Matrix-analytic Methods in Stochastic Models

Covering sex allocation, sex determination and operational sex ratios, this multi-author volume provides both a conceptual context and an instruction in methods for many aspects of sex ratio research. Theory, statistical analysis and genetics are each explained and discussed in the first three sections. The remaining chapters each focus on research in one of a wide spectrum of animal, plant and microbial taxa, including sex ratio distorting bacteria in invertebrates, malarial parasites, birds, human and other mammals, giving critical appraisals of such research. Sex Ratios: Concepts and Research Methods is primarily intended for graduate and professional behavioural and evolutionary ecologists in this field, but it will also be useful to biologists building evolutionary models, and researchers analysing data involving proportions or comparisons across phylogenetically related species.

Covering sex allocation, sex determination and operational sex ratios, this multi-author volume provides both a conceptual context and an instruction in methods for many aspects of sex ratio research. Theory, statistical analysis and genetics are each explained and discussed in the first three sections. The remaining chapters each focus on research in one of a wide spectrum of animal, plant and microbial taxa, including sex ratio distorting bacteria in invertebrates, malarial parasites, birds, human and other mammals, giving critical appraisals of such research. Sex Ratios: Concepts and Research Methods is primarily intended for graduate and professional behavioural and evolutionary ecologists in this field, but it will also be useful to biologists building evolutionary models, and researchers analysing data involving proportions or comparisons across phylogenetically related species.

Engineers and scientists need powerful formalisms to make conceptual models of systems in order to analyse and design them. These models can be used to verify the behaviour of the systems, or as an executable specification of them. In this textbook, Professor van Hee concentrates on discrete dynamic systems, e.g. computer hardware, and information and logistical systems. He develops an integrated formalism which can be used as a prototyping language. It has three components: Petri nets, extended with time, token values and hierarchy; a specification language that is a subset of Z; and a binary data model, extended with complex objects. Much attention is paid to methods for constructing models of systems and analysing their behaviour, i.e. putting the theory into practice. The text is designed for use by advanced undergraduate and beginning graduate students, in computer science, electrical and industrial engineering, or applied mathematics; indeed, it is based on courses taught by the

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.

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

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.

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 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 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.

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.

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.

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of

International edition of Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets 7th Edition. Hillier is especially known for his classic, award-winning text, Introduction to Operations Research, co-authored with the late Gerald J. Lieberman, which has been translated into well over a dozen languages and is currently in its 8th edition. The 6th edition won honorable mention for the 1995 Lanchester Prize (best English-language publication of any kind in the field) and Dr. Hillier also was awarded the 2004 INFORMS Expository Writing Award for the 8th edition. His other books include The Evaluation of Risky Interrelated Investments, Queueing Tables and Graphs, Introduction to Stochastic Models in Operations Research, and Introduction to Mathematical Programming. He received his BS in industrial engineering and doctorate specializing in operations research and management science from Stanford University. The winner of many awards in high school and colleg

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

This is a graduate text surveying both the theoretical and experimental aspects of chaotic behaviour. Over the course of the past two decades it has been discovered that relatively simple, deterministic, nonlinear mathematical models that describe dynamic phenomena in various physical, chemical, biological and other systems yield solutions which are aperiodic and depend very sensitively on the initial conditions. This phenomenon is known as deterministic chaos. The authors present chaos as a model of many seemingly random processes in nature. Basic notions from the theory of dynamical systems and bifurcation theory, together with the properties of chaotic solutions, are then described and are illustrated by examples. A review of the numerical methods used both in studies of mathematical models and in the interpretation of experimental data is also provided.

For a number of years, French mathematicians have run regular number theory conferences to which they have invited number theorists from many countries. To repay their hospitality, the London Mathematical Society arranged for the 1980 'Journees Arithmeiques' to be held in Exeter. The papers published here are either based on the main invited lectures or on selected research talks given at the conference. They cover all branches of the subject: combinatorial and elementary methods; analytic number theory; transcendence theory; Galois module theory and algebraic number theory in general; elliptic curves and modular functions; local fields; additive number theory; Diophantine geometry, and uniform distribution. It will be necessary reading for all those undertaking research in number theory.

