Functional Analysis Methods for Reliability Models

This book has two components: stochastic dynamics and stochastic random combinatorial analysis. The first discusses evolving patterns of interactions of a large but finite number of agents of several types. Changes of agent types or their choices or decisions over time are formulated as jump Markov processes with suitably specified transition rates: optimisations by agents make these rates generally endogenous. Probabilistic equilibrium selection rules are also discussed, together with the distributions of relative sizes of the bases of attraction. As the number of agents approaches infinity, we recover deterministic macroeconomic relations of more conventional economic models. The second component analyses how agents form clusters of various sizes. This has applications for discussing sizes or shares of markets by various agents which involve some combinatorial analysis patterned after the population genetics literature. These are shown to be relevant to distributions of returns to as

The third edition of this successful textbook is fully updated and includes important recent developments in cosmology. It begins with an introduction to cosmology and general relativity, and goes on to cover the mathematical models of standard cosmology. The physical aspects of cosmology, including primordial nucleosynthesis, the astroparticle physics of inflation, and the current ideas on structure formation are discussed. Alternative models of cosmology are reviewed, including the model of Quasi-Steady State Cosmology, which has recently been proposed as an alternative to Big Bang Cosmology. The final chapters discuss observational cosmology, and debate theory versus observational methods. The book includes 400 problems and numerous worked examples. This introductory textbook describes modern cosmology at a level suitable for advanced undergraduates and graduates who are familiar with mathematical methods and basic theoretical physics. It is intended for use on courses in theoretic

Contain s current methods of analysis for new formulations of cosmetics, perfumes, creams, and lotions!With contributions from world-renowned experts in the field, Topical Absorption of Dermatological

This book provides a clear and detailed survey of basic neural network architectures and learning rules. In it, the authors emphasize mathematical analysis of networks, methods for training netw

What are the requirements for a just response to criminal wrongdoing? Drawing on comparative and empirical analysis of existing models of global practice, this book offers an approach aimed at restric

Almost every artifact in archaeological analysis originates in or on the ground. While there are elaborate methods for extracting and analyzing artifacts, treatment of the matrix within which they are

The Handbook is a definitive reference source and teaching aid for econometricians. It examines models, estimation theory, data analysis and field applications in econometrics. Comprehensive surv

The central tradition of mainline economics deals with one way of making a living; producing goods and services. But there is another way of getting ahead through conflict or the 'dark side', by appropriating what others have produced. Parallel to military aggression and resistance, the dark side includes non-military activities such as litigation, strikes and lockouts, takeover contests, and bureaucratic back-biting struggles. This volume brings the analysis of conflict into the mainstream of economics. Part I explores the causes, conduct, and consequences of conflict as an economic activity. Part II delves deeply into the evolutionary sources of our capacities, physical and mental, for both conflict and cooperation. The introductory chapter of the volume, which outlines the significance of the dark side, was the author's 1993 Presidential Address to the Western Economic Association. Other chapters investigate economic models, historical discussions, experimental tests, and applicatio

Market Models provides an authoritative and up-to-date treatment of the use of market data to develop models for financial analysis. Written by a leading figure in the field of financial data analysi

The central tradition of mainline economics deals with one way of making a living; producing goods and services. But there is another way of getting ahead through conflict or the 'dark side', by appropriating what others have produced. Parallel to military aggression and resistance, the dark side includes non-military activities such as litigation, strikes and lockouts, takeover contests, and bureaucratic back-biting struggles. This volume brings the analysis of conflict into the mainstream of economics. Part I explores the causes, conduct, and consequences of conflict as an economic activity. Part II delves deeply into the evolutionary sources of our capacities, physical and mental, for both conflict and cooperation. The introductory chapter of the volume, which outlines the significance of the dark side, was the author's 1993 Presidential Address to the Western Economic Association. Other chapters investigate economic models, historical discussions, experimental tests, and applicatio

In the clinical neurosciences, decision-making becomes ever more complicated because of rapidly emerging new diagnostic tests and treatments and increasing demands from patients to participate in their management. This concise but wide-ranging handbook reviews the epidemiology of neurological disease and the treatment and prognosis of all major diseases of the nervous system. Part one offers essential guidance for clinicians to quantitative methods in research, including genetic epidemiology, decision analysis, meta-analysis, outcomes research and survival analysis, and thus provides a good understanding of the evidence underlying clinical management. The second part is devoted to individual neurological diseases, covering etiology, diagnosis, prognosis, interventions, and implications for clinical practice. With contributions from leading international authorities, this book is an invaluable guide to clinical decision-making for neurologists and others involved in the management of ne

