Stochastic Modelling of Reaction–Diffusion Processes

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Publisher : Cambridge University Press
ISBN 13 : 1108572995
Total Pages : 322 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Stochastic Modelling of Reaction–Diffusion Processes by : Radek Erban

Download or read book Stochastic Modelling of Reaction–Diffusion Processes written by Radek Erban and published by Cambridge University Press. This book was released on 2020-01-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Integral And Differential Equations In Mathematical Modelling

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Publisher : World Scientific
ISBN 13 : 1800613598
Total Pages : 319 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Stochastic Integral And Differential Equations In Mathematical Modelling by : Santanu Saha Ray

Download or read book Stochastic Integral And Differential Equations In Mathematical Modelling written by Santanu Saha Ray and published by World Scientific. This book was released on 2023-04-25 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes — either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.

Dissertation Abstracts International

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Publisher :
ISBN 13 :
Total Pages : 820 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Dissertation Abstracts International by :

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2001 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines

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Publisher : Springer Nature
ISBN 13 : 9811965536
Total Pages : 312 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines by : Jamal Amani Rad

Download or read book Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines written by Jamal Amani Rad and published by Springer Nature. This book was released on 2023-03-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions—Chebyshev, Legendre, Gegenbauer, and Jacobi—are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

American Doctoral Dissertations

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Publisher :
ISBN 13 :
Total Pages : 816 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis American Doctoral Dissertations by :

Download or read book American Doctoral Dissertations written by and published by . This book was released on 2000 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

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Publisher :
ISBN 13 :
Total Pages : 704 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Time-Fractional Order Biological Systems with Uncertain Parameters

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Publisher : Springer Nature
ISBN 13 : 3031024230
Total Pages : 144 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Time-Fractional Order Biological Systems with Uncertain Parameters by : Snehashish Chakraverty

Download or read book Time-Fractional Order Biological Systems with Uncertain Parameters written by Snehashish Chakraverty and published by Springer Nature. This book was released on 2022-06-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, λμ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters. However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge. In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.

Splitting Methods for Partial Differential Equations with Rough Solutions

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Publisher : European Mathematical Society
ISBN 13 : 9783037190784
Total Pages : 238 pages
Book Rating : 4.1/5 (97 download)

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Book Synopsis Splitting Methods for Partial Differential Equations with Rough Solutions by : Helge Holden

Download or read book Splitting Methods for Partial Differential Equations with Rough Solutions written by Helge Holden and published by European Mathematical Society. This book was released on 2010 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated Web page that provides MATLABR codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

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Publisher : Springer
ISBN 13 : 3319626272
Total Pages : 377 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology by : David Holcman

Download or read book Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology written by David Holcman and published by Springer. This book was released on 2017-10-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Random Partial Differential Equations

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Publisher : Birkhäuser
ISBN 13 : 3034864132
Total Pages : 168 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Random Partial Differential Equations by : HORNUNG

Download or read book Random Partial Differential Equations written by HORNUNG and published by Birkhäuser. This book was released on 2013-11-22 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Modeling of Genetic and Biochemical Networks

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Publisher : MIT Press
ISBN 13 : 9780262524230
Total Pages : 386 pages
Book Rating : 4.5/5 (242 download)

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Book Synopsis Computational Modeling of Genetic and Biochemical Networks by : James M. Bower

Download or read book Computational Modeling of Genetic and Biochemical Networks written by James M. Bower and published by MIT Press. This book was released on 2001 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: How new modeling techniques can be used to explore functionally relevant molecular and cellular relationships.

Bayesian Time Series Models

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Publisher : Cambridge University Press
ISBN 13 : 0521196760
Total Pages : 432 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Bayesian Time Series Models by : David Barber

Download or read book Bayesian Time Series Models written by David Barber and published by Cambridge University Press. This book was released on 2011-08-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.

Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations

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Publisher : Frontiers Media SA
ISBN 13 : 2832514588
Total Pages : 209 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations by : André H. Erhardt

Download or read book Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations written by André H. Erhardt and published by Frontiers Media SA. This book was released on 2023-02-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Processes in Cell Biology

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Publisher : Springer
ISBN 13 : 3319084887
Total Pages : 688 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Stochastic Processes in Cell Biology by : Paul C. Bressloff

Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer. This book was released on 2014-08-22 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily aimed at graduate students and researchers working in mathematical biology and applied mathematicians interested in stochastic modeling. Applied probabilists and theoretical physicists should also find it of interest. It assumes no prior background in statistical physics and introduces concepts in stochastic 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.

First Congress of Greek Mathematicians

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110663074
Total Pages : 286 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis First Congress of Greek Mathematicians by : Ioannis Emmanouil

Download or read book First Congress of Greek Mathematicians written by Ioannis Emmanouil and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-03-23 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interesting collection of up-to-date survey articles on various topics of current mathematical research presents extended versions of the plenary talks given by important Greek mathematicians at the congress held in Athens, Greece, on occasion of the celebration for the 100 years of the Hellenic Mathematical Society.

High-Performance Computing and Big Data Analysis

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Publisher : Springer Nature
ISBN 13 : 3030334953
Total Pages : 520 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis High-Performance Computing and Big Data Analysis by : Lucio Grandinetti

Download or read book High-Performance Computing and Big Data Analysis written by Lucio Grandinetti and published by Springer Nature. This book was released on 2019-10-19 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised and selected papers from the Second International Congress on High-Performance Computing and Big Data Analysis, TopHPC 2019, held in Tehran, Iran, in April 2019. The 37 full papers and 2 short papers presented in this volume were carefully reviewed and selected from a total of 103 submissions. The papers in the volume are organized acording to the following topical headings: deep learning; big data analytics; Internet of Things.- data mining, neural network and genetic algorithms; performance issuesand quantum computing.

The Directory of Graduate Studies

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Publisher :
ISBN 13 :
Total Pages : 1876 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Directory of Graduate Studies by :

Download or read book The Directory of Graduate Studies written by and published by . This book was released on 1999 with total page 1876 pages. Available in PDF, EPUB and Kindle. Book excerpt: