Matrix-analytic Methods in Stochastic Models

This introduction to the field of many-body atomic physics is suitable for researchers and graduate students. Drawing from three major subject areas, atomic structure, atomic photoionization, and electron-atom collisions, this book begins with an introduction to many-body diagrams, and continues with several chapters devoted to each subject area written by leading theorists in that field. Topics in atomic structure include the relativistic theory for highly charged atomic ions and calculations of parity nonconservation. Topics in atomic photoionization include single and double photoionization processes, and photoelectron angular distributions. Topics in electron-atom collisions include the theory of electron impact ionization, perturbation series methods, target dependence of the triply differential cross section, Thomas processes, R-matrix theory, close coupling, and distorted-wave theory. This coherent and carefully edited volume has been prepared by leading atomic physicists as a t

A growing number of art therapists are also trained in group analytic psychotherapy. This book explores the new theories and models for practice arising from the merging of these two disciplines.Contr

Human Demography and Disease offers an interdisciplinary and integrated perspective on the relationship between historical populations and the dynamics of epidemiological processes. It brings the techniques of time-series analysis and computer matrix modelling to historical demography and geography to extract detailed information concerning the oscillations in births, deaths, migrations and epidemics from parish registers and other data series and to build mathematical models of the population cycles. This book presents a new way of studying pre-industrial communities and explores the subtle, and hitherto undetected effects of fluctuating nutritional levels on mortality patterns and the dynamics of infectious diseases. It will be of interest to researchers, teachers and students in the fields of demography, anthropology, historical geography, social history, population biology and epidemiology.

This social history of earliest Christianity radically re-evaluates both the methods and models of other studies. Justin Meggitt draws on the most recent research in classical studies on the economy a

Nations at War provides an explanation of war in international politics grounded on data-based, empirical research. The book classifies and synthesizes the research findings of over 500 quantitative analyses of war at the analytic level of the state, dyad, region, and international system. Because wars follow from political decisions, two basic decision-making models - the rational and the non-rational - are examined in relation to the explanatory framework of the volume. In addition, case analyses of two wars - the Iran/Iraq War (1980), and World War I (1914) - are provided as demonstrations of scientifically-based explanations of historical events. The primary structural factors responsible for the onset and seriousness of war are identified and the explanations are developed according to the scientific model of 'covering laws'. The conclusion presents a discussion of the potential for probabilistic conditional predictions of conflict within the context of war and peace studies.

Nations at War provides an explanation of war in international politics grounded on data-based, empirical research. The book classifies and synthesizes the research findings of over 500 quantitative analyses of war at the analytic level of the state, dyad, region, and international system. Because wars follow from political decisions, two basic decision-making models - the rational and the non-rational - are examined in relation to the explanatory framework of the volume. In addition, case analyses of two wars - the Iran/Iraq War (1980), and World War I (1914) - are provided as demonstrations of scientifically-based explanations of historical events. The primary structural factors responsible for the onset and seriousness of war are identified and the explanations are developed according to the scientific model of 'covering laws'. The conclusion presents a discussion of the potential for probabilistic conditional predictions of conflict within the context of war and peace studies.

This book studies the development of ideas on freedom, coercion and power in the history of economic thought. It focuses on the exchange of goods and services and on terms of exchange (interest rates, prices and wages) and examines the nature of choice, that is, the state of the will of economic actors making exchange decisions. In a social context, anyone's range of choice is restricted by the choices made by others. The first to raise the question of the will in this economic context were the medieval scholastics, drawing on non-economic analytic models inherited from antiquity and mainly from Aristotle. From these origins, views on economic choice, coercion and power are recorded, as they gradually change over the centuries, until they manifest themselves in more contemporary disputes between different branches of institutional economics.

This book is about the ways in which many animals form groups; for instance, schools of fish, flocks of birds, and swarms of insects. Covering both invertebrate and vertebrate species, the authors investigate three-dimensional animal aggregations from a variety of disciplines, from physics to mathematics to biology. The first section is devoted to the various methods, mainly optical and acoustic, used to collect three-dimensional data over time. The second section focuses on analytical methods used to quantify pattern, group kinetics, and interindividual interactions within the group. The section on behavioural ecology and evolution deals with the functions of aggregative behaviour from the point of view of an inherently selfish individual member. The final section uses models to elucidate how group dynamics at the individual level creates emergent pattern at the level of the group.