This volume of essays reflects the increasing breadth and scope of Bach research. The fifteen essays by American and European scholars address a wide range of topics and issues: Magnificat, Cantata, and Passion; Parody and Genre; The Well-Tempered Clavier; and Transmission and Reception. Many of the authors focus on works which due to the Bach chronology - can now be examined in a fresh light. Seen as a whole, the essays combine source - critical and analytic methods with historical and theological interpretation to consider problems of genesis and style, as well as questions of transmission and reception.

This introductory overview explores the methods, models and interdisciplinary links of artificial economics, a new way of doing economics in which the interactions of artificial economic agents are computationally simulated to study their individual and group behavior patterns. Conceptually and intuitively, and with simple examples, Mercado addresses the differences between the basic assumptions and methods of artificial economics and those of mainstream economics. He goes on to explore various disciplines from which the concepts and methods of artificial economics originate; for example cognitive science, neuroscience, artificial intelligence, evolutionary science and complexity science. Introductory discussions on several controversial issues are offered, such as the application of the concepts of evolution and complexity in economics and the relationship between artificial intelligence and the philosophies of mind. This is one of the first books to fully address artificial economics

With the current push toward educational reform, there is great potential for innovation and change, particularly in large scale testing. One area where change is possible is in cognitive diagnostic assessment. Researchers in educational measurement and cognitive psychology are finally in a position to design tests targeted specifically for providing valuable information about students' cognitive strengths and weaknesses. This self-contained volume organizes what is known about cognitive diagnostic assessment in education, including its conceptual and philosophical basis, methods, and applications. The complete list of topics includes educational demand, philosophical rationale, construct validity, cognitive methods, test construction, statistical models, and unresolved issues (e.g., how to best translate diagnostic information into teaching practices). Leighton and Gierl present a comprehensive and up-to-date examination of cognitive diagnostic assessment in education.

With the current push toward educational reform, there is great potential for innovation and change, particularly in large scale testing. One area where change is possible is in cognitive diagnostic assessment. Researchers in educational measurement and cognitive psychology are finally in a position to design tests targeted specifically for providing valuable information about students' cognitive strengths and weaknesses. This self-contained volume organizes what is known about cognitive diagnostic assessment in education, including its conceptual and philosophical basis, methods, and applications. The complete list of topics includes educational demand, philosophical rationale, construct validity, cognitive methods, test construction, statistical models, and unresolved issues (e.g., how to best translate diagnostic information into teaching practices). Leighton and Gierl present a comprehensive and up-to-date examination of cognitive diagnostic assessment in education.

Fully updated and expanded, this new edition presents a cutting-edge summary of planetary rings, including results from Cassini's Saturn System, Equinox and Solstice missions, and the New Horizons flyby of Jupiter. The book introduces basic physical processes and simple mathematical approaches in an accessible manner, including N-body and stochastic models of ring dynamics. Further revised chapters present highlighted topics including Saturn's F ring, Uranus' rings and moons, Neptune's partial rings, dusty rings, and Jupiter's ring-moon system after Galileo and New Horizons. Cassini results are fully integrated throughout, including new images in color, and a new Afterword links ring images in the Cassini 'Hall of Fame' gallery to the relevant explanation in the text. An online cache of images and videos from NASA's collection makes it easy to locate relevant and beautiful illustrative materials. This is a key resource for students, researchers and professionals in planetary science, a

Fully updated and expanded, this new edition presents a cutting-edge summary of planetary rings, including results from Cassini's Saturn System, Equinox and Solstice missions, and the New Horizons flyby of Jupiter. The book introduces basic physical processes and simple mathematical approaches in an accessible manner, including N-body and stochastic models of ring dynamics. Further revised chapters present highlighted topics including Saturn's F ring, Uranus' rings and moons, Neptune's partial rings, dusty rings, and Jupiter's ring-moon system after Galileo and New Horizons. Cassini results are fully integrated throughout, including new images in color, and a new Afterword links ring images in the Cassini 'Hall of Fame' gallery to the relevant explanation in the text. An online cache of images and videos from NASA's collection makes it easy to locate relevant and beautiful illustrative materials. This is a key resource for students, researchers and professionals in planetary science, a

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are cover

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.

