Download or read book Branching Processes in Biology written by Marek Kimmel and published by Springer. This book was released on 2015-02-17 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) “This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences.” (Short Book Reviews of the ISI, Vol. 23 (2), 2003)
Download or read book Branching Processes in Biology written by Marek Kimmel and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.
Download or read book Branching Processes with Biological Applications written by Peter Jagers and published by . This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Workshop on Branching Processes and Their Applications written by Miguel González and published by Springer Science & Business Media. This book was released on 2010-03-02 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.
Download or read book Branching Processes in Biology written by Marek Kimmel and published by Springer. This book was released on 2015-02-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) “This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences.” (Short Book Reviews of the ISI, Vol. 23 (2), 2003)
Download or read book Branching Processes written by Patsy Haccou and published by Cambridge University Press. This book was released on 2005-05-19 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Download or read book Branching Processes and Their Applications written by Inés M. del Puerto and published by Springer. This book was released on 2016-09-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.
Download or read book Biological Applications of Branching Processes written by Anthony Pakes and published by . This book was released on 2000 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Branching Processes with Biological Applications written by Peter Jagers and published by Wiley-Interscience. This book was released on 1975 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer Nature. This book was released on 2022-01-04 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes – Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.
Download or read book Introduction to Stochastic Processes with R written by Robert P. Dobrow and published by John Wiley & Sons. This book was released on 2016-03-07 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.
Download or read book Branching Process Models of Cancer written by Richard Durrett and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the authors calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the authors evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time. Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
Download or read book The Theory of Branching Processes written by Theodore Edward 1919- Harris and published by Hassell Street Press. This book was released on 2021-09-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Branching Processes in Random Environment written by Kersting Gotz and published by Iste Press - Elsevier. This book was released on 2017-10-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several books devoted to the theory of branching processes. However, the theory of branching processes in random environment is rather pour reflected in these books. During the last two decades an essential progress was achieved on this field in particular, owing to the efforts of the authors of the proposal. We develop in this book a unique and new approach to study branching processes in random environment To compare properties of branching processes in random environment with properties of ordinary random walks This approach, combined with the properties of random walks conditioned to stay nonnegative or negative allows to find the probability of survival of the critical and subcritical branching processes in random environment as well as Yaglom-type limit theorems for the mentioned classes of processes
Download or read book Branching Processes and Neutral Evolution written by Ziad Taib and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F. Galton as problem 4001 in the Educational Times (17, 1873). In 1875, an attempt to solve this problem was made by H. W. Watson but as it turned out, his conclusion was incorrect. Half a century later, R. A. Fisher made use of the Galton-Watson process to determine the extinction probability of the progeny of a mutant gene. However, it was J. B. S. Haldane who finally gave the first sketch of the correct conclusion. J. B. S. Haldane also predicted that mathematical genetics might some day develop into a "respectable branch of applied mathematics" (quoted in M. Kimura & T. Ohta, Theoretical Aspects of Population Genetics. Princeton, 1971). Since the time of Fisher and Haldane, the two fields of branching processes and mathematical genetics have attained a high degree of sophistication but in different directions. This monograph is a first attempt to apply the current state of knowledge concerning single-type branching processes to a particular area of mathematical genetics: neutral evolution. The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. Following the advice of an anonymous referee, I have enlarged my original version of the introduction (Chapter Zero) in order to make it accessible to a larger audience. G6teborg, Sweden, November 1991.
Download or read book An Introduction to Stochastic Processes with Applications to Biology written by Linda J. S. Allen and published by CRC Press. This book was released on 2010-12-02 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and
Download or read book Stochastic Population and Epidemic Models written by Linda J. S. Allen and published by Springer. This book was released on 2015-08-20 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics at Texas Tech University, USA.