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

A concise survey of compliant mechanisms-from fundamentals to state-of-the-art applicationsThis volume presents the newest and most effective methods for the analysis and design of compliant mechanism

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thou

The world of intelligence has been completely transformed by the end of the Cold War and the onset of an age of information. Prior to the 1990s, US government intelligence had one principal target, the Soviet Union; a narrow set of 'customers', the political and military officials of the US government; and a limited set of information from the sources they owned, spy satellites and spies. Today, world intelligence has many targets, numerous consumers - not all of whom are American or in the government - and too much information, most of which is not owned by the U.S. government and is of widely varying reliability. In this bold and penetrating study, Gregory Treverton, former Vice Chair of the National Intelligence Council and Senate investigator, offers his insider's views on how intelligence gathering and analysis must change. He suggests why intelligence needs to be both contrarian, leaning against the conventional wisdom, and attentive to the longer term, leaning against the growin

This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.

Mechanisms are fundamental components of machines. They are used to transmit forces and moments and to manipulate objects in industrial machinery, robots, automobiles, aircraft, mechatronics devices and biomechanical systems. A knowledge of the kinematic and dynamic properties of mechanisms is essential for their design and control. This book describes methods and algorithms for the analysis of kinematic systems. Beginning with basic concepts, the book then discusses a variety of problem-solving approaches and computational techniques. Its distinctive feature is its focus on the contour equation as a powerful, computationally efficient tool that will help the reader to design complex spatial mechanisms. This handy text will be useful for senior or graduate students, researchers and practising engineers working in robotics, vehicle dynamics, mechatronics and machine design.

This book, first published in 2001, explores two shifts in the paradigms of governance in Western bureaucracies. They are the widespread use of privatisation, private firms and market methods to run core public services, and the conscious attempt to transform the role of citizenship from ideals of entitlement and security to notions of mutual obligation, selectivity and risk. Considine examines the most important service of the modern welfare state - unemployment assistance - to explain and theorise the nature of these radical changes. He undertakes research in the United Kingdom, the Netherlands, Australia and New Zealand, four countries which have been among the boldest reformers within the OECD, yet each adopting different models. Each case is a break from the standards of responsible democracy and legal-rational bureaucracy, with at least one government opting for a commercial paradigm based on targets and economic incentives and another opting for a model based on network governan

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this mon

This is a 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. It is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included.

This is a 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. It is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included.

This book provides an introduction to the analysis of interaction effects in logistic regression by focusing on the interpretation of the coefficients of interactive logistic models for a wide range

When a structure is put under an increasing compressive load, it becomes unstable and buckling occurs. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that exist in real systems. The techniques are based on two complementary theories which are developed in the text. First, the probabilistic theory of stability is presented, with particular emphasis on reliability. Both theoretical and computational issues are discussed. Secondly, the authors present the alternative to probability based on the notion of 'anti-optimization', a theory that is valid when the necessary information for probabilistic analysis is absent, that is, when only scant data are available. Design engineers, researchers, and graduate students in aerospace, mechanical, marine, and civil engineering who are concerned with iss

Natural Language Semantics discusses fundamental concepts for linguistic semantics. This book combines theoretical explanations of several methods of inquiry with detailed semantic analysis and emphas

Natural Language Semantics discusses fundamental concepts for linguistic semantics. This book combines theoretical explanations of several methods of inquiry with detailed semantic analysis and emphas

This book provides a powerful theoretical framework for understanding cross-national cultural differences. Focusing on France and America, it analyses how the people of these two different cultures mobilise national 'repertoires of evaluation' to make judgements about politics, economics, morals and aesthetics. The analysis draws on eight case studies by eleven French and American researchers who have worked together over a number of years to develop systematic comparisons between these countries. The topics are wide-ranging, comparing how individuals use the cultural tools at their disposal to answer questions such as: are races equal? What constitutes sexual harassment? What is the value of contemporary art? Should journalists be neutral? How can the defense of the environment be reconciled with economic imperatives? Moving beyond simplistic essentialist models of national character, this comparative approach offers important insights that will interest not only sociologists but also

This book provides a powerful theoretical framework for understanding cross-national cultural differences. Focusing on France and America, it analyses how the people of these two different cultures mobilise national 'repertoires of evaluation' to make judgements about politics, economics, morals and aesthetics. The analysis draws on eight case studies by eleven French and American researchers who have worked together over a number of years to develop systematic comparisons between these countries. The topics are wide-ranging, comparing how individuals use the cultural tools at their disposal to answer questions such as: are races equal? What constitutes sexual harassment? What is the value of contemporary art? Should journalists be neutral? How can the defense of the environment be reconciled with economic imperatives? Moving beyond simplistic essentialist models of national character, this comparative approach offers important insights that will interest not only sociologists but also

