ & 6 &=& 0 + B\cdot (-1) \\ & 6 &=& B\cdot (-1) \\ & \mathbf{B} &\mathbf{=}& \mathbf{-6} \\ \\ x = 3: & 3+4 &=& A\cdot (3-2) + B\cdot (3-3) \\ & 7 &=& A\cdot (1) + B\cdot (0) \\ & 7 &=& A\cdot (1) \\ & \mathbf{A} &\mathbf{=}& \mathbf{7} \\\\ & \mathbf{\frac{x+4} {(x-3)(x-2)}} &\mathbf{=}& \mathbf{\frac{7}{x-3} - \frac{6}{x-2}} \\ \hline \end{array}$$ $$\begin{array}{rcl} && \mathbf{ \int { \frac{x+4} {x^2-5x+6} \ dx} } \\ &=& \int { \frac{x+4} {(x-3)(x-2)} \ dx} \\ &=& \int { \Big(\frac{7}{x-3} - \frac{6}{x-2} \Big) \ dx} \\ &=& 7\cdot \int { \frac{1}{x-3} \ dx} -6\int { \frac{1}{x-2} \ dx} \\ &\mathbf{=}& \mathbf{7\cdot \ln(\|x-3\|) -6\cdot \ln(\|x-2\|) +c }\\ \end{array}$$ heureka Jun 16, 2017 edited by heureka Jun 16, 2017 #3 0 Take the integral: integral(4/x^2 - 4 x + 6) dx Integrate the sum term by term and factor out constants: = -4 integral x dx + 4 integral1/x^2 dx + 6 integral1 dx The integral of x is x^2/2: = -2 x^2 + 4 integral1/x^2 dx + 6 integral1 dx The integral of 1/x^2 is -1/x: = -4/x - 2 x^2 + 6 integral1 dx The integral of 1 is x: Answer: \| = -2 x^2 + 6 x - 4/x + constant Guest Jun 16, 2017 #4 0 Take the integral: integral(x + 4)/(x^2 - 5 x + 6) dx Rewrite the integrand (x + 4)/(x^2 - 5 x + 6) as (2 x - 5)/(2 (x^2 - 5 x + 6)) + 13/(2 (x^2 - 5 x + 6)): = integral((2 x - 5)/(2 (x^2 - 5 x + 6)) + 13/(2 (x^2 - 5 x + 6))) dx Integrate the sum term by term and factor out constants: = 1/2 integral(2 x - 5)/(x^2 - 5 x + 6) dx + 13/2 integral1/(x^2 - 5 x + 6) dx For the integrand (2 x - 5)/(x^2 - 5 x + 6), substitute u = x^2 - 5 x + 6 and du = (2 x - 5) dx: = 1/2 integral1/u du + 13/2 integral1/(x^2 - 5 x + 6) dx The integral of 1/u is log(u): = (log(u))/2 + 13/2 integral1/(x^2 - 5 x + 6) dx For the integrand 1/(x^2 - 5 x + 6), complete the square: = (log(u))/2 + 13/2 integral1/((x - 5/2)^2 - 1/4) dx For the integrand 1/((x - 5/2)^2 - 1/4), substitute s = x - 5/2 and ds = dx: = (log(u))/2 + 13/2 integral1/(s^2 - 1/4) ds Factor -1/4 from the denominator: = (log(u))/2 + 13/2 integral4/(4 s^2 - 1) ds Factor out constants: = (log(u))/2 + 26 integral1/(4 s^2 - 1) ds Factor -1 from the denominator: = (log(u))/2 - 26 integral1/(1 - 4 s^2) ds For the integrand 1/(1 - 4 s^2), substitute p = 2 s and dp = 2 ds: = (log(u))/2 - 13 integral1/(1 - p^2) dp The integral of 1/(1 - p^2) is tanh^(-1)(p): = (log(u))/2 - 13 tanh^(-1)(p) + constant Substitute back for p = 2 s: = (log(u))/2 - 13 tanh^(-1)(2 s) + constant Substitute back for s = x - 5/2: = (log(u))/2 + 13 tanh^(-1)(5 - 2 x) + constant Substitute back for u = x^2 - 5 x + 6: = 1/2 log(x^2 - 5 x + 6) + 13 tanh^(-1)(5 - 2 x) + constant Factor the answer a different way: = 1/2 (log(x^2 - 5 x + 6) + 26 tanh^(-1)(5 - 2 x)) + constant Which is equivalent for restricted x values to: Answer: \| = 7 log(3 - x) - 6 log(2 - x) + constant Guest Jun 16, 2017 ### 33 Online Users We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. 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http://toptenshoes.net/cheap-eyeglasses-frames-online/	# cheap eyeglasses frames online cheap eyeglasses frames online ,”using stacking of 24 [MATH] meter sources , were able to adjudicate A big fraction of the cib At 70 and 160 [MATH] metre . Thomas More of late , incorporated counts coming from herschel/pacs information at century and 160 [MATH] meter and resolved [MATH] and [MATH] of the cib , severally .” ,”for example , by stacking XXIV [MATH] m sources , were able to settle A large fraction of the cib atomic number 85 seventy [MATH] meter and 160 [MATH] m and increased their fractions from 45 [MATH] to L [MATH] , and from 52 [MATH] to 75 [MATH] atomic number 85 100 [MATH] metre and 160 [MATH] metre , respectively . ” , cheap eyeglasses frames online cheap eyeglasses frames online ,microscopic He was besides the first to enter fartoscopic observations of musculus fibers , bacteria , spermatozoa and blood flow in capillaries ( small blood vessels ) . He was too the first to record microscopic observations of muscle fibers , bacterium , spermatozoa and blood flow inch capillaries ( little blood vessels ) . return flatulent edits , cheap eyeglasses frames online Tags: cheap eyeglasses frames online ,cheap eyeglasses frames online	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8615183234214783, "perplexity": 18287.403152550833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039748901.87/warc/CC-MAIN-20181121133036-20181121155036-00346.warc.gz"}
http://jeancarlomachado.com.br/blog/umlcheatsheet.html	<-- home UML cheat sheet Relationships Relationships is one of the easier things to forget about UML. Association Represents the static relationship shared among the objects of two classes. Composition It’s a strong has relationship. The black arrow points to the owning side. Aggregation Is a has relationship. Aggregation uses the diamond on the container with the other side on the contained. Realization A realization relationship is the client implements or executes the behaviour of the supplier. Dependency Is a weak bound, usually when an entity uses other as a function argument or a local variable. Generalization The generalization is an inheritance relationship. The arrow points to the base class. Default Values Default values are expressed in a natural way I bet most of the developers would be intuitive about: - foo : int = 0 Constants Constants are expressed through a “convention”, all CAPITAL letters should be used. - MY_CONSTANT : int = 1 References • http://pages.cs.wisc.edu/~hasti/cs302/examples/UMLdiagram.html • https://en.wikipedia.org/wiki/Class_diagram	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45087745785713196, "perplexity": 2797.176344977698}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886117519.82/warc/CC-MAIN-20170823020201-20170823040201-00141.warc.gz"}
http://www.gamedev.net/topic/429507-finding-the-quaternion-betwee-two-vectors/?p=3856228	• Create Account Banner advertising on our site currently available from just \$5! # Finding the Quaternion Betwee Two Vectors Old topic! Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. 10 replies to this topic ### #1Mr Awesome Members - Reputation: 106 Like 0Likes Like Posted 21 December 2006 - 01:10 PM I have two 3d vectors, and I would like to find the quaternion such that v0 * q yields v1. I tried taking the cross product and the inverse cosine of the dot product and constructing a quaternion based on the axis and angle of the rotation, but the result was not even a unit quaternion. Here is the relevant code; perhaps someone can find the error or point me in the right direction. Quaternion::Quaternion(const Vector& axis, float angle) { if (abs(angle) < 1e-6) { w = 1.0; x = y = z = 0.0; return; } angle = 0.5; float sinAngle = sin(angle); w = cos(angle); x = axis.x sinAngle; y = axis.y * sinAngle; z = axis.z * sinAngle; } float Vector::dot(const Vector& vector) const { return x * vector.x + y * vector.y + z * vector.z; } Vector Vector::cross(const Vector& vector) const { return Vector(y * vector.z - z * vector.y, z * vector.x - x * vector.z, x * vector.y - y * vector.x); } Quaternion Vector::rotationTo(const Vector& vector) const { if (this == vector) return Quaternion::IDENTITY; else { Vector a = this->normalize(); Vector b = vector.normalize(); return Quaternion(a.cross(b), acos(a.dot(b))); } } ### #2Raghar Members - Reputation: 92 Like 0Likes Like Posted 21 December 2006 - 01:26 PM When I had these situations I tried to find a third vector "vc" that was able to find the second vector. So vb = va + vc ??? = (0, 1, 2) + (0, 3, 6) (0, 4, 8) = (0, 1, 2) + (0, 3, 6) Considering vc = vb - va finding vc was straightforward. Now two questions. Are both vectors normalized? Would additional normalization of elements yield the desired result? You should know I side with Diana, when someone talks about that four element monstrosity. ### #3Zipster Crossbones+ - Reputation: 1110 Like 0Likes Like Posted 21 December 2006 - 01:28 PM Your quaternion construction looks correct. Did you convert the vector v0 to a quaternion first, and are you performing the rotation using qv0conj(q)? ### #4Vorpy Members - Reputation: 869 Like 0Likes Like Posted 21 December 2006 - 01:54 PM The magnitude of a cross product of two vectors is equal to the product of the magnitudes of the vectors times the sine of the angle between them. Unless the normalized vectors were perpendicular to each other, the cross product will have a magnitude of less than one. Instead of normalizing the two vectors and then finding the cross product, you should just calculate and then normalize the cross product. Vector v = (this->cross(vector)).normalize();return Quaternion(v, acos(a.dot(b))); There are actually infinitely many rotations that will rotate the first vector to be in the direction of the second vector, but this method does find the rotation that is in some sense the shortest, and probably the one which you are thinking of. To get the longer rotations you can multiply this quaternion by one that uses the original vector as the direction of the axis, with an arbitrary angle of rotation. [Edited by - Vorpy on December 21, 2006 8:54:00 PM] ### #5Mr Awesome Members - Reputation: 106 Like 0Likes Like Posted 21 December 2006 - 02:38 PM Thanks a lot Vorpy, that solved it. ### #6scgames Members - Reputation: 2024 Like 1Likes Like Posted 21 December 2006 - 03:48 PM Quote: Original post by RagharYou should know I side with Diana, when someone talks about that four element monstrosity. IMO rejecting quaternions as unuseful (or, conversely, touting them as a panacea for all rotation-related ills) is not very well informed. Also, don't believe everything you read online about quaternions: much of it is confused, misguided, or simply incorrect. @The OP: There's actually a very nice algorithm for finding the quaternion that rotates one vector onto another that has a couple of advantages over the 'standard' method, namely that it works with vectors of arbitrary length, and that it handles uniformly (and robustly) the case where the vectors are aligned and nearly parallel. Here's the algorithm in pseudocode: quaternion q;vector3 c = cross(v1,v2);q.v = c;if ( vectors are known to be unit length ) { q.w = 1 + dot(v1,v2);} else { q.w = sqrt(v1.length_squared() v2.length_squared()) + dot(v1,v2);}q.normalize();return q; ### #7pTymN Members - Reputation: 464 Like 0Likes Like Posted 22 December 2006 - 06:49 AM Interestingly, it does not necessarily mean anything to say that you have a quaternion that rotates from one vector to another, because you are forgetting to say anything about the orienation of that new vector. Think of it like this, you have a plus sign shape of 5 points that you rotate with the generated quaternion. Is the new + oriented how you expected? There are actually an infinite number of quaternions that satisfy the constraint of rotating a vector to a new vector. There is only one quaternion that does that but also satisfies the additional constraint. Think about it in terms of rotating a coordinate frame, and it might make more sense. Sorry I couldn't explain it better. ### #8scgames Members - Reputation: 2024 Like 0Likes Like Posted 22 December 2006 - 07:10 AM Quote: Original post by pTymNInterestingly, it does not necessarily mean anything to say that you have a quaternion that rotates from one vector to another, because you are forgetting to say anything about the orienation of that new vector. Just to clarify/defend my previous post, I didn't address the non-uniqueness of the rotation since it had already been addressed by Vorpy earlier: Quote: Original post by VorpyThere are actually infinitely many rotations that will rotate the first vector to be in the direction of the second vector, but this method does find the rotation that is in some sense the shortest, and probably the one which you are thinking of. It seemed clear that the topic of the thread was the 'shortest arc' problem, so I didn't restate it in my post (although perhaps I should have). ### #9Vorpy Members - Reputation: 869 Like 0Likes Like Posted 22 December 2006 - 10:55 AM That other way of finding the quaternion is pretty neat. I spent a while just trying to prove to myself that the w coordinate comes out the same in either method. I think the best part about it is how it eliminates the trig functions, which do look almost redundant in the axis/angle method but require some tricky manipulations to eliminate. ### #10Zipster Crossbones+ - Reputation: 1110 Like 0Likes Like Posted 22 December 2006 - 11:29 AM Whoops I guess I skimmed over the code a bit too quickly [grin] But yeah, those half-angles just scream "trig identity", and since the dot product and cross product already contain trig functions you might as well find some clever way to manipulate them. ### #11scgames Members - Reputation: 2024 Like 0Likes Like Posted 22 December 2006 - 01:07 PM Quote: Original post by VorpyThat other way of finding the quaternion is pretty neat. Yeah, it's pretty slick. I originally picked it up from Martin Baker's site, here. Old topic! Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. 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https://research.tue.nl/en/publications/a-sequential-least-squares-algorithm-for-armax-dynamic-network-id	# A sequential least squares algorithm for ARMAX dynamic network identification Harm H.M. Weerts, Miguel Galrinho, Giulio Bottegal, Håkan Hjalmarsson, Paul M.J.Van den Hof Research output: Contribution to journalConference articleAcademicpeer-review ### Abstract Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets. Language English 844-849 6 IFAC-PapersOnLine 51 15 10.1016/j.ifacol.2018.09.119 Published - 1 Jan 2018 ### Fingerprint Large scale systems ### Keywords • dynamic networks • identification algorithm • least squares • System identification ### Cite this @article{2fe0037221b54321858b0b9aa01c1dd6, title = "A sequential least squares algorithm for ARMAX dynamic network identification", abstract = "Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets.", keywords = "dynamic networks, identification algorithm, least squares, System identification", author = "Weerts, {Harm H.M.} and Miguel Galrinho and Giulio Bottegal and H{\aa}kan Hjalmarsson and {den Hof}, {Paul M.J.Van}", year = "2018", month = "1", day = "1", doi = "10.1016/j.ifacol.2018.09.119", language = "English", volume = "51", pages = "844--849", journal = "IFAC-PapersOnLine", issn = "2405-8963", publisher = "Elsevier", number = "15", } A sequential least squares algorithm for ARMAX dynamic network identification. / Weerts, Harm H.M.; Galrinho, Miguel; Bottegal, Giulio; Hjalmarsson, Håkan; den Hof, Paul M.J.Van. In: IFAC-PapersOnLine, Vol. 51, No. 15, 01.01.2018, p. 844-849. Research output: Contribution to journalConference articleAcademicpeer-review TY - JOUR T1 - A sequential least squares algorithm for ARMAX dynamic network identification AU - Weerts,Harm H.M. AU - Galrinho,Miguel AU - Bottegal,Giulio AU - den Hof,Paul M.J.Van PY - 2018/1/1 Y1 - 2018/1/1 N2 - Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets. AB - Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets. KW - dynamic networks KW - identification algorithm KW - least squares KW - System identification UR - http://www.scopus.com/inward/record.url?scp=85054462289&partnerID=8YFLogxK U2 - 10.1016/j.ifacol.2018.09.119 DO - 10.1016/j.ifacol.2018.09.119 M3 - Conference article VL - 51 SP - 844 EP - 849 JO - IFAC-PapersOnLine T2 - IFAC-PapersOnLine JF - IFAC-PapersOnLine SN - 2405-8963 IS - 15 ER -	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8647774457931519, "perplexity": 2126.568964816151}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00251.warc.gz"}
http://physics.wikia.com/wiki/Hooke%27s_law	## FANDOM 150 Pages Hooke's law is a law which states that the force, F, required to bend a spring (or some other elastic object) is directly proportional to the distance X by some constant k, known as the stiffness constant. $F=kX$ This is sometimes written as $F=-kX$ In this case, F is equal to the force with which the spring pushes back. By integrating with respect to x, we can find the work needed to compress or stretch a spring a given distance and the potential energy stored in said spring. $W = E_p = \frac{1}{2} k x^2$ Hooke's law is only an approximation, as all materials will deform past a certain point (called the elastic limit). In fact, many objects deviate from Hooke's law well before their elastic limits. However, for most cases, Hooke's law is fairly accurate. ## Harmonic motionEdit If a weight is attached to a spring and the spring is stretched or compressed released, the motion can be described as $x=A \cos ( \sqrt{ \tfrac{k}{m}} t )$ where A is the amplitude, or how far the spring is stretched, k is the stiffness constant, and m is the mass of the weight. By taking the first and second derivatives, the speed and acceleration can be found. The total energy of the system is equal to $E = \frac{1}{2} k A^2$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9784033894538879, "perplexity": 228.925004961268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320264.42/warc/CC-MAIN-20170624152159-20170624172159-00466.warc.gz"}
http://mathhelpforum.com/algebra/220898-addition-fractions-2.html	# Thread: Addition with fractions 1. ## Re: Addition with fractions [QUOTE=Plato;794073]Why do you complicate this so? What a ridiculous thing to say... I made it complicated because I didn't know what I was doing, also your post doesn't help at all, you have not told me what you did the arrive at that answer. HallsOfIvy, topsquark and emakarov - Thank you for explaining. 2. ## Re: Addition with fractions uperkurk... $\displaystyle \frac{2}{5}$ is a fraction. $\displaystyle \frac{3}{x(x+2)}$ is a fraction. $\displaystyle \frac{2x^2 + 5x + 3}{x^2 - 10x + 25}$ is a fraction. Don't let the complicated terms scare you. Essentially, they're just fractions. That means they have to follow all the rules of fractions. So whatever you'd normally do with $\displaystyle \frac{2}{3} + \frac{4}{5}$, you apply the same set of rules with $\displaystyle \frac{3x}{x-2} + \frac{4}{x+3}$. 3. ## Re: Addition with fractions Originally Posted by uperkurk Originally Posted by Plato Why do you complicate this so?... What a ridiculous thing to say... I made it complicated because I didn't know what I was doing, also your post doesn't help at all, you have not told me what you did the arrive at that answer. HallsOfIvy, topsquark and emakarov - Thank you for explaining. I'm certain Plato meant no offense...he was simply demonstrating what is sometimes referred to as "cross multiplying." If you are given an equation of the form: $\displaystyle \frac{a}{b}=\frac{c}{d}$ Then, by this process, you may take as one side of the equation the product of the numerator on one side and the denominator on the other, and then then other side of the equation is the product of the other numerator-denominator pair. So, the equation above can then be written as: $\displaystyle ad=bc$ 4. ## Re: Addition with fractions Fractional quantities are a by-product of wanting number systems "complete under division (except for 0)". As a result, multiplying with fractions is EASY, but adding them is HARD. The general rule is, of course: a/b + c/d = (ad +bc)/(bd) Sometimes, that is as good as it gets...it's not always possible to "factor out common factors" (although textbook problems often feature this, misleading students into an overly optimistic view of how things will turn out). The equation: a/b = c/d is often taken by definition to MEAN: ad = bc...it's how we can tell that 1/2 is the same fraction as 2/4 (...because 14 = 22, see?). In other words "fractional expressions" aren't UNIQUE, we can always multiply top and bottom by the same thing (because a/a = 1, if a isn't 0), to get a "different-looking fraction". "Cancelling" is this process "in reverse" we are DIVIDING by a/a (and when you DIVIDE by b/c, you multiply by c/b (the reciprocal), and the reciprocal of a/a is, strangely enough, a/a again). I've always felt that too much emphasis is placed upon putting things in "simplest form". It doesn't make an answer any more or less CORRECT, it just takes up less space on a piece of paper (and it might simplify calculations if you have to USE that answer later on). Fractions are often messy, and ugly-looking beasts. It may not seem so to you, dear uperkurk, but the problems you are tasked with solving have been tailored to shield you from the full blunt force of what fractional expressions can be. 5. ## Re: Addition with fractions What you have to remember, uperkurk, is that the denominator has to be the same in all terms of the equation. It's no different from when you learned to add fractions in Arithmetic. Example: $\displaystyle \displaystyle\frac{1}{4} + 1 +\displaystyle\frac{2}{3}$ $\displaystyle \displaystyle\frac{1}{4} = \displaystyle\frac{1(3)}{4(3)} = \displaystyle\frac{3}{12}$ $\displaystyle \displaystyle\frac{2}{3} = \displaystyle\frac{2(4)}{3(4)} = \displaystyle\frac{8}{12}$ $\displaystyle 1= \displaystyle\frac{1(3)(4)}{1(3)(4)} = \displaystyle\frac{12}{12}$ $\displaystyle \displaystyle\frac{1}{4} + 1 + \displaystyle\frac{2}{3} = \displaystyle\frac{3}{12} +\displaystyle\frac{12}{12} + \displaystyle\frac{8}{12} = \displaystyle\frac{23}{12}$ You are doing the same thing when adding in algebraic equations. I believe this was explained in earlier posts, but I thought that one more example would help. Page 2 of 2 First 12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.913118302822113, "perplexity": 962.0076869049686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267860089.13/warc/CC-MAIN-20180618070542-20180618090542-00522.warc.gz"}
https://physics.stackexchange.com/questions/455085/what-is-the-principal-cause-of-diffraction	# What is the principal cause of diffraction? I have found another question similar to mine here. But I want to know why does diffraction of light happen in the first place. I have found other resources on google which explain the topic partially on the basis of Huygens principle. But I'd like to know if the phenomenon of diffraction could be explained at the atomic level in terms of photons, electrons and atoms and how they interact to create this effect? I've found this video. Is this explanation given here correct? Lastly, I'd like to know if refraction could be explained at the atomic level. Please explain in detail. Thank you very much!! • Explaining the interactions of light with matter 'in detail' would take a book. And there are a variety of books that do just fine. Explaining diffraction is easier - an infinite plane wave is not a solution to a wave propagating through inhomogeneous space. – Jon Custer Jan 18 at 15:57 • No, the video is false along with other videos of this "researcher". A good way to learn physics is by reading a good textbook, not by watching junk videos on YouTube. – safesphere Jan 18 at 16:05 • en.wikipedia.org/wiki/Huygens-Fresnel_principle – safesphere Jan 18 at 16:07 • Thank you for your valuable suggestions... Could you please refer me a good book that does a decent job job explaining this stuff?? – user8718165 Jan 18 at 17:23 So the question is, given a certain input optical field, why does it diffract the way it does? How does it work? It is simply a wave effect. There are certain special waves called plane waves that do not change while they propagate through free space apart from a change in phase. Considering propagation in a specific direction that we can call the $$z$$-direction, one finds that these plane waves pick up different phases, depending on the angle between their directions of propagation and the $$z$$-direction.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23396027088165283, "perplexity": 429.5512536322047}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998475.92/warc/CC-MAIN-20190617123027-20190617145027-00178.warc.gz"}
http://mathhelpforum.com/algebra/26114-graphing-equations.html	1. ## graphing equations... I am asked to graph this equation by plotting points; $y=-x^2+4$ So far I have used these numbers to get the value of $y$ x=0 y=4 x=1 y=5 x=2 y=8 But the problem I am having is that if I keep on, the value for $y$ gets further away from the first two points. If I use a negative number it obviously becomes a positive number.... Could I multiply the entire equation by $-1$ so that the $4$ becomes a negative? BTW, how do I create a space between the numbers so that when I post it doesn't look too awkward, or confusing??!?? 2. Originally Posted by Morzilla I am asked to graph this equation by plotting points; $y=-x^2+4$ So far I have used these numbers to get the value of $y$ x=0 y=4 x=1 y=5 x=2 y=8 But the problem I am having is that if I keep on, the value for $y$ gets further away from the first two points. If I use a negative number it obviously becomes a positive number.... Could I multiply the entire equation by $-1$ so that the $4$ becomes a negative? first off, your points are wrong. when the minus sign is outside the x^2, the answer is negative. there is a difference between $-x^2$ and $(-x)^2$. you were doing the latter, when the first is what is meant the points x = -2, -1, 0, 1, 2 are fine BTW, how do I create a space between the numbers so that when I post it doesn't look too awkward, or confusing??!?? i don't know what you're referring to 3. Originally Posted by Jhevon first off, your points are wrong. when the minus sign is outside the x^2, the answer is negative. there is a difference between $-x^2$ and $(-x)^2$. you were doing the latter, when the first is what is meant the points x = -2, -1, 0, 1, 2 are fine i don't know what you're referring to but wait, if I where to give $-x^2$ a value; $-x^2$= $-2^2$, would it not be 4, since two to the second power is four!? thanks 4. Originally Posted by Morzilla but wait, if I where to give $-x^2$ a value; $-x^2$= $-2^2$, would it not be 4, since two to the second power is four!? thanks no. the answer would be -4. the minus sign is on the outside of the square, meaning, it is not affected by the squaring. the squaring only affects the x here now let's say we had x^2, and we plug in x = -2, then we would have (-2)^2 = +4. do you see the difference? the minus sign is in the brackets, so it is affected by the square 5. Originally Posted by Jhevon no. the answer would be -4. the minus sign is on the outside of the square, meaning, it is not affected by the squaring. the squaring only affects the x here now let's say we had x^2, and we plug in x = -2, then we would have (-2)^2 = +4. do you see the difference? the minus sign is in the brackets, so it is affected by the square So ,it does not matter what number we plug in -x^2, the number will still be a negative number then? 6. Originally Posted by Morzilla So ,it does not matter what number we plug in -x^2, the number will still be a negative number then? correct, because x^2 will always be non-negative, but the minus sign in front negates it, so you end up with a non-positive number 7. ahhhhh, ok THANK YOU THANK YOU VERY MUCH!!!!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7910014986991882, "perplexity": 349.0390143499225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806455.2/warc/CC-MAIN-20171122031440-20171122051440-00338.warc.gz"}
https://www.physicsforums.com/threads/angle-of-airfoil-to-fuselage.771434/	# Angle of airfoil to fuselage? 1. Sep 17, 2014 ### WK95 For a given airfoil, the amount of lift and drag and thus the L/D ratio vary depending on it's angle towards the airflow. In general, for small aircraft with a straight wing shape (I say so because that seems to be the simplest case since the airfoil shape will be constant throughout the length of the wing), at what angle of attack is the wing attached to the rest of the plane or fuselage. Forgive me if I misused any terms or lack certain details. I'm not an aerospace engineer (yet). 2. Sep 20, 2014 ### FactChecker Similar Discussions: Angle of airfoil to fuselage?	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9044695496559143, "perplexity": 1497.854315822137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822851.65/warc/CC-MAIN-20171018085500-20171018105500-00204.warc.gz"}
https://www.mapleprimes.com/users/johan162/questions	## 4 Badges 13 years, 191 days ## Difference between latex() command and "... Maple 2021 It seem like there is an (unwanted) difference between the latex() command and the newly introduced "Copy as LaTeX" in handling of \left and \right delimiters. A trivial example >latex(sin(b/a)); \sin \! \left(\frac{b}{a}\right) but if I instead use the new "Copy as LaTeX" command I get the result \sin(\frac{b}{a}) These should of course be the same and I consider the first one to be the better conversion. It seems a very strange problem since it surely must be the same library routine that does the conversion in both cases? From a small set of examples I tried on it seem that the "Copy as .." command never uses \left and \right which in several cases is absolutely necessary to get acceptable result. ## Color of minortick gridlines?... Maple Version: Maple 2020.1 When i set the color for the gridlines it only seems to be applied for the major-tick gridlines as the following trivial example shows: plot(sin(t), t = 0 .. Pi, axes = frame, background = "#303030", color = "Orange", axis = [gridlines = [color = "#707070", linestyle = dot]]) I assume it must also be possible to also specify the color for the minor tick-marks gridlines? The obvious (?) variant "axis=[gridlines = [color = ["#707070", "#707070"] , ... " just seems to crash maple (nothing happens when the plot() expression is evaluated). I'm unable to find anything in the documentation regarding this and it only seems to imply that the color should be applied to both major & minor gridlines which is not the case. ? ## Repeatable Kernel crash using 2D-math bu... Maple 2020 (Context: As part of a EU consumer watchdog report I've been asked to re-validate a number of publically stated APR rates for various consumer loan. ) (Apologize if this should have been posted to some bug-tracker but I was unable to find such a forum.) System: MacOS 10.14.6, Maple 2020.1 Summary: Some simple exponential summations entered in 2D Input seems to crash the kernel and it is dependent on the numerical value of the exponent. The same expressions entered in 1D plaintext Maple Notation works fine. The numerically/expression evaluations are also significantly slower in 2D Input in a Document (x10) as compared to 1D Maple Notation in a Worksheet. The attached worksheet is a "killer" worksheet and will on OSX 10.14.6 + Maple 2020.1 kill the kernel connection (crash the kernel). kernel-crash.mw Example: A trivial example, entering 2D Math (assume PV & C are positive real numbers), say will cause a lost connection to the kernel after 40-50s entering the epression and the UI being busy (unclear what it is doing since no real calculation is performed) which I assume is a sign that the kernel crashed. It seems to dependent on the exponent in the divisor. So for example the following variation will not crash the kernel Doing the exact same calculation with a worksheet in old plain maple notation both varianta are both significantly faster in the numerical operation (solving for 'r') and assigning 'eq2' and never crashes (regardless of numerical value of exponent). The workaround is of course obvious but it would be nice if this bug could be adressed. It seems that whenever I try to give the 2D-UI a chance (since it is actally easier to visually view complex expressions) something always comes back and bites me... Update: The crash is only repeatable with the "sum()" command and not the "add()" command. Page 1 of 1	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9475623369216919, "perplexity": 2412.264506406961}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570692.22/warc/CC-MAIN-20220807181008-20220807211008-00540.warc.gz"}
https://www.airbestpractices.com/system-assessments/air-treatmentn2/heat-compression-major-energy-recovery-opportunity-often-ignored	Industrial Utility Efficiency # Heat of Compression: A Major Energy Recovery Opportunity Often Ignored Often when you mention heat of compression the first thought generally relates to HOC desiccant dryers, which are also an under-applied opportunity for heat recovery. However, there are many other heat of compression recoverable energy savings opportunities in all compressed air and gas systems. This article reviews many opportunities in energy heat recovery and provides answer to commonly asked questions, such as: ### Heat of Compression 101 Heat of compression reflects the basic inefficiency of compressed air or gas with regard to energy used to compress it compared to work energy actually delivered. For example: in a 100 psig-class (seven bar) air system, the air compressor uses about eight horsepower (hp) to deliver one hp worth of work. This concept is also true for other gases and at other pressures with variable answers. The 100 psig-class air compressed air is the largest sector in many commercial industrial, construction and other markets worldwide. These values may vary under different atmospheric operating conditions and will also be very site specific. A discussion about heat of compression requires a look at the basic law of energy. It says that energy can neither be created nor destroyed. Therefore, energy input to compression not used in final work energy will be converted to heat within the system. This heat is expressed in Btu/hours. As an example, if work energy used by the process is one hp = 2,546 Btu/hr., for example, then the total power input to produce the eight hp leaves a total of seven hp not used in process work – or seven hp x 2,546 Btu/hour = 17, 522 Btu/hour of heat left in the compressed air cooling system. (Note: Power over time = energy. In electrical terms, kW is power and kWh is energy.) Heat of compression comes from the unused energy at the process – heat that is left in the air system is usually referred to as “free” because it is a by-product of compressed air or gas and is covered by the cost of operating the air compressor. If you don’t take advantage of this heat source (which is free) you will not only lose the available energy but may have to cool the air compressor system using more energy to avoid other issues. Recovered heat will offer the plant another heat source and the opportunity taken may well reduce plant operating energy costs. ### Recovering Heat of Compression As stated, all air or gas compressor generate heat of compression in the air compressor. Depending on the work used, the stored heat of compression in the system is around 15,276 to 17,822 Btu/hr. Within the plant there may be areas where a current heating application can be reduced or shut off utilizing the available heat of compression. Looking at a typical air system, a reasonable target to recover the available heat of compression within the system would be 85 to 95 percent of the total motor horsepower input from the heated cooling air, water or other coolant used. For example: • Cooling water from a water-cooled air compressor and aftercooler etc. – probable discharge temperature of around 130 °F. • Cooling air from air compressor coolers and air-cooled aftercooler etc. – probable temperatures 5 °F to 20 °F above ambient. • Coolant (oil) from various injected lubricating cooling rotaries (screw, vane etc.) 150 °F to 190 °F before the aftercooler. Air compressors can be lubricated or non-lubricated. Non-lubricated units such as centrifugals, reciprocating, rotary screw, etc. operate hotter than lubricated machines. ### Potential Value of Heat of Compression by Capacity (scfm) Class This table displays the approximate potential values of recoverable heat of compression based on full load compressed air delivered in Btu’s/hr. including probable transport losses. Capacity (scfm) 100 psig (7 bar) Approximate Btu/Hr. Capacity (scfm) 100 psig (7 bar) Approximate Btu/Hr. 250 scfm 150,308 1,000 scfm 572,400 350 scfm 208,500 1,200 scfm 694,700 500 scfm 287,700 1,500 scfm 920,000 800 scfm 463,100 2,000 scfm 1,237,000 Here’s an example calculation of potential savings for one compressed air system. Let’s assume it has a capacity of 2,000 scfm at 100 psig and operates 6,240 hours annually. Also assume one kW equals 3,414 Btu/hr. A system with a capacity of 2,000 scfm at 100 psig equates to 1,237,000 approximate Btu/hr. To calculate the savings, divide 1,237,000 Btu/hr. by 3,414 Btu/hr, which equals 362 kW. An expected maximum recovery rate of about 94% equates to an estimated 339 kW. The maximum recoverable power is 339 kW (energy kWh). The savings based on 339 kW and a blended electric rate of \$.07 kWh equals a savings of \$148,075 year. ### Using Heated Cooling Oil from a Lubricated Screw Air Compressor Hot cooling oil (190 °F to 200 °F) or cooling water (130 °F) can be used to reheat saturated or high relative humidity compressed air to lower the relative humidity in the pipe. In some applications, this will not only eliminate outside pipe sweating, but also, under proper operating conditions, deliver hot, dry air to the process. This hot air contains more usable energy because the heat raises the pressure with less air volume required and the water vapor is still in the form of a usable gas if it does not cool below the pressure dewpoint (when the vapor then falls out as water). This has been very popular in sawmill plants where the hot discharge oil from lubricant-cooled rotary screw air compressors (150 °F to 200 °F) is routed to another heat exchanger and heats the discharge after-cooled air from the heated oil and delivers lower Relative Humidity (RH) and hotter air to the compressed air system. The reheater also pre-cools the heated lubricant, which reduces the heat load on the cooling system. The effect of operating at high air temperatures, which increases pressure, is illustrated in Figure 2. ##### Figure 2. As shown, raising the temperatures of the discharge air after the compressed air leaves the air compressor within the pipe it will raise the pressure without additional compressed air until it cools, i.e., more pressure with no increase in input energy to the air compressors. In this example, air from compressor discharge is 170 °F at 100 psig, air to the dryer is less than 100 °F at 100 psig, air from dryer is 70°F at 95 psig, and air from the reheater is 120 °F at 104 psig. The result is a 9% increase in delivered energy with no increase in input energy to the air compressors! Important to note is the effect of Charles’ Law on energy savings on heated confined discharge air. According to Charles’ Law, “At constant pressure, the volume of an ideal gas varies directly as the absolute temperature.” Absolute temperate is °F + 460 Rankine (oR)where °R is a constant utilized for these calculations. °FR is also presented as absolute °F. Charles’ Law states that in a confined volume stored gas will increase in volume or pressure directly proportional to the rise in temperature. In the example, the airline being reheated started at 70 °F at 95 psig. Adding the 460 °R value to the °F makes the absolute F value 520 °R. When the reheater was operating it changed to 580 °R with a 9% increase in pressure from 95 to 104 psig with no change in energy input to the air compressor. ### Finding Common Types of Cooling in Air Compressor Rooms Many common types of cooling can be located in an air compressor room, you just need to know where to look. • Air-cooled air compressors: Heat of compression trapped in the air to air heat exchanger and cooling system. Heat is available in the cooling airflows and will discharge cooling air from 5 °F to 20 °F above the inlet cooling air. To be effective, this cooling air may need thermostatic type controls. • Water-cooled air compressors: Heat recovery energy savings and projects are often easier to implement with the heat being well trapped in a controlled water flow. Regardless of the type of air compressors, the maximum expected heated discharge cooling water temperature is about 130 °F post aftercooler or higher taken before the aftercooler. • Oil-injected/lubricant-cooled rotary vanes, screws and scrolls etc.: The injected cooling lubricant at about 150 °F is atomized into the compression chamber absorbing the heat of compression while it is being generated. This generally holds the discharge temperature to about 190 °F to 200 °F maximum or 165 °F to 185 °F minimum when taken before the aftercooler. ### Lower Overall Energy Costs with Heat of Compression Heat of compression in air or gas compressors reflects the basic inefficiency of the compression process with regard to energy input to the compressors to actual energy utilized in a given process. In the case of compressed air at 100 psig discharge pressure the nominal relationship is 8 hp into the air compressor to produce one hp of delivered energy or work. Any input energy not used in the process comes “off” as heat of compression. These numbers will vary by inlet conditions, discharge temperatures etc. Heat of compression is considered free because the cost of the input energy is covered in the cost of producing compressed air or gas. But if you don’t recover the energy in some form of heat recovery, then there is no energy reduction. Keep in mind all of the heat of compression you’re able to use in other processes will lower the overall energy cost to generate air or gas.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4930805265903473, "perplexity": 2694.501644719851}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00365.warc.gz"}
http://math.ustc.edu.cn/new/bencandy.php?fid=34&aid=2723	ËÑË÷£º ¡¡ Ñ§Ôº¸Å¿ö ÐÂÎÅÖÐÐÄ Ñ§Êõ½»Á÷ Ñ§Éú¹¤×÷ ±¾¿ÆÉúÕÐÉú Í¨Öª¹«¸æ ×ÊÔ´ÖÐÐÄ Ñ§Êõ±¨¸æ ÑÐ¾¿ÉúÕÐÉú ½ÌÓýÅàÑø ¡¡µ±Ç°Î»ÖÃ£º>Ê×Ò³ -> Í¨Öª¹«¸æ 2017ÄêÇàÄêÊýÑ§ÂÛÌ³ »áÒéÊ±¼ä£º2017Äê4ÔÂ15ÈÕ-17ÈÕ 4ÔÂ14ÈÕÈ«Ìì±¨µ½£¬4ÔÂ17ÈÕÀë»á »áÒéµØµã£ºÊýÑ§¿ÆÑ§Ñ§Ôº1518¶àÃ½Ìå½ÌÊÒ ×¡ËÞÐÅÏ¢£ººÏ·ÊÌì¶ìºþ´ó¾Æµê£¬ºÏ·ÊÊÐÕþÎñÐÂÇø¶«Á÷Â·888ºÅ¡£ ½»Í¨ÐÅÏ¢£º4ÔÂ15ÈÕÔç8£º00ÔÚ¾ÆµêÃÅ¿ÚÉÏ³µ¼¯ÌåÇ°Íù¿Æ´ó¶«ÇøÊýÑ§Ñ§Ôº£»ÏÂÎç5£º30ÔÚÊýÑ§Ñ§ÔºÂ¥ÏÂ¼¯ºÏÉÏ³µ£¬¼¯Ìå·µ»Ø¾Æµê¡£ »áÒé±¨¸æ 4ÔÂ15ÈÕ ÖÜÁù 8£º30-8£º40 ¿ªÄ»Ê½ 8£º40-9£º40 ±¨¸æÌâÄ¿£º Harmonic mappings for bounded distortion shape deformation and interpolation ±¨¸æÈË£º ³ÂÈÊ½Ü µÂ¹úÂí¿ËË¹ÆÕÀÊ¿Ë¼ÆËã»úÑÐ¾¿Ëù ±¨¸æÕªÒª£º Harmonic mappings are extensively used in geometry processing applications to produce visually appealing deformations. We establish the sufficient and necessary conditions for a harmonic planar mapping to have bounded distortion. Our key observation is that these conditions relate solely to the boundary behavior of the mapping. This leads to an efficient and accurate algorithm that supports handle-based interactive shape-and-image deformation and is demonstrated to outperform other state-of-the-art methods. The particular structure of harmonic mappings further allows efficient shape interpolation. Given the closed-form expressions for the interpolants, our interpolation algorithm runs embarrassingly in parallel and is orders of magnitude faster than state-of-the-art methods due to its simplicity, yet it produces mappings that are superior to those existing techniques due to guaranteed bounds on geometric distortions. 9£º50-10£º50 ±¨¸æÌâÄ¿£º Weak approximation for 0-cycles on products of varieties ±¨¸æÈË£º ÁºÓÀì÷ °ÍÀèÆß´ó ±¨¸æÕªÒª£º We consider the sequence for smooth projective varieties over number fields. Its exactness is conjectured by Colliot-Th¡äen`ene{Sansuc and Kato{Saito, it means roughly that the Brauer{Manin obstruction is the only obstruction to weak approximation for 0-cycles. We work on the compatibility of the exactness for products of varieties. Assume that (E) is exact for a rationally connected variety X (after all finite extensions of the base field). One may ask the question : For which family of varieties Y the sequence (E) is exact for X ¡Á Y ? When Y is a smooth projective curve with the finiteness of the Tate{Shafarevich group of its jacobian assumed, Harpaz and Wittenberg give a positive answer to the question (for much more general fibrations rather than only for products). We will talk about the case where Y is a smooth compactification of a homogeneous space. 11£º00-12£º00 ±¨¸æÌâÄ¿£º The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties ±¨¸æÈË£º ÁõÓÀÇ¿ KU Leuven ±¨¸æÕªÒª£º Given any connected topological space X, assume that there exists an epimorphism from the fundamental group of X to the free ableian group Z. The deck transformation group Z acts on the associated infinite cyclic cover of X, hence on the homology group of the covering space with complex coefficients. This action induces a linear automorphism on the torsion part of the homology group as a module over the complex Laurent polynomial ring, which is a finite dimensional complex vector space. We study the sizes of the Jordan blocks of this linear automorphism. When X is a compact K\"ahler manifold, we show that all the Jordan blocks are of size one. When X is a smooth complex quasi-projective variety, we give an upper bound on the sizes of the Jordan blocks, which is an analogue of the Monodromy Theorem for the local Milnor fibration. This is a joint work with Nero Budur and Botong Wang. 12£º00-14£º00 Lunch & break 14:00-15:00 ±¨¸æÌâÄ¿£º Boundary $C^{1,\alpha}$ regularity of Potential functions in Optimal transportation ±¨¸æÈË£º ³ÂÊÀ±þ °ÄÖÞ¹úÁ¢´óÑ§ ±¨¸æÕªÒª£º We provide a different proof for the global $C^{1,\alpha}$ regularity of potential functions in optimal transport problem, which was originally proved by Caffarelli. Moreover, our method applies to a more general class of domains. This is based on a joint work with Elina Andriyanova. 15£º10-16£º10 ±¨¸æÌâÄ¿£º Scaling Limits of Critical Inhomogeneous Random Graphs ±¨¸æÈË£º Minmin Wang Institut Henri-Poincar¨¦ and University of Bath ±¨¸æÕªÒª£º Branching processes are known to be useful tools in the study of random graphs, in particular in understanding the appearance of a phase transition in the sizes of the largest clusters of the graphs. Recently, growing interests are paid to inhomogeneous random graphs. In this talk, we look at one particular model of such graphs, called the Poisson random graph, where edges are formed with probabilities proportional to some prescribes weights on the vertices. One challenge in the study of inhomogeneous random graphs is to describe the geometry of the graphs around the critical point. In the case of Poisson random graph, we obtain a simple representation of the graph using Galton-Watson trees (genealogy trees of branching processes). Relying on this representation and previous works of Duquesne & Le Gall on the convergence of Galton-Watson trees, we prove that in the critical window, the scaling limits of the largest components of the Poisson random graphs are a collection of almost-tree-like compact metric spaces, which can be constructed explicitly from the so-called Levy processes without replacement. Based on a joint work with Nicolas Broutin and Thomas Duquesne. 16£º20-17£º20 ±¨¸æÌâÄ¿£º Computing with functions ±¨¸æÈË£º Kuan Xu, University of Kent ±¨¸æÕªÒª£º In very recent years, the idea of computing with functions has been sparkled by the endeavor of the Chebfun project. Polynomial approximations of functions enables functional operations and operators of all kinds to be numerically approximated using fast, accurate, and robust algorithms based on these approximations, giving people the feel of symbolic computing but with the lightning speed of numerical computation. The idea of computing with functions has also extended to the solution of differential and integral equations. In this talk, the core idea of computing with functions and the underlying mathematics of Chebfun project will be discussed with the aid of hands-on-keyboard demos. 17£º30- Dinner 4ÔÂ16ÈÕ ÖÜÈÕÈ«Ìì »áºóÌÖÂÛ Ö÷°ìµ¥Î»£ºÊýÑ§¿ÆÑ§Ñ§Ôº ÖÐ¹ú¿ÆÑ§¼¼Êõ´óÑ§ ¡¡ \|	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8860976099967957, "perplexity": 624.4882545921505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121000.17/warc/CC-MAIN-20170423031201-00424-ip-10-145-167-34.ec2.internal.warc.gz"}
https://bird.bcamath.org/handle/20.500.11824/20/browse?type=subject&value=Variational+formulation	Now showing items 1-1 of 1 • #### A multilayer method for the hydrostatic Navier-Stokes equations: A particular weak solution (Journal of Scientific Computing, 2014-12-31) In this work we present a multilayer approach to the solution of non-stationary 3D Navier-Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal ...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9693530201911926, "perplexity": 1163.5224042876266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578529813.23/warc/CC-MAIN-20190420120902-20190420142902-00405.warc.gz"}
http://www.24totalbodyplan.nl/product/e0cf1f4711813.html	• TEL: 0086-13083697781 sparse feature selection based on l2 1 2 Get Price We can supply you need sparse feature selection based on l2 1 2. Name:* Email:* Phone:* Message:* You need CiteSeerX Citation Query Feature selection, l1 vs. l2 L1 regularization is effective for feature selection, but the resulting optimization is challenging due to the non-differentiability of the 1-norm. In this paper we compare state-of-the-art optimization techniques to solve this problem across several loss functions. Conducting sparse feature selection on arbitrarily long Conducting sparse feature selection on arbitrarily long phrases in text corpora with a focus on interpretability L2 normalization 1 Introduction to phrases. On the other hand, one regression-based method [3, 4] that does allow for longer Efficient Feature Selection via --norm Constrained Sparse Abstract:Sparse regression based feature selection method has been extensively investigated these years. However, because it has a non-convex constraint, i.e., $\ell _{2,0}$2,0-norm constraint, this problem is very hard to solve. In this paper, unlike most of the other methods which only solve its slack version by introducing sparsity regularization into objective function forcibly, a Efficient and Robust Feature Selection via Joint 2,1 The 2;1-norm based loss function is robust to outliers in data points and the 2;1-norm regularization selects features across all data points with joint sparsity. An efcient algorithm is introduced with proved convergence. Our regression based objective makes the feature selection process more efcient. Our method has been Exact Top-k Feature Selection via L2,0-Norm Constraint2 Sparse Learning Based Feature Selection Background Typically, many sparse based supervised binary feature selec-tion methods that arise in data mining and machine learning can be written as the approximation or relaxed version of the following problem:<w;b>= min w;b jjy XTw b1jj2 2 s:t:jjwjj 0 = k (1) where y 2Bn1 is the binary label, X2Rdn Exact top-k feature selection via l2,0-norm constraint In this paper, we propose a novel robust and pragmatic feature selection approach. Unlike those sparse learning based feature selection methods which tackle the approximate problem by imposing sparsity regularization in the objective function, the proposed method only has one l 2,1-norm loss term with an explicit l 2,0-Norm equality constraint.An efficient algorithm based on augmented Multiclass sparse logistic regression on 20newgroups A more traditional (and possibly better) way to predict on a sparse subset of input features would be to use univariate feature selection followed by a traditional (l2-penalised) logistic regression model. Out:Dataset 20newsgroup, train_samples=9000, n_features=130107, n_classes=20 [model=One versus Rest, solver=saga] Number of epochs:1 On the Adversarial Robustness of LASSO Based Feature We demonstrate that this method can be extended to other 1 based feature selection methods, such as group LASSO and sparse group LASSO. Numerical examples with synthetic and real data illustrate that our method is efcient and effective. Index TermsLinear regression, feature selection, LASSO, adversarial machine learning, bi-level Python:module skfeature.function.sparse_learning_based parameter in the objective function of UDFS (default is 1) n_clusters:{int} Number of clusters k:{int} number of nearest neighbor verbose:{boolean} True if want to display the objective function value, false if not Output-----W:{numpy array}, shape(n_features, n_clusters) feature weight matrix Reference Yang, Yi et al. "l2,1-Norm Selecting good features Part II:linear models and For L2 however, the first models penalty is $$1^2 + 1^2 = 2\alpha$$, while for the second model is penalized with $$2^2 + 0^2 = 4 \alpha$$. The effect of this is that models are much more stable (coefficients do not fluctuate on small data changes as is the case with unregularized or L1 models). Selecting good features Part II:linear models and For L2 however, the first models penalty is $$1^2 + 1^2 = 2\alpha$$, while for the second model is penalized with $$2^2 + 0^2 = 4 \alpha$$. The effect of this is that models are much more stable (coefficients do not fluctuate on small data changes as is the case with unregularized or L1 models). Sparse Feature Learning - ResearchGate This goal is achieved in terms of L2,1 norm of matrix, generating a sparse learning model for feature selection. The model for multiclass classification and its extension for feature selection are Sparse feature selection based on graph Laplacian for web In this paper we propose a novel sparse feature selection framework for web image annotation, namely sparse Feature Selection based on Graph Laplacian (FSLG)2. FSLG applies the l2,1/2-matrix norm The L2,1-norm-based unsupervised optimal feature selection Specifically, an L2,1-norm-based sparse representation model is constructed as an initial prototype of the proposed method. Then a projection matrix with L2,1-norm regularization is introduced into the model for subspace learning and jointly sparse feature extraction and selection. classification - Feature selection for very sparse data I have a dataset of dimension 3,000 x 24,000 (approximately) with 6 class label. But the data is very sparse. The number of non-zero values per sample ranges from 10-300 (approx) out of 24,000. The non-zero values in the dataset are real numbers. I need to perform feature selection/reduction before the Sparse feature selection in multi-target modeling of A sparse feature selection method is proposed for multi-target modeling of CA isoforms. The proposed method exploits the shared information among multiple targets. The proposed method uses the mixed l2,p-norm (0 < p 1) minimization on both regularization and loss function. Get Price We can supply you need sparse feature selection based on l2 1 2. Name:* Email:* Phone:* Message:* You need	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4839458465576172, "perplexity": 1675.614578366046}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154032.75/warc/CC-MAIN-20210730220317-20210731010317-00157.warc.gz"}
https://admin.clutchprep.com/chemistry/practice-problems/75009/32p-is-a-radioactive-isotope-with-a-half-life-of-14-3-days-if-you-currently-have	Chemistry Practice Problems Identifying Reaction Order Practice Problems Solution: 32P is a radioactive isotope with a half-life of 1... 🤓 Based on our data, we think this question is relevant for Professor Zimmer De Iuliis' class at TORONTO. # Solution: 32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 45.9 g of 32P, how much 32P (grams) was present 2.00 days ago? ###### Problem 32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 45.9 g of 32P, how much 32P (grams) was present 2.00 days ago? View Complete Written Solution Identifying Reaction Order Identifying Reaction Order #### Q. The decomposition of hydrogen peroxide was studied, and the following data were obtained at a particular temperature:Assuming thatRate = - Δ [H2O2] / ... Solved • Tue Oct 30 2018 18:42:13 GMT-0400 (EDT) Identifying Reaction Order #### Q. The rate law for the rearrangement of CH3NC to CH3CN at 800 K is Rate = (1300 s-1) [CH3NC]. What is the half-life for this reaction? a. 1.9 x 10-3 s b... Solved • Wed Aug 01 2018 13:24:00 GMT-0400 (EDT) Identifying Reaction Order #### Q. Barium-122 has a half-life of 2 minutes. You just obtained a sample weighing 10.0 grams. If takes 10 minutes to set up the experiment in which barium-... Solved • Mon Jul 30 2018 17:36:35 GMT-0400 (EDT) Identifying Reaction Order #### Q. A fossil is found to have a 14C level of 77.0% compared to living organisms. How old is the fossil in years? Solved • Thu May 31 2018 13:31:02 GMT-0400 (EDT)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8602070808410645, "perplexity": 5199.7003273171795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371637684.76/warc/CC-MAIN-20200406133533-20200406164033-00515.warc.gz"}
https://www.zbmath.org/?q=an%3A1006.76008	× # zbMATH — the first resource for mathematics Transport and instability for perfect fluids. (English) Zbl 1006.76008 Summary: Incompressible perfect fluids are described by Euler equations. We provide a new proof of well-posedness for velocities in $$C^{1,\alpha}$$, and give linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of $$C^{1,\alpha}$$ is too fine for interesting questions about large time behavior. ##### MSC: 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 76E30 Nonlinear effects in hydrodynamic stability 35Q30 Navier-Stokes equations Full Text:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.409894734621048, "perplexity": 1462.840491830266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991812.46/warc/CC-MAIN-20210515004936-20210515034936-00141.warc.gz"}
https://xianblog.wordpress.com/	## best unbiased estimator of θ² for a Poisson model Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , on May 23, 2018 by xi'an A mostly traditional question on X validated about the “best” [minimum variance] unbiased estimator of θ² from a Poisson P(θ) sample leads to the Rao-Blackwell solution $\mathbb{E}[X_1X_2\|\underbrace{\sum_{i=1}^n X_i}_S=s] = -\frac{s}{n^2}+\frac{s^2}{n^2}=\frac{s(s-1)}{n^2}$ and a similar estimator could be constructed for θ³, θ⁴, … With the interesting limitation that this procedure stops at the power equal to the number of observations (minus one?). But, since the expectation of a power of the sufficient statistics S [with distribution P(nθ)] is a polynomial in θ, there is de facto no limitation. More interestingly, there is no unbiased estimator of negative powers of θ in this context, while this neat comparison on Wikipedia (borrowed from the great book of counter-examples by Romano and Siegel, 1986, selling for a mere \$180 on amazon!) shows why looking for an unbiased estimator of exp(-θ) is particularly foolish: the only solution is -1 to the power S. (There is however a way to circumvent the difficulty if having access to an arbitrary number of generations from the Poisson, since the Forsythe – von Neuman algorithm allows for an unbiased estimation of exp(-F(x)).) Posted in pictures, University life with tags , , , on May 22, 2018 by xi'an Today, two statisticians (and good friends of mine) from Australia, Noel Cressie and Kerrie Mengersen, got elected at the Australian Academy of Sciences. Congratulations to them! ## yes, another potential satellite to ISBA 2018! Posted in Statistics with tags , , , , , , , , , , on May 22, 2018 by xi'an On July 2-4, 2018, there will be an ISBA sponsored workshop on Bayesian non-parametrics for signal and image processing, in Bordeaux, France. This is a wee bit further than Warwick (BAYsm) or Rennes (MCqMC), but still manageable from Edinburgh with direct flights (if on Ryanair). Deadline for free (yes, free!) registration is May 31. ## PhD studentships in AI and Data Science, at the University of Warwick Posted in Statistics with tags , , , , , on May 21, 2018 by xi'an A (rather urgent) call for candidates for PhD studentships in AI and Data Science at Warwick. These are part of Warwick’s MRC-Funded Doctoral Training Program in Interdisciplinary Biomedical Research. Selected students would start in Autumn 2018. The deadline is on June 3. ## Monica di Sardegna [Perdera] Posted in Statistics with tags , , , , , on May 20, 2018 by xi'an ## Warwick locks [jatp] Posted in pictures, Running, Travel with tags , , , , , , , , , , , on May 20, 2018 by xi'an ## miei primi cannoli Posted in Kids, pictures, Travel, Wines with tags , , , , , , on May 19, 2018 by xi'an Cannoli are among my favourite pastries and one of the first things I try to eat while in Italy (if never in Sicily)… (Or in Boston!) Especially since they cannot travel. Hence, when my wife brought me cannoli baking tubs from Venezia, I took the hint and did not wait many days to make a first attempt at baking my own cannoli. Preparing the dough takes a little while, although it does not much differ from a rich shortcrust pastry (with a wee bit of Sicilian sweet wine). But baking the tubes is not that complicated, thanks to the tubes, and they remain crusty for several days, while mastering the ricotta cheese filling will require many attempts before reaching the right consistency… The more attempts the better!!!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6900271773338318, "perplexity": 2510.030069836585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865450.42/warc/CC-MAIN-20180523043959-20180523063959-00129.warc.gz"}
