Population Dynamics Algebraic And Probabilistic Approach

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Population Dynamics: Algebraic And Probabilistic Approach

Author : Utkir A Rozikov
Publisher : World Scientific
ISBN 13 : 9811211248
Total Pages : 458 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Population Dynamics: Algebraic And Probabilistic Approach by : Utkir A Rozikov

Download or read book Population Dynamics: Algebraic And Probabilistic Approach written by Utkir A Rozikov and published by World Scientific. This book was released on 2020-04-22 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.

Modelling Population Dynamics

Author : K. B. Newman
Publisher : Springer
ISBN 13 : 1493909770
Total Pages : 223 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Modelling Population Dynamics by : K. B. Newman

Download or read book Modelling Population Dynamics written by K. B. Newman and published by Springer. This book was released on 2014-07-16 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models). The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.

Stochastic Differential Equations

Author : Michael J. Panik
Publisher : John Wiley & Sons
ISBN 13 : 1119377382
Total Pages : 303 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Stochastic Differential Equations by : Michael J. Panik

Download or read book Stochastic Differential Equations written by Michael J. Panik and published by John Wiley & Sons. This book was released on 2017-04-03 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

Gibbs Measures In Biology And Physics: The Potts Model

Author : Utkir A Rozikov
Publisher : World Scientific
ISBN 13 : 9811251258
Total Pages : 367 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Gibbs Measures In Biology And Physics: The Potts Model by : Utkir A Rozikov

Download or read book Gibbs Measures In Biology And Physics: The Potts Model written by Utkir A Rozikov and published by World Scientific. This book was released on 2022-07-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

An Introduction to Structured Population Dynamics

Author : J. M. Cushing
Publisher : SIAM
ISBN 13 : 9781611970005
Total Pages : 106 pages
Book Rating : 4.9/5 (7 download)

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Book Synopsis An Introduction to Structured Population Dynamics by : J. M. Cushing

Download or read book An Introduction to Structured Population Dynamics written by J. M. Cushing and published by SIAM. This book was released on 1998-01-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Infinite Dimensional Analysis, Quantum Probability and Applications

Author : Luigi Accardi
Publisher : Springer Nature
ISBN 13 : 3031061705
Total Pages : 369 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Infinite Dimensional Analysis, Quantum Probability and Applications by : Luigi Accardi

Download or read book Infinite Dimensional Analysis, Quantum Probability and Applications written by Luigi Accardi and published by Springer Nature. This book was released on 2022-10-04 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more. By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.

Population Dynamics

Author : T. N. E. Greville
Publisher : Elsevier
ISBN 13 : 1483273814
Total Pages : 456 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Population Dynamics by : T. N. E. Greville

Download or read book Population Dynamics written by T. N. E. Greville and published by Elsevier. This book was released on 2014-05-12 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population Dynamics covers the proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison on June 19-21, 1972. The book focuses on the application of mathematics to the study of human population growth. The selection first offers information on population waves and the properties of a stochastic attraction model. Discussions focus on social distance, limiting behavior of the model, mathematical development, population increase and retirement pensions, natural periodicity in the demographic system, trends in generational stability, mobility in unstable populations, and the Easterlin effect. The text then takes a look at the sampling frame as a determinant of observed distributions of duration variables and comparison of alternative marriage models, including plausible marriage models, axioms for marriage functions, birth intervals, and computer simulation of prospective and interior birth interval lengths. The manuscript ponders on contraceptive impact over several generations, estimation of the risk of conception from censored data, and influence of cause of death structure on age-patterns of mortality. Topics include distributions of conception times, simulation of experiments, potential fertility of users, and length of protection. The selection is a valuable reference for researchers interested in population dynamics.

Mathematical Methods of Population Biology

Author : Frank Charles Hoppensteadt
Publisher : Cambridge University Press
ISBN 13 : 9780521282567
Total Pages : 162 pages
Book Rating : 4.2/5 (825 download)

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Book Synopsis Mathematical Methods of Population Biology by : Frank Charles Hoppensteadt

Download or read book Mathematical Methods of Population Biology written by Frank Charles Hoppensteadt and published by Cambridge University Press. This book was released on 1982-02-26 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to mathematical methods used in the study of population phenomena including models of total population and population age structure, models of random population events presented in terms of Markov chains, and methods used to uncover qualitative behavior of more complicated difference equations.

Theory of Nonlinear Age-Dependent Population Dynamics

Author : Glenn F. Webb
Publisher : CRC Press
ISBN 13 : 9780824772901
Total Pages : 312 pages
Book Rating : 4.7/5 (729 download)

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Book Synopsis Theory of Nonlinear Age-Dependent Population Dynamics by : Glenn F. Webb

Download or read book Theory of Nonlinear Age-Dependent Population Dynamics written by Glenn F. Webb and published by CRC Press. This book was released on 1985-01-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

mathematical population dynamics

Author : Ovide Arino
Publisher : CRC Press
ISBN 13 : 1000154254
Total Pages : 812 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis mathematical population dynamics by : Ovide Arino

Download or read book mathematical population dynamics written by Ovide Arino and published by CRC Press. This book was released on 2020-12-18 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.

