Matrix-analytic Methods in Stochastic Models

Describing the processes in stars which produce the chemical elements for planets and life, this book shows how similar processes may be reproduced in laboratories using exotic beams, and how these results can be analyzed. Beginning with one-channel scattering theory, the book builds up to multi-channel reactions. Emphasis is placed on using transfer and breakup reactions to probe structure and predict capture processes, as well as R-matrix methods for modeling compound nucleus dynamics described by Hauser-Feshbach methods. Practical applications are prominent in this book, confronting theory predictions with data throughout. The associated reaction program Fresco is described, allowing readers to apply the methods to practical cases. Each chapter ends with exercises so readers can test their understanding of the materials covered. Supplementary materials at www.cambridge.org/9780521856355 include the Fresco program, input and output files for the examples given in the book, and hints

Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distributions of unobserved random variables. Often, it is

The authoritative reference on NEURON, the simulation environment for modeling biological neurons and neural networks that enjoys wide use in the experimental and computational neuroscience communities. This book shows how to use NEURON to construct and apply empirically based models. Written primarily for neuroscience investigators, teachers, and students, it assumes no previous knowledge of computer programming or numerical methods. Readers with a background in the physical sciences or mathematics, who have some knowledge about brain cells and circuits and are interested in computational modeling, will also find it helpful. The NEURON Book covers material that ranges from the inner workings of this program, to practical considerations involved in specifying the anatomical and biophysical properties that are to be represented in models. It uses a problem-solving approach, with many working examples that readers can try for themselves.

First published in 1961, this book gives an account of the theory of the physical properties of the ions of metals having partly filled d shells in some or all of their compounds. It concentrates on non-cooperative phenomena, such as paramagnetism and single optical spectra, but a study of the theory is also desirable to an understanding of cooperative phenomena, such as ferro- and anti-ferro-magnetism. The extensive development and use of techniques in the theory of finite groups and their matrix representations is noteworthy. It leads to simple methods of deducing many known and new results and to the formulation of general theorems. While the book will be of interest primarily to mathematical physicists and theoretical chemists, the large amount of data in it, including 80 tables, will make it a valuable reference book for inorganic and physical chemists, biochemists and experimental physicists.

First published in 1985, this book provides the psychiatrist with a basic knowledge of the methods and concepts used in the sphere of artificial intelligence. The techniques not only involve building models of the mind (and hence aid hypothesis testing) but also incorporate programs to assist the everyday work of psychiatrists. Knowledge representation, natural language understanding, search and planning, computer-assisted diagnosis, simulation and teaching are discussed. Enough basic theory is outlined to enable readers to understand and to carry out research in the area and to take part in the major ethical debate which will affect the direction of research in the area.

Are you involved in designing the next generation of wireless networks? With spectrum becoming an ever scarcer resource, it is critical that new systems utilize all available frequency bands as efficiently as possible. The revolutionary technology presented in this book will be at the cutting edge of future wireless communications. Dynamic Spectrum Access and Management in Cognitive Radio Networks provides you with an all-inclusive introduction to this emerging technology, outlining the fundamentals of cognitive radio-based wireless communication and networking, spectrum sharing models, and the requirements for dynamic spectrum access. In addition to the different techniques and their applications in designing dynamic spectrum access methods, you'll also find state-of-the-art dynamic spectrum access schemes, including classifications of the different schemes and the technical details of each scheme. This is a perfect introduction for graduate students and researchers, as well as a usef

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. This second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Structural Modeling by Example offers a comprehensive overview of the application of structural equation models in the social and behavioural sciences and in educational research. It is devoted in roughly equal proportions to substantive issues and to methodological ones. The substantive section comprises case studies of the use of these models in a number of disciplines. The authors emphasize the reasons for modeling by these methods, the processes involved in defining the model, and the interpretation of the results. Each substantive chapter includes an exemplary data set and formal model construction of give readers practice in setting up the models and interpreting the results. The methodological section comprises investigations of the behaviour of structural equation modeling methods under a number of conditions. The aim is to clarify the situations in which these methods can usefully be applied and the interpretations that can be made.

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. This second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

How can we make sure that the software we build does what it is supposed to? This book provides an insight into established techniques which help developers to overcome the complexity of software development by constructing models of software systems in early design stages. It uses one of the leading formal methods, VDM (Vienna Development Method), and combines training in the formalism with industry-strength tool support and examples derived from real industrial applications. The principles taught here also apply to many of the current generation of formal methods. This second edition has been updated to include advanced online tool support for formal modelling as well as up-to-date reports on real commercial applications in areas as diverse as business information systems and firmware design.

Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.