This pioneering book is based upon very extensive analysis of the famous 1851 Census of Religious Worship and earlier sources such as the 1676 Compton Census. The authors stress contextual and regional understanding of religion. Among the subjects covered for all of England and Wales are the geography of the Church of England, Roman Catholicism, the old and new dissenting denominations, the spatial complementarity of denominations, and their importance for political history. A range of further questions are then analysed, such as regional continuities in religion, the growth of religious pluralism, Sunday schools and child labour during industrialisation, free and appropriated church sittings, landownership and religion, and urbanisation and regional 'secularisation'. This book's advanced methods and findings will have far-reaching influence within the disciplines of history, historical and cultural geography, religious sociology and in the social science community general.

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, first published in 2000, is based on the modern conceptual understanding of crystal fields. It provides readers with clear instructions and a set of computer programs for the phenomenological analysis of energy spectra of magnetic ions in solids. The text clarifies several issues that have historically produced confusion in this area, particularly the effects of covalency and ligand polarization on the energy spectra of magnetic ions. Readers are shown how to employ a hierarchy of parametrized models to extract as much information as possible from observed lanthanide and actinide spectra. This book of crystal field theory describes all of the available phenomenological models, together with the conceptual and computational tools necessary for their use. It will be of particular interest to graduate students and researchers working in the development of opto-electronic systems and magnetic materials.

This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra.

Modern policy problems require analysts to capture the interactions between policy and the complexities of economic and social life, as well as between policies of different types. Increasingly, microsimulation is employed to analyse these problems. This book brings together examples of microsimulation modelling that are at the frontiers of developments in the field, either because they extend the range of techniques available to modellers, or because they demonstrate new applications for established methods. It represents the state of the art with chapters on the use of microsimulation for comparative policy research and for challenging conventional assumptions, combining microsimulation with other types of economic models and the much-neglected subjects of model alignment and validation. Data and case studies are taken from regions including Asia-Pacific, Europe and North America.

The theory of competition has held a central place in economic analysis since Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of perfect competition. Beginning with a concise survey of how the theory of competition has evolved, Gale makes extensive and rigorous use of dynamic matching and bargaining models to provide a more complete description of how a competitive equlibrium is achieved. Whereas economists have made use of a macroscopic description of markets in which certain behavioral characteristics, such as price-taking behavior, are taken for granted, Gale uses game theory to re-evaluate this assumption, beginning with individual agents and modelling their strategic interaction. A strategic foundation for competitive equilibrium shows how such interaction leads to competitive, price-taking behavior. Essential reading for graduate courses in game

The theory of competition has held a central place in economic analysis since Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of perfect competition. Beginning with a concise survey of how the theory of competition has evolved, Gale makes extensive and rigorous use of dynamic matching and bargaining models to provide a more complete description of how a competitive equlibrium is achieved. Whereas economists have made use of a macroscopic description of markets in which certain behavioral characteristics, such as price-taking behavior, are taken for granted, Gale uses game theory to re-evaluate this assumption, beginning with individual agents and modelling their strategic interaction. A strategic foundation for competitive equilibrium shows how such interaction leads to competitive, price-taking behavior. Essential reading for graduate courses in game

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.

Macroeconomic modelling has been one of the most important and influential areas of economic research. This book presents contributions from the leading researchers working in this area as part of the ongoing research project sponsored by the Economic and Social Research Council, Bank of England and UK Treasury. The papers combine a description of the latest techniques used in modelling the economy with an account of the way that models can be used for purposes of policy analysis. Designed for use by advanced students and professional economists, the book considers issues including: why 'bad' forecasters, i.e. those with no coherent and properly articulated view of the functioning of the macroeconomy, do so well; reconciling short term dynamics with economic theory; modelling tax policy; and the stabilisation costs of European Monetary Union.

The concepts of rents and rent-seeking are central to any discussion of the processes of economic development. Yet conventional models of rent-seeking are unable to explain how it can drive decades of rapid growth in some countries, and at other times be associated with spectacular economic crises. This book argues that the rent-seeking framework has to be radically extended by incorporating insights developed by political scientists, institutional economists and political economists if it is to explain the anomalous role played by rent-seeking in Asian countries. It includes detailed analysis of Thailand, Malaysia, the Philippines, the Indian sub-continent, Indonesia and South Korea. This new critical and multidisciplinary approach has important policy implications for the debates over institutional reform in developing countries. It brings together leading international scholars in economics and political science, and will be of great interest to readers in the social sciences and As

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.