On The Stochastic Modelling Of Reaction Diffusion Processes

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Stochastic Modelling Of Reaction Diffusion Processes

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Author : Radek Erban
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-30

Stochastic Modelling Of Reaction Diffusion Processes written by Radek Erban and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.

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

On The Stochastic Modelling Of Reaction Diffusion Processes

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Author :
language : en
Publisher:
Release Date : 2007

On The Stochastic Modelling Of Reaction Diffusion Processes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Chemical processes categories.

Stochastic Processes In Cell Biology

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Author : Paul C. Bressloff
language : en
Publisher: Springer Nature
Release Date : 2022-01-04

Stochastic Processes In Cell Biology written by Paul C. Bressloff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.

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.

Stochastic Dynamics In Computational Biology

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Author : Stefanie Winkelmann
language : en
Publisher: Springer Nature
Release Date : 2021-01-04

Stochastic Dynamics In Computational Biology written by Stefanie Winkelmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.

The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.

Spatial Dynamics And Pattern Formation In Biological Populations

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Author : Ranjit Kumar Upadhyay
language : en
Publisher: CRC Press
Release Date : 2021-02-23

Spatial Dynamics And Pattern Formation In Biological Populations written by Ranjit Kumar Upadhyay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Mathematics categories.

The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

Bioinformatics And Computational Biology

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Author : Tamer Aldwairi
language : en
Publisher: Springer Nature
Release Date : 2025-08-24

Bioinformatics And Computational Biology written by Tamer Aldwairi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-24 with Computers categories.

This book constitutes the refereed proceedings of the 17th International Conference on Bioinformatics and Computational Biology, BICOB 2025, held in San Francisco, CA, USA, on March 17, 2025. The 18 full papers presented in this book were carefully reviewed and selected from 38 submissions. The papers cover a wide range of bioinformatics and computational biology topics, including bioinformatics algorithms, genomics, machine learning applications in bioinformatics, and medical informatics.

Biological Modeling And Simulation

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Author : Russell Schwartz
language : en
Publisher: MIT Press
Release Date : 2008-07-25

Biological Modeling And Simulation written by Russell Schwartz and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-25 with Science categories.

A practice-oriented survey of techniques for computational modeling and simulation suitable for a broad range of biological problems. There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention has been paid to training aspiring computational biologists to handle new and unanticipated problems. This text is intended to fill that gap by teaching students how to reason about developing formal mathematical models of biological systems that are amenable to computational analysis. It collects in one place a selection of broadly useful models, algorithms, and theoretical analysis tools normally found scattered among many other disciplines. It thereby gives the aspiring student a bag of tricks that will serve him or her well in modeling problems drawn from numerous subfields of biology. These techniques are taught from the perspective of what the practitioner needs to know to use them effectively, supplemented with references for further reading on more advanced use of each method covered. The text, which grew out of a class taught at Carnegie Mellon University, covers models for optimization, simulation and sampling, and parameter tuning. These topics provide a general framework for learning how to formulate mathematical models of biological systems, what techniques are available to work with these models, and how to fit the models to particular systems. Their application is illustrated by many examples drawn from a variety of biological disciplines and several extended case studies that show how the methods described have been applied to real problems in biology.

Next Generation Data Science

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Author : Henry Han
language : en
Publisher: Springer Nature
Release Date : 2024-06-26

Next Generation Data Science written by Henry Han and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Computers categories.

This book constitutes the refereed proceedings of the Sescond Southwest Data Science Conference, SDSC 2023, held in Waco, TX, USa, during March 24-25, 2023. The 16 full and 1 short paper included in this book were carefully reviewed and selected from 72 submissions. They were oragnized in topical sections named: Business social and foundation data science; and applied data science, artifiicial intelligence and data engineering.

Simulation Algorithms For Computational Systems Biology

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Author : Luca Marchetti
language : en
Publisher: Springer
Release Date : 2017-09-27

Simulation Algorithms For Computational Systems Biology written by Luca Marchetti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-27 with Computers categories.

This book explains the state-of-the-art algorithms used to simulate biological dynamics. Each technique is theoretically introduced and applied to a set of modeling cases. Starting from basic simulation algorithms, the book also introduces more advanced techniques that support delays, diffusion in space, or that are based on hybrid simulation strategies. This is a valuable self-contained resource for graduate students and practitioners in computer science, biology and bioinformatics. An appendix covers the mathematical background, and the authors include further reading sections in each chapter.

Mathematical Methods For Cancer Evolution

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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2017-06-13

Mathematical Methods For Cancer Evolution written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-13 with Mathematics categories.

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.