Population Dynamics: Algebraic And Probabilistic Approach
Population Dynamics: Algebraic And Probabilistic Approach

Author: Utkir A Rozikov

Publisher: World Scientific

Published: 2020-04-22

Total Pages: 458

ISBN-13: 9811211248

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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.

Infinite Dimensional Analysis, Quantum Probability and Applications
Infinite Dimensional Analysis, Quantum Probability and Applications

Author: Luigi Accardi

Publisher: Springer Nature

Published: 2022-10-04

Total Pages: 369

ISBN-13: 3031061705

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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.

Gibbs Measures In Biology And Physics: The Potts Model
Gibbs Measures In Biology And Physics: The Potts Model

Author: Utkir A Rozikov

Publisher: World Scientific

Published: 2022-07-28

Total Pages: 367

ISBN-13: 9811251258

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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.

Algebraic Biology
Algebraic Biology

Author: Katsuhisa Horimoto

Publisher: Springer

Published: 2008-07-30

Total Pages: 256

ISBN-13: 3540851011

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This volume contains the proceedings of the Third International Conference on Algebraic Biology (AB 2008). Jointly organized by the National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, and the Research Institute for Symbolic Computation (RISC), Hagenberg, Austria, it was held from July 31 to August 2, 2008 in the Castle of Hagenberg. Algebraic biology is an interdisciplinary forum for research on all aspects of applying symbolic computation in biology. The ?rst conference on algebraic biology (AB 2005) was held November 28–30, 2005 in Tokyo, the second during July 2–4, 2007 in Hagenberg. The AB conference series is intended as a bridge between life sciences and symbolic computation: On the one hand, new insights inbiologyarefoundbypowerfulsymbolicmethods;ontheotherhand,biological problems suggestnew algebraicstructures andalgorithms.While this pro?le has been established in the previous proceedings, the papers in the present volume demonstrate the continuous growth of algebraic biology. We received 27 submissions from 14 countries (Australia, Austria, Canada, China, Colombia, France, Germany, Italy, Japan, Norway, Russia, Switzerland, UK, USA), and 14 papers were accepted for publication. Each submission was assigned to at least three ProgramCommittee members, who carefully reviewed the papers, in many cases with the help of external referees. The reviews were discussedby the ProgramCommittee for oneweekvia the EasyChairconference management system.

Stochastic Processes
Stochastic Processes

Author: Pierre Del Moral

Publisher: CRC Press

Published: 2017-02-24

Total Pages: 1026

ISBN-13: 1498701868

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Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

A Short History of Mathematical Population Dynamics
A Short History of Mathematical Population Dynamics

Author: Nicolas Bacaër

Publisher: Springer Science & Business Media

Published: 2011-02-01

Total Pages: 160

ISBN-13: 0857291157

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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.

Software Engineering and Formal Methods
Software Engineering and Formal Methods

Author: Carlos Canal

Publisher: Springer

Published: 2015-01-31

Total Pages: 426

ISBN-13: 3319152017

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This book constitutes revised selected papers from the workshops collocated with the SEFM 2014 conference on Software Engineering and Formal Methods, held in Grenoble, France, in September 2014. The 26 papers included in this volume were carefully reviewed and selected from 49 submissions. They are from the following workshops: the 1st Workshop on Human-Oriented Formal Methods - From Readability to Automation, HOFM 2014, the 3rd International Symposium on Modelling and Knowledge Management Applications - Systems and Domains, MoKMaSD 2014, the 8th International Workshop on Foundations and Techniques for Open Source Software Certification, Open Cert 2014, the 1st Workshop on Safety and Formal Methods, SaFoMe 2014 and the 4th Workshop on Formal Methods in the Development of Software, WS-FMDS 2014.

Sensitivity Analysis: Matrix Methods in Demography and Ecology
Sensitivity Analysis: Matrix Methods in Demography and Ecology

Author: Hal Caswell

Publisher: Springer

Published: 2019-04-02

Total Pages: 308

ISBN-13: 3030105342

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This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.