Matrix-analytic Methods in Stochastic Models

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 is a fully revised and updated version of Hans van der Doel's Democracy and Welfare Economics. It presents the economic theory of political decision-making (otherwise knownn as new political economy, or public choice), providing students with an accessible and clear introduction to this important subject. The authors identify four different methods of decision-making by which the political process transforms the demands of individual citizens into government policy and public goods and services: negotiation, majority decision, representations and bureaucratic implementation. These are analysed, in turn, as independent decision-making models whose effectiveness is examined with reference to economic theory. A final chapter draws conclusions from this analysis, arguing that the size of the public sector is a result of forces that work in different directions at different stages of the political process.

Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Oceanographers are increasingly turning to inverse methods for combining these observations with numerical models of ocean circulation. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modelling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development. Thus this book will be invaluable for environmental scientists and engineers, advanced underg

An introduction to analysis techniques used in the design of linear feedback control systems with an emphasis on both classical and matrix methods. After introducing general state space and input-outp

This book outlines the basic science underlying the prediction of stress and velocity distributions in granular materials. It takes the form of a textbook suitable for postgraduate courses, research workers and for use in design offices. The nature of a rigid-plastic material is discussed and a comparison is made between the Coulomb and conical (extended Von Mises) models. The methods of measuring material properties are described and an interpretation of the experimental results is considered in the context of the Critical State Theory. The book will be an invaluable text for all those working with or doing research into granular materials. Exercises and solutions are provided which will be particularly useful for the student.

This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual ne

This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual ne

Developed fifty years ago by the National Bureau of Economic Research, the analytic methods of business cycles and economic indicators enable economists to forecast economic trends by examining the repetitive sequences that occur in business cycles. The methodology has proven to be an inexpensive and useful tool that is now used extensively throughout the world. In recent years, however, significant new developments have emerged in the field of business cycles and economic indicators. This volume contains twenty-two articles by international experts who are working with new and innovative approaches to indicator research. They cover advances in three broad areas of research: the use of new developments in economic theory and time-series analysis to rationalise existing systems of indicators; more appropriate methods to evaluate the forecasting records of leading indicators, particularly of turning point probability; and the development of new indicators.

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

These volumes contain a collection of essays by many of the closest co-workers of Raphael Høegh-Krohn, 1938–88, one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose, and content - some are surveys where leading experts sum up and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Many of the papers are based on talks given at a symposium in honor of Høegh-Krohn at the University of Oslo: however the final volumes are far more than proceedings and great care has been taken to attract contributions from the leading researchers.

These volumes contain a collection of essays by many of the closest co-workers of Raphael Høegh-Krohn, 1938–88, one of the outstanding mathematical physicists of our age. The contributions vary in style, purpose and content - some are surveys where leading experts sum up and clarify a subject area, others are new and adventurous expeditions into unknown territory. The topics cover most aspects of modern mathematical physics with special emphasis on methods from operator theory and stochastic analysis. Many of the papers are based on talks given at a symposium in honour of Høegh-Krohn at the University of Oslo; however the final volumes are far more than proceedings and great care has been taken to attract contributions from the leading researchers.

This book presents statistical methods for analysis of the duration of events. The primary focus is on models for single-spell data, events in which individual agents are observed for a single duration. Some attention is also given to multiple-spell data. The first part of the book covers model specification, including both structural and reduced form models and models with and without neglected heterogeneity. The book next deals with likelihood based inference about such models, with sections on full and semiparametric specification. A final section treats graphical and numerical methods of specification testing. This is the first published exposition of current econometric methods for the study of duration data.

This book provides students and research workers in the biological, medical and social sciences with the statistical background needed to collect and analyse data in an intelligent and critical manner. Key examples and case studies are used to illustrate commonly encountered research problems and to explain how they may be solved or even avoided altogether. Professor Manly also presents a clear understanding of the opportunities and limitations of different research designs, as well as an introduction to some new methods of analysis that are proving increasingly popular. Topics covered include the differences between observational and experimental studies; the design of sample surveys; multiple regression and its generalizations to log-linear and logistic models; experimental and quasi-experimental designs; interrupted time series; computer intensive methods of statistical inference; and the ethical considerations of research. In the final chapter, there is a useful discussion of how t

The interaction between light and electrons in semiconductors forms the basis for many interesting and practically significant properties. This book examines the fundamental physics underlying this rich complexity of photoelectronic properties of semiconductors, and will familiarise the reader with the relatively simple models that are useful in describing these fundamentals. The basic physics is also illustrated with typical recent examples of experimental data and observations. Following introductory material on the basic concepts, the book moves on to consider a wide range of phenomena, including photoconductivity, recombination effects, photoelectronic methods of defect analysis, photoeffects at grain boundaries, amorphous semiconductors, photovoltaic effects and photoeffects in quantum wells and superlattices. The author is Professor of Materials Science and Electrical Engineering at Stanford University, and has taught this material for many years. He is an experienced author, his