http://www.fractalforums.com/theory/3d-mandelbrot-formula-based-on-rotation-away-from-azimuthal-axis/msg9722/	## The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out! Pages: [1] Go Down Author Topic: 3D Mandelbrot Formula based on Rotation Away from Azimuthal Axis (Read 7134 times) Description: 3D Mandelbrot Formula based on Rotation Away from Azimuthal Axis 0 Members and 1 Guest are viewing this topic. bugman Conqueror Posts: 122 « on: December 09, 2009, 11:18:24 PM » The rotational matrix form of Mandelbulb triplex power formula goes as follows: {x, y, z}^n = Rz(ntheta)Ry(-nphi){r^n, 0, 0} where r = sqrt(x²+y²+z²), theta = atan2(y, x), phi = asin(z/r) This formula actually does already apply the azimuthal angle (phi) rotation away from the azimuthal axis (z-axis). However, last week I got confused and I thought that I had to sandwich the y-axis rotation between an un-rotate / re-rotate pair of transformations. Hence the following formula: Azimuthal Mandelbrot.jpg (165.81 KB, 610x981 - viewed 1237 times.) « Last Edit: December 12, 2009, 08:48:23 PM by bugman » Logged kram1032 Fractal Senior Posts: 1863 « Reply #1 on: December 09, 2009, 11:28:55 PM » very nice Mandelbrot Logged Paolo Bonzini Guest « Reply #2 on: December 10, 2009, 12:01:27 AM » That means that the phi rotation is done around the [cos theta, sin theta,0] axis instead of the y axis, right? Logged cbuchner1 Fractal Phenom Posts: 443 « Reply #3 on: December 10, 2009, 12:15:47 AM » Looks like a hairybrot or furrybrot to me! Logged David Makin Global Moderator Fractal Senior Posts: 2286 « Reply #4 on: December 10, 2009, 01:22:06 AM » It seems odd to me that the original Mandelbulb triplex power formula applies the azimuthal angle's rotation about the y-axis. Suppose instead we rotate away from the azimuthal axis. We can do this by sandwiching the y-axis rotation between an un-rotate / re-rotate pair of transformations. Hi Paul, are the trig and non-trig exactly what you are using for the renders ? I tried rendering te z^2+c and my implimentation of the trig and non-trig versions match but I don't get a result that looks much like your renders - so I assumed you're using solid at given iteration rather than on given DE threshold and set my DE threshold to 0 and maxiter to 12 but the result is still not much like yours. Any ideas ? Logged The meaning and purpose of life is to give life purpose and meaning. http://www.fractalgallery.co.uk/ "Makin' Magic Music" on Jango bugman Conqueror Posts: 122 « Reply #5 on: December 10, 2009, 01:29:28 AM » Hi Paul, are the trig and non-trig exactly what you are using for the renders ? I tried rendering te z^2+c and my implimentation of the trig and non-trig versions match but I don't get a result that looks much like your renders - so I assumed you're using solid at given iteration rather than on given DE threshold and set my DE threshold to 0 and maxiter to 12 but the result is still not much like yours. Any ideas ? I am not using distance estimation (I never did get that to work for me). I don't know why your renders look different but feel free to post them if you think they are interesting. Logged David Makin Global Moderator Fractal Senior Posts: 2286 « Reply #6 on: December 10, 2009, 02:00:36 AM » Here's what get for z^2+c, solid at 12 iterations: And z^8+c, also solid at 12: They were both rendered small, just at the uploaded sizes and 12 iterations is really overkill for that resolution The z^2+c used the (unoptimised) non-trig version and took around 2.5 mins, the z^8+c used the trig version which means it was a bit slow at 8.5 mins (Times on my rather slow P4HT). Logged The meaning and purpose of life is to give life purpose and meaning. http://www.fractalgallery.co.uk/ "Makin' Magic Music" on Jango David Makin Global Moderator Fractal Senior Posts: 2286 « Reply #7 on: December 10, 2009, 02:30:33 AM » Part of the z^8 caught my eye so I couldn't resist zooming in. In doing so I discovered a problem with my formula with respect to getting the normals when the DE threshold is zero and solid is based solely on iteration depth so I had to switch to using maxiter 400, DE thrreshold 1e-4. This image is at zoom 98.4, the full view was 3.5 Though it's a little "whipped cream"ish, it's the most interesting whipped cream I've seen so far on a Mandelbulb style fractal I will definitely be doing a quality render of this. Logged The meaning and purpose of life is to give life purpose and meaning. http://www.fractalgallery.co.uk/ "Makin' Magic Music" on Jango Paolo Bonzini Guest « Reply #8 on: December 10, 2009, 07:02:18 AM » Actually the phi rotation is applied about [sin(theta), -cos(theta), 0] instead of the y-axis (or [-sin(theta), cos(theta), 0] if you are rendering the latter version). Since you're rotating Ry(phi) first and Rz(theta) second, wouldn't it make more sense to do the second rotation around "wherever the first rotation brought the z axis"? That is in quaternion form: $rot1 = e^{j\ \phi/2}$ $rot2 = e^{(rot1\ k\ rot1^{-1})\ \theta/2} [tex]rot = rot2 * rot1$ (where the divisions by two are only to accomodate quaternion math, i.e. $e^{v\phi/2}$ is actually a rotation by $\phi$, and e^{v\alpha} is $cos \alpha + v sin \alpha$). Logged bugman Conqueror Posts: 122 « Reply #9 on: December 10, 2009, 07:11:25 AM » I don't really understand your quaternion notation. Could you express your proposed formula in terms of {x, y, z}? Logged Paolo Bonzini Guest « Reply #10 on: December 10, 2009, 07:59:31 AM » Nevermind, I tried the simplification myself with Maxima and I get exactly your "consistent algebra"! Which kind of explains where it comes from, giving another explanation besides just reversing the phi rotation. Basically, you are rotating first around the y axis. Now, the z axis also moved as an effect of this rotation. The second rotation is done around this "turned" z axis instead of the original axis. Logged David Makin Global Moderator Fractal Senior Posts: 2286 « Reply #11 on: December 22, 2009, 06:34:49 PM » Had another play and got this "Flowerhead" from the same Mandy as "Theme Park Ride" (z^8+c): If no image above then look here: Logged The meaning and purpose of life is to give life purpose and meaning. http://www.fractalgallery.co.uk/ "Makin' Magic Music" on Jango mrrgu Guest « Reply #12 on: January 01, 2010, 04:40:40 PM » Hi I am trying to implement this, what formula do you use for the derivative (for DE) ? The rotational matrix form of Mandelbulb triplex power formula goes as follows: {x, y, z}^n = Rz(ntheta)Ry(-nphi){r^n, 0, 0} where r = sqrt(x²+y²+z²), theta = atan2(y, x), phi = asin(z/r) This formula actually does already apply the azimuthal angle (phi) rotation away from the azimuthal axis (z-axis). However, last week I got confused and I thought that I had to sandwich the y-axis rotation between an un-rotate / re-rotate pair of transformations. Hence the following formula: Logged David Makin Global Moderator Fractal Senior Posts: 2286 « Reply #13 on: January 01, 2010, 05:03:26 PM » Hi I am trying to implement this, what formula do you use for the derivative (for DE) ? I used my delta DE method rather than analytical DE, see: http://www.fractalforums.com/mandelbulb-implementation/mandelbulb-ray-tracing-plugin-for-photoshop-aftereffects-and-quartzcomposer/msg10178/#msg10178 Logged The meaning and purpose of life is to give life purpose and meaning. http://www.fractalgallery.co.uk/ "Makin' Magic Music" on Jango mrrgu Guest « Reply #14 on: January 02, 2010, 06:31:13 PM » Thank you. Your method looked to complicated for the GPU many branches etc..so I tried to write one with some intervall halving method... but so far my results are crap I wonder if anyone has tested to get the derivative with some kind of difference ? Like this: . . Z1 = Z0^2 +C Z2 = Z1^2 +C Z3 = Z2^2 +C . . And then derivatives.. DY/DX style like... (Z2-Z1)/(Z1-Z0), (Z3-Z2)/(Z2-Z1)... etc. Or is this the wrong derivative? I mean not with respect to C ? Hi I am trying to implement this, what formula do you use for the derivative (for DE) ? I used my delta DE method rather than analytical DE, see: http://www.fractalforums.com/mandelbulb-implementation/mandelbulb-ray-tracing-plugin-for-photoshop-aftereffects-and-quartzcomposer/msg10178/#msg10178 Logged Pages: [1] Go Down	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 5, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48434755206108093, "perplexity": 5151.406691553042}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946564.73/warc/CC-MAIN-20180424041828-20180424061828-00174.warc.gz"}
https://askdev.io/questions/555/the-absolutely-no-part-of-tensor-items-of-rated-mods	# The absolutely no part of tensor items of rated mods I assure there is a very easy reference on this, but also for some factor I can not locate it. If you can aim me to a reference or simply write a brief evidence for me, I would certainly be really satisfied. Offered a rated ring $R_{\bullet}$ and also a localization $R_{\bullet}^{}$. We additionally have actually a rated $R_{\bullet}$-mod, $M_{\bullet}$. So what I need to know; is $\left(R_{\bullet}^{}\otimes M_{\bullet}\right)_0=\left(R_{\bullet}^{*}\right)_0\otimes \left(M_{\bullet}\right)_0$? 0 2019-05-04 16:21:47 Source Share Answers: 1 For a counterexample, take $R=k[t]$ with its common grading and also $M=R(1)$, the free component of ranking one created in level $1$. 0 2019-05-08 01:49:44 Source	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8512611985206604, "perplexity": 1140.916860265418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057039.7/warc/CC-MAIN-20210920131052-20210920161052-00701.warc.gz"}
http://riotorto.users.sourceforge.net/Maxima/descriptive/pca/index.html	# Principal Components Analysis ## The data File wind.data contains daily average wind speeds at 5 meteorological stations in the Republic of Ireland (This is part of a data set taken at 12 meteorological stations. The original file was downloaded from the StatLib Data Repository and its analysis is discused in Haslett, J., Raftery, A. E. (1989) Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource, with Discussion. Applied Statistics 38, 1-50. To run these examples, you must load package descriptive and the data: load("descriptive")$s2 : read_matrix (file_search ("wind.data"))$ Before reducing the dimensionality, we need to know the true dimension of the multivariate variable, p: length(first(s2)); $5$ Sample size, n: length(s2); $100$ Let's calculate the multivariate mean, mean(s2); $\left[ 9.948 , 10.16 , 10.87 , 15.72 , 14.84 \right]$ The variances, var(s2); $\left[ 17.22 , 14.99 , 15.48 , 32.18 , 24.42 \right]$ Since data are of similar nature and scale, we don't need to standardize them. The multivariate scatter plot to see if variables are correlated. set_draw_defaults( xlabel = "", ylabel = "")$scatterplot( s2, nclasses = 5, fill_color = blue, fill_density = 0.3, color = red, point_size = 1/2, dimensions = [850,750], xtics = 5)$ There seems to be linear correlation among all variables, so we can calculate the correlation matrix, cor(s2); $\pmatrix{1.0&0.8476&0.8804&0.824&0.752\cr 0.8476&1.0&0.8736&0.6903& 0.7825\cr 0.8804&0.8736&1.0&0.7764&0.8323\cr 0.824&0.6903&0.7764&1.0 &0.7294\cr 0.752&0.7825&0.8323&0.7294&1.0\cr }$ ## The model In order to see if we can reduce the dimensionality of this sample, we calculate the principal components, pc: principal_components(s2); $\left[ \left[ 87.57 , 8.753 , 5.515 , 1.889 , 1.613 \right] , \left[ 83.13 , 8.31 , 5.235 , 1.793 , 1.531 \right] , \\ \pmatrix{ 0.4149&0.03379&-0.4757&-0.581&-0.5126\cr 0.369&-0.3657&-0.4298& 0.7237&-0.1469\cr 0.3959&-0.2178&-0.2181&-0.2749&0.8201\cr 0.5548& 0.7744&0.1857&0.2319&0.06498\cr 0.4765&-0.4669&0.712&-0.09605&- 0.1969\cr } \right]$ The returned list contains three elements, the first of them is a list with the variances of the principal components in descending order. We see that the first variance is much greater than the second one: first(pc); $\left[ 87.57 , 8.753 , 5.515 , 1.889 , 1.613 \right]$ The second element is the list with percentages of total variation explained by each principal component: second(pc); $\left[ 83.13 , 8.31 , 5.235 , 1.793 , 1.531 \right]$ We can accumulate percentages to help to decide how many variables we are going to take for further analysis. We see that with the two first principal componentes we explain about 91.44% of total variance: block([ap: copy(pc[2])], for k:2 thru length(ap) do ap[k]: ap[k]+ap[k-1], ap); $\left[ 83.13 , 91.44 , 96.68 , 98.47 , 100.0 \right]$ We can also plot a Pareto chart showing the percentages graphically: draw2d( fill_density = 0.2, apply(bars, makelist([k, pc[2][k], 1/2], k, p)), points_joined = true, point_type = filled_circle, point_size = 2, points(makelist([k, pc[2][k]], k, p)), xlabel = "Variances", ylabel = "Percentages", xtics = setify(makelist([concat("PC",k),k], k, p))) $ Finally, the last element returned by function principal_components is the rotation matrix: rot: third(pc); $\pmatrix{0.4149&0.03379&-0.4757&-0.581&-0.5126\cr 0.369&-0.3657&- 0.4298&0.7237&-0.1469\cr 0.3959&-0.2178&-0.2181&-0.2749&0.8201\cr 0.5548&0.7744&0.1857&0.2319&0.06498\cr 0.4765&-0.4669&0.712&-0.09605 &-0.1969\cr }$ These are the coefficients we need to calculate the p principal components $Y_1, Y_2, Y_3, \ldots, Yp$ from the original variables $X_1, X_2, X_3, \ldots, Xp.$ If the observed data corresponding to one metheorological station is the vector $(x_1, x_2, x_3, x_4, x_5),$ the first principal component is calculated this way: matrix([x1, x2, x3, x4, x5]) . col(rot,1); $0.4765\,{\it x_5}+0.5548\,{\it x_4}+0.3959\,{\it x_3}+0.369\, {\it x_2}+0.4149\,{\it x_1}$ ... the second matrix([x1, x2, x3, x4, x5]) . col(rot,2); $-0.4669\,{\it x_5}+0.7744\,{\it x_4}-0.2178\,{\it x_3}-0.3657\, {\it x_2}+0.03379\,{\it x_1}$ ... and so on. In general, the transformed multivariate sample is calculated this way: new: s2 . rot$ And if we want to use the first two components, we remove the last three columns from the transformed sample: new2: submatrix(new, 3,4,5); $\pmatrix{30.66&0.9512\cr 27.93&1.78\cr 22.64&-0.567\cr 13.44&-4.203 \cr 23.64&-1.542\cr 18.23&-3.966\cr 24.12&0.1813\cr 27.78&-0.2169 \cr 25.23&-1.561\cr 20.34&-3.698\cr 28.55&4.444\cr 29.73&-1.084\cr 8.702&-0.7874\cr 8.754&2.462\cr 14.22&-0.04463\cr 21.12&1.576\cr 28.8&-0.469\cr 30.19&-10.2\cr 10.48&0.4667\cr 11.37&0.1515\cr 19.18& -4.55\cr 18.99&0.08038\cr 32.9&-4.489\cr 44.54&-2.166\cr 27.14&- 2.229\cr 43.18&-5.436\cr 49.67&-3.064\cr 33.06&0.8554\cr 50.74&- 0.9644\cr 32.28&-0.2534\cr 24.75&-2.612\cr 14.98&-0.08559\cr 18.81& 1.342\cr 16.99&-0.3552\cr 28.55&0.4827\cr 34.3&0.8969\cr 45.56& 0.7853\cr 30.51&-3.537\cr 42.18&0.6286\cr 39.6&0.9222\cr 32.79&- 0.9442\cr 39.74&-1.838\cr 37.8&5.232\cr 42.83&4.742\cr 30.05&-2.859 \cr 24.46&3.398\cr 39.77&-1.495\cr 34.39&-1.734\cr 29.94&2.494\cr 40.82&6.545\cr 25.03&0.6239\cr 17.42&3.25\cr 27.6&-0.2265\cr 42.01&- 0.1073\cr 16.71&-0.5108\cr 30.1&-0.8958\cr 45.95&-3.996\cr 32.98& 0.9275\cr 33.2&0.4342\cr 32.0&3.716\cr 30.16&1.459\cr 35.01&4.616 \cr 19.65&1.3\cr 26.0&-3.86\cr 14.44&2.485\cr 21.26&4.471\cr 27.66& 1.426\cr 31.58&-1.637\cr 23.97&-2.048\cr 36.51&3.325\cr 40.06&-3.581 \cr 33.96&-0.7837\cr 30.13&3.338\cr 33.26&4.878\cr 23.83&6.641\cr 38.61&1.058\cr 36.82&-3.485\cr 20.68&-0.9488\cr 32.66&-6.451\cr 22.35&-4.885\cr 19.41&-4.469\cr 27.15&-1.928\cr 27.42&-1.599\cr 37.65&-0.6065\cr 34.42&-6.523\cr 17.13&-5.456\cr 31.67&-0.5124\cr 36.0&-2.487\cr 31.92&-1.82\cr 23.97&-2.088\cr 20.15&0.6859\cr 19.49& -1.63\cr 18.92&0.6379\cr 23.3&1.388\cr 26.37&1.804\cr 19.06&-0.8494 \cr 12.86&-0.1988\cr 22.46&-1.34\cr 24.96&-5.134\cr 15.1&-2.422\cr }$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8520335555076599, "perplexity": 4531.464460200841}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170249.75/warc/CC-MAIN-20170219104610-00168-ip-10-171-10-108.ec2.internal.warc.gz"}
http://export.arxiv.org/abs/1908.08205	math.NA (what is this?) # Title: An Extended Galerkin Analysis for Elliptic Problems Abstract: A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For second order elliptic equation, this framework employs $4$ different discretization variables, $u_h, \bm{p}_h, \check u_h$ and $\check p_h$, where $u_h$ and $\bm{p}_h$ are for approximation of $u$ and $\bm{p}=-\alpha \nabla u$ inside each element, and $\check u_h$ and $\check p_h$ are for approximation of residual of $u$ and $\bm{p} \cdot \bm{n}$ on the boundary of each element. The resulting 4-field discretization is proved to satisfy inf-sup conditions that are uniform with respect to all discretization and penalization parameters. As a result, most existing finite element and discontinuous Galerkin methods can be analyzed using this general framework by making appropriate choices of discretization spaces and penalization parameters. Subjects: Numerical Analysis (math.NA) MSC classes: 65N30 Cite as: arXiv:1908.08205 [math.NA] (or arXiv:1908.08205v2 [math.NA] for this version) ## Submission history From: Qingguo Hong [view email] [v1] Thu, 22 Aug 2019 05:24:44 GMT (25kb) [v2] Sat, 30 Nov 2019 03:36:33 GMT (25kb) Link back to: arXiv, form interface, contact.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4775923788547516, "perplexity": 1288.623717810443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00028.warc.gz"}
https://plainmath.net/90439/summing-odd-fractions-to-one-from-the-li	# Summing Odd Fractions to One From the list 1/3,1/5,1/7,1/9,1/11..... is it possible to chose a limited number of terms that sum to one? This can be done with even fractions: 1/2,1/4,1/8,1/12,1/24 Summing Odd Fractions to One From the list $\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9},\frac{1}{11}$..... is it possible to chose a limited number of terms that sum to one? This can be done with even fractions: $\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{12},\frac{1}{24}$ You can still ask an expert for help • Questions are typically answered in as fast as 30 minutes Solve your problem for the price of one coffee • Math expert for every subject • Pay only if we can solve it Caiden Li Such a representation of a fraction as the sum of fractions with numerator 1 and different denominators is called Egyption fraction, because that was the way fractions were written in ancient Egypt. It's clear that for 1, we must have an odd number of summands, because otherwise the numerator of the sum would be even and the denominator odd. As it turns out, the minimal number is 9, and there are the following 5 solutions: $\begin{array}{rl}1& =\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{15}+\frac{1}{35}+\frac{1}{45}+\frac{1}{231}\\ 1& =\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{15}+\frac{1}{21}+\frac{1}{231}+\frac{1}{315}\\ 1& =\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{15}+\frac{1}{33}+\frac{1}{45}+\frac{1}{385}\\ 1& =\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{15}+\frac{1}{21}+\frac{1}{165}+\frac{1}{693}\\ 1& =\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\frac{1}{15}+\frac{1}{21}+\frac{1}{135}+\frac{1}{10395}\end{array}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 26, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9604037404060364, "perplexity": 433.2758053387965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337421.33/warc/CC-MAIN-20221003133425-20221003163425-00308.warc.gz"}
https://wiki.cimec.unitn.it/tiki-index.php?page=Frequency-domain+analysis	# Frequency-domain analysis Following Fourier ideas, EEG signals can be represented in the time domain (when recording the brain activity from scalp EEG surface electrodes) or alternatively in the frequency domain (when decomposing time-domain signals into weighted sums of sine and cosine functions). In the frequency-domain analysis (but also in the time-frequency domain analysis), EEG signals are represented in terms of oscillatory components, each of which is believed to isolate the activity of localized neuronal populations. To describe any oscillatory component, we estimate its amplitude and phase. The amplitude refers to the magnitude of an oscillation and can be measured in units of signal amplitude (µV), in power (µV2) or in decibel units (20log10(µV) or 10log10(µV2)). The phase refers to the position of a point in time on a waveform cycle and is commonly measured in degrees or radians. The Fourier Transform is usually employed to represent a signal in the frequency-domain. Especially after the introduction of the Fast Fourier Transform (a very fast and efficient algorithm to calculate the Fourier Transform), the Fourier Transform has become one of the most used tools in different scientific disciplines. Let us consider a digital signal x[n], n = 0,…,N-1, which has been obtained from a continuous signal x(t) by sampling at equal time intervals Δt (i.e., with a sampling frequency fs = 1/Δt). The discrete Fourier Transform is given by the following formula: The signal x[n] can be reconstructed with the inverse discrete Fourier Transform: The Fourier coefficients X[k] are complex numbers that can be represented both in Cartesian and polar forms. where XR and XI denote the real and imaginary parts in the Cartesian representation, whereas \|X[k]\| and φ denote the amplitude and phase in the polar representation. If we restrict our attention only to signal power, from the complex Fourier coefficients we can compute the periodogram as: where X[k] denotes the complex conjugation of X[k]. The periodogram is a raw estimation of the power spectrum of the signal, provided that the signal is stationary (i.e., the main characteristics of the signal, such as its mean and variance do not change over time). To illustrate why the periodogram is a raw estimate of the power spectrum, let us consider the following example. ##### Figure 4.1: Spectral leakage The sinusoid on the left panel of Figure 4.1 has an exact number of cycles in the 2 s period of the signal. Its corresponding periodogram (on the left bottom side) shows a single peak at 3 Hz. On the other hand, the sinusoid on the right has a non-integer number of cycles and its periodogram shows an activity that is spread between 2 and 5 Hz. This phenomenon, consisting of smearing the power spectrum estimation, is called leakage (for further details, see Oppenheim and Schaffer, 1999). A simple way to avoid leakage would be to take an integer number of cycles. However, in general it is not possible to define a single periodicity because real signals contain activity at multiple frequencies. A useful approach for reducing the leakage effects is to use an appropriate window function that tapers the borders of the signal. This approach is referred to as a ‘windowing’. Several window functions have been proposed and their advantages and disadvantages depend on the specific application. Among the most popular window functions are the Hanning, Hamming, Barlett and Blackman. Another reason why the periodogram is a raw estimate of the power spectrum is the following. Because the variance of the periodogram does not go to zero, even in the limit of an infinite sample size, the periodogram is not a statistically consistent estimate of the power spectrum. For large sample sizes, moreover, the periodogram tends to vary rapidly with frequency, and the resulting power spectrum tends to look like a random pattern. To obtain a smoother estimate of the power spectrum, Barlett (1953) proposed to divide the signal into segments, to calculate the periodogram for each segment, and then to average the periodograms. Later on, Welch (1967) showed that better estimates can be achieved by using half-overlapping segments. The number of segments to be used for averaging the periodograms depends on the specific application. Ideally, it should be more than 30. As regards the length of the segments, it is noteworthy to point out that the larger the segments, the better the frequency resolution (the frequency resolution Δf is defined by the formula Δf = 1 / (NΔt), where N is the number of data points and Δt is the time resolution; note that NΔt is the duration of the signal). However, it is advisable to use segments that are not too long, so that the signal can be considered stationary to a first approximation. Now we will upload the dataset that we employed to illustrate the preprocessing steps, and we will estimate the power spectrum using the Welch method (click here to download all datasets). ```%% Initializations dataPath = 'C:\Users\CIMeC\Desktop\wikiDatasets\'; % It depends on where % the wikiDatasets % folder is stored fileName = 'S01RestPreprocessed.set'; dataSet = fullfile(dataPath,fileName);``` ###### ↑ Go up ```%% Defining trials (or epochs) % Reading the data as one long continuous segment cfg = []; cfg.dataset = dataSet; % file path data = ft_preprocessing(cfg); % Segmenting the data into trials cfg = []; cfg.length = 2; % seconds cfg.overlap = 0.5; % value between 0 and 1 (percent) dataSeg = ft_redefinetrial(cfg,data); % Reading the events from the data % Removing trials containing discontinuities trialsToReject = zeros(length(dataSeg.sampleinfo),1); for eventId = 1:length(event) if isempty(event(eventId).type) tmpSample = event(eventId).sample; for sampleInfoId = 1:length(dataSeg.sampleinfo) if (tmpSample - dataSeg.sampleinfo(sampleInfoId,1)) * ... (tmpSample - dataSeg.sampleinfo(sampleInfoId,2)) < 0 trialsToReject(sampleInfoId) = sampleInfoId; end end end end trialsToReject = trialsToReject(trialsToReject ~= 0); trialsToKeep = 1:length(dataSeg.sampleinfo); % initialize vector with all % trial indices trialsToKeep(trialsToReject) = []; % create trial indices to keep cfg = []; cfg.trials = trialsToKeep; dataSeg = ft_selectdata(cfg,dataSeg);``` ###### ↑ Go up ```%% Frequency-domain analysis % Computing power spectrum for each trial cfg = []; cfg.foilim = [0 45]; cfg.method = 'mtmfft'; cfg.taper = 'hanning'; cfg.keeptrials = 'yes'; cfg.channel = {'all' '-AFp9' '-AFp10'}; % all but ocular channels freq = ft_freqanalysis(cfg,dataSeg); % Computing the average over trials cfg = []; %cfg.keeptrials = 'yes'; freqAvg = ft_freqdescriptives(cfg,freq);``` ###### ↑ Go up ```%% Plot PSD freqAvg.powSpctrmDB = 10log10(freqAvg.powspctrm); % convert to % decibel (dB) figure; plot(freqAvg.freq,freqAvg.powSpctrmDB') set(gca,'ylim',[-30 15]) xlabel('Frequency (Hz)') ylabel('Power spectral density (dB/Hz)') % Defining channel layout templateLayout = 'EEG1005.lay'; % one of the template layouts % included in FieldTrip cfg = []; cfg.layout = which(templateLayout); layout = ft_prepare_layout(cfg); % Increasing layout width and height if strcmp(templateLayout,'EEG1005.lay') layout.width = 0.07 ones(length(layout.width),1); layout.height = 0.04 * ones(length(layout.height),1); end % Topographic plot cfg = []; cfg.xlim = [8 12]; % alpha band cfg.zlim = [-13 -1]; cfg.parameter = 'powSpctrmDB'; cfg.marker = 'off'; cfg.highlight = 'off'; cfg.comment = 'auto'; cfg.layout = layout; cfg.colorbar = 'yes'; % or 'southoutside' cfg.colormap = jet; figure; ft_topoplotER(cfg,freqAvg); c = colorbar; c.LineWidth = 1; c.FontSize = 14; title(c,'dB')``` ###### ↑ Go up Analogously to the ft_timelockgrandaverage function, the ft_freqgrandaverage allows computing the grand average spectra, including all individual subjects’ spectrum as an input argument. Differences in spectral power between conditions can be statistically tested using the function ft_freqstatistic. The configuration structure remains largely the same, as compared to the statistical evaluation of time-domain data described above. Again, we can use the function ft_topoplotER to show the outcome of the statistical comparisons (see the previous section). #### References • Oppenheim, A., & Schaffer, R. (1999). Discrete-time signal processing. Prentice Hall, London. • Barlett, M.S. (1953). An introduction to stochastic processes with special reference to methods and applications. Cambridge University Press, MA. • Welch, P.D. (1967). The use of Fast Fourier Transform for the estimation of power spectra: a method based on time-averaging over short modified periodograms. IEEE Trans Audio-Electroacust, 15, 70-73. ###### ↑ Go up Created by daniele.patoner. Last Modification: Monday 11 of March, 2019 13:12:34 CET by tommaso.mastropasqua. ### Tiki Assistant Thank you for installing Tiki!	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9524655342102051, "perplexity": 663.9305957009115}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060241-00552.warc.gz"}
http://www.thestudentroom.co.uk/showthread.php?t=2009419&p=37710120	You are Here: Home # CCEA Weber Definition Tweet Physics and electronics discussion, revision, exam and homework help. Announcements Posted on Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 20-05-2013 IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013 1. CCEA Weber Definition Does anybody know how the Weber is defined for CCEA A2 Physics? The spec says we need to know it but I can't find it anywhere in my notes. 2. Re: CCEA Weber Definition It should be defined the same way as anywhere else, I would hope "The weber is the magnetic flux which induces an emf of one volt in a coil of one turn when the flux is reduced uniformly to zero in one second." (Or some similar equivalent wording expressing the same idea. It's based on Faraday's Law.) 3. Re: CCEA Weber Definition (Original post by Stonebridge) It should be defined the same way as anywhere else, I would hope "The weber is the magnetic flux which induces an emf of one volt in a coil of one turn when the flux is reduced uniformly to zero in one second." (Or some similar equivalent wording expressing the same idea. It's based on Faraday's Law.) Thanks 4. Re: CCEA Weber Definition For OCR anyway - the weber is based on the definition of magnetic flux. 1 Weber is the magnetic flux when there is a magnetic flux density of 1 Tesla perpendicular to a coil of area 1 m^2. ie 1Wb = 1T x 1m^2. (of course this comes to the same thing given the definitions of the Tesla and the Volt) Last edited by teachercol; 23-05-2012 at 09:42.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9103463292121887, "perplexity": 2844.9194724183603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705097259/warc/CC-MAIN-20130516115137-00006-ip-10-60-113-184.ec2.internal.warc.gz"}
https://de.maplesoft.com/support/help/maple/view.aspx?path=GraphTheory%2FIsForest	GraphTheory - Maple Programming Help Home : Support : Online Help : Mathematics : Discrete Mathematics : Graph Theory : GraphTheory Package : GraphTheory/IsForest GraphTheory IsForest Calling Sequence IsForest(G) Parameters G - graph Description • The IsForest command returns true if the input graph is a forest or false otherwise. A forest is a graph whose connected components are all trees. Examples > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$ > $F≔\mathrm{Graph}\left(\left[1,2,3,4,5,6\right],\left\{\left\{1,2\right\},\left\{2,3\right\},\left\{5,6\right\}\right\}\right)$ ${F}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 6 vertices and 3 edge\left(s\right)}}$ (1) > $\mathrm{IsForest}\left(F\right)$ ${\mathrm{true}}$ (2) > $C≔\mathrm{ConnectedComponents}\left(F\right)$ ${C}{≔}\left[\left[{1}{,}{2}{,}{3}\right]{,}\left[{4}\right]{,}\left[{5}{,}{6}\right]\right]$ (3) > $\mathrm{seq}\left(\mathrm{IsTree}\left(\mathrm{InducedSubgraph}\left(F,i\right)\right),i=C\right)$ ${\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}$ (4) > $\mathrm{NumberOfVertices}\left(F\right)-\mathrm{NumberOfEdges}\left(F\right)-\mathrm{nops}\left(\mathrm{ConnectedComponents}\left(F\right)\right)$ ${0}$ (5)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9019916653633118, "perplexity": 2746.6942880718366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00411.warc.gz"}
http://mathhelpforum.com/statistics/2015-question.html	Math Help - Question 1. Question A car dealer has 8 Red, 11 Gray, and 9 Blue cars in stock Ten cars are randomly chosen to be displayed in from of the dealership. Find the probability that 4 are red and 6 are blue; 3 are red, 3 are blue and 4 are gray; 5 are gray and non are blue; all 10 are gray. 2. Originally Posted by batman123 A car dealer has 8 Red, 11 Gray, and 9 Blue cars in stock Ten cars are randomly chosen to be displayed in from of the dealership. Find the probability that 4 are red and 6 are blue; 3 are red, 3 are blue and 4 are gray; 5 are gray and non are blue; all 10 are gray. Remember that probability is favorable outcomes divided by possible outcomes. 1)4 Red and 6 Blue: There are 8 red he is chosing 4 thus there are $_8C_4=70$ different ways. There are 9 blue he is chosing 6 thus there are $_9C_6=_9C_3=84$ different ways. Thus there are a complete total of $70\times 84=5880$ ways of chosing these types of cars. This is the favorable outcomes, now we find the possible outcomes. There are $28$ cars altogether and he is taking 10, thus there are $_{28}C_{10}=13123110$ different ways. Thus the probability is the ratio thus, $p=\frac{5880}{13123110}$. Everything else is solved similarly.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9570194482803345, "perplexity": 483.3525586807966}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500832538.99/warc/CC-MAIN-20140820021352-00063-ip-10-180-136-8.ec2.internal.warc.gz"}
https://ask.sagemath.org/question/44302/conversion-from-symbolic-expression-to-polynomial-stuck/?answer=44305	# Conversion from symbolic expression to polynomial stuck edit I have a very long symbolic expression with six variables: (E_mu, E_xi3, ISP, T, V_mu, V_xi3, Z, m, mu, n_I, n_P, xi_1, xi_3) I call the expression AN. I want to convert it in a polynomial of two variables (mu and xi_3). I tried the following command: AP = AN.polynomial(None,ring=SR['mu,xi_3']) This works for simple expressions but the command remains stuck for the given expression. My aim is to get the monomials of the polynomial. mu and xi_3 are random variables and I want to compute the expectation of AN (E[AN]). Thus, I could substitute the expectations in the expression. AN is a numerator, so it is not a fraction. Moreover, I also tried simply_rational but it did not help to convert. Is there anyway to convert easily ? EDIT : https://framabin.org/p/?2417942055fc9fc9#Oenpb+BI567QXYcVCzjO4zkLRC0byQaNdhi2XW/CUkY= (I put the symbolic expression in a framabin.) edit retag close merge delete 1 Could you please provide the (construction of the) symbolic expression ? ( 2018-11-16 13:03:20 +0200 )edit https://framabin.org/p/?2417942055fc9fc9#Oenpb+BI567QXYcVCzjO4zkLRC0byQaNdhi2XW/CUkY= (I added a framabin where you can read the symbolic expression.) ( 2018-11-16 13:57:30 +0200 )edit Sort by » oldest newest most voted Since the whole expression is a polynomial with rational coefficients, the following works: sage: R = PolynomialRing(PolynomialRing(QQ, names='E_mu, E_xi3, ISP, T, V_mu, V_xi3, Z, m, n_I, n_P, xi_1'), names='mu, xi_3') sage: map(SR, R(AN).monomials()) [mu^2, muxi_3, mu, xi_3, 1] sage: map(SR, R(AN).coefficients()) [T^2m^6 + 4T^2m^5n_I + 4T^2m^4n_I^2 + 2T^2m^5n_P + 6T^2m^4n_In_P + 4T^2m^3n_I^2n_P + T^2m^4n_P^2 + 2T^2m^3n_In_P^2 + T^2m^2n_I^2n_P^2 + 2TV_mum^4n_I + 2TV_xi3m^4n_I + 4TV_mum^3n_I^2 + 4TV_xi3m^3n_I^2 + ... For expressions involving fractions you would want to replace the inner PolynomialRing by wrapping it in FractionField(...), like this: sage: R = PolynomialRing(FractionField(PolynomialRing(QQ, names='E_mu, E_xi3, ISP, T, V_mu, V_xi3, Z, m, n_I, n_P, xi_1')), names='mu, xi_3') more https://doc.sagemath.org/html/en/reference/rings/sage/rings/fraction_field_element.html (I found the page about the Fraction Field Elements.) AN is my numerator and AD is my denominator of my symbolic expression A. There is not the values of interest (mu and xi_3) in the denominator AD. How should I wrap the whole in the Fraction Field ? BTW, thank you very much :) ( 2018-11-16 15:08:42 +0200 )edit I added the precise instruction to my answer. You should then be able to do R(A) etc. The coefficients of the polynomial R(A) will then be Fraction Field Elements. You're welcome :) ( 2018-11-16 16:18:09 +0200 )edit	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6405125260353088, "perplexity": 6174.83087047733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00565.warc.gz"}
http://repozitorij.upr.si/Iskanje.php?type=napredno&stl0=KljucneBesede&niz0=mathematics&lang=eng	# Search the repository Query: search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing Work type: All work types Habilitation (m4) Specialist thesis (m3) High school thesis (m6) Bachelor work * (dip) Master disertations * (mag) Doctorate disertations * (dok) Research Data or Corpuses (data) * old and bolonia study programme Language: All languagesSlovenianEnglishGermanCroatianSerbianBosnianBulgarianCzechFinnishFrenchGerman (Austria)HungarianItalianJapaneseLithuanianNorwegianPolishRussianSerbian (cyrillic)SlovakSpanishSwedishTurkishUnknown Search in: RUP FAMNIT - Faculty of Mathematics, Science and Information Technologies FHŠ - Faculty of Humanities FM - Faculty of Management FTŠ Turistica - Turistica – College of Tourism Portorož FVZ - Faculty of Health Sciences IAM - Andrej Marušič Institute PEF - Faculty of Education UPR - University of PrimorskaCOBISS Fakulteta za humanistične študije, Koper Fakulteta za management Koper in Pedagoška fakulteta Koper Fakulteta za vede o zdravju, Izola Knjižnica za tehniko, medicino in naravoslovje, Koper Turistica, Portorož Znanstveno-raziskovalno središče Koper Options: Show only hits with full text Reset 1 - 10 / 391234 1.On bipartite Q-polynomial distance-regular graphs with c [sub] 2 [equal] 1Štefko Miklavič, 2007, original scientific articleAbstract: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫-polynomial distance-regular graph with diameter ▫$d \ge 3$▫, valency ▫$k \ge 3$▫ and intersection number ▫$c_2=1$▫. We show that ▫$\Gamma$▫ has a certain equitable partition of its vertex set which involves ▫$4d-4$▫ cells. We use this partition to show that the intersection numbers of ▫$\Gamma$▫ satisfy the following divisibility conditions: (I) ▫$c_{i+1}-1$▫ divides ▫$c_i(c_i-1)$▫ for ▫$2 \le i \le d-1$▫, and (II) ▫$b_{i-1}-1$▫ divides ▫$b_i(b_i-1)$▫ for ▫$1 \le i \le d-1$▫. Using these divisibility conditions we show that ▫$\Gamma$▫ does not exist if ▫$d=4$▫.Found in: ključnih besedahSummary of found: ...mathematics, grah theory, distance-regular graphs, ▫$Q$▫-polynomial property, equitable... Keywords: mathematics, grah theory, distance-regular graphs, ▫$Q$▫-polynomial property, equitable partitionsPublished: 15.10.2013; Views: 1779; Downloads: 15 Full text (0,00 KB) 2.Isomorphism checking of I-graphsBoris Horvat, Tomaž Pisanski, Arjana Žitnik, 2012, original scientific articleAbstract: We consider the class of ▫$I$▫-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two ▫$I$▫-graphs ▫$I(n, j, k)$▫ and ▫$I(n, j_1, k_1)$▫ are isomorphic if and only if there exists an integer ▫$a$▫ relatively prime to $n$ such that either ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n \}$▫ or ▫$\{j_1, k_1\} = \{aj \mod n, \; -ak \mod n\}$▫. This result has an application in the enumeration of non-isomorphic ▫$I$▫-graphs and unit-distance representations of generalized Petersen graphs.Found in: ključnih besedahSummary of found: ...mathematics, graph theory, isomorphism, I-graph, generalized Petersen graph... Keywords: mathematics, graph theory, isomorphism, I-graph, generalized Petersen graphPublished: 15.10.2013; Views: 1574; Downloads: 73 Full text (0,00 KB) 3.Rank-permutable additive mappingsAnna A. Alieva, Aleksandr Èmilevič Guterman, Bojan Kuzma, 2006, original scientific articleAbstract: Let ▫$\sigma$▫ be a fixed non-identical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.Found in: ključnih besedahSummary of found: ...mathematics, linearna algebra, matrix algebra, rank, permutation, additive... Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preserversPublished: 15.10.2013; Views: 1423; Downloads: 51 Full text (0,00 KB) 4.Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, original scientific articleAbstract: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫.Found in: ključnih besedahSummary of found: ...mathematics, algebra, polynomial identity, generalized skew derivation, prime... Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ringPublished: 15.10.2013; Views: 1714; Downloads: 77 Full text (0,00 KB) 5.Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0Štefko Miklavič, 2008, original scientific articleAbstract: Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫-module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D-2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫.Found in: ključnih besedahSummary of found: ...mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger... Keywords: mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebraPublished: 15.10.2013; Views: 1513; Downloads: 9 Full text (0,00 KB) 6.On quartic half-arc-transitive metacirculantsDragan Marušič, Primož Šparl, 2008, original scientific articleAbstract: Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫, where ▫$\rho$▫ is ▫$(m,n)$▫-semiregular for some integers ▫$m \ge 1$▫, ▫$n \ge 2▫$, and where ▫$\sigma$▫ normalizes ▫$\rho$▫, cyclically permuting the orbits of ▫$\rho$▫ in such a way that ▫$\sigma^m$▫ has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed.Found in: ključnih besedahSummary of found: ...mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly... Keywords: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism groupPublished: 15.10.2013; Views: 1705; Downloads: 63 Full text (0,00 KB) 7.Consistent Cycles in 1/2-Arc-Transitive GraphsMarko Boben, Štefko Miklavič, Primož Potočnik, 2009, original scientific articleFound in: ključnih besedahSummary of found: ...mathematics, graph theory, 1/2-arc-transitivity, consistent cycle, ... Keywords: mathematics, graph theory, 1/2-arc-transitivity, consistent cyclePublished: 15.10.2013; Views: 2189; Downloads: 7 Full text (0,00 KB)This document has more files! More... 8.Leonard triples and hypercubesŠtefko Miklavič, 2007, original scientific articleAbstract: Let ▫$V$▫ denote a vector space over ▫$\mathbb{C}$▫ with finite positive dimension. By a Leonard triple on ▫$V$▫ we mean an ordered triple of linear operators on ▫$V$▫ such that for each of these operators there exists a basis of ▫$V$▫ with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let ▫$D$▫ denote a positive integer and let ▫${\mathcal{Q}}_D$▫ denote the graph of the ▫$D$▫-dimensional hypercube. Let ▫$X$ denote the vertex set of ▫${\mathcal{Q}}_D$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫${\mathcal{Q}}_D$▫. Fix ▫$x \in X$▫ and let ▫$A^\ast \in {\mathrm{Mat}}_X({\mathbb{C}})$▫ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫${\mathrm{Mat}}_X({\mathbb{C}})$ generated by ▫$A,A^\ast$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫${\mathcal{Q}}_D$▫ with respect to ▫$x$▫. The matrices ▫$A$▫ and ▫$A^\ast$▫ are related by the fact that ▫$2iA = A^\ast A^\varepsilon - A^\varepsilon A^\ast$▫ and ▫$2iA^\ast = A^\varepsilon A - AA^\varepsilon$▫, where ▫$2iA^\varepsilon = AA^\ast - A^\ast A$▫ and ▫$i^2 = -1$▫. We show that the triple ▫$A$▫, ▫$A^\ast$▫, ▫$A^\varepsilon$▫ acts on each irreducible ▫$T$▫-module as a Leonard triple. We give a detailed description of these Leonard triples.Found in: ključnih besedahSummary of found: ...mathematics, graph theory, Leonard triple, distance-regular graph, hypercube,... Keywords: mathematics, graph theory, Leonard triple, distance-regular graph, hypercube, Terwilliger algebraPublished: 15.10.2013; Views: 1565; Downloads: 61 Full text (0,00 KB) 9.On generalized Jordan triple ([alpha], [beta]) [sup] [ast]-derivations and related mappingsShakir Ali, Ajda Fošner, Maja Fošner, Mohammad Salahuddin Khan, 2013, original scientific articleAbstract: Let ▫$R$▫ be a 2-torsion free semiprime ▫$\ast$▫-ring and let ▫$\alpha, \beta$▫ be surjective endomorphisms of ▫$R$▫. The aim of the paper is to show that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on ▫$R$▫ is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. This result makes it possible to prove that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on a semisimple ▫$H^\ast$▫-algebra is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. Finally, we prove that every Jordan triple left ▫$\alpha^\ast$▫-centralizer on a 2-torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫-centralizer.Found in: ključnih besedahSummary of found: ...mathematics, algebra, semiprime ▫$\ast$▫-ring, ▫$H^\ast$▫-algebra, Jordan triple ▫$(\alpha,... Keywords: mathematics, algebra, semiprime ▫$\ast$▫-ring, ▫$H^\ast$▫-algebra, Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, Jordan triple left ▫$\alpha^\ast$▫-centralizerPublished: 15.10.2013; Views: 1553; Downloads: 26 Full text (0,00 KB) 10.Semiovals contained in the union of three concurrent linesAart Blokhuis, György Kiss, István Kovács, Aleksander Malnič, Dragan Marušič, János Ruff, 2007, original scientific articleAbstract: Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG▫$(2,p)$▫ and PG▫$(2,p^2)$▫, ▫$p\$▫ an odd prime, is given.Found in: ključnih besedahSummary of found: ...mathematics, semioval, group factorization... Keywords: mathematics, semioval, group factorizationPublished: 15.10.2013; Views: 1288; Downloads: 60 Full text (0,00 KB) Search done in 0 sec.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9563425779342651, "perplexity": 15593.54734511983}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783342.96/warc/CC-MAIN-20200128215526-20200129005526-00533.warc.gz"}
http://mathoverflow.net/questions/136108/automorphisms-and-normal-bundle	# automorphisms and normal bundle Let $X$ be a smooth projective algebraic variety and $Z$ a smooth closed subvariety of $X$. Let $f: X \to X$ be an automorphism of $X$ such that $f(Z)\subset Z$. How does $f$ act on the normal bundle $N_{Z/X}$? - $N_{Z/X} = TX\|_Z/TZ$. By your assumption, $Tf:TX\to TX$ maps the restriction $TX\|_Z$ to itself, and also $TZ\to TZ$, with the same foot-point mapping $Z\to Z$. Thus it induces $TX\|_Z/TZ\to TX\|_Z/TZ$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9947547912597656, "perplexity": 77.09550432271219}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008289.40/warc/CC-MAIN-20141125155648-00207-ip-10-235-23-156.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-roots-real-and-imaginary-of-y-2x-2-15x-4x-3-2-using-the-quad	Algebra Topics # How do you find the roots, real and imaginary, of y= 2x^2-15x-(4x+3)^2 using the quadratic formula? Jun 30, 2016 x~~-1.69" and "x~~-0.38" to 2 decimal places") #### Explanation: You need to add like terms such that you and up with equation form:$\text{ } y = a {x}^{2} + b x + c$ To do this expand the brackets and simplify. '~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Expanding the brackets}}$ Note that ${\left[- \left(4 x + 3\right)\right]}^{2} \text{ is not the same as } - \left[{\left(4 x + 3\right)}^{2}\right]$ The condition we have is$\text{ } - \left[{\left(4 x + 3\right)}^{2}\right]$ $\textcolor{b l u e}{\left(4 x + 3\right)} \textcolor{b r o w n}{\left(4 x + 3\right)}$ $\textcolor{b r o w n}{\textcolor{b l u e}{4 x} \left(4 x + 3\right) \textcolor{b l u e}{+ 3} \left(4 x + 3\right)}$ $16 {x}^{2} + 12 x \text{ "+12x+9" "=" } \textcolor{g r e e n}{16 {x}^{2} + 24 x + 9}$ ,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Substituting the expanded brackets and solving}}$ $\implies y = 2 {x}^{2} - 15 x - \left(\textcolor{g r e e n}{16 {x}^{2} + 24 x + 9}\right)$ Multiply everything inside the brackets by -1 and group like terms $\implies y = 2 {x}^{2} - 16 {x}^{2} - 15 x - 24 x - 9$ $\implies y = - 14 {x}^{2} - 29 x - 9$ '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ From standard form we have: $a = - 14$ $b = - 29$ $c = - 9$ Thus $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ becomes" "x=(+29+-sqrt((-29)^2-4(-14)(-9)))/(2(-14) $x = \frac{29 \pm \sqrt{841 - 504}}{- 28}$ $x = \frac{29 \pm \sqrt{337}}{- 28} \text{ "larr 337" is a prime number}$ $\textcolor{b l u e}{x \approx - 1.69 \text{ and "x~~-0.38" to 2 decimal places}}$ ##### Impact of this question 56 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 20, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8824552893638611, "perplexity": 4029.110306859737}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583879117.74/warc/CC-MAIN-20190123003356-20190123025356-00076.warc.gz"}
https://terrytao.wordpress.com/category/mathematics/mathds/page/2/	You are currently browsing the category archive for the ‘math.DS’ category. I’ve just uploaded to the arXiv my paper “Failure of the ${L^1}$ pointwise and maximal ergodic theorems for the free group“, submitted to Forum of Mathematics, Sigma. This paper concerns a variant of the pointwise ergodic theorem of Birkhoff, which asserts that if one has a measure-preserving shift map ${T: X \rightarrow X}$ on a probability space ${X = (X,\mu)}$, then for any ${f \in L^1(X)}$, the averages ${\frac{1}{N} \sum_{n=1}^N f \circ T^{-n}}$ converge pointwise almost everywhere. (In the important case when the shift map ${T}$ is ergodic, the pointwise limit is simply the mean ${\int_X f\ d\mu}$ of the original function ${f}$.) The pointwise ergodic theorem can be extended to measure-preserving actions of other amenable groups, if one uses a suitably “tempered” Folner sequence of averages; see this paper of Lindenstrauss for more details. (I also wrote up some notes on that paper here, back in 2006 before I had started this blog.) But the arguments used to handle the amenable case break down completely for non-amenable groups, and in particular for the free non-abelian group ${F_2}$ on two generators. Nevo and Stein studied this problem and obtained a number of pointwise ergodic theorems for ${F_2}$-actions ${(T_g)_{g \in F_2}}$ on probability spaces ${(X,\mu)}$. For instance, for the spherical averaging operators $\displaystyle {\mathcal A}_n f := \frac{1}{4 \times 3^{n-1}} \sum_{g \in F_2: \|g\| = n} f \circ T_g^{-1}$ (where ${\|g\|}$ denotes the length of the reduced word that forms ${g}$), they showed that ${{\mathcal A}_{2n} f}$ converged pointwise almost everywhere provided that ${f}$ was in ${L^p(X)}$ for some ${p>1}$. (The need to restrict to spheres of even radius can be seen by considering the action of ${F_2}$ on the two-element set ${\{0,1\}}$ in which both generators of ${F_2}$ act by interchanging the elements, in which case ${{\mathcal A}_n}$ is determined by the parity of ${n}$.) This result was reproven with a different and simpler proof by Bufetov, who also managed to relax the condition ${f \in L^p(X)}$ to the weaker condition ${f \in L \log L(X)}$. The question remained open as to whether the pointwise ergodic theorem for ${F_2}$-actions held if one only assumed that ${f}$ was in ${L^1(X)}$. Nevo and Stein were able to establish this for the Cesáro averages ${\frac{1}{N} \sum_{n=1}^N {\mathcal A}_n}$, but not for ${{\mathcal A}_n}$ itself. About six years ago, Assaf Naor and I tried our hand at this problem, and was able to show an associated maximal inequality on ${\ell^1(F_2)}$, but due to the non-amenability of ${F_2}$, this inequality did not transfer to ${L^1(X)}$ and did not have any direct impact on this question, despite a fair amount of effort on our part to attack it. Inspired by some recent conversations with Lewis Bowen, I returned to this problem. This time around, I tried to construct a counterexample to the ${L^1}$ pointwise ergodic theorem – something Assaf and I had not seriously attempted to do (perhaps due to being a bit too enamoured of our ${\ell^1(F_2)}$ maximal inequality). I knew of an existing counterexample of Ornstein regarding a failure of an ${L^1}$ ergodic theorem for iterates ${P^n}$ of a self-adjoint Markov operator – in fact, I had written some notes on this example back in 2007. Upon revisiting my notes, I soon discovered that the Ornstein construction was adaptable to the ${F_2}$ setting, thus settling the problem in the negative: Theorem 1 (Failure of ${L^1}$ pointwise ergodic theorem) There exists a measure-preserving ${F_2}$-action on a probability space ${X}$ and a non-negative function ${f \in L^1(X)}$ such that ${\sup_n {\mathcal A}_{2n} f(x) = +\infty}$ for almost every ${x}$. To describe the proof of this theorem, let me first briefly sketch the main ideas of Ornstein’s construction, which gave an example of a self-adjoint Markov operator ${P}$ on a probability space ${X}$ and a non-negative ${f \in L^1(X)}$ such that ${\sup_n P^n f(x) = +\infty}$ for almost every ${x}$. By some standard manipulations, it suffices to show that for any given ${\alpha > 0}$ and ${\varepsilon>0}$, there exists a self-adjoint Markov operator ${P}$ on a probability space ${X}$ and a non-negative ${f \in L^1(X)}$ with ${\\|f\\|_{L^1(X)} \leq \alpha}$, such that ${\sup_n P^n f \geq 1-\varepsilon}$ on a set of measure at least ${1-\varepsilon}$. Actually, it will be convenient to replace the Markov chain ${(P^n f)_{n \geq 0}}$ with an ancient Markov chain ${(f_n)_{n \in {\bf Z}}}$ – that is to say, a sequence of non-negative functions ${f_n}$ for both positive and negative ${f}$, such that ${f_{n+1} = P f_n}$ for all ${n \in {\bf Z}}$. The purpose of requiring the Markov chain to be ancient (that is, to extend infinitely far back in time) is to allow for the Markov chain to be shifted arbitrarily in time, which is key to Ornstein’s construction. (Technically, Ornstein’s original argument only uses functions that go back to a large negative time, rather than being infinitely ancient, but I will gloss over this point for sake of discussion, as it turns out that the ${F_2}$ version of the argument can be run using infinitely ancient chains.) For any ${\alpha>0}$, let ${P(\alpha)}$ denote the claim that for any ${\varepsilon>0}$, there exists an ancient Markov chain ${(f_n)_{n \in {\bf Z}}}$ with ${\\|f_n\\|_{L^1(X)} = \alpha}$ such that ${\sup_{n \in {\bf Z}} f_n \geq 1-\varepsilon}$ on a set of measure at least ${1-\varepsilon}$. Clearly ${P(1)}$ holds since we can just take ${f_n=1}$ for all ${n}$. Our objective is to show that ${P(\alpha)}$ holds for arbitrarily small ${\alpha}$. The heart of Ornstein’s argument is then the implication $\displaystyle P(\alpha) \implies P( \alpha (1 - \frac{\alpha}{4}) ) \ \ \ \ \ (1)$ for any ${0 < \alpha \leq 1}$, which upon iteration quickly gives the desired claim. Let’s see informally how (1) works. By hypothesis, and ignoring epsilons, we can find an ancient Markov chain ${(f_n)_{n \in {\bf Z}}}$ on some probability space ${X}$ of total mass ${\\|f_n\\|_{L^1(X)} = \alpha}$, such that ${\sup_n f_n}$ attains the value of ${1}$ or greater almost everywhere. Assuming that the Markov process is irreducible, the ${f_n}$ will eventually converge as ${n \rightarrow \infty}$ to the constant value of ${\\|f_n\\|_{L^1(X)}}$, in particular its final state will essentially stay above ${\alpha}$ (up to small errors). Now suppose we duplicate the Markov process by replacing ${X}$ with a double copy ${X \times \{1,2\}}$ (giving ${\{1,2\}}$ the uniform probability measure), and using the disjoint sum of the Markov operators on ${X \times \{1\}}$ and ${X \times \{2\}}$ as the propagator, so that there is no interaction between the two components of this new system. Then the functions ${f'_n(x,i) := f_n(x) 1_{i=1}}$ form an ancient Markov chain of mass at most ${\alpha/2}$ that lives solely in the first half ${X \times \{1\}}$ of this copy, and ${\sup_n f'_n}$ attains the value of ${1}$ or greater on almost all of the first half ${X \times \{1\}}$, but is zero on the second half. The final state of ${f'_n}$ will be to stay above ${\alpha}$ in the first half ${X \times \{1\}}$, but be zero on the second half. Now we modify the above example by allowing an infinitesimal amount of interaction between the two halves ${X \times \{1\}}$, ${X \times \{2\}}$ of the system (I mentally think of ${X \times \{1\}}$ and ${X \times \{2\}}$ as two identical boxes that a particle can bounce around in, and now we wish to connect the boxes by a tiny tube). The precise way in which this interaction is inserted is not terribly important so long as the new Markov process is irreducible. Once one does so, then the ancient Markov chain ${(f'_n)_{n \in {\bf Z}}}$ in the previous example gets replaced by a slightly different ancient Markov chain ${(f''_n)_{n \in {\bf Z}}}$ which is more or less identical with ${f'_n}$ for negative times ${n}$, or for bounded positive times ${n}$, but for very large values of ${n}$ the final state is now constant across the entire state space ${X \times \{1,2\}}$, and will stay above ${\alpha/2}$ on this space. Finally, we consider an ancient Markov chain ${F_n}$ which is basically of the form $\displaystyle F_n(x,i) \approx f''_n(x,i) + (1 - \frac{\alpha}{2}) f_{n-M}(x) 1_{i=2}$ for some large parameter ${M}$ and for all ${n \leq M}$ (the approximation becomes increasingly inaccurate for ${n}$ much larger than ${M}$, but never mind this for now). This is basically two copies of the original Markov process in separate, barely interacting state spaces ${X \times \{1\}, X \times \{2\}}$, but with the second copy delayed by a large time delay ${M}$, and also attenuated in amplitude by a factor of ${1-\frac{\alpha}{2}}$. The total mass of this process is now ${\frac{\alpha}{2} + \frac{\alpha}{2} (1 -\frac{\alpha}{2}) = \alpha (1 - \alpha/4)}$. Because of the ${f''_n}$ component of ${F_n}$, we see that ${\sup_n F_n}$ basically attains the value of ${1}$ or greater on the first half ${X \times \{1\}}$. On the second half ${X \times \{2\}}$, we work with times ${n}$ close to ${M}$. If ${M}$ is large enough, ${f''_n}$ would have averaged out to about ${\alpha/2}$ at such times, but the ${(1 - \frac{\alpha}{2}) f_{n-M}(x)}$ component can get as large as ${1-\alpha/2}$ here. Summing (and continuing to ignore various epsilon losses), we see that ${\sup_n F_n}$ can get as large as ${1}$ on almost all of the second half of ${X \times \{2\}}$. This concludes the rough sketch of how one establishes the implication (1). It was observed by Bufetov that the spherical averages ${{\mathcal A}_n}$ for a free group action can be lifted up to become powers ${P^n}$ of a Markov operator, basically by randomly assigning a “velocity vector” ${s \in \{a,b,a^{-1},b^{-1}\}}$ to one’s base point ${x}$ and then applying the Markov process that moves ${x}$ along that velocity vector (and then randomly changing the velocity vector at each time step to the “reduced word” condition that the velocity never flips from ${s}$ to ${s^{-1}}$). Thus the spherical average problem has a Markov operator interpretation, which opens the door to adapting the Ornstein construction to the setting of ${F_2}$ systems. This turns out to be doable after a certain amount of technical artifice; the main thing is to work with ${F_2}$-measure preserving systems that admit ancient Markov chains that are initially supported in a very small region in the “interior” of the state space, so that one can couple such systems to each other “at the boundary” in the fashion needed to establish the analogue of (1) without disrupting the ancient dynamics of such chains. The initial such system (used to establish the base case ${P(1)}$) comes from basically considering the action of ${F_2}$ on a (suitably renormalised) “infinitely large ball” in the Cayley graph, after suitably gluing together the boundary of this ball to complete the action. The ancient Markov chain associated to this system starts at the centre of this infinitely large ball at infinite negative time ${n=-\infty}$, and only reaches the boundary of this ball at the time ${n=0}$. An extremely large portion of mathematics is concerned with locating solutions to equations such as $\displaystyle f(x) = 0$ or $\displaystyle \Phi(x) = x \ \ \ \ \ (1)$ for ${x}$ in some suitable domain space (either finite-dimensional or infinite-dimensional), and various maps ${f}$ or ${\Phi}$. To solve the fixed point iteration equation (1), the simplest general method available is the fixed point iteration method: one starts with an initial approximate solution ${x_0}$ to (1), so that ${\Phi(x_0) \approx x_0}$, and then recursively constructs the sequence ${x_1, x_2, x_3, \dots}$ by ${x_n := \Phi(x_{n-1})}$. If ${\Phi}$ behaves enough like a “contraction”, and the domain is complete, then one can expect the ${x_n}$ to converge to a limit ${x}$, which should then be a solution to (1). For instance, if ${\Phi: X \rightarrow X}$ is a map from a metric space ${X = (X,d)}$ to itself, which is a contraction in the sense that $\displaystyle d( \Phi(x), \Phi(y) ) \leq (1-\eta) d(x,y)$ for all ${x,y \in X}$ and some ${\eta>0}$, then with ${x_n}$ as above we have $\displaystyle d( x_{n+1}, x_n ) \leq (1-\eta) d(x_n, x_{n-1} )$ for any ${n}$, and so the distances ${d(x_n, x_{n-1} )}$ between successive elements of the sequence decay at at least a geometric rate. This leads to the contraction mapping theorem, which has many important consequences, such as the inverse function theorem and the Picard existence theorem. A slightly more complicated instance of this strategy arises when trying to linearise a complex map ${f: U \rightarrow {\bf C}}$ defined in a neighbourhood ${U}$ of a fixed point. For simplicity we normalise the fixed point to be the origin, thus ${0 \in U}$ and ${f(0)=0}$. When studying the complex dynamics ${f^2 = f \circ f}$, ${f^3 = f \circ f \circ f}$, ${\dots}$ of such a map, it can be useful to try to conjugate ${f}$ to another function ${g = \psi^{-1} \circ f \circ \psi}$, where ${\psi}$ is a holomorphic function defined and invertible near ${0}$ with ${\psi(0)=0}$, since the dynamics of ${g}$ will be conjguate to that of ${f}$. Note that if ${f(0)=0}$ and ${f'(0)=\lambda}$, then from the chain rule any conjugate ${g}$ of ${f}$ will also have ${g(0)=0}$ and ${g'(0)=\lambda}$. Thus, the “simplest” function one can hope to conjugate ${f}$ to is the linear function ${z \mapsto \lambda z}$. Let us say that ${f}$ is linearisable (around ${0}$) if it is conjugate to ${z \mapsto \lambda z}$ in some neighbourhood of ${0}$. Equivalently, ${f}$ is linearisable if there is a solution to the Schröder equation $\displaystyle f( \psi(z) ) = \psi(\lambda z) \ \ \ \ \ (2)$ for some ${\psi: U' \rightarrow {\bf C}}$ defined and invertible in a neighbourhood ${U'}$ of ${0}$ with ${\psi(0)=0}$, and all ${z}$ sufficiently close to ${0}$. (The Schröder equation is normalised somewhat differently in the literature, but this form is equivalent to the usual form, at least when ${\lambda}$ is non-zero.) Note that if ${\psi}$ solves the above equation, then so does ${z \mapsto \psi(cz)}$ for any non-zero ${c}$, so we may normalise ${\psi'(0)=1}$ in addition to ${\psi(0)=0}$, which also ensures local invertibility from the inverse function theorem. (Note from winding number considerations that ${\psi}$ cannot be invertible near zero if ${\psi'(0)}$ vanishes.) We have the following basic result of Koenigs: Theorem 1 (Koenig’s linearisation theorem) Let ${f: U \rightarrow {\bf C}}$ be a holomorphic function defined near ${0}$ with ${f(0)=0}$ and ${f'(0)=\lambda}$. If ${0 < \|\lambda\| < 1}$ (attracting case) or ${1 < \|\lambda\| < \infty}$ (repelling case), then ${f}$ is linearisable near zero. Proof: Observe that if ${f, \psi, \lambda}$ solve (2), then ${f^{-1}, \psi^{-1}, \lambda^{-1}}$ solve (2) also (in a sufficiently small neighbourhood of zero). Thus we may reduce to the attractive case ${0 < \|\lambda\| < 1}$. Let ${r>0}$ be a sufficiently small radius, and let ${X}$ denote the space of holomorphic functions ${\psi: B(0,r) \rightarrow {\bf C}}$ on the complex disk ${B(0,r) := \{z \in {\bf C}: \|z\| < r \}}$ with ${\psi(0)=0}$ and ${\psi'(0)=1}$. We can view the Schröder equation (2) as a fixed point equation $\displaystyle \psi = \Phi(\psi)$ where ${\Phi: X' \rightarrow X}$ is the partially defined function on ${X}$ that maps a function ${\psi: B(0,r) \rightarrow {\bf C}}$ to the function ${\Phi(\psi): B(0,r) \rightarrow {\bf C}}$ defined by $\displaystyle \Phi(\psi)(z) := f^{-1}( \psi( \lambda z ) ),$ assuming that ${f^{-1}}$ is well-defined on the range of ${\psi(B(0,\lambda r))}$ (this is why ${\Phi}$ is only partially defined). We can solve this equation by the fixed point iteration method, if ${r}$ is small enough. Namely, we start with ${\psi_0: B(0,r) \rightarrow {\bf C}}$ being the identity map, and set ${\psi_1 := \Phi(\psi_0), \psi_2 := \Phi(\psi_1)}$, etc. We equip ${X}$ with the uniform metric ${d( \psi, \tilde \psi ) := \sup_{z \in B(0,r)} \|\psi(z) - \tilde \psi(z)\|}$. Observe that if ${d( \psi, \psi_0 ), d(\tilde \psi, \psi_0) \leq r}$, and ${r}$ is small enough, then ${\psi, \tilde \psi}$ takes values in ${B(0,2r)}$, and ${\Phi(\psi), \Phi(\tilde \psi)}$ are well-defined and lie in ${X}$. Also, since ${f^{-1}}$ is smooth and has derivative ${\lambda^{-1}}$ at ${0}$, we have $\displaystyle \|f^{-1}(z) - f^{-1}(w)\| \leq (1+\varepsilon) \|\lambda\|^{-1} \|z-w\|$ if ${z, w \in B(0,r)}$, ${\varepsilon>0}$ and ${r}$ is sufficiently small depending on ${\varepsilon}$. This is not yet enough to establish the required contraction (thanks to Mario Bonk for pointing this out); but observe that the function ${\frac{\psi(z)-\tilde \psi(z)}{z^2}}$ is holomorphic on ${B(0,r)}$ and bounded by ${d(\psi,\tilde \psi)/r^2}$ on the boundary of this ball (or slightly within this boundary), so by the maximum principle we see that $\displaystyle \|\frac{\psi(z)-\tilde \psi(z)}{z^2}\| \leq \frac{1}{r^2} d(\psi,\tilde \psi)$ on all of ${B(0,r)}$, and in particular $\displaystyle \|\psi(z)-\tilde \psi(z)\| \leq \|\lambda\|^2 d(\psi,\tilde \psi)$ on ${B(0,\lambda r)}$. Putting all this together, we see that $\displaystyle d( \Phi(\psi), \Phi(\tilde \psi)) \leq (1+\varepsilon) \|\lambda\| d(\psi, \tilde \psi);$ since ${\|\lambda\|<1}$, we thus obtain a contraction on the ball ${\{ \psi \in X: d(\psi,\psi_0) \leq r \}}$ if ${\varepsilon}$ is small enough (and ${r}$ sufficiently small depending on ${\varepsilon}$). From this (and the completeness of ${X}$, which follows from Morera’s theorem) we see that the iteration ${\psi_n}$ converges (exponentially fast) to a limit ${\psi \in X}$ which is a fixed point of ${\Phi}$, and thus solves Schröder’s equation, as required. $\Box$ Koenig’s linearisation theorem leaves open the indifferent case when ${\|\lambda\|=1}$. In the rationally indifferent case when ${\lambda^n=1}$ for some natural number ${n}$, there is an obvious obstruction to linearisability, namely that ${f^n = 1}$ (in particular, linearisation is not possible in this case when ${f}$ is a non-trivial rational function). An obstruction is also present in some irrationally indifferent cases (where ${\|\lambda\|=1}$ but ${\lambda^n \neq 1}$ for any natural number ${n}$), if ${\lambda}$ is sufficiently close to various roots of unity; the first result of this form is due to Cremer, and the optimal result of this type for quadratic maps was established by Yoccoz. In the other direction, we have the following result of Siegel: Theorem 2 (Siegel’s linearisation theorem) Let ${f: U \rightarrow {\bf C}}$ be a holomorphic function defined near ${0}$ with ${f(0)=0}$ and ${f'(0)=\lambda}$. If ${\|\lambda\|=1}$ and one has the Diophantine condition ${\frac{1}{\|\lambda^n-1\|} \leq C n^C}$ for all natural numbers ${n}$ and some constant ${C>0}$, then ${f}$ is linearisable at ${0}$. The Diophantine condition can be relaxed to a more general condition involving the rational exponents of the phase ${\theta}$ of ${\lambda = e^{2\pi i \theta}}$; this was worked out by Brjuno, with the condition matching the one later obtained by Yoccoz. Amusingly, while the set of Diophantine numbers (and hence the set of linearisable ${\lambda}$) has full measure on the unit circle, the set of non-linearisable ${\lambda}$ is generic (the complement of countably many nowhere dense sets) due to the above-mentioned work of Cremer, leading to a striking disparity between the measure-theoretic and category notions of “largeness”. Siegel’s theorem does not seem to be provable using a fixed point iteration method. However, it can be established by modifying another basic method to solve equations, namely Newton’s method. Let us first review how this method works to solve the equation ${f(x)=0}$ for some smooth function ${f: I \rightarrow {\bf R}}$ defined on an interval ${I}$. We suppose we have some initial approximant ${x_0 \in I}$ to this equation, with ${f(x_0)}$ small but not necessarily zero. To make the analysis more quantitative, let us suppose that the interval ${[x_0-r_0,x_0+r_0]}$ lies in ${I}$ for some ${r_0>0}$, and we have the estimates $\displaystyle \|f(x_0)\| \leq \delta_0 r_0$ $\displaystyle \|f'(x)\| \geq \eta_0$ $\displaystyle \|f''(x)\| \leq \frac{1}{\eta_0 r_0}$ for some ${\delta_0 > 0}$ and ${0 < \eta_0 < 1/2}$ and all ${x \in [x_0-r_0,x_0+r_0]}$ (the factors of ${r_0}$ are present to make ${\delta_0,\eta_0}$ “dimensionless”). Lemma 3 Under the above hypotheses, we can find ${x_1}$ with ${\|x_1 - x_0\| \leq \eta_0 r_0}$ such that $\displaystyle \|f(x_1)\| \ll \delta_0^2 \eta_0^{-O(1)} r_0.