Modelling With The Master Equation

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Modelling with the Master Equation

Günter Haag
Modelling with the Master Equation Book PDF

Author : Günter Haag
Publisher : Springer
Page : 342 pages
File Size : 49,6 Mb
Release : 2017-07-31
Category : Social Science
ISBN : 9783319603001

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Modelling with the Master Equation by Günter Haag Pdf

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

Interactive Macroeconomics

Corrado Di Guilmi,Mauro Gallegati,Simone Landini
Interactive Macroeconomics Book PDF

Author : Corrado Di Guilmi,Mauro Gallegati,Simone Landini
Publisher : Cambridge University Press
Page : 307 pages
File Size : 46,9 Mb
Release : 2017-04-04
Category : Business & Economics
ISBN : 9781107198944

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Interactive Macroeconomics by Corrado Di Guilmi,Mauro Gallegati,Simone Landini Pdf

This book describes the analysis of macroeconomic agent based models using the tools of statistical mechanics.

Chemical Master Equation for Large Biological Networks

Don Kulasiri,Rahul Kosarwal
Chemical Master Equation for Large Biological Networks Book PDF

Author : Don Kulasiri,Rahul Kosarwal
Publisher : Springer
Page : 0 pages
File Size : 50,6 Mb
Release : 2022-09-13
Category : Science
ISBN : 9811653534

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Chemical Master Equation for Large Biological Networks by Don Kulasiri,Rahul Kosarwal Pdf

This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.

Chemical Master Equation for Large Biological Networks

Don Kulasiri,Rahul Kosarwal
Chemical Master Equation for Large Biological Networks Book PDF

Author : Don Kulasiri,Rahul Kosarwal
Publisher : Springer Nature
Page : 231 pages
File Size : 42,5 Mb
Release : 2021-09-12
Category : Science
ISBN : 9789811653513

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Chemical Master Equation for Large Biological Networks by Don Kulasiri,Rahul Kosarwal Pdf

This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.

The Master Equation and the Convergence Problem in Mean Field Games

Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
The Master Equation and the Convergence Problem in Mean Field Games Book PDF

Author : Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
Publisher : Princeton University Press
Page : 224 pages
File Size : 46,7 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9780691190716

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The Master Equation and the Convergence Problem in Mean Field Games by Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions Pdf

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Modelling Degradation of Bioresorbable Polymeric Medical Devices

J Pan
Modelling Degradation of Bioresorbable Polymeric Medical Devices Book PDF

Author : J Pan
Publisher : Elsevier
Page : 260 pages
File Size : 42,9 Mb
Release : 2014-10-24
Category : Technology & Engineering
ISBN : 9781782420255

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Modelling Degradation of Bioresorbable Polymeric Medical Devices by J Pan Pdf

The use of bioresorbable polymers in stents, fixation devices and tissue engineering is revolutionising medicine. Both industry and academic researchers are interested in using computer modelling to replace some experiments which are costly and time consuming. This book provides readers with a comprehensive review of modelling polymers and polymeric medical devices as an alternative to practical experiments. Chapters in part one provide readers with an overview of the fundamentals of biodegradation. Part two looks at a wide range of degradation theories for bioresorbable polymers and devices. The final set of chapters look at advances in modelling biodegradation of bioresorbable polymers. This book is an essential guide to those concerned with replacing tests and experiments with modelling. Provides a comprehensive mathematical framework for computer modelling of polymers and polymeric medical devices that can significantly reduce the number of experiments needed. Reviews the fundamental methods of modelling degradation, and applies these to particular materials including amorphous bioresorbable polyesters, semicrystalline biodegradable polyesters, and composite materials made of biodegradable polyesters and triclcium phosphates

Identifiability and Regression Analysis of Biological Systems Models

Paola Lecca
Identifiability and Regression Analysis of Biological Systems Models Book PDF

Author : Paola Lecca
Publisher : Springer Nature
Page : 90 pages
File Size : 51,8 Mb
Release : 2020-03-05
Category : Medical
ISBN : 9783030412555

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Identifiability and Regression Analysis of Biological Systems Models by Paola Lecca Pdf

This richly illustrated book presents the objectives of, and the latest techniques for, the identifiability analysis and standard and robust regression analysis of complex dynamical models. The book first provides a definition of complexity in dynamic systems by introducing readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature of determination. In turn, it presents the mathematical foundations of and algorithmic procedures for model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection. Although the main fields of application discussed in the book are biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to deal with problems such as determining the identifiability conditions, searching for an identifiable model, and conducting their own regression analysis and diagnostics without supervision. Featuring a wealth of real-world examples, exercises, and codes in R, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Readers should be familiar with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R.

Master Equation Models of Macromolecular Dynamics from Atomistic Simulation

John D. Chodera
Master Equation Models of Macromolecular Dynamics from Atomistic Simulation Book PDF

Author : John D. Chodera
Publisher : Unknown
Page : 324 pages
File Size : 41,7 Mb
Release : 2006
Category : Electronic
ISBN : UCAL:X85387

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Master Equation Models of Macromolecular Dynamics from Atomistic Simulation by John D. Chodera Pdf

This dissertation is concerned with the construction, validation, and use of master equation models for the study of macromolecular conformational dynamics. The master equation formalism is a powerful tool for describing the dynamics of a system that can be characterized by a discrete-state, continuous-time Markov process. Once constructed from a large quantities of short trajectories, the evolution of experimentally measurable dynamical observables can be computed and compared with experiment. Additionally, information not yet directly accessible to experiment but which may be useful in aiding understanding or the generation of novel hypotheses, such as folding pathways, transiently populated conformations, and mean first passage times, can also be easily obtained. We demonstrate that a master equation model constructed from short trajectories can describe slow conformational dynamics for a solvated alanine peptide over long times, propose a number of tests to tell whether a model constructed from short trajectories will adequately describe dynamics over long times, and describe an algorithm for the automatic construction of these models from simulation data. While the focus here is on protein folding and dynamics, these techniques are very general, and can be broadly applied to problems in biomolecular dynamics.

