Stochastic Modelling of Reaction–Diffusion Processes PDF Download

Author: Radek Erban
Publisher: Cambridge University Press
ISBN: 1108572995
Category : Mathematics
Languages : en
Pages : 322

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Book Description
This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Author: Radek Erban
Publisher: Cambridge University Press
ISBN: 1108498124
Category : Mathematics
Languages : en
Pages : 321

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Book Description
Practical introduction for advanced undergraduate or beginning graduate students of applied mathematics, developed at the University of Oxford.

Author: Paola Lecca
Publisher: Elsevier
ISBN: 1908818212
Category : Mathematics
Languages : en
Pages : 411

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Book Description
Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples Presents recently developed discrete stochastic formalisms for modelling biological systems and processes Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

Author: Christiane Fuchs
Publisher: Springer Science & Business Media
ISBN: 3642259693
Category : Mathematics
Languages : en
Pages : 439

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Book Description
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.

Author: Kurt Jacobs
Publisher: Cambridge University Press
ISBN: 1139486799
Category : Science
Languages : en
Pages : 203

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Book Description
Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

Author: Paul C. Bressloff
Publisher: Springer Nature
ISBN: 3030725154
Category : Mathematics
Languages : en
Pages : 773

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Book Description
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.

Author: Howard M. Taylor
Publisher: Academic Press
ISBN: 1483269272
Category : Mathematics
Languages : en
Pages : 410

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Book Description
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.

Author: Darren J. Wilkinson
Publisher: CRC Press
ISBN: 1351000896
Category : Mathematics
Languages : en
Pages : 366

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Book Description
Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book. New in the Third Edition New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC Updated R package, including code relating to all of the new material New R package for parsing SBML models into simulatable stochastic Petri net models New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

Author: Péter Érdi
Publisher: Manchester University Press
ISBN: 9780719022081
Category : Science
Languages : en
Pages : 296

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Book Description

Author: Richard Durrett
Publisher: Springer
ISBN: 3319456148
Category : Mathematics
Languages : en
Pages : 282

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Book Description
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.