Modelling with the Master Equation

Modelling with the Master Equation

Author: Günter Haag

Publisher: Springer

Published: 2017-07-31

Total Pages: 342

ISBN-13: 3319603000

DOWNLOAD EBOOK

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.


Book Synopsis Modelling with the Master Equation by : Günter Haag

Download or read book Modelling with the Master Equation written by Günter Haag and published by Springer. This book was released on 2017-07-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Interactive Macroeconomics

Author: Corrado Di Guilmi

Publisher: Cambridge University Press

Published: 2017-04-04

Total Pages: 307

ISBN-13: 1107198941

DOWNLOAD EBOOK

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


Book Synopsis Interactive Macroeconomics by : Corrado Di Guilmi

Download or read book Interactive Macroeconomics written by Corrado Di Guilmi and published by Cambridge University Press. This book was released on 2017-04-04 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the analysis of macroeconomic agent based models using the tools of statistical mechanics.

Chemical Master Equation for Large Biological Networks

Chemical Master Equation for Large Biological Networks

Author: Don Kulasiri

Publisher: Springer

Published: 2022-09-13

Total Pages: 0

ISBN-13: 9789811653537

DOWNLOAD EBOOK

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.


Book Synopsis Chemical Master Equation for Large Biological Networks by : Don Kulasiri

Download or read book Chemical Master Equation for Large Biological Networks written by Don Kulasiri and published by Springer. This book was released on 2022-09-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Master Equation and the Convergence Problem in Mean Field Games

Author: Pierre Cardaliaguet

Publisher: Princeton University Press

Published: 2019-08-13

Total Pages: 224

ISBN-13: 0691190712

DOWNLOAD EBOOK

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.


Book Synopsis The Master Equation and the Convergence Problem in Mean Field Games by : Pierre Cardaliaguet

Download or read book The Master Equation and the Convergence Problem in Mean Field Games written by Pierre Cardaliaguet and published by Princeton University Press. This book was released on 2019-08-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Statistical Methods in Quantum Optics 1

Statistical Methods in Quantum Optics 1

Author: Howard J. Carmichael

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 384

ISBN-13: 3662038757

DOWNLOAD EBOOK

This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.


Book Synopsis Statistical Methods in Quantum Optics 1 by : Howard J. Carmichael

Download or read book Statistical Methods in Quantum Optics 1 written by Howard J. Carmichael and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.

Chemical Master Equation for Large Biological Networks

Chemical Master Equation for Large Biological Networks

Author: Don Kulasiri

Publisher: Springer Nature

Published: 2021-09-12

Total Pages: 231

ISBN-13: 9811653518

DOWNLOAD EBOOK

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.


Book Synopsis Chemical Master Equation for Large Biological Networks by : Don Kulasiri

Download or read book Chemical Master Equation for Large Biological Networks written by Don Kulasiri and published by Springer Nature. This book was released on 2021-09-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Encyclopedia of Systems Biology

Encyclopedia of Systems Biology

Author: Werner Dubitzky

Publisher: Springer

Published: 2013-06-05

Total Pages: 0

ISBN-13: 9781441998620

DOWNLOAD EBOOK

Systems biology refers to the quantitative analysis of the dynamic interactions among several components of a biological system and aims to understand the behavior of the system as a whole. Systems biology involves the development and application of systems theory concepts for the study of complex biological systems through iteration over mathematical modeling, computational simulation and biological experimentation. Systems biology could be viewed as a tool to increase our understanding of biological systems, to develop more directed experiments, and to allow accurate predictions. The Encyclopedia of Systems Biology is conceived as a comprehensive reference work covering all aspects of systems biology, in particular the investigation of living matter involving a tight coupling of biological experimentation, mathematical modeling and computational analysis and simulation. The main goal of the Encyclopedia is to provide a complete reference of established knowledge in systems biology – a ‘one-stop shop’ for someone seeking information on key concepts of systems biology. As a result, the Encyclopedia comprises a broad range of topics relevant in the context of systems biology. The audience targeted by the Encyclopedia includes researchers, developers, teachers, students and practitioners who are interested or working in the field of systems biology. Keeping in mind the varying needs of the potential readership, we have structured and presented the content in a way that is accessible to readers from wide range of backgrounds. In contrast to encyclopedic online resources, which often rely on the general public to author their content, a key consideration in the development of the Encyclopedia of Systems Biology was to have subject matter experts define the concepts and subjects of systems biology.


Book Synopsis Encyclopedia of Systems Biology by : Werner Dubitzky

Download or read book Encyclopedia of Systems Biology written by Werner Dubitzky and published by Springer. This book was released on 2013-06-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems biology refers to the quantitative analysis of the dynamic interactions among several components of a biological system and aims to understand the behavior of the system as a whole. Systems biology involves the development and application of systems theory concepts for the study of complex biological systems through iteration over mathematical modeling, computational simulation and biological experimentation. Systems biology could be viewed as a tool to increase our understanding of biological systems, to develop more directed experiments, and to allow accurate predictions. The Encyclopedia of Systems Biology is conceived as a comprehensive reference work covering all aspects of systems biology, in particular the investigation of living matter involving a tight coupling of biological experimentation, mathematical modeling and computational analysis and simulation. The main goal of the Encyclopedia is to provide a complete reference of established knowledge in systems biology – a ‘one-stop shop’ for someone seeking information on key concepts of systems biology. As a result, the Encyclopedia comprises a broad range of topics relevant in the context of systems biology. The audience targeted by the Encyclopedia includes researchers, developers, teachers, students and practitioners who are interested or working in the field of systems biology. Keeping in mind the varying needs of the potential readership, we have structured and presented the content in a way that is accessible to readers from wide range of backgrounds. In contrast to encyclopedic online resources, which often rely on the general public to author their content, a key consideration in the development of the Encyclopedia of Systems Biology was to have subject matter experts define the concepts and subjects of systems biology.

Probabilistic Theory of Mean Field Games with Applications II

Probabilistic Theory of Mean Field Games with Applications II

Author: René Carmona

Publisher: Springer

Published: 2018-03-08

Total Pages: 700

ISBN-13: 3319564366

DOWNLOAD EBOOK

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.


Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona and published by Springer. This book was released on 2018-03-08 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Identifiability and Regression Analysis of Biological Systems Models

Identifiability and Regression Analysis of Biological Systems Models

Author: Paola Lecca

Publisher: Springer Nature

Published: 2020-03-05

Total Pages: 90

ISBN-13: 3030412555

DOWNLOAD EBOOK

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.


Book Synopsis Identifiability and Regression Analysis of Biological Systems Models by : Paola Lecca

Download or read book Identifiability and Regression Analysis of Biological Systems Models written by Paola Lecca and published by Springer Nature. This book was released on 2020-03-05 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modelling Degradation of Bioresorbable Polymeric Medical Devices

Modelling Degradation of Bioresorbable Polymeric Medical Devices

Author: J Pan

Publisher: Elsevier

Published: 2014-10-24

Total Pages: 271

ISBN-13: 1782420258

DOWNLOAD EBOOK

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


Book Synopsis Modelling Degradation of Bioresorbable Polymeric Medical Devices by : J Pan

Download or read book Modelling Degradation of Bioresorbable Polymeric Medical Devices written by J Pan and published by Elsevier. This book was released on 2014-10-24 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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