Information Geometry and Population Genetics: The Mathematical Structure of the

Description: Information Geometry and Population Genetics by Julian Hofrichter, Tat Dat Tran, JÜrgen Jost The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amaris and Chentsovs information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field. Back Cover The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amaris and Chentsovs information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field. Author Biography J. Jost: Studies of mathematics, physics, economics and philosophy; PhD and habilitation in mathematics (University of Bonn); professor for mathematics at Ruhr-University Bonn; since 1996 director at the MPI for Mathematics in the Sciences, Leipzig, and honorary professor at the University of Leipzig; external faculty member of the Santa Fe InstituteJ. Hofrichter: Studies of mathematics and physics in Heidelberg, Granada and Muenster/Westph., diploma in mathematics; graduate studies in mathematics in Leipzig, PhD 2014; postdoctoral researcher at the MPI for Mathematics in the Sciences, LeipzigT. D. Tran: Studies of mathematics in Hanoi (Vietnam), bachelor and master degree in mathematics; graduate studies in mathematics in Leipzig, PhD 2012; postdoctoral researcher at the MPI for Mathematics in the Sciences, Leipzig Table of Contents 1. Introduction.- 2. The Wright–Fisher model.- 3. Geometric structures and information geometry.- 4. Continuous approximations.- 5. Recombination.- 6. Moment generating and free energy functionals.- 7. Large deviation theory.- 8. The forward equation.- 9. The backward equation.- 10.Applications.- Appendix.- A. Hypergeometric functions and their generalizations.- Bibliography. Review "Information Geometry and Population Genetics masterfully explores the stochastic dynamics of the progressive distribution of alleles over generations through a geometric perspective on the traditional Wright-Fisher model. … The present book is a useful piece of literature for applied biologists with a fair understanding of calculus, who are looking toward the exploration of new dimensions in research on genetic evolution." (Ranjita Pandey, Canadian Studies in Population, Vol. 45 (1-2), 2018) Review Quote "Information Geometry and Population Genetics masterfully explores the stochastic dynamics of the progressive distribution of alleles over generations through a geometric perspective on the traditional Wright-Fisher model. ... The present book is a useful piece of literature for applied biologists with a fair understanding of calculus, who are looking toward the exploration of new dimensions in research on genetic evolution." (Ranjita Pandey, Canadian Studies in Population, Vol. 45 (1-2), 2018) Feature Provides a new systematic and geometric approach to the Wright--Fisher model of population genetics Introduces new tools from information geometry and statistical mechanics that lead to a deeper understanding Includes precise formulas and a detailed analysis of the boundary behavior (loss of allele events) Provides a solid and broad working basis for graduate students and researchers interested in this field. Details ISBN3319848054 Author JÜrgen Jost Series Understanding Complex Systems ISBN-10 3319848054 ISBN-13 9783319848051 Format Paperback Subtitle The Mathematical Structure of the Wright-Fisher Model DEWEY 515 Pages 320 Publisher Springer International Publishing AG Year 2018 Publication Date 2018-07-18 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Short Title Information Geometry and Population Genetics Language English UK Release Date 2018-07-18 Illustrations 2 Illustrations, color; 1 Illustrations, black and white; XII, 320 p. 3 illus., 2 illus. in color. Edition Description Softcover reprint of the original 1st ed. 2017 Alternative 9783319520445 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:128955476;

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