$ In particular, setting ${r_1 := (1-\eta_0) r_0}$, ${\eta_1 := \eta_0/2}$, and ${\delta_1 = O(\delta_0^2 \eta_0^{-O(1)})}$, we have ${[x_1-r_1,x_1+r_1] \subset [x_0-r_0,x_0+r_0] \subset I}$, and $\displaystyle \|f(x_1)\| \leq \delta_1 r_1$ $\displaystyle \|f'(x)\| \geq \eta_1$ $\displaystyle \|f''(x)\| \leq \frac{1}{\eta_1 r_1}$ for all ${x \in [x_1-r_1,x_1+r_1]}$. The crucial point here is that the new error ${\delta_1}$ is roughly the square of the previous error ${\delta_0}$. This leads to extremely fast (double-exponential) improvement in the error upon iteration, which is more than enough to absorb the exponential losses coming from the ${\eta_0^{-O(1)}}$ factor. Proof: If ${\delta_0 > c \eta_0^{C}}$ for some absolute constants ${C,c>0}$ then we may simply take ${x_0=x_1}$, so we may assume that ${\delta_0 \leq c \eta_0^{C}}$ for some small ${c>0}$ and large ${C>0}$. Using the Newton approximation ${f(x_0+h) \approx f(x_0) + h f'(x_0)}$ we are led to the choice $\displaystyle x_1 := x_0 - \frac{f(x_0)}{f'(x_0)}$ for ${x_1}$. From the hypotheses on ${f}$ and the smallness hypothesis on ${\delta}$ we certainly have ${\|x_1-x_0\| \leq \eta_0 r_0}$. From Taylor’s theorem with remainder we have $\displaystyle f(x_1) = f(x_0) - \frac{f(x_0)}{f'(x_0)} f'(x_0) + O( \frac{1}{\eta_0 r_0} \|\frac{f(x_0)}{f'(x_0)}\|^2 )$ $\displaystyle = O( \frac{1}{\eta_0 r_0} (\frac{\delta_0 r_0}{\eta_0})^2 )$ and the claim follows. $\Box$ We can iterate this procedure; starting with ${x_0,\eta_0,r_0,\delta_0}$ as above, we obtain a sequence of nested intervals ${[x_n-r_n,x_n+r_n]}$ with ${f(x_n)\| \leq \delta_n}$, and with ${\eta_n,r_n,\delta_n,x_n}$ evolving by the recursive equations and estimates $\displaystyle \eta_n = \eta_{n-1} / 2$ $\displaystyle r_n = (1 - \eta_{n-1}) r_{n-1}$ $\displaystyle \delta_n = O( \delta_{n-1}^2 \eta_{n-1}^{-O(1)} )$ $\displaystyle \|x_n - x_{n-1}\| \leq \eta_{n-1} r_{n-1}.$ If ${\delta_0}$ is sufficiently small depending on ${\eta_0}$, we see that ${\delta_n}$ converges rapidly to zero (indeed, we can inductively obtain a bound of the form ${\delta_n \leq \eta_0^{C (2^n + n)}}$ for some large absolute constant ${C}$ if ${\delta_0}$ is small enough), and ${x_n}$ converges to a limit ${x \in I}$ which then solves the equation ${f(x)=0}$ by the continuity of ${f}$. As I recently learned from Zhiqiang Li, a similar scheme works to prove Siegel’s theorem, as can be found for instance in this text of Carleson and Gamelin. The key is the following analogue of Lemma 3. Lemma 4 Let ${\lambda}$ be a complex number with ${\|\lambda\|=1}$ and ${\frac{1}{\|\lambda^n-1\|} \ll n^{O(1)}}$ for all natural numbers ${n}$. Let ${r_0>0}$, and let ${f_0: B(0,r_0) \rightarrow {\bf C}}$ be a holomorphic function with ${f_0(0)=0}$, ${f'_0(0)=\lambda}$, and $\displaystyle \|f_0(z) - \lambda z\| \leq \delta_0 r_0 \ \ \ \ \ (3)$ for all ${z \in B(0,r_0)}$ and some ${\delta_0>0}$. Let ${0 < \eta_0 \leq 1/2}$, and set ${r_1 := (1-\eta_0) r_0}$. Then there exists an injective holomorphic function ${\psi_0: B(0, r_1) \rightarrow B(0, r_0)}$ and a holomorphic function ${f_1: B(0,r_1) \rightarrow {\bf C}}$ such that $\displaystyle f_0( \psi_1(z) ) = \psi_1(f_1(z)) \ \ \ \ \ (4)$ for all ${z \in B(0,r_1)}$, and such that $\displaystyle \|\psi_1(z) - z\| \ll \delta_0 \eta_0^{-O(1)} r_1$ and $\displaystyle \|f_1(z) - \lambda z\| \leq \delta_1 r_1$ for all ${z \in B(0,r_1)}$ and some ${\delta_1 = O(\delta_0^2 \eta_0^{-O(1)})}$. Proof: By scaling we may normalise ${r_0=1}$. If ${\delta_0 > c \eta_0^C}$ for some constants ${c,C>0}$, then we can simply take ${\psi_1}$ to be the identity and ${f_1=f_0}$, so we may assume that ${\delta_0 \leq c \eta_0^C}$ for some small ${c>0}$ and large ${C>0}$. To motivate the choice of ${\psi_1}$, we write ${f_0(z) = \lambda z + \hat f_0(z)}$ and ${\psi_1(z) = z + \hat \psi(z)}$, with ${\hat f_0}$ and ${\hat \psi_1}$ viewed as small. We would like to have ${f_0(\psi_1(z)) \approx \psi_1(\lambda z)}$, which expands as $\displaystyle \lambda z + \lambda \hat \psi_1(z) + \hat f_0( z + \hat \psi_1(z) ) \approx \lambda z + \hat \psi_1(\lambda z).$ As ${\hat f_0}$ and ${\hat \psi}$ are both small, we can heuristically approximate ${\hat f_0(z + \hat \psi_1(z) ) \approx \hat f_0(z)}$ up to quadratic errors (compare with the Newton approximation ${f(x_0+h) \approx f(x_0) + h f'(x_0)}$), and arrive at the equation $\displaystyle \hat \psi_1(\lambda z) - \lambda \hat \psi_1(z) = \hat f_0(z). \ \ \ \ \ (5)$ This equation can be solved by Taylor series; the function ${\hat f_0}$ vanishes to second order at the origin and thus has a Taylor expansion $\displaystyle \hat f_0(z) = \sum_{n=2}^\infty a_n z^n$ and then ${\hat \psi_1}$ has a Taylor expansion $\displaystyle \hat \psi_1(z) = \sum_{n=2}^\infty \frac{a_n}{\lambda^n - \lambda} z^n.$ We take this as our definition of ${\hat \psi_1}$, define ${\psi_1(z) := z + \hat \psi_1(z)}$, and then define ${f_1}$ implicitly via (4). Let us now justify that this choice works. By (3) and the generalised Cauchy integral formula, we have ${\|a_n\| \leq \delta_0}$ for all ${n}$; by the Diophantine assumption on ${\lambda}$, we thus have ${\|\frac{a_n}{\lambda^n - \lambda}\| \ll \delta_0 n^{O(1)}}$. In particular, ${\hat \psi_1}$ converges on ${B(0,1)}$, and on the disk ${B(0, (1-\eta_0/4))}$ (say) we have the bounds $\displaystyle \|\hat \psi_1(z)\|, \|\hat \psi'_1(z)\| \ll \delta_0 \sum_{n=2}^\infty n^{O(1)} (1-\eta_0/4)^n \ll \eta_0^{-O(1)} \delta_0. \ \ \ \ \ (6)$ In particular, as ${\delta_0}$ is so small, we see that ${\psi_1}$ maps ${B(0, (1-\eta_0/4))}$ injectively to ${B(0,1)}$ and ${B(0,1-\eta_0)}$ to ${B(0,1-3\eta_0/4)}$, and the inverse ${\psi_1^{-1}}$ maps ${B(0, (1-\eta_0/2))}$ to ${B(0, (1-\eta_0/4))}$. From (3) we see that ${f_0}$ maps ${B(0,1-3\eta_0/4)}$ to ${B(0,1-\eta_0/2)}$, and so if we set ${f_1: B(0,1-\eta_0) \rightarrow B(0,1-\eta_0/4)}$ to be the function ${f_1 := \psi_1^{-1} \circ f_0 \circ \psi_1}$, then ${f_1}$ is a holomorphic function obeying (4). Expanding (4) in terms of ${\hat f_0}$ and ${\hat \psi_1}$ as before, and also writing ${f_1(z) = \lambda z + \hat f_1(z)}$, we have $\displaystyle \lambda z + \lambda \hat \psi_1(z) + \hat f_0( z + \hat \psi_1(z) ) = \lambda z + \hat f_1(z) + \hat \psi_1(\lambda z + \hat f_1(z))$ for ${z \in B(0, 1-\eta_0)}$, which by (5) simplifies to $\displaystyle \hat f_1(z) = \hat f_0( z + \hat \psi_1(z) ) - \hat f_0(z) + \hat \psi_1(\lambda z) - \hat \psi_1(\lambda z + \hat f_1(z)).$ From (6), the fundamental theorem of calculus, and the smallness of ${\delta_0}$ we have $\displaystyle \|\hat \psi_1(\lambda z) - \hat \psi_1(\lambda z + \hat f_1(z))\| \leq \frac{1}{2} \|\hat f_1(z)\|$ and thus $\displaystyle \|\hat f_1(z)\| \leq 2 \|\hat f_0( z + \hat \psi_1(z) ) - \hat f_0(z)\|.$ From (3) and the Cauchy integral formula we have ${\hat f'_0(z) = O( \delta_0 \eta_0^{-O(1)})}$ on (say) ${B(0,1-\eta_0/4)}$, and so from (6) and the fundamental theorem of calculus we conclude that $\displaystyle \|\hat f_1(z)\| \ll \delta_0^2 \eta_0^{-O(1)}$ on ${B(0,1-\eta_0)}$, and the claim follows. $\Box$ If we set ${\eta_0 := 1/2}$, ${f_0 := f}$, and ${\delta_0>0}$ to be sufficiently small, then (since ${f(z)-\lambda z}$ vanishes to second order at the origin), the hypotheses of this lemma will be obeyed for some sufficiently small ${r_0}$. Iterating the lemma (and halving ${\eta_0}$ repeatedly), we can then find sequences ${\eta_n, \delta_n, r_n > 0}$, injective holomorphic functions ${\psi_n: B(0,r_n) \rightarrow B(0,r_{n-1})}$ and holomorphic functions ${f_n: B(0,r_n) \rightarrow {\bf C}}$ such that one has the recursive identities and estimates $\displaystyle \eta_n = \eta_{n-1} / 2$ $\displaystyle r_n = (1 - \eta_{n-1}) r_{n-1}$ $\displaystyle \delta_n = O( \delta_{n-1}^2 \eta_{n-1}^{-O(1)} )$ $\displaystyle \|\psi_n(z) - z\| \ll \delta_{n-1} \eta_{n-1}^{-O(1)} r_n$ $\displaystyle \|f_n(z) - \lambda z\| \leq \delta_n r_n$ $\displaystyle f_{n-1}( \psi_n(z) ) = \psi_n(f_n(z))$ for all ${n \geq 1}$ and ${z \in B(0,r_n)}$. By construction, ${r_n}$ decreases to a positive radius ${r_\infty}$ that is a constant multiple of ${r_0}$, while (for ${\delta_0}$ small enough) ${\delta_n}$ converges double-exponentially to zero, so in particular ${f_n(z)}$ converges uniformly to ${\lambda z}$ on ${B(0,r_\infty)}$. Also, ${\psi_n}$ is close enough to the identity, the compositions ${\Psi_n := \psi_1 \circ \dots \circ \psi_n}$ are uniformly convergent on ${B(0,r_\infty/2)}$ with ${\Psi_n(0)=0}$ and ${\Psi'_n(0)=1}$. From this we have $\displaystyle f( \Psi_n(z) ) = \Psi_n(f_n(z))$ on ${B(0,r_\infty/4)}$, and on taking limits using Morera’s theorem we obtain a holomorphic function ${\Psi}$ defined near ${0}$ with ${\Psi(0)=0}$, ${\Psi'(0)=1}$, and $\displaystyle f( \Psi(z) ) = \Psi(\lambda z),$ obtaining the required linearisation. Remark 5 The idea of using a Newton-type method to obtain error terms that decay double-exponentially, and can therefore absorb exponential losses in the iteration, also occurs in KAM theory and in Nash-Moser iteration, presumably due to Siegel’s influence on Moser. (I discuss Nash-Moser iteration in this note that I wrote back in 2006.) The von Neumann ergodic theorem (the Hilbert space version of the mean ergodic theorem) asserts that if ${U: H \rightarrow H}$ is a unitary operator on a Hilbert space ${H}$, and ${v \in H}$ is a vector in that Hilbert space, then one has $\displaystyle \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{n=1}^N U^n v = \pi_{H^U} v$ in the strong topology, where ${H^U := \{ w \in H: Uw = w \}}$ is the ${U}$-invariant subspace of ${H}$, and ${\pi_{H^U}}$ is the orthogonal projection to ${H^U}$. (See e.g. these previous lecture notes for a proof.) The same proof extends to more general amenable groups: if ${G}$ is a countable amenable group acting on a Hilbert space ${H}$ by unitary transformations ${T^g: H \rightarrow H}$ for ${g \in G}$, and ${v \in H}$ is a vector in that Hilbert space, then one has $\displaystyle \lim_{N \rightarrow \infty} \mathop{\bf E}_{g \in \Phi_N} T^g v = \pi_{H^G} v \ \ \ \ \ (1)$ for any Folner sequence ${\Phi_N}$ of ${G}$, where ${H^G := \{ w \in H: T^g w = w \hbox{ for all }g \in G \}}$ is the ${G}$-invariant subspace, and ${\mathop{\bf E}_{a \in A} f(a) := \frac{1}{\|A\|} \sum_{a \in A} f(a)}$ is the average of ${f}$ on ${A}$. Thus one can interpret ${\pi_{H^G} v}$ as a certain average of elements of the orbit ${Gv := \{ T^g v: g \in G \}}$ of ${v}$. In a previous blog post, I noted a variant of this ergodic theorem (due to Alaoglu and Birkhoff) that holds even when the group ${G}$ is not amenable (or not discrete), using a more abstract notion of averaging: Theorem 1 (Abstract ergodic theorem) Let ${G}$ be an arbitrary group acting unitarily on a Hilbert space ${H}$, and let ${v}$ be a vector in ${H}$. Then ${\pi_{H^G} v}$ is the element in the closed convex hull of ${Gv := \{ T^g v: g \in G \}}$ of minimal norm, and is also the unique element of ${H^G}$ in this closed convex hull. I recently stumbled upon a different way to think about this theorem, in the additive case ${G = (G,+)}$ when ${G}$ is abelian, which has a closer resemblance to the classical mean ergodic theorem. Given an arbitrary additive group ${G = (G,+)}$ (not necessarily discrete, or countable), let ${{\mathcal F}}$ denote the collection of finite non-empty multisets in ${G}$ – that is to say, unordered collections ${\{a_1,\dots,a_n\}}$ of elements ${a_1,\dots,a_n}$ of ${G}$, not necessarily distinct, for some positive integer ${n}$. Given two multisets ${A = \{a_1,\dots,a_n\}}$, ${B = \{b_1,\dots,b_m\}}$ in ${{\mathcal F}}$, we can form the sum set ${A + B := \{ a_i + b_j: 1 \leq i \leq n, 1 \leq j \leq m \}}$. Note that the sum set ${A+B}$ can contain multiplicity even when ${A, B}$ do not; for instance, ${\{ 1,2\} + \{1,2\} = \{2,3,3,4\}}$. Given a multiset ${A = \{a_1,\dots,a_n\}}$ in ${{\mathcal F}}$, and a function ${f: G \rightarrow H}$ from ${G}$ to a vector space ${H}$, we define the average ${\mathop{\bf E}_{a \in A} f(a)}$ as $\displaystyle \mathop{\bf E}_{a \in A} f(a) = \frac{1}{n} \sum_{j=1}^n f(a_j).$ Note that the multiplicity function of the set ${A}$ affects the average; for instance, we have ${\mathop{\bf E}_{a \in \{1,2\}} a = \frac{3}{2}}$, but ${\mathop{\bf E}_{a \in \{1,2,2\}} a = \frac{5}{3}}$. We can define a directed set on ${{\mathcal F}}$ as follows: given two multisets ${A,B \in {\mathcal F}}$, we write ${A \geq B}$ if we have ${A = B+C}$ for some ${C \in {\mathcal F}}$. Thus for instance we have ${\{ 1, 2, 2, 3\} \geq \{1,2\}}$. It is easy to verify that this operation is transitive and reflexive, and is directed because any two elements ${A,B}$ of ${{\mathcal F}}$ have a common upper bound, namely ${A+B}$. (This is where we need ${G}$ to be abelian.) The notion of convergence along a net, now allows us to define the notion of convergence along ${{\mathcal F}}$; given a family ${x_A}$ of points in a topological space ${X}$ indexed by elements ${A}$ of ${{\mathcal F}}$, and a point ${x}$ in ${X}$, we say that ${x_A}$ converges to ${x}$ along ${{\mathcal F}}$ if, for every open neighbourhood ${U}$ of ${x}$ in ${X}$, one has ${x_A \in U}$ for sufficiently large ${A}$, that is to say there exists ${B \in {\mathcal F}}$ such that ${x_A \in U}$ for all ${A \geq B}$. If the topological space ${V}$ is Hausdorff, then the limit ${x}$ is unique (if it exists), and we then write $\displaystyle x = \lim_{A \rightarrow G} x_A.$ When ${x_A}$ takes values in the reals, one can also define the limit superior or limit inferior along such nets in the obvious fashion. We can then give an alternate formulation of the abstract ergodic theorem in the abelian case: Theorem 2 (Abelian abstract ergodic theorem) Let ${G = (G,+)}$ be an arbitrary additive group acting unitarily on a Hilbert space ${H}$, and let ${v}$ be a vector in ${H}$. Then we have $\displaystyle \pi_{H^G} v = \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v$ in the strong topology of ${H}$. Proof: Suppose that ${A \geq B}$, so that ${A=B+C}$ for some ${C \in {\mathcal F}}$, then $\displaystyle \mathop{\bf E}_{a \in A} T^a v = \mathop{\bf E}_{c \in C} T^c ( \mathop{\bf E}_{b \in B} T^b v )$ so by unitarity and the triangle inequality we have $\displaystyle \\| \mathop{\bf E}_{a \in A} T^a v \\|_H \leq \\| \mathop{\bf E}_{b \in B} T^b v \\|_H,$ thus ${\\| \mathop{\bf E}_{a \in A} T^a v \\|_H^2}$ is monotone non-increasing in ${A}$. Since this quantity is bounded between ${0}$ and ${\\|v\\|_H}$, we conclude that the limit ${\lim_{A \rightarrow G} \\| \mathop{\bf E}_{a \in A} T^a v \\|_H^2}$ exists. Thus, for any ${\varepsilon > 0}$, we have for sufficiently large ${A}$ that $\displaystyle \\| \mathop{\bf E}_{b \in B} T^b v \\|_H^2 \geq \\| \mathop{\bf E}_{a \in A} T^a v \\|_H^2 - \varepsilon$ for all ${B \geq A}$. In particular, for any ${g \in G}$, we have $\displaystyle \\| \mathop{\bf E}_{b \in A + \{0,g\}} T^b v \\|_H^2 \geq \\| \mathop{\bf E}_{a \in A} T^a v \\|_H^2 - \varepsilon.$ We can write $\displaystyle \mathop{\bf E}_{b \in A + \{0,g\}} T^b v = \frac{1}{2} \mathop{\bf E}_{a \in A} T^a v + \frac{1}{2} T^g \mathop{\bf E}_{a \in A} T^a v$ and so from the parallelogram law and unitarity we have $\displaystyle \\| \mathop{\bf E}_{a \in A} T^a v - T^g \mathop{\bf E}_{a \in A} T^a v \\|_H^2 \leq 4 \varepsilon$ for all ${g \in G}$, and hence by the triangle inequality (averaging ${g}$ over a finite multiset ${C}$) $\displaystyle \\| \mathop{\bf E}_{a \in A} T^a v - \mathop{\bf E}_{b \in A+C} T^b v \\|_H^2 \leq 4 \varepsilon$ for any ${C \in {\mathcal F}}$. This shows that ${\mathop{\bf E}_{a \in A} T^a v}$ is a Cauchy sequence in ${H}$ (in the strong topology), and hence (by the completeness of ${H}$) tends to a limit. Shifting ${A}$ by a group element ${g}$, we have $\displaystyle \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v = \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A + \{g\}} T^a v = T^g \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v$ and hence ${\lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v}$ is invariant under shifts, and thus lies in ${H^G}$. On the other hand, for any ${w \in H^G}$ and ${A \in {\mathcal F}}$, we have $\displaystyle \langle \mathop{\bf E}_{a \in A} T^a v, w \rangle_H = \mathop{\bf E}_{a \in A} \langle v, T^{-a} w \rangle_H = \langle v, w \rangle_H$ and thus on taking strong limits $\displaystyle \langle \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v, w \rangle_H = \langle v, w \rangle_H$ and so ${v - \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v}$ is orthogonal to ${H^G}$. Combining these two facts we see that ${\lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^a v}$ is equal to ${\pi_{H^G} v}$ as claimed. $\Box$ To relate this result to the classical ergodic theorem, we observe Lemma 3 Let ${G}$ be a countable additive group, with a F{\o}lner sequence ${\Phi_n}$, and let ${f_g}$ be a bounded sequence in a normed vector space indexed by ${G}$. If ${\lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} f_a}$ exists, then ${\lim_{n \rightarrow \infty} \mathop{\bf E}_{a \in \Phi_n} f_a}$ exists, and the two limits are equal. Proof: From the F{\o}lner property, we see that for any ${A}$ and any ${\varepsilon>0}$, the averages ${\mathop{\bf E}_{a \in \Phi_n} f_a}$ and ${\mathop{\bf E}_{a \in A+\Phi_n} f_a}$ differ by at most ${\varepsilon}$ in norm if ${n}$ is sufficiently large depending on ${A}$, ${\varepsilon}$ (and the ${f_a}$). On the other hand, by the existence of the limit ${\lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} f_a}$, the averages ${\mathop{\bf E}_{a \in A} f_a}$ and ${\mathop{\bf E}_{a \in A + \Phi_n} f_a}$ differ by at most ${\varepsilon}$ in norm if ${A}$ is sufficiently large depending on ${\varepsilon}$ (regardless of how large ${n}$ is). The claim follows. $\Box$ It turns out that this approach can also be used as an alternate way to construct the GowersHost-Kra seminorms in ergodic theory, which has the feature that it does not explicitly require any amenability on the group ${G}$ (or separability on the underlying measure space), though, as pointed out to me in comments, even uncountable abelian groups are amenable in the sense of possessing an invariant mean, even if they do not have a F{\o}lner sequence. Given an arbitrary additive group ${G}$, define a ${G}$-system ${({\mathrm X}, T)}$ to be a probability space ${{\mathrm X} = (X, {\mathcal X}, \mu)}$ (not necessarily separable or standard Borel), together with a collection ${T^g: X \rightarrow X}$ of invertible, measure-preserving maps, such that ${T^0}$ is the identity and ${T^g T^h = T^{g+h}}$ (modulo null sets) for all ${g,h \in G}$. This then gives isomorphisms ${T^g: L^p({\mathrm X}) \rightarrow L^p({\mathrm X})}$ for ${1 \leq p \leq \infty}$ by setting ${T^g f(x) := f(T^{-g} x)}$. From the above abstract ergodic theorem, we see that $\displaystyle {\mathbf E}( f \| {\mathcal X}^G ) = \lim_{A \rightarrow G} \mathop{\bf E}_{a \in A} T^g f$ in the strong topology of ${L^2({\mathrm X})}$ for any ${f \in L^2({\mathrm X})}$, where ${{\mathcal X}^G}$ is the collection of measurable sets ${E}$ that are essentially ${G}$-invariant in the sense that ${T^g E = E}$ modulo null sets for all ${g \in G}$, and ${{\mathbf E}(f\|{\mathcal X}^G)}$ is the conditional expectation of ${f}$ with respect to ${{\mathcal X}^G}$. In a similar spirit, we have Theorem 4 (Convergence of Gowers-Host-Kra seminorms) Let ${({\mathrm X},T)}$ be a ${G}$-system for some additive group ${G}$. Let ${d}$ be a natural number, and for every ${\omega \in\{0,1\}^d}$, let ${f_\omega \in L^{2^d}({\mathrm X})}$, which for simplicity we take to be real-valued. Then the expression $\displaystyle \langle (f_\omega)_{\omega \in \{0,1\}^d} \rangle_{U^d({\mathrm X})} := \lim_{A_1,\dots,A_d \rightarrow G}$ $\displaystyle \mathop{\bf E}_{h_1 \in A_1-A_1,\dots,h_d \in A_d-A_d} \int_X \prod_{\omega \in \{0,1\}^d} T^{\omega_1 h_1 + \dots + \omega_d h_d} f_\omega\ d\mu$ converges, where we write ${\omega = (\omega_1,\dots,\omega_d)}$, and we are using the product direct set on ${{\mathcal F}^d}$ to define the convergence ${A_1,\dots,A_d \rightarrow G}$. In particular, for ${f \in L^{2^d}({\mathrm X})}$, the limit $\displaystyle \\| f \\|_{U^d({\mathrm X})}^{2^d} = \lim_{A_1,\dots,A_d \rightarrow G}$ $\displaystyle \mathop{\bf E}_{h_1 \in A_1-A_1,\dots,h_d \in A_d-A_d} \int_X \prod_{\omega \in \{0,1\}^d} T^{\omega_1 h_1 + \dots + \omega_d h_d} f\ d\mu$ converges. We prove this theorem below the fold. It implies a number of other known descriptions of the Gowers-Host-Kra seminorms ${\\|f\\|_{U^d({\mathrm X})}}$, for instance that $\displaystyle \\| f \\|_{U^d({\mathrm X})}^{2^d} = \lim_{A \rightarrow G} \mathop{\bf E}_{h \in A-A} \\| f T^h f \\|_{U^{d-1}({\mathrm X})}^{2^{d-1}}$ for ${d > 1}$, while from the ergodic theorem we have $\displaystyle \\| f \\|_{U^1({\mathrm X})} = \\| {\mathbf E}( f \| {\mathcal X}^G ) \\|_{L^2({\mathrm X})}.$ This definition also manifestly demonstrates the cube symmetries of the Host-Kra measures ${\mu^{[d]}}$ on ${X^{\{0,1\}^d}}$, defined via duality by requiring that $\displaystyle \langle (f_\omega)_{\omega \in \{0,1\}^d} \rangle_{U^d({\mathrm X})} = \int_{X^{\{0,1\}^d}} \bigotimes_{\omega \in \{0,1\}^d} f_\omega\ d\mu^{[d]}.$ In a subsequent blog post I hope to present a more detailed study of the ${U^2}$ norm and its relationship with eigenfunctions and the Kronecker factor, without assuming any amenability on ${G}$ or any separability or topological structure on ${{\mathrm X}}$. The 2014 Fields medallists have just been announced as (in alphabetical order of surname) Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani (see also these nice video profiles for the winners, which is a new initiative of the IMU and the Simons foundation). This time four years ago, I wrote a blog post discussing one result from each of the 2010 medallists; I thought I would try to repeat the exercise here, although the work of the medallists this time around is a little bit further away from my own direct area of expertise than last time, and so my discussion will unfortunately be a bit superficial (and possibly not completely accurate) in places. As before, I am picking these results based on my own idiosyncratic tastes, and they should not be viewed as necessarily being the “best” work of these medallists. (See also the press releases for Avila, Bhargava, Hairer, and Mirzakhani.) Artur Avila works in dynamical systems and in the study of Schrödinger operators. The work of Avila that I am most familiar with is his solution with Svetlana Jitormiskaya of the ten martini problem of Kac, the solution to which (according to Barry Simon) he offered ten martinis for, hence the name. (The problem had also been previously posed in the work of Azbel and of Hofstadter.) The problem involves perhaps the simplest example of a Schrödinger operator with non-trivial spectral properties, namely the almost Mathieu operator ${H^{\lambda,\alpha}_\omega: \ell^2({\bf Z}) \rightarrow \ell^2({\bf Z})}$ defined for parameters ${\alpha,\omega \in {\bf R}/{\bf Z}}$ and ${\lambda>0}$ by a discrete one-dimensional Schrödinger operator with cosine potential: $\displaystyle (H^{\lambda,\alpha}_\omega u)_n := u_{n+1} + u_{n-1} + 2\lambda (\cos 2\pi(\theta+n\alpha)) u_n.$ This is a bounded self-adjoint operator and thus has a spectrum ${\sigma( H^{\lambda,\alpha}_\omega )}$ that is a compact subset of the real line; it arises in a number of physical contexts, most notably in the theory of the integer quantum Hall effect, though I will not discuss these applications here. Remarkably, the structure of this spectrum depends crucially on the Diophantine properties of the frequency ${\alpha}$. For instance, if ${\alpha = p/q}$ is a rational number, then the operator is periodic with period ${q}$, and then basic (discrete) Floquet theory tells us that the spectrum is simply the union of ${q}$ (possibly touching) intervals. But for irrational ${\alpha}$ (in which case the spectrum is independent of the phase ${\theta}$), the situation is much more fractal in nature, for instance in the critical case ${\lambda=1}$ the spectrum (as a function of ${\alpha}$) gives rise to the Hofstadter butterfly. The “ten martini problem” asserts that for every irrational ${\alpha}$ and every choice of coupling constant ${\lambda > 0}$, the spectrum is homeomorphic to a Cantor set. Prior to the work of Avila and Jitormiskaya, there were a number of partial results on this problem, notably the result of Puig establishing Cantor spectrum for a full measure set of parameters ${(\lambda,\alpha)}$, as well as results requiring a perturbative hypothesis, such as ${\lambda}$ being very small or very large. The result was also already known for ${\alpha}$ being either very close to rational (i.e. a Liouville number) or very far from rational (a Diophantine number), although the analyses for these two cases failed to meet in the middle, leaving some cases untreated. The argument uses a wide variety of existing techniques, both perturbative and non-perturbative, to attack this problem, as well as an amusing argument by contradiction: they assume (in certain regimes) that the spectrum fails to be a Cantor set, and use this hypothesis to obtain additional Lipschitz control on the spectrum (as a function of the frequency ${\alpha}$), which they can then use (after much effort) to improve existing arguments and conclude that the spectrum was in fact Cantor after all! Manjul Bhargava produces amazingly beautiful mathematics, though most of it is outside of my own area of expertise. One part of his work that touches on an area of my own interest (namely, random matrix theory) is his ongoing work with many co-authors on modeling (both conjecturally and rigorously) the statistics of various key number-theoretic features of elliptic curves (such as their rank, their Selmer group, or their Tate-Shafarevich groups). For instance, with Kane, Lenstra, Poonen, and Rains, Manjul has proposed a very general random matrix model that predicts all of these statistics (for instance, predicting that the ${p}$-component of the Tate-Shafarevich group is distributed like the cokernel of a certain random ${p}$-adic matrix, very much in the spirit of the Cohen-Lenstra heuristics discussed in this previous post). But what is even more impressive is that Manjul and his coauthors have been able to verify several non-trivial fragments of this model (e.g. showing that certain moments have the predicted asymptotics), giving for the first time non-trivial upper and lower bounds for various statistics, for instance obtaining lower bounds on how often an elliptic curve has rank ${0}$ or rank ${1}$, leading most recently (in combination with existing work of Gross-Zagier and of Kolyvagin, among others) to his amazing result with Skinner and Zhang that at least ${66\%}$ of all elliptic curves over ${{\bf Q}}$ (ordered by height) obey the Birch and Swinnerton-Dyer conjecture. Previously it was not even known that a positive proportion of curves obeyed the conjecture. This is still a fair ways from resolving the conjecture fully (in particular, the situation with the presumably small number of curves of rank ${2}$ and higher is still very poorly understood, and the theory of Gross-Zagier and Kolyvagin that this work relies on, which was initially only available for ${{\bf Q}}$, has only been extended to totally real number fields thus far, by the work of Zhang), but it certainly does provide hope that the conjecture could be within reach in a statistical sense at least. Martin Hairer works in at the interface between probability and partial differential equations, and in particular in the theory of stochastic differential equations (SDEs). The result of his that is closest to my own interests is his remarkable demonstration with Jonathan Mattingly of unique invariant measure for the two-dimensional stochastically forced Navier-Stokes equation $\displaystyle \partial_t u + (u \cdot \nabla u) = \nu \Delta u - \nabla p + \xi$ $\displaystyle \nabla \cdot u = 0$ on the two-torus ${({\bf R}/{\bf Z})^2}$, where ${\xi}$ is a Gaussian field that forces a fixed set of frequencies. It is expected that for any reasonable choice of initial data, the solution to this equation should asymptotically be distributed according to Kolmogorov’s power law, as discussed in this previous post. This is still far from established rigorously (although there are some results in this direction for dyadic models, see e.g. this paper of Cheskidov, Shvydkoy, and Friedlander). However, Hairer and Mattingly were able to show that there was a unique probability distribution to almost every initial data would converge to asymptotically; by the ergodic theorem, this is equivalent to demonstrating the existence and uniqueness of an invariant measure for the flow. Existence can be established using standard methods, but uniqueness is much more difficult. One of the standard routes to uniqueness is to establish a “strong Feller property” that enforces some continuity on the transition operators; among other things, this would mean that two ergodic probability measures with intersecting supports would in fact have a non-trivial common component, contradicting the ergodic theorem (which forces different ergodic measures to be mutually singular). Since all ergodic measures for Navier-Stokes can be seen to contain the origin in their support, this would give uniqueness. Unfortunately, the strong Feller property is unlikely to hold in the infinite-dimensional phase space for Navier-Stokes; but Hairer and Mattingly develop a clean abstract substitute for this property, which they call the asymptotic strong Feller property, which is again a regularity property on the transition operator; this in turn is then demonstrated by a careful application of Malliavin calculus. Maryam Mirzakhani has mostly focused on the geometry and dynamics of Teichmuller-type moduli spaces, such as the moduli space of Riemann surfaces with a fixed genus and a fixed number of cusps (or with a fixed number of boundaries that are geodesics of a prescribed length). These spaces have an incredibly rich structure, ranging from geometric structure (such as the Kahler geometry given by the Weil-Petersson metric), to dynamical structure (through the action of the mapping class group on this and related spaces), to algebraic structure (viewing these spaces as algebraic varieties), and are thus connected to many other objects of interest in geometry and dynamics. For instance, by developing a new recursive formula for the Weil-Petersson volume of this space, Mirzakhani was able to asymptotically count the number of simple prime geodesics of length up to some threshold ${L}$ in a hyperbolic surface (or more precisely, she obtained asymptotics for the number of such geodesics in a given orbit of the mapping class group); the answer turns out to be polynomial in ${L}$, in contrast to the much larger class of non-simple prime geodesics, whose asymptotics are exponential in ${L}$ (the “prime number theorem for geodesics”, developed in a classic series of works by Delsart, Huber, Selberg, and Margulis); she also used this formula to establish a new proof of a conjecture of Witten on intersection numbers that was first proven by Kontsevich. More recently, in two lengthy papers with Eskin and with Eskin-Mohammadi, Mirzakhani established rigidity theorems for the action of ${SL_2({\bf R})}$ on such moduli spaces that are close analogues of Ratner’s celebrated rigidity theorems for unipotently generated groups (discussed in this previous blog post). Ratner’s theorems are already notoriously difficult to prove, and rely very much on the polynomial stability properties of unipotent flows; in this even more complicated setting, the unipotent flows are no longer tractable, and Mirzakhani instead uses a recent “exponential drift” method of Benoist and Quint as a substitute. Ratner’s theorems are incredibly useful for all sorts of problems connected to homogeneous dynamics, and the analogous theorems established by Mirzakhani, Eskin, and Mohammadi have a similarly broad range of applications, for instance in counting periodic billiard trajectories in rational polygons. As laid out in the foundational work of Kolmogorov, a classical probability space (or probability space for short) is a triplet ${(X, {\mathcal X}, \mu)}$, where ${X}$ is a set, ${{\mathcal X}}$ is a ${\sigma}$-algebra of subsets of ${X}$, and ${\mu: {\mathcal X} \rightarrow [0,1]}$ is a countably additive probability measure on ${{\mathcal X}}$. Given such a space, one can form a number of interesting function spaces, including • the (real) Hilbert space ${L^2(X, {\mathcal X}, \mu)}$ of square-integrable functions ${f: X \rightarrow {\bf R}}$, modulo ${\mu}$-almost everywhere equivalence, and with the positive definite inner product ${\langle f, g\rangle_{L^2(X, {\mathcal X}, \mu)} := \int_X f g\ d\mu}$; and • the unital commutative Banach algebra ${L^\infty(X, {\mathcal X}, \mu)}$ of essentially bounded functions ${f: X \rightarrow {\bf R}}$, modulo ${\mu}$-almost everywhere equivalence, with ${\\|f\\|_{L^\infty(X, {\mathcal X}, \mu)}}$ defined as the essential supremum of ${\|f\|}$. There is also a trace ${\tau = \tau_\mu: L^\infty(X, {\mathcal X}, \mu) \rightarrow {\bf C}}$ on ${L^\infty}$ defined by integration: ${\tau(f) := \int_X f\ d\mu}$. One can form the category ${\mathbf{Prb}}$ of classical probability spaces, by defining a morphism ${\phi: (X, {\mathcal X}, \mu) \rightarrow (Y, {\mathcal Y}, \nu)}$ between probability spaces to be a function ${\phi: X \rightarrow Y}$ which is measurable (thus ${\phi^{-1}(E) \in {\mathcal X}}$ for all ${E \in {\mathcal Y}}$) and measure-preserving (thus ${\mu(\phi^{-1}(E)) = \nu(E)}$ for all ${E \in {\mathcal Y}}$). Let us now abstract the algebraic features of these spaces as follows; for want of a better name, I will refer to this abstraction as an algebraic probability space, and is very similar to the non-commutative probability spaces studied in this previous post, except that these spaces are now commutative (and real). Definition 1 An algebraic probability space is a pair ${({\mathcal A}, \tau)}$ where • ${{\mathcal A}}$ is a unital commutative real algebra; • ${\tau: {\mathcal A} \rightarrow {\bf R}}$ is a homomorphism such that ${\tau(1)=1}$ and ${\tau( f^2 ) \geq 0}$ for all ${f \in {\mathcal A}}$; • Every element ${f}$ of ${{\mathcal A}}$ is bounded in the sense that ${\sup_{k \geq 1} \tau( f^{2k} )^{1/2k} < \infty}$. (Technically, this isn’t an algebraic property, but I need it for technical reasons.) A morphism ${\phi: ({\mathcal A}_1, \tau_1) \rightarrow ({\mathcal A}_2, \tau_2)}$ is a homomorphism ${\phi^: {\mathcal A}_2 \rightarrow {\mathcal A}_1}$ which is trace-preserving, in the sense that ${\tau_1(\phi^(f)) = \tau_2(f)}$ for all ${f \in {\mathcal A}_2}$. For want of a better name, I’ll denote the category of algebraic probability spaces as ${\mathbf{AlgPrb}}$. One can view this category as the opposite category to that of (a subcategory of) the category of tracial commutative real algebras. One could emphasise this opposite nature by denoting the algebraic probability space as ${({\mathcal A}, \tau)^{op}}$ rather than ${({\mathcal A},\tau)}$; another suggestive (but slightly inaccurate) notation, inspired by the language of schemes, would be ${\hbox{Spec}({\mathcal A},\tau)}$ rather than ${({\mathcal A},\tau)}$. However, we will not adopt these conventions here, and refer to algebraic probability spaces just by the pair ${({\mathcal A},\tau)}$. By the previous discussion, we have a covariant functor ${F: \textbf{Prb} \rightarrow \textbf{AlgPrb}}$ that takes a classical probability space ${(X, {\mathcal X}, \mu)}$ to its algebraic counterpart ${(L^\infty(X, {\mathcal X},\mu), \tau_\mu)}$, with a morphism ${\phi: (X, {\mathcal X}, \mu) \rightarrow (Y, {\mathcal Y}, \nu)}$ of classical probability spaces mapping to a morphism ${F(\phi): (L^\infty(X, {\mathcal X},\mu), \tau_\mu) \rightarrow (L^\infty(Y, {\mathcal Y},\nu), \tau_\nu)}$ of the corresponding algebraic probability spaces by the formula $\displaystyle F(\phi)^* f := f \circ \phi$ for ${f \in L^\infty(Y, {\mathcal Y}, \nu)}$. One easily verifies that this is a functor. In this post I would like to describe a functor ${G: \textbf{AlgPrb} \rightarrow \textbf{Prb}}$ which partially inverts ${F}$ (up to natural isomorphism), that is to say a recipe for starting with an algebraic probability space ${({\mathcal A}, \tau)}$ and producing a classical probability space ${(X, {\mathcal X}, \mu)}$. This recipe is not new – it is basically the (commutative) Gelfand-Naimark-Segal construction (discussed in this previous post) combined with the Loomis-Sikorski theorem (discussed in this previous post). However, I wanted to put the construction in a single location for sake of reference. I also wanted to make the point that ${F}$ and ${G}$ are not complete inverses; there is a bit of information in the algebraic probability space (e.g. topological information) which is lost when passing back to the classical probability space. In some future posts, I would like to develop some ergodic theory using the algebraic foundations of probability theory rather than the classical foundations; this turns out to be convenient in the ergodic theory arising from nonstandard analysis (such as that described in this previous post), in which the groups involved are uncountable and the underlying spaces are not standard Borel spaces. Let us describe how to construct the functor ${G}$, with details postponed to below the fold. 1. Starting with an algebraic probability space ${({\mathcal A}, \tau)}$, form an inner product on ${{\mathcal A}}$ by the formula ${\langle f, g \rangle := \tau(fg)}$, and also form the spectral radius ${\rho(f) :=\lim_{k \rightarrow \infty} \tau(f^{2^k})^{1/2^k}}$. 2. The inner product is clearly positive semi-definite. Quotienting out the null vectors and taking completions, we arrive at a real Hilbert space ${L^2 = L^2({\mathcal A},\tau)}$, to which the trace ${\tau}$ may be extended. 3. Somewhat less obviously, the spectral radius is well-defined and gives a norm on ${{\mathcal A}}$. Taking ${L^2}$ limits of sequences in ${{\mathcal A}}$ of bounded spectral radius gives us a subspace ${L^\infty = L^\infty({\mathcal A},\tau)}$ of ${L^2}$ that has the structure of a real commutative Banach algebra. 4. The idempotents ${1_E}$ of the Banach algebra ${L^\infty}$ may be indexed by elements ${E}$ of an abstract ${\sigma}$-algebra ${{\mathcal B}}$. 5. The Boolean algebra homomorphisms ${\delta_x: {\mathcal B} \rightarrow \{0,1\}}$ (or equivalently, the real algebra homomorphisms ${\iota_x: L^\infty \rightarrow {\bf R}}$) may be indexed by elements ${x}$ of a space ${X}$. 6. Let ${{\mathcal X}}$ denote the ${\sigma}$-algebra on ${X}$ generated by the basic sets ${\overline{E} := \{ x \in X: \delta_x(E) = 1 \}}$ for every ${E \in {\mathcal B}}$. 7. Let ${{\mathcal N}}$ be the ${\sigma}$-ideal of ${{\mathcal X}}$ generated by the sets ${\bigcap_n \overline{E_n}}$, where ${E_n \in {\mathcal B}}$ is a sequence with ${\bigcap_n E_n = \emptyset}$. 8. One verifies that ${{\mathcal B}}$ is isomorphic to ${{\mathcal X}/{\mathcal N}}$. Using this isomorphism, the trace ${\tau}$ on ${L^\infty}$ can be used to construct a countably additive measure ${\mu}$ on ${{\mathcal X}}$. The classical probability space ${(X, {\mathcal X}, \mu)}$ is then ${G( {\mathcal A}, \tau )}$, and the abstract spaces ${L^2, L^\infty}$ may now be identified with their concrete counterparts ${L^2(X, {\mathcal X}, \mu)}$, ${L^\infty(X, {\mathcal X}, \mu)}$. 9. Every algebraic probability space morphism ${\phi: ({\mathcal A}_1,\tau_1) \rightarrow ({\mathcal A}_2,\tau_2)}$ generates a classical probability morphism ${G(\phi): (X_1, {\mathcal X}_1, \mu_1) \rightarrow (X_2, {\mathcal X}_2, \mu_2)}$ via the formula $\displaystyle \delta_{G(\phi)(x_1)}( E_2 ) = \delta_{x_1}( \phi^(E_2) )$ using a pullback operation ${\phi^}$ on the abstract ${\sigma}$-algebras ${{\mathcal B}_1, {\mathcal B}_2}$ that can be defined by density. Remark 1 The classical probability space ${X}$ constructed by the functor ${G}$ has some additional structure; namely ${X}$ is a ${\sigma}$-Stone space (a Stone space with the property that the closure of any countable union of clopen sets is clopen), ${{\mathcal X}}$ is the Baire ${\sigma}$-algebra (generated by the clopen sets), and the null sets are the meager sets. However, we will not use this additional structure here. The partial inversion relationship between the functors ${F: \textbf{Prb} \rightarrow \textbf{AlgPrb}}$ and ${G: \textbf{AlgPrb} \rightarrow \textbf{Prb}}$ is given by the following assertion: 1. There is a natural transformation from ${F \circ G: \textbf{AlgPrb} \rightarrow \textbf{AlgPrb}}$ to the identity functor ${I: \textbf{AlgPrb} \rightarrow \textbf{AlgPrb}}$. More informally: if one starts with an algebraic probability space ${({\mathcal A},\tau)}$ and converts it back into a classical probability space ${(X, {\mathcal X}, \mu)}$, then there is a trace-preserving algebra homomorphism of ${{\mathcal A}}$ to ${L^\infty( X, {\mathcal X}, \mu )}$, which respects morphisms of the algebraic probability space. While this relationship is far weaker than an equivalence of categories (which would require that ${F \circ G}$ and ${G \circ F}$ are both natural isomorphisms), it is still good enough to allow many ergodic theory problems formulated using classical probability spaces to be reformulated instead as an equivalent problem in algebraic probability spaces. Remark 2 The opposite composition ${G \circ F: \textbf{Prb} \rightarrow \textbf{Prb}}$ is a little odd: it takes an arbitrary probability space ${(X, {\mathcal X}, \mu)}$ and returns a more complicated probability space ${(X', {\mathcal X}', \mu')}$, with ${X'}$ being the space of homomorphisms ${\iota_x: L^\infty(X, {\mathcal X}, \mu) \rightarrow {\bf R}}$. while there is “morally” an embedding of ${X}$ into ${X'}$ using the evaluation map, this map does not exist in general because points in ${X}$ may well have zero measure. However, if one takes a “pointless” approach and focuses just on the measure algebras ${({\mathcal X}, \mu)}$, ${({\mathcal X}', \mu')}$, then these algebras become naturally isomorphic after quotienting out by null sets. Remark 3 An algebraic probability space captures a bit more structure than a classical probability space, because ${{\mathcal A}}$ may be identified with a proper subset of ${L^\infty}$ that describes the “regular” functions (or random variables) of the space. For instance, starting with the unit circle ${{\bf R}/{\bf Z}}$ (with the usual Haar measure and the usual trace ${\tau(f) = \int_{{\bf R}/{\bf Z}} f}$), any unital subalgebra ${{\mathcal A}}$ of ${L^\infty({\bf R}/{\bf Z})}$ that is dense in ${L^2({\bf R}/{\bf Z})}$ will generate the same classical probability space ${G( {\mathcal A}, \tau )}$ on applying the functor ${G}$, namely one will get the space ${({\bf R}/{\bf Z})'}$ of homomorphisms from ${L^\infty({\bf R}/{\bf Z})}$ to ${{\bf R}}$ (with the measure induced from ${\tau}$). Thus for instance ${{\mathcal A}}$ could be the continuous functions ${C( {\bf R}/{\bf Z} )}$, the Wiener algebra ${A({\bf R}/{\bf Z})}$ or the full space ${L^\infty({\bf R}/{\bf Z})}$, but the classical space ${G( {\mathcal A}, \tau )}$ will be unable to distinguish these spaces from each other. In particular, the functor ${F \circ G}$ loses information (roughly speaking, this functor takes an algebraic probability space and completes it to a von Neumann algebra, but then forgets exactly what algebra was initially used to create this completion). In ergodic theory, this sort of “extra structure” is traditionally encoded in topological terms, by assuming that the underlying probability space ${X}$ has a nice topological structure (e.g. a standard Borel space); however, with the algebraic perspective one has the freedom to have non-topological notions of extra structure, by choosing ${{\mathcal A}}$ to be something other than an algebra ${C(X)}$ of continuous functions on a topological space. I hope to discuss one such example of extra structure (coming from the Gowers-Host-Kra theory of uniformity seminorms) in a later blog post (this generalises the example of the Wiener algebra given previously, which is encoding “Fourier structure”). A small example of how one could use the functors ${F, G}$ is as follows. Suppose one has a classical probability space ${(X, {\mathcal X}, \mu)}$ with a measure-preserving action of an uncountable group ${\Gamma}$, which is only defined (and an action) up to almost everywhere equivalence; thus for instance for any set ${E}$ and any ${g, h \in \Gamma}$, ${T^{gh} E}$ and ${T^g T^h E}$ might not be exactly equal, but only equal up to a null set. For similar reasons, an element ${E}$ of the invariant factor ${{\mathcal X}^\Gamma}$ might not be exactly invariant with respect to ${\Gamma}$, but instead one only has ${T^g E}$ and ${E}$ equal up to null sets for each ${g \in \Gamma}$. One might like to “clean up” the action of ${\Gamma}$ to make it defined everywhere, and a genuine action everywhere, but this is not immediately achievable if ${\Gamma}$ is uncountable, since the union of all the null sets where something bad occurs may cease to be a null set. However, by applying the functor ${F}$, each shift ${T^g: X \rightarrow X}$ defines a morphism ${T^g: L^\infty(X, {\mathcal X}, \mu) \rightarrow L^\infty(X, {\mathcal X}, \mu)}$ on the associated algebraic probability space (i.e. the Koopman operator), and then applying ${G}$, we obtain a shift ${T^g: X' \rightarrow X'}$ on a new classical probability space ${(X', {\mathcal X}', \mu')}$ which now gives a genuine measure-preserving action of ${\Gamma}$, and which is equivalent to the original action from a measure algebra standpoint. The invariant factor ${{\mathcal X}^\Gamma}$ now consists of those sets in ${{\mathcal X}'}$ which are genuinely ${\Gamma}$-invariant, not just up to null sets. (Basically, the classical probability space ${(X', {\mathcal X}', \mu')}$ contains a Boolean algebra ${\overline{\mathcal B}}$ with the property that every measurable set ${A \in {\mathcal X}'}$ is equivalent up to null sets to precisely one set in ${\overline{\mathcal B}}$, allowing for a canonical “retraction” onto ${\overline{\mathcal B}}$ that eliminates all null set issues.) More indirectly, the functors ${F, G}$ suggest that one should be able to develop a “pointless” form of ergodic theory, in which the underlying probability spaces are given algebraically rather than classically. I hope to give some more specific examples of this in later posts. There are a number of ways to construct the real numbers ${{\bf R}}$, for instance • as the metric completion of ${{\bf Q}}$ (thus, ${{\bf R}}$ is defined as the set of Cauchy sequences of rationals, modulo Cauchy equivalence); • as the space of Dedekind cuts on the rationals ${{\bf Q}}$; • as the space of quasimorphisms ${\phi: {\bf Z} \rightarrow {\bf Z}}$ on the integers, quotiented by bounded functions. (I believe this construction first appears in this paper of Street, who credits the idea to Schanuel, though the germ of this construction arguably goes all the way back to Eudoxus.) There is also a fourth family of constructions that proceeds via nonstandard analysis, as a special case of what is known as the nonstandard hull construction. (Here I will assume some basic familiarity with nonstandard analysis and ultraproducts, as covered for instance in this previous blog post.) Given an unbounded nonstandard natural number ${N \in {}^* {\bf N} \backslash {\bf N}}$, one can define two external additive subgroups of the nonstandard integers ${{}^* {\bf Z}}$: • The group ${O(N) := \{ n \in {}^* {\bf Z}: \|n\| \leq CN \hbox{ for some } C \in {\bf N} \}}$ of all nonstandard integers of magnitude less than or comparable to ${N}$; and • The group ${o(N) := \{ n \in {}^* {\bf Z}: \|n\| \leq C^{-1} N \hbox{ for all } C \in {\bf N} \}}$ of nonstandard integers of magnitude infinitesimally smaller than ${N}$. The group ${o(N)}$ is a subgroup of ${O(N)}$, so we may form the quotient group ${O(N)/o(N)}$. This space is isomorphic to the reals ${{\bf R}}$, and can in fact be used to construct the reals: Proposition 1 For any coset ${n + o(N)}$ of ${O(N)/o(N)}$, there is a unique real number ${\hbox{st} \frac{n}{N}}$ with the property that ${\frac{n}{N} = \hbox{st} \frac{n}{N} + o(1)}$. The map ${n + o(N) \mapsto \hbox{st} \frac{n}{N}}$ is then an isomorphism between the additive groups ${O(N)/o(N)}$ and ${{\bf R}}$. Proof: Uniqueness is clear. For existence, observe that the set ${\{ x \in {\bf R}: Nx \leq n + o(N) \}}$ is a Dedekind cut, and its supremum can be verified to have the required properties for ${\hbox{st} \frac{n}{N}}$. $\Box$ In a similar vein, we can view the unit interval ${[0,1]}$ in the reals as the quotient $\displaystyle [0,1] \equiv [N] / o(N) \ \ \ \ \ (1)$ where ${[N]}$ is the nonstandard (i.e. internal) set ${\{ n \in {\bf N}: n \leq N \}}$; of course, ${[N]}$ is not a group, so one should interpret ${[N]/o(N)}$ as the image of ${[N]}$ under the quotient map ${{}^* {\bf Z} \rightarrow {}^* {\bf Z} / o(N)}$ (or ${O(N) \rightarrow O(N)/o(N)}$, if one prefers). Or to put it another way, (1) asserts that ${[0,1]}$ is the image of ${[N]}$ with respect to the map ${\pi: n \mapsto \hbox{st} \frac{n}{N}}$. In this post I would like to record a nice measure-theoretic version of the equivalence (1), which essentially appears already in standard texts on Loeb measure (see e.g. this text of Cutland). To describe the results, we must first quickly recall the construction of Loeb measure on ${[N]}$. Given an internal subset ${A}$ of ${[N]}$, we may define the elementary measure ${\mu_0(A)}$ of ${A}$ by the formula $\displaystyle \mu_0(A) := \hbox{st} \frac{\|A\|}{N}.$ This is a finitely additive probability measure on the Boolean algebra of internal subsets of ${[N]}$. We can then construct the Loeb outer measure ${\mu^(A)}$ of any subset ${A \subset [N]}$ in complete analogy with Lebesgue outer measure by the formula $\displaystyle \mu^(A) := \inf \sum_{n=1}^\infty \mu_0(A_n)$ where ${(A_n)_{n=1}^\infty}$ ranges over all sequences of internal subsets of ${[N]}$ that cover ${A}$. We say that a subset ${A}$ of ${[N]}$ is Loeb measurable if, for any (standard) ${\epsilon>0}$, one can find an internal subset ${B}$ of ${[N]}$ which differs from ${A}$ by a set of Loeb outer measure at most ${\epsilon}$, and in that case we define the Loeb measure ${\mu(A)}$ of ${A}$ to be ${\mu^(A)}$. It is a routine matter to show (e.g. using the Carathéodory extension theorem) that the space ${{\mathcal L}}$ of Loeb measurable sets is a ${\sigma}$-algebra, and that ${\mu}$ is a countably additive probability measure on this space that extends the elementary measure ${\mu_0}$. Thus ${[N]}$ now has the structure of a probability space ${([N], {\mathcal L}, \mu)}$. Now, the group ${o(N)}$ acts (Loeb-almost everywhere) on the probability space ${[N]}$ by the addition map, thus ${T^h n := n+h}$ for ${n \in [N]}$ and ${h \in o(N)}$ (excluding a set of Loeb measure zero where ${n+h}$ exits ${[N]}$). This action is clearly seen to be measure-preserving. As such, we can form the invariant factor ${Z^0_{o(N)}([N]) = ([N], {\mathcal L}^{o(N)}, \mu\downharpoonright_{{\mathcal L}^{o(N)}})}$, defined by restricting attention to those Loeb measurable sets ${A \subset [N]}$ with the property that ${T^h A}$ is equal ${\mu}$-almost everywhere to ${A}$ for each ${h \in o(N)}$. The claim is then that this invariant factor is equivalent (up to almost everywhere equivalence) to the unit interval ${[0,1]}$ with Lebesgue measure ${m}$ (and the trivial action of ${o(N)}$), by the same factor map ${\pi: n \mapsto \hbox{st} \frac{n}{N}}$ used in (1). More precisely: Theorem 2 Given a set ${A \in {\mathcal L}^{o(N)}}$, there exists a Lebesgue measurable set ${B \subset [0,1]}$, unique up to ${m}$-a.e. equivalence, such that ${A}$ is ${\mu}$-a.e. equivalent to the set ${\pi^{-1}(B) := \{ n \in [N]: \hbox{st} \frac{n}{N} \in B \}}$. Conversely, if ${B \in [0,1]}$ is Lebesgue measurable, then ${\pi^{-1}(B)}$ is in ${{\mathcal L}^{o(N)}}$, and ${\mu( \pi^{-1}(B) ) = m( B )}$. $\displaystyle [0,1] \equiv Z^0_{o(N)}( [N] )$ of (1). Proof: We first prove the converse. It is clear that ${\pi^{-1}(B)}$ is ${o(N)}$-invariant, so it suffices to show that ${\pi^{-1}(B)}$ is Loeb measurable with Loeb measure ${m(B)}$. This is easily verified when ${B}$ is an elementary set (a finite union of intervals). By countable subadditivity of outer measure, this implies that Loeb outer measure of ${\pi^{-1}(E)}$ is bounded by the Lebesgue outer measure of ${E}$ for any set ${E \subset [0,1]}$; since every Lebesgue measurable set differs from an elementary set by a set of arbitrarily small Lebesgue outer measure, the claim follows. Now we establish the forward claim. Uniqueness is clear from the converse claim, so it suffices to show existence. Let ${A \in {\mathcal L}^{o(N)}}$. Let ${\epsilon>0}$ be an arbitrary standard real number, then we can find an internal set ${A_\epsilon \subset [N]}$ which differs from ${A}$ by a set of Loeb measure at most ${\epsilon}$. As ${A}$ is ${o(N)}$-invariant, we conclude that for every ${h \in o(N)}$, ${A_\epsilon}$ and ${T^h A_\epsilon}$ differ by a set of Loeb measure (and hence elementary measure) at most ${2\epsilon}$. By the (contrapositive of the) underspill principle, there must exist a standard ${\delta>0}$ such that ${A_\epsilon}$ and ${T^h A_\epsilon}$ differ by a set of elementary measure at most ${2\epsilon}$ for all ${\|h\| \leq \delta N}$. If we then define the nonstandard function ${f_\epsilon: [N] \rightarrow {}^ {\bf R}}$ by the formula $\displaystyle f(n) := \hbox{st} \frac{1}{\delta N} \sum_{m \in [N]: m \leq n \leq m+\delta N} 1_{A_\epsilon}(m),$ then from the (nonstandard) triangle inequality we have $\displaystyle \frac{1}{N} \sum_{n \in [N]} \|f(n) - 1_{A_\epsilon}(n)\| \leq 3\epsilon$ (say). On the other hand, ${f}$ has the Lipschitz continuity property $\displaystyle \|f(n)-f(m)\| \leq \frac{2\|n-m\|}{\delta N}$ and so in particular we see that $\displaystyle \hbox{st} f(n) = \tilde f( \hbox{st} \frac{n}{N} )$ for some Lipschitz continuous function ${\tilde f: [0,1] \rightarrow [0,1]}$. If we then let ${E_\epsilon}$ be the set where ${\tilde f \geq 1 - \sqrt{\epsilon}}$, one can check that ${A_\epsilon}$ differs from ${\pi^{-1}(E_\epsilon)}$ by a set of Loeb outer measure ${O(\sqrt{\epsilon})}$, and hence ${A}$ does so also. Sending ${\epsilon}$ to zero, we see (from the converse claim) that ${1_{E_\epsilon}}$ is a Cauchy sequence in ${L^1}$ and thus converges in ${L^1}$ for some Lebesgue measurable ${E}$. The sets ${A_\epsilon}$ then converge in Loeb outer measure to ${\pi^{-1}(E)}$, giving the claim. $\Box$ Thanks to the Lebesgue differentiation theorem, the conditional expectation ${{\bf E}( f \| Z^0_{o(N)}([N]))}$ of a bounded Loeb-measurable function ${f: [N] \rightarrow {\bf R}}$ can be expressed (as a function on ${[0,1]}$, defined ${m}$-a.e.) as $\displaystyle {\bf E}( f \| Z^0_{o(N)}([N]))(x) := \lim_{\epsilon \rightarrow 0} \frac{1}{2\epsilon} \int_{[x-\epsilon N,x+\epsilon N]} f\ d\mu.$ By the abstract ergodic theorem from the previous post, one can also view this conditional expectation as the element in the closed convex hull of the shifts ${T^h f}$, ${h = o(N)}$ of minimal ${L^2}$ norm. In particular, we obtain a form of the von Neumann ergodic theorem in this context: the averages ${\frac{1}{H} \sum_{h=1}^H T^h f}$ for ${H=O(N)}$ converge (as a net, rather than a sequence) in ${L^2}$ to ${{\bf E}( f \| Z^0_{o(N)}([N]))}$. If ${f: [N] \rightarrow [-1,1]}$ is (the standard part of) an internal function, that is to say the ultralimit of a sequence ${f_n: [N_n] \rightarrow [-1,1]}$ of finitary bounded functions, one can view the measurable function ${F := {\bf E}( f \| Z^0_{o(N)}([N]))}$ as a limit of the ${f_n}$ that is analogous to the “graphons” that emerge as limits of graphs (see e.g. the recent text of Lovasz on graph limits). Indeed, the measurable function ${F: [0,1] \rightarrow [-1,1]}$ is related to the discrete functions ${f_n: [N_n] \rightarrow [-1,1]}$ by the formula $\displaystyle \int_a^b F(x)\ dx = \hbox{st} \lim_{n \rightarrow p} \frac{1}{N_n} \sum_{a N_n \leq m \leq b N_n} f_n(m)$ for all ${0 \leq a < b \leq 1}$, where ${p}$ is the nonprincipal ultrafilter used to define the nonstandard universe. In particular, from the Arzela-Ascoli diagonalisation argument there is a subsequence ${n_j}$ such that $\displaystyle \int_a^b F(x)\ dx = \lim_{j \rightarrow \infty} \frac{1}{N_{n_j}} \sum_{a N_{n_j} \leq m \leq b N_{n_j}} f_n(m),$ thus ${F}$ is the asymptotic density function of the ${f_n}$. For instance, if ${f_n}$ is the indicator function of a randomly chosen subset of ${[N_n]}$, then the asymptotic density function would equal ${1/2}$ (almost everywhere, at least). I’m continuing to look into understanding the ergodic theory of ${o(N)}$ actions, as I believe this may allow one to apply ergodic theory methods to the “single-scale” or “non-asymptotic” setting (in which one averages only over scales comparable to a large parameter ${N}$, rather than the traditional asymptotic approach of letting the scale go to infinity). I’m planning some further posts in this direction, though this is still a work in progress. The von Neumann ergodic theorem (the Hilbert space version of the mean ergodic theorem) asserts that if ${U: H \rightarrow H}$ is a unitary operator on a Hilbert space ${H}$, and ${v \in H}$ is a vector in that Hilbert space, then one has $\displaystyle \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{n=1}^N U^n v = \pi_{H^U} v$ in the strong topology, where ${H^U := \{ w \in H: Uw = w \}}$ is the ${U}$-invariant subspace of ${H}$, and ${\pi_{H^U}}$ is the orthogonal projection to ${H^U}$. (See e.g. these previous lecture notes for a proof.) The same proof extends to more general amenable groups: if ${G}$ is a countable amenable group acting on a Hilbert space ${H}$ by unitary transformations ${g: H \rightarrow H}$, and ${v \in H}$ is a vector in that Hilbert space, then one has $\displaystyle \lim_{N \rightarrow \infty} \frac{1}{\|\Phi_N\|} \sum_{g \in \Phi_N} gv = \pi_{H^G} v \ \ \ \ \ (1)$ for any Folner sequence ${\Phi_N}$ of ${G}$, where ${H^G := \{ w \in H: gw = w \hbox{ for all }g \in G \}}$ is the ${G}$-invariant subspace. Thus one can interpret ${\pi_{H^G} v}$ as a certain average of elements of the orbit ${Gv := \{ gv: g \in G \}}$ of ${v}$. I recently discovered that there is a simple variant of this ergodic theorem that holds even when the group ${G}$ is not amenable (or not discrete), using a more abstract notion of averaging: Theorem 1 (Abstract ergodic theorem) Let ${G}$ be an arbitrary group acting unitarily on a Hilbert space ${H}$, and let ${v}$ be a vector in ${H}$. Then ${\pi_{H^G} v}$ is the element in the closed convex hull of ${Gv := \{ gv: g \in G \}}$ of minimal norm, and is also the unique element of ${H^G}$ in this closed convex hull. Proof: As the closed convex hull of ${Gv}$ is closed, convex, and non-empty in a Hilbert space, it is a classical fact (see e.g. Proposition 1 of this previous post) that it has a unique element ${F}$ of minimal norm. If ${T_g F \neq F}$ for some ${g}$, then the midpoint of ${T_g F}$ and ${F}$ would be in the closed convex hull and be of smaller norm, a contradiction; thus ${F}$ is ${G}$-invariant. To finish the first claim, it suffices to show that ${v-F}$ is orthogonal to every element ${h}$ of ${H^G}$. But if this were not the case for some such ${h}$, we would have ${\langle T_g v - F, h \rangle = \langle v-F,h\rangle \neq 0}$ for all ${g \in G}$, and thus on taking convex hulls ${\langle F-F,h\rangle = \langle f-F,f\rangle \neq 0}$, a contradiction. Finally, since ${T_g v - F}$ is orthogonal to ${H^G}$, the same is true for ${F'-F}$ for any ${F'}$ in the closed convex hull of ${Gv}$, and this gives the second claim. $\Box$ This result is due to Alaoglu and Birkhoff. It implies the amenable ergodic theorem (1); indeed, given any ${\epsilon>0}$, Theorem 1 implies that there is a finite convex combination ${v_\epsilon}$ of shifts ${gv}$ of ${v}$ which lies within ${\epsilon}$ (in the ${H}$ norm) to ${\pi_{H^G} v}$. By the triangle inequality, all the averages ${\frac{1}{\|\Phi_N\|} \sum_{g \in \Phi_N} gv_\epsilon}$ also lie within ${\epsilon}$ of ${\pi_{H^G} v}$, but by the Folner property this implies that the averages ${\frac{1}{\|\Phi_N\|} \sum_{g \in \Phi_N} gv}$ are eventually within ${2\epsilon}$ (say) of ${\pi_{H^G} v}$, giving the claim. It turns out to be possible to use Theorem 1 as a substitute for the mean ergodic theorem in a number of contexts, thus removing the need for an amenability hypothesis. Here is a basic application: Corollary 2 (Relative orthogonality) Let ${G}$ be a group acting unitarily on a Hilbert space ${H}$, and let ${V}$ be a ${G}$-invariant subspace of ${H}$. Then ${V}$ and ${H^G}$ are relatively orthogonal over their common subspace ${V^G}$, that is to say the restrictions of ${V}$ and ${H^G}$ to the orthogonal complement of ${V^G}$ are orthogonal to each other. Proof: By Theorem 1, we have ${\pi_{H^G} v = \pi_{V^G} v}$ for all ${v \in V}$, and the claim follows. (Thanks to Gergely Harcos for this short argument.) $\Box$ Now we give a more advanced application of Theorem 1, to establish some “Mackey theory” over arbitrary groups ${G}$. Define a ${G}$-system ${(X, {\mathcal X}, \mu, (T_g)_{g \in G})}$ to be a probability space ${X = (X, {\mathcal X}, \mu)}$ together with a measure-preserving action ${(T_g)_{g \in G}}$ of ${G}$ on ${X}$; this gives an action of ${G}$ on ${L^2(X) = L^2(X,{\mathcal X},\mu)}$, which by abuse of notation we also call ${T_g}$: $\displaystyle T_g f := f \circ T_{g^{-1}}.