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Titlebook: An Operator Semigroup in Mathematical Genetics; Adam Bobrowski,Marek Kimmel Book 2015 The Author(s) 2015 Differential Lyapunov Equation.Mi

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发表于 2025-3-21 16:49:33 | 显示全部楼层 |阅读模式
期刊全称An Operator Semigroup in Mathematical Genetics
影响因子2023Adam Bobrowski,Marek Kimmel
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发行地址Combines genetic models with advanced mathematics.Contains examples based on human evolution data.Written by leading experts in the field.Includes supplementary material:
学科分类SpringerBriefs in Applied Sciences and Technology
图书封面Titlebook: An Operator Semigroup in Mathematical Genetics;  Adam Bobrowski,Marek Kimmel Book 2015 The Author(s) 2015 Differential Lyapunov Equation.Mi
影响因子.This authored monograph presents a mathematical description of the time evolution of neutral genomic regions in terms of the differential Lyapunov equation. The qualitative behavior of its solutions, with respect to different mutation models and demographic patterns, can be characterized using operator semi group theory..Mutation and drift are two of the main genetic forces, which act on genes of individuals in populations. Their effects are influenced by population dynamics. This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions. The effects of demographic change to the asymptotic of the distribution are also covered. The target audience primarily covers researchers and experts in the field but the book may also be beneficial for graduate students..
Pindex Book 2015
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Motivating Example: Population Bottlenecks in the History of Modern Humans, Use of the Imbalance Inex they introduced. Three major groups of population, Asians, Africans, and Europeans, were considered for this purpose. The analysis shows that the data are consistent with a population bottleneck in modern humanity history and gradual settling of Europe and Asia.
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Mathematical Tools,ups of operators related to Markov chains at the end of the chapter. Since these semigroups act in the space of absolutely summable sequences, which is a particularly simple Banach space, some results of the theory of semigroups of operators can be proved in a simpler way here.
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Epilogue, recombination. The principles are simple, and encompass various versions of the Wright-Fisher and Moran Models of drift, with Markovian mutations, Haldane model for recombination and several types of selection. However, when combined, these principles lead to very complicated and frequently puzzling models some with very interesting mathematics.
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