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Modelling With The Master Equation
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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.
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.
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.
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.
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.
Book Synopsis The Theory of Open Quantum Systems by : Heinz-Peter Breuer
Download or read book The Theory of Open Quantum Systems written by Heinz-Peter Breuer and published by Oxford University Press, USA. This book was released on 2002 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.
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 260 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
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.
Book Synopsis Master Equation Models of Macromolecular Dynamics from Atomistic Simulation by : John D. Chodera
Download or read book Master Equation Models of Macromolecular Dynamics from Atomistic Simulation written by John D. Chodera and published by . This book was released on 2006 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Economic Dynamics and Financial Modelling by : Roberto Dieci
Download or read book Nonlinear Economic Dynamics and Financial Modelling written by Roberto Dieci and published by Springer. This book was released on 2014-07-26 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Single-Cell-Based Models in Biology and Medicine by : Alexander Anderson
Download or read book Single-Cell-Based Models in Biology and Medicine written by Alexander Anderson and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Modelling for Systems Biology by : Darren J. Wilkinson
Download or read book Stochastic Modelling for Systems Biology written by Darren J. Wilkinson and published by CRC Press. This book was released on 2006-04-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Simple Mathematical Models of Gene Regulatory Dynamics by : Michael C. Mackey
Download or read book Simple Mathematical Models of Gene Regulatory Dynamics written by Michael C. Mackey and published by Springer. This book was released on 2016-11-09 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Composite-Based Structural Equation Modeling by : Jörg Henseler
Download or read book Composite-Based Structural Equation Modeling written by Jörg Henseler and published by Guilford Publications. This book was released on 2020-12-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Approaches to Macroeconomic Modeling by : Masanao Aoki
Download or read book New Approaches to Macroeconomic Modeling written by Masanao Aoki and published by Cambridge University Press. This book was released on 1998-02-13 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a method for modeling large collections of heterogeneous agents subject to non-pairwise externality called field effects.
Author :Maximilian Schlosshauer Publisher :Springer Science & Business Media ISBN 13 :3540357734 Total Pages :428 pages Book Rating :4.5/5 (43 download)
Book Synopsis Decoherence by : Maximilian Schlosshauer
Download or read book Decoherence written by Maximilian Schlosshauer and published by Springer Science & Business Media. This book was released on 2007 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantitative Sociodynamics by : D. Helbing
Download or read book Quantitative Sociodynamics written by D. Helbing and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the logistic equation, the gravity model, some diffusion models, the evolutionary game theory and the social field theory, but it also implies numerous new results. Examples concerning opinion formation, migration, social field theory; the self-organization of behavioural conventions as well as the behaviour of customers and voters are presented and illustrated by computer simulations. Quantitative Sociodynamics is relevant both for social scientists and natural scientists who are interested in the application of stochastic and synergetics concepts to interdisciplinary topics.