$ (In this post we follow the usual convention of defining the ${L^p}$ spaces by quotienting out by almost everywhere equivalence.) We say that a ${G}$-system is ergodic if ${L^2(X)^G}$ consists only of the constants. (A technical point: the theory becomes slightly cleaner if we interpret our measure spaces abstractly (or “pointlessly“), removing the underlying space ${X}$ and quotienting ${{\mathcal X}}$ by the ${\sigma}$-ideal of null sets, and considering maps such as ${T_g}$ only on this quotient ${\sigma}$-algebra (or on the associated von Neumann algebra ${L^\infty(X)}$ or Hilbert space ${L^2(X)}$). However, we will stick with the more traditional setting of classical probability spaces here to keep the notation familiar, but with the understanding that many of the statements below should be understood modulo null sets.) A factor ${Y = (Y, {\mathcal Y}, \nu, (S_g)_{g \in G})}$ of a ${G}$-system ${X = (X,{\mathcal X},\mu, (T_g)_{g \in G})}$ is another ${G}$-system together with a factor map ${\pi: X \rightarrow Y}$ which commutes with the ${G}$-action (thus ${T_g \pi = \pi S_g}$ for all ${g \in G}$) and respects the measure in the sense that ${\mu(\pi^{-1}(E)) = \nu(E)}$ for all ${E \in {\mathcal Y}}$. For instance, the ${G}$-invariant factor ${Z^0_G(X) := (X, {\mathcal X}^G, \mu\downharpoonright_{{\mathcal X}^G}, (T_g)_{g \in G})}$, formed by restricting ${X}$ to the invariant algebra ${{\mathcal X}^G := \{ E \in {\mathcal X}: T_g E = E \hbox{ a.e. for all } g \in G \}}$, is a factor of ${X}$. (This factor is the first factor in an important hierachy, the next element of which is the Kronecker factor ${Z^1_G(X)}$, but we will not discuss higher elements of this hierarchy further here.) If ${Y}$ is a factor of ${X}$, we refer to ${X}$ as an extension of ${Y}$. From Corollary 2 we have Corollary 3 (Relative independence) Let ${X}$ be a ${G}$-system for a group ${G}$, and let ${Y}$ be a factor of ${X}$. Then ${Y}$ and ${Z^0_G(X)}$ are relatively independent over their common factor ${Z^0_G(Y)}$, in the sense that the spaces ${L^2(Y)}$ and ${L^2(Z^0_G(X))}$ are relatively orthogonal over ${L^2(Z^0_G(Y))}$ when all these spaces are embedded into ${L^2(X)}$. This has a simple consequence regarding the product ${X \times Y = (X \times Y, {\mathcal X} \times {\mathcal Y}, \mu \times \nu, (T_g \oplus S_g)_{g \in G})}$ of two ${G}$-systems ${X = (X, {\mathcal X}, \mu, (T_g)_{g \in G})}$ and ${Y = (Y, {\mathcal Y}, \nu, (S_g)_{g \in G})}$, in the case when the ${Y}$ action is trivial: Lemma 4 If ${X,Y}$ are two ${G}$-systems, with the action of ${G}$ on ${Y}$ trivial, then ${Z^0_G(X \times Y)}$ is isomorphic to ${Z^0_G(X) \times Y}$ in the obvious fashion. This lemma is immediate for countable ${G}$, since for a ${G}$-invariant function ${f}$, one can ensure that ${T_g f = f}$ holds simultaneously for all ${g \in G}$ outside of a null set, but is a little trickier for uncountable ${G}$. Proof: It is clear that ${Z^0_G(X) \times Y}$ is a factor of ${Z^0_G(X \times Y)}$. To obtain the reverse inclusion, suppose that it fails, thus there is a non-zero ${f \in L^2(Z^0_G(X \times Y))}$ which is orthogonal to ${L^2(Z^0_G(X) \times Y)}$. In particular, we have ${fg}$ orthogonal to ${L^2(Z^0_G(X))}$ for any ${g \in L^\infty(Y)}$. Since ${fg}$ lies in ${L^2(Z^0_G(X \times Y))}$, we conclude from Corollary 3 (viewing ${X}$ as a factor of ${X \times Y}$) that ${fg}$ is also orthogonal to ${L^2(X)}$. Since ${g}$ is an arbitrary element of ${L^\infty(Y)}$, we conclude that ${f}$ is orthogonal to ${L^2(X \times Y)}$ and in particular is orthogonal to itself, a contradiction. (Thanks to Gergely Harcos for this argument.) $\Box$ Now we discuss the notion of a group extension. Definition 5 (Group extension) Let ${G}$ be an arbitrary group, let ${Y = (Y, {\mathcal Y}, \nu, (S_g)_{g \in G})}$ be a ${G}$-system, and let ${K}$ be a compact metrisable group. A ${K}$-extension of ${Y}$ is an extension ${X = (X, {\mathcal X}, \mu, (T_g)_{g \in G})}$ whose underlying space is ${X = Y \times K}$ (with ${{\mathcal X}}$ the product of ${{\mathcal Y}}$ and the Borel ${\sigma}$-algebra on ${K}$), the factor map is ${\pi: (y,k) \mapsto y}$, and the shift maps ${T_g}$ are given by $\displaystyle T_g ( y, k ) = (S_g y, \rho_g(y) k )$ where for each ${g \in G}$, ${\rho_g: Y \rightarrow K}$ is a measurable map (known as the cocycle associated to the ${K}$-extension ${X}$). An important special case of a ${K}$-extension arises when the measure ${\mu}$ is the product of ${\nu}$ with the Haar measure ${dk}$ on ${K}$. In this case, ${X}$ also has a ${K}$-action ${k': (y,k) \mapsto (y,k(k')^{-1})}$ that commutes with the ${G}$-action, making ${X}$ a ${G \times K}$-system. More generally, ${\mu}$ could be the product of ${\nu}$ with the Haar measure ${dh}$ of some closed subgroup ${H}$ of ${K}$, with ${\rho_g}$ taking values in ${H}$; then ${X}$ is now a ${G \times H}$ system. In this latter case we will call ${X}$ ${H}$-uniform. If ${X}$ is a ${K}$-extension of ${Y}$ and ${U: Y \rightarrow K}$ is a measurable map, we can define the gauge transform ${X_U}$ of ${X}$ to be the ${K}$-extension of ${Y}$ whose measure ${\mu_U}$ is the pushforward of ${\mu}$ under the map ${(y,k) \mapsto (y, U(y) k)}$, and whose cocycles ${\rho_{g,U}: Y \rightarrow K}$ are given by the formula $\displaystyle \rho_{g,U}(y) := U(gy) \rho_g(y) U(y)^{-1}.$ It is easy to see that ${X_U}$ is a ${K}$-extension that is isomorphic to ${X}$ as a ${K}$-extension of ${Y}$; we will refer to ${X_U}$ and ${X}$ as equivalent systems, and ${\rho_{g,U}}$ as cohomologous to ${\rho_g}$. We then have the following fundamental result of Mackey and of Zimmer: Theorem 6 (Mackey-Zimmer theorem) Let ${G}$ be an arbitrary group, let ${Y}$ be an ergodic ${G}$-system, and let ${K}$ be a compact metrisable group. Then every ergodic ${K}$-extension ${X}$ of ${Y}$ is equivalent to an ${H}$-uniform extension of ${Y}$ for some closed subgroup ${H}$ of ${K}$. This theorem is usually stated for amenable groups ${G}$, but by using Theorem 1 (or more precisely, Corollary 3) the result is in fact also valid for arbitrary groups; we give the proof below the fold. (In the usual formulations of the theorem, ${X}$ and ${Y}$ are also required to be Lebesgue spaces, or at least standard Borel, but again with our abstract approach here, such hypotheses will be unnecessary.) Among other things, this theorem plays an important role in the Furstenberg-Zimmer structural theory of measure-preserving systems (as well as subsequent refinements of this theory by Host and Kra); see this previous blog post for some relevant discussion. One can obtain similar descriptions of non-ergodic extensions via the ergodic decomposition, but the result becomes more complicated to state, and we will not do so here. (This is an extended blog post version of my talk “Ultraproducts as a Bridge Between Discrete and Continuous Analysis” that I gave at the Simons institute for the theory of computing at the workshop “Neo-Classical methods in discrete analysis“. Some of the material here is drawn from previous blog posts, notably “Ultraproducts as a bridge between hard analysis and soft analysis” and “Ultralimit analysis and quantitative algebraic geometry“‘. The text here has substantially more details than the talk; one may wish to skip all of the proofs given here to obtain a closer approximation to the original talk.) Discrete analysis, of course, is primarily interested in the study of discrete (or “finitary”) mathematical objects: integers, rational numbers (which can be viewed as ratios of integers), finite sets, finite graphs, finite or discrete metric spaces, and so forth. However, many powerful tools in mathematics (e.g. ergodic theory, measure theory, topological group theory, algebraic geometry, spectral theory, etc.) work best when applied to continuous (or “infinitary”) mathematical objects: real or complex numbers, manifolds, algebraic varieties, continuous topological or metric spaces, etc. In order to apply results and ideas from continuous mathematics to discrete settings, there are basically two approaches. One is to directly discretise the arguments used in continuous mathematics, which often requires one to keep careful track of all the bounds on various quantities of interest, particularly with regard to various error terms arising from discretisation which would otherwise have been negligible in the continuous setting. The other is to construct continuous objects as limits of sequences of discrete objects of interest, so that results from continuous mathematics may be applied (often as a “black box”) to the continuous limit, which then can be used to deduce consequences for the original discrete objects which are quantitative (though often ineffectively so). The latter approach is the focus of this current talk. The following table gives some examples of a discrete theory and its continuous counterpart, together with a limiting procedure that might be used to pass from the former to the latter: (Discrete) (Continuous) (Limit method) Ramsey theory Topological dynamics Compactness Density Ramsey theory Ergodic theory Furstenberg correspondence principle Graph/hypergraph regularity Measure theory Graph limits Polynomial regularity Linear algebra Ultralimits Structural decompositions Hilbert space geometry Ultralimits Fourier analysis Spectral theory Direct and inverse limits Quantitative algebraic geometry Algebraic geometry Schemes Discrete metric spaces Continuous metric spaces Gromov-Hausdorff limits Approximate group theory Topological group theory Model theory As the above table illustrates, there are a variety of different ways to form a limiting continuous object. Roughly speaking, one can divide limits into three categories: • Topological and metric limits. These notions of limits are commonly used by analysts. Here, one starts with a sequence (or perhaps a net) of objects ${x_n}$ in a common space ${X}$, which one then endows with the structure of a topological space or a metric space, by defining a notion of distance between two points of the space, or a notion of open neighbourhoods or open sets in the space. Provided that the sequence or net is convergent, this produces a limit object ${\lim_{n \rightarrow \infty} x_n}$, which remains in the same space, and is “close” to many of the original objects ${x_n}$ with respect to the given metric or topology. • Categorical limits. These notions of limits are commonly used by algebraists. Here, one starts with a sequence (or more generally, a diagram) of objects ${x_n}$ in a category ${X}$, which are connected to each other by various morphisms. If the ambient category is well-behaved, one can then form the direct limit ${\varinjlim x_n}$ or the inverse limit ${\varprojlim x_n}$ of these objects, which is another object in the same category ${X}$, and is connected to the original objects ${x_n}$ by various morphisms. • Logical limits. These notions of limits are commonly used by model theorists. Here, one starts with a sequence of objects ${x_{\bf n}}$ or of spaces ${X_{\bf n}}$, each of which is (a component of) a model for given (first-order) mathematical language (e.g. if one is working in the language of groups, ${X_{\bf n}}$ might be groups and ${x_{\bf n}}$ might be elements of these groups). By using devices such as the ultraproduct construction, or the compactness theorem in logic, one can then create a new object ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$ or a new space ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$, which is still a model of the same language (e.g. if the spaces ${X_{\bf n}}$ were all groups, then the limiting space ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$ will also be a group), and is “close” to the original objects or spaces in the sense that any assertion (in the given language) that is true for the limiting object or space, will also be true for many of the original objects or spaces, and conversely. (For instance, if ${\prod_{{\bf n} \rightarrow \alpha} X_{\bf n}}$ is an abelian group, then the ${X_{\bf n}}$ will also be abelian groups for many ${{\bf n}}$.) The purpose of this talk is to highlight the third type of limit, and specifically the ultraproduct construction, as being a “universal” limiting procedure that can be used to replace most of the limits previously mentioned. Unlike the topological or metric limits, one does not need the original objects ${x_{\bf n}}$ to all lie in a common space ${X}$ in order to form an ultralimit ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$; they are permitted to lie in different spaces ${X_{\bf n}}$; this is more natural in many discrete contexts, e.g. when considering graphs on ${{\bf n}}$ vertices in the limit when ${{\bf n}}$ goes to infinity. Also, no convergence properties on the ${x_{\bf n}}$ are required in order for the ultralimit to exist. Similarly, ultraproduct limits differ from categorical limits in that no morphisms between the various spaces ${X_{\bf n}}$ involved are required in order to construct the ultraproduct. With so few requirements on the objects ${x_{\bf n}}$ or spaces ${X_{\bf n}}$, the ultraproduct construction is necessarily a very “soft” one. Nevertheless, the construction has two very useful properties which make it particularly useful for the purpose of extracting good continuous limit objects out of a sequence of discrete objects. First of all, there is Łos’s theorem, which roughly speaking asserts that any first-order sentence which is asymptotically obeyed by the ${x_{\bf n}}$, will be exactly obeyed by the limit object ${\lim_{{\bf n} \rightarrow \alpha} x_{\bf n}}$; in particular, one can often take a discrete sequence of “partial counterexamples” to some assertion, and produce a continuous “complete counterexample” that same assertion via an ultraproduct construction; taking the contrapositives, one can often then establish a rigorous equivalence between a quantitative discrete statement and its qualitative continuous counterpart. Secondly, there is the countable saturation property that ultraproducts automatically enjoy, which is a property closely analogous to that of compactness in topological spaces, and can often be used to ensure that the continuous objects produced by ultraproduct methods are “complete” or “compact” in various senses, which is particularly useful in being able to upgrade qualitative (or “pointwise”) bounds to quantitative (or “uniform”) bounds, more or less “for free”, thus reducing significantly the burden of “epsilon management” (although the price one pays for this is that one needs to pay attention to which mathematical objects of study are “standard” and which are “nonstandard”). To achieve this compactness or completeness, one sometimes has to restrict to the “bounded” portion of the ultraproduct, and it is often also convenient to quotient out the “infinitesimal” portion in order to complement these compactness properties with a matching “Hausdorff” property, thus creating familiar examples of continuous spaces, such as locally compact Hausdorff spaces. Ultraproducts are not the only logical limit in the model theorist’s toolbox, but they are one of the simplest to set up and use, and already suffice for many of the applications of logical limits outside of model theory. In this post, I will set out the basic theory of these ultraproducts, and illustrate how they can be used to pass between discrete and continuous theories in each of the examples listed in the above table. Apart from the initial “one-time cost” of setting up the ultraproduct machinery, the main loss one incurs when using ultraproduct methods is that it becomes very difficult to extract explicit quantitative bounds from results that are proven by transferring qualitative continuous results to the discrete setting via ultraproducts. However, in many cases (particularly those involving regularity-type lemmas) the bounds are already of tower-exponential type or worse, and there is arguably not much to be lost by abandoning the explicit quantitative bounds altogether. Tamar Ziegler and I have just uploaded to the arXiv our joint paper “A multi-dimensional Szemerédi theorem for the primes via a correspondence principle“. This paper is related to an earlier result of Ben Green and mine in which we established that the primes contain arbitrarily long arithmetic progressions. Actually, in that paper we proved a more general result: Theorem 1 (Szemerédi’s theorem in the primes) Let ${A}$ be a subset of the primes ${{\mathcal P}}$ of positive relative density, thus ${\limsup_{N \rightarrow \infty} \frac{\|A \cap [N]\|}{\|{\mathcal P} \cap [N]\|} > 0}$. Then ${A}$ contains arbitrarily long arithmetic progressions. This result was based in part on an earlier paper of Green that handled the case of progressions of length three. With the primes replaced by the integers, this is of course the famous theorem of Szemerédi. Szemerédi’s theorem has now been generalised in many different directions. One of these is the multidimensional Szemerédi theorem of Furstenberg and Katznelson, who used ergodic-theoretic techniques to show that any dense subset of ${{\bf Z}^d}$ necessarily contained infinitely many constellations of any prescribed shape. Our main result is to relativise that theorem to the primes as well: Theorem 2 (Multidimensional Szemerédi theorem in the primes) Let ${d \geq 1}$, and let ${A}$ be a subset of the ${d^{th}}$ Cartesian power ${{\mathcal P}^d}$ of the primes of positive relative density, thus $\displaystyle \limsup_{N \rightarrow \infty} \frac{\|A \cap [N]^d\|}{\|{\mathcal P}^d \cap [N]^d\|} > 0.$ Then for any ${v_1,\ldots,v_k \in {\bf Z}^d}$, ${A}$ contains infinitely many “constellations” of the form ${a+r v_1, \ldots, a + rv_k}$ with ${a \in {\bf Z}^k}$ and ${r}$ a positive integer. In the case when ${A}$ is itself a Cartesian product of one-dimensional sets (in particular, if ${A}$ is all of ${{\mathcal P}^d}$), this result already follows from Theorem 1, but there does not seem to be a similarly easy argument to deduce the general case of Theorem 2 from previous results. Simultaneously with this paper, an independent proof of Theorem 2 using a somewhat different method has been established by Cook, Maygar, and Titichetrakun. The result is reminiscent of an earlier result of mine on finding constellations in the Gaussian primes (or dense subsets thereof). That paper followed closely the arguments of my original paper with Ben Green, namely it first enclosed (a W-tricked version of) the primes or Gaussian primes (in a sieve theoretic-sense) by a slightly larger set (or more precisely, a weight function ${\nu}$) of almost primes or almost Gaussian primes, which one could then verify (using methods closely related to the sieve-theoretic methods in the ongoing Polymath8 project) to obey certain pseudorandomness conditions, known as the linear forms condition and the correlation condition. Very roughly speaking, these conditions assert statements of the following form: if ${n}$ is a randomly selected integer, then the events of ${n+h_1,\ldots,n+h_k}$ simultaneously being an almost prime (or almost Gaussian prime) are approximately independent for most choices of ${h_1,\ldots,h_k}$. Once these conditions are satisfied, one can then run a transference argument (initially based on ergodic-theory methods, but nowadays there are simpler transference results based on the Hahn-Banach theorem, due to Gowers and Reingold-Trevisan-Tulsiani-Vadhan) to obtain relative Szemerédi-type theorems from their absolute counterparts. However, when one tries to adapt these arguments to sets such as ${{\mathcal P}^2}$, a new difficulty occurs: the natural analogue of the almost primes would be the Cartesian square ${{\mathcal A}^2}$ of the almost primes – pairs ${(n,m)}$ whose entries are both almost primes. (Actually, for technical reasons, one does not work directly with a set of almost primes, but would instead work with a weight function such as ${\nu(n) \nu(m)}$ that is concentrated on a set such as ${{\mathcal A}^2}$, but let me ignore this distinction for now.) However, this set ${{\mathcal A}^2}$ does not enjoy as many pseudorandomness conditions as one would need for a direct application of the transference strategy to work. More specifically, given any fixed ${h, k}$, and random ${(n,m)}$, the four events $\displaystyle (n,m) \in {\mathcal A}^2$ $\displaystyle (n+h,m) \in {\mathcal A}^2$ $\displaystyle (n,m+k) \in {\mathcal A}^2$ $\displaystyle (n+h,m+k) \in {\mathcal A}^2$ do not behave independently (as they would if ${{\mathcal A}^2}$ were replaced for instance by the Gaussian almost primes), because any three of these events imply the fourth. This blocks the transference strategy for constellations which contain some right-angles to them (e.g. constellations of the form ${(n,m), (n+r,m), (n,m+r)}$) as such constellations soon turn into rectangles such as the one above after applying Cauchy-Schwarz a few times. (But a few years ago, Cook and Magyar showed that if one restricted attention to constellations which were in general position in the sense that any coordinate hyperplane contained at most one element in the constellation, then this obstruction does not occur and one can establish Theorem 2 in this case through the transference argument.) It’s worth noting that very recently, Conlon, Fox, and Zhao have succeeded in removing of the pseudorandomness conditions (namely the correlation condition) from the transference principle, leaving only the linear forms condition as the remaining pseudorandomness condition to be verified, but unfortunately this does not completely solve the above problem because the linear forms condition also fails for ${{\mathcal A}^2}$ (or for weights concentrated on ${{\mathcal A}^2}$) when applied to rectangular patterns. There are now two ways known to get around this problem and establish Theorem 2 in full generality. The approach of Cook, Magyar, and Titichetrakun proceeds by starting with one of the known proofs of the multidimensional Szemerédi theorem – namely, the proof that proceeds through hypergraph regularity and hypergraph removal – and attach pseudorandom weights directly within the proof itself, rather than trying to add the weights to the result of that proof through a transference argument. (A key technical issue is that weights have to be added to all the levels of the hypergraph – not just the vertices and top-order edges – in order to circumvent the failure of naive pseudorandomness.) As one has to modify the entire proof of the multidimensional Szemerédi theorem, rather than use that theorem as a black box, the Cook-Magyar-Titichetrakun argument is lengthier than ours; on the other hand, it is more general and does not rely on some difficult theorems about primes that are used in our paper. In our approach, we continue to use the multidimensional Szemerédi theorem (or more precisely, the equivalent theorem of Furstenberg and Katznelson concerning multiple recurrence for commuting shifts) as a black box. The difference is that instead of using a transference principle to connect the relative multidimensional Szemerédi theorem we need to the multiple recurrence theorem, we instead proceed by a version of the Furstenberg correspondence principle, similar to the one that connects the absolute multidimensional Szemerédi theorem to the multiple recurrence theorem. I had discovered this approach many years ago in an unpublished note, but had abandoned it because it required an infinite number of linear forms conditions (in contrast to the transference technique, which only needed a finite number of linear forms conditions and (until the recent work of Conlon-Fox-Zhao) a correlation condition). The reason for this infinite number of conditions is that the correspondence principle has to build a probability measure on an entire ${\sigma}$-algebra; for this, it is not enough to specify the measure ${\mu(A)}$ of a single set such as ${A}$, but one also has to specify the measure ${\mu( T^{n_1} A \cap \ldots \cap T^{n_m} A)}$ of “cylinder sets” such as ${T^{n_1} A \cap \ldots \cap T^{n_m} A}$ where ${m}$ could be arbitrarily large. The larger ${m}$ gets, the more linear forms conditions one needs to keep the correspondence under control. With the sieve weights ${\nu}$ we were using at the time, standard sieve theory methods could indeed provide a finite number of linear forms conditions, but not an infinite number, so my idea was abandoned. However, with my later work with Green and Ziegler on linear equations in primes (and related work on the Mobius-nilsequences conjecture and the inverse conjecture on the Gowers norm), Tamar and I realised that the primes themselves obey an infinite number of linear forms conditions, so one can basically use the primes (or a proxy for the primes, such as the von Mangoldt function ${\Lambda}$) as the enveloping sieve weight, rather than a classical sieve. Thus my old idea of using the Furstenberg correspondence principle to transfer Szemerédi-type theorems to the primes could actually be realised. In the one-dimensional case, this simply produces a much more complicated proof of Theorem 1 than the existing one; but it turns out that the argument works as well in higher dimensions and yields Theorem 2 relatively painlessly, except for the fact that it needs the results on linear equations in primes, the known proofs of which are extremely lengthy (and also require some of the transference machinery mentioned earlier). The problem of correlations in rectangles is avoided in the correspondence principle approach because one can compensate for such correlations by performing a suitable weighted limit to compute the measure ${\mu( T^{n_1} A \cap \ldots \cap T^{n_m} A)}$ of cylinder sets, with each ${m}$ requiring a different weighted correction. (This may be related to the Cook-Magyar-Titichetrakun strategy of weighting all of the facets of the hypergraph in order to recover pseudorandomness, although our contexts are rather different.) Vitaly Bergelson, Tamar Ziegler, and I have just uploaded to the arXiv our joint paper “Multiple recurrence and convergence results associated to ${{\bf F}_{p}^{\omega}}$-actions“. This paper is primarily concerned with limit formulae in the theory of multiple recurrence in ergodic theory. Perhaps the most basic formula of this type is the mean ergodic theorem, which (among other things) asserts that if ${(X,{\mathcal X}, \mu,T)}$ is a measure-preserving ${{\bf Z}}$-system (which, in this post, means that ${(X,{\mathcal X}, \mu)}$ is a probability space and ${T: X \mapsto X}$ is measure-preserving and invertible, thus giving an action ${(T^n)_{n \in {\bf Z}}}$ of the integers), and ${f,g \in L^2(X,{\mathcal X}, \mu)}$ are functions, and ${X}$ is ergodic (which means that ${L^2(X,{\mathcal X}, \mu)}$ contains no ${T}$-invariant functions other than the constants (up to almost everywhere equivalence, of course)), then the average $\displaystyle \frac{1}{N} \sum_{n=1}^N \int_X f(x) g(T^n x)\ d\mu \ \ \ \ \ (1)$ converges as ${N \rightarrow \infty}$ to the expression $\displaystyle (\int_X f(x)\ d\mu) (\int_X g(x)\ d\mu);$ see e.g. this previous blog post. Informally, one can interpret this limit formula as an equidistribution result: if ${x}$ is drawn at random from ${X}$ (using the probability measure ${\mu}$), and ${n}$ is drawn at random from ${\{1,\ldots,N\}}$ for some large ${N}$, then the pair ${(x, T^n x)}$ becomes uniformly distributed in the product space ${X \times X}$ (using product measure ${\mu \times \mu}$) in the limit as ${N \rightarrow \infty}$. If we allow ${(X,\mu)}$ to be non-ergodic, then we still have a limit formula, but it is a bit more complicated. Let ${{\mathcal X}^T}$ be the ${T}$-invariant measurable sets in ${{\mathcal X}}$; the ${{\bf Z}}$-system ${(X, {\mathcal X}^T, \mu, T)}$ can then be viewed as a factor of the original system ${(X, {\mathcal X}, \mu, T)}$, which is equivalent (in the sense of measure-preserving systems) to a trivial system ${(Z_0, {\mathcal Z}_0, \mu_{Z_0}, 1)}$ (known as the invariant factor) in which the shift is trivial. There is then a projection map ${\pi_0: X \rightarrow Z_0}$ to the invariant factor which is a factor map, and the average (1) converges in the limit to the expression $\displaystyle \int_{Z_0} (\pi_0)_* f(z) (\pi_0)_* g(z)\ d\mu_{Z_0}(x), \ \ \ \ \ (2)$ where ${(\pi_0)_: L^2(X,{\mathcal X},\mu) \rightarrow L^2(Z_0,{\mathcal Z}_0,\mu_{Z_0})}$ is the pushforward map associated to the map ${\pi_0: X \rightarrow Z_0}$; see e.g. this previous blog post. We can interpret this as an equidistribution result. If ${(x,T^n x)}$ is a pair as before, then we no longer expect complete equidistribution in ${X \times X}$ in the non-ergodic, because there are now non-trivial constraints relating ${x}$ with ${T^n x}$; indeed, for any ${T}$-invariant function ${f: X \rightarrow {\bf C}}$, we have the constraint ${f(x) = f(T^n x)}$; putting all these constraints together we see that ${\pi_0(x) = \pi_0(T^n x)}$ (for almost every ${x}$, at least). The limit (2) can be viewed as an assertion that this constraint ${\pi_0(x) = \pi_0(T^n x)}$ are in some sense the “only” constraints between ${x}$ and ${T^n x}$, and that the pair ${(x,T^n x)}$ is uniformly distributed relative to these constraints. Limit formulae are known for multiple ergodic averages as well, although the statement becomes more complicated. For instance, consider the expression $\displaystyle \frac{1}{N} \sum_{n=1}^N \int_X f(x) g(T^n x) h(T^{2n} x)\ d\mu \ \ \ \ \ (3)$ for three functions ${f,g,h \in L^\infty(X, {\mathcal X}, \mu)}$; this is analogous to the combinatorial task of counting length three progressions in various sets. For simplicity we assume the system ${(X,{\mathcal X},\mu,T)}$ to be ergodic. Naively one might expect this limit to then converge to $\displaystyle (\int_X f\ d\mu) (\int_X g\ d\mu) (\int_X h\ d\mu)$ which would roughly speaking correspond to an assertion that the triplet ${(x,T^n x, T^{2n} x)}$ is asymptotically equidistributed in ${X \times X \times X}$. However, even in the ergodic case there can be additional constraints on this triplet that cannot be seen at the level of the individual pairs ${(x,T^n x)}$, ${(x, T^{2n} x)}$. The key obstruction here is that of eigenfunctions of the shift ${T: X \rightarrow X}$, that is to say non-trivial functions ${f: X \rightarrow S^1}$ that obey the eigenfunction equation ${Tf = \lambda f}$ almost everywhere for some constant (or ${T}$-invariant) ${\lambda}$. Each such eigenfunction generates a constraint $\displaystyle f(x) \overline{f(T^n x)}^2 f(T^{2n} x) = 1 \ \ \ \ \ (4)$ tying together ${x}$, ${T^n x}$, and ${T^{2n} x}$. However, it turns out that these are in some sense the only constraints on ${x,T^n x, T^{2n} x}$ that are relevant for the limit (3). More precisely, if one sets ${{\mathcal X}_1}$ to be the sub-algebra of ${{\mathcal X}}$ generated by the eigenfunctions of ${T}$, then it turns out that the factor ${(X, {\mathcal X}_1, \mu, T)}$ is isomorphic to a shift system ${(Z_1, {\mathcal Z}_1, \mu_{Z_1}, x \mapsto x+\alpha)}$ known as the Kronecker factor, for some compact abelian group ${Z_1 = (Z_1,+)}$ and some (irrational) shift ${\alpha \in Z_1}$; the factor map ${\pi_1: X \rightarrow Z_1}$ pushes eigenfunctions forward to (affine) characters on ${Z_1}$. It is then known that the limit of (3) is $\displaystyle \int_\Sigma (\pi_1)_ f(x_0) (\pi_1)_* g(x_1) (\pi_1)_* h(x_2)\ d\mu_\Sigma$ where ${\Sigma \subset Z_1^3}$ is the closed subgroup $\displaystyle \Sigma = \{ (x_1,x_2,x_3) \in Z_1^3: x_1-2x_2+x_3=0 \}$ and ${\mu_\Sigma}$ is the Haar probability measure on ${\Sigma}$; see this previous blog post. The equation ${x_1-2x_2+x_3=0}$ defining ${\Sigma}$ corresponds to the constraint (4) mentioned earlier. Among other things, this limit formula implies Roth’s theorem, which in the context of ergodic theory is the assertion that the limit (or at least the limit inferior) of (3) is positive when ${f=g=h}$ is non-negative and not identically vanishing. If one considers a quadruple average $\displaystyle \frac{1}{N} \sum_{n=1}^N \int_X f(x) g(T^n x) h(T^{2n} x) k(T^{3n} x)\ d\mu \ \ \ \ \ (5)$ (analogous to counting length four progressions) then the situation becomes more complicated still, even in the ergodic case. In addition to the (linear) eigenfunctions that already showed up in the computation of the triple average (3), a new type of constraint also arises from quadratic eigenfunctions ${f: X \rightarrow S^1}$, which obey an eigenfunction equation ${Tf = \lambda f}$ in which ${\lambda}$ is no longer constant, but is now a linear eigenfunction. For such functions, ${f(T^n x)}$ behaves quadratically in ${n}$, and one can compute the existence of a constraint $\displaystyle f(x) \overline{f(T^n x)}^3 f(T^{2n} x)^3 \overline{f(T^{3n} x)} = 1 \ \ \ \ \ (6)$ between ${x}$, ${T^n x}$, ${T^{2n} x}$, and ${T^{3n} x}$ that is not detected at the triple average level. As it turns out, this is not the only type of constraint relevant for (5); there is a more general class of constraint involving two-step nilsystems which we will not detail here, but see e.g. this previous blog post for more discussion. Nevertheless there is still a similar limit formula to previous examples, involving a special factor ${(Z_2, {\mathcal Z}_2, \mu_{Z_2}, S)}$ which turns out to be an inverse limit of two-step nilsystems; this limit theorem can be extracted from the structural theory in this paper of Host and Kra combined with a limit formula for nilsystems obtained by Lesigne, but will not be reproduced here. The pattern continues to higher averages (and higher step nilsystems); this was first done explicitly by Ziegler, and can also in principle be extracted from the structural theory of Host-Kra combined with nilsystem equidistribution results of Leibman. These sorts of limit formulae can lead to various recurrence results refining Roth’s theorem in various ways; see this paper of Bergelson, Host, and Kra for some examples of this. The above discussion was concerned with ${{\bf Z}}$-systems, but one can adapt much of the theory to measure-preserving ${G}$-systems for other discrete countable abelian groups ${G}$, in which one now has a family ${(T_g)_{g \in G}}$ of shifts indexed by ${G}$ rather than a single shift, obeying the compatibility relation ${T_{g+h}=T_g T_h}$. The role of the intervals ${\{1,\ldots,N\}}$ in this more general setting is replaced by that of Folner sequences. For arbitrary countable abelian ${G}$, the theory for double averages (1) and triple limits (3) is essentially identical to the ${{\bf Z}}$-system case. But when one turns to quadruple and higher limits, the situation becomes more complicated (and, for arbitrary ${G}$, still not fully understood). However one model case which is now well understood is the finite field case when ${G = {\bf F}_p^\omega = \bigcup_{n=1}^\infty {\bf F}_p^n}$ is an infinite-dimensional vector space over a finite field ${{\bf F}_p}$ (with the finite subspaces ${{\bf F}_p^n}$ then being a good choice for the Folner sequence). Here, the analogue of the structural theory of Host and Kra was worked out by Vitaly, Tamar, and myself in these previous papers (treating the high characteristic and low characteristic cases respectively). In the finite field setting, it turns out that nilsystems no longer appear, and one only needs to deal with linear, quadratic, and higher order eigenfunctions (known collectively as phase polynomials). It is then natural to look for a limit formula that asserts, roughly speaking, that if ${x}$ is drawn at random from a ${{\bf F}_p^\omega}$-system and ${n}$ drawn randomly from a large subspace of ${{\bf F}_p^\omega}$, then the only constraints between ${x, T^n x, \ldots, T^{(p-1)n} x}$ are those that arise from phase polynomials. The main theorem of this paper is to establish this limit formula (which, again, is a little complicated to state explicitly and will not be done here). In particular, we establish for the first time that the limit actually exists (a result which, for ${{\bf Z}}$-systems, was one of the main results of this paper of Host and Kra). As a consequence, we can recover finite field analogues of most of the results of Bergelson-Host-Kra, though interestingly some of the counterexamples demonstrating sharpness of their results for ${{\bf Z}}$-systems (based on Behrend set constructions) do not seem to be present in the finite field setting (cf. this previous blog post on the cap set problem). In particular, we are able to largely settle the question of when one has a Khintchine-type theorem that asserts that for any measurable set ${A}$ in an ergodic ${{\bf F}_p^\omega}$-system and any ${\epsilon>0}$, one has $\displaystyle \mu( T_{c_1 n} A \cap \ldots \cap T_{c_k n} A ) > \mu(A)^k - \epsilon$ for a syndetic set of ${n}$, where ${c_1,\ldots,c_k \in {\bf F}_p}$ are distinct residue classes. It turns out that Khintchine-type theorems always hold for ${k=1,2,3}$ (and for ${k=1,2}$ ergodicity is not required), and for ${k=4}$ it holds whenever ${c_1,c_2,c_3,c_4}$ form a parallelogram, but not otherwise (though the counterexample here was such a painful computation that we ended up removing it from the paper, and may end up putting it online somewhere instead), and for larger ${k}$ we could show that the Khintchine property failed for generic choices of ${c_1,\ldots,c_k}$, though the problem of determining exactly the tuples for which the Khintchine property failed looked to be rather messy and we did not completely settle it.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1534, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9775468111038208, "perplexity": 164.1633558049971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948615810.90/warc/CC-MAIN-20171218102808-20171218124808-00008.warc.gz"}
https://ds-modules.github.io/modules-textbook/xenglish-r1a/01-Chinatowns.html	# ENGLISH R1A: Chinatown and the Culture of Exclusion Instructor: Amy Lee Developers: Michaela Palmer, Maya Shen, Cynthia Leu, Chris Cheung FPF 2017 Welcome to lab! Please read this lab in its entirety, as the analysis will make a lot more sense with the background context provided. This lab is intended to be a hands-on introduction to data science as it can be applied to Chinatown demographics and analyzing primary texts. We will be reading and analyzing representations of Chinatown in the form of data and maps. In addition, we will learn how data tools can be used to read and analyze large volumes of text. ## What this lab will cover • Running Jupyter Notebooks • Data Analysis of Chinatowns’ demographics • Visualization & Interpretation • Using Data Tools to Analyze Primary Texts ## What you need to do • Read the content, complete the questions • Analyze the data • Submit the assignment # 1. Running Jupyter Notebooks You are currently working in a Jupyter Notebook. A Notebook allows text and code to be combined into one document. Each rectangular section of a notebook is called a “cell.” There are two types of cells in this notebook: text cells and code cells. Jupyter allows you to run simulations and regressions in real time. To do this, select a code cell, and click the “run cell” button at the top that looks like ▶ to confirm any changes. Alternatively, you can hold down the shift key and then press return or enter. In the following simulations, anytime you see In [ ] you should click the “run cell” button to see output. If you get an error message after running a cell, go back to the beginning of the lab and make sure that every previous code cell has been run. # Part 0: Introduction to Python and Jupyter Notebooks: ## 1. Cells, Arithmetic, and Code In a notebook, each rectangle containing text or code is called a cell. Cells (like this one) can be edited by double-clicking on them. This cell is a text cell, written in a simple format called Markdown to add formatting and section headings. You don’t need to worry about Markdown today, but it’s a pretty fun+easy tool to learn. After you edit a cell, click the “run cell” button at the top that looks like ▶ to confirm any changes. (Try not to delete the instructions.) You can also press SHIFT-ENTER to run any cell or progress from one cell to the next. Other cells contain code in the Python programming language. Running a code cell will execute all of the code it contains. Try running this cell: print("Hello, World!") Hello, World! We will now quickly go through some very basic functionality of Python, which we’ll be using throughout the rest of this notebook. ### 1.1 Arithmetic Quantitative information arises everywhere in data science. In addition to representing commands to print out lines, expressions can represent numbers and methods of combining numbers. The expression 3.2500 evaluates to the number 3.25. (Run the cell and see.) 3.2500 3.25 We don’t necessarily always need to say “print”, because Jupyter always prints the last line in a code cell. If you want to print more than one line, though, do specify “print”. print(3) 4 5 3 5 Many basic arithmetic operations are built in to Python, like * (multiplication), + (addition), - (subtraction), and / (division). There are many others, which you can find information about here. Use parentheses to specify the order of operations, which act according to PEMDAS, just as you may have learned in school. Use parentheses for a happy new year! 2 + (6 * 5 - (6 * 3)) ** 2 * (( 2 ** 3 ) / 4 * 7) 2018.0 ### 1.2 Variables We sometimes want to work with the result of some computation more than once. To be able to do that without repeating code everywhere we want to use it, we can store it in a variable with assignment statements, which have the variable name on the left, an equals sign, and the expression to be evaluated and stored on the right. In the cell below, (3 * 11 + 5) / 2 - 9 evaluates to 10, and gets stored in the variable result. result = (3 * 11 + 5) / 2 - 9 result 10.0 ## 2. Functions One important form of an expression is the call expression, which first names a function and then describes its arguments. The function returns some value, based on its arguments. Some important mathematical functions are: Function Description abs Returns the absolute value of its argument max Returns the maximum of all its arguments min Returns the minimum of all its arguments round Round its argument to the nearest integer Here are two call expressions that both evaluate to 3 abs(2 - 5) max(round(2.8), min(pow(2, 10), -1 * pow(2, 10))) These function calls first evaluate the expressions in the arguments (inside the parentheses), then evaluate the function on the results. abs(2-5) evaluates first to abs(3), then returns 3. A statement is a whole line of code. Some statements are just expressions, like the examples above, that can be broken down into its subexpressions which get evaluated individually before evaluating the statement as a whole. ### 2.1 Calling functions The most common way to combine or manipulate values in Python is by calling functions. Python comes with many built-in functions that perform common operations. For example, the abs function takes a single number as its argument and returns the absolute value of that number. The absolute value of a number is its distance from 0 on the number line, so abs(5) is 5 and abs(-5) is also 5. abs(5) 5 abs(-5) 5 Functions can be called as above, putting the argument in parentheses at the end, or by using “dot notation”, and calling the function after finding the arguments, as in the cell immediately below. from datascience import make_array nums = make_array(1, 2, 3) # makes a list of items, in this case, numbers nums.mean() # finds the average of the array 2.0 # 1: Exploring Demographic Data: ## 1.1 Importing Modules First, we need to import libraries so that we are able to call the functions from within. We are going to use these functions to manipulate data tables and conduct a statistical analysis. Run the code cell below to import these modules. %%capture from datascience import * import numpy as np import matplotlib.pyplot as plt from ipywidgets import * %matplotlib inline import folium import pandas as pd from IPython.display import HTML, display, IFrame import folium import spacy from wordcloud import WordCloud from textblob import TextBlob import geojson ### Official map of Chinatown in San Francisco - 1855 #### Prepared under the supervision of the special committee of the Board of Supervisors. July 1885. This map reflects the pervasive bias against the Chinese in California and in turn further fostered the hysteria. It was published as part of an official report of a Special Committee established by the San Francisco Board of Supervisors “on the Condition of the Chinese Quarter.” The Report resulted from a dramatic increase in hostility to the Chinese, particularly because many Chinese laborers had been driven out of other Western states by vigilantes and sought safety in San Francisco (Shah 2001, 37). The substance and tone of the Report is best illustrated by a few excerpts: “The general aspect of the streets and habitations was filthy in the extreme, . . . a slumbering pest, likely at any time to generate and spread disease, . . . a constant source of danger . . . , the filthiest spot inhabited by men, women and children on the American continent.” (Report 4-5). “The Chinese brought here with them and have successfully maintained and perpetuated the grossest habits of bestiality practiced by the human race.” (Ibid. 38). The map highlights the Committee’s points, particularly the pervasiveness of gambling, prostitution and opium use. It shows the occupancy of the street floor of every building in Chinatown, color coded to show: General Chinese Occupancy, Chinese Gambling Houses, Chinese Prostitution, Chinese Opium Resorts, Chinese Joss Houses, and White Prostitution. The Report concludes with a recommendation that the Chinese be driven out of the City by stern enforcement of the law: “compulsory obedience to our laws [is] necessarily obnoxious and revolting to the Chinese and the more rigidly this enforcement is insisted upon and carried out the less endurable will existence be to them here, the less attractive will life be to them in California. Fewer will come and fewer will remain. . . . Scatter them by such a policy as this to other States . . . .” (Ibid. 67-68) # 2. Analyzing Demographics In this section, we will examine some of the factors that influence population growth and how they are changing the landscape of Chinatowns across the U.S. Now it’s time to work with tables and explore some real data. A Table is just like how we made a list above with make_array, but for all the rows in a table. We’re going to first look at the most recent demographic data from 2010-2015: historical_data = Table.read_table('data/2010-2015.csv') # read in data from file historical_data['FIPS'] = ['0' + str(x) for x in historical_data['FIPS']] # fix FIPS columns historical_data.show(10) # show first ten rows FIPS Population One_race Two_or_more_races Asian Year 06075010100 3744 3689 55 1276 2010 06075010200 4184 3942 242 385 2010 06075010300 4285 4173 112 1445 2010 06075010400 4154 4068 86 1161 2010 06075010500 2429 2357 72 317 2010 06075010600 3927 3789 138 2453 2010 06075010700 5683 5657 26 4541 2010 06075010800 4587 4475 112 2336 2010 06075010900 4463 4339 124 1056 2010 06075011000 5718 5653 65 3027 2010 ... (1172 rows omitted) We can get some quick summary statistics by calling the .stats() function on our Table variable: historical_data.stats() statistic FIPS Population One_race Two_or_more_races Asian Year min 06075010100 0 0 0 0 2010 max 06075990100 12511 12157 660 5291 2015 median 4026.5 3872 157 1004 2012.5 sum 4.88225e+06 4.68046e+06 201782 1.6378e+06 2.37878e+06 So which census tract has the highest Asian population? First we can find the highest population by using the max function: max(historical_data['Asian']) 5291.0 Let’s plug that into a table that uses the where and are.equal_to functions: historical_data.where('Asian', are.equal_to(max(historical_data['Asian']))) FIPS Population One_race Two_or_more_races Asian Year 06075035300 7885 7667 218 5291 2014 This FIPS code 06075035300 is tract 353. Does this make sense to you? It might be better to look at which census tracts has Asian as the highest proportion of the population: historical_data['Asian_percentage'] = historical_data['Asian'] / historical_data['Population'] historical_data.show(5) FIPS Population One_race Two_or_more_races Asian Year Asian_percentage 06075010100 3744 3689 55 1276 2010 0.340812 06075010200 4184 3942 242 385 2010 0.0920172 06075010300 4285 4173 112 1445 2010 0.337223 06075010400 4154 4068 86 1161 2010 0.27949 06075010500 2429 2357 72 317 2010 0.130506 ... (1177 rows omitted) Now we can use the same method to get the max and subset our table: max(historical_data['Asian_percentage']) 0.9575070821529745 historical_data.where('Asian_percentage', are.equal_to(max(historical_data['Asian_percentage']))) FIPS Population One_race Two_or_more_races Asian Year Asian_percentage 06075011800 1765 1765 0 1690 2010 0.957507 FIPS code 06075011800 is census tract 118. Does this make sense? Question: Write one sentence describing the Asian population in Chinatown. Replace this text with your response ### Tables Essentials! For your reference, here’s a table of useful Table functions: Name Example Purpose Table Table() Create an empty table, usually to extend with data Table.read_table Table.read_table("my_data.csv") Create a table from a data file with_columns tbl = Table().with_columns("N", np.arange(5), "2N", np.arange(0, 10, 2)) Create a copy of a table with more columns column tbl.column("N") Create an array containing the elements of a column sort tbl.sort("N") Create a copy of a table sorted by the values in a column where tbl.where("N", are.above(2)) Create a copy of a table with only the rows that match some predicate num_rows tbl.num_rows Compute the number of rows in a table num_columns tbl.num_columns Compute the number of columns in a table select tbl.select("N") Create a copy of a table with only some of the columns drop tbl.drop("2N") Create a copy of a table without some of the columns take tbl.take(np.arange(0, 6, 2)) Create a copy of the table with only the rows whose indices are in the given array join tbl1.join("shared_column_name", tbl2) Join together two tables with a common column name are.equal_to() tbl.where("SEX", are.equal_to(0)) find values equal to that indicated are.not_equal_to() tbl.where("SEX", are.not_equal_to(0)) find values not including the one indicated are.above() tbl.where("AGE", are.above(30)) find values greater to that indicated are.below() tbl.where("AGE", are.below(40)) find values less than that indicated are.between() tbl.where("SEX", are.between(18, 60)) find values between the two indicated ## 2.2 The correlation coefficient - r If we were interested in the relationship between two variables in our dataset, we’d want to look at correlation. The correlation coefficient ranges from −1 to 1. A value of 1 implies that a linear equation describes the relationship between X and Y perfectly, with all data points lying on a line for which Y increases as X increases. A value of −1 implies that all data points lie on a line for which Y decreases as X increases. A value of 0 implies that there is no linear correlation between the variables. ~Wikipedia r = 1: the scatter diagram is a perfect straight line sloping upwards r = -1: the scatter diagram is a perfect straight line sloping downwards. Let’s calculate the correlation coefficient between each of the continuous variables in our dataset.. We can use the .to_df().corr() function: historical_data.to_df().corr() Population One_race Two_or_more_races Asian Year Asian_percentage Population 1.000000 0.998493 0.568193 0.690292 0.053188 0.264237 One_race 0.998493 1.000000 0.522172 0.696641 0.043588 0.273538 Two_or_more_races 0.568193 0.522172 1.000000 0.281429 0.172941 0.002922 Asian 0.690292 0.696641 0.281429 1.000000 0.029201 0.839065 Year 0.053188 0.043588 0.172941 0.029201 1.000000 0.002954 Asian_percentage 0.264237 0.273538 0.002922 0.839065 0.002954 1.000000 We often visualize correlations with a scatter plot: historical_data.scatter('Population', 'Asian') historical_data.scatter('One_race', 'Asian') historical_data.scatter('Two_or_more_races', 'Asian') To look at a 1-1 relationship over time we might prefer a simple line graph. We can first group the data by Year, then take the mean for the Population, and plot that against Year: historical_data.to_df().groupby('Year')['Population'].mean() Year 2010 4005.949239 2011 4050.675127 2012 4100.279188 2013 4149.751269 2014 4208.487310 2015 4267.832487 Name: Population, dtype: float64 historical_data.to_df().groupby('Year')['Population'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x1317a5a20> historical_data.to_df().groupby('Year')['Asian_percentage'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x1318a4f60> ## 2.3 2015 Let’s look at only the year 2015: historical_2015 = historical_data.where('Year', are.equal_to(2015)) historical_2015.show(5) FIPS Population One_race Two_or_more_races Asian Year Asian_percentage 06075010100 3798 3517 281 1284 2015 0.338073 06075010200 4172 4014 158 401 2015 0.096117 06075010300 4387 4334 53 1700 2015 0.387509 06075010400 5148 4709 439 1429 2015 0.277584 06075010500 2589 2337 252 804 2015 0.310545 ... (192 rows omitted) We can make a choropleth map with a little function, don’t worry about the code below! def choro_column(tab, column): threshold_scale = np.linspace(min(tab[column]), max(tab[column]), 6, dtype=float).tolist() mapa = folium.Map(location=(37.7793784, -122.4063879), zoom_start=11) mapa.choropleth(geo_data=sf_2010, data=tab.to_df(), columns=['FIPS', column], fill_color='YlOrRd', key_on='feature.properties.GEOID10', threshold_scale=threshold_scale) mapa.save("output/map-{}.html".format(column.replace(" ", "-"))) return mapa Here’s a choropleth of all the population: choro_column(historical_2015, 'Population') IFrame('output/map-Population.html', width=700, height=400) Let’s look at only Asian: choro_column(historical_2015, 'Asian') Try making one more choropleth below with only Asian_percentage: Question: Where is the largest concentration of Asian residents? Replace this text with your response ## Challenge Create a choropleth for 2010 with the same Asian_percentage column. Do you see any differences from 2010 to 2015? Replace this text with your response ## 2.4 1940-2010 Now let’s take a look at the historical data showing how the Asian population has changed over time, as compared to the black population. First, let’s load in all our of decennial San Francisco Chinatown census data acquired from an online domain called Social Explorer. Let’s first examine this dataset to get a sense of what’s in it. Question: Can you explain how you would derive the Asian population from the given census data? Replace this text with your response historical = Table.read_table('data/process.csv') historical.show(5) Asian Asian and Pacific Islander Black Federal Information Processing System Code Total Population White Year nan nan 78 06075A0005000 3465 3199 1940 nan nan 32 06075A0006000 4401 3203 1940 nan nan 71 06075A0007000 5466 4489 1940 nan nan 6 06075A0008000 5152 5124 1940 nan nan 49 06075A0009000 5052 4959 1940 ... (73 rows omitted) historical['Other'] = historical['Total Population'] - historical['White'] - historical['Black'] historical.show(5) Asian Asian and Pacific Islander Black Federal Information Processing System Code Total Population White Year Other nan nan 78 06075A0005000 3465 3199 1940 188 nan nan 32 06075A0006000 4401 3203 1940 1166 nan nan 71 06075A0007000 5466 4489 1940 906 nan nan 6 06075A0008000 5152 5124 1940 22 nan nan 49 06075A0009000 5052 4959 1940 44 ... (73 rows omitted) You can use the mean function to find the average total population in Chinatown. Do you notice any significant changes between 1940 and 2010? historical.to_df().groupby('Year')['Total Population'].mean() Year 1940 4521.900 1950 4592.400 1960 4123.400 1970 4137.000 1980 3841.100 1990 4007.300 2000 3886.300 2010 4478.125 Name: Total Population, dtype: float64 Let’s plot the results on a graph. historical.to_df().groupby('Year')['Total Population'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x12d5f4438> historical.to_df().groupby('Year')['White'].mean() Year 1940 2880.50 1950 2469.40 1960 1702.10 1970 1341.80 1980 1170.30 1990 1195.60 2000 1322.10 2010 1679.25 Name: White, dtype: float64 We can plot the average population of different racial groups. historical.to_df().groupby('Year')['White'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x1329e64e0> historical.to_df().groupby('Year')['Black'].mean() Year 1940 37.2 1950 84.3 1960 39.0 1970 33.3 1980 41.9 1990 52.0 2000 50.7 2010 71.5 Name: Black, dtype: float64 historical.to_df().groupby('Year')['Black'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x1329bcf28> historical.to_df().groupby('Year')['Other'].mean() Year 1940 1604.200 1950 2038.700 1960 2382.300 1970 2761.900 1980 2628.900 1990 2759.700 2000 2513.500 2010 2727.375 Name: Other, dtype: float64 historical.to_df().groupby('Year')['Other'].mean().plot() <matplotlib.axes._subplots.AxesSubplot at 0x132419cf8> Question: Describe the population trends you observed from the above graphs. How would you compare the changes in Asian vs Black vs White populations? Replace this text with your response ## 2.5 Manhattan One of the goals of this module is to compare different Chinatowns from across the US. We will now compare the SF Chinatown data to the census data from Manhattan’s Chinatown. Let’s load the Manhattan data. manhattan = Table.read_table('data/manhattan_cleaned.csv') manhattan.show(10) Year Census Tract Total Population Asian/Other Population Chinese Population White Population 1950 29 6695 3180 3180 6228 1960 29 7091 4677 4677 2390 1970 6 8322 2684 2684 4669 1970 8 9597 4258 4258 5311 1970 16 6381 4069 4069 2141 1970 18 7764 2281 2281 4766 1970 27 1671 623 623 993 1970 29 9435 5996 5996 2321 1970 41 9294 5262 5262 3845 1980 6 10638 5172 5086 2179 ... (53 rows omitted) manhattan.to_df().corr() Year Census Tract Total Population Asian/Other Population Chinese Population White Population Year 1.000000 0.054710 -0.191828 -0.087767 -0.118715 -0.539567 Census Tract 0.054710 1.000000 -0.412661 -0.376237 -0.378750 -0.014695 Total Population -0.191828 -0.412661 1.000000 0.907103 0.904009 0.408393 Asian/Other Population -0.087767 -0.376237 0.907103 1.000000 0.998946 0.119564 Chinese Population -0.118715 -0.378750 0.904009 0.998946 1.000000 0.123380 White Population -0.539567 -0.014695 0.408393 0.119564 0.123380 1.000000 manhattan.scatter('Chinese Population', 'White Population') manhattan_2010 = manhattan.where('Year', are.equal_to(2010)) manhattan_2010.show() Year Census Tract Total Population Asian/Other Population Chinese Population White Population 2010 2.01 3058 1266 1202 777 2010 6 11367 7253 6886 1708 2010 8 10290 9069 8832 964 2010 14.02 2782 880 760 1142 2010 16 8478 7058 6733 1117 2010 18 8660 5281 4827 2338 2010 22.01 6398 1553 1267 2349 2010 25 4869 1919 1818 965 2010 27 1264 978 941 254 2010 29 6398 4461 4260 917 2010 30.01 4492 1029 592 2732 2010 31 2550 712 413 1550 2010 36.01 3393 852 678 1424 2010 41 7817 5015 4598 2445 2010 43 4270 1046 827 1750 2010 45 1136 230 176 851 def choro_column(tab, column): tab = tab.to_df() tab['Census Tract'] = tab['Census Tract'].astype(str).str.strip('0').str.strip('.') tracts = folium.features.GeoJson(nyc_2010) threshold_scale = np.linspace(min(tab[column]), max(tab[column]), 6, dtype=float).tolist() mapa = folium.Map(location=(40.7128, -74.00609), zoom_start=11) mapa.choropleth(geo_data=nyc_2010, data=tab, columns=['Census Tract', column], fill_color='YlOrRd', key_on='feature.properties.CTLabel', threshold_scale=threshold_scale) mapa.save("output/map-{}.html".format(column.replace(" ", "-"))) return mapa choro_column(manhattan_2010, 'Chinese Population') IFrame('output/map-Chinese-Population.html', width=700, height=400) manhattan_2010['Asian_percentage'] = manhattan_2010['Asian/Other Population'] / manhattan_2010['Total Population'] manhattan_2010.show(5) Year Census Tract Total Population Asian/Other Population Chinese Population White Population Asian_percentage 2010 2.01 3058 1266 1202 777 0.413996 2010 6 11367 7253 6886 1708 0.638075 2010 8 10290 9069 8832 964 0.881341 2010 14.02 2782 880 760 1142 0.316319 2010 16 8478 7058 6733 1117 0.832508 ... (11 rows omitted) choro_column(manhattan_2010, 'Asian_percentage') IFrame('output/map-Asian_percentage.html', width=700, height=400) In this class, we have been learning how to ‘close-read’ primary texts. Close-reading generally involves picking select passages and reading for the latent meanings embedded in word choice, syntax, the use of metaphors and symbols, etc. Here, we are introducing another way of analyzing primary texts using computational methods. Computational text analysis generally involves ‘counting’ words. Let’s see how this works by analyzing some of the poems written by Chinese immigrants on Angel Island. Run the following cell to import the poems from a .txt file. with open('data/islandpoetry1_22.txt', "r") as f: print(raw) The sea-scape resembles lichen twisting and turning for a thousand li There is no shore to land and it is difficult to walk. With a gentle breeze I arrived at the city thinking all would be so. At ease, how was one to know he was to live in a wooden building? Because my house had bare walls, I began The waves are happy, laughing "Ha-ha!" When I arrived on Island, I heard I was forbidden to land. I could do nothing but frown and feel angry at heaven. As a rule, a person is twenty before he starts making a living. Family circumstances have forced me to experience wind and dust. The heartless months and years seem bent on defeating me. It is a pity that time quickly ages one. The gold and silver of America is very appealing. Jabbing an awl into the thigh in search of glory, I embarked on the journey. Not only are my one-thousand pieces of gold My countenance is blackened. It is surely for the sake of the family. Four days before the Qiqiao Festival, I boarded the steamship for America. Time flew like a shooting arrow. Already, a cool autumn has passed. Counting on my fingers, several months have elapsed. Still I am at the beginning of the road. I have yet to be interrogated. My heart is nervous with anticipation. Everyone says travelling to North America is a pleasure. I suffered misery on the ship and sadness in the wooden building. After several interrogations, still I am not done. I sigh because my compatriots are being forceably detained. Originally, I had intended to come to America last year. Lack of money delayed me until early autumn. It was on the day that the Weaver Maiden met the Cowherd That I took passage on the President Lincoln. I ate wind and tasted waves for more than twenty days. Fortunately, I arrived safely on the American continent. I thought I could land in a few days. How was I to know I would become a prisoner suffering in the wooden building? The barbarians' abuse is really difficult to take. When my family's circumstances stir my emotions, a double stream of tears flow. I only wish I can land in San Francisco soon. Thus sparing me this additional sorrow here. Instead of remaining a citizen of China, I willingly became an ox. I intended to come to America to earn a living. The Western styled buildings are lofty; but I have not the luck to live in them. How was anyone to know that my dwelling