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and patt

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathem

Introduces matrix theory combining algebraic and analytic aspects and provides concise exposition of the basic ideas, results, and techniques in the subject. Presumes no knowledge beyond some familiar

This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

Misspecification tests play an important role in detecting unreliable and inadequate economic models. This book brings together many results from the growing literature in econometrics on misspecification testing. It provides theoretical analyses and convenient methods for application. The main emphasis is on the Lagrange multiplier principle, which provides considerable unification, although several other approaches are also considered. The author also examines general checks for model adequacy that do not involve formulation of an alternative hypothesis. General and specific tests are discussed in the context of multiple regression models, systems of simultaneous equations, and models with qualitative or limited dependent variables.

This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

The application of time series techniques in economics has become increasingly important, both for forecasting purposes and in the empirical analysis of time series in general. In this book, Terence Mills not only brings together recent research at the frontiers of the subject, but also analyses the areas of most importance to applied economics. It is an up-to-date text which extends the basic techniques of analysis to cover the development of methods that can be used to analyse a wide range of economic problems. The book analyses three basic areas of time series analysis: univariate models, multivariate models, and non-linear models. In each case the basic theory is outlined and then extended to cover recent developments. Particular emphasis is placed on applications of the theory to important areas of applied economics and on the computer software and programs needed to implement the techniques. This book clearly distinguishes itself from its competitors by emphasising the techniques

This book describes the main methods of one- and two-dimensional high-resolution nuclear magnetic resonance spectroscopy in liquids within the quantum-mechanical formalism of the density matrix. In vi

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

This book provides an introduction to the methods employed in forecasting the future state of the economy. It provides a comprehensive coverage of methods and applications in this fast-growing area and is intended for use in postgraduate and upper-level undergraduate courses. Part I outlines the available techniques, particularly those used in business forecasting and econometric forecasting. The state of the art in time series modelling is reviewed and includes a discussion of Box-Jenkins models, the vector autogressive approach and cointegration. Ways of combining forecasts are also examined in detail. Part II considers the most important applications of forecasting. Applications in microeconomics include demand and sales forecasting, the use of anticipations data, leading indicators and scenario analysis. In macroeconomics the emphasis is on why errors occur in forecasting asset market prices, including implications of the efficient markets hypothesis for foreign markets, stock mark

This classic book, now re-issued in paperback, presents a detailed account of the mathematical theory of viscosity, thermal conduction and diffusion in non-uniform gases based on the solution of the Maxwell–Boltzmann equations. The theory of Chapman and Enskog, describing work on dense gases, quantum theory of collisions and the theory of conduction and diffusion in ionized gases in the presence of electric and magnetic fields, is extended in the later chapters. The third edition was first published in 1970 and included revisions to take account of extensions of the theory to fresh molecular models and of new methods used in discussing dense gases and plasmas. This reprint will therefore be of value to mathematicians, theoretical physicists and chemical engineers interested in gas theory and its applications.

Time Series: Theory and Methods is a systematic account of linear time series models and their application to the modelling and prediction of data collected sequentially in time. The aim is to provid

This book presents a novel approach to the teaching of dynamic aspects of the operation of semiconductor and opto-electronic devices. Such dynamic aspects often determine the steady state conditions. Also, the dynamical operation of such devices is of increasing importance as modern methods of communicating data and information require electronic devices that switch electrical or optical signals at ever faster rates. The author discusses the rates at which electrons and holes can reach equilibrium, the rates at which transistors and diodes can switch, and the rates at which electrons and holes can interact with photons, and with protons. He also applies the rate equations in a unified way to models of light-emitting diodes, injection lasers and photodiodes. Finally, the author discusses more-advanced topics on the photon statistics of injection lasers, mode-locking and the application of rate equations and Maxwell's equations to opto-electronic devices.

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

This collection of essays, written between 1975 and 1987, covers the doctrine of analogy; the Trinity; 'theological realism'; the problems of evil and suffering; the doctrine of God, tragedy and Christian life; the doctrine of the atonement, christology, the theology of religions, ecclesiology, discipleship and the so-called theistic 'proofs'. The earlier essays reflect the author's training as a philosopher in the Anglo-American 'analytic' tradition. Later essays have a more explicitly theological focus, and they represent an attempt to come to terms with, and to proceed beyond, this tradition. More importance is attached to issues in hermeneutics and literary and social theory in the later essays. This collection therefore tends to address a wider list of topics than is usual in works of philosophical theology, and it is also distinctive in respect of the methods and approaches used in considering these topics.

