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010   $a3-319-52045-8
024 7 $a10.1007/978-3-319-52045-2
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035   $a(DE-He213)978-3-319-52045-2
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035   $a(OCoLC)974463474
035   $a(PPN)198869622
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100   $a20170224d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aInformation Geometry and Population Genetics $eThe Mathematical Structure of the Wright-Fisher Model /$fby Julian Hofrichter, Jürgen Jost, Tat Dat Tran
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XII, 320 p. 3 illus., 2 illus. in color.)
225 1 $aUnderstanding Complex Systems,$x1860-0840
311 08$a3-319-52044-X 
320   $aIncludes bibliographical references and index.
327   $a1. 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.
330   $aThe present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.
410  0$aUnderstanding Complex Systems,$x1860-0840
606   $aBiomathematics
606   $aStatistics
606   $aMedical genetics
606   $aMathematical analysis
606   $aGeometry
606   $aProbabilities
606   $aMathematical and Computational Biology
606   $aStatistical Theory and Methods
606   $aMedical Genetics
606   $aAnalysis
606   $aGeometry
606   $aProbability Theory
615  0$aBiomathematics.
615  0$aStatistics.
615  0$aMedical genetics.
615  0$aMathematical analysis.
615  0$aGeometry.
615  0$aProbabilities.
615 14$aMathematical and Computational Biology.
615 24$aStatistical Theory and Methods.
615 24$aMedical Genetics.
615 24$aAnalysis.
615 24$aGeometry.
615 24$aProbability Theory.
676   $a576.58015118
700   $aHofrichter$b Julian$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767161
702   $aJost$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aTran$b Tat Dat$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254291003321
996   $aInformation Geometry and Population Genetics$92174112
997   $aUNINA