When we do something as apparently simple as sketching a map, constructing a working diagram, or drawing an imaginary face to amuse ourselves, we utilise a complex set of abilities: perceptual, mechanical, strategic, representational, pragmatic. Peter van Sommers sets out to distinguish and describe the various layers of organisation in the drawing performances of ordinary people - adults and children. Drawings, like language, have a multi-layered structure. Because much of the structure represents tacit knowledge, a variety of special observational and analytic methods must be developed to provide a comprehensive empirical account of graphic production. This book illuminates the link between laboratory methods and the study of an important skill exercised in the real world. It will be of interest to a wide range of cognitive psychologists as well as to many neuropsychologists and others concerned with art, aesthetics, writing and script evolution.

The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of Sequences by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to research workers or graduate students in number theory.

This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modelling, and the pitfalls. The discussion shows you how to think about the critical issues - including the connection (or lack of it) between the statistical models and the real phenomena. The book is written for advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences.

This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modelling, and the pitfalls. The discussion shows you how to think about the critical issues - including the connection (or lack of it) between the statistical models and the real phenomena. The book is written for advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences.

Reveals How HMMs Can Be Used as General-Purpose Time Series ModelsImplements all methods in RHidden Markov Models for Time Series: An Introduction Using R applies hidden Markov models (HMMs) to a wide

This book presents a new computational approach to solving large-scale Auerbach-Kotlikoff Overlapping Generations (OLG) models in a complementarity format. Unlike with integrated solution methods, the

Weeds are a major constraint to agricultural production, particularly in the developing world. Cost-efficient biological control is a self-sustaining way to reduce this problem, and produces fewer non-target effects than chemical methods, which can cause serious damage to the environment. This book covers the origin, distribution, and ecology of twenty model invasive weed species, which occur in habitats from tropical to temperate to aquatic. Sustainable biological control of each weed using one or more arthropods is discussed. The aim is to provide ecological management models for use across the tropical world, and to assist in the assessment of potential risks to native and economic plants. This is a valuable resource for scientists and policy makers concerned with the biological control of invasive tropical plants.

This rigourous and self-contained book describes mathematical and, in particular, stochastic methods to assess the performance of networked systems. It consists of three parts. The first part is a review on probability theory. Part two covers the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory), which are considered to be the basic building blocks for performance evaluation studies. Part three focuses on the relatively new field of the physics of networks. This part deals with the recently obtained insights that many very different large complex networks - such as the Internet, World Wide Web, proteins, utility infrastructures, social networks - evolve and behave according to more general common scaling laws. This understanding is useful when assessing the end-to-end quality of communications services, for example, in Internet telephony, real-time video and interacting games. Containing problems and solutions, this book is ideal for graduate studen

This comprehensive textbook, now in its sixth edition, combines classical and matrix-based methods of structural analysis and develops them concurrently. New solved examples and problems have been add

The sign-solvability of a linear system implies that the signs of the entries of the solution are determined solely on the basis of the signs of the coefficients of the system. That it might be worthwhile and possible to investigate such linear systems was recognised by Samuelson in his classic book Foundations of Economic Analysis. Sign-solvability is part of a larger study which seeks to understand the special circumstances under which an algebraic, analytic or geometric property of a matrix can be determined from the combinatorial arrangement of the positive, negative and zero elements of the matrix. The large and diffuse body of literature connected with sign-solvability is presented as a coherent whole for the first time in this book, displaying it as a beautiful interplay between combinatorics and linear algebra. One of the features of this book is that algorithms that are implicit in many of the proofs have been explicitly described and their complexity has been commented on.

As a tradition modernism has fostered particularly polarised impulses - though the great modernist poems offer impressive models, modernist principles, epitomised in Ezra Pound's exhortation to 'make it new', encourage poets to reject the methods of their immediate predecessors. Re-making it New explores the impact of this polarised tradition on contemporary American poets by examining the careers of John Ashbery, Elizabeth Bishop, Robert Creeley and James Merrill. To demonstrate how these four have extended modernist attitudes to create a distinctive post-modern art, each one's poetry is compared with that of a modernist who has been an important influence: Ashbery is discussed in conjunction with Wallace Stevens, Bishop with Marianne Moore, Creeley with William Carlos Williams and Merrill with W. H. Auden. Lynn Keller's book shows that contemporary poets have chosen not to reach for order as their modernist predecessors did; instead, they attempt to dissolve hierarchical distinction

Geared toward theoretical physicists, this advanced text explores the value of modern group-theoretical methods in quantum theory. It explains the theory of groups and their matrix representations, de

In this book David Currie and Paul Levine address a broad range of issues concerning the design and conduct of macroeconomic policy in open economies. Adopting neo-Keynesian models for which monetary and fiscal policy have short-term real effects, they analyse active stabilisation policies in both a single- and multi-country context. Questions addressed include: the merits of simple policy rules, policy design in the face of uncertainty and international policy coordination. A central feature of the book is the treatment of credibility and the effect of a policy-maker's reputation for sticking to announced policies. These considerations are integrated with coordination issues to produce a unique synthesis. The volume develops optimal control methods and dynamic game theory to handle relationships between governments and a conscious rational private sector and produces a unified, coherent approach to the subject. This book will be of interest to students and teachers of open economy mac

This collection provides detailed descriptions of both standard and advanced meta-analytic methods and their implementation in Stata. Readers will gain access to the statistical methods behind the rap

This classic text and reference collects the many formulae and methods that can be found in the scientific literature on stochastic methods. This fourth edition has been thoroughly updated and restruc

Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the ass

This authoritative handbook covers all aspects of immunosenescence, with contributions from experts in the research and clinical areas. It examines methods and models for studying immunosenescence; g

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.