Professor Roemer's goal in this book is to give a rigorous view of classical Marxian economic theory by presenting specific analytic models. The theory is not extended to deal with new problems, but it is deepened: Marxian theory is given micro-foundations and upon those foundations the author begins to rebuild a tightly constructed Marxian economics. The book begins, after a methodological introduction, with an examination of the Marxian notion of equilibrium and the theory of exploitation, and goes on to deal with the theory of the falling rate of profit. The next section explores one of the points made in the first section of the book, that the Marxian theory of exploitation can be constructed completely independently of the labor theory of value as a theory of exchange. Technical study of this problem allows comment on various issues, such as the relative importance of 'marginal utilities' and 'class struggle' in determining relative prices. The final part examines models of variou

Papers of the April 1988, Reno, Nevada meeting. They deal with: novel processing methods for metal based composites; deformation mechanisms in metal matrix composites; ceramic composite mechanical per

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researc

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Although the complexity and capability of flight simulators have matched the growth of aerospace technology, there has until now been no textbook dealing specifically with the design and construction of flight simulators. This is a primary purpose of Flight Simulation. Written in collaboration with a number of internationally known specialists, the book considers the subject in three sections. Firstly it introduces the concept of simulation in order to identify the essential elements which make up the modern flight simulator. The development of these elements is also traced through the historical evolution of flight simulation. The main section of the book commences with an exposition of the mathematical models into dynamic physical devices capable of representing the response of a specific aircraft and its systems. The simulation of the flight environment is also covered in relation to cockpit motion systems and methods of representing the external visual scene. Another important aspe

This book represents a comprehensive examination of interest-group politics in France. Rather than the narrow case studies usually employed to study group politics, the book focuses on the overall pattern of interaction between interest groups and government. Drawing upon extensive interviews with French interest-group leaders and politicians, Wilson examines the structures and methods of group politics, the perspectives and attitudes of group leaders, and the place of interest groups in the broader pattern of French politics. He concludes that neither of the two major conceptualizations of interest-group/government relations is adequate to explain group politics in France. He suggests that the French state is much more powerful than recognized by these or other models of interest-group politics. Political influence is difficult for groups to develop and, once achieved, is fleeting. Consequently, groups engage in a wide range of activities, some of which are pluralist, others corporati

This 1987 book is a self-contained text on the probabilistic modelling method. It provides the reader with an understanding of the available results as well as with examples of their application. The only background assumed is a knowledge of basic calculus. The necessary fundamentals of probability are presented followed by an introduction to stochastic processes. The remainder of the book is devoted to the treatment of various single-station and their application to uni-programmed and multi-programmed systems and local and wide-area networks. Both exact and approximate solution methods are discussed, with as much emphasis on explaining the ideas and providing information, as on derivations and proofs. This book will still be of use for anyone with an interest in the history of computer science.

The place of money capital in the theory of the firm has remained a relatively neglected question in traditions of economic analysis. In this highly integrative work, issues in production, pricing, capital investment and financial theory are brought to new levels of interdependence. Developing a three-part argument, Money Capital in the Theory of the Firm deals successively with the theoretical issues and analytic motivation, the neoclassical tradition and postclassical perspectives. In doing so, it presents a self-contained foundation in the basic structures of microeconomic analysis relating to optimize decision making in the firm and in the accounting concepts and statistical apparatus of probability theory relevant to the neoclassical aspects of the argument. Additionally, the book provides the essential mathematical development of such advanced topics as utility functions defined over stochastic arguments, the equilibrium theory of financial asset prices and yields, the cost of mo

The papers in this volume, a multidisciplinary collaboration of anthropologists, linguists, and psychologists, explore the ways in which cultural knowledge is organized and used in everyday language and understanding. Employing a variety of methods, which rely heavily on linguistic data, the authors offer analyses of domains of knowledge ranging across the physical, social, and psychological worlds, and reveal the importance of tacit, presupposed knowledge in the conduct of everyday life. The authors argue that cultural knowledge is organized in 'cultural models' - storylike chains of prototypical events that unfold in simplified worlds - and explore the nature and role of these models. They demonstrate that cultural knowledge may take either proposition-schematic or image-schematic form, each enabling the performance of different kinds of cognitive tasks. Metaphor and metonymy are shown to have special roles in the construction of cultural models. The authors also demonstrates that so

This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.

This book presents a novel approach to the teaching of dynamic aspects of the operation of semiconductor and opto-electronic devices. Such dynamic aspects often determine the steady state conditions. Also, the dynamical operation of such devices is of increasing importance as modern methods of communicating data and information require electronic devices that switch electrical or optical signals at ever faster rates. The author discusses the rates at which electrons and holes can reach equilibrium, the rates at which transistors and diodes can switch, and the rates at which electrons and holes can interact with photons, and with protons. He also applies the rate equations in a unified way to models of light-emitting diodes, injection lasers and photodiodes. Finally, the author discusses more-advanced topics on the photon statistics of injection lasers, mode-locking and the application of rate equations and Maxwell's equations to opto-electronic devices.