Probabilistic modelling is the most cost-effective means of performance and reliability evaluation of complex dynamic systems. This self-contained text will be welcomed by students and teachers for its no-nonsense treatment of the basic results and examples of their application. The only mathematical background that is assumed is basic calculus. The necessary fundamentals of probability theory are included, as well as an introduction to renewal, Poisson and Markov processes. Models arising in the fields of manufacturing, computing and communications, involving single or multiple service stations and one or more customer classes, are examined in some detail. Both exact and approximate solution methods are discussed, including recent techniques such as spectral expansion. Special attention is devoted to models of systems subject to breakdowns and repairs. Throughout the book, strong emphasis is placed on explaining the ideas behind the results and helping the reader to use them, making t

Probabilistic modelling is the most cost-effective means of performance and reliability evaluation of complex dynamic systems. This self-contained text will be welcomed by students and teachers for its no-nonsense treatment of the basic results and examples of their application. The only mathematical background that is assumed is basic calculus. The necessary fundamentals of probability theory are included, as well as an introduction to renewal, Poisson and Markov processes. Models arising in the fields of manufacturing, computing and communications, involving single or multiple service stations and one or more customer classes, are examined in some detail. Both exact and approximate solution methods are discussed, including recent techniques such as spectral expansion. Special attention is devoted to models of systems subject to breakdowns and repairs. Throughout the book, strong emphasis is placed on explaining the ideas behind the results and helping the reader to use them, making t

Bootstrap methods are computer-intensive methods of statistical analysis, which use simulation to calculate standard errors, confidence intervals, and significance tests. The methods apply for any level of modelling, and so can be used for fully parametric, semiparametric, and completely nonparametric analysis. This 1997 book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. S-Plus programs for implementing the

Engineers and applied geophysicists routinely encounter interpolation and estimation problems when analysing data from field observations. Introduction to Geostatistics presents practical techniques for the estimation of spatial functions from sparse data. The author's unique approach is a synthesis of classic and geostatistical methods with a focus on the most practical linear minimum-variance estimation methods, and includes suggestions on how to test and extend the applicability of such methods. The author includes many useful methods (often not covered in other geostatistics books) such as estimating variogram parameters, evaluating the need for a variable mean, parameter estimation and model testing in complex cases (e.g. anisotropy, variable mean, and multiple variables), and using information from deterministic mathematical models. Well illustrated with exercises and worked examples taken from hydrogeology, Introduction to Geostatistics assumes no background in statistics and

An exploration of the use of smoothing methods in testing the fit of parametric regression models. The book reviews many of the existing methods for testing lack-of-fit and also proposes a number of n

Numerical Methods in Finance has emerged as a discipline at the intersection of probability theory, finance and numerical analysis. This book, based on lectures given at the Newton Institute as part of a broader programme, describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially of American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures; identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Articles have been written in a pedagogic style and made reasonably self-contained, covering both mathematical matters and practical issues in numerical problems. Thus the book has something to offer economists, probabilists and applied mathematicians working in finance.

Attempts to model the effects of global change are inhibited by a lack of information about how individual plant and animal species will respond. One way of reducing the problem is to develop models treating a smaller number of groups or 'functional types' with similar characteristics. This 1977 book describes approaches and methods for defining these functional types in ways which maximize our potential to predict accurately the responses of real vegetation with real species diversity.

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review articles at an advanced research level, describing results for one-dimensional models of dynamical processes such as chemical reactions and catalysis, kinetic ising models, phase separation and cluster growth, monolayer and multilayer adsorption with added relaxation, surface and hard-core particle dynamics, diffusional transport, random systems and experimental results. It also covers experimental results for systems ranging from chemical reactions to adsorption and reactions on polymer chains, steps on crystalline surfaces, and DNA. All chapters are written by leading scientists in the field. They present a self-contained review of this subject that will guide a reader from basic concepts, ideas, methods and models to the forefront o

This volume comprises the proceedings of the 1995 Cardiff symposium on sieve methods, exponential sums, and their applications in number theory. Included are contributions from many leading international figures in this area which encompasses the main branches of analytic number theory. In particular, many of the papers reflect the interaction between the different fields of sieve theory, Dirichlet series (including the Riemann Zeta-function), and exponential sums, whilst displaying the subtle interplay between the additive and multiplicative aspects of the subjects. The fundamental problems discussed include recent work on Waring's problem, primes in arithmetical progressions, Goldbach numbers in short intervals, the ABC conjecture, and the moments of the Riemann Zeta-function.