The Basic Approach to Age-Structured Population Dynamics

Author : Mimmo Iannelli
Publisher : Springer
ISBN 13 : 9402411461
Total Pages : 350 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis The Basic Approach to Age-Structured Population Dynamics by : Mimmo Iannelli

Download or read book The Basic Approach to Age-Structured Population Dynamics written by Mimmo Iannelli and published by Springer. This book was released on 2017-08-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.

Stochastic Models for Structured Populations

Author : Sylvie Meleard
Publisher : Springer
ISBN 13 : 9783319217109
Total Pages : 0 pages
Book Rating : 4.2/5 (171 download)

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Book Synopsis Stochastic Models for Structured Populations by : Sylvie Meleard

Download or read book Stochastic Models for Structured Populations written by Sylvie Meleard and published by Springer. This book was released on 2015-09-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.

Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains

Author : Harkaran Singh
Publisher : CRC Press
ISBN 13 : 1351251694
Total Pages : 274 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains by : Harkaran Singh

Download or read book Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains written by Harkaran Singh and published by CRC Press. This book was released on 2018-12-07 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.

Algebraic Biology

Author : Katsuhisa Horimoto
Publisher : Springer Science & Business Media
ISBN 13 : 3540851003
Total Pages : 256 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Algebraic Biology by : Katsuhisa Horimoto

Download or read book Algebraic Biology written by Katsuhisa Horimoto and published by Springer Science & Business Media. This book was released on 2008-07-18 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Algebraic Biology, AB 2008, held at the Castle of Hagenberg, Austria in July 2008 as part of the RISC Summer 2008, organized by the Research Institute for Symbolic Computation. The 14 revised full papers presented together with 3 tutorial lectures were carefully reviewed and selected from 27 submissions. The conference is the interdisciplinary forum for the presentation of research on all aspects of applications of symbolic computation (computer algebra, computational logic, and related methods) to various issues in biology and life sciences as well as other problems in biology being approached with symbolic methods.

Population Dynamics and the Tribolium Model: Genetics and Demography

Author : Robert F. Costantino
Publisher : Springer
ISBN 13 : 9781461278238
Total Pages : 0 pages
Book Rating : 4.2/5 (782 download)

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Book Synopsis Population Dynamics and the Tribolium Model: Genetics and Demography by : Robert F. Costantino

Download or read book Population Dynamics and the Tribolium Model: Genetics and Demography written by Robert F. Costantino and published by Springer. This book was released on 2011-09-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of populations is becoming increasingly focused on dynamics. We believe there are two reasons for this trend. The ftrst is the impactof nonlinear dynamics with its exciting ideas and colorful language: bifurcations, domains of attraction, chaos, fractals, strange attractors. Complexity, which is so very much a part of biology, now seems to be also a part of mathematics. A second trend is the accessibility of the new concepts. Thebarriers tocommunicationbetween theoristandexperimentalistseemless impenetrable. The active participationofthe experimentalist means that the theory will obtain substance. Our role is the application of the theory of dynamics to the analysis ofbiological populations. We began our work early in 1979 by writing an ordinary differential equation for the rateofchange in adult numbers which was based on an equilibrium model proposed adecadeearlier. Duringthenextfewmonths weftlledournotebookswithstraightforward deductions from the model and its associated biological implications. Slowly, some of the biological observations were explained and papers followed on a variety of topics: genetic and demographic stability, stationary probability distributions for population size,population growth asabirth-deathprocess, natural selectionanddensity-dependent population growth, genetic disequilibrium, and the stationary stochastic dynamics of adult numbers.

Population Dynamics in Variable Environments

Author : Professor Shripad Tuljapurkar
Publisher : Springer
ISBN 13 : 9783642516535
Total Pages : 160 pages
Book Rating : 4.5/5 (165 download)

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Book Synopsis Population Dynamics in Variable Environments by : Professor Shripad Tuljapurkar

Download or read book Population Dynamics in Variable Environments written by Professor Shripad Tuljapurkar and published by Springer. This book was released on 2014-01-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gender-structured Population Modeling

Author : M. Iannelli
Publisher : SIAM
ISBN 13 : 0898715776
Total Pages : 186 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Gender-structured Population Modeling by : M. Iannelli

Download or read book Gender-structured Population Modeling written by M. Iannelli and published by SIAM. This book was released on 2005-04-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unified presentation of, and mathematical framework for, modeling population growth by couple formation, summarizing both past and present modeling results. It provides results on model analysis, gives an up-to-date review of mathematical demography, discusses numerical methods, and puts deterministic modeling of human populations into historical perspective.