Matrix-analytic Methods in Stochastic Models

There is a certain body of knowledge and methods that finds application in most branches of fluid mechanics. This book aims to supply a proper theoretical understanding that will permit sensible simplifications to be made in the formulation of problems, and enable the reader to develop analytical models of practical significance. Such analyses can be used to guide more detailed experimental and numerical investigations. As in most technical subjects, such understanding is acquired by detailed study of highly simplified 'model problems'. The first part (Chapters 1-4) is concerned entirely with the incompressible flow of a homogeneous fluid. It was written for the Boston University introductory graduate level course 'Advanced Fluid Mechanics'. The remaining Chapters 5 and 6 deal with dispersive waves and acoustics, and are unashamedly inspired by James Lighthill's masterpiece, Waves in Fluids.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

There is growing consensus in the development economics literature that ethnic diversity is a very significant factor in explaining Africa's poor economic performance. Ethnic Diversity and Economic Instability in Africa challenges this conventional wisdom. Drawing on the insights of historians, anthropologists and political scientists as well as development economists, this book questions whether ethnicity is the most useful organising principle by which to examine the economic development of Africa, arguing that it is a more fluid and contingent concept than economic models allow. Instead, the authors explore the actual experience of ethnicity in Africa and propose new methods of measuring ethnic diversity and inequalities. Finally some tentative conclusions are reached regarding appropriate policy reforms.

Presenting a systematic model reduction and hierarchical controller design framework for broad classes of integrated process systems encountered in practice, this book first studies process systems with large material recycle and/or with small purge streams, followed by systems with energy integration. Step-by-step model reduction procedures are developed to derive nonlinear reduced models of the dynamics in each time scale. Hierarchical control architectures consisting of coordinated levels of control action in different time scales are proposed for each class of process systems considered to enforce stability, tracking performance and disturbance rejection. Numerous process applications are discussed in detail to illustrate the application of the methods and their potential to improve process operations. MATLAB codes are also presented to guide further application of the methods developed and facilitate practical implementations.

Over the past forty years, scientists have developed models of human reasoning based on the principle that human languages and classical logic involve fundamentally different concepts and different methods of interpretation. In The Emergence of Meaning Stephen Crain challenges this view, arguing that a common logical nativism underpins human language and logical reasoning. The approach which Crain takes is twofold. Firstly, he uncovers the underlying meanings of logical expressions and logical principles that appear in typologically different languages - English and Mandarin Chinese - and he demonstrates that these meanings and principles directly correspond to the expressions and structures of classical logic. Secondly he reports the findings of new experimental studies which investigate how children acquire the logical concepts of these languages. A step-by-step introduction to logic and a comprehensive review of the literature on child language acquisition make this work accessible

The traditional view of the relationship between business and the arts is very much a one-way affair: organisations may endorse, fund or publicise the arts but the arts have nothing to offer from a business perspective. The Value of Arts for Business challenges this view by showing how the arts, in the form of Arts-based Initiatives (ABIs), can be used to enhance value-creation capacity and boost business performance. The book introduces and explains three models that show how organisations can successfully implement and manage ABIs. Firstly, the Arts Value Matrix enables managers to see how organisational value-drivers are affected by ABIs. Secondly, the Arts Benefits Constellation shows how to assess the benefits of using ABIs. Finally, the Arts Value Map shows how ABIs can be integrated and aligned with organisational strategy and operations. These models lay the foundations for a new research area exploring the links between arts and business.

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 book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9781107407350.

?In this brief we consider some stochastic models that may be used to study problems related to environmental matters, in particular, air pollution. The impact of exposure to air pollutants on people

Quantitative modeling techniques and methods are central to the study and development of process engineering, including mineral processing. Models in mineral processing have been difficult to develop

Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing an

The small sample properties of estimators and tests are frequently too complex to be useful or are unknown. Much econometric theory is therefore developed for very large or asymptotic samples where it is assumed that the behaviour of estimators and tests will adequately represent their properties in small samples. Refined asymptotic methods adopt an intermediate position by providing improved approximations to small sample behaviour using asymptotic expansions. Dedicated to the memory of Michael Magdalinos, whose work is a major contribution to this area, this book contains chapters directly concerned with refined asymptotic methods. In addition, there are chapters focusing on new asymptotic results; the exploration through simulation of the small sample behaviour of estimators and tests in panel data models; and improvements in methodology. With contributions from leading econometricians, this collection will be essential reading for researchers and graduate students concerned with th

Recent research on joint or dyadic decision making has received renewed attention from behavioral scientists. This interest is due mostly to the advances in analytic and conceptual models used to stud

Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short-term risk modelling, model-based pricing, risk-sharing, ruin theory and credibility. It covers much of the international syllabuses for professional actuarial examinations in risk models, but goes into further depth, with worked examples, exercises and detailed case studies. The authors also use the statistical package R to demonstrate how simple code and functions can be used profitably in an actuarial context. The authors' engaging and pragmatic approach, balancing rigour and intuition and developed over many years of teaching the subject, makes this book ideal for self-study or for students taking courses in risk modelling.