This comprehensive textbook, now in its sixth edition, combines classical and matrix-based methods of structural analysis and develops them concurrently. New solved examples and problems have been add

Since economies are dynamic processes driven by creativity, social norms, and emotions as well as rational calculation, why do economists largely study them using static equilibrium models and narrow rationalistic assumptions? Economic activity is as much a function of imagination and social sentiments as of the rational optimisation of given preferences and goods. In this book, Richard Bronk argues that economists can best model and explain these creative and social aspects of markets by using new structuring assumptions and metaphors derived from the poetry and philosophy of the Romantics. By bridging the divide between literature and science, and between Romanticism and narrow forms of Rationalism, economists can access grounding assumptions, models, and research methods suitable for comprehending the creativity and social dimensions of economic activity. This is a guide to how economists and other social scientists can broaden their analytical repertoire to encompass the vital role

Since economies are dynamic processes driven by creativity, social norms, and emotions as well as rational calculation, why do economists largely study them using static equilibrium models and narrow rationalistic assumptions? Economic activity is as much a function of imagination and social sentiments as of the rational optimisation of given preferences and goods. In this book, Richard Bronk argues that economists can best model and explain these creative and social aspects of markets by using new structuring assumptions and metaphors derived from the poetry and philosophy of the Romantics. By bridging the divide between literature and science, and between Romanticism and narrow forms of Rationalism, economists can access grounding assumptions, models, and research methods suitable for comprehending the creativity and social dimensions of economic activity. This is a guide to how economists and other social scientists can broaden their analytical repertoire to encompass the vital role

Amiria Henare explores the role of material cultural research in anthropology and related disciplines from the late eighteenth century to the present. Grounded in a historical ethnography of museums in New Zealand and Scotland, the work traces the movement of artefacts now held in contemporary collections through space and time, demonstrating how and why things were bought, exchanged and stolen and carried across oceans to arrive in present-day museums. The collecting of artefacts and their study both in museums and the the field are emphasised as key strategies in the development of anthropological thought, While much late twentieth-century writing in anthropology has employed analytic models and methodologies derived from the study of language, this work belongs to a growing body of research drawing on the epistemological potency of artefacts, the distinctive insights afforded by engagement with material things.

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanc

Methods of non-equilibrium statistical mechanics play an increasingly important role in modern turbulence research, yet the range of relevant tools and methods is so wide and developing so fast that until now there has not been a single book covering the subject. As an introduction to modern methods of statistical mechanics in turbulence, this volume rectifies that situation. The book comprises three harmonised lecture courses by world class experts in statistical physics and turbulence: John Cardy introduces Field Theory and Non-Equilibrium Statistical Mechanics; Gregory Falkovich discusses Turbulence Theory as part of Statistical Physics; and Krzysztof Gawedzki examines Soluble Models of Turbulent Transport. To encourage readers to deepen their understanding of the theoretical material, each chapter contains exercises with solutions. Essential reading for students and researchers in the field of theoretical turbulence, this volume will also interest any scientist or engineer who appl

Dependence with complete connections is a more general type of stochastic process than the well-known Markovian dependence, accounting for a complete history of a stochastic evolution. This book is an authoritative survey of knowledge of the subject, dealing with the basic theoretical understanding and also with applications. These arise in a variety of situations as diverse as stochastic models of learning, branching processes in random environments, continued fractions and dynamical systems. Thus the book will appeal to mathematicians working in probability theory, ergodic theory and number theory, as well as applied mathematicians, engineers, biologists and social scientists interested in applications of stochastic methods.

If you're looking to understand photonic crystals, this systematic, rigorous, and pedagogical introduction is a must. Here you'll find intuitive analytical and semi-analytical models applied to complex and practically relevant photonic crystal structures. You will also be shown how to use various analytical methods borrowed from quantum mechanics, such as perturbation theory, asymptotic analysis, and group theory, to investigate many of the limiting properties of photonic crystals which are otherwise difficult to rationalize using only numerical simulations. An introductory review of nonlinear guiding in photonic lattices is also presented, as are the fabrication and application of photonic crystals. In addition, end-of-chapter exercise problems with detailed analytical and numerical solutions allow you to monitor your understanding of the material presented. This accessible text is ideal for researchers and graduate students studying photonic crystals in departments of electrical engi

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time