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Information geometry and population ...

Hofrichter, Julian.

Information geometry and population geneticsthe mathematical structure of the Wright-Fisher model /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Information geometry and population geneticsby Julian Hofrichter, Jurgen Jost, Tat Dat Tran.
其他題名:	the mathematical structure of the Wright-Fisher model /
作者:	Hofrichter, Julian.
其他作者:	Jost, Jurgen.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xii, 319 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Population geneticsMathematical models.
電子資源:	http://dx.doi.org/10.1007/978-3-319-52045-2
ISBN:	9783319520452$q(electronic bk.)

Information geometry and population geneticsthe mathematical structure of the Wright-Fisher model /
Hofrichter, Julian.

Information geometry and population geneticsthe mathematical structure of the Wright-Fisher model /[electronic resource] :by Julian Hofrichter, Jurgen Jost, Tat Dat Tran. - Cham :Springer International Publishing :2017. - xii, 319 p. :ill., digital ;24 cm. - Understanding complex systems,1860-0832. - Understanding complex systems..

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.

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 Amari's and Chentsov's 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.

ISBN: 9783319520452$q(electronic bk.)

Standard No.: 10.1007/978-3-319-52045-2doiSubjects--Topical Terms:

277724
Population genetics
--Mathematical models.

LC Class. No.: QH455

Dewey Class. No.: 576.58015118

Information geometry and population geneticsthe mathematical structure of the Wright-Fisher model /
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520 $a 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 Amari's and Chentsov's 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.
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