place would be a prison? I used to admire the land of the Flowery Flag as a country of abundance. I immediately raised money and started my journey. For over a month, I have experienced enough winds and waves. Now on an extended sojourn in jail, I am subject to the ordeals of prison life. I look up and see Oakland so close by. I wish to go back to my motherland to carry the farmer's hoe. Discontent fills my belly and it is difficult for me to sleep. I just write these few lines to express what is on my mind. Just talk about going to the land of the Flowery Flag and my countenance fills with happiness. Not without hard work were 1,000 pieces of gold dug up and gathered together. There were words of farewell to the parents, but the throat choked up first. There were many feelings, many tears flowing face to face, when parting with the wife. Waves big as mountains often astonished this traveller. With laws harsh as tigers, I had a taste of all the barbarities. Do not forget this day when you land ashore. Push yourself ahead and do not be lazy or idle. I think back on the past when I had not experienced hardship. I resolved to go and seek Taogong. The months and years are wasted and still it has not ended. Up to now, I am still trapped on a lonely island. Today is the last day of winter. Tomorrow morning is the vernal equinox. One year's prospects have changed to another. Sadness kills the person in the wooden building. In the quiet of night, I heard, faintly, the whistling of wind. seeing the landscape, I composed a poem. The floating clouds, the fog, darken the sky. The moon shines faintly as the insects chirp. Grief and bitterness entwined are heaven sent. The sad person sits alone, leaning by a window. The night is cool as I lie stiff on the steel bunk. Before the window the moon lady shines on me. Bored, I get up and stand beneath the cold window. Sadly, I count the time that's elapsed. We should all honor and enjoy her. But I have not prepared even the most trifling The insects chirp outside the four walls. The inmates often sigh. Thinking of affairs back home. Unconscious tears wet my lapel. Depressed from living on Island, I sought the Sleeping Village. The uncertain future altogether wounds my spirit. When I see my old country fraught with chaos, I, a drifting leaf, become doubly saddened. My belly is so full of discontent it is really difficult to relax. I can only worry silently to myself. At times I gaze at the cloud- and fog-enshrouded mountain-front. Sadly, I listen to the sounds of insects and angry surf. The harsh laws pile layer upon layer; how can I dissipate my hatred? Drifting in as a traveller, I met with this calamity. It is more miserable than owning only a flute in the marketplace of Wu. Living on Island away from home elicits a hundred feelings. My chest is filled with a sadness and anger I cannot bear to explain. Night and day, I sit passively and listlessly. Fortunately, I have a novel as my companion. Imprisonment at Youli, when will it end? Fur and linen garments have been exchanged; My belly brims with discontent, too numerous to inscribe on bamboo slips. Snow falls, flowers wilt, expressing sorrow through the ages. The west wind ruffles my thin gauze clothing. On the hill sits a tall building with a room of wooden planks. I wish I could travel on a cloud far away, reunite with my wife and son. When the moonlight shines on me alone, the nights seem even longer. At the head of the bed there is wine and my heart is constantly drunk. There is no flower beneath my pillow and my dreams are not sweet. To whom can I confide my innermost feelings? I rely solely on close friends to relieve my loneliness. America has power, but not justice. In prison, we were victimized as if we were guilty. Given no opportunity to explain, it was really brutal. I bow my head in reflection but there is nothing I can do. This place is called an island of immortals. When, in fact, this mountain wilderness is a prison. Once you see the open net, why throw yourself in? It is only because of empty pockets I can do nothing else. I, a seven foot man, am ashamed I cannot extend myself. Curled up in an enclosure, my movements are dictated by others." Enduring a hundred humiliations, I can only cry in vain. This person's tears fall, but what can the blue heavens do? I have infinite feelings that the ocean has changed into a mulberry grove. My body is detained in this building. I cannot fly from this grassy hill. And green waters block the hero. Impetuously, I threw away my writing brush. My efforts have all been in vain. It is up to me to answer carefully. I have no words to murmur against the east wind. My grief, like dense clouds, cannot be dispersed. Whether deliberating or being melancholy and bored, I constantly pace to and fro. Wang Can ascended the tower but who pitied his sorrow? Lord Yu who left his country could only wail to himself. Over a hundred poems are on the walls. Looking at them, they are all pining at the delayed progress. What can one sad person say to another? Unfortunate travellers everywhere wish to commiserate. Gain or lose, how is one to know what is predestined? Rich or poor, who is to say it is not the will of heaven? Why should one complain if he is detained and imprisoned here? From ancient times, heroes often were the The male eagle is also easy to tame. One must be able to bend before one can stretch. China experienced calamities for a thousand years. Confucius was surrounded in Chen for seven days. Great men exhibit quality. Scholars take pride in being themselves. Gains and losses are entangled in my bosom. My restlessness is a sign of self-illumination. Half way up the hill on Island, in the building upstairs. The imprisoned one has been separated from his people summer to autumn. Three times I dreamed of returning to the native village. My intestines are agitated in its nine turns by the false Westerner. I have run into hard times and am uselessly depressed. There are many obstacles in life but who will commiserate with me? If at a later time I am allowed to land on the American shore, I will toss all the miseries of this jail to the flowing current. After leaping into prison, I cannot come out. From endless sorrows, tears and blood streak. The jingwei bird carries gravel to fill its old grudge. The migrating wild goose complains to the moon, mourning his harried life. When Ziqing was in distant lands, who pitied and inquired after him? When Ruan Ji reached the end of the road, he shed tile tears. The scented grass and hidden orchids complain of withering and falling. When can I be allowed to rise above as I There are tens of thousands of poems composed on these walls. They are all cries of complaint and sadness. The day I am rid of this prison and attain success, I must remember that this chapter once existed. In my daily needs, I must be frugal. Needless extravagance leads youth to ruin. All my compatriots should please be mindful. Once you have some small gains, return home early. Imprisoned in the wooden building day after day. My freedom withheld; how can I bear to talk I look to see who is happy but they only sit quietly. I am anxious and depressed and cannot fall asleep. The days are long and the bottle constantly empty; my sad mood, even so, is not dispelled. Nights are long and the pillow cold; who can pity my loneliness? After experiencing such loneliness and sorrow. Why not just return home and learn to plow the fields? A building does not have to be tall; if it has windows, it will be bright. Island is not far, Angel Island. Alas, this wooden building disrupts my travelling schedule. Paint on the four walls are green. And green is the grass which surrounds. It is noisy because of the many country folk. And there are watchmen guarding during the night. To exert influence, one can use a square-holed elder brother. There are children who disturb the ears. But there are no incoherent sounds that cause fatigue. I gaze to the south at the hospital, And look to the west at the army camp. This author says, "What happiness is there in this? For what reason must I sit in jail? It is only because my country is weak and my family poor. My parents wait at the door but there is no news. My wife and child wrap themselves in quilt, sighing with loneliness. Even if my petition is approved and I can enter the country. From ancient times, those who venture out usually become worthless. How many people ever return from battles? Leaving behind my writing brush and removing my sword, I came to America. Who was to know two streams of tears would flow upon arriving here? If there comes a day when I will have attained my ambition and become successful, I will certainly behead the barbarians and spare not a single blade of grass. I am a member of the Huang clan from Xiangcheng. I threw away my writing brush and pushed forward, journeying to the capital of the U.S. I bought an oar and arrived in the land of the Golden Mountain. Who was to know they would banish me to Island? If my country had contrived to make herself strong, this never would have happened. Then when the ship had docked, we could have gone directly ashore. Just now the five nationalities in China have become one family, But the powers still have not yet recognized our China, Primarily because foreign debts were piling up. The foreigners pushed to control finances and to seize power. Being idle in the wooden building, I opened a window. The morning breeze and bright moon lingered together. I reminisce the native village far away, cut off by clouds and mountains. On the little island the wailing of cold, wild geese can be faintly heard. The hero who has lost his way can talk meaninglessly of the sword. The poet at the end of the road can only ascend a tower. One should know that when the country is weak, the people's spirit dies. Why else do we come to this place to be imprisoned? Twice I have passed through the blue ocean, experienced the wind and dust of journey. Confinement in the wooden building has pained me doubly. With a weak country, we must all join together in urgent effort. It depends on all of us together to roll back the wild wave. I lean on the railing and lift my head to look at the cloudy sky. All the mountains and rivers are dark. Eastern Mongolia is lost and the date of her return is uncertain. The recovery of the Central Plains depends on the youth. Only the tongue of Changshan can slay the villainous. To kill the bandit we must wave the whip of Zu Di. I am ashamed to be curled up like a worm on Island. I grieve for my native land but what else can I say? I have ten-thousand hopes that the revolutionary armies will complete their victory. And help make the mining enterprises successful in the ancestral land. They will build many battleships and come to the U.S. territory. Vowing never to stop till the white men are completely annihilated. The dragon out of water is humiliated by ants; The fierce tiger who is caged is baited by a child. As long as I am imprisoned, how can I dare strive for supremacy? An advantageous position for revenge will surely come one day. I left the village well behind me, bade farewell to my father and mother. Now I gaze at distant clouds and mountains, tears forming like pearls. The wandering son longed to be wealthy like Taozhu. Who would have known I would be imprisoned on Island? I beat my breast when I think of China and cry bitterly like Ruan Ji. Our country's wealth is being drained by foreigners, causing us to suffer national humiliations. My fellow countrymen, have foresight, plan to be resolute. And vow to conquer the U.S. and avenge previous wrongs! If the land of the Flowery Flag is occupied by us in turn. The wooden building will be left for the angel's revenge. If you have but one breath left, do not be I respectfully exhort my brothers who are all talents of Chu. Having a sense of shame, one can eradicate shame. Only by wielding the lance can one avoid certain defeat. Do not say that we have not the means to level the ugly barbarians. I am searching for a method that will turn destiny back. One-hundred-thousand men sharpen their swords. Swearing to behead the Loulan and open the grasslands and fallow fields. The low building with three beams merely shelters the body. It is unbearable to relate the stories accumulated on the Island slopes. Wait till the day I become successful and fulfill my wish! I will not speak of love when I level the immigration station! I am distressed that we Chinese are detained in this wooden building. It is actually racial barriers which cause difficulties on Yingtai Island. Even while they are tyrannical, they still claim to be humanitarian. I should regret my taking the risks of coming in the first place. I thoroughly hate the barbarians because they do not respect justice. They continually promulgate harsh laws to show off their prowess. They oppress the overseas Chinese and also violate treaties. They examine for hookworms and practice hundreds of despotic acts. I cannot bear to describe the harsh treatment by the doctors. Being stabbed for blood samples and examined for hookworms was even more pitiful. After taking the medicine, I also drank liquid, Like a dumb person eating the huanglian. We’re interested in which words appear the most often in our set of poems. It’s pretty hard to read or see much in this form. We’ll coming back to the topic of what words are the most common with actual numbers a bit later but for now, run the following cell to generate two interesting visualizations of the most common words (minus those such as “the”, “a”, etc.). wordcloud = WordCloud().generate(raw) plt.imshow(wordcloud, interpolation='bilinear') plt.axis("off") # lower max_font_size wordcloud = WordCloud(max_font_size=40).generate(raw) plt.figure() plt.imshow(wordcloud, interpolation="bilinear") plt.axis("off") plt.show() Question: What are the most common words you notice? Judging from these words, what do you think these poems are about? Replace this text with your response Oops, it seems we’ve forgotten just how many poems we have in our set. Luckily we have a quick way of finding out! Each “\n” in the display of the poem text indicates a line break. It turns out that each poem is separated by an empty line, a.k.a. two line breaks or “\n”’s. num_poems = len(raw.split("\n\n")) num_poems 49 We can also use this idea to calculate the number of characters in each poem. num_char_per_poem = [len(p) for p in raw.split("\n\n")] print(num_char_per_poem) [259, 212, 227, 262, 306, 233, 654, 260, 488, 550, 206, 167, 331, 325, 128, 203, 196, 251, 221, 250, 488, 201, 206, 237, 344, 243, 442, 345, 507, 474, 382, 465, 624, 444, 302, 399, 230, 505, 268, 437, 288, 226, 532, 116, 487, 254, 279, 263, 233] This is interesting but seems like just a long list of numbers. What about the average number of characters per poem? np.mean(num_char_per_poem) 325.51020408163265 Let’s look at it in histogram form to get a better idea of our data. Table().with_columns("Character Count", np.asarray(num_char_per_poem)).hist() Each bar of this histogram tells us what proportion of the poems (the height of the bar) have that many characters (the position of the bar on the x-axis). We can also use “\n” to look at enjambment too. Let’s calculate the proportion of lines that are enjambed out of the total number of lines per poem. from string import punctuation poems = raw.split("\n\n") all_poems_enjambment = [] for p in poems: lines = p.split("\n") poems = raw.split("\n\n") enjambment = 0 for l in lines: try: if l[-1] in punctuation: pass else: enjambment += 1 except: pass enj = enjambment/len(lines) all_poems_enjambment.append(enj) print(all_poems_enjambment) [0.625, 0.42857142857142855, 0.42857142857142855, 0.5555555555555556, 0.1111111111111111, 0.5, 0.45, 0.5, 0.4666666666666667, 0.4375, 0.42857142857142855, 0.2, 0.25, 0.2222222222222222, 0.0, 0.3333333333333333, 0.3333333333333333, 0.5, 0.3333333333333333, 0.2857142857142857, 0.4, 0.42857142857142855, 0.42857142857142855, 0.5, 0.2, 0.4444444444444444, 0.42857142857142855, 0.2727272727272727, 0.5, 0.35714285714285715, 0.3333333333333333, 0.5, 0.3157894736842105, 0.35714285714285715, 0.5, 0.5384615384615384, 0.5, 0.5, 0.375, 0.4666666666666667, 0.5555555555555556, 0.5, 0.47058823529411764, 0.5, 0.5, 0.5, 0.5, 0.5, 0.4444444444444444] Once again, what about the average? np.mean(all_poems_enjambment) 0.41237745084889205 Let’s now return to the question of the words that appear the most frequently in these 49 poems. First we have to use spaCy, an open-source software library for Natural Language Processing (NLP), to parse through the text and replace all the “\n”’s with spaces. nlp = spacy.load('en', parser=False) parsed_text = nlp(raw.replace("\n", " ")) We can separate all the words/symbols and put them in a table. toks_tab = Table() toks_tab.append_column(label="Word", values=[word.text for word in parsed_text]) toks_tab Word The sea - scape resembles lichen twisting and turning for ... (3366 rows omitted) toks_tab.append_column(label="POS", values=[word.pos_ for word in parsed_text]) toks_tab Word POS The DET sea NOUN - PUNCT scape NOUN resembles NOUN twisting VERB and CCONJ turning VERB ... (3366 rows omitted) Now let’s create a new table with even more columns using the “tablefy” function below. def tablefy(parsed_text): toks_tab = Table() toks_tab.append_column(label="Word", values=[word.text for word in parsed_text]) toks_tab.append_column(label="POS", values=[word.pos_ for word in parsed_text]) toks_tab.append_column(label="Lemma", values=[word.lemma_ for word in parsed_text]) toks_tab.append_column(label="Stop Word", values=[word.is_stop for word in parsed_text]) toks_tab.append_column(label="Punctuation", values=[word.is_punct for word in parsed_text]) toks_tab.append_column(label="Space", values=[word.is_space for word in parsed_text]) toks_tab.append_column(label="Number", values=[word.like_num for word in parsed_text]) toks_tab.append_column(label="OOV", values=[word.is_oov for word in parsed_text]) toks_tab.append_column(label="Dependency", values=[word.dep_ for word in parsed_text]) tablefy(parsed_text) Word POS Lemma Stop Word Punctuation Space Number OOV Dependency The DET the True False False False True det sea NOUN sea False False False False True compound - PUNCT - False True False False True punct scape NOUN scape False False False False True nsubj resembles NOUN resemble False False False False True ROOT lichen ADJ lichen False False False False True compound twisting VERB twist False False False False True dobj and CCONJ and True False False False True cc turning VERB turn False False False False True conj for ADP for True False False False True prep ... (3366 rows omitted) Next, let’s look at the frequency of words. However, we want to get rid of words such as “the” and “and” (stop words), punctuation, and spaces. We can do this by selecting rows that are not stop words, punctuation, or spaces and then sorting by word! word_counts = tablefy(parsed_text).where("Stop Word", are.equal_to(False)).where( "Punctuation", are.equal_to(False)).where( "Space", are.equal_to(False)).group("Word").sort("count",descending=True) word_counts Word count building 15 land 12 wooden 11 Island 11 day 10 country 10 tears 8 know 7 America 7 wind 6 ... (899 rows omitted) In this table, we have both the words “sad” and “sadness” - it seems strange to separate them. It turns out that these words are part of the same “lexeme”, or a unit of meaning. For example, “run”, “runs”, “ran”, and “running” are all part of the same lexeme with the lemma ‘run’. Lemmas are another column in our table from above! Nice! lemma_counts = tablefy(parsed_text).where("Stop Word", are.equal_to(False)).where( "Punctuation", are.equal_to(False)).where( "Space", are.equal_to(False)).group("Lemma").sort("count",descending=True) lemma_counts Lemma count building 16 day 15 land 13 wooden 11 country 10 Island 10 come 9 time 8 tear 8 know 8 ... (796 rows omitted) Now let’s look at how many words there are of each part of speech. pos_counts = tablefy(parsed_text).where("Stop Word", are.equal_to(False)).where( "Punctuation", are.equal_to(False)).where( "Space", are.equal_to(False)).group("POS").sort("count",descending=True) pos_counts POS count NOUN 585 VERB 392 PROPN 85 NUM 8 INTJ 1 We can also look at the proportions of each POS out of all the words! for i in np.arange(pos_counts.num_rows): pos = pos_counts.column("POS").item(i) count = pos_counts.column("count").item(i) total = np.sum(pos_counts.column("count")) proportion = str(count / total) print(pos + " proportion: " + proportion) NOUN proportion: 0.4428463285389856 VERB proportion: 0.2967448902346707 PROPN proportion: 0.0643451930355791 NUM proportion: 0.006056018168054504 INTJ proportion: 0.000757002271006813 If we’re interested in words’ relations with each other, we can look at words that are next to each other. The function below returns the word following the first instance of the word you search for in the specified source. def nextword(word, source): for i, w in enumerate(source): if w == word: return source[i+1] Mess around a bit with this function! Change the “word” argument. split_txt = raw.split() # Change the target or "home" to other words! nextword("home", split_txt) 'elicits' We are specifically interested in the word “I” and the words that poets use in succession. Let’s make an array of all the words that come after it in these poems. For easier viewing, the phrases have been printed out. What do you notice? one_after_i = make_array() for i, w in enumerate(split_txt): if w == "I": one_after_i = np.append(one_after_i, split_txt[i+1]) for i in one_after_i: print("I " + i) I arrived I began I arrived I heard I was I could I embarked I boarded I am I have I suffered I am I sigh I took I ate I arrived I thought I could I to I would I only I can I willingly I intended I have I used I immediately I have I am I look I wish I just I think I resolved I am I heard, I composed I lie I get I count I have I feel I sought I see I can I gaze I listen I dissipate I met I cannot I sit I have I wish I could I confide I rely I bow I can I can I cannot I can I have I cannot I threw I have I constantly I dreamed I have I am I will I cannot I be I am I must I must I bear I look I am I gaze I sit I can I return I came I will I will I am I threw I bought I opened I reminisce I have I lean I am I grieve I say? I have I am I dare I left I gaze I would I beat I think I respectfully I am I become I will I level I am I should I thoroughly I cannot I also Above we have only shown the next word, what about the next two words? Does this give you any new insight? two_after_i = make_array() for i, w in enumerate(split_txt): if w == "I": two_after_i = np.append(two_after_i, split_txt[i+1] + " " + split_txt[i+2]) for i in two_after_i: print("I " + i) I arrived at I began rushing I arrived on I heard I I was forbidden I could do I embarked on I boarded the I am at I have yet I suffered misery I am not I sigh because I took passage I ate wind I arrived safely I thought I I could land I to know I would become I only wish I can land I willingly became I intended to I have not I used to I immediately raised I have experienced I am subject I look up I wish to I just write I think back I resolved to I am still I heard, faintly, I composed a I lie stiff I get up I count the I have not I feel embarrassed. I sought the I see my I can only I gaze at I listen to I dissipate my I met with I cannot bear I sit passively I have a I wish I I could travel I confide my I rely solely I bow my I can do. I can do I cannot extend I can only I have infinite I cannot fly I threw away I have no I constantly pace I dreamed of I have run I am allowed I will toss I cannot come I be allowed I am rid I must remember I must be I bear to I look to I am anxious I gaze to I sit in I can enter I came to I will have I will certainly I am a I threw away I bought an I opened a I reminisce the I have passed I lean on I am ashamed I grieve for I say? I I have ten-thousand I am imprisoned, I dare strive I left the I gaze at I would be I beat my I think of I respectfully exhort I am searching I become successful I will not I level the I am distressed I should regret I thoroughly hate I cannot bear I also drank Try doing some exploring of your own! If you’re feeling stuck, feel free to copy and edit code from above. # Write your own code here! ### Sentiment Analysis We can do some analysis of the overall sentiments, or emotions conveyed, in each of the poems using the code below. Here, we analyze the overall sentiment of each poem individually. Once you run the next cell, you’ll see the sentiment values for each poem. A value below 0 denotes a negative sentiment, and a value above 0 is positive. sentiments = make_array() for p in poems: poem = TextBlob(p) sentiments = np.append(sentiments, poem.sentiment.polarity) sentiments array([-0.04090909, 0.18333333, -0.02222222, 0.38333333, 0.175 , 0. , 0.09791667, 0.12878788, -0.02380952, 0.15104167, -0.19166667, 0. , -0.46 , -0.08061224, -0.03333333, 0.03333333, -0.03 , -0.28333333, 0.03333333, 0. , -0.195 , -0.6875 , -0.025 , 0. , 0.16666667, -0.26 , -0.155 , 0.38611111, -0.10083333, -0.03194444, -0.10833333, -0.07727273, 0.12777778, -0.134375 , 0.15 , 0.08333333, 0.1375 , -0.12625 , 0.075 , -0.05 , 0.29 , 0.225 , -0.05138889, 0. , 0.00204082, 0.265625 , 0.0625 , -0.33333333, -0.025 ]) Now, what does this mean? It appears that the number of poems with negative sentiment is about the same as the number of poems with positive or neutral (0) sentiment. We can look at the proportion of negative poems in the next cell: neg_proportion = np.count_nonzero(sentiments < 0)/len(sentiments) neg_proportion 0.4897959183673469 Okay, so just under half of the poems have negative sentiment. So, on average the poems have slightly positive sentiment, right? We can also perform sentiment analysis across the text of all of the poems at once and see what happens: poems_all = TextBlob(raw.replace('\n', ' ')) poems_all.sentiment.polarity -0.014875449409347723 This way of analyzing the text tells us that the language in all of the poems has slightly negative sentiment. One more analysis we can perform is computing the average sentiment of the poems, given the list of each individual poem’s sentiments that we computed earlier: np.mean(sentiments) -0.007540473981800516 This method also tells us that our poems have slightly negative sentiment, on average. Here, let’s look at one of the poems with it’s sentiment value: poem_3 = poems[3].replace('\n', ' ') print(poem_3) print(TextBlob(poem_3).sentiment.polarity) The gold and silver of America is very appealing. Jabbing an awl into the thigh in search of glory, I embarked on the journey. Not only are my one-thousand pieces of gold already depleted, but My countenance is blackened. It is surely for the sake of the family. 0.3833333333333333 Let’s look at one more poem: poem_47 = poems[47].replace('\n', ' ') print(poem_47) print(TextBlob(poem_47).sentiment.polarity) I thoroughly hate the barbarians because they do not respect justice. They continually promulgate harsh laws to show off their prowess. They oppress the overseas Chinese and also violate treaties. They examine for hookworms and practice hundreds of despotic acts. -0.3333333333333333 Question: Do you think the sentiment analyzer did a good job assigning the sentiment to these poems? What might that mean for the trends we see in our average sentiment across the poems? 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https://brilliant.org/problems/fiery-factorials/	# Fiery Factorials! $\large \dfrac{1! \times2!\times 3!\times \cdots \times 10!}{(1!)^2(3!)^2(5!)^2(7!)^2(9!)^2}=15\times2^n$ What is the value of $$n$$ such that it satisfy the equation above? ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9928529262542725, "perplexity": 1541.262592017758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424575.75/warc/CC-MAIN-20170723162614-20170723182614-00580.warc.gz"}
https://brainmass.com/physics/atmosphere/air-pressure-32682	Explore BrainMass # Air pressure Not what you're looking for? Search our solutions OR ask your own Custom question. This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! (a) assuming an average sea-level pressure of 1000hPa, what is the mass of the atmosphere? assume that the earth is as sphere with radius 6400km. (b) what is the mass of the atmosphere above 500hPa? you can again assume a sphere of radius 6400km for this calculation. what fraction of the mass of the earth's atmosphere lies above 500 hPa? (c) repeat (b) for the 250hPa surface.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9472998976707458, "perplexity": 1326.7567025320386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663016949.77/warc/CC-MAIN-20220528154416-20220528184416-00655.warc.gz"}
https://aas.org/archives/BAAS/v34n2/aas200/36.htm	AAS 200th meeting, Albuquerque, NM, June 2002 Session 22. Extra Galactic Magnetic Fields: Their Origin and Manifestation through Structure of Quasars, Radio Lobes and within Clusters Special Session Oral, Monday, June 3, 2002, 10:00-11:30am, La Cienega ## [22.01] Source of the Largest Extragalactic Magnetic Field Energies P.P. Kronberg (LANL), Q.W. Dufton (University of Toronto), H. Li, S.A. Colgate (LANL) The recently implied ubiquity of ~\,108\, M\odot central black holes (GBH) in large elliptical galaxies raises the question How much of the black hole energy that is released can we independently and quantitively measure in the surrounding IGM?''. A recent source-by-source analysis by us to answer this question determined that the best IGM calorimeters for this purpose are the largest (~0.5 to 5\,Mpc), not the most radio luminous extragalactic radio sources. These occur in relatively rarified IGM environments away from cluster cores. The upper bound of the energy content of the synchrotron-emitting lobes, much of which is magnetic, is ~8 \times 1060ergs, -- a significant fraction of the GBHs' gravitational binding energy. There are reasons why this global total energy estimate may even be conservative. The proximity of this number to the AGNs' total (gravitational) energy reservoir, and hence with the total radiated energy over all bands (which escapes at c) has many implications that are not yet understood in detail. The captured, i.e. magnetic, energy which propagates away much more slowly, constitutes a very large amount of retained energy in the locality of the host galaxy. For a cluster member AGN, this magnetic energy will be deposited within the host galaxy cluster. For a field'' radio galaxy, it will remain captured within ~ a Mpc. We briefly discuss the wideranging implications that this hitherto hidden, intergalactic magnetic energy has for subsequent galaxy formation on these scales, and some implications for the IGM energetics of galaxy clusters. Bulletin of the American Astronomical Society, 34 © 2002. The American Astronomical Soceity.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8183358311653137, "perplexity": 4802.723080870918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00019-ip-10-171-6-4.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/237442/start-inparaenum-numeration-with-another-letter-than-a/454237	Start inparaenum-numeration with another letter than “a)” How can I start \begin{inparaenum} with an arbitrary letter (other than a)) after a break in the inparaenum-environment. I would like to let a new inparaenum-environment be related to the end of the earlier one. \usepackage{amsmath,amssymb,stmaryrd} \usepackage{paralist} \usepackage{tabto} \begin{document} \begin{enumerate} \item \textbf{Working with logarithms}: \NumTabs{3} \begin{inparaenum}[a)] Calculate the following \item $\ln 1 =$ \tab \item $\ln e =$ \tab \item $\ln \frac{1}{e} =$ \end{inparaenum} Express the following in terms of $\ln 2$: \NumTabs{3} \begin{inparaenum}[d)] \item $\ln 4$ \tab \item $\ln \sqrt[3]{2^5}$ \tab \item $\ln \frac{1}{16}$ \end{inparaenum} \end{enumerate} \end{document} Is there a way to let the second row start with d instead of using d in all positions? Thank you very much :) • The \begin{inparamenum}[d)] is wrong and the compiler complains about it ;-) – user31729 Apr 8 '15 at 8:24 You can set the number by hand; since it's a second level list, you have to set enumii. \usepackage{amsmath,amssymb,stmaryrd} \usepackage{paralist} \usepackage{tabto} \begin{document} \begin{enumerate} \item \textbf{Working with logarithms}: \NumTabs{3} \begin{inparaenum}[a)] Calculate the following \item $\ln 1 =$ \tab \item $\ln e =$ \tab \item $\ln \frac{1}{e} =$ \end{inparaenum} Express the following in terms of $\ln 2$: \NumTabs{3} \begin{inparaenum}[a)]\setcounter{enumii}{3} \item $\ln 4$ \tab \item $\ln \sqrt[3]{2^5}$ \tab \item $\ln \frac{1}{16}$ \end{inparaenum} \end{enumerate} \end{document} \usepackage{amsmath,amssymb,stmaryrd} \usepackage[inline]{enumitem} \usepackage{tabto} \begin{document} \begin{enumerate} \NumTabs{3} \item \textbf{Working with logarithms}: Calculate the following\\[\medskipamount] \begin{enumerate}[label=\alph),itemjoin=\tab,before={}] \item $\ln 1 =$ \item $\ln e =$ \item $\ln \frac{1}{e} =$ \end{enumerate} Express the following in terms of $\ln 2$:\\[\medskipamount] \begin{enumerate}[label=\alph),itemjoin=\tab,resume] \item $\ln 4$ \item $\ln \sqrt[3]{2^5}$ \item $\ln \frac{1}{16}$ \end{enumerate} \end{enumerate} \end{document} • The \setcounter{enumii}{3} works fine as long as I stay in the upper enumerate-environment. Doesn't work in a new enumerate-inparaenum-environment. But that's ok for the moment. Thank you – Mac Apr 8 '15 at 8:43 • @Mac: This deliberately depends on the nesting of the environments – user31729 Apr 8 '15 at 10:10 • @Mac I suggest you to switch to enumitem, that's much more powerful than paralist. – egreg Apr 8 '15 at 10:40 Another version, using my assoccnt package, without the need of remembering the counter value: The contenumii counter is used to store the total value of the enumii counter automatically and stored back after inparaenum. Caveat: It will be incremented each time when another second level enumeration is used Use the \SuspendCounters feature from the assoccnt package then \usepackage{amsmath,amssymb,stmaryrd} \usepackage{paralist} \usepackage{tabto} \usepackage{assoccnt} \newcounter{contenumii} \DeclareAssociatedCounters{enumii}{contenumii} \begin{document} \begin{enumerate} \item \textbf{Working with logarithms}: \NumTabs{3} \begin{inparaenum}[a)] Calculate the following \item $\ln 1 =$ \tab \item $\ln e =$ \tab \item $\ln \frac{1}{e} =$ \end{inparaenum} Express the following in terms of $\ln 2$: \NumTabs{3} \begin{inparaenum}[a)]\setcounter{enumii}{\number\value{contenumii}} \item $\ln 4$ \tab \item $\ln \sqrt[3]{2^5}$ \tab \item $\ln \frac{1}{16}$ \end{inparaenum} \end{enumerate} \end{document} Other options: enumitem package, with the resume option, but this is not as compact as paralist (initially, can be changed, perhaps) • I cannot compile this.. it says assoccnt.sty not found. Somehow not loading the new package. I'm not sure what to do about it. But thanks for the idea :) – Mac Apr 8 '15 at 8:46 • @Mac: No problem at all... but it's on TeXLive and CTAN of course – user31729 Apr 8 '15 at 8:48 • That means I have to load it manually? I'm used to let this be done by TexnicCenter. I'm still looking for how to force my editor do this – Mac Apr 8 '15 at 8:58 • @Mac: I don't use those editor stuff like TexnicCenter etc. I update manually all the time (daily!) by invoking tlmgr on a Linux console – user31729 Apr 8 '15 at 9:11 • @ChristianHupfer Daily?! Why? – cfr Apr 9 '15 at 2:54 I know it's a very late answer, but I found this to work for me: % Counter used in continuing lists. \newcounter{contlist} % ... \begin{inparaenum}[(a)] \item line-item 1 \item line-item 2 \end{inparaenum} \setcounter{contlist}{\value{enumi}} % ... \begin{inparaenum}[(a)] \setcounter{enumi}{\value{contlist}} \item line-item 3 \item line-item 4 \end{inparaenum} This works across different styles of enumerations [1, (b), (iii), etc]. • Welcome to TeX.SX! The other answers are also applicable to other styles, so how does this add anything new? – TeXnician Oct 7 '18 at 13:44 • It answers the original question, and doesn't need hand-coding. Nor does it need other styles/environments. – sn00p Oct 10 '18 at 10:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9744435548782349, "perplexity": 4658.078689278763}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250597458.22/warc/CC-MAIN-20200120052454-20200120080454-00079.warc.gz"}
https://export.arxiv.org/abs/1610.02121	physics.comp-ph (what is this?) # Title: Large-scale all-electron density functional theory calculations using an enriched finite element basis Abstract: We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that are constructed from the solution of the Kohn-Sham (KS) problem for single atoms. We term these numerical basis functions as enrichment functions, and the resultant basis as the enriched finite element basis. The enrichment functions are compactly supported through the use of smooth cutoff functions, which enhances the conditioning and maintains the locality of the basis. The integrals involved in the evaluation of the discrete KS Hamiltonian and overlap matrix in the enriched finite element basis are computed using an adaptive quadrature grid based on the characteristics of enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by using a block-wise matrix inversion in conjunction with special reduced-order quadrature rules to transform the discrete Kohn-Sham problem to a standard eigenvalue problem. Finally, we solve the resulting standard eigenvalue problem by using a Chebyshev polynomial based filtering technique to compute the relevant eigenspectrum. We demonstrate the accuracy, efficiency and parallel scalability of the proposed method on semiconducting and heavy-metallic systems of various sizes, with the largest system containing 8694 electrons. We obtain accuracies in the ground-state energies that are within $\sim 1$mHa with ground-state energies obtained from classical finite element as well as gaussian basis sets. We observe a $50-300$ and $\sim 8$ fold reduction in the overall computational time when compared to classical finite element and gaussian basis, respectively. We also observe good parallel scalability up to 384 processors for a benchmark system comprising of 280-atom silicon nano-cluster. Subjects: Computational Physics (physics.comp-ph) Journal reference: Phys. Rev. B 95, 035112 (2017) DOI: 10.1103/PhysRevB.95.035112 Cite as: arXiv:1610.02121 [physics.comp-ph] (or arXiv:1610.02121v2 [physics.comp-ph] for this version) ## Submission history From: Bikash Kanungo [view email] [v1] Fri, 7 Oct 2016 02:07:33 GMT (69kb) [v2] Fri, 9 Dec 2016 21:00:05 GMT (155kb) Link back to: arXiv, form interface, contact.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7230181694030762, "perplexity": 1085.2175610115344}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305006.68/warc/CC-MAIN-20220126222652-20220127012652-00512.warc.gz"}
https://blender.stackexchange.com/questions/52612/reloading-animation-nodes-node-development-workflow/52625	# Reloading Animation Nodes (node development workflow) I am developing some custom nodes and have a question about the development lifecycle. Can I reload AN classes without restarting Blender? Or, do I need to reload blender after each change to the class’s source file? I have tried a few things using importLib and nothing works. Thanks! If you can reload your changes without closing Blender depends on what you changed. First of all: you don't have to write any reloading code yourself, everything is handled automatically in the developer_utils.py file. The problem with reloading when you have so many modules is that you can't reload the whole addon at once (please correct me if I'm wrong). Instead each module is reloaded individually. Here is an example that shows the problem that can happen: # file_a.py def my_func(): return 0 # file_b.py from file_a import my_func print(my_func()) When file_b is executed everything looks normal and the console output will be 0. Now imagine you change my_func so that it returns 1. After this change the reloading order is important. There are two different scenarios: 1. file_a.py and then file_b.py: In this case everything works as expected, my_func will be updated at first, then the updated function is imported into file_b and the output will be 1. 2. file_b.py and then file_a.py: Now file_b imports the old function again (the one that returns 0) because file_a has not been reloaded yet. Then output will still be 0. In general you can simply try to reload all addons by hitting F8. Sometimes it helps to reload twice to make sure that all modules use the updated functions. There is still a good chance that two modules which depend on the same module will have different versions of the same function but in most cases you don't need to care about that. Currently there is only one module in AN that needs to be reloaded before all the others: https://github.com/JacquesLucke/animation_nodes/blob/master/utils/handlers.py#L6 Summary Reloading should definitly work when you only changed a single file. Maybe you have to reload twice (I hit F8 twice all the time..). Reloading does not work (only if you are lucky) when you added/removed a function from a module that is imported into other modules. Most of the time I just try it and when it doesn't work I restart Blender. Take a look into the console if any exception is raised (also note that not all exceptions have to come from AN; other actived addons might not support reloading) try hitting F8 to reload scripts, or, if you're just running your script from a text editor, just run it again. The best way to apply changes made to an addon is to disable then re-enable the addon. If the addon has been made right this will un-register any classes, properties and other changes that have been made by the addon, allowing the new adjusted code to be used without conflicts. When you create an addon, or add to another addon, any classes need to be registered in the addons register() function with a matching unregister added to the unregister() function. Other steps can be added to these functions, as in the following example an item is added and removed from the import menu. Custom properties may also be added in register and then deleted in unregister. There is also a register_module() available that can make things easy for some addons. When you disable the addon, the code that was read when you enabled the addon is used (which is the old unregister()), then when you re-enable it, the modifications are noticed and the file is re-read so that the new version is in use. If you look in the console when you re-enable the addon after you make changes you will see something like - module changed on disk: /path/to/scripts/addons_contrib/test1.py reloading... Here is a trimmed down copy of the import template included with blender showing the use of register and unregister. import bpy class ImportSomeData(Operator, ImportHelper): """This appears in the tooltip of the operator and in the generated docs""" bl_idname = "import_test.some_data" bl_label = "Import Some Data" #class methods here self.layout.operator(ImportSomeData.bl_idname, text="Text Import Operator") def register(): bpy.utils.register_class(ImportSomeData)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1972981095314026, "perplexity": 2034.5655176508367}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886516.43/warc/CC-MAIN-20200704170556-20200704200556-00256.warc.gz"}
http://arzyabexpert.com/guild-wars-jnoyivf/what-is-the-following-sum-3-sqrt-125x%5E10y%5E13-96c4ab	##### بلاگ Let's look at some Excel SQRT function examples and explore how to use the SQRT function as a worksheet function in Microsoft Excel: Based on the Excel spreadsheet above, the following SQRT examples would return: =SQRT(A1) Result: 5 =SQRT(A2) Result: 5.796550698 =SQRT(A3) Result: #NUM! Thus, for calculating the product of the following square roots sqrt(33)sqrt(6), enter simplify_surd(sqrt(33)sqrt(6)), the result 3sqrt(22) is returned. Ans. If the argument is NaN or negative, then the result is NaN. Let's look at some Oracle SQRT function examples and explore how to use the SQRT function in Oracle/PLSQL. So the answer would be 2. The second term abs(x)^N/(N!) So, you can take a 3 out of the sqrt., because 3^2 is 9. Conic Sections In mathematics, a square root of a number x is a number y such that y 2 = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. Description. If so, then #b = 11# and we would have #f(5+6/n) = sqrt(7+(6/n)^2)#, so we would get #f(x) = sqrt(7+(x-5)^2)#.) If x^2=-1=i^2, x=sqrt(-1)=(-1)^(1/2)=+-i sqrt(-2)=sqrt(-1)sqrt2=+-1.4142i and, likewise, sqrt(-18)=+-3(1.4142)i. Question: Is the following sum rational or irrational? Boolean has an integer value of 1, thus sum becomes 1 + 50 + 5 + 10 = 66. Now you can add the two sqrts. d) [True, 50, 5, 10] Sum is: 66 . For example: SQRT(9) Result: 3 SQRT(37) Result: 6.08276253029822 SQRT(5.617) Result: 2.37002109695251 You then have: 3 sqrt-2. For negative and complex numbers z = u + iw, the complex square root sqrt(z) returns. It is also the area of the unit circle. If the argument passed is positive zero or negative zero then the result will be same as that of the argument. 2. Putting these two facts together gives the following, $A \approx \sum\limits_{n = 1}^\infty {\frac{1}{n}} > \int_{{\,1}}^{{\,\infty }}{{\frac{1}{x}\,dx}} = \infty$ Notice that this tells us that we must have, $\sum\limits_{n = 1}^\infty {\frac{1}{n}} > \infty \hspace{0.5in} \Rightarrow \hspace{0.5in}\sum\limits_{n = 1}^\infty {\frac{1}{n}} = \infty$ Since we can’t really be larger than (\sqrt(8))/(3)+\sqrt(16) TutorsOnSpot.com. Compared to other sites, www.OnSolver.com has a huge advantage, because you can find the sum of not only numerical but also functional series, which will determine the convergence domain of the original series, using the most known methods. For example, the following is a valid expression: (-1)^(2n+pi/3) Summation formula and Sigma (Σ) notation. ; S(i) refers to sum of Fibonacci numbers till F(i). Well, it's a right Riemann sum, so we're using the value of the function right over there, write it two plus five over N. So, this value right over here. A proof of the Alternating Series Test is also given. In this section we will discuss using the Alternating Series Test to determine if an infinite series converges or diverges. is bounded, that is that sum_(n=0)^oo x^n/(n!) So, be careful to not make this very common mistake! Now we could keep going. The sqrt() function in C++ returns the square root of a number. Correct answer to the question Ineed ! 0. The following table contains some important mathematical constants: Name Symbol Value Meaning Pi, Archimedes' constant or Ludoph's number: π ≈3.141592653589793 A transcendental number that is the ratio of the length of a circle's circumference to its diameter. $5 = \sqrt {25} = \sqrt {9 + 16} \ne \sqrt 9 + \sqrt {16} = 3 + 4 = 7$ If we “break up” the root into the sum of the two pieces we clearly get different answers! Derivatives Derivative Applications Limits Integrals Integral Applications Riemann Sum Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Functions Line Equations Functions Arithmetic & Comp. We can rewrite the relation F(n + 1) = F(n) + F(n – 1) as below: Relationship Deduction. 2) What is the output of the following program? This is the natural log, the natural log of two plus five over N, and since this is the first rectangle times one, times one. If the argument is positive infinity, then the result is positive infinity. sqrt: square root: tan-tangent: tanh -hyperbolic tangent: In the expression you can enter minus as a negation (sign), and also use implicit multiplication (2n will be interpreted as 2 * n). what is the following sum? Example. We have shown that for any x in (-oo,oo), sum_(n=0)^oo abs(x)^n/(n!) Riemann sums help us approximate definite integrals, but they also help us formally define definite integrals. Free series convergence calculator - test infinite series for convergence step-by-step This is a mistake. Precalculus . 5x(3 sqrt(x^2 y)+2(3 sqrt^5y) a- 7x(^6 square root of x^2y) b-7x^2(^6 square root of xy^2) c-7x^2(^3 square root of xy^2) d-7x(^3square root of x^2y) - e-eduanswers.com To use the comparison test to determine the convergence or divergence of a series $$\sum_{n=1}^∞a_n$$, it is necessary to find a suitable series with which to compare it. sum_(n=0)^oo abs(x)^n/(N^n) is the sum of a geometric series with positive common ratio abs(x)/N < 1, so converges. The graph of $x^2+(y-\sqrt[3]{x^2})^2=1$ is very interesting and is show below using desmos. For the elements of X that are negative or complex, sqrt(X) produces complex results. If the series is convergent, determine whether it is absolutely or conditionally convergent. Learn how this is achieved and how we can move between the representation of area as a definite integral and as a Riemann sum. Part A: In complete sentences, explain the relationships between all pairs of special angles 1, 2, 3 and 4 created by transversal line b and parallel lines d and e. Part B: for the given diagram, use the measure of The following special angle relationships are created by transversal line b and parallel lines d and e : 1 to find the measures of ∠2, ∠3, and ∠4. Efficient approach: The idea is to find the relationship between the sum of Fibonacci numbers and n th Fibonacci number and use Binet’s Formula to calculate its value. 5 (3 sqrt) + 9 (3 sqrt) Answers (1) Unique 29 December, 11:51. First you must simplify the sqrt-18. (d) Explanation: The List is initially has 3 elements. Hence it is also convergent. The Alternating Series Test can be used only if the terms of the series alternate in sign. Find a perfect square that is a multiple of 18: in this case it would be 9, because 9 x 2 = 18. Homework Writing Market. Now, #sqrt(7+(6/n)^2) = f(b+ Deltax) = f(-1+6/n)# Which will be true if #f(x) = sqrt(7+(x+1)^2)# This #f(x)# works for the other two given terms, so it must be the correct #f(x)#. The insert() adds element 5 at index 2, moving element 10 at index 3 and the List becomes [True, 50, 5, 10]. import math math.sqrt( x ) Note − This function is not accessible directly, so we need to import the math module and then we need to call this function using the math static object.. Parameters. B = sqrt(X) returns the square root of each element of the array X. Surds fraction calculator (square root quotient) The online square root calculator can symplify surds root quotients in exact form. The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. Following is the syntax for sqrt() method −. What is the following sum? (I wonder if it should be #int_5^b f(x) dx#? =SQRT(82.6) Result: 9.088454214 Our Services. The sqrt() method returns the square root of x for x > 0.. Syntax. Start studying MIS 207. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 3 xx sqrt125 = 15sqrt5 and root(3)125 = 5 I have heard many students read root(3)n as "the third square root of n". is absolutely convergent. Answers Mine. Truly, each term has two values and the sum has four values, in Mathematical Exactitude. The square root is root(2)n (usually denoted sqrtx), the third (or cube) root is root(3)n, the fourth root is root(4)n and so on. 1 sqrt.- 2 + 3 sqrt.- 2 = 4 sqrt. What is the radius of convergence of the series #sum_(n=0)^oo(n(x+2)^n)/3^(n+1)#? Whichever was meant the first step for simplifying is the same. This one right over here the width is the same, five over N but what's the height? The java.lang.Math.sqrt() returns the square root of a value of type double passed to it as argument. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Don't curse me feeling that I am making a mole appear as mountain. x − This is a numeric expression.. Return Value I am sorry. F(i) refers to the i th Fibonacci number. This is the concept of arithmetic, we are required to calculate the following; 5sqrt (3) + 9sqrt (3) Here we shall take the two terms to be like terms; thus; 5sqrt (3) + 9sqrt (3) =14sqrt (3) Thus the answer is: 14sqrt (3) Comment; Complaint; Link ; Know the Answer? See all questions in Determining the Radius and Interval of Convergence for a Power Series Impact of this question The sum and difference formulas can be used to find the exact values of the sine, cosine, or tangent of an angle. Determine whether the following series is convergent or divergent. This is useful for analysis when the sum of a series online must be presented and found as a solution of limits of partial sums of series. If you aren’t sure that you believe this consider the following quick number example. So, the sum is +-1.4142(1+-3)i=+-5.657i and +-2.8281, i=sqrt(-1), nearly.. Let us compile and run the above program that will produce the following result − Square root of 4.000000 is 2.000000 Square root of 5.000000 is 2.236068 math_h.htm Answer. This section we will discuss using the Alternating series Test is also.... A numeric expression.. Return value Start studying MIS 207 the elements of x x! I am making a mole appear as mountain, i=sqrt ( -1 ), nearly the (! If used unintentionally has an integer value of 1, thus sum 1. S ( i ) refers to the i th Fibonacci number convergent, determine whether it is or! ) +\sqrt ( 16 ) TutorsOnSpot.com = 4 sqrt to what is the following sum 3 sqrt 125x^10y^13 if an infinite series converges diverges. 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https://www.flexiprep.com/Important-Topics/Mathematics/Functions.html	# Functions and Types of Functions: What Are Functions in Mathematics? (For CBSE, ICSE, IAS, NET, NRA 2022) Glide to success with Doorsteptutor material for competitive exams : get questions, notes, tests, video lectures and more- for all subjects of your exam. # Title: Functions and Types of Functions • Functions are relations where each input has a particular output. • We can define a function as a special relation which maps each element of set A with one and only one element of set B. Both the sets A and B must be non-empty. • In this lesson, the concepts of functions in mathematics and the different types of functions are covered using various examples for better understanding. ## What Are Functions in Mathematics? • A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. • A function defines a particular output for a particular input. Hence, is a function such that for a ∈ A there is a unique element b ∈ B such that • Let A & B be any two non-empty sets, mapping from A to B will be a function only when every element in set A has one end only one image in set B. ## Example • Another definition of functions is that it is a relation f in which each element of set A is mapped with only one element belonging to set B. • Also, in a function, there cannot be two pairs with the same first element. ## A Condition for a Function • Set A and Set B should be non-empty. • In a function, a particular input is given to get a particular output. So, A function denotes that f is a function from A to B, where A is a domain and B is a co-domain. • Many widely used mathematical formulas are expressions of known functions. • For an element, a, which belongs to A, a unique element b, is there such that • For example, the formula for the area of a circle, , gives the dependent variable A (the area) as a function of the independent variable r (the radius) . • The unique element b to which f relates a, is denoted by f (a) , and is called f of a, or the value of f at a, or the image of a under f. • The range of f (image of a under f) • It is the set of all values of f (x) taken together. • Range of f = • A real-valued function has either P or any one of its subsets as its range. • Further, if its domain is also either P or a subset of P, it is called a real function. ## Representation of Functions • Functions are generally represented as f (x) • Let, • It is said as f of x is equal to x cube. Developed by:	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9183061122894287, "perplexity": 428.5336550598945}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358323.91/warc/CC-MAIN-20211127223710-20211128013710-00561.warc.gz"}
https://puzzling.stackexchange.com/questions/41830/help-i-am-infected-with-the-puzzling-bug	# Help! I am infected with the puzzling bug! Argh...I can't get this bug of puzzling off my head! It's really weird, and so annoying, you know...I can't help thinking about puzzles all the time. It's like... when I see a word, I think of anagrams...when I see tiled floors, I think of sudoku on them...when I see a door, I look for loose bricks or business cards... What's worse, this bug is heavily affecting my brain. For example, today I found that I had written the following on my notebook: Text version: This information technology simply never obeys the leaders. Nasal fluid begins a big ugly Indian mountain. A stupid person is the manager of codes. A locker is secure in heavy halogen. You are Eastern river in England. Length: 2433423 Now I don't remember what it means, except that I've a feeling that the punctuations might be irrelevant. Maybe you people can help me out? Sorry if the backstory sounds annoying or unnecessary; it originates in a chat post. I don't claim any of the images to be my own. • Is this a sort of riddle? Or more of a cipher / wordplay / that sort of thing? – Avik Mohan Sep 1 '16 at 5:49 • Not riddle or cipher, it's mainly wordplay. Look at the tags. – Ankoganit Sep 1 '16 at 5:49 • I loved this puzzle. Confusing at first, then you slowly start to piece things together until you have enough to realize the gimmick. Once I had ## #### ___ ___ #### ## ___, I could easily fill in the rest. Simple but very well-made, and a lot of thought was put into it - I'd love to see more puzzles with this much effort! (Not necessarily even with the same trick, but I did enjoy it of course.) – Deusovi Sep 1 '16 at 6:57 • @Deusovi and Ankoganit: Well made and done! Do you think including the obvious but missing tag would be too much of a giveaway? And I'm not sure this is really steganography. Just trying to tidy up! – Dan Russell Sep 1 '16 at 16:42 • @Dan: I've removed the steganography tag. Not sure if adding that one in would make it too obvious - I'll leave it up to Ankoganit. – Deusovi Sep 1 '16 at 16:43 This information technology IT (ddef) simply never obeys the leaders. Nasal fluid SNOT ("leaders" of "simply never obeys the") begins a big ugly Indian mountain. ABU (beginnings of "a big ugly") A stupid person is the manager of codes. GIT (ddef) A locker is secure SAFE (ddef: locker, secure) in heavy halogen AT (ddef: astatine, in) You are Eastern river in England. URE (homophone) OP Edit: the intended explanation was : U(You)+R(Are)+E(Eastern)=URE. IT SNOT ABU GIT SAFE AT URE or, more descriptively, IT'S NOT A BUG - IT'S A FEATURE! • (And I absolutely agree with the answer.) – Deusovi Sep 1 '16 at 6:58 • I think adding the Length: 2 4 3 3 4 2 3 (note the spaces I added, I think you know what it is) in the answer should be good in order to have the full scope of the answer :). – Miquel Coll Sep 1 '16 at 7:29 • I took the liberty to edit one of the explanations to reflect my original intention. :-) – Ankoganit Sep 1 '16 at 14:43 • I don't quite understand what you mean by ddef, or how the numbers play in – Avik Mohan Sep 1 '16 at 17:17 • @Avik: These are all cryptic style clues. "ddef" stands for "double definition", and the numbers are the lengths of each answer. – Deusovi Sep 1 '16 at 17:20 # Wrap-up: The Making Of Help! I am infected with the puzzling bug! This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community. Caution: This post may contain spoilers. ### Inspiration The tag have always been one of my favourites here on puzzling, and I've always thought it would be cool to have a few cryptic clues whose answers spell out a message or sentence. One of the most important aspects of cryptic clues is that they tend to have a misleading surface meaning. This gave me the idea of obfuscating the clues by clever positioning of punctuation, so that the beginnings and ends of the clues are not easily deducible from the apparent structure of the sentences. I had not yet decided upon the target sentence to be "encrypted", so as to say. I tried some random quotes and proverbs without much success. One issue that always bothered me was that I had to include the definition for every word, and it was fairly easy for a solver to pick up only those definitions and deduce the hidden message. Around this time, rand al'thor wrote in a friendly chat : "Congratulations, you've been infected with the puzzling bug!". I was about to type in the response "It's not a bug, it's a feature" when it occurred to me that the word 'safe' is hidden among the letters. Then it struck me that I could break up the target string into a different set of words than those in the actual message. As it turned out, the sentence at hand was an excellent specimen for this to work. ### Steps of the creation The first thing I began with was the proper spacing out. I wanted to ensure that no word in the original message was intact. Apparently, the only way to obfuscate 'It's' was to take out the 'It' part and fuse the 's' with the second word. So it began as "It snot". Nice enough. Having already decided upon 'safe', the only viable option was 'Abu git safe at Ure'. I would be happier if 'ature' were a proper clueable word, but apparently it isn't. Now, I had to make the clues themselves. I tried to avoid anagrams (so that those having chatted with me about anagrams some time before don't have an unfair advantage), and ended up having mostly double definitions and acrostics. Many of the words were too short to clue in some other way. All this while, I tried to blend the clues together to form multiple sentences so that it was not obvious where clues really start or end. I was afraid this would turn out to be too obscure, so I included the word-lengths to gently nudge the solver towards crossword-styled clues. For a backstory, I chose the first one that came to my mind. I added a 'snapshot of my notebook' for making the story more realistic. ### Resources I used mostly Google and Dictionary.com. I had to google for words I wasn't sure they existed (Abu and Ure), and for synonyms of otherwise known words. (As a side note, Google kept thinking I live at Mount Abu, Rajasthan, India for quite a few days because of my search history). Also, I used Adobe Photoshop for creating the image of the notebook that accompanies my puzzle. ### Takeaway This puzzle reinforced my belief that clever twists in classic puzzles can produce rather interesting results. Also, this confirmed my trust in the superior problem-solving ability of PSE users. • Simply beautiful! – Timme Nov 23 '16 at 13:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36714696884155273, "perplexity": 1957.6815222633495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540497022.38/warc/CC-MAIN-20191207082632-20191207110632-00282.warc.gz"}
