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An Operator Semigroup in Mathematical Genetics

  • Adam Bobrowski
  • Marek Kimmel

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Mathematical Methods book sub series (BRIEFSMATHMETH)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Adam Bobrowski, Marek Kimmel
    Pages 1-2
  3. Adam Bobrowski, Marek Kimmel
    Pages 3-18
  4. Adam Bobrowski, Marek Kimmel
    Pages 23-65
  5. Adam Bobrowski, Marek Kimmel
    Pages 67-83
  6. Adam Bobrowski, Marek Kimmel
    Pages 85-85
  7. Back Matter
    Pages 87-88

About this book

Introduction

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.

Keywords

Differential Lyapunov Equation Microsatellite Loci Mutation Models Mutation and Drift Single-base Substitions Time Evolution of Neutral Genomic Regions

Authors and affiliations

  • Adam Bobrowski
    • 1
  • Marek Kimmel
    • 2
  1. 1.Faculty of Electrical Engineering and Computer Science, Department of Mathematics, Lublin University of TechnologyNadbystrzycka 38A, LublinPoland
  2. 2.Systems Engineering group, Silesian University of Technology, Gliwice, PolandDepartment of Statistics, Rice UniversityHoustonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-35958-3
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-35957-6
  • Online ISBN 978-3-642-35958-3
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site