Matrix-analytic Methods in Stochastic Models

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Vladimir Gribov was one of the founding fathers of high-energy elementary particle physics. This book derives from a lecture course he delivered to graduate students in the 1970s. It thus provides today's graduate students and researchers with the opportunity to learn from the teaching of one of the twentieth century's greatest physicists. Its content is still deeply relevant to modern research, for example exploring properties of the relativistic theory of hadron interactions in a domain of peripheral collisions and large distances that quantum chromodynamics has barely approached. It covers a combination of topics not treated elsewhere, whilst remaining self-contained and thus accessible at graduate level. In guiding the reader, step-by-step, from the basics of quantum mechanics and relativistic kinematics to the most challenging problems of high-energy hadron interactions with simplifying models and physical analogies, it demonstrates general methods of addressing difficult problems

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

Statistical ideas and methods underlie just about every aspect of modern life. From randomized clinical trials in medical research, to statistical models of risk in banking and hedge fund industries,

Weaver (learning and information services, U. of Cumbria, UK) compiles 13 chapters that outline methods and models to help librarians, faculty, and staff in higher education adapt their learning suppo

The authors of this tract present a treatment of generalised Clifford parallelism within the framework of complex projective geometry. After a brief survey of the necessary preliminary material, the principal properties of systems of mutually Clifford parallel spaces are developed, centred round discussion of an extended form of the Hurwitz - Radon matrix equations. Later chapters deal with methods for the construction and representation of such systems. Much of the work in the tract is previously unpublished. Some emphasis has been placed throughout on special cases (particularly on the exceptionally interesting parallelisms that exist in spaces of seven and fifteen dimensions). Numerous exercises give the reader a clear insight into the fresh ideas presented. The tract will be of interest to advanced undergraduates and graduates with special interests in algebraic and projective geometry or in the geometry of matrices.

Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of

Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. In order to solve these models, economists need to use many mathematical tools. This book presents va

The book contains papers that focus explicitly on the last achievements (methods, algorithms, models, systems) with respect to the Third Dimension. Motivated by the rapid developments in 3D, the organ

Stochastic process models are a kind of mathematics that offers enormous opportunities for application to a wide range of problems in the real world, says Solberg (Purdue U.), but almost no one knows

Vibration problems arise in the design of almost all engineering machinery and structures. Many of these problems are extremely complex but their solution is essential if a safe and satisfactory design is to be achieved. The equations of motion are often insoluble by the classical methods of the calculus and so it is necessary to approximate on order to reduce them to a set of linear equations. The use of matrices simplifies the solution of sets of linear equations. This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades,

Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathemat

An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black–Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to b

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.

Longitudinal Analysis of Labor Market Data presents a set of papers by leading scholars on methods for analysing the longitudinal data that is available on numerous topics of interest to social scientists. Because many sources of longitudinal data record labour market phenomena such as unemployment, labour supply, earnings mobility, job turnover and participation in training programmes, all of the papers collected in this volume focus on models of the labour market. The main methodological points, however, are more general and apply to such diverse areas as demography, life science analysis and training evaluation, to name only a few, potential avenues of application. The book contains important methodological contributions to the emerging field of longitudinal analysis and is of interest to a wide range of social scientists.