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Workshop on Branching Processes and Their Applications

Workshop on Branching Processes and Their Applications
Author: Miguel González
Publisher: Springer Science & Business Media
Total Pages: 304
Release: 2010-03-02
Genre: Mathematics
ISBN: 3642111564
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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.

Branching Processes and Their Applications

Branching Processes and Their Applications
Author: Inés M. del Puerto
Publisher: Springer
Total Pages: 332
Release: 2016-09-06
Genre: Mathematics
ISBN: 3319316419
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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.

Classical and Modern Branching Processes

Classical and Modern Branching Processes
Author: Krishna B. Athreya
Publisher: Springer Science & Business Media
Total Pages: 340
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461218624
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This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13-171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes.

Discrete Time Branching Processes in Random Environment

Discrete Time Branching Processes in Random Environment
Author: Götz Kersting
Publisher: John Wiley & Sons
Total Pages: 388
Release: 2017-10-30
Genre: Mathematics
ISBN: 1119473551
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Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.

Controlled Branching Processes

Controlled Branching Processes
Author: Miguel González Velasco
Publisher: John Wiley & Sons
Total Pages: 240
Release: 2018-03-13
Genre: Mathematics
ISBN: 1786302535
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The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

Branching Processes in Biology

Branching Processes in Biology
Author: Marek Kimmel
Publisher: Springer
Total Pages: 293
Release: 2015-02-17
Genre: Mathematics
ISBN: 1493915592
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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)

Nonlinear Dynamics of Electronic Systems

Nonlinear Dynamics of Electronic Systems
Author: Valeri M. Mladenov
Publisher: Springer
Total Pages: 416
Release: 2014-06-30
Genre: Computers
ISBN: 3319086723
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This book constitutes the refereed proceedings of the 22nd International Conference on Nonlinear Dynamics of Electronic Systems, NDES 2014, held in Albena, Bulgaria, in July 2014. The 47 revised full papers presented were carefully reviewed and selected from 65 submissions. The papers are organized in topical sections on nonlinear oscillators, circuits and electronic systems; networks and nonlinear dynamics and nonlinear phenomena in biological and physiological systems.

The Mathematics of the Uncertain

The Mathematics of the Uncertain
Author: Eduardo Gil
Publisher: Springer
Total Pages: 917
Release: 2018-02-28
Genre: Technology & Engineering
ISBN: 3319738488
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This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.

Multivariate Nonparametric Methods with R

Multivariate Nonparametric Methods with R
Author: Hannu Oja
Publisher: Springer Science & Business Media
Total Pages: 239
Release: 2010-03-25
Genre: Mathematics
ISBN: 1441904689
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This book offers a new, fairly efficient, and robust alternative to analyzing multivariate data. The analysis of data based on multivariate spatial signs and ranks proceeds very much as does a traditional multivariate analysis relying on the assumption of multivariate normality; the regular L2 norm is just replaced by different L1 norms, observation vectors are replaced by spatial signs and ranks, and so on. A unified methodology starting with the simple one-sample multivariate location problem and proceeding to the general multivariate multiple linear regression case is presented. Companion estimates and tests for scatter matrices are considered as well. The R package MNM is available for computation of the procedures. This monograph provides an up-to-date overview of the theory of multivariate nonparametric methods based on spatial signs and ranks. The classical book by Puri and Sen (1971) uses marginal signs and ranks and different type of L1 norm. The book may serve as a textbook and a general reference for the latest developments in the area. Readers are assumed to have a good knowledge of basic statistical theory as well as matrix theory. Hannu Oja is an academy professor and a professor in biometry in the University of Tampere. He has authored and coauthored numerous research articles in multivariate nonparametrical and robust methods as well as in biostatistics.