[PDF] Modelling With The Master Equation eBook

Author : Günter Haag
Publisher : Springer
Page : 355 pages
File Size : 45,72 MB
Release : 2017-07-31
Category : Social Science
ISBN : 3319603000

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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.

Author : Don Kulasiri
Publisher : Springer
Page : 0 pages
File Size : 39,95 MB
Release : 2022-09-13
Category : Science
ISBN : 9789811653537

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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.

Author : Corrado Di Guilmi
Publisher : Cambridge University Press
Page : 307 pages
File Size : 45,8 MB
Release : 2017-04-04
Category : Business & Economics
ISBN : 1107198941

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

Author : Howard J. Carmichael
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 18,96 MB
Release : 2013-04-17
Category : Science
ISBN : 3662038757

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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.

Author : John D. Chodera
Publisher :
Page : 324 pages
File Size : 46,81 MB
Release : 2006
Category :
ISBN :

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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.

Author : Pierre Cardaliaguet
Publisher : Princeton University Press
Page : 224 pages
File Size : 32,57 MB
Release : 2019-08-13
Category : Mathematics
ISBN : 0691190712

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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.

Author : Don Kulasiri
Publisher : Springer Nature
Page : 231 pages
File Size : 34,88 MB
Release : 2021-09-12
Category : Science
ISBN : 9811653518

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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.

Author : Jörg Henseler
Publisher : Guilford Publications
Page : 387 pages
File Size : 10,68 MB
Release : 2020-12-24
Category : Social Science
ISBN : 1462545610

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This book presents powerful tools for integrating interrelated composites--such as capabilities, policies, treatments, indices, and systems--into structural equation modeling (SEM). Jörg Henseler introduces the types of research questions that can be addressed with composite-based SEM and explores the differences between composite- and factor-based SEM, variance- and covariance-based SEM, and emergent and latent variables. Using rich illustrations and walked-through data sets, the book covers how to specify, identify, estimate, and assess composite models using partial least squares path modeling, maximum likelihood, and other estimators, as well as how to interpret findings and report the results. Advanced topics include confirmatory composite analysis, mediation analysis, second-order constructs, interaction effects, and importance–performance analysis. Most chapters conclude with software tutorials for ADANCO and the R package cSEM. The companion website includes data files and syntax for the book's examples, along with presentation slides.