Download or read book Information Geometry and Population Genetics written by Julian Hofrichter and published by Springer. This book was released on 2017-02-23 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Riemannian Geometry and Geometric Analysis written by Jürgen Jost and published by Springer. This book was released on 2017-10-13 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik
Download or read book Our Genes written by Rasmus Grønfeldt Winther and published by Cambridge University Press. This book was released on 2022-12-31 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Situated at the intersection of natural science and philosophy, Our Genes explores historical practices, investigates current trends, and imagines future work in genetic research to answer persistent, political questions about human diversity. Readers are guided through fascinating thought experiments, complex measures and metrics, fundamental evolutionary patterns, and in-depth treatment of exciting case studies. The work culminates in a philosophical rationale, based on scientific evidence, for a moderate position about the explanatory power of genes that is often left unarticulated. Simply put, human evolutionary genomics - our genes - can tell us much about who we are as individuals and as collectives. However, while they convey scientific certainty in the popular imagination, genes cannot answer some of our most important questions. Alternating between an up-close and a zoomed-out focus on genes and genomes, individuals and collectives, species and populations, Our Genes argues that the answers we seek point to rich, necessary work ahead.
Download or read book A Short History of Mathematical Population Dynamics written by Nicolas Bacaër and published by Springer Science & Business Media. This book was released on 2011-02-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.
Download or read book Evolutionstheorie und Dynamische Systeme written by Josef Hofbauer and published by . This book was released on 1988 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy–Weinberg law, the Lotka–Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Download or read book Introduction to Probability written by David F. Anderson and published by Cambridge University Press. This book was released on 2017-11-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Download or read book Mathematical Contributions to the Theory of Evolution written by Karl Pearson and published by . This book was released on 1904 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Population Processes written by Thomas G. Kurtz and published by SIAM. This book was released on 1981-01-01 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population processes are stochastic models for systems involving a number of similar particles. Examples include models for chemical reactions and for epidemics. The model may involve a finite number of attributes, or even a continuum. This monograph considers approximations that are possible when the number of particles is large. The models considered will involve a finite number of different types of particles.
Download or read book Quantum Adaptivity in Biology From Genetics to Cognition written by Masanari Asano and published by Springer. This book was released on 2015-04-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines information processing performed by bio-systems at all scales: from genomes, cells and proteins to cognitive and even social systems. It introduces a theoretical/conceptual principle based on quantum information and non-Kolmogorov probability theory to explain information processing phenomena in biology as a whole. The book begins with an introduction followed by two chapters devoted to fundamentals, one covering classical and quantum probability, which also contains a brief introduction to quantum formalism, and another on an information approach to molecular biology, genetics and epigenetics. It then goes on to examine adaptive dynamics, including applications to biology, and non-Kolmogorov probability theory. Next, the book discusses the possibility to apply the quantum formalism to model biological evolution, especially at the cellular level: genetic and epigenetic evolutions. It also presents a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. The last two chapters of the book explore foundational problems of quantum mechanics and demonstrate the power of usage of positive operator valued measures (POVMs) in biological science. This book will appeal to a diverse group of readers including experts in biology, cognitive science, decision making, sociology, psychology, and physics; mathematicians working on problems of quantum probability and information and researchers in quantum foundations.
Download or read book Information Geometry written by Nihat Ay and published by Springer. This book was released on 2017-08-25 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Download or read book Handbook of Statistical Genetics written by David J. Balding and published by John Wiley & Sons. This book was released on 2008-06-10 with total page 1616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook for Statistical Genetics is widely regarded as the reference work in the field. However, the field has developed considerably over the past three years. In particular the modeling of genetic networks has advanced considerably via the evolution of microarray analysis. As a consequence the 3rd edition of the handbook contains a much expanded section on Network Modeling, including 5 new chapters covering metabolic networks, graphical modeling and inference and simulation of pedigrees and genealogies. Other chapters new to the 3rd edition include Human Population Genetics, Genome-wide Association Studies, Family-based Association Studies, Pharmacogenetics, Epigenetics, Ethic and Insurance. As with the second Edition, the Handbook includes a glossary of terms, acronyms and abbreviations, and features extensive cross-referencing between the chapters, tying the different areas together. With heavy use of up-to-date examples, real-life case studies and references to web-based resources, this continues to be must-have reference in a vital area of research. Edited by the leading international authorities in the field. David Balding - Department of Epidemiology & Public Health, Imperial College An advisor for our Probability & Statistics series, Professor Balding is also a previous Wiley author, having written Weight-of-Evidence for Forensic DNA Profiles, as well as having edited the two previous editions of HSG. With over 20 years teaching experience, he’s also had dozens of articles published in numerous international journals. Martin Bishop – Head of the Bioinformatics Division at the HGMP Resource Centre As well as the first two editions of HSG, Dr Bishop has edited a number of introductory books on the application of informatics to molecular biology and genetics. He is the Associate Editor of the journal Bioinformatics and Managing Editor of Briefings in Bioinformatics. Chris Cannings – Division of Genomic Medicine, University of Sheffield With over 40 years teaching in the area, Professor Cannings has published over 100 papers and is on the editorial board of many related journals. Co-editor of the two previous editions of HSG, he also authored a book on this topic.
Download or read book Chance in Evolution written by Grant Ramsey and published by University of Chicago Press. This book was released on 2016-10-25 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This illuminating volume explores the effects of chance on evolution, covering diverse perspectives from scientists, philosophers, and historians. The evolution of species, from single-celled organisms to multicellular animals and plants, is the result of a long and highly chancy history. But how profoundly has chance shaped life on earth? And what, precisely, do we mean by chance? Bringing together biologists, philosophers of science, and historians of science, Chance in Evolution is the first book to untangle the far-reaching effects of chance, contingency, and randomness on the evolution of life. The book begins by placing chance in historical context, starting with the ancients and moving through Darwin to contemporary biology. It documents the shifts in our understanding of chance as Darwin’s theory of evolution developed into the modern synthesis, and how the acceptance of chance in Darwinian theory affected theological resistance to it. Other chapters discuss how chance relates to the concepts of genetic drift, mutation, and parallel evolution—as well as recent work in paleobiology and the experimental evolution of microbes. By engaging in collaboration across biology, history, philosophy, and theology, this book offers a comprehensive overview both of the history of chance in evolution and of our current understanding of the impact of chance on life.
Download or read book The Genetic Structure of Populations written by A. Jacquard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is part of the ideology of science that it is an international enterprise, carried out by a community that knows no barriers of nation or culture. But the reality is somewhat different. Despite the best intentions of scientists to form a single community, unseparated by differences of national and political viewpoint, they are, in fact, separated by language. Scientific literature in German is not generally assimilated by French workers, nor that appearing in French by those whose native language is English. The problem appears to have become more severe since the last war, because the ascendance of the United States as the preeminent economic power led, in a time of big and expensive science, to a pre dominance of American scientific production and a growing tendency (at least among English-speakers) to regard English as the international language of science. International congresses and journals of world circulation have come more and more to take English as their standard or official language. As a result, students and scientific workers in the English speaking world have become more linguistically parochial than ever before and have been cut off from a considerable scientific literature. Population genetics has been no exception to the rule. The elegant and extremely innovative theoreticaI work of Malecot, for example, is only now being properly assimilated by population biologists outside France. It was therefore with some sense of frustration that I read Prof.
Download or read book Elementary Probability for Applications written by Rick Durrett and published by Cambridge University Press. This book was released on 2009-07-31 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.
Download or read book Mixture Models written by Bruce G. Lindsay and published by IMS. This book was released on 1995 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