Nonlinear Economic Dynamics and Financial Modelling

Roberto Dieci,Xue-Zhong He,Cars Hommes
Nonlinear Economic Dynamics and Financial Modelling Book PDF

Author : Roberto Dieci,Xue-Zhong He,Cars Hommes
Publisher : Springer
Page : 389 pages
File Size : 50,5 Mb
Release : 2014-07-26
Category : Business & Economics
ISBN : 9783319074702

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Nonlinear Economic Dynamics and Financial Modelling by Roberto Dieci,Xue-Zhong He,Cars Hommes Pdf

This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly rational heterogeneous agents to estimation, time series modelling and empirical analysis and from risk management of interest-rate products, futures price volatility and American option pricing with stochastic volatility to evaluation of risk and derivatives of electricity market. The book illustrates some of the most recent research tools in these areas and will be of interest to economists working in economic dynamics and financial market modelling, to mathematicians who are interested in applying complexity theory to economics and finance and to market practitioners and researchers in quantitative finance interested in limit order, futures and electricity market modelling, derivative pricing and risk management.

Probabilistic Theory of Mean Field Games with Applications II

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications II Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 700 pages
File Size : 40,7 Mb
Release : 2018-03-08
Category : Mathematics
ISBN : 9783319564364

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Probabilistic Theory of Mean Field Games with Applications II by René Carmona,François Delarue Pdf

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Single-Cell-Based Models in Biology and Medicine

Alexander Anderson,Katarzyna Rejniak
Single Cell Based Models in Biology and Medicine Book PDF

Author : Alexander Anderson,Katarzyna Rejniak
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 54,5 Mb
Release : 2007-08-08
Category : Mathematics
ISBN : 9783764381233

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Single-Cell-Based Models in Biology and Medicine by Alexander Anderson,Katarzyna Rejniak Pdf

Aimed at postgraduate students in a variety of biology-related disciplines, this volume presents a collection of mathematical and computational single-cell-based models and their application. The main sections cover four general model groupings: hybrid cellular automata, cellular potts, lattice-free cells, and viscoelastic cells. Each section is introduced by a discussion of the applicability of the particular modelling approach and its advantages and disadvantages, which will make the book suitable for students starting research in mathematical biology as well as scientists modelling multicellular processes.

Stochastic Modelling for Systems Biology

Darren J. Wilkinson
Stochastic Modelling for Systems Biology Book PDF

Author : Darren J. Wilkinson
Publisher : CRC Press
Page : 296 pages
File Size : 44,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 1584885408

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Stochastic Modelling for Systems Biology by Darren J. Wilkinson Pdf

Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective. Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modelling using examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications. While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source.

Simple Mathematical Models of Gene Regulatory Dynamics

Michael C. Mackey,Moisés Santillán,Marta Tyran-Kamińska,Eduardo S. Zeron
Simple Mathematical Models of Gene Regulatory Dynamics Book PDF

Author : Michael C. Mackey,Moisés Santillán,Marta Tyran-Kamińska,Eduardo S. Zeron
Publisher : Springer
Page : 124 pages
File Size : 55,7 Mb
Release : 2016-11-09
Category : Medical
ISBN : 9783319453187

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Simple Mathematical Models of Gene Regulatory Dynamics by Michael C. Mackey,Moisés Santillán,Marta Tyran-Kamińska,Eduardo S. Zeron Pdf

This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduates students and young researchers with a solid mathematical background (calculus, ordinary differential equations, and probability theory at a minimum), as well as with basic notions of biochemistry, cell biology, and molecular biology. They are meant to serve as a readable and brief entry point into a field that is currently highly active, and will allow the reader to grasp the current state of research and so prepare them for defining and tackling new research problems.

New Approaches to Macroeconomic Modeling

Masanao Aoki
New Approaches to Macroeconomic Modeling Book PDF

Author : Masanao Aoki
Publisher : Cambridge University Press
Page : 312 pages
File Size : 55,9 Mb
Release : 1998-02-13
Category : Business & Economics
ISBN : 0521637694

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New Approaches to Macroeconomic Modeling by Masanao Aoki Pdf

This book provides a method for modeling large collections of heterogeneous agents subject to non-pairwise externality called field effects.

Decoherence

Maximilian Schlosshauer
Decoherence Book PDF

Author : Maximilian Schlosshauer
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 42,8 Mb
Release : 2007
Category : Computers
ISBN : 9783540357735

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Decoherence by Maximilian Schlosshauer Pdf

This detailed, accessible introduction to the field of quantum decoherence reviews the basics and then explains the essential consequences of the phenomenon for our understanding of the world. The discussion includes, among other things: How the classical world of our experience can emerge from quantum mechanics; the implications of decoherence for various interpretations of quantum mechanics; recent experiments confirming the puzzling consequences of the quantum superposition principle and making decoherence processes directly observable.