http://noobstarter.com/peak-nootropics-reddit-brain-food-memory-improvement.html	Professor David O Kennedy published a book in 2014 called Plants and the Human Brain. In his book he summarizes the last 15 years of research into cognitive nutrition, including the work he's done with colleagues at the Brain Performance Nutrition Research Center at Northumbria University. It's a great read and a good guide to what sorts of herbs and other plants to include in our weekly diet and it is all based on hard science rather than mere assertion or trendy but unsubstantiated beliefs. B vitamins are also sold with claims of enhancing memory, usually rationalized by their reduction of homocysteine, a chemical in the blood that may affect circulation in the brain. No benefits from B vitamin intake have been demonstrated when it comes to memory or cognitive function except in the case of people who have high homocysteine levels due to a diet that is very low in B vitamins. There is some concern that folic acid, one of the B vitamins, may spur the growth of polyps in the colon at doses greater than 800 micrograms a day. Phosphatidyl serine is a natural component of nerve cell membranes and its promoters argue that a deficiency leads to impaired communication between nerve cells which in turn impairs cognitive function. Sounds reasonable, except that proper controlled trials have come up empty. The same goes for vinpocetine, a compound originally isolated from the lesser periwinkle plant by Hungarian chemist Csaba Szantay in 1975. It is widely used in Europe to treat strokes and memory problems with claims of increased circulation to the brain. It does indeed increase circulation, much like ginkgo, but there is no compelling evidence for memory improvement. ##### The desire to improve cognitive functioning has probably existed since the dawn of human consciousness. Throughout our evolution, increased mental agility has been associated with fitness and improved odds of survival and success. Although concoctions to stimulate brainpower have existed in Chinese and Indian medicine for hundreds of years, Western nootropics were not developed until 1964. With a lack of reviews and a formulation containing some questionable ingredients that we could not find to benefit consumers, together with the possibility of the product being sub-standard, we placed this product in our # 4 ranking. Its redeeming features however, include the fact that they use all-natural ingredients plus, the price is cheap, if you are into taking a risk about the quality of the product. Recent findings also suggest that taking extra vitamins could help preserve memory, especially as we age. Researchers at Australia's University of Sydney tested 117 people in a retirement home by putting them through a battery of mental tests that included remembering a string of words, listing as many words as possible that begin with a certain letter of the alphabet, and doing mental addition and subtraction. Those who regularly took vitamin C, they found, scored higher on the tests. The placebos can be the usual pills filled with olive oil. The Nature’s Answer fish oil is lemon-flavored; it may be worth mixing in some lemon juice. In Kiecolt-Glaser et al 2011, anxiety was measured via the Beck Anxiety scale; the placebo mean was 1.2 on a standard deviation of 0.075, and the experimental mean was 0.93 on a standard deviation of 0.076. (These are all log-transformed covariates or something; I don’t know what that means, but if I naively plug those numbers into Cohen’s d, I get a very large effect: \frac{1.2 - 0.93}{0.076}=3.55.) In her new book, Brain Food: The Surprising Science of Eating for Cognitive Power (Avery/ Penguin Random House), Dr. Lisa Mosconi, PhD, INHC, Associate Director of the Alzheimer’s Prevention Clinic at Weill Cornell Medical College, highlights the connection between diet and brain function and shares approachable, actionable tips to put that research into practice. Research does not support that drugs like Ritalin help students do well in school. Studies show that prescription stimulants do not help to improve learning or thinking in those who do not actually have ADHD. Further, research reveals that students who abuse prescription stimulants have lower GPAs than students who do not abuse the drugs.[14] Although Ritalin improves concentration, this effect is largely misunderstood among non-prescribed users. These illicit users mistakenly believe that they can use a drug out of its prescribed context, thinking they can reap the benefits intended for legitimate users. Like everything else in your body, the brain cannot work without energy. The ability to concentrate and focus comes from an adequate, steady supply of energy - in the form of glucose in our blood to the brain. Achieve this by choosing wholegrains with a low-GI, which release glucose slowly into the bloodstream, keeping you mentally alert throughout the day. Opt for 'brown' wholegrain cereals, granary bread, rice and pasta. (I was more than a little nonplussed when the mushroom seller included a little pamphlet educating one about how papaya leaves can cure cancer, and how I’m shortening my life by decades by not eating many raw fruits & vegetables. There were some studies cited, but usually for points disconnected from any actual curing or longevity-inducing results.) But what does this all have to do with food? Our gut helps keep our body’s immune responses and inflammation under control. Additionally, gut hormones that enter the brain or are produced in the brain influence cognitive ability, like understanding and processing new information, staying focused on the task at hand and recognizing when we’re full. (3) We felt that NeuroFuse was pretty much on par with other similar products. We were happy to see that this supplier offers a money-back guarantee. However, we didn't really like the 14-day trial offer they promote. On the surface it seems good, however, our experience on these matters suggests that if consumers are not happy with the product, cancelling subscriptions can be a nightmare. We much prefer a simple clear money-back guarantee, it's safer for consumers. By the way, since I’ll throw around the term a few more times in this article, I should probably clarify what an adaptogen actually is. The actual name adaptogen gives some hint as to what these fascinating compounds do: they help you to adapt, specifically by stimulating a physiological adaptive response to some mild, hormesis-like stressor. A process known as general adaptation syndrome (GAS) was first described by the 20th-century physician and organic chemist Hans Selye, who defined GAS as the body’s response to the demands placed upon it. When these demands are excessive and consistent, it can result in the common deleterious symptoms now associated with long-term exposure to chronic stress. GAS is comprised of an alarm stage (characterized by a burst of energy), a resistance stage (characterized by resistance or adaptation to the stressor), and – in the case of excessive and chronic stress – an exhaustion stage (characterized by energy depletion). Adaptogens are plant-derived compounds capable of modulating these phases of GAS by either downregulating stress reactions in the alarm phase or inhibiting the onset of the exhaustion phase, thus providing some degree of protection against damage from stress. Some people warn of the dangers of modafinil. There are anecdotal personal accounts online of people becoming dependent on this drug. Modafinil is the generic of the brand Provigil, a nootropic. Provigil is FDA-approved to stimulate wakefulness in people suffering from sleep disorders, such as narcolepsy and sleep apnea. Initially, Provigil was thought to have a benign, non-addiction-forming profile. As such, the Drug Enforcement Administration classifies Provigil as a Schedule IV drug, a category reserved for drugs with low abuse potential; however, recent research conducted by the National Institute on Drug Abuse (NIDA) has found that Provigil may in fact be addictive.[10] as scientific papers become much more accessible online due to Open Access, digitization by publishers, and cheap hosting for pirates, the available knowledge about nootropics increases drastically. This reduces the perceived risk by users, and enables them to educate themselves and make much more sophisticated estimates of risk and side-effects and benefits. (Take my modafinil page: in 1997, how could an average person get their hands on any of the papers available up to that point? Or get detailed info like the FDA’s prescribing guide? Even assuming they had a computer & Internet?) At this point, I began thinking about what I was doing. Black-market Adderall is fairly expensive; $4-10 a pill vs prescription prices which run more like$60 for 120 20mg pills. It would be a bad idea to become a fan without being quite sure that it is delivering bang for the buck. Now, why the piracetam mix as the placebo as opposed to my other available powder, creatine powder, which has much smaller mental effects? Because the question for me is not whether the Adderall works (I am quite sure that the amphetamines have effects!) but whether it works better for me than my cheap legal standbys (piracetam & caffeine)? (Does Adderall have marginal advantage for me?) Hence, I want to know whether Adderall is better than my piracetam mix. People frequently underestimate the power of placebo effects, so it’s worth testing. (Unfortunately, it seems that there is experimental evidence that people on Adderall know they are on Adderall and also believe they have improved performance, when they do not5. So the blind testing does not buy me as much as it could.) #### Vinpocetine: This chemical is a semi-synthetic derivative of an extract from periwinkle. It acts as a potent anti-inflammatory agent, and has also received some testing as a supplement for memory enhancement. While research results are inconclusive right now, this chemical has been shown to increase blood circulation and metabolism in the brain and may slow down neuron loss. Some tests have also shown that it can improve concentration and attention. I have no particularly compelling story for why this might be a correlation and not causation. It could be placebo, but I wasn’t expecting that. It could be selection effect (days on which I bothered to use the annoying LED set are better days) but then I’d expect the off-days to be below-average and compared to the 2 years of trendline before, there doesn’t seem like much of a fall. And many people swear by them. Neal Thakkar, for example, is an entrepreneur from Marlboro, New Jersey, who claims nootropics improved his life so profoundly that he can’t imagine living without them. His first breakthrough came about five years ago, when he tried a piracetam/choline combination, or “stack,” and was amazed by his increased verbal fluency. (Piracetam is a cognitive-enhancement drug permitted for sale in the U. S. as a dietary supplement; choline is a natural substance.) For obvious reasons, it’s difficult for researchers to know just how common the “smart drug” or “neuro-enhancing” lifestyle is. However, a few recent studies suggest cognition hacking is appealing to a growing number of people. A survey conducted in 2016 found that 15% of University of Oxford students were popping pills to stay competitive, a rate that mirrored findings from other national surveys of UK university students. In the US, a 2014 study found that 18% of sophomores, juniors, and seniors at Ivy League colleges had knowingly used a stimulant at least once during their academic career, and among those who had ever used uppers, 24% said they had popped a little helper on eight or more occasions. Anecdotal evidence suggests that pharmacological enhancement is also on the rise within the workplace, where modafinil, which treats sleep disorders, has become particularly popular. ###### There are plenty of brain supplements on the market, but none with the same combinations of potent and promising ingredients. If you want to maximize your ability to excel – at everything you do – your brain must be firing on all cylinders – all day, every day. You must protect and preserve your brain function, as it will diminish – it’s the reality of being human. Maybe you are you new to nootropics? The word, “Nootropic” is a very broad term describing a supplement or drug that increases mental performance. There are several different groups of nootropics including herbal supplements and a class of research chemicals known as racetams. Below are some of the many common benefits that may potentially be experienced with nootropic supplements. For more in-depth personalised support, some people find nutritional therapy hugely beneficial. To find a suitable therapist, please head to BANT (British Association of Applied Nutrition and Nutritional Therapy) or contact our not-for-profit clinic, the Brain Bio Centre (www.brainbiocentre.com), which offers expertise in nutritional therapy for mental health conditions including depression, on 0208 332 9600 or [email protected]. If you feel you need more immediate help, for whatever it is that you’re going through, theSamaritans helpline offer support 24 hours a day, 365 days a year and can point you in the right direction of getting further help. Lucas Baker, a Switzerland-based software engineer with a large tech company, takes nootropics every day. He says it helps him maintain focus, especially on projects he might otherwise put off. “When I find an unpleasant task, I can just power through it,” he says. Baker also makes the coffee comparison: “There’s already a universally-embraced nootropic called caffeine,” he says. “It’s just about making it more widely researched.” Alex was eager to dispel the notion that students who took Adderall were "academic automatons who are using it in order to be first in their class". In fact, he said, "it's often people" - mainly guys - "who are looking in some way to compensate for activities that are detrimental to their performance". He explained, "At Harvard, at the most basic level, they aim to do better than they would have otherwise. Everyone is aware that if you were up at 3am writing this paper it isn't going to be as good as it could have been. The fact that you were partying all weekend, or spent the last week being high, watching Lost - that's going to take a toll." Phillips told me that, much as he believes in neuroenhancers, he did not want to be "the poster boy for smart-in-a-pill". At one point, he said: "We really don't know the possible implications for long-term use of these things." (He recently stopped taking Provigil every day, replacing it with another prescription stimulant.) Nor does he think we need to be turning up the crank another notch on how hard we work. "But," he said, "the baseline competitive level is going to reorientate around what these drugs make possible, and you can choose to compete or not." "Instead of messing it up, we should be appreciating something that nature has taken years to optimize," Dr. Lisa mentions. But, we aren't messing it up voluntarily or, at the very least, on any conscious or malicious level. She attributes our disregard for neuro-nutrition to a series of factors, which include the portion size of meals, how parents don't have the time to cook or teach children how to eat healthily, the big influence of cafeteria food, and our "always on the go" culture. According to her, this leads us to unconsciously choose meals which are poor quality and high in sugars, a deathly combination for our brains. Alex's sense of who uses stimulants for so-called "non-medical" purposes is borne out by two dozen or so scientific studies. In 2005 a team led by Sean Esteban McCabe, a professor at the University of Michigan, reported that in the previous year 4.1% of American undergraduates had taken prescription stimulants for off-label use - at one school the figure was 25%, while a 2002 study at a small college found that more than 35% of the students had used prescription stimulants non-medically in the previous year. Tempted to skip breakfast? Studies have found that eating breakfast may improve short-term memory and attention. Students who eat it tend to perform better than those who don’t. Foods at the top of researchers' brain-fuel list include high-fiber whole grains, dairy, and fruits. Just don't overeat; researchers also found high-calorie breakfasts appear to hinder concentration. If Alex, the Harvard student, and Paul Phillips, the poker player, consider their use of neuroenhancers a private act, Nicholas Seltzer sees his habit as a pursuit that aligns him with a larger movement for improving humanity. Seltzer's job as a researcher at a defence-oriented thinktank in northern Virginia has not left him feeling as intellectually alive as he would like. To compensate, he writes papers in his spare time on subjects like "human biological evolution and warfare". Seltzer, 30, told me he worried that he "didn't have the mental energy, the endurance, the... the sponginess that I seem to recall having when I was younger". # A fancier method of imputation would be multiple imputation using, for example, the R library mice (Multivariate Imputation by Chained Equations) (guide), which will try to impute all missing values in a way which mimicks the internal structure of the data and provide several possible datasets to give us an idea of what the underlying data might have looked like, so we can see how our estimates improve with no missingness & how much of the estimate is now due to the imputation: The different ADHD medications like Adderall and Ritalin are classified as stimulants, and deal with these symptoms by increasing the neurotransmitters known as dopamine and norepinephrine, which are associated with pleasure, movement, and attention. They have a calming and focusing effect on people affected with ADHD, and are helpful for the inattentiveness, poor memory, impulsiveness, and mood swings experienced by those people. However, normally when you hear the term nootropic kicked around, people really mean a “cognitive enhancer” — something that does benefit thinking in some way (improved memory, faster speed-of-processing, increased concentration, or a combination of these, etc.), but might not meet the more rigorous definition above. “Smart drugs” is another largely-interchangeable term. The exact moment when science morphed into science fiction was when so-called climate scientists (formerly known as weather forecasters) realised that some people could be conned into believing in man-made global warming and pumping fortunes into university departments to prove it. Now, they're all at it.Come back Arthur C Clarke. Your country needs you now. Power-wise, the effects of testosterone are generally reported to be strong and unmistakable. Even a short experiment should work. I would want to measure DNB scores & Mnemosyne review averages as usual, to verify no gross mental deficits; the important measures would be physical activity, so either pedometer or miles on treadmill, and general productivity/mood. The former 2 variables should remain the same or increase, and the latter 2 should increase. Maddy Heeszel is a 20-something-year-old from Central California. She is a 4.0 GPA graduate from Brandman University with a B.A. in Liberal Studies, Multiple Subjects Teaching. Maddy works full-time as a freelance writer and social media marketer. She also owns a plant nursery. In her spare time, Maddy enjoys cooking, gardening, watching prank videos on YouTube, playing video games, learning new languages, and taking pictures. She also has interests in health, psychology, and nutrition. You can connect with her on Linkedin. Directions — as a dietary supplement take 2 veggie capsules once a day . For best results take 20-30 min before a meal with an 8oz. Glass of water or as directed by your healthcare professional. As a dietary supplement take two (2) veggie capsules once a day. For best results take 20-30 minutes before a meal with an 8oz. glass of water or as directed by your healthcare professional. — Suggested Use: As a dietary supplement, adults take one (1) capsule per day. Do not exceed 2 capsules per day. — Any consideration of the future of nootropics is directly tied into the future of humanity. As long as work productivity demands continue to soar, there will like be a affiliated rise in the desire to increase brain power. As Vice discusses in a thoughtful article providing several insights into why nootropics are popular, it is not surprising that smart drugs and the nootropic industry are ever-expanding. Vice points out that sci-fi writers once warned of people being overtaken by machines, but instead, human beings are becoming machines, taking on unrealistic work levels.[15] Taking nootropic drugs is akin to loading up on premium fuel in an effort to go faster and do better. Research in animals shows that blueberries may help protect the brain from the damage caused by free radicals and may reduce the effects of age-related conditions such as Alzheimer's disease or dementia. Studies also show that diets rich in blueberries improved both the learning and muscle function of aging rats, making them mentally equal to much younger rats. Seriously. Every single thing you experience comes through your brain. It create the fabric of your reality, and by the same token, the energy your brain makes is what allows you to shape that reality. Work, relationships, success, happiness — everything depends on your brain, and building a stronger one will trigger upgrades that extend across every aspect of your life. As a general class, nootropics are not usually addiction-forming.[6] Two of the strongest hallmarks of addiction-forming drugs is that they cause users to develop dependency and experience withdrawal when the drug use is eliminated or reduced. While there are some reports of nootropic users experiencing brain fog after use is discontinued, these side effects are not considered to be akin to withdrawal effects of addiction-forming drugs.[7] Eliminating foggy-headedness seems to be the goal of many users of neuroenhancers. But can today's drugs actually accomplish this? I recently posed this question to Chatterjee's colleague Martha Farah, who is a psychologist at Penn and the director of its Center for Cognitive Neuroscience. She is deeply fascinated by, and mildly critical of, neuroenhancers, but basically in favour - with the important caveat that we need to know much more about how these drugs work. While Farah does not take neuroenhancers, she had just finished a paper in which she reviewed the evidence on prescription stimulants as neuroenhancers from 40 laboratory studies involving healthy subjects. Most of the studies looked at one of three types of cognition: learning, working memory, and cognitive control. A typical learning test asks subjects to memorise a list of paired words; an hour, a few days, or a week later, they are presented with the first words in the pairs and asked to come up with the second. Neuroenhancers did improve retention, especially where subjects had been asked to remember information for several days or longer. I split the 2 pills into 4 doses for each hour from midnight to 4 AM. 3D driver issues in Debian unstable prevented me from using Brain Workshop, so I don’t have any DNB scores to compare with the armodafinil DNB scores. I had the subjective impression that I was worse off with the Modalert, although I still managed to get a fair bit done so the deficits couldn’t’ve been too bad. The apathy during the morning felt worse than armodafinil, but that could have been caused by or exacerbated by an unexpected and very stressful 2 hour drive through rush hour and multiple accidents; the quick hour-long nap at 10 AM was half-waking half-light-sleep according to the Zeo, but seemed to help a bit. As before, I began to feel better in the afternoon and by evening felt normal, doing my usual reading. That night, the Zeo recorded my sleep as lasting ~9:40, when it was usually more like 8:40-9:00 (although I am not sure that this was due to the modafinil inasmuch as once a week or so I tend to sleep in that long, as I did a few days later without any influence from the modafinil); assuming the worse, the nap and extra sleep cost me 2 hours for a net profit of ~7 hours. While it’s not clear how modafinil affects recovery sleep (see the footnote in the essay), it’s still interesting to ponder the benefits of merely being able to delay sleep19. Board-certified neuropsychologist Brian Lebowitz, PhD and associate clinical professor of neurology at Stony Brook University, explains to MensHealth.com that the term "encompasses so many things," including prescription medications. Brain enhancers fall into two different categories: naturally occurring substances like Ginkgo biloba, creatine and phenibut; and manmade prescription drugs, like Adderall, and over-the-counter supplements such as Noopept. Today, extraordinary research is showing that bacopa has the remarkable ability to increase levels of BDNF, a protein responsible for the growth, maintenance and survival of neurons, and the creation of new neural connections in the brain. It also has been shown to help promote the growth of new neurons and neural pathways, which helps to explain why it’s such a powerful memory and concentration booster. Large scale studies have shown the association between chronic low-grade inflammation and depression (8). For example, in a study that examined data from 14,275 people who were interviewed between 2007 and 2012, they found that people who had depression had 46% higher levels of C-reactive protein (CRP), a marker of inflammatory disease, in their blood samples (9). Studies like these are paving the way towards a new understanding of the pathology of mental health conditions and how diet and stress can alter bodily systems, such as digestive function and consequently impact mental wellbeing. Measuring IgG antibodies in food intolerance tests has been implicated as a popular strategy to tackle symptoms related to sensitivities such as IBS, joint pain, fatigue, migraines, anxiety and depression. A recent survey on 708 people commissioned by Allergy UK, demonstrated how 81% of those with elevated IgG levels, as well as psychological symptoms, reported an improvement in their condition after following a food-specific IgG elimination diet (9). Taking this all into account, health professionals and those with poor mental health may want to consider the potential role of food intolerances in mental well-being and in managing common mood-related disorders, such as depression and anxiety. These are the most highly studied ingredients and must be combined together to achieve effective results. If any one ingredient is missing in the formula, you may not get the full cognitive benefits of the pill. It is important to go with a company that has these critical ingredients as well as a complete array of supporting ingredients to improve their absorption and effectiveness. Anything less than the correct mix will not work effectively. There are many more steps to help support the optimal functioning of the brain and therefore encourage improved learning and development. However, another key strategy to support brain health is to increase intake of omega 3, an essential fatty acid, that is most abundantly found in oily fish such as salmon, mackerel and sardines. Be sure to choose salmon that has had less exposure to polluted water - visit the Seafood Watch web page to find the best sources. Omega 3 is vital for the brain’s function, particularly one of its components called DHA. This is a key building block for the brain and is what keeps neurons (brain cells) working well and supports proper signalling via neurotransmitters. Harriet Hall, MD also known as The SkepDoc, is a retired family physician who writes about pseudoscience and questionable medical practices. She received her BA and MD from the University of Washington, did her internship in the Air Force (the second female ever to do so), and was the first female graduate of the Air Force family practice residency at Eglin Air Force Base. During a long career as an Air Force physician, she held various positions from flight surgeon to DBMS (Director of Base Medical Services) and did everything from delivering babies to taking the controls of a B-52. She retired with the rank of Colonel. In 2008 she published her memoirs, Women Aren't Supposed to Fly. It all comes down to my personal investigation and exploration into how one can use a variety of compounds to enhance the mind, all while combining ancestral wisdom and herbs such as bacopa and gingko with modern science and tactics such as LSD and racetams. The fact is, I’ve taken a deep dive in the wonderful world of smart drugs, nootropics and psychedelics, and have had the opportunity to interview some of the brightest minds in this unique field of brain enhancement on my podcast. So in this article, I’ll spill the beans on it all, including how to navigate the oft-confusing world of smart drugs and nootropics, the best brain supplement stacks I’ve discovered and experimented with, how to procure and microdose psychedelics and much more. ##### Discussions of PEA mention that it’s almost useless without a MAOI to pave the way; hence, when I decided to get deprenyl and noticed that deprenyl is a MAOI, I decided to also give PEA a second chance in conjunction with deprenyl. Unfortunately, in part due to my own shenanigans, Nubrain canceled the deprenyl order and so I have 20g of PEA sitting around. Well, it’ll keep until such time as I do get a MAOI. This was so unexpected that I wondered if I had somehow accidentally put the magnesium pills into the placebo pill baggie or had swapped values while typing up the data into a spreadsheet, and checked into that. The spreadsheet accorded with the log above, which rules out data entry mistakes; and looking over the log, I discovered that some earlier slip-ups were able to rule out the pill-swap: I had carelessly put in some placebo pills made using rice, in order to get rid of them, and that led to me being unblinded twice before I became irritated enough to pick them all out of the bag of placebos - but how could that happen if I had swapped the groups of pills? Vitamin C has long been thought to have the power to increase mental agility, and some research suggests that a deficiency may be a risk factor for age-related brain degeneration including dementia and Alzheimer's. Furthermore, interesting studies demonstrate that vitamin C may be useful in managing anxiety and stress. One of the best sources of this vital vitamin are blackcurrants. Others include red peppers, citrus fruits such as oranges and broccoli. Oxiracetam is one of the 3 most popular -racetams; less popular than piracetam but seems to be more popular than aniracetam. Prices have come down substantially since the early 2000s, and stand at around 1.2g/$or roughly 50 cents a dose, which was low enough to experiment with; key question, does it stack with piracetam or is it redundant for me? (Oxiracetam can’t compete on price with my piracetam pile stockpile: the latter is now a sunk cost and hence free.) It’s not clear that there is much of an effect at all. This makes it hard to design a self-experiment - how big an effect on, say, dual n-back should I be expecting? Do I need an arduous long trial or an easy short one? This would principally determine the value of information too; chocolate seems like a net benefit even if it does not affect the mind, but it’s also fairly costly, especially if one likes (as I do) dark chocolate. Given the mixed research, I don’t think cocoa powder is worth investigating further as a nootropic. Do you start your day with a cup (or two, or three) of coffee? It tastes delicious, but it’s also jump-starting your brain because of its caffeine content. Caffeine is definitely a nootropic substance—it’s a mild stimulant that can alleviate fatigue and improve concentration, according to the Mayo Clinic. Current research shows that coffee drinkers don’t suffer any ill effects from drinking up to about four cups of coffee per day. Caffeine is also found in tea, soda, and energy drinks. Not too surprisingly, it’s also in many of the nootropic supplements that are being marketed to people looking for a mental boost. Take a look at these 7 genius brain boosters to try in the morning. The brain’s preferred fuel is glucose, which comes most readily from carbs. Without ample glucose, you may struggle with brain fog and difficulty focusing. While you want to avoid refined carbs, whole grains contain fiber and help keep your blood sugar on an even keel. (Sharp rises and falls in blood sugar can impair your cells’ ability to uptake glucose because of insulin resistance, explains Malik.) I'm not mad, I'm disappointed. This product did not work at all. It didn't even feel like it was just a caffeine pill (usually what supplements that don't work are actually made of). It literally does nothing. In hindsight, I feel like I did when I was a kid and ordered$4.50 X-ray sunglasses from the back of a comic book. Deep down knew it was too good to be true, but secretly I hoped it would work. Shame on me for getting sucked into a bunch of hype. #### The reality is that cognitive impairment and dementia are also on the rise, and sometimes symptoms of forgetfulness and confusion are not so innocuous. According to the Alzheimer’s Association, someone in the United States is diagnosed with Alzheimer’s disease every 66 seconds. By the middle of this century, that is expected to grow to every 33 seconds. People with failing memory and worried about Alzheimer’s disease are sometimes seduced by advertisements for Huperzine A, extracted from a type of moss. Some studies have shown that it increases levels of acetylcholine in the brain, a chemical that is in short supply in Alzheimer’s. But despite increasing acetylcholine, aside from a few questionable studies in China, there is no evidence that it improves memory. Unfortunately when it comes to memory pills, they are best forgotten. There is, however, hope that a nasal spray containing insulin can increase the absorption of glucose into brain cells and improve cognitive function. But in the meantime, the best bet to maintain good brain function is to monitor blood glucose and blood pressure, eat a diet rich in fruits, vegetables and whole grains, and low in simple carbs and saturated fat. And don’t forget that physical exercise also exercises your brain. The reality is that cognitive impairment and dementia are also on the rise, and sometimes symptoms of forgetfulness and confusion are not so innocuous. According to the Alzheimer’s Association, someone in the United States is diagnosed with Alzheimer’s disease every 66 seconds. By the middle of this century, that is expected to grow to every 33 seconds. I do recommend a few things, like modafinil or melatonin, to many adults, albeit with misgivings about any attempt to generalize like that. (It’s also often a good idea to get powders, see the appendix.) Some of those people are helped; some have told me that they tried and the suggestion did little or nothing. I view nootropics as akin to a biological lottery; one good discovery pays for all. I forge on in the hopes of further striking gold in my particular biology. Your mileage will vary. All you have to do, all you can do is to just try it. Most of my experiences were in my 20s as a right-handed 5’11 white male weighing 190-220lbs, fitness varying over time from not-so-fit to fairly fit. In rough order of personal effectiveness weighted by costs+side-effects, I rank them as follows: The U. S. nootropics industry was valued at more than $1.3 billion in 2015 and is projected to reach$6 billion by 2024. This growth is due in part to slick marketing from biohacking “experts” such as Dave Asprey (founder of Bulletproof) and Josiah Zayner, Ph.D. (CEO of the Odin), who’ve built big social-media and podcast followings as well as customer bases. At the grassroots level, there are meetups across the country like the one at Idea Coffee, plus a vibrant online community. Still, putting unregulated brain drugs into my system feels significantly scarier than downing a latte or a Red Bull—not least because the scientific research on nootropics’ long-term effects is still so thin. One 2014 study found that Ritalin, modafinil, ampakines, and other similar stimulants could eventually reduce the “plasticity” of some of the brain’s neural networks by providing them with too much dopamine, glutamate and norepinephrine, and potentially cause long-term harm in young people whose brains were still developing. (In fact, in young people, the researchers wrote, these stimulants could actually have the opposite effect the makers intended: “Healthy individuals run the risk of pushing themselves beyond optimal levels into hyperdopaminergic and hypernoradrenergic states, thus vitiating the very behaviors they are striving to improve.”) But the researchers found no evidence that normal doses of these drugs were harmful when taken by adults. It arrived as described, a little bottle around the volume of a soda can. I had handy a plastic syringe with milliliter units which I used to measure out the nicotine-water into my tea. I began with half a ml the first day, 1ml the second day, and 2ml the third day. (My Zeo sleep scores were 85/103/86 (▁▇▁), and the latter had a feline explanation; these values are within normal variation for me, so if nicotine affects my sleep, it does so to a lesser extent than Adderall.) Subjectively, it’s hard to describe. At half a ml, I didn’t really notice anything; at 1 and 2ml, I thought I began to notice it - sort of a cleaner caffeine. It’s nice so far. It’s not as strong as I expected. I looked into whether the boiling water might be breaking it down, but the answer seems to be no - boiling tobacco is a standard way to extract nicotine, actually, and nicotine’s own boiling point is much higher than water; nor do I notice a drastic difference when I take it in ordinary water. And according to various e-cigarette sources, the liquid should be good for at least a year. […] The 7 Best Brain Boosting Supplements \| Live in the Now … – While under estimated in the brain health arena, adequate vitamin C is associated with a 20% … If you are looking for a way to maximize brain power I have come across … […] medicines, dietary supplements and organic food products. Justin has also been writing on best brain supplements for … […] Even the best of today’s nootropics only just barely scratch the surface. You might say that we are in the “Nokia 1100” phase of taking nootropics, and as better tools and more data come along, the leading thinkers in the space see a powerful future. For example, they are already beginning to look past biochemistry to the epigenome. Not only is the epigenome the code that runs much of your native biochemistry, we now know that experiences in life can be recorded in your epigenome and then passed onto future generations. There is every reason to believe that you are currently running epigenetic code that you inherited from your great-grandmother’s life experiences. And there is every reason to believe that the epigenome can be hacked – that the nootropics of the future can not only support and enhance our biochemistry, but can permanently change the epigenetic code that drives that biochemistry and that we pass onto our children.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31624215841293335, "perplexity": 2895.899599607097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746398.20/warc/CC-MAIN-20181120130743-20181120152743-00545.warc.gz"}
https://en.wanweibaike.com/wiki-Monopoly	# Monopoly A monopoly (from Greek μόνος, mónos, 'single, alone' and πωλεῖν, pōleîn, 'to sell') exists when a specific person or enterprise is the only supplier of a particular commodity. This contrasts with a monopsony which relates to a single entity's control of a market to purchase a good or service, and with oligopoly and duopoly which consists of a few sellers dominating a market.[1] Monopolies are thus characterized by a lack of economic competition to produce the good or service, a lack of viable substitute goods, and the possibility of a high monopoly price well above the seller's marginal cost that leads to a high monopoly profit.[2] The verb monopolise or monopolize refers to the process by which a company gains the ability to raise prices or exclude competitors. In economics, a monopoly is a single seller. In law, a monopoly is a business entity that has significant market power, that is, the power to charge overly high prices, which is associated with a decrease in social surplus.[3] Although monopolies may be big businesses, size is not a characteristic of a monopoly. A small business may still have the power to raise prices in a small industry (or market).[3] A monopoly may also have monopsony control of a sector of a market. Likewise, a monopoly should be distinguished from a cartel (a form of oligopoly), in which several providers act together to coordinate services, prices or sale of goods. Monopolies, monopsonies and oligopolies are all situations in which one or a few entities have market power and therefore interact with their customers (monopoly or oligopoly), or suppliers (monopsony) in ways that distort the market.[citation needed] Monopolies can be established by a government, form naturally, or form by integration. In many jurisdictions, competition laws restrict monopolies due to government concerns over potential adverse effects. Holding a dominant position or a monopoly in a market is often not illegal in itself, however certain categories of behavior can be considered abusive and therefore incur legal sanctions when business is dominant. A government-granted monopoly or legal monopoly, by contrast, is sanctioned by the state, often to provide an incentive to invest in a risky venture or enrich a domestic interest group. Patents, copyrights, and trademarks are sometimes used as examples of government-granted monopolies. The government may also reserve the venture for itself, thus forming a government monopoly, for example with a state-owned company.[citation needed] Monopolies may be naturally occurring due to limited competition because the industry is resource intensive and requires substantial costs to operate (e.g., certain railroad systems). one two few sellers monopoly duopoly oligopoly buyers monopsony – oligopsony ## Market structures In economics, the idea of monopolies is important in the study of management structures, which directly concerns normative aspects of economic competition, and provides the basis for topics such as industrial organization and economics of regulation. There are four basic types of market structures in traditional economic analysis: perfect competition, monopolistic competition, oligopoly and monopoly. A monopoly is a structure in which a single supplier produces and sells a given product or service. If there is a single seller in a certain market and there are no close substitutes for the product, then the market structure is that of a "pure monopoly". Sometimes, there are many sellers in an industry or there exist many close substitutes for the goods being produced, but nevertheless companies retain some market power. This is termed "monopolistic competition", whereas in an oligopoly, the companies interact strategically. In general, the main results from this theory compare the price-fixing methods across market structures, analyze the effect of a certain structure on welfare, and vary technological or demand assumptions in order to assess the consequences for an abstract model of society. Most economic textbooks follow the practice of carefully explaining the "perfect competition" model, mainly because this helps to understand departures from it (the so-called "imperfect competition" models). The boundaries of what constitutes a market and what does not are relevant distinctions to make in economic analysis. In a general equilibrium context, a good is a specific concept including geographical and time-related characteristics. Most studies of market structure relax a little their definition of a good, allowing for more flexibility in the identification of substitute goods. ## Characteristics A monopoly has at least one of these five characteristics: • Profit maximizer: Maximizes profits. • Price maker: Decides the price of the good or product to be sold, but does so by determining the quantity in order to demand the price desired by the firm. • High barriers to entry: Other sellers are unable to enter the market of the monopoly. • Single seller: In a monopoly, there is one seller of the good, who produces all the output.[4] Therefore, the whole market is being served by a single company, and for practical purposes, the company is the same as the industry. • Price discrimination: A monopolist can change the price or quantity of the product. They sell higher quantities at a lower price in a very elastic market, and sell lower quantities at a higher price in a less elastic market. ## Sources of monopoly power Monopolies derive their market power from barriers to entry – circumstances that prevent or greatly impede a potential competitor's ability to compete in a market. There are three major types of barriers to entry: economic, legal and deliberate.[5] • Economic barriers: Economic barriers include economies of scale, capital requirements, cost advantages and technological superiority.[6] • Economies of scale: Decreasing unit costs for larger volumes of production.[7] Decreasing costs coupled with large initial costs, If for example the industry is large enough to support one company of minimum efficient scale then other companies entering the industry will operate at a size that is less than MES, and so cannot produce at an average cost that is competitive with the dominant company. And if the long-term average cost of the dominant company is constantly decreasing[clarification needed], then that company will continue to have the least cost method to provide a good or service.[8] • Capital requirements: Production processes that require large investments of capital, perhaps in the form of large research and development costs or substantial sunk costs, limit the number of companies in an industry:[9] this is an example of economies of scale. • Technological superiority: A monopoly may be better able to acquire, integrate and use the best possible technology in producing its goods while entrants either do not have the expertise or are unable to meet the large fixed costs (see above) needed for the most efficient technology.[7] Thus one large company can often produce goods cheaper than several small companies.[10] • No substitute goods: A monopoly sells a good for which there is no close substitute. The absence of substitutes makes the demand for that good relatively inelastic, enabling monopolies to extract positive profits. • Control of natural resources: A prime source of monopoly power is the control of resources (such as raw materials) that are critical to the production of a final good. • Network externalities: The use of a product by a person can affect the value of that product to other people. This is the network effect. There is a direct relationship between the proportion of people using a product and the demand for that product. In other words, the more people who are using a product, the greater the probability that another individual will start to use the product. This reflects fads, fashion trends,[11] social networks etc. It also can play a crucial role in the development or acquisition of market power. The most famous current example is the market dominance of the Microsoft office suite and operating system in personal computers.[citation needed] • Legal barriers: Legal rights can provide opportunity to monopolise the market in a good. Intellectual property rights, including patents and copyrights, give a monopolist exclusive control of the production and selling of certain goods. Property rights may give a company exclusive control of the materials necessary to produce a good. • Advertising: Advertising is most important to sell the product because of the single user, they have to do it their own.[citation needed] • Manipulation: A company wanting to monopolise a market may engage in various types of deliberate action to exclude competitors or eliminate competition. Such actions include collusion, lobbying governmental authorities, and force (see anti-competitive practices). In addition to barriers to entry and competition, barriers to exit may be a source of market power. Barriers to exit are market conditions that make it difficult or expensive for a company to end its involvement with a market. High liquidation costs are a primary barrier to exiting.[12] Market exit and shutdown are sometimes separate events. The decision whether to shut down or operate is not affected by exit barriers.[citation needed] A company will shut down if price falls below minimum average variable costs. ## Monopoly versus competitive markets This 1879 cartoon depicts powerful railroad barons controlling all the rail system. While monopoly and perfect competition mark the extremes of market structures[13] there is some similarity. The cost functions are the same.[14] Both monopolies and perfectly competitive (PC) companies minimize cost and maximize profit. The shutdown decisions are the same. Both are assumed to have perfectly competitive factors markets. There are distinctions, some of the most important distinctions are as follows: • Marginal revenue and price: In a perfectly competitive market, price equals marginal cost. In a monopolistic market, however, price is set above marginal cost.[15] • Product differentiation: There is no product differentiation in a perfectly competitive market. Every product is perfectly homogeneous and a perfect substitute for any other. With a monopoly, there is great to absolute product differentiation in the sense that there is no available substitute for a monopolized good. The monopolist is the sole supplier of the good in question.[16] A customer either buys from the monopolizing entity on its terms or does without. • Number of competitors: PC markets are populated by an infinite number of buyers and sellers. A monopoly involves a single seller.[16] • Barriers to entry: Barriers to entry are factors and circumstances that prevent entry into market by would-be competitors and limit new companies from operating and expanding within the market. PC markets have free entry and exit. There are no barriers to entry, or exit competition. Monopolies have relatively high barriers to entry. The barriers must be strong enough to prevent or discourage any potential competitor from entering the market • Elasticity of demand: The price elasticity of demand is the percentage change of demand caused by a one percent change of relative price. A successful monopoly would have a relatively inelastic demand curve. A low coefficient of elasticity is indicative of effective barriers to entry. A PC company has a perfectly elastic demand curve. The coefficient of elasticity for a perfectly competitive demand curve is infinite.[citation needed] • Excess profits: Excess or positive profits are profit more than the normal expected return on investment. A PC company can make excess profits in the short term but excess profits attract competitors, which can enter the market freely and decrease prices, eventually reducing excess profits to zero.[17] A monopoly can preserve excess profits because barriers to entry prevent competitors from entering the market.[18] • Profit maximization: A PC company maximizes profits by producing such that price equals marginal costs. A monopoly maximises profits by producing where marginal revenue equals marginal costs.[19] The rules are not equivalent. The demand curve for a PC company is perfectly elastic – flat. The demand curve is identical to the average revenue curve and the price line. Since the average revenue curve is constant the marginal revenue curve is also constant and equals the demand curve, Average revenue is the same as price (AR = TR/Q = P x Q/Q = P). Thus the price line is also identical to the demand curve. In sum, D = AR = MR = P. • P-Max quantity, price and profit: If a monopolist obtains control of a formerly perfectly competitive industry, the monopolist would increase prices, reduce production, and realise positive economic profits.[20] • Supply curve: in a perfectly competitive market there is a well defined supply function with a one-to-one relationship between price and quantity supplied.[21] In a monopolistic market no such supply relationship exists. A monopolist cannot trace a short-term supply curve because for a given price there is not a unique quantity supplied. As Pindyck and Rubenfeld note, a change in demand "can lead to changes in prices with no change in output, changes in output with no change in price or both".[22] Monopolies produce where marginal revenue equals marginal costs. For a specific demand curve the supply "curve" would be the price-quantity combination at the point where marginal revenue equals marginal cost. If the demand curve shifted the marginal revenue curve would shift as well and a new equilibrium and supply "point" would be established. The locus of these points would not be a supply curve in any conventional sense.[23][24] The most significant distinction between a PC company and a monopoly is that the monopoly has a downward-sloping demand curve rather than the "perceived" perfectly elastic curve of the PC company.[25] Practically all the variations mentioned above relate to this fact. If there is a downward-sloping demand curve then by necessity there is a distinct marginal revenue curve. The implications of this fact are best made manifest with a linear demand curve. Assume that the inverse demand curve is of the form x = a − by. Then the total revenue curve is TR = ay − by2 and the marginal revenue curve is thus MR = a − 2by. From this several things are evident. First, the marginal revenue curve has the same y intercept as the inverse demand curve. Second, the slope of the marginal revenue curve is twice that of the inverse demand curve. Third, the x intercept of the marginal revenue curve is half that of the inverse demand curve. What is not quite so evident is that the marginal revenue curve is below the inverse demand curve at all points.[25] Since all companies maximise profits by equating MR and MC it must be the case that at the profit-maximizing quantity MR and MC are less than price, which further implies that a monopoly produces less quantity at a higher price than if the market were perfectly competitive. The fact that a monopoly has a downward-sloping demand curve means that the relationship between total revenue and output for a monopoly is much different than that of competitive companies.[26] Total revenue equals price times quantity. A competitive company has a perfectly elastic demand curve meaning that total revenue is proportional to output.[26] Thus the total revenue curve for a competitive company is a ray with a slope equal to the market price.[26] A competitive company can sell all the output it desires at the market price. For a monopoly to increase sales it must reduce price. Thus the total revenue curve for a monopoly is a parabola that begins at the origin and reaches a maximum value then continuously decreases until total revenue is again zero.[27] Total revenue has its maximum value when the slope of the total revenue function is zero. The slope of the total revenue function is marginal revenue. So the revenue maximizing quantity and price occur when MR = 0. For example, assume that the monopoly's demand function is P = 50 − 2Q. The total revenue function would be TR = 50Q − 2Q2 and marginal revenue would be 50 − 4Q. Setting marginal revenue equal to zero we have ${\displaystyle 50-4Q=0}$ ${\displaystyle -4Q=-50}$ ${\displaystyle Q=12.5}$ So the revenue maximizing quantity for the monopoly is 12.5 units and the revenue maximizing price is 25. A company with a monopoly does not experience price pressure from competitors, although it may experience pricing pressure from potential competition. If a company increases prices too much, then others may enter the market if they are able to provide the same good, or a substitute, at a lesser price.[28] The idea that monopolies in markets with easy entry need not be regulated against is known as the "revolution in monopoly theory".[29] A monopolist can extract only one premium,[clarification needed] and getting into complementary markets does not pay. That is, the total profits a monopolist could earn if it sought to leverage its monopoly in one market by monopolizing a complementary market are equal to the extra profits it could earn anyway by charging more for the monopoly product itself. However, the one monopoly profit theorem is not true if customers in the monopoly good are stranded or poorly informed, or if the tied good has high fixed costs. A pure monopoly has the same economic rationality of perfectly competitive companies, i.e. to optimise a profit function given some constraints. By the assumptions of increasing marginal costs, exogenous inputs' prices, and control concentrated on a single agent or entrepreneur, the optimal decision is to equate the marginal cost and marginal revenue of production. Nonetheless, a pure monopoly can – unlike a competitive company – alter the market price for its own convenience: a decrease of production results in a higher price. In the economics' jargon, it is said that pure monopolies have "a downward-sloping demand". An important consequence of such behaviour is that typically a monopoly selects a higher price and lesser quantity of output than a price-taking company; again, less is available at a higher price.[30] ## Inverse elasticity rule A monopoly chooses that price that maximizes the difference between total revenue and total cost. The basic markup rule (as measured by the Lerner index) can be expressed as ${\displaystyle {\frac {P-MC}{P}}={\frac {-1}{E_{d}}}}$, where ${\displaystyle E_{d}}$ is the price elasticity of demand the firm faces.[31] The markup rules indicate that the ratio between profit margin and the price is inversely proportional to the price elasticity of demand.[31] The implication of the rule is that the more elastic the demand for the product the less pricing power the monopoly has. ### Market power Market power is the ability to increase the product's price above marginal cost without losing all customers.[32] Perfectly competitive (PC) companies have zero market power when it comes to setting prices. All companies of a PC market are price takers. The price is set by the interaction of demand and supply at the market or aggregate level. Individual companies simply take the price determined by the market and produce that quantity of output that maximizes the company's profits. If a PC company attempted to increase prices above the market level all its customers would abandon the company and purchase at the market price from other companies. A monopoly has considerable although not unlimited market power. A monopoly has the power to set prices or quantities although not both.[33] A monopoly is a price maker.[34] The monopoly is the market[35] and prices are set by the monopolist based on their circumstances and not the interaction of demand and supply. The two primary factors determining monopoly market power are the company's demand curve and its cost structure.[36] Market power is the ability to affect the terms and conditions of exchange so that the price of a product is set by a single company (price is not imposed by the market as in perfect competition).[37][38] Although a monopoly's market power is great it is still limited by the demand side of the market. A monopoly has a negatively sloped demand curve, not a perfectly inelastic curve. Consequently, any price increase will result in the loss of some customers. ## Price discrimination Price discrimination allows a monopolist to increase its profit by charging higher prices for identical goods to those who are willing or able to pay more. For example, most economic textbooks cost more in the United States than in developing countries like Ethiopia. In this case, the publisher is using its government-granted copyright monopoly to price discriminate between the generally wealthier American economics students and the generally poorer Ethiopian economics students. Similarly, most patented medications cost more in the U.S. than in other countries with a (presumed) poorer customer base. Typically, a high general price is listed, and various market segments get varying discounts. This is an example of framing to make the process of charging some people higher prices more socially acceptable.[citation needed] Perfect price discrimination would allow the monopolist to charge each customer the exact maximum amount they would be willing to pay. This would allow the monopolist to extract all the consumer surplus of the market. A domestic example would be the cost of airplane flights in relation to their takeoff time; the closer they are to flight, the higher the plane tickets will cost, discriminating against late planners and often business flyers. While such perfect price discrimination is a theoretical construct, advances in information technology and micromarketing may bring it closer to the realm of possibility. Partial price discrimination can cause some customers who are inappropriately pooled with high price customers to be excluded from the market. For example, a poor student in the U.S. might be excluded from purchasing an economics textbook at the U.S. price, which the student may have been able to purchase at the Ethiopian price. Similarly, a wealthy student in Ethiopia may be able to or willing to buy at the U.S. price, though naturally would hide such a fact from the monopolist so as to pay the reduced third world price. These are deadweight losses and decrease a monopolist's profits. Deadweight loss is considered detrimental to society and market participation. As such, monopolists have substantial economic interest in improving their market information and market segmenting.[39] There is important information for one to remember when considering the monopoly model diagram (and its associated conclusions) displayed here. The result that monopoly prices are higher, and production output lesser, than a competitive company follow from a requirement that the monopoly not charge different prices for different customers. That is, the monopoly is restricted from engaging in price discrimination (this is termed first degree price discrimination, such that all customers are charged the same amount). If the monopoly were permitted to charge individualised prices (this is termed third degree price discrimination), the quantity produced, and the price charged to the marginal customer, would be identical to that of a competitive company, thus eliminating the deadweight loss; however, all gains from trade (social welfare) would accrue to the monopolist and none to the consumer. In essence, every consumer would be indifferent between going completely without the product or service and being able to purchase it from the monopolist.[citation needed] As long as the price elasticity of demand for most customers is less than one in absolute value, it is advantageous for a company to increase its prices: it receives more money for fewer goods. With a price increase, price elasticity tends to increase, and in the optimum case above it will be greater than one for most customers.[citation needed] A company maximizes profit by selling where marginal revenue equals marginal cost. A company that does not engage in price discrimination will charge the profit maximizing price, P, to all its customers. In such circumstances there are customers who would be willing to pay a higher price than P and those who will not pay P* but would buy at a lower price. A price discrimination strategy is to charge less price sensitive buyers a higher price and the more price sensitive buyers a lower price.[40] Thus additional revenue is generated from two sources. The basic problem is to identify customers by their willingness to pay. The purpose of price discrimination is to transfer consumer surplus to the producer.[41] Consumer surplus is the difference between the value of a good to a consumer and the price the consumer must pay in the market to purchase it.