Matrix-analytic Methods in Stochastic Models

This introduction to the field of many-body atomic physics is suitable for researchers and graduate students. Drawing from three major subject areas, atomic structure, atomic photoionization, and electron-atom collisions, this book begins with an introduction to many-body diagrams, and continues with several chapters devoted to each subject area written by leading theorists in that field. Topics in atomic structure include the relativistic theory for highly charged atomic ions and calculations of parity nonconservation. Topics in atomic photoionization include single and double photoionization processes, and photoelectron angular distributions. Topics in electron-atom collisions include the theory of electron impact ionization, perturbation series methods, target dependence of the triply differential cross section, Thomas processes, R-matrix theory, close coupling, and distorted-wave theory. This coherent and carefully edited volume has been prepared by leading atomic physicists as a t

This book describes a major method in modelling the flow of water and transport of solutes in the subsurface, a subject of considerable interest in the exploitation and preservation of water resources. The stochastic approach allows the uncertainty which affects various properties and parameters to be incorporated in models of subsurface flow and transport. These much more realistic models are of greater use in, for example, modelling the transport and build-up of contaminants in groundwater. The volume is based on the second Kovacs Colloquium organised by the International Hydrological Programme (UNESCO) and the International Association of Hydrological Sciences. Fifteen leading scientists with international reputations review the latest developments in this area. The book is a valuable reference work for graduate students, research workers and professionals in government and public institutions, interested in hydrology, environmental issues, soil physics, petroleum engineering, geolo

An important problem in computational biology is identifying short DNA sequences (mathematically, 'words') associated to a biological function. One approach consists in determining whether a particular word is simply random or is of statistical significance, for example, because of its frequency or location. This book introduces the mathematical and statistical ideas used in solving this so-called exceptional word problem. It begins with a detailed description of the principal models used in sequence analysis: Markovian models are central here and capture compositional information on the sequence being analysed. There follows an introduction to several statistical methods that are used for finding exceptional words with respect to the model used. The second half of the book is illustrated with numerous examples provided from the analysis of bacterial genomes, making this a practical guide for users facing a real situation and needing to make an adequate procedure choice.

Studies of dental and skeletal growth and development have often been treated as independent disciplines within the literature. Human Growth in the Past, first published in 1999, brings together these two related fields of enquiry in a single volume whose purpose is to place methodological issues of growth and development in past populations within a strong theoretical framework. Contributions examine a variety of aspects of human growth in the past, drawing from both palaeoanthropological and bioarchaeological data. The book covers a wide spectrum of topics, from patterns of growth in humans and their close relatives, innovative methods and applications of techniques and models for the study of growth, to estimation of age-at-death in subadults and infant mortality in archaeological samples. Human Growth in the Past will be of interest to biological anthropologists, and those in the related fields of dental anatomy, evolutionary biology and developmental biology.

This textbook provides a clear and concise introduction to computer architecture and implementation. Two important themes are interwoven throughout the book. The first is an overview of the major concepts and design philosophies of computer architecture and organization. The second is the early introduction and use of analytic modeling of computer performance. The author begins by describing the classic von Neumann architecture, and then presents in detail a number of performance models and evaluation techniques. He goes on