Effective participatory water management requires effective co-engineering – the collective process whereby organisational decisions are made on how to bring stakeholders together. This trans-disciplinary book highlights the challenges involved in the collective initiation, design, implementation and evaluation of water planning and management processes. It demonstrates how successful management requires the effective handling of two participatory processes: the stakeholder water management process and the co-engineering process required to organise this. The book provides practical methods for supporting improved participatory processes, including the application of theory and models to aid decision-making. International case studies of these applications from Australia, Europe and all over the world, including Africa, are used to examine negotiations and leadership approaches, and their effects on the participatory stakeholder processes. This international review of participatory wat

Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process a

This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

Democratization and Research Methods is a coherent survey and critique of both democratization research and the methodology of comparative politics. The two themes enhance each other: the democratization literature illustrates the advantages and disadvantages of various methodological approaches, and the critique of methods makes sense of the vast and bewildering democratization field. Michael Coppedge argues that each of the three main approaches in comparative politics - case studies and comparative histories, formal modeling and large-sample statistical analysis - accomplishes one fundamental research goal relatively well: 'thickness', integration and generalization, respectively. Throughout the book, comprehensive surveys of democratization research demonstrate that each approach accomplishes one of these goals well but the other two poorly. Chapters cover conceptualization and measurement, case studies and comparative histories, formal models and theories, political culture and su

Democratization and Research Methods is a coherent survey and critique of both democratization research and the methodology of comparative politics. The two themes enhance each other: the democratization literature illustrates the advantages and disadvantages of various methodological approaches, and the critique of methods makes sense of the vast and bewildering democratization field. Michael Coppedge argues that each of the three main approaches in comparative politics - case studies and comparative histories, formal modeling and large-sample statistical analysis - accomplishes one fundamental research goal relatively well: 'thickness', integration and generalization, respectively. Throughout the book, comprehensive surveys of democratization research demonstrate that each approach accomplishes one of these goals well but the other two poorly. Chapters cover conceptualization and measurement, case studies and comparative histories, formal models and theories, political culture and su

Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving err

This book describes the tectonic landforms resulting from major internal and external forces acting on the outer layers of solid bodies throughout the Solar System. It presents a detailed survey of tectonic structures at a range of length scales found on Mercury, Venus, the Moon, Mars, the outer planet satellites, and asteroids. A diverse range of models for the sources of tectonic stresses acting on silicate and icy crusts is outlined, comparing processes acting throughout the Solar System. Rheological and mechanical properties of planetary crusts and lithospheres are discussed to understand how and why tectonic stresses manifest themselves differently on various bodies. Results from fault population data are assessed in detail. The book provides methods for mapping and analysing planetary tectonic features, and is illustrated with diagrams and spectacular images returned by manned and robotic spacecraft. It forms an essential reference for researchers and students in planetary geolog

This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behaviour of continuous materials. This self-contained textbook is tailored for advanced undergraduate or first-year graduate students with numerous step-by-step derivations and worked-out examples. The author presents both the general continuum theory and the mathematics needed to apply it in practice. The derivation of constitutive models for ideal gases, fluids, solids and biological materials, and the numerical methods required to solve the resulting differential equations, are also detailed. Specifically, the text presents the theory and numerical implementation for the finite difference and the finite element methods in the Matlab® programming language. It includes thirteen detailed Matlab® programs illustrating how constitutive models are used in practice.

Stochastic Averaging and Extremum Seeking treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments.

"Risk analysis is crucial in stochastic supply chain models. Over the past few years, the pace has quickened for research attempting to explore risk analysis issues in supply chain management problem

Giving a detailed overview of the subject, this book takes in the results and methods that have arisen since the term 'self-organised criticality' was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the famous Bak-Tang-Wiesenfeld sandpile, ten key models are carefully defined, together with their results and applications. Comprehensive tables of numerical results are collected in one volume for the first time, making the information readily accessible to readers. Written for graduate students and practising researchers in a range of disciplines, from physics and mathematics to biology, sociology, finance, medicine and engineering, the book gives a practical, hands-on approach throughout. Methods and results are applied in ways that will relate to the reader's own research.

Understanding damage and failure of composite materials is critical for reliable and cost-effective engineering design. Bringing together materials mechanics and modeling, this book provides a complete guide to damage, fatigue and failure of composite materials. Early chapters focus on the underlying principles governing composite damage, reviewing basic equations and mechanics theory, before describing mechanisms of damage such as cracking, breakage and buckling. In subsequent chapters, the physical mechanisms underlying the formation and progression of damage under mechanical loads are described with ample experimental data, and micro- and macro-level damage models are combined. Finally, fatigue of composite materials is discussed using fatigue-life diagrams. While there is a special emphasis on polymer matrix composites, metal and ceramic matrix composites are also described. Outlining methods for more reliable design of composite structures, this is a valuable resource for engineer

This book introduces the basic tools of dynamic optimization in economics to study environmental problems, applies econometric methods to estimate and test the models derived by dynamic optimization,

Astronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced und

How can I supercharge the therapy I currently use?This volume distils the core principles, methods, and vision of the approach. Each Functional Analytic Psychotherapy (FAP) principle is presented in t

How can I supercharge the therapy I currently use?This volume distils the core principles, methods, and vision of the approach. Each Functional Analytic Psychotherapy (FAP) principle is presented in t

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Explorin

This books covers the broad range of research in stochastic models and optimization. Applications presented include networks, financial engineering, production planning, and supply chain management. E

Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic p

The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic diffe

This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox–Ross–Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox–Ross–Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.

The stone tools and fossil bones from the earliest archaeological sites in Africa have been used over the past fifty years to create models that interpret how early hominins lived, foraged, behaved and communicated and how early and modern humans evolved. In this book, an international team of archaeologists and primatologists examines early Stone Age tools and bones and uses scientific methods to test alternative hypotheses that explain the archaeological record. By focusing on both lithics and faunal records, this volume presents the most holistic view to date of the archaeology of human origins.

A textbook for studentsand a reference guide for professionals, this text builds a foundation in the key methods and models of quantitative finance from the perspective of their implementation i