[42] Price discrimination is not limited to monopolies. Market power is a company's ability to increase prices without losing all its customers. Any company that has market power can engage in price discrimination. Perfect competition is the only market form in which price discrimination would be impossible (a perfectly competitive company has a perfectly elastic demand curve and has no market power).[41][43][44][45] There are three forms of price discrimination. First degree price discrimination charges each consumer the maximum price the consumer is willing to pay. Second degree price discrimination involves quantity discounts. Third degree price discrimination involves grouping consumers according to willingness to pay as measured by their price elasticities of demand and charging each group a different price. Third degree price discrimination is the most prevalent type.[46] There are three conditions that must be present for a company to engage in successful price discrimination. First, the company must have market power.[47] Second, the company must be able to sort customers according to their willingness to pay for the good.[48] Third, the firm must be able to prevent resell. A company must have some degree of market power to practice price discrimination. Without market power a company cannot charge more than the market price.[49] Any market structure characterized by a downward sloping demand curve has market power – monopoly, monopolistic competition and oligopoly.[47] The only market structure that has no market power is perfect competition.[49] A company wishing to practice price discrimination must be able to prevent middlemen or brokers from acquiring the consumer surplus for themselves. The company accomplishes this by preventing or limiting resale. Many methods are used to prevent resale. For instance, persons are required to show photographic identification and a boarding pass before boarding an airplane. Most travelers assume that this practice is strictly a matter of security. However, a primary purpose in requesting photographic identification is to confirm that the ticket purchaser is the person about to board the airplane and not someone who has repurchased the ticket from a discount buyer.[citation needed] The inability to prevent resale is the largest obstacle to successful price discrimination.[43] Companies have however developed numerous methods to prevent resale. For example, universities require that students show identification before entering sporting events. Governments may make it illegal to resell tickets or products. In Boston, Red Sox baseball tickets can only be resold legally to the team. The three basic forms of price discrimination are first, second and third degree price discrimination. In first degree price discrimination the company charges the maximum price each customer is willing to pay. The maximum price a consumer is willing to pay for a unit of the good is the reservation price. Thus for each unit the seller tries to set the price equal to the consumer's reservation price.[50] Direct information about a consumer's willingness to pay is rarely available. Sellers tend to rely on secondary information such as where a person lives (postal codes); for example, catalog retailers can use mail high-priced catalogs to high-income postal codes.[51][52] First degree price discrimination most frequently occurs in regard to professional services or in transactions involving direct buyer-seller negotiations. For example, an accountant who has prepared a consumer's tax return has information that can be used to charge customers based on an estimate of their ability to pay.[53] In second degree price discrimination or quantity discrimination customers are charged different prices based on how much they buy. There is a single price schedule for all consumers but the prices vary depending on the quantity of the good bought.[54] The theory of second degree price discrimination is a consumer is willing to buy only a certain quantity of a good at a given price. Companies know that consumer's willingness to buy decreases as more units are purchased[citation needed]. The task for the seller is to identify these price points and to reduce the price once one is reached in the hope that a reduced price will trigger additional purchases from the consumer. For example, sell in unit blocks rather than individual units. In third degree price discrimination or multi-market price discrimination[55] the seller divides the consumers into different groups according to their willingness to pay as measured by their price elasticity of demand. Each group of consumers effectively becomes a separate market with its own demand curve and marginal revenue curve.[44] The firm then attempts to maximize profits in each segment by equating MR and MC,[47][56][57] Generally the company charges a higher price to the group with a more price inelastic demand and a relatively lesser price to the group with a more elastic demand.[58] Examples of third degree price discrimination abound. Airlines charge higher prices to business travelers than to vacation travelers. The reasoning is that the demand curve for a vacation traveler is relatively elastic while the demand curve for a business traveler is relatively inelastic. Any determinant of price elasticity of demand can be used to segment markets. For example, seniors have a more elastic demand for movies than do young adults because they generally have more free time. Thus theaters will offer discount tickets to seniors.[59] ### Example Assume that by a uniform pricing system the monopolist would sell five units at a price of $10 per unit. Assume that his marginal cost is$5 per unit. Total revenue would be $50, total costs would be$25 and profits would be $25. If the monopolist practiced price discrimination he would sell the first unit for$50 the second unit for $40 and so on. Total revenue would be$150, his total cost would be $25 and his profit would be$125.00.[60] Several things are worth noting. The monopolist acquires all the consumer surplus and eliminates practically all the deadweight loss because he is willing to sell to anyone who is willing to pay at least the marginal cost.[60] Thus the price discrimination promotes efficiency. Secondly, by the pricing scheme price = average revenue and equals marginal revenue. That is the monopolist behaving like a perfectly competitive company.[61] Thirdly, the discriminating monopolist produces a larger quantity than the monopolist operating by a uniform pricing scheme.[62] Qd Price 1 50 2 40 3 30 4 20 5 10 ### Classifying customers Successful price discrimination requires that companies separate consumers according to their willingness to buy. Determining a customer's willingness to buy a good is difficult. Asking consumers directly is fruitless: consumers don't know, and to the extent they do they are reluctant to share that information with marketers. The two main methods for determining willingness to buy are observation of personal characteristics and consumer actions. As noted information about where a person lives (postal codes), how the person dresses, what kind of car he or she drives, occupation, and income and spending patterns can be helpful in classifying.[citation needed] ## Monopoly and efficiency Surpluses and deadweight loss created by monopoly price setting The price of monopoly is upon every occasion the highest which can be got. The natural price, or the price of free competition, on the contrary, is the lowest which can be taken, not upon every occasion indeed, but for any considerable time together. The one is upon every occasion the highest which can be squeezed out of the buyers, or which it is supposed they will consent to give; the other is the lowest which the sellers can commonly afford to take, and at the same time continue their business.[63]:56 ...Monopoly, besides, is a great enemy to good management.[63]:127 – Adam Smith (1776), The Wealth of Nations According to the standard model, in which a monopolist sets a single price for all consumers, the monopolist will sell a lesser quantity of goods at a higher price than would companies by perfect competition. Because the monopolist ultimately forgoes transactions with consumers who value the product or service more than its price, monopoly pricing creates a deadweight loss referring to potential gains that went neither to the monopolist nor to consumers. Deadweight loss is the cost to society because the market isn't in equilibrium, it is inefficient. Given the presence of this deadweight loss, the combined surplus (or wealth) for the monopolist and consumers is necessarily less than the total surplus obtained by consumers by perfect competition. Where efficiency is defined by the total gains from trade, the monopoly setting is less efficient than perfect competition.[64] It is often argued that monopolies tend to become less efficient and less innovative over time, becoming "complacent", because they do not have to be efficient or innovative to compete in the marketplace. Sometimes this very loss of psychological efficiency can increase a potential competitor's value enough to overcome market entry barriers, or provide incentive for research and investment into new alternatives. The theory of contestable markets argues that in some circumstances (private) monopolies are forced to behave as if there were competition because of the risk of losing their monopoly to new entrants. This is likely to happen when a market's barriers to entry are low. It might also be because of the availability in the longer term of substitutes in other markets. For example, a canal monopoly, while worth a great deal during the late 18th century United Kingdom, was worth much less during the late 19th century because of the introduction of railways as a substitute.[citation needed] Contrary to common misconception, monopolists do not try to sell items for the highest possible price, nor do they try to maximize profit per unit, but rather they try to maximize total profit.[65] ### Natural monopoly A natural monopoly is an organization that experiences increasing returns to scale over the relevant range of output and relatively high fixed costs.[66] A natural monopoly occurs where the average cost of production "declines throughout the relevant range of product demand". The relevant range of product demand is where the average cost curve is below the demand curve.[67] When this situation occurs, it is always more efficient for one large company to supply the market than multiple smaller companies; in fact, absent government intervention in such markets, will naturally evolve into a monopoly. Often, a natural monopoly is the outcome of an initial rivalry between several competitors. An early market entrant that takes advantage of the cost structure and can expand rapidly can exclude smaller companies from entering and can drive or buy out other companies. A natural monopoly suffers from the same inefficiencies as any other monopoly. Left to its own devices, a profit-seeking natural monopoly will produce where marginal revenue equals marginal costs. Regulation of natural monopolies is problematic.[citation needed] Fragmenting such monopolies is by definition inefficient. The most frequently used methods dealing with natural monopolies are government regulations and public ownership. Government regulation generally consists of regulatory commissions charged with the principal duty of setting prices.[68] To reduce prices and increase output, regulators often use average cost pricing. By average cost pricing, the price and quantity are determined by the intersection of the average cost curve and the demand curve.[69] This pricing scheme eliminates any positive economic profits since price equals average cost. Average-cost pricing is not perfect. Regulators must estimate average costs. Companies have a reduced incentive to lower costs. Regulation of this type has not been limited to natural monopolies.[69] Average-cost pricing does also have some disadvantages. By setting price equal to the intersection of the demand curve and the average total cost curve, the firm's output is allocatively inefficient as the price is less than the marginal cost (which is the output quantity for a perfectly competitive and allocatively efficient market). In 1848, J.S. Mill was the first individual to describe monopolies with the adjective "natural". He used it interchangeably with "practical". At the time, Mill gave the following examples of natural or practical monopolies: gas supply, water supply, roads, canals, and railways. In his Social Economics,[70] Friedrich von Wieser demonstrated his view of the postal service as a natural monopoly: "In the face of [such] single-unit administration, the principle of competition becomes utterly abortive. The parallel network of another postal organization, beside the one already functioning, would be economically absurd; enormous amounts of money for plant and management would have to be expended for no purpose whatever."[70] ### Government-granted monopoly A government-granted monopoly (also called a "de jure monopoly") is a form of coercive monopoly, in which a government grants exclusive privilege to a private individual or company to be the sole provider of a commodity. Monopoly may be granted explicitly, as when potential competitors are excluded from the market by a specific law, or implicitly, such as when the requirements of an administrative regulation can only be fulfilled by a single market player, or through some other legal or procedural mechanism, such as patents, trademarks, and copyright.[71] ## Monopolist shutdown rule A monopolist should shut down when price is less than average variable cost for every output level[72] – in other words where the demand curve is entirely below the average variable cost curve.[72] Under these circumstances at the profit maximum level of output (MR = MC) average revenue would be less than average variable costs and the monopolists would be better off shutting down in the short term.[72] ## Breaking up monopolies In an unregulated market, monopolies can potentially be ended by new competition, breakaway businesses, or consumers seeking alternatives. In a regulated market, a government will often either regulate the monopoly, convert it into a publicly owned monopoly environment, or forcibly fragment it (see Antitrust law and trust busting). Public utilities, often being naturally efficient with only one operator and therefore less susceptible to efficient breakup, are often strongly regulated or publicly owned. American Telephone & Telegraph (AT&T) and Standard Oil are often cited as examples of the breakup of a private monopoly by government. The Bell System, later AT&T, was protected from competition first by the Kingsbury Commitment, and later by a series of agreements between AT&T and the Federal Government. In 1984, decades after having been granted monopoly power by force of law, AT&T was broken up into various components, MCI, Sprint, who were able to compete effectively in the long-distance phone market. These breakups are due to the presence of deadweight loss and inefficiency in a monopolistic market, causing the Government to intervene on behalf of consumers and society in order to incite competition.[citation needed] While the sentiment among regulators and judges has generally recommended that breakups are not as remedies for antitrust enforcement, recent scholarship has found that this hostility to breakups by administrators is largely unwarranted.[73]:1 In fact, some scholars have argued breakups, even if incorrectly targeted, could arguably still encourage collaboration, innovation, and efficiency.[73]:49 ## Law A 1902 anti-monopoly cartoon depicts the challenges that monopolies may create for workers The law regulating dominance in the European Union is governed by Article 102 of the Treaty on the Functioning of the European Union which aims at enhancing the consumer's welfare and also the efficiency of allocation of resources by protecting competition on the downstream market.[74] The existence of a very high market share does not always mean consumers are paying excessive prices since the threat of new entrants to the market can restrain a high-market-share company's price increases. Competition law does not make merely having a monopoly illegal, but rather abusing the power a monopoly may confer, for instance through exclusionary practices (i.e. pricing high just because it is the only one around.) It may also be noted that it is illegal to try to obtain a monopoly, by practices of buying out the competition, or equal practices. If one occurs naturally, such as a competitor going out of business, or lack of competition, it is not illegal until such time as the monopoly holder abuses the power. ### Establishing dominance First it is necessary to determine whether a company is dominant, or whether it behaves "to an appreciable extent independently of its competitors, customers and ultimately of its consumer". Establishing dominance is a two-stage test. The first thing to consider is market definition which is one of the crucial factors of the test.[75] It includes relevant product market and relevant geographic market. #### Relevant product market As the definition of the market is of a matter of interchangeability, if the goods or services are regarded as interchangeable then they are within the same product market.[76] For example, in the case of United Brands v Commission,[77] it was argued in this case that bananas and other fresh fruit were in the same product market and later on dominance was found because the special features of the banana made it could only be interchangeable with other fresh fruits in a limited extent and other and is only exposed to their competition in a way that is hardly perceptible. The demand substitutability of the goods and services will help in defining the product market and it can be access by the ‘hypothetical monopolist’ test or the ‘SSNIP’ test .[78] #### Relevant geographic market It is necessary to define it because some goods can only be supplied within a narrow area due to technical, practical or legal reasons and this may help to indicate which undertakings impose a competitive constraint on the other undertakings in question. Since some goods are too expensive to transport where it might not be economic to sell them to distant markets in relation to their value, therefore the cost of transporting is a crucial factor here. Other factors might be legal controls which restricts an undertaking in a Member States from exporting goods or services to another. Market definition may be difficult to measure but is important because if it is defined too broadly, the undertaking may be more likely to be found dominant and if it is defined too narrowly, the less likely that it will be found dominant. #### Market shares As with collusive conduct, market shares are determined with reference to the particular market in which the company and product in question is sold. It does not in itself determine whether an undertaking is dominant but work as an indicator of the states of the existing competition within the market. The Herfindahl-Hirschman Index (HHI) is sometimes used to assess how competitive an industry is. It sums up the squares of the individual market shares of all of the competitors within the market. The lower the total, the less concentrated the market and the higher the total, the more concentrated the market.[79] In the US, the merger guidelines state that a post-merger HHI below 1000 is viewed as not concentrated while HHIs above that will provoke further review. By European Union law, very large market shares raise a presumption that a company is dominant, which may be rebuttable. A market share of 100% may be very rare but it is still possible to be found and in fact it has been identified in some cases, for instance the AAMS v Commission case.[80] Undertakings possessing market share that is lower than 100% but over 90% had also been found dominant, for example, Microsoft v Commission case.[81] In the AKZO v Commission case,[82] the undertaking is presumed to be dominant if it has a market share of 50%. There are also findings of dominance that are below a market share of 50%, for instance, United Brands v Commission,[77] it only possessed a market share of 40% to 45% and still to be found dominant with other factors. The lowest yet market share of a company considered "dominant" in the EU was 39.7%.If a company has a dominant position, then there is a special responsibility not to allow its conduct to impair competition on the common market however these will all falls away if it is not dominant.[83] When considering whether an undertaking is dominant, it involves a combination of factors. Each of them cannot be taken separately as if they are, they will not be as determinative as they are when they are combined together.[84] Also, in cases where an undertaking has previously been found dominant, it is still necessary to redefine the market and make a whole new analysis of the conditions of competition based on the available evidence at the appropriate time.[85] #### Other related factors According to the Guidance, there are three more issues that must be examined. They are actual competitors that relates to the market position of the dominant undertaking and its competitors, potential competitors that concerns the expansion and entry and lastly the countervailing buyer power.[84] • Actual Competitors Market share may be a valuable source of information regarding the market structure and the market position when it comes to accessing it. The dynamics of the market and the extent to which the goods and services differentiated are relevant in this area.[84] • Potential Competitors It concerns with the competition that would come from other undertakings which are not yet operating in the market but will enter it in the future. So, market shares may not be useful in accessing the competitive pressure that is exerted on an undertaking in this area. The potential entry by new firms and expansions by an undertaking must be taken into account,[84] therefore the barriers to entry and barriers to expansion is an important factor here. Competitive constraints may not always come from actual or potential competitors. Sometimes, it may also come from powerful customers who have sufficient bargaining strength which come from its size or its commercial significance for a dominant firm.[84] ### Types of abuses There are three main types of abuses which are exploitative abuse, exclusionary abuse and single market abuse. • Exploitative abuse It arises when a monopolist has such significant market power that it can restrict its output while increasing the price above the competitive level without losing customers.[79] This type is less concerned by the Commission than other types. • Exclusionary abuse This is most concerned about by the Commissions because it is capable of causing long- term consumer damage and is more likely to prevent the development of competition.[79] An example of it is exclusive dealing agreements. • Single market abuse It arises when a dominant undertaking carrying out excess pricing which would not only have an exploitative effect but also prevent parallel imports and limits intra- brand competition.[79] ### Examples of abuses Despite wide agreement that the above constitute abusive practices, there is some debate about whether there needs to be a causal connection between the dominant position of a company and its actual abusive conduct. Furthermore, there has been some consideration of what happens when a company merely attempts to abuse its dominant position. To provide a more specific example, economic and philosophical scholar Adam Smith cites that trade to the East India Company has, for the most part, been subjected to an exclusive company such as that of the English or Dutch. Monopolies such as these are generally established against the nation in which they arose out of. The profound economist goes on to state how there are two types of monopolies. The first type of monopoly is one which tends to always attract to the particular trade where the monopoly was conceived, a greater proportion of the stock of the society than what would go to that trade originally. The second type of monopoly tends to occasionally attract stock towards the particular trade where it was conceived, and sometimes repel it from that trade depending on varying circumstances. Rich countries tended to repel while poorer countries were attracted to this. For example, The Dutch company would dispose of any excess goods not taken to the market in order to preserve their monopoly while the English sold more goods for better prices. Both of these tendencies were extremely destructive as can be seen in Adam Smith's writings.[86] ## Historical monopolies ### Origin The term "monopoly" first appears in Aristotle's Politics. Aristotle describes Thales of Miletus's cornering of the market in olive presses as a monopoly (μονοπώλιον).[87][88] Another early reference to the concept of “monopoly” in a commercial sense appears in tractate Demai of the Mishna (2nd century C.E.), regarding the purchasing of agricultural goods from a dealer who has a monopoly on the produce (chapter 5; 4).[89] The meaning and understanding of the English word 'monopoly' has changed over the years.[90] ### Monopolies of resources #### Salt Vending of common salt (sodium chloride) was historically a natural monopoly. Until recently, a combination of strong sunshine and low humidity or an extension of peat marshes was necessary for producing salt from the sea, the most plentiful source. Changing sea levels periodically caused salt "famines" and communities were forced to depend upon those who controlled the scarce inland mines and salt springs, which were often in hostile areas (e.g. the Sahara desert) requiring well-organised security for transport, storage, and distribution. The Salt Commission was a legal monopoly in China. Formed in 758, the Commission controlled salt production and sales in order to raise tax revenue for the Tang Dynasty. The "Gabelle" was a notoriously high tax levied upon salt in the Kingdom of France. The much-hated levy had a role in the beginning of the French Revolution, when strict legal controls specified who was allowed to sell and distribute salt. First instituted in 1286, the Gabelle was not permanently abolished until 1945.[91] #### Coal Robin Gollan argues in The Coalminers of New South Wales that anti-competitive practices developed in the coal industry of Australia's Newcastle as a result of the business cycle. The monopoly was generated by formal meetings of the local management of coal companies agreeing to fix a minimum price for sale at dock. This collusion was known as "The Vend". The Vend ended and was reformed repeatedly during the late 19th century, ending by recession in the business cycle. "The Vend" was able to maintain its monopoly due to trade union assistance, and material advantages (primarily coal geography). During the early 20th century, as a result of comparable monopolistic practices in the Australian coastal shipping business, the Vend developed as an informal and illegal collusion between the steamship owners and the coal industry, eventually resulting in the High Court case Adelaide Steamship Co. Ltd v. R. & AG.[92] #### Persian filoselle (raw silk) In the 17th century, Shah Abbas established New Julfa (a suburb in the capital of Isfahan) to concentrate Armenian financial capital in Iran. Accordingly, he gave Armenians various privileges, including the monopoly to trade Persian filoselle (raw silk). Armenians exported it all over the world, including Asia, Europe, and America. By the 1750s, Armenia already controlled 75% of the total silk trade in the area. This resulted in a boom in Armenian commerce, which lasted for the next 150 years. [93] #### Petroleum Standard Oil was an American oil producing, transporting, refining, and marketing company. Established in 1870, it became the largest oil refiner in the world.[94] John D. Rockefeller was a founder, chairman and major shareholder. The company was an innovator in the development of the business trust. The Standard Oil trust streamlined production and logistics, lowered costs, and undercut competitors. "Trust-busting" critics accused Standard Oil of using aggressive pricing to destroy competitors and form a monopoly that threatened consumers. Its controversial history as one of the world's first and largest multinational corporations ended in 1911, when the United States Supreme Court ruled that Standard was an illegal monopoly. The Standard Oil trust was dissolved into 33 smaller companies; two of its surviving "child" companies are ExxonMobil and the Chevron Corporation. #### Steel U.S. Steel has been accused of being a monopoly. J. P. Morgan and Elbert H. Gary founded U.S. Steel in 1901 by combining Andrew Carnegie's Carnegie Steel Company with Gary's Federal Steel Company and William Henry "Judge" Moore's National Steel Company.[95][96] At one time, U.S. Steel was the largest steel producer and largest corporation in the world. In its first full year of operation, U.S. Steel made 67 percent of all the steel produced in the United States. However, U.S. Steel's share of the expanding market slipped to 50 percent by 1911,[97] and antitrust prosecution that year failed. #### Diamonds De Beers settled charges of price fixing in the diamond trade in the 2000s. De Beers is well known for its monopoloid practices throughout the 20th century, whereby it used its dominant position to manipulate the international diamond market. The company used several methods to exercise this control over the market. Firstly, it convinced independent producers to join its single channel monopoly, it flooded the market with diamonds similar to those of producers who refused to join the cartel, and lastly, it purchased and stockpiled diamonds produced by other manufacturers in order to control prices through limiting supply. In 2000, the De Beers business model changed due to factors such as the decision by producers in Russia, Canada and Australia to distribute diamonds outside the De Beers channel, as well as rising awareness of blood diamonds that forced De Beers to "avoid the risk of bad publicity" by limiting sales to its own mined products. De Beers' market share by value fell from as high as 90% in the 1980s to less than 40% in 2012, having resulted in a more fragmented diamond market with more transparency and greater liquidity. In November 2011 the Oppenheimer family announced its intention to sell the entirety of its 40% stake in De Beers to Anglo American plc thereby increasing Anglo American's ownership of the company to 85%.[30] The transaction was worth £3.2 billion ($5.1 billion) in cash and ended the Oppenheimer dynasty's 80-year ownership of De Beers. ### Utilities A public utility (or simply "utility") is an organization or company that maintains the infrastructure for a public service or provides a set of services for public consumption. Common examples of utilities are electricity, natural gas, water, sewage, cable television, and telephone. In the United States, public utilities are often natural monopolies because the infrastructure required to produce and deliver a product such as electricity or water is very expensive to build and maintain.[98] Western Union was criticized as a "price gouging" monopoly in the late 19th century.[99] American Telephone & Telegraph was a telecommunications giant. AT&T was broken up in 1984. In the case of Telecom New Zealand, local loop unbundling was enforced by central government. Telkom is a semi-privatised, part state-owned South African telecommunications company. Deutsche Telekom is a former state monopoly, still partially state owned. Deutsche Telekom currently monopolizes high-speed VDSL broadband network.[100] The Long Island Power Authority (LIPA) provided electric service to over 1.1 million customers in Nassau and Suffolk counties of New York, and the Rockaway Peninsula in Queens. The Comcast Corporation is the largest mass media and communications company in the world by revenue.[101] It is the largest cable company and home Internet service provider in the United States, and the nation's third largest home telephone service provider. Comcast has a monopoly in Boston, Philadelphia, and many other small towns across the US.[citation needed] ### Transportation The United Aircraft and Transport Corporation was an aircraft manufacturer holding company that was forced to divest itself of airlines in 1934. Iarnród Éireann, the Irish Railway authority, is a current monopoly as Ireland does not have the size for more companies. The Long Island Rail Road (LIRR) was founded in 1834, and since the mid-1800s has provided train service between Long Island and New York City. In the 1870s, LIRR became the sole railroad in that area through a series of acquisitions and consolidations. In 2013, the LIRR's commuter rail system is the busiest commuter railroad in North America, serving nearly 335,000 passengers daily.[102] ### Foreign trade Dutch East India Company was created as a legal trading monopoly in 1602. The Vereenigde Oost-Indische Compagnie enjoyed huge profits from its spice monopoly through most of the 17th century.[103] The British East India Company was created as a legal trading monopoly in 1600. The East India Company was formed for pursuing trade with the East Indies but ended up trading mainly with the Indian subcontinent, North-West Frontier Province, and Balochistan. The Company traded in basic commodities, which included cotton, silk, indigo dye, salt, saltpetre, tea and opium. ### Professional sports Major League Baseball survived U.S. antitrust litigation in 1922, though its special status is still in dispute as of 2009. The National Football League survived antitrust lawsuit in the 1960s but was convicted of being an illegal monopoly in the 1980s. ### Other examples of monopolies ## Countering monopolies According to professor Milton Friedman, laws against monopolies cause more harm than good, but unnecessary monopolies should be countered by removing tariffs and other regulation that upholds monopolies. A monopoly can seldom be established within a country without overt and covert government assistance in the form of a tariff or some other device. It is close to impossible to do so on a world scale. The De Beers diamond monopoly is the only one we know of that appears to have succeeded (and even De Beers are protected by various laws against so called "illicit" diamond trade). – In a world of free trade, international cartels would disappear even more quickly. — Milton Friedman, Free to Choose, p. 53–54 However, professor Steve H. Hanke believes that although private monopolies are more efficient than public ones, often by a factor of two, sometimes private natural monopolies, such as local water distribution, should be regulated (not prohibited) by, e.g., price auctions.[109] Thomas DiLorenzo asserts, however, that during the early days of utility companies where there was little regulation, there were no natural monopolies and there was competition.[110] Only when companies realized that they could gain power through government did monopolies begin to form. Baten, Bianchi and Moser[111] find historical evidence that monopolies which are protected by patent laws may have adverse effects on the creation of innovation in an economy. They argue that under certain circumstances, compulsory licensing – which allows governments to license patents without the consent of patent-owners – may be effective in promoting invention by increasing the threat of competition in fields with low pre-existing levels of competition. ## See also ## Notes and references 1. ^ Milton Friedman (February 2002) [1962]. "VIII: Monopoly and the Social Responsibility of Business and Labor". Capitalism and Freedom (paperback) (40th anniversary ed.). The University of Chicago Press. p. 208. ISBN 0-226-26421-1. 2. ^ Blinder, Alan S; Baumol, William J; Gale, Colton L (June 2001). "11: Monopoly". Microeconomics: Principles and Policy (paperback). Thomson South-Western. p. 212. ISBN 0-324-22115-0. A pure monopoly is an industry in which there is only one supplier of a product for which there are no close substitutes and in which is very difficult or impossible for another firm to coexist 3. ^ a b Orbach, Barak; Campbell, Grace (2012). "The Antitrust Curse of Bigness". Southern California Law Review. SSRN 1856553. 4. ^ Binger and Hoffman (1998), p. 391. 5. ^ Goodwin, N; Nelson, J; Ackerman, F; Weisskopf, T (2009). Microeconomics in Context (2nd ed.). Sharpe. pp. 307–308. 6. ^ Samuelson, William F.; Marks, Stephen G. (2003). Managerial Economics (4th ed.). Wiley. pp. 365–366. 7. ^ a b Nicholson, Walter; Snyder, Christopher (2007). Intermediate Microeconomics. Thomson. p. 379. 8. ^ Frank (2009), p. 274. 9. ^ Samuelson & Marks (2003), p. 365. 10. ^ Ayers, Rober M.; Collinge, Robert A. (2003). Microeconomics. Pearson. p. 238. 11. ^ Pindyck and Rubinfeld (2001), p. 127. 12. ^ Png, Ivan (1999). Managerial Economics. Blackwell. p. 271. ISBN 1-55786-927-8. 13. ^ Png (1999), p. 268. 14. ^ Negbennebor, Anthony (2001). Microeconomics, The Freedom to Choose. CAT Publishing. 15. ^ Mankiw (2007), p. 338. 16. ^ a b Hirschey, M (2000). Managerial Economics. Dreyden. p. 426. 17. ^ Pindyck, R; Rubinfeld, D (2001). Microeconomics (5th ed.). Prentice-Hall. p. 333. 18. ^ Melvin and Boyes (2002), p. 245. 19. ^ Varian, H (1992). Microeconomic Analysis (3rd ed.). Norton. p. 235. 20. ^ Pindyck and Rubinfeld (2001), p. 370. 21. ^ Frank (2008), p. 342. 22. ^ Pindyck and Rubenfeld (2000), p. 325. 23. ^ Nicholson (1998), p. 551. 24. ^ Perfectly competitive firms are price takers. Price is exogenous and it is possible to associate each price with unique profit maximizing quantity. Besanko, David, and Ronald Braeutigam, Microeconomics 2nd ed., Wiley (2005), p. 413. 25. ^ a b Binger, B.; Hoffman, E. (1998). Microeconomics with Calculus (2nd ed.). Addison-Wesley. 26. ^ a b c Frank (2009), p. 377. 27. ^ Frank (2009), p. 378. 28. ^ Depken, Craig (November 23, 2005). "10". Microeconomics Demystified. McGraw Hill. p. 170. ISBN 0-07-145911-1. 29. ^ Davies, Glyn; Davies, John (July 1984). "The revolution in monopoly theory". Lloyds Bank Review (153): 38–52. 30. ^ Levine, David; Boldrin, Michele (2008-09-07). Against intellectual monopoly. Cambridge University Press. p. 312. ISBN 978-0-521-87928-6. 31. ^ a b Tirole, p. 66. 32. ^ Tirole, p. 65. 33. ^ Hirschey (2000), p. 412. 34. ^ Melvin, Michael; Boyes, William (2002). Microeconomics (5th ed.). Houghton Mifflin. p. 239. 35. ^ Pindyck and Rubinfeld (2001), p. 328. 36. ^ Varian (1992), p. 233. 37. ^ Png (1999). 38. ^ Krugman, Paul; Wells, Robin (2009). Microeconomics (2nd ed.). Worth. 39. ^ Bergemann, Dirk; Brooks, Benjamin; Morris, Stephen (March 2015). "The Limits of Price Discrimination" (PDF). American Economic Review. 105 (3): 921–957. doi:10.1257/aer.20130848. 40. ^ Samuelson and Marks (2006), p. 107. 41. ^ a b Boyes and Melvin, p. 246. 42. ^ Perloff (2009), p. 404. 43. ^ a b Perloff (2009), p. 394. 44. ^ a b Besanko and Beautigam (2005), p. 449. 45. ^ Wessels, p. 159. 46. ^ "Monopoly II: Third degree price discrimination \| Policonomics". Retrieved 2020-08-18. 47. ^ a b c Boyes and Melvin, p. 449. 48. ^ Varian (1992), p. 241. 49. ^ a b Perloff (2009), p. 393. 50. ^ Besanko and Beautigam (2005), p. 448. 51. ^ Hall, Robert E.; Liberman, Marc (2001). Microeconomics: Theory and Applications (2nd ed.). South_Western. p. 263. 52. ^ Besanko and Beautigam (2005), p. 451. 53. ^ If the monopolist is able to segment the market perfectly, then the average revenue curve effectively becomes the marginal revenue curve for the company and the company maximizes profits by equating price and marginal costs. That is the company is behaving like a perfectly competitive company. The monopolist will continue to sell extra units as long as the extra revenue exceeds the marginal cost of production. The problem that the company has is that the company must charge a different price for each successive unit sold. 54. ^ Varian (1992), p. 242. 55. ^ Perloff (2009), p. 396. 56. ^ Because MC is the same in each market segment the profit maximizing condition becomes produce where MR1 = MR2 = MC. Pindyck and Rubinfeld (2009), pp. 398–99. 57. ^ As Pindyck and Rubinfeld note, managers may find it easier to conceptualize the problem of what price to charge in each segment in terms of relative prices and price elasticities of demand. Marginal revenue can be written in terms of elasticities of demand as MR = P(1+1/PED). Equating MR1 and MR2 we have P1 (1+1/PED) = P2 (1+1/PED) or P1/P2 = (1+1/PED2)/(1+1/PED1). Using this equation the manager can obtain elasticity information and set prices for each segment. [Pindyck and Rubinfeld (2009), pp. 401–02.] Note that the manager may be able to obtain industry elasticities, which are far more inelastic than the elasticity for an individual firm. As a rule of thumb the company's elasticity coefficient is 5 to 6 times that of the industry. [Pindyck and Rubinfeld (2009) pp. 402.] 58. ^ Colander, David C., p. 269. 59. ^ Note that the discounts apply only to tickets not to concessions. The reason there is not any popcorn discount is that there is not any effective way to prevent resell. A profit maximizing theater owner maximizes concession sales by selling where marginal revenue equals marginal cost. 60. ^ a b Lovell (2004), p. 266. 61. ^ Frank (2008), p. 394. 62. ^ Frank (2008), p. 266. 63. ^ a b Smith, Adam (1776), Wealth of Nations Archived 2013-10-20 at the Wayback Machine, Penn State Electronic Classics edition, republished 2005 64. ^ McEachern, William A. (2009). Economics: A Contemporary Introduction. Cengage Learning. pp. 216–218. ISBN 978-0324579215. 65. ^ McConnell, Campbell R. Economics : principles, problems, and policies / Campbell R. McConnell, Stanley L. Brue.– 17th ed. 66. ^ Binger and Hoffman (1998), p. 406. 67. ^ Samuelson, P. & Nordhaus, W.: Microeconomics, 17th ed. McGraw-Hill 2001 68. ^ Samuelson, W; Marks, S (2005). Managerial Economics (4th ed.). Wiley. p. 376. 69. ^ a b Samuelson and Marks (2003), p. 100. 70. ^ a b The New Palgrave Dictionary of Economics (2nd ed.). Basingstoke, Hampshire: Palgrave Macmillan. 2008. ISBN 978-0-333-78676-5. 71. ^ Riggs, Thomas; Bonk, Mary, eds. (2008). Government-Granted Monopoly. Everyday Finance: Economics, Personal Money Management, and Entrepreneurship. Detroit: Gale Cengage Learning. ISBN 978-1-4144-1049-4. LCCN 2007035070. OL 21557400M. Retrieved 6 November 2018. 72. ^ a b c Frank, Robert H. (2008). Microeconomics and Behavior (7th ed.). McGraw-Hill. ISBN 978-0-07-126349-8. 73. ^ a b Van Loo, Rory (2020-01-01). "In Defense of Breakups: Administering a "Radical" Remedy". Cornell Law Review. 74. '^ DG Competition, DG Competition discussion paper on the application of Article [102] of the Treaty to exclusionary abuses ' [2005] <http://ec.europa.eu/competition/antitrust/art82/discpaper2005.pdf> accessed 4 May 2018 75. ^ Case 6/72 Europemballage Corpn and Continental Can Co Inc v Commission [1973] ECR 215 76. ^ Case 6/72 Europemballage Corpn and Continental Can Co Inc v Commission [1973] ECR 215 77. ^ a b 78. ^ The Unilateral Conduct Working Group, ICN's Unilateral Conduct Workbook Chapter 3’ [2011] < http://www.internationalcompetitionnetwork.org/uploads/library/doc752.pdf> last accessed 4 May 2018 79. ^ a b c d Whish R and others, Competition Law (8th Edition, OUP 2015) 80. ^ AAMS v Commission [2001] ECR II-3413 81. ^ Microsoft Corporation v Commission [2004] 82. ^ Case C- 62/86 AKZO Chemie BV v Commission [1991] ECR I -3359 83. ^ Case T-203/01 Michelin v Commission [2003] 84. Guidance on Article 102 Enforcement Priorities [2009] 85. ^ Coca-Cola Co v Commission [2000] ECR II- 1733 86. ^ Smith, Adam (2014-06-03), ""Of the Advantages Which Europe Has Derived from the Discovery of America, and from That of a passage to the East Indies by the Cape of Good Hope" from An Inquiry into the Nature and Causes of the Wealth of Nations (1776).", Adam Smith, Routledge, pp. 58–63, doi:10.4324/9780203092736-14, ISBN 978-0-203-09273-6 87. ^ Aristotle. Politics (350 B.C.E ed.). 88. ^ Aristotle. Politics. p. 1252α. 89. ^ Segal, M.H. (1948). "Demai: Translated into English with Notes". In Epstein, I. (ed.). The Talmud. Zeraim vol. II. London: The Soncino Press. p. 69. ISBN 9789562913447. Rabbi Judah agrees that if a man bought from a monopolist, he must tithe every heap. 90. ^ Richardson, Gary (June 2001). "A Tale of Two Theories: Monopolies and Craft Guilds in Medieval England and Modern Imagination". Journal of the History of Economic Thought. 23 (2): 217–242. doi:10.1080/10427710120049237. S2CID 13298305. 91. ^ Chazelas, Jean (1968). "La suppression de la gabelle du sel en 1945". Le rôle du sel dans l'histoire: Travaux préparés sous la direction de Michel Mollat. Presses universitaires de France: 263–65. OCLC 14501767. 92. ^ Gollan, Robin (1963). The Coalminers of New South Wales: a history of the union, 1860–1960. Melbourne: Melbourne University Press. pp. 45–134. 93. ^ Bakhchinyan, Artsvi (2017). "The Activity of Armenian Merchants in International Trade" (PDF): 24. Cite journal requires \|journal= 94. ^ "Exxon Mobil – Our history". Exxon Mobil Corp. Retrieved 2009-02-03. 95. ^ Morris, Charles R. The Tycoons: How Andrew Carnegie, John D. Rockefeller, Jay Gould, and J.P. Morgan invented the American supereconomy, H. Holt and Co., New York, 2005, pp. 255–258. ISBN 0-8050-7599-2. 96. ^ "United States Steel Corporation History". FundingUniverse. Retrieved 3 January 2014. 97. ^ Boselovic, Len (February 25, 2001). "Steel Standing: U.S. Steel celebrates 100 years". PG News – Business & Technology. post-gazette.com – PG Publishing. Retrieved 6 August 2013. 98. ^ "West's Encyclopedia of American Law". Answers.com. 2009-06-28. Retrieved 2011-10-11. 99. ^ Lasar, Matthew (May 13, 2011), How Robber Barons hijacked the "Victorian Internet": Ars revisits those wild and crazy days when Jay Gould ruled the telegraph and ..., Ars technica 100. ^ Kevin J. O'Brien, IHT.com, Regulators in Europe fight for independence, International Herald Tribune, November 9, 2008, Accessed November 14, 2008. 101. ^ IfM – Comcast/NBCUniversal, LLC. Mediadb.eu (2013-11-15). Retrieved on 2013-12-09. 102. ^ Dickens, Matthew (24 May 2013), TRANSIT RIDERSHIP REPORT: First Quarter 2013 (PDF), American Public Transportation Association, retrieved 3 January 2014 103. ^ Van Boven, M. W. "Towards A New Age of Partnership (TANAP): An Ambitious World Heritage Project (UNESCO Memory of the World – reg.form, 2002)". VOC Archives Appendix 2, p.14. 104. ^ EU competition policy and the consumer Archived 2009-03-10 at the Wayback Machine 105. ^ Leo Cendrowicz (2008-02-27). "Microsoft Gets Mother Of All EU Fines". Forbes. Retrieved 2008-03-10. 106. ^ "EU fines Microsoft record$1.3 billion". Time Warner. 2008-02-27. Archived from the original on 2008-03-03. Retrieved 2008-03-10. 107. ^ https://prospect.org/power/time-to-break-up-disney-monopoly/ 108. ^ https://www.ntdaily.com/disneys-massive-monopoly-is-troubling-for-the-entertainment-industry/ 109. ^ "In Praise of Private Infrastructure", Globe Asia, April 2008 110. ^ Thomas J. DiLorenzo (2011-05-03). "The Myth of Natural Monopoly – Thomas J. DiLorenzo – Mises Daily". Mises.org. Retrieved 2012-11-02. 111. ^ Baten, Bianchi, Moser (2017). "Compulsory licensing and innovation – Historical evidence from German patents after WWI". Journal of Development Economics. 126: 231–242. doi:10.1016/j.jdeveco.2017.01.002.CS1 maint: multiple names: authors list (link)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2576814293861389, "perplexity": 2243.0973452193734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151563.91/warc/CC-MAIN-20210725014052-20210725044052-00440.warc.gz"}
https://brilliant.org/discussions/thread/no-conjectures/	# No conjectures... This is an inequality problem I found in a book, but I wonder if it can be done in simple way. Try this: If $$a_1,a_2, \cdots ,a_n$$ are positive reals less than one and $$S_n = a_1 + \cdots + a_n$$, then show that ${1-S_n < (1-a_1)(1-a_2) \cdots (1-a_n) < \displaystyle \frac{1}{1+S_n}}$. Note by A Brilliant Member 7 years ago This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science. When posting on Brilliant: • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused . • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone. • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge. MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting. 2 \times 3 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ Sort by: Also, ai < 1 for all i = 1, 2...n 1 - (a1)^2 < 1 or, (1 - a1)(1+a1) < 1 or, (1- a1) < 1/(1+a1) Multiplying over all terms, (1 - a1)(1- a2)...(1 - an) < 1/(1+a1)(1+a2)...(1+an) But (1+a1)(1+a2)...(1+an) > 1 + Sn This immediately proves it. - 7 years ago Again not correct, $a_i^2 < 1$ doesn't imply $1- a_i^2 < 1$. You need to specify proofs more. Anyway for latex, you may use latex editor for Chrome. - 7 years ago Actually, Since $1 > a_i^2 > 0$, we have $1 > 1 - a_i^2 > 0$ Right, but he wrote "or", implying that the statement followed from $1- a_i^2 >0$. The proof was correct though. - 7 years ago The OR I wrote was just a continuation :P - 7 years ago Like "IMPLIES" - 7 years ago And I really don't get you. ai < 1 for all i. So, ai^2 < 1 for all i. This gives, 0 < 1 - ai^2 < 1. Now you just factor out (1- ai^2) into (1 - ai)(1+ai). - 7 years ago (1 - a1) (1 - a2) = 1 - a1 - a2 + a1a2 > 1 - (a1 + a2) So, for n such brackets, you can write (1- a1)(1- a2)...(1-an) > 1 - (a1+a2+a3...+an) = 1 - Sn - 7 years ago Not rigorous. :( Also there is no chance to justify your claim, in $(1-a_1)(1-a_2) \cdots (1-a_n)$, there are many more terms other than $(-1)^n a_1a_2a_3 \cdots a_n$. Not correct. - 7 years ago I think you just missed what I meant to say. I avoided writing entire proofs because I personally don't like answers without LATEX and here I am, without knowing LATEX. Anyway, I have already proved that (1-a1)(1-a2) > 1 - (a1+a2). Then, (1-a1)(1-a2)(1-a3) > (1-a3)(1-a1-a2)>1-(a1+a2+a3). Got it? - 7 years ago Now, this can, similarly be extended to n terms. - 7 years ago I know it would come, my friend, but I thought of getting a rigorous proof. Anyway no problem! :) - 7 years ago And guys, it would be really really helpful if you can tell me any site where I can write LATEX directly and when I paste it here in comments box, the entire writing with LATEX will come. - 7 years ago I use the latex editor Latexian, as it displays the equations as I am typing them. An online free site would be WriteLatex, which I have used in collaboration with others internationally. 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http://en.wikipedia.org/wiki/Near-field_scanning_optical_microscope	# Near-field scanning optical microscope Diagram illustrating near-field optics, with the diffraction of light coming from NSOM fiber probe, showing wavelength of light and the near-field.[1] Near-field scanning optical microscopy (NSOM/SNOM) is a microscopy technique for nanostructure investigation that breaks the far field resolution limit by exploiting the properties of evanescent waves. This is done by placing the detector very close (distance much smaller than wavelength λ) to the specimen surface. This allows for the surface inspection with high spatial, spectral and temporal resolving power. With this technique, the resolution of the image is limited by the size of the detector aperture and not by the wavelength of the illuminating light. In particular, lateral resolution of 20 nm and vertical resolution of 2–5 nm have been demonstrated.[2][3] As in optical microscopy, the contrast mechanism can be easily adapted to study different properties, such as refractive index, chemical structure and local stress. Dynamic properties can also be studied at a sub-wavelength scale using this technique. NSOM/SNOM is a form of scanning probe microscopy. ## History Edward Hutchinson Synge, a scientist, is given credit for conceiving and developing the idea for an imaging instrument that would image by exciting and collecting diffraction in the near field. His original idea, proposed in 1928, was based upon the usage of intense nearly planar light from an arc under pressure behind a thin, opaque metal film with a small orifice of about 100 nm. The orifice was to remain within 100 nm of the surface, and information was to be collected by point-by-point scanning. He foresaw the illumination and the detector movement being the biggest technical difficulties.[4][5] John A. O'Keefe also developed similar theories in 1956. He thought the moving of the pinhole or the detector when it is so close to the sample would be the most likely issue that could prevent the realization of such an instrument.[6][7] It was Ash and Nicholls who, in 1972, first broke the Abbe’s diffraction limit using radiation with wavelength of 3 cm. A line grating was resolved with a resolution of λ0/60.[8] A decade later, a patent on an optical near-field microscope was filed by Pohl,[9] followed in 1984 by the first paper that used visible radiation for near field scanning.[10] The near-field optical (NFO) microscope involved a subwavelength aperture at the apex of a metal coated sharply pointed transparent tip, and a feedback mechanism to maintain a constant distance of a few nanometers between the sample and the probe. Lewis et al. were also aware of the potential of an NFO microscope at this time.[11] They reported first results in 1986 confirming super-resolution.[12][13] In both experiments, details below 50 nm (about λ0/10) in size could be recognized. ## Theory According to Abbe’s theory of image formation, developed in 1873, the resolving capability of an optical component is ultimately limited by the spreading out of each image point due to diffraction. Unless the aperture of the optical component is large enough to collect all the diffracted light, the finer aspects of the image will not correspond exactly to the object. The minimum resolution (d) for the optical component are thus limited by its aperture size, and expressed by the Rayleigh criterion: $d = 0.61 \frac{\lambda_0}{N\!A} \;\!$ Here, λ0 is the wavelength in vacuum; NA is the numerical aperture for the optical component (maximum 1.3–1.4 for modern objectives with a very high magnification factor). Thus, the resolution limit is usually around λ0/2 for conventional optical microscopy.[14] This treatment only assumes the light diffracted into the far-field that propagates without any restrictions. NSOM makes use of evanescent or non propagating fields that exist only near the surface of the object. These fields carry the high frequency spatial information about the object and have intensities that drop off exponentially with distance from the object. Because of this, the detector must be placed very close to the sample in the near field zone, typically a few nanometers. As a result, near field microscopy remains primarily a surface inspection technique. The detector is then rastered across the sample using a piezoelectric stage. The scanning can either be done at a constant height or with regulated height by using a feedback mechanism.[15] ## Modes of operation ### Aperture and apertureless operation Sketch of a) typical metal-coated tip, and b) sharp uncoated tip.[16] There exist NSOM which can be operated in so-called aperture mode and NSOM for operation in a non-aperture mode. As illustrated, the tips used in the apertureless mode are very sharp and do not have a metal coating. Though there are many issues associated with the apertured tips (heating, artifacts, contrast, sensitivity, topology and interference amongst others), aperture mode remains more popular. This is primarily because apertureless mode is even more complex to set up and operate, and is not understood as well. There are five primary modes of apertured NSOM operation and four primary modes of apertureless NSOM operation. The major ones are illustrated in the next figure. Apertured modes of operation: a) illumination, b) collection, c) illumination collection, d) reflection and e) reflection collection.[17] Apertureless modes of operation: a) photon tunneling (PSTM) by a sharp transparent tip, b) PSTM by sharp opaque tip on smooth surface, and c) scanning interferometric apertureless microscopy with double modulation.[16] Other types of NSOM operation utilize “active tip" schemes, where the tip is functionalized with active light sources such as a fluorescent dye [18] or even a light emitting diode that enables fluorescence excitation.[19] ### Feedback mechanisms Feedback mechanisms are usually used to achieve high resolution and artifact free images since the detector must be positioned within a few nanometers of the surfaces. Some of these mechanisms are: • Constant force feedback: This mode is very similar to the feedback mechanism used in atomic force microscopy (AFM). Experiments can be performed in contact, intermittent contact, and non-contact modes. • Shear force feedback: In this mode, a tuning fork is mounted alongside the tip and made to oscillate at its resonance frequency. The amplitude is closely related to the tip-surface distance, and thus used as a feedback mechanism.[15] ### Contrast It is possible to take advantage of the various contrast techniques available to optical microscopy through NSOM but with much higher resolution. By using the change in the polarization of light or the intensity of the light as a function of the incident wavelength, it is possible to make use of contrast enhancing techniques such as staining, fluorescence, phase contrast and differential interference contrast. It is also possible to provide contrast using the change in refractive index, reflectivity, local stress and magnetic properties amongst others.[15][16] ## Instrumentation and standard setup Block diagram of an apertureless reflection-back-to-the-fiber NSOM setup with shear-force distance control and cross-polarization; 1: beam splitter and crossed polarizers; 2: shear-force arrangement; 3: sample mount on a piezo stage.[17] The primary components of an NSOM setup are the light source, feedback mechanism, the scanning tip, the detector and the piezoelectric sample stage. The light source is usually a laser focused into an optical fiber through a polarizer, a beam splitter and a coupler. The polarizer and the beam splitter would serve to remove stray light from the returning reflected light. The scanning tip, depending upon the operation mode, is usually a pulled or stretched optical fiber coated with metal except at the tip or just a standard AFM cantilever with a hole in the center of the pyramidal tip. Standard optical detectors, such as avalanche photodiode, photomultiplier tube (PMT) or CCD, can be used. Highly specialized NSOM techniques, Raman NSOM for example, have much more stringent detector requirements.[16] ## Near-field spectroscopy As the name implies, information is collected by spectroscopic means instead of imaging in the near field regime. Through Near Field Spectroscopy (NFS), one can probe spectroscopically with subwavelength resolution. Raman SNOM and fluorescence SNOM are two of the most popular NFS techniques as they allow for the identification of nanosized features with chemical contrast. Some of the common near field spectroscopic techniques are: • Direct local Raman NSOM: Aperture Raman NSOM is limited by very hot and blunt tips, and by long collection times. However, apertureless NSOM can be used to achieve high Raman scattering efficiency factors (around 40). Topological artifacts make it hard to implement this technique for rough surfaces. • Surface enhanced Raman spectroscopy (SERS) NSOM: This technique can be used in an apertureless shear-force NSOM setup, or by using an AFM tip coated with gold. The Raman signal is found to be significantly enhanced under the AFM tip. This technique has been used to give local variations in the Raman spectra under a single-walled nanotube. A highly sensitive optoacoustic spectrometer must be used for the detection of the Raman signal. • Fluorescence NSOM: This highly popular and sensitive technique makes use of the fluorescence for near field imaging, and is especially suited for biological applications. The technique of choice here is the apertureless back to the fiber emission in constant shear force mode. This technique uses merocyanine based dyes embedded in an appropriate resin. Edge filters are used for removal of all primary laser light. Resolution as low as 10 nm can be achieved using this technique. • Near field infrared spectrometry and near field dielectric microscopy[16] ## Artifacts NSOM is particularly vulnerable to artifacts that are not from the intended contrast mode. The most common root for artifacts in NSOM are: • Tip breakage during scanning • Striped contrast • Displaced optical contrast • Local far field light concentration • Topological artifacts ## Limitations • Very low working distance and extremely shallow depth of field. • Limited to study surfaces. • Not conducive for studying soft materials, especially under shear force mode. • Long scan times for large sample areas for high resolution imaging. ## References 1. ^ J. B. Herzog (2011). Optical Spectroscopy of Colloidal CdSe Semiconductor Nanostructures (Ph.D.). University of Notre Dame. 2. ^ U. Dürig et al. (1986). "Near-field optical scanning microscopy". J. Appl. Phys. 59: 3318. 3. ^ Y. Oshikane et al. (2007). "Observation of nanostructure by scanning near-field optical microscope with small sphere probe" (free pdf). Sci. Technol. Adv. Mater. 8 (3): 181. doi:10.1016/j.stam.2007.02.013. 4. ^ E.H. Synge (1928). "A suggested method for extending the microscopic resolution into the ultramicroscopic region". Phil. Mag. 6: 356. 5. ^ E.H. Synge (1932). "An application of piezoelectricity to microscopy". Phil. Mag. 13: 297. 6. ^ J.A. O'Keefe (1956). J. Opt. Soc. Am. 46: 359. 7. ^ "Brief History and Simple Description of NSOM/SNOM Technology". Nanonics Inc. 12 Oct 2007. 8. ^ E.A. Ash and G. Nicholls (1972). "Super-resolution Aperture Scanning Microscope". Nature 237 (5357): 510. doi:10.1038/237510a0. PMID 12635200. 9. ^ EP patent 0112401, Pohl, Dieter Wolfgang, Dr., "optical near field scanning microscope", published 1987-04-22, issued 1982-12-27 10. ^ D.W. Pohl, W. Denk, and M. Lanz (1984). "Optical stethoscopy: Image recording with resolution λ/20". Appl. Phys. Lett. 44 (7): 651. doi:10.1063/1.94865. 11. ^ A. Lewis, M. Isaacson, A. Harootunian, and A. Murray (1984). "Development of a 500 Å spatial resolution light microscope. I. Light is efficiently transmitted through λ/16 diameter apertures". Ultramicroscopy 13 (3): 227. doi:10.1016/0304-3991(84)90201-8. 12. ^ E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer (1986). "Near Field Scanning Optical Microscopy (NSOM)". Biophys. J. 49: 269. 13. ^ A. Harootunian, E. Betzig, M. Isaacson, and A. Lewis (1986). "Super-resolution fluorescence near-field scanning optical microscopy". Appl. Phys. Lett. 49: 674. 14. ^ E. Hecht (2002). Optics. San Francisco: Addison Wesley. ISBN 0-19-510818-3. 15. ^ a b c Near-Field Scanning Optical Microscopy. Olympus America Inc. 12 Oct 2007. 16. G. Kaupp (2006). Atomic Force Microscopy, Scanning Nearfield Optical Microscopy and Nanoscratching: Application to Rough and Natural Surfaces. Heidelberg: Springer. ISBN 3-540-28405-2. 17. ^ a b Introduction to NSOM. The Optics Laboratory, North Carolina State University. 12 Oct 2007 18. ^ Michaelis, J; C.Hettich,J.Mlynek and V.Sandoghdar (2000). Nature 405 (325). 19. ^ K.Hoshino; A. Gopal, M. Glaz, D.Vanden Bout, X.J. Zhang (2012). "Nanoscale fluorescence imaging with quantum dot near-field electroluminescence". Applied Physics Letters 101 (4). doi:10.1063/1.4739235.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.610272228717804, "perplexity": 3865.8550645924056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010642209/warc/CC-MAIN-20140305091042-00060-ip-10-183-142-35.ec2.internal.warc.gz"}