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Intended for researchers and practitioners in interaction design, this book shows how Bayesian models can be brought to bear on problems of interface design and user modelling. It introduces and motivates Bayesian modelling and illustrates how powerful these ideas can be in thinking about human-computer interaction, especially in representing and manipulating uncertainty. Bayesian methods are increasingly practical as computational tools to implement them become more widely available, and offer a principled foundation to reason about interaction design. The book opens with a self-contained tutorial on Bayesian concepts and their practical implementation, tailored for the background and needs of interaction designers. The contributed chapters cover the use of Bayesian probabilistic modelling in a diverse set of applications, including improving pointing-based interfaces; efficient text entry using modern language models; advanced interface design using cutting-edge techniques in Bayesia

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.

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.

This 2004 volume offers a broad overview of developments in the theory and applications of state space modeling. With fourteen chapters from twenty-three contributors, it offers a unique synthesis of state space methods and unobserved component models that are important in a wide range of subjects, including economics, finance, environmental science, medicine and engineering. The book is divided into four sections: introductory papers, testing, Bayesian inference and the bootstrap, and applications. It will give those unfamiliar with state space models a flavour of the work being carried out as well as providing experts with valuable state of the art summaries of different topics. Offering a useful reference for all, this accessible volume makes a significant contribution to the literature of this discipline.

This 2004 volume offers a broad overview of developments in the theory and applications of state space modeling. With fourteen chapters from twenty-three contributors, it offers a unique synthesis of state space methods and unobserved component models that are important in a wide range of subjects, including economics, finance, environmental science, medicine and engineering. The book is divided into four sections: introductory papers, testing, Bayesian inference and the bootstrap, and applications. It will give those unfamiliar with state space models a flavour of the work being carried out as well as providing experts with valuable state of the art summaries of different topics. Offering a useful reference for all, this accessible volume makes a significant contribution to the literature of this discipline.

The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researc

Attempts by ecologists to establish models for predicting the growth of a population or the fluctuations of a natural resource can be confounded by environmental heterogeneity. Spatio-Temporal Heterogeneity explores a range of available statistical methods to help ecologists in the attempt to unravel complexities, demonstrating how to place these changes into an understandable statistical framework. It addresses several key questions, including how to interpret the parameters of statistical models in relation to the biological and environmental realities, how to design a study to collect the best sample data and how to avoid pitfalls in modelling, design, statistical assessment and interpretation. Dutilleul uses a variety of examples to facilitate understanding, from plant ecology, earth and atmospheric sciences, animal biology, forestry and limnology. The accompanying CD-ROM contains MATLAB and SAS codes to aid analyses.

Attempts by ecologists to establish models for predicting the growth of a population or the fluctuations of a natural resource can be confounded by environmental heterogeneity. Spatio-Temporal Heterogeneity explores a range of available statistical methods to help ecologists in the attempt to unravel complexities, demonstrating how to place these changes into an understandable statistical framework. It addresses several key questions, including how to interpret the parameters of statistical models in relation to the biological and environmental realities, how to design a study to collect the best sample data and how to avoid pitfalls in modelling, design, statistical assessment and interpretation. Dutilleul uses a variety of examples to facilitate understanding, from plant ecology, earth and atmospheric sciences, animal biology, forestry and limnology. The accompanying CD-ROM contains MATLAB and SAS codes to aid analyses.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

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.