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

Currency crises in Europe and Mexico during the 1990s provided stark reminders of the importance and the fragility of international financial markets. These experiences led some commentators to conclude that open international capital markets are incompatible with financial stability. But the pre-1914 gold standard is an obvious challenge to the notion that open capital markets are sources of instability. To deepen our understanding of how this system worked, this volume draws together recent research on the gold standard. Theoretical models are used to guide qualitative discussions of historical experience, while econometric methods are used to help the historical data speak clearly. The result is an overview of the gold standard, a survey of the relevant applied research in international macroeconomics, and a demonstration of how the past can help to inform the present.

The aim of this book is to present a substantial part of matrix analysis that is functional analytic in spirit. Much of this will be of interest to graduate students and research workers in operator t

The data analytic methods routinely applied in the analysis of recidivism data in criminology have been expanded to include immune individuals. This book describes the theory and methods of incorporat

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.

Modern geochemistry aims to provide an accurate description of geological processes, and a set of models and quantitative rules that help predict the evolution of geological systems. This work is an introduction to the mathematical methods of geochemical modeling, largely based on examples presented with full solutions. It shows how geochemical problems, dealing with mass balance, equilibrium, fractionation, dynamics, and transport in the igneous, sedimentary and oceanic environments, can be reformulated in terms of equations. Its practical approach then leads to simple but efficient methods of solution. This book should help the motivated reader to overcome the formal difficulties of geochemical modeling, and bring state-of-the-art methods within reach of advanced students in geochemistry and geophysics, as well as in physics and chemistry.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.

Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.

This book describes the most reliable methods available for evaluating the transport properties, such as viscosity, thermal conductivity and diffusion, of pure gases and fluid mixtures. Particular emphasis is placed on recent theoretical advances in our understanding of fluid transport properties in all the different regions of temperature and pressure. In addition to the important theoretical tools, the different methods of data representation are also covered, followed by a section which demonstrates the application of selected models in a range of circumstances. Case studies of transport property analysis for real fluids are then given, and the book concludes with a discussion of various international data banks and prediction packages. Advanced students of kinetic theory, as well as engineers and scientists involved with the design of process equipment or the interpretation of measurements of fluid transport properties, will find this book indispensable.

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the s

This book summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike tra

Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered

This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; invariant measures for specific models. The focus is on models of dynamical processes affected by white noise, which are described by partial differential equations such as the reaction-diffusion equations or Navier–Stokes equations. Besides existence and uniqueness questions, special attention is paid to the asymptotic behaviour of the solutions, to invariant measures and ergodicity. Some of the results found here are presented for the first time. For all whose research interests involve stochastic modelling, dynamical systems, or ergodic theory, this book will be an essential purchase.

Major scholars on Japan explore the Japanese style of learning in this important volume, drawing upon ethnographic and experimental studies of learning throughout the lifespan. The reader will get an inside view of Japanese teaching methods, where the emphasis is on the process of learning, rather than the end product. Applications across contexts - from religion to music, to mathematics, to guidance - are very differently handled than in the West. Contributors analyze various models of learning within and without the Japanese school system. The examples considered here allow us to understand better the rich coherence and variety of educational experiences in the broader social context. A carefully articulated introduction and conclusion by the editors provide salient comparisons of East and West and caution, that we do not simplify our model of either one. Teaching and Learning in Japanwill be of interest to educators, Japan scholars, and to educational psychologists.

Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a r

The first edition of this book was reviewed in 1982 as 'the most extensive treatment of Padé approximants actually available'. This second edition has been thoroughly updated, with a substantial chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches, to the analysi

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.