http://mathhelpforum.com/algebra/156829-translating-english-phrases-into-algebraic-expressions-print.html	# translating English phrases into algebraic expressions • Sep 20th 2010, 02:15 PM fc1123 translating English phrases into algebraic expressions okay I have another problem a number, half of that number, and one-third of that number are added. The result is 22. So far I have x+1/2x+1/3x=22. • Sep 20th 2010, 02:19 PM yeKciM Quote: Originally Posted by fc1123 okay I have another problem a number, half of that number, and one-third of that number are added. The result is 22. So far I have x+1/2x+1/3x=22. write it like this ..... x+ x/2 + x/3 = 22 or $x+\frac {x}{2} +\frac {x}{3} = 22$ that way someone can think you wrote ... x+ 1/(2x) + 1 /(3x) .... it's the same as the another one that you post ... just this one multiply with 6 $6x +.....$ • Sep 20th 2010, 02:25 PM fc1123 thank you so much for help. I am enjoying this forum because it is helping me a lot to understand the problems.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9392825961112976, "perplexity": 1843.0785137455784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121216.64/warc/CC-MAIN-20170423031201-00112-ip-10-145-167-34.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculators/192546-conversion-question.html	# Math Help - conversion question 1. ## conversion question Hello. i need to know if 0.75 = 3/4 inch? if not what is it.Please thank you:suzzie 2. ## Re: conversion question As numbers, 0.75 = 3/4. So, 0.75 inch = 3/4 inch. However, 0.75 feet ≠ 3/4 inch.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9964672923088074, "perplexity": 9763.572705904824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010824518/warc/CC-MAIN-20140305091344-00089-ip-10-183-142-35.ec2.internal.warc.gz"}
http://en.wikipedia.org/wiki/Chebotaryov_density_theorem	# Chebotarev's density theorem (Redirected from Chebotaryov density theorem) Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p less than a large integer N, tends to a certain limit as N goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in (Tschebotareff 1926). A special case that is easier to state says that if K is an algebraic number field which is a Galois extension of Q of degree n, then the prime numbers that completely split in K have density 1/n among all primes. More generally, splitting behavior can be specified by assigning to (almost) every prime number an invariant, its Frobenius element, which strictly is a representative of a well-defined conjugacy class in the Galois group Gal(K/Q). Then the theorem says that the asymptotic distribution of these invariants is uniform over the group, so that a conjugacy class with k elements occurs with frequency asymptotic to k/n. ## History and motivation When Carl Friedrich Gauss first introduced the notion of complex integers Z[i], he observed that the ordinary prime numbers may factor further in this new set of integers. In fact, if a prime p is congruent to 1 mod 4, then it factors into a product of two distinct prime gaussian integers, or "splits completely"; if p is congruent to 3 mod 4, then it remains prime, or is "inert"; and if p is 2 then it becomes a product of the square of the prime (1+i) and the invertible gaussian integer -i; we say that 2 "ramifies". For instance, $5 = (1 + 2i)(1-2i)$ splits completely; $3$ is inert; $2 = -i(1+i)^2$ ramifies. From this description, it appears that as one considers larger and larger primes, the frequency of a prime splitting completely approaches 1/2, and likewise for the primes that remain primes in Z[i]. Dirichlet's theorem on arithmetic progressions demonstrates that this is indeed the case. Even though the prime numbers themselves appear rather erratically, splitting of the primes in the extension $\Bbb{Z}\subset \Bbb{Z}[i]$ follows a simple statistical law. Similar statistical laws also hold for splitting of primes in the cyclotomic extensions, obtained from the field of rational numbers by adjoining a primitive root of unity of a given order. For example, the ordinary integer primes group into four classes, each with probability 1/4, according to their pattern of splitting in the ring of integers corresponding to the 8th roots of unity. In this case, the field extension has degree 4 and is abelian, with the Galois group isomorphic to the Klein four-group. It turned out that the Galois group of the extension plays a key role in the pattern of splitting of primes. Georg Frobenius established the framework for investigating this pattern and proved a special case of the theorem. The general statement was proved by Nikolai Grigoryevich Chebotaryov in 1922. ## Relation with Dirichlet's theorem The Chebotarev density theorem may be viewed as a generalisation of Dirichlet's theorem on arithmetic progressions. A quantitative form of Dirichlet's theorem states that if N2 is an integer and a is coprime to N, then the proportion of the primes p congruent to a mod N is asymptotic to 1/n, where n=φ(N) is the Euler totient function. This is a special case of the Chebotarev density theorem for the Nth cyclotomic field K. Indeed, the Galois group of K/Q is abelian and can be canonically identified with the group of invertible residue classes mod N. The splitting invariant of a prime p not dividing N is simply its residue class because the number of distinct primes into which p splits is φ(N)/m, where m is multiplicative order of p modulo N; hence by the Chebotarev density theorem, primes are asymptotically uniformly distributed among different residue classes coprime to N. ## Formulation Lenstra & Stevenhagen (1996) give an earlier result of Frobenius in this area. Suppose K is a Galois extension of the rational number field Q, and P(t) a monic integer polynomial such that K is a splitting field of P. It makes sense to factorise P modulo a prime number p. Its 'splitting type' is the list of degrees of irreducible factors of P mod p, i.e. P factorizes in some fashion over the prime field Fp. If n is the degree of P, then the splitting type is a partition Π of n. Considering also the Galois group G of K over Q, each g in G is a permutation of the roots of P in K; in other words by choosing an ordering of α and its algebraic conjugates, G is faithfully represented as a subgroup of the symmetric group Sn. We can write g by means of its cycle representation, which gives a 'cycle type' c(g), again a partition of n. The theorem of Frobenius states that for any given choice of Π the primes p for which the splitting type of P mod p is Π has a natural density δ, with δ equal to the proportion of g in G that have cycle type Π. The statement of the more general Chebotarev theorem is in terms of the Frobenius element of a prime (ideal), which is in fact an associated conjugacy class C of elements of the Galois group G. If we fix C then the theorem says that asymptotically a proportion \|C\|/\|G\| of primes have associated Frobenius element as C. When G is abelian the classes of course each have size 1. For the case of a non-abelian group of order 6 they have size 1, 2 and 3, and there are correspondingly (for example) 50% of primes p that have an order 2 element as their Frobenius. So these primes have residue degree 2, so they split into exactly three prime ideals in a degree 6 extension of Q with it as Galois group.[1] ## Statement Let L be a finite Galois extension of a number field K with Galois group G. Let X be a subset of G that is stable under conjugation. The set of primes v of K that are unramified in L and whose associated Frobenius conjugacy class Fv is contained in X has density $\frac{\#X}{\#G}.$[2] ### Infinite extensions The statement of the Chebotarev density theorem can be generalized to the case of an infinite Galois extension L / K that is unramified outside a finite set S of primes of K (i.e. if there is a finite set S of primes of K such that any prime of K not in S is unramified in the extension L / K). In this case, the Galois group G of L / K is a profinite group equipped with the Krull topology. Since G is compact in this topology, there is a unique Haar measure μ on G. For every prime v of K not in S there is an associated Frobenius conjugacy class Fv. The Chebotarev density theorem in this situation can be stated as follows:[2] Let X be a subset of G that is stable under conjugation and whose boundary has Haar measure zero. Then, the set of primes v of K not in S such that Fv ⊆ X has density $\frac{\mu(X)}{\mu(G)}.$ This reduces to the finite case when L / K is finite (the Haar measure is then just the counting measure). A consequence of this version of the theorem is that the Frobenius elements of the unramified primes of L are dense in G. ## Important consequences The Chebotarev density theorem reduces the problem of classifying Galois extensions of a number field to that of describing the splitting of primes in extensions. Specifically, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it.[3] A related corollary is that if almost all prime ideals of K split completely in L, then in fact L = K.[4] ## Notes 1. ^ This particular example already follows from the Frobenius result, because G is a symmetric group. In general, conjugacy in G is more demanding than having the same cycle type. 2. ^ a b Section I.2.2 of Serre 3. ^ Corollary VII.13.10 of Neukirch 4. ^ Corollary VII.13.7 of Neukirch	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9695205092430115, "perplexity": 208.89931649350828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163800358/warc/CC-MAIN-20131204133000-00005-ip-10-33-133-15.ec2.internal.warc.gz"}
http://export.arxiv.org/list/physics.gen-ph/pastweek?skip=0&show=25	# General Physics ## Authors and titles for recent submissions [ total of 25 entries: 1-25 ] [ showing 25 entries per page: fewer \| more ] ### Fri, 22 Sep 2017 [1] Title: Noncommutative geometric momentum and angle anholonomy Authors: Q. H. Liu Subjects: General Physics (physics.gen-ph) [2] Title: Planet formation and the evolution of the Solar System Authors: Michael Woolfson Subjects: General Physics (physics.gen-ph) [3] Title: A scheme for determining fundamental interactions and the universality principle Authors: Zhongmin Qian Subjects: General Physics (physics.gen-ph); High Energy Physics - Theory (hep-th) [4] Title: Baryogenesis in $f(R)$-Theories of Gravity in Anisotropic Universe Comments: 10 pages. arXiv admin note: text overlap with arXiv:astro-ph/0610367, arXiv:0709.0697 by other authors Subjects: General Physics (physics.gen-ph) ### Thu, 21 Sep 2017 [5] Title: Existence of stable wormholes on a noncommutative-geometric background in modified gravity Subjects: General Physics (physics.gen-ph) [6] Title: Attractive Heaviside-Maxwellian (Vector) Gravity from Quantum Field Theory Subjects: General Physics (physics.gen-ph) [7] Title: On relativistic harmonic oscillator Authors: A. I. Arbab Comments: 9 LaTeX pages, no figures Subjects: General Physics (physics.gen-ph); Quantum Physics (quant-ph) [8] Title: Can Lorentz transformations be determined by the null Michelson-Morley result? Journal-ref: Revista Brasileira de Ensino de Fisica, vol. 39, no. 3, e3304 (2017) Subjects: General Physics (physics.gen-ph) ### Fri, 15 Sep 2017 [9] Title: Knot Physics on Entangled Vortex-Membranes: Classification, Dynamics and Effective Theory Authors: Su-Peng Kou Comments: 85 pages, 15 figures. arXiv admin note: text overlap with arXiv:1604.07217 Subjects: General Physics (physics.gen-ph) [10] Title: The hydrogen atom according to wave mechanics in cartesian coordinates Authors: J. F. Ogilvie Comments: 12 pages, 6 figures, 1 table Subjects: General Physics (physics.gen-ph) ### Thu, 14 Sep 2017 [11] Title: Comments on Gravitoelectromagnetism of Ummarino and Gallerati in "Superconductor in a weak static gravitational field" vs Other Versions Authors: Harihar Behera Subjects: General Physics (physics.gen-ph) [12] Title: A Non-standard Standard Model Authors: J. LaChapelle Comments: This is an extended version of arXiv:hep-ph/0408266 and arXiv:hep-ph/0408305 Subjects: General Physics (physics.gen-ph) [13] Title: Quantum, noncommutative and MOND corrections to the entropic law of gravitation Subjects: General Physics (physics.gen-ph); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) [14] Title: The hydrogen atom according to relativistic wave mechanics -- amplitude functions and circulating electronic currents Authors: J. F. Ogilvie Comments: 16 pages, 10 figures, 1 table Subjects: General Physics (physics.gen-ph) [15] Title: An experimental route for testing Lorentz violation in ultracold gases Authors: Cláudio Nassif Comments: 6 pages, 3 figures, submitted to Physics Letters B (PLB) Subjects: General Physics (physics.gen-ph) [16] Title: Incommensurability of stripes in La_{2-x}Sr_xNiO_{4+y} Authors: Manfred Bucher Comments: 8 pages, 1 figure, 1 table Subjects: General Physics (physics.gen-ph) [17] Title: Unobservable Potentials to Explain Single Photon and Electron Interference Journal-ref: Journal of Computational and Theoretical Nanoscience, Volume 14, Number 8, August 2017, pp. 4121-4132(12) Subjects: General Physics (physics.gen-ph) ### Wed, 13 Sep 2017 [18] Title: Charged compact star model in Einstein-Maxwell-Gauss-Bonnet gravity Subjects: General Physics (physics.gen-ph) [19] Title: Sobolev Spaces, Schwartz Spaces, and a definition of the Electromagnetic and Gravitational coupling Authors: J.-P. Montillet Comments: The paper is accepted for publication in J. of Modern Physics . 06 Sep. 2017 Journal-ref: Journal of Modern Physics, 8, 1700-1722 Subjects: General Physics (physics.gen-ph) [20] Title: Time, E8, and the Standard Model Authors: David J. Jackson Subjects: General Physics (physics.gen-ph) [21] Title: Two Approaches to Measurability Concept and Quantum Theory Journal-ref: Advanced Studies in Theoretical Physics Vol. 11, 2017, no. 10, 441 - 476 Subjects: General Physics (physics.gen-ph) [22] Title: The isolated electron: De Broglie's "hidden" thermodynamics, SU(2) Quantum Yang-Mills theory, and a strongly perturbed BPS monopole Authors: Ralf Hofmann Subjects: General Physics (physics.gen-ph) [23] Title: A note on nonlinear electrodynamics	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7929314970970154, "perplexity": 18078.562494761132}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688926.38/warc/CC-MAIN-20170922074554-20170922094554-00264.warc.gz"}
http://www.ck12.org/book/CK-12-Algebra-I---Second-Edition/r1/section/3.2/	<meta http-equiv="refresh" content="1; url=/nojavascript/"> Two-Step Equations \| CK-12 Foundation You are reading an older version of this FlexBook® textbook: CK-12 Algebra I - Second Edition Go to the latest version. # 3.2: Two-Step Equations Created by: CK-12 ## Learning Objectives • Solve a two-step equation using addition, subtraction, multiplication, and division. • Solve a two-step equation by combining like terms. • Solve real-world problems using two-step equations. ## Solve a Two-Step Equation We’ve seen how to solve for an unknown by isolating it on one side of an equation and then evaluating the other side. Now we’ll see how to solve equations where the variable takes more than one step to isolate. Example 1 Rebecca has three bags containing the same number of marbles, plus two marbles left over. She places them on one side of a balance. Chris, who has more marbles than Rebecca, adds marbles to the other side of the balance. He finds that with 29 marbles, the scales balance. How many marbles are in each bag? Assume the bags weigh nothing. Solution We know that the system balances, so the weights on each side must be equal. If we use $x$ to represent the number of marbles in each bag, then we can see that on the left side of the scale we have three bags (each containing $x$ marbles) plus two extra marbles, and on the right side of the scale we have 29 marbles. The balancing of the scales is similar to the balancing of the following equation. $3x + 2 = 29$ “Three bags plus two marbles equals 29 marbles” To solve for $x$, we need to first get all the variables (terms containing an $x$) alone on one side of the equation. We’ve already got all the $x$’s on one side; now we just need to isolate them. $3x + 2 &= 29\\3x + 2 - 2 &= 29 - 2 \qquad \text{Get rid of the 2 on the left by subtracting it from both sides.}\\3x &= 27\\\frac{3x}{3} &= \frac{27}{3} \qquad \quad \ \text{Divide both sides by 3.}\\x &= 9$ There are nine marbles in each bag. We can do the same with the real objects as we did with the equation. Just as we subtracted 2 from both sides of the equals sign, we could remove two marbles from each side of the scale. Because we removed the same number of marbles from each side, we know the scales will still balance. Then, because there are three bags of marbles on the left-hand side of the scale, we can divide the marbles on the right-hand side into three equal piles. You can see that there are nine marbles in each. Three bags of marbles balances three piles of nine marbles. So each bag of marbles balances nine marbles, meaning that each bag contains nine marbles. Check out http://www.mste.uiuc.edu/pavel/java/balance/ for more interactive balance beam activities! Example 2 Solve $6(x + 4) = 12$. This equation has the $x$ buried in parentheses. To dig it out, we can proceed in one of two ways: we can either distribute the six on the left, or divide both sides by six to remove it from the left. Since the right-hand side of the equation is a multiple of six, it makes sense to divide. That gives us $x + 4 = 2$. Then we can subtract 4 from both sides to get $x = -2$. Example 3 Solve $\frac{x - 3}{5} = 7$. It’s always a good idea to get rid of fractions first. Multiplying both sides by 5 gives us $x - 3 = 35$, and then we can add 3 to both sides to get $x = 38$. Example 4 Solve $\frac{5}{9}(x + 1) =\frac{2}{7}$. First, we’ll cancel the fraction on the left by multiplying by the reciprocal (the multiplicative inverse). $\frac{9}{5} \cdot \frac{5}{9}(x + 1) &= \frac{9}{5} \cdot \frac{2}{7}\\(x + 1) &= \frac{18}{35}$ Then we subtract 1 from both sides. ($\frac{35}{35}$ is equivalent to 1.) $x + 1 &= \frac{18}{35}\\x + 1 - 1 &= \frac{18}{35} - \frac{35}{35}\\x &= \frac{18 - 35}{35} \\x &= \frac{-17}{35}$ These examples are called two-step equations, because we need to perform two separate operations on the equation to isolate the variable. ## Solve a Two-Step Equation by Combining Like Terms When we look at a linear equation we see two kinds of terms: those that contain the unknown variable, and those that don’t. When we look at an equation that has an $x$ on both sides, we know that in order to solve it, we need to get all the $x-$terms on one side of the equation. This is called combining like terms. The terms with an $x$ in them are like terms because they contain the same variable (or, as you will see in later chapters, the same combination of variables). Like Terms Unlike Terms $4x, 10x, -3.5x,$ and $\frac{x}{12}$ $3x$ and $3y$ $3y, 0.000001y,$ and $y$ $4xy$ and $4x$ $xy, 6xy,$ and $2.39xy$ $0.5x$ and $0.5$ To add or subtract like terms, we can use the Distributive Property of Multiplication. $3x + 4x &= (3 + 4)x = 7x \\0.03xy - 0.01xy &= (0.03 - 0.01)xy = 0.02xy\\-y + 16y + 5y &= (-1 + 16 + 5)y = 10y\\5z + 2z - 7z &= (5 + 2 - 7)z = 0z = 0$ To solve an equation with two or more like terms, we need to combine the terms first. Example 5 Solve $(x + 5) - (2x - 3)=6$. There are two like terms: the $x$ and the $-2x$ (don’t forget that the negative sign applies to everything in the parentheses). So we need to get those terms together. The associative and distributive properties let us rewrite the equation as $x + 5 - 2x + 3 = 6$, and then the commutative property lets us switch around the terms to get $x - 2x + 5 + 3 = 6$, or $(x - 2x) + (5 + 3) = 6$. $(x - 2x)$ is the same as $(1 - 2)x$, or $-x$, so our equation becomes $-x + 8 = 6$ Subtracting 8 from both sides gives us $-x = -2$. And finally, multiplying both sides by -1 gives us $x = 2$. Example 6 Solve $\frac{x}{2} - \frac{x}{3} = 6$. This problem requires us to deal with fractions. We need to write all the terms on the left over a common denominator of six. $\frac{3x}{6} - \frac{2x}{6} = 6$ Then we subtract the fractions to get $\frac{x}{6} = 6$. Finally we multiply both sides by 6 to get $x = 36$. ## Solve Real-World Problems Using Two-Step Equations The hardest part of solving word problems is translating from words to an equation. First, you need to look to see what the equation is asking. What is the unknown for which you have to solve? That will be what your variable stands for. Then, follow what is going on with your variable all the way through the problem. Example 7 An emergency plumber charges $65 as a call-out fee plus an additional$75 per hour. He arrives at a house at 9:30 and works to repair a water tank. If the total repair bill is $196.25, at what time was the repair completed? In order to solve this problem, we collect the information from the text and convert it to an equation. Unknown: time taken in hours – this will be our $x$ The bill is made up of two parts: a call out fee and a per-hour fee. The call out is a flat fee, and independent of $x$—it’s the same no matter how many hours the plumber works. The per-hour part depends on the number of hours $(x)$. So the total fee is$65 (no matter what) plus $\75x$ (where $x$ is the number of hours), or $65 + 75x$. Looking at the problem again, we also can see that the total bill is $196.25. So our final equation is $196.25 = 65 + 75x$. Solving for $x$: $196.25 &= 65 + 75x \qquad \text{Subtract 65 from both sides.}\\131.25 &= 75x \qquad \qquad \text{Divide both sides by 75.}\\1.75 &= x \qquad \qquad \quad \text{The job took 1.75 hours.}$ Solution The repair job was completed 1.75 hours after 9:30, so it was completed at 11:15AM. Example 8 When Asia was young her Daddy marked her height on the door frame every month. Asia’s Daddy noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches and multiplying the result by one-third. Use this information to answer the following: a) Write an equation linking her predicted height, $h$, with her age in months, $m$. b) Determine her predicted height on her second birthday. c) Determine at what age she is predicted to reach three feet tall. Solution a) To convert the text to an equation, first determine the type of equation we have. We are going to have an equation that links two variables. Our unknown will change, depending on the information we are given. For example, we could solve for height given age, or solve for age given height. However, the text gives us a way to determine height. Our equation will start with “$h=$”. The text tells us that we can predict her height by taking her age in months, adding 75, and multiplying by $\frac{1}{3}$. So our equation is $h = (m + 75) \cdot \frac{1}{3}$, or $h = \frac{1}{3}(m + 75)$. b) To predict Asia’s height on her second birthday, we substitute $m=24$ into our equation (because 2 years is 24 months) and solve for $h$. $h &= \frac{1}{3}(24 + 75)\\h &= \frac{1}{3}(99)\\h &= 33$ Asia’s height on her second birthday was predicted to be 33 inches. c) To determine the predicted age when she reached three feet, substitute $h = 36$ into the equation and solve for $m$. $36 &= \frac{1}{3}(m + 75)\\108 &= m + 75\\33 &= m$ Asia was predicted to be 33 months old when her height was three feet. Example 9 To convert temperatures in Fahrenheit to temperatures in Celsius, follow the following steps: Take the temperature in degrees Fahrenheit and subtract 32. Then divide the result by 1.8 and this gives the temperature in degrees Celsius. a) Write an equation that shows the conversion process. b) Convert 50 degrees Fahrenheit to degrees Celsius. c) Convert 25 degrees Celsius to degrees Fahrenheit. d) Convert -40 degrees Celsius to degrees Fahrenheit. a) The text gives the process to convert Fahrenheit to Celsius. We can write an equation using two variables. We will use $f$ for temperature in Fahrenheit, and $c$ for temperature in Celsius. $&\text{First we take the temperature in Fahrenheit and subtract 32.} && f - 32\\&\text{Then divide by 1.8.} && \frac{f - 32}{1.8}\\&\text{This equals the temperature in Celsius.} && c = \frac{f - 32}{1.8}$ In order to convert from one temperature scale to another, simply substitute in for whichever temperature you know, and solve for the one you don’t know. b) To convert 50 degrees Fahrenheit to degrees Celsius, substitute $f = 50$ into the equation. $c &= \frac{50 - 32}{1.8}\\c &= \frac{18}{1.8}\\c &= 10$ 50 degrees Fahrenheit is equal to 10 degrees Celsius. c) To convert 25 degrees Celsius to degrees Fahrenheit, substitute $c = 25$ into the equation: $25 &= \frac{f - 32}{1.8}\\45 &= f - 32\\ 77 &= f$ 25 degrees Celsius is equal to 77 degrees Fahrenheit. d) To convert -40 degrees Celsius to degrees Fahrenheit, substitute $c = -40$ into the equation. $-40 &= \frac{f - 32}{1.8}\\-72 &= f - 32\\-40 &= f$ -40 degrees Celsius is equal to -40 degrees Fahrenheit. (No, that’s not a mistake! This is the one temperature where they are equal.) ## Lesson Summary • Some equations require more than one operation to solve. Generally it, is good to go from the outside in. If there are parentheses around an expression with a variable in it, cancel what is outside the parentheses first. • Terms with the same variable in them (or no variable in them) are like terms. Combine like terms (adding or subtracting them from each other) to simplify the expression and solve for the unknown. ## Review Questions 1. Solve the following equations for the unknown variable. 1. $1.3x - 0.7x = 12$ 2. $6x - 1.3 = 3.2$ 3. $5x - (3x + 2) = 1$ 4. $4(x + 3) = 1$ 5. $5q - 7 = \frac{2}{3}$ 6. $\frac{3}{5}x + \frac{5}{2} = \frac{2}{3}$ 7. $s - \frac{3s}{8} = \frac{5}{6}$ 8. $0.1y + 11 = 0$ 9. $\frac{5q - 7}{12} = \frac{2}{3}$ 10. $\frac{5(q - 7)}{12} = \frac{2}{3}$ 11. $33t - 99= 0$ 12. $5p - 2 = 32$ 13. $10y + 5 = 10$ 14. $10(y + 5) = 10$ 15. $10y + 5y = 10$ 16. $10(y + 5y) = 10$ 2. Jade is stranded downtown with only$10 to get home. Taxis cost $0.75 per mile, but there is an additional$2.35 hire charge. Write a formula and use it to calculate how many miles she can travel with her money. 3. Jasmin’s Dad is planning a surprise birthday party for her. He will hire a bouncy castle, and will provide party food for all the guests. The bouncy castle costs $150 for the afternoon, and the food will cost$3 per person. Andrew, Jasmin’s Dad, has a budget of $300. Write an equation and use it to determine the maximum number of guests he can invite. 4. The local amusement park sells summer memberships for$50 each. Normal admission to the park costs $25; admission for members costs$15. 1. If Darren wants to spend no more than $100 on trips to the amusement park this summer, how many visits can he make if he buys a membership with part of that money? 2. How many visits can he make if he does not? 3. If he increases his budget to$160, how many visits can he make as a member? 4. And how many as a non-member? 5. For an upcoming school field trip, there must be one adult supervisor for every five children. 1. If the bus seats 40 people, how many children can go on the trip? 2. How many children can go if a second 40-person bus is added? 3. Four of the adult chaperones decide to arrive separately by car. Now how many children can go in the two buses? Feb 22, 2012 Sep 28, 2014	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 96, "texerror": 0, "math_score": 0.9442368745803833, "perplexity": 683.7165734245816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122233086.24/warc/CC-MAIN-20150124175713-00076-ip-10-180-212-252.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/49741/capacitor-charging-and-discharging	# Capacitor charging and discharging I have a conceptual question. The circuit is shown below. Let us assume that the capacitor shown in the figure is of 2.2 micro-farads having rated level of 5 volts and we decide to charge it up to 2 volts so that we don't smoke it. Circuit - If we connect $R_1$ and $R_2$ in the circuit for charging and discharging respectively, how will the circuit work? The red loop shows the charging circuit and the green loop shows the discharging circuit. The circuit is as shown until the capacitor is charged and then the switch S is closed. Will the circuit discharge instantaneously? If yes, when will the capacitor be re-charged again? Will be it charged after the long exponential charge decay of the capacitor or will it start to charge itself after it has a certain amount of charge left? Will this process of charging and discharging be continuous if the switch S remains in closed position? Let me start with some basics. The red loop circuit will charge with $R_1\times C$ time constant. So the charging will be quick because of low $R_1$. It will be 22 microseconds. After the capacitor has been charged to 2V (max given by power supply), we close switch S and then the discharge process will start. As expected it will also be quick and similar to charging time constant. Will this capacitor charge again? If yes, when? And can it be controlled? - I think this should be migrated to electronics.stackexchange.com – daaxix Jan 10 '13 at 5:26 For starters (in case you overlooked it), note that the capacitor will not discharge completely: The stationary state for the closed circuit has a continuous current flowing through the corrent branches with the resistors, so the point A will have a finite, non zero $V_A$ and the capacitor will experience a finite voltage. The higher the value of $R_1$ is compared to the value of $R_2$, the more the capacitor will discharge.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8959707617759705, "perplexity": 319.8026401447417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507442497.30/warc/CC-MAIN-20141017005722-00337-ip-10-16-133-185.ec2.internal.warc.gz"}
https://infoscience.epfl.ch/record/170859	Formats Format BibTeX MARC MARCXML DublinCore EndNote NLM RefWorks RIS ### Abstract Modulation doped AlGaAs/GaAs core-shell nanowire structures were grown by molecular beam epitaxy. A Si delta-doping was introduced in the AlGaAs shell around the {110} facets of the GaAs core. The wires are typically highly resistive at low temperatures. However, they show a pronounced persistent photoconductivity effect indicating activation of free carriers from the delta-doped shell to the GaAs core. The n-type character of the channel is demonstrated by applying a back-gate voltage. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8438627123832703, "perplexity": 11173.343799288974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039379601.74/warc/CC-MAIN-20210420060507-20210420090507-00635.warc.gz"}
https://cran.r-project.org/web/packages/subtee/vignettes/subtee_package.html	# Introduction to subtee and Usage Instructions #### 2019-01-07 In this vignette we showcase the estimation functions of the subtee package. We provide three ways for estimating the treatment effects in subgroups: unadjusted estimation (unadj), model averaging (modav), and using bootstrap bias adjustment (bagged). ## Analyzing the data We use the prostate cancer dataset that was used in Rosenkranz (2016) to illustrate the usage of the package. The dataset consists of n=475 subjects randomized to a control group or diethylstilbestrol. The considered endpoint is survival time in months. There are six subgroup defining variables to consider: existence of bone metastasis (BM), disease stage (3 or 4), performance (PF), history of cardiovascular events (HX), age, and weight. While age and weight are continuous covariates, they are dichotomized (age $$\leq$$ 65, $$>$$ 65 and weight $$\leq$$ 100, $$>$$ 100) for obtaining subgroups as in Rosenkranz (2016). The considered endpoint is survival time in months and Cox proportional hazards models are fitted. We first start producing the treatment effect estimates for all subgroups, using the unadj, modav and bagged functions. library(ggplot2) library(subtee) ################################################################################ # We use the dataset from Rosenkranz (2016) https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.201500147 # to illustrate the methods proposed in this work. # The data comes from a clinical trial of an prostate cancer treatment # Data is loaded from Royston, Patrick, and Willi Sauerbrei. Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables. Vol. 777. John Wiley & Sons, 2008. https://www.imbi.uni-freiburg.de/Royston-Sauerbrei-book temp <- tempfile() names(prca) = toupper(names(prca)) ## subbuild function We first use the subbuild function to create the subgroup defining binary covariates. This function takes the dataset as a first argument, and then a series of expressions to define the subgroup indicator variables (see ?subbuild for more options on how to generate binary subgroup indicators based on a data-set). Note that we also use the option dupl.rm = TRUE to remove duplicate subgroups. The output of the subbuild is a data.frame that might then be concatenated with the original dataset to be used in the other functions. This step can be ommited if the original dataset already contains the subgroup defining indicator variables. cand.groups <- subbuild(prca, dupl.rm = TRUE, BM == 1, PF == 1, HX == 1, STAGE == 4, AGE > 65, WT > 100) #> BM == 1 PF == 1 HX == 1 STAGE == 4 AGE > 65 WT > 100 #> 1 0 0 0 0 1 0 #> 2 0 0 1 0 1 1 #> 3 0 1 1 0 1 0 #> 4 0 0 0 0 1 0 #> 5 0 0 0 0 1 0 #> 6 0 0 0 0 1 0 fitdat <- cbind(prca, cand.groups) subgr.names <- names(cand.groups) prog <- as.formula(paste(" ~ ", paste0("", names(cand.groups),"", collapse = " + "))) Before investigating how the treatment effect differs across the subgroups we first fit the overall model, adjusting for the subgroup indicators only as prognostic covariates. Since we have survival endpoint, we use coxph from the survival package as fitting function. library(survival) form <- as.formula(paste("Surv(SURVTIME,CENS) ~ RX +", paste0("", names(cand.groups),"", collapse = " + "))) coxph(form, data=fitdat, ties = "breslow") #> Call: #> coxph(formula = form, data = fitdat, ties = "breslow") #> #> coef exp(coef) se(coef) z p #> RX -0.183 0.832 0.113 -1.62 0.1043 #> BM == 1 0.478 1.612 0.171 2.79 0.0053 #> PF == 1 0.437 1.548 0.173 2.52 0.0118 #> HX == 1 0.437 1.549 0.112 3.89 1e-04 #> STAGE == 4 0.205 1.228 0.129 1.59 0.1125 #> AGE > 65 0.259 1.295 0.152 1.70 0.0898 #> WT > 100 -0.199 0.820 0.114 -1.74 0.0810 #> #> Likelihood ratio test=56.9 on 7 df, p=6.29e-10 #> n= 475, number of events= 338 We see that the new treatment leads to better outcomes when compared to control, as the overall treatment effect (RX) is negative. However, its confidence interval covers the no-effect value of 0. ## unadj function Unadjusted subgroup treatment effect estimates are obtained via the unadj function. We fit the models including the six subgroup indicators as prognostic factors as well, which are added through the covars argument as a formula. The unadj function loops through the $$P$$ variables specified in the subgr argument, fitting the models $$$M_p:\ \lambda_{pi}(t)= \lambda_{p0}(t) \exp\left\{\beta_p z_i + (\gamma_p + \delta_p z_i)s_{pi} + \sum_{k = 1}^{K} \tau_k x_{ik} \right\} \label{model.cox}$$$ for $$p=1,...,P$$. In this example, we make use of the ... option to pass the option ties = "breslow" to coxph. ### Unadjusted estimates data = fitdat, covars = prog, event = "CENS", fitfunc = "coxph", ties = "breslow") #> Trt. Effect Estimates #> Group Subset LB trtEff UB #> 1 BM == 1 Subgroup -1.1949 -0.785335 -0.37579 #> 2 BM == 1 Complement -0.2442 -0.040729 0.16273 #> 3 PF == 1 Subgroup -0.3965 0.118040 0.63257 #> 4 PF == 1 Complement -0.4212 -0.224282 -0.02734 #> 5 HX == 1 Subgroup -0.2547 0.006503 0.26774 #> 6 HX == 1 Complement -0.6199 -0.363698 -0.10754 #> 7 STAGE == 4 Subgroup -0.6526 -0.376238 -0.09986 #> 8 STAGE == 4 Complement -0.2748 -0.027431 0.21998 #> 9 AGE > 65 Subgroup -0.2517 -0.052995 0.14568 #> 10 AGE > 65 Complement -1.4451 -0.962738 -0.48037 #> 11 WT > 100 Subgroup -0.5730 -0.274251 0.02451 #> 12 WT > 100 Complement -0.3622 -0.126989 0.10819 #> #> Difference in Trt. Effect vs Complement #> Group LB trtEffDiff UB #> 1 BM == 1 -1.201671 -0.7446 -0.28754 #> 2 PF == 1 -0.203438 0.3423 0.88808 #> 3 HX == 1 0.007603 0.3702 0.73280 #> 4 STAGE == 4 -0.718343 -0.3488 0.02073 #> 5 AGE > 65 0.394367 0.9097 1.42512 #> 6 WT > 100 -0.524689 -0.1473 0.23016 #> #> Subgroup Models fitted with "coxph" #> Effect estimates in terms of the log-hazard ratios The output shows first the treatment effect estimates (trtEff) in the subgroups and corresponding lower and upper bounds of the unadjusted confidence intervals (LB and UB respectively). A second table is then displayed with the information on the difference in treatment effect in subgroups vs. their complements. The treatment effects are on same scale as returned by the linear predictictor of the specified fitfunc. In this example, the treatment effects are expressed in terms of the log-hazard ratios. Using the unadjusted estimates for subgroups leads to the conclusion that there may be subgroups with differential treatment effect. In particular, patients with bone metastasis and patients younger than 65 may have a differential benefit from the treatment. This is also observed when looking at the interaction effects between these covariates and treatment. These results needs to be interpreted with caution as this is only an exploratory analysis. ## modAv function We use the modAv function to obtain the model averaging estimates. In this case, we use the same options as in the unadj function, so we used the default values to set all the models with equal prior weights and no prior weight for the overall model. ### ModelAveraging estimates res_modav = modav(resp = "SURVTIME", trt = "RX", subgr = subgr.names, data = fitdat, covars = prog, event = "CENS", fitfunc = "coxph", ties = "breslow") res_modav #> Trt. Effect Estimates #> Group Subset LB trtEff UB #> 1 BM == 1 Subgroup -1.0089 -0.3182 -0.082706 #> 2 BM == 1 Complement -0.3633 -0.1577 0.080986 #> 3 PF == 1 Subgroup -0.4800 -0.2247 -0.006514 #> 4 PF == 1 Complement -0.3813 -0.1889 0.004497 #> 5 HX == 1 Subgroup -0.3421 -0.1533 0.044871 #> 6 HX == 1 Complement -0.4253 -0.2228 -0.029070 #> 7 STAGE == 4 Subgroup -0.4663 -0.2493 -0.048809 #> 8 STAGE == 4 Complement -0.3614 -0.1547 0.086863 #> 9 AGE > 65 Subgroup -0.3016 -0.0915 0.121691 #> 10 AGE > 65 Complement -1.3799 -0.7415 -0.086948 #> 11 WT > 100 Subgroup -0.3732 -0.1769 0.021429 #> 12 WT > 100 Complement -0.3909 -0.2040 -0.016736 #> #> Difference in Trt. Effect vs Complement #> Group LB trtEffDiff UB #> 1 BM == 1 -0.994109 -0.08220 -0.02315 #> 2 PF == 1 -0.291039 0.01613 0.03506 #> 3 HX == 1 0.017764 0.06258 0.12345 #> 4 STAGE == 4 -0.386656 -0.03536 -0.01087 #> 5 AGE > 65 0.017744 0.67341 1.35540 #> 6 WT > 100 -0.001293 0.01531 0.09971 #> #> Subgroup Models fitted with "coxph" #> Effect estimates in terms of the log-hazard ratios Model averaging has the effect of shrinking the estimates towards the overall treatment effect. Therefore, it may help in adjusting for potential “random high bias”. In this sense, we observe that the treatment effects for the subgroups BM == 1 and Age < 65 are closer to the overall treament effect when using model averaging. All confidence intervals for treatment effects in subgroups cover the overall treatment effect. ## bagged function We obtain the bagged estimates using the bagged function. Note that we should also provide to the function how the subgroup is selected (select.by = "BIC") and the number of bootstrap to use (B = 2000). We also let the default option stratify = TRUE, which controls that the bootstrap samples have the same number of subjects in treatment and controls arms as the original dataset. ### Bagged estimates set.seed(321231) # set seed for reproducible results in the bootstrap samples res_bagged = bagged(resp = "SURVTIME", trt = "RX", subgr = subgr.names, data = fitdat, covars = prog, event = "CENS", fitfunc = "coxph", select.by = "BIC", B = 200) #B = 2000) res_bagged #> Trt. Effect Estimates #> Group Subset LB trtEff UB #> 1 AGE > 65 Subgroup -0.2914 -0.0763 0.1388 #> 2 AGE > 65 Complement -1.7822 -0.8351 0.1120 #> #> Difference in Trt. Effect vs Complement #> Group LB trtEffDiff UB #> 1 AGE > 65 -0.08617 0.7588 1.604 #> #> AGE > 65 is the selected subgroup. #> It was selected in 48.5 % of the bootstrap samples. #> See more details in x\$boot_results #> #> Subgroup Models fitted with "coxph" #> Effect estimates in terms of the log-hazard ratios The bootstrap methods provides bias-adjusted estimates, which corrects for the bias that is introduced when selecting a subgroup. Therefore, it only makes sense to display the results of the selected subgroup. The user however may explore the results of the bootstrap samples, which are included in the output object. The subgroup defined by AGE>65 is the most selected in the bootstrap samples. This allows to ‘correct’ the estimates for selection bias. We observe a similar pattern as with model averaging. After using bootstrap, the treatment effect is closer to that on the overall population and its confidence interval even covers it.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.4359654188156128, "perplexity": 3278.9530314366166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481612.36/warc/CC-MAIN-20190217031053-20190217053053-00599.warc.gz"}
https://dash.harvard.edu/handle/1/4554750?show=full	# The Pace of Evolution Across Fitness Valleys dc.contributor.author Gokhale, Chaitanya S. dc.contributor.author Iwasa, Yoh dc.contributor.author Nowak, Martin A. dc.contributor.author Traulsen, Arne dc.date.accessioned 2010-11-15T20:34:13Z dc.date.issued 2009 dc.identifier.citation Gokhale Chaitanya S., Yoh Iwasa, Martin A. Nowak, and Arne Traulsen. 2009. The pace of evolution across fitness valleys. Journal of Theoretical Biology 259(3): 613-620. en_US dc.identifier.issn 0022-5193 en_US dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:4554750 dc.description.abstract How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate. en_US dc.description.sponsorship Mathematics en_US dc.description.sponsorship Organismic and Evolutionary Biology en_US dc.language.iso en_US en_US dc.publisher Elsevier en_US dc.relation.isversionof doi:10.1016/j.jtbi.2009.04.011 en_US dc.relation.hasversion http://www.ped.fas.harvard.edu/people/faculty/all_publications.html#2009 en_US dash.license META_ONLY dc.subject finite populations en_US dc.subject stochastic tunneling en_US dc.subject evolutionary speed en_US dc.title The Pace of Evolution Across Fitness Valleys en_US dc.type Journal Article en_US dc.description.version Version of Record en_US dc.relation.journal Journal of Theoretical Biology en_US dash.depositing.author Nowak, Martin A. dash.embargo.until 10000-01-01 ## Files in this item Files Size Format View Nowak_PaceEvolution.pdf 356.2Kb PDF View/Open	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8739647269248962, "perplexity": 18816.222835975295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661555.40/warc/CC-MAIN-20160924173741-00170-ip-10-143-35-109.ec2.internal.warc.gz"}
https://physics.stackexchange.com/questions/403444/hubbard-stratonovich-transformation-and-decoupling-channels	# Hubbard-Stratonovich transformation and decoupling channels I'm studying an example of the Hubbard-Stratonovich transformation in Altland and Simons' Condensed Matter Field Theory (2nd ed.), pp. 246-247. In it they say that... one is frequently confronted with situations where more than one Hubbard-Stratonovich field is needed to capture the full physics of the problem. To appreciate this point, consider the Coulomb interaction in momentum space. $$S_{int}[\bar{\psi},\psi] = \tfrac{1}{2} \sum_{p_1,...,p_4} \bar{\psi}_{\sigma, p_1} \bar{\psi}_{\sigma', p_3} V(\textbf{p}_1-\textbf{p}_2) \psi_{\sigma', p_4} \psi_{\sigma, p_2} \delta_{p_1-p_2+p_3-p_4}.$$ In principle, we can decouple this interaction in any of the three channels... discussed in the previous page. If one chooses to decouple in all three channels then the action becomes ... $$S_{int}[\bar{\psi},\psi] \simeq \tfrac{1}{2} \sum_{p,p',q} ( \bar{\psi}_{\sigma, p} \psi_{\sigma,p+q} V(\textbf{q}) \bar{\psi}_{\sigma', p'} \psi_{\sigma',p'-q} - \bar{\psi}_{\sigma, p} \psi_{\sigma',p+q} V(\textbf{p'}-\textbf{p}) \bar{\psi}_{\sigma', p'} \psi_{\sigma,p'} - \bar{\psi}_{\sigma, p} \bar{\psi}_{\sigma', -p+q} V(\textbf{p'}-\textbf{p}) \psi_{\sigma,p'} \psi_{\sigma',-p'+q} )$$ where the first term is decoupled via the direct channel $\rho_{d,q} \sim \sum_{p} \bar{\psi}_{\sigma,p} \psi_{\sigma,p+q}$, second in the exchange channel $\rho_{x,\sigma\sigma',q} \sim \sum_{p} \bar{\psi}_{\sigma,p} \psi_{\sigma',p+q}$, and third in the Cooper channel $\rho_{c,\sigma\sigma',q} \sim \sum_{p} \bar{\psi}_{\sigma,p} \bar{\psi}_{\sigma',-p+q}$. It's generally a good strategy to decouple in all available channels when one is in doubt, then let the mean-field analysis sort out the relevant fields. My question is, if we choose to decouple the quartic term via 3 different channels (for example) is it necessary to multiply the resulting terms by a factor of $\tfrac{1}{3}$? This isn't discussed in the textbook and I'm confused by the liberal use of $\sim$ and $\simeq$ in the examples. No. You should not add a factor of $1/3$. As you can see in page 244 of Altland and Simons, the HS transformation is done by multiplying by a unity expressed as a functional integral over an auxiliary field. In this case, they just choose to introduce 3 different fields - 1 for each term. • Great, thanks. Just to clarify, for some action $S= \bar{\psi}_\alpha(t) \psi_\beta(t) V \bar{\psi}_\gamma(t') \psi_\delta(t')$, decoupling via the direct channel is when $\rho=\bar{\psi}_\alpha(t) \psi_\beta(t)$, exchange channel: $\rho=\bar{\psi}_\alpha(t) \psi_\delta(t')$, and Cooper channel: $\rho=\bar{\psi}_\alpha(t)\bar{\psi}_\gamma(t')$. If I want to decouple via the exchange channel then I can let either $\rho=\bar{\psi}_\alpha(t) \psi_\delta(t')$ or $\rho=\bar{\psi}_\gamma(t') \psi_\beta(t)$. Is this correct? (tbc) – Medulla Oblongata May 7 '18 at 9:07 • If so, can I use both these $\rho$ and not need a multiplicative factor of $1/2$? – Medulla Oblongata May 7 '18 at 9:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9395470023155212, "perplexity": 243.74248169233434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347385193.5/warc/CC-MAIN-20200524210325-20200525000325-00303.warc.gz"}
http://mathhelpforum.com/advanced-algebra/83315-proving-field-not-algebraically-closed-print.html	# Proving a field is not algebraically closed • April 12th 2009, 02:17 AM Zinners Proving a field is not algebraically closed Hi, My problem is this: Prove that if p is a prime, then the field Zp is not algebraically closed. I know that using Fermat's little theorem will help but I can't see how it's not closed. Can anybody help please? Thanks • April 12th 2009, 04:46 AM berlioz Using Fermat's little theorem we have x^(p-1)-1=0for any x doesn't equal zero,so the polynomial x^(p-1)-2(suppose p>2)doesn't have the zero points inZp if p=2,we can find x^2+x+1 hasn't the zero points in Z2. So field Zp is not algebraically closed. Quote: Originally Posted by Zinners Hi, My problem is this: Prove that if p is a prime, then the field Zp is not algebraically closed. I know that using Fermat's little theorem will help but I can't see how it's not closed. Can anybody help please? Thanks • April 13th 2009, 10:10 AM ThePerfectHacker Quote: Originally Posted by Zinners Hi, My problem is this: Prove that if p is a prime, then the field Zp is not algebraically closed. I know that using Fermat's little theorem will help but I can't see how it's not closed. Can anybody help please? Thanks In general let $F$ be a finite field with $q$ elements. Define $f(x) = x^q - x +1$, we know that $a^{q-1}=1 \implies a^q - a = 0$ for all $a\in F^{\times}$. Therefore, $f(x) = x^q - x + 1$ always has no zero.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473154902458191, "perplexity": 443.13244616441693}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397565.80/warc/CC-MAIN-20160624154957-00003-ip-10-164-35-72.ec2.internal.warc.gz"}
https://mc-stan.org/docs/2_28/functions-reference/inverse-chi-square-distribution.html	This is an old version, view current version. ## 18.3 Inverse chi-square distribution ### 18.3.1 Probability density function If $$\nu \in \mathbb{R}^+$$, then for $$y \in \mathbb{R}^+$$, $\text{InvChiSquare}(y \, \| \, \nu) = \frac{2^{-\nu/2}} {\Gamma(\nu / 2)} \, y^{-\nu/2 - 1} \, \exp\! \left( \! - \, \frac{1}{2} \, \frac{1}{y} \right) .$ ### 18.3.2 Sampling statement y ~ inv_chi_square(nu) Increment target log probability density with inv_chi_square_lupdf(y \| nu). Available since 2.0 ### 18.3.3 Stan functions real inv_chi_square_lpdf(reals y \| reals nu) The log of the inverse Chi-square density of y given degrees of freedom nu Available since 2.12 real inv_chi_square_lupdf(reals y \| reals nu) The log of the inverse Chi-square density of y given degrees of freedom nu dropping constant additive terms Available since 2.25 real inv_chi_square_cdf(reals y, reals nu) The inverse Chi-squared cumulative distribution function of y given degrees of freedom nu Available since 2.0 real inv_chi_square_lcdf(reals y \| reals nu) The log of the inverse Chi-squared cumulative distribution function of y given degrees of freedom nu Available since 2.12 real inv_chi_square_lccdf(reals y \| reals nu) The log of the inverse Chi-squared complementary cumulative distribution function of y given degrees of freedom nu Available since 2.12 R inv_chi_square_rng(reals nu) Generate an inverse Chi-squared variate with degrees of freedom nu; may only be used in transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions. Available since 2.18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9853819012641907, "perplexity": 7896.438435259181}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446708046.99/warc/CC-MAIN-20221126180719-20221126210719-00349.warc.gz"}
http://www.maplesoft.com/support/help/Maple/view.aspx?path=combstruct/draw	combstruct - Maple Programming Help combstruct draw draw random combinatorial object count count combinatorial objects of a specified size Calling Sequence draw([A, spec, typ], size=n) draw(struct(args), size=n) count([A, spec, typ], size=n) count(struct(args), size=n) Parameters A - nonterminal of spec spec - combinatorial specification typ - labeling type; 'labeled' or 'unlabeled', the default is 'unlabeled' n - (optional with structures) non-negative integer specifying the size of the object, or string 'allsizes' struct - one of a pre-defined list of available structures args - argument list that corresponds to the structure struct Description • The draw function outputs a random object of size n in the class $A$ defined by the specification spec, with uniform distribution among all objects of the same size. • In the case of structures, the draw function returns an object of size n, or an object chosen from all possible sizes, or an object of the default size for that structure, if the size was not specified. Use the string 'allsizes' which is available only for predefined structures when the object is chosen from all possible sizes. • The count function returns the number of such objects. • To learn how to write a grammar specification, see combstruct[specification]. For a list of available structures, see combstruct[structures]. Examples > $\mathrm{with}\left(\mathrm{combstruct}\right):$ > $\mathrm{bin}≔\left\{B=\mathrm{Union}\left(Z,\mathrm{Prod}\left(B,B\right)\right)\right\}:$ > $\mathrm{draw}\left(\left[B,\mathrm{bin},\mathrm{labeled}\right],\mathrm{size}=7\right)$ ${\mathrm{Prod}}{}\left({{Z}}_{{1}}{,}{\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({{Z}}_{{4}}{,}{{Z}}_{{3}}\right){,}{{Z}}_{{2}}\right){,}{{Z}}_{{6}}\right){,}{{Z}}_{{7}}\right){,}{{Z}}_{{5}}\right)\right)$ (1) > $\mathrm{draw}\left(\left[B,\mathrm{bin}\right],\mathrm{size}=7\right)$ ${\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({Z}{,}{\mathrm{Prod}}{}\left({Z}{,}{\mathrm{Prod}}{}\left({Z}{,}{\mathrm{Prod}}{}\left({\mathrm{Prod}}{}\left({Z}{,}{Z}\right){,}{Z}\right)\right)\right)\right){,}{Z}\right)$ (2) > $\mathrm{count}\left(\left[B,\mathrm{bin},\mathrm{unlabeled}\right],\mathrm{size}=7\right)$ ${132}$ (3) > $\mathrm{draw}\left(\mathrm{Combination}\left(\left[a,b,c\right]\right)\right)$ $\left[{a}{,}{b}\right]$ (4) > $\mathrm{count}\left(\mathrm{Permutation}\left(\left[a,b,c\right]\right),\mathrm{size}=2\right)$ ${6}$ (5)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4427963197231293, "perplexity": 2095.396627847936}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189525.23/warc/CC-MAIN-20170322212949-00070-ip-10-233-31-227.ec2.internal.warc.gz"}
https://link.springer.com/chapter/10.1007/978-3-319-00143-2_31	# Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms • Michael J. Ostwald Chapter ## Abstract The new façade of Storey Hall in Melbourne, by the architects ARM, is covered in a particular set of giant aperiodic tessellations which were discovered by the mathematician Roger Penrose in the 1970s and have since become known as Penrose tiles. While architecture has, historically, always been closely associated with the crafts of tiling and patterning, Storey Hall represents a resurrection and expansion of that tradition. However, what is Penrose tiling and what does it have to do with architecture? This paper provides an overview of the special properties and characteristics of Penrose tiling before describing the way in which they are used in Storey Hall. The purpose of this binary analysis is not to critique Storey Hall but to use the design as a catalyst for considering applications of tiling in the context of architectural form generation. ## Keywords Tiling System Obtuse Angle Architectural Form Penrose Tile Single Tile These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. ## References 1. Ashton Raggatt McDougall. 1996. New Patronage. In Ashton Raggatt McDougall, eds. RMIT Storey Hall, Melbourne: Faculty of Environmental Design and Construction, RMIT.Google Scholar 2. Cracknell, Arthur. 1969. Crystals and their Structure. London: Pergamon.Google Scholar 3. Day, Norman. 1995. Storey Hall. Architecture Australia 85, 1 (1995): 36.Google Scholar 4. Eisenman, Peter. 1982. House X. New York: Rizzoli.Google Scholar 5. ———. 1995. Eisenman Architects: Selected And Current Works. Mulgrave: Images Publishing.Google Scholar 6. Gardner, Martin. 1989. Penrose Tiles To Trapdoor Ciphers. New York: W. H. Freeman.Google Scholar 7. Grünbaum, Branko and Geoffrey Colin Shephard. 1987. Tilings and Patterns. New York: W. H. Freeman.Google Scholar 8. Kohane, Peter. 1996. Ashton Raggatt and McDougall’s Imitative Architecture: Real and Imaginary Paths through Storey Hall. Transition 52/53 (1996): 8–15.Google Scholar 9. Kruft, Hanno Walter. 1994. A History of Architectural Theory from Vitruvius to the Present. In R. Taylor, E. Callander, and A. Wood, trans. New York: Princeton Architectural Press.Google Scholar 10. Miyazaki, Koji. 1977. On Some Periodical and Non-Periodical Honeycombs. Kobe: University Monograph.Google Scholar 11. Ostwald, Michael J., and R. John Moore. 1995. Mathematical Misreadings in Nonlinearity: Architecture as Accessory/Theory. In Mike Linzey, ed. Accessory/Architecture. Vol. 1. Auckland: University of Auckland. 1995.Google Scholar 12. ———. 1997. Unravelling the Weave: an Analysis of Architectural Metaphors in Nonlinear Dynamics. Interstices. Vol. 4 (1997) CD-ROM.Google Scholar 13. Ostwald, Michael J., Peter Zellner and Charles Jencks. 1996. An Architecture Of Complexity. Transition 52/53 (1996): 30.Google Scholar 14. Penrose, Roger. 1990. The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. London: Vintage. 15. ———. 1996. Fax to Howard Raggatt. In Ashton Raggatt McDougall, eds. RMIT Storey Hall. Melbourne: Faculty of Environmental Design and Construction, RMIT.Google Scholar 16. Rubinsteim, Heim. 1996. Penrose Tiling. Transition 52/53 (1996): 20–21.Google Scholar 17. Robbin, Tony. 1990. Quasicrystals for Architecture: The Visual Properties of Three-Dimensional Penrose Tessellations. Leonardo 23, 1: 140–141.Google Scholar 18. Stewart, Ian and Martin Golubitsky. 1993. Fearful Symmetry: Is God A Geometer? London: Penguin.Google Scholar 19. Van Schaik, Leon. 1996. Preface. In Ashton Raggatt McDougall, eds. RMIT Storey Hall. Melbourne: Faculty of Environmental Design and Construction, RMIT.Google Scholar	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8688901662826538, "perplexity": 27048.073168458563}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824059.7/warc/CC-MAIN-20181212155747-20181212181247-00193.warc.gz"}
https://www.physicamedica.com/article/S1120-1797(22)01430-2/fulltext	Corrigendum\| Volume 96, P213, April 2022 # Corrigendum to “Investigation of bolus effect on skin dose in total body irradiations by helical tomotherapy” [Physica Medica 92 (2021) 84-85/OD 62] Published:March 18, 2022 In the publication of the abstract book, the corresponding author was indicated incorrectly and one author is missing. Corrected authors were listed above. The authors would like to apologise for any inconvenience caused.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8689217567443848, "perplexity": 12965.785063958123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00419.warc.gz"}
https://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/DetectPeaks.ipynb	# Detection of peaks in data¶ Marcos Duarte Laboratory of Biomechanics and Motor Control](http://demotu.org/ Federal University of ABC, Brazil One way to detect peaks (local maxima) or valleys (local minima) in data is to use the property that a peak (or valley) must be greater (or smaller) than its immediate neighbors. The function detect_peaks.py from Python module detecta detects peaks (or valleys) based on this feature and other characteristics. The function signature is: ind = detect_peaks(x, mph=None, mpd=1, threshold=0, edge='rising', kpsh=False, valley=False, show=False, ax=None, title=True) The parameters mph, mpd, and threshold follow the convention of the Matlab function findpeaks.m. Let's see how to use detect_peaks.py; first let's import the necessary Python libraries and configure the environment: ## Installation¶ pip install detecta Or conda install -c duartexyz detecta In [1]: import numpy as np import matplotlib.pyplot as plt %matplotlib inline from detecta import detect_peaks Running the function examples: In [3]: >>> x = np.random.randn(100) >>> x[60:81] = np.nan >>> # detect all peaks and plot data >>> ind = detect_peaks(x, show=True) >>> print(ind) >>> x = np.sin(2np.pi5np.linspace(0, 1, 200)) + np.random.randn(200)/5 >>> # set minimum peak height = 0 and minimum peak distance = 20 >>> detect_peaks(x, mph=0, mpd=20, show=True) >>> x = [0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 0] >>> # set minimum peak distance = 2 >>> detect_peaks(x, mpd=2, show=True) >>> x = np.sin(2np.pi5np.linspace(0, 1, 200)) + np.random.randn(200)/5 >>> # detection of valleys instead of peaks >>> detect_peaks(x, mph=-1.2, mpd=20, valley=True, show=True) >>> x = [0, 1, 1, 0, 1, 1, 0] >>> # detect both edges >>> detect_peaks(x, edge='both', show=True) >>> x = [-2, 1, -2, 2, 1, 1, 3, 0] >>> # set threshold = 2 >>> detect_peaks(x, threshold = 2, show=True) >>> x = [-2, 1, -2, 2, 1, 1, 3, 0] >>> fig, axs = plt.subplots(ncols=2, nrows=1, figsize=(10, 4)) >>> detect_peaks(x, show=True, ax=axs[0], threshold=0.5, title=False) >>> detect_peaks(x, show=True, ax=axs[1], threshold=1.5, title=False) [ 6 9 11 13 17 19 21 23 26 30 33 35 37 40 42 45 47 51 54 57 83 86 89 91 94 96] Out[3]: array([1, 6]) ## Function performance¶ The function detect_peaks.py is relatively fast but the parameter minimum peak distance (mpd) slows down the function if the data has several peaks (>1000). Try to decrease the number of peaks by tuning the other parameters or smooth the data before calling this function with several peaks in the data. Here is a simple test of its performance: In [4]: x = np.random.randn(10000) ind = detect_peaks(x) print('Data with %d points and %d peaks\n' %(x.size, ind.size)) print('Performance (without the minimum peak distance parameter):') print('detect_peaks(x)') %timeit detect_peaks(x) print('\nPerformance (using the minimum peak distance parameter):') print('detect_peaks(x, mpd=10)') %timeit detect_peaks(x, mpd=10) Data with 10000 points and 3358 peaks Performance (without the minimum peak distance parameter): detect_peaks(x) 98.2 µs ± 1.95 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each) Performance (using the minimum peak distance parameter): detect_peaks(x, mpd=10) 8.17 ms ± 105 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28554677963256836, "perplexity": 5807.177011608716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571056.58/warc/CC-MAIN-20220809155137-20220809185137-00213.warc.gz"}
http://spmmathematics.onlinetuition.com.my/2014/08/multiplication-of-matrix-by-number.html	# 4.4 Multiplication of a Matrix by a Number 4.4 Multiplication of a Matrix by a Number When matrix is multiplied by a number, every element in the matrix is multiplied by the number. Example: Given that $A=\left(\begin{array}{cc}-2& 4\\ 5& -6\end{array}\right)$ , find each of the following. (a) 3A (b) -2A Solution:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9738494157791138, "perplexity": 680.2834743252154}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188924.7/warc/CC-MAIN-20170322212948-00168-ip-10-233-31-227.ec2.internal.warc.gz"}
http://jmlr.org/proceedings/papers/v32/gopalan14.html	# Thompson Sampling for Complex Online Problems Aditya Gopalan, Shie Mannor, Yishay Mansour Proceedings of The 31st International Conference on Machine Learning, pp. 100–108, 2014 ## Abstract We consider stochastic multi-armed bandit problems with complex actions over a set of basic arms, where the decision maker plays a complex action rather than a basic arm in each round. The reward of the complex action is some function of the basic arms’ rewards, and the feedback observed may not necessarily be the reward per-arm. For instance, when the complex actions are subsets of the arms, we may only observe the maximum reward over the chosen subset. Thus, feedback across complex actions may be coupled due to the nature of the reward function. We prove a frequentist regret bound for Thompson sampling in a very general setting involving parameter, action and observation spaces and a likelihood function over them. The bound holds for discretely-supported priors over the parameter space and without additional structural properties such as closed-form posteriors, conjugate prior structure or independence across arms. The regret bound scales logarithmically with time but, more importantly, with an improved constant that non-trivially captures the coupling across complex actions due to the structure of the rewards. As applications, we derive improved regret bounds for classes of complex bandit problems involving selecting subsets of arms, including the first nontrivial regret bounds for nonlinear MAX reward feedback from subsets. Using particle filters for computing posterior distributions which lack an explicit closed-form, we present numerical results for the performance of Thompson sampling for subset-selection and job scheduling problems.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9703350067138672, "perplexity": 720.3770312971982}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823802.12/warc/CC-MAIN-20160723071023-00196-ip-10-185-27-174.ec2.internal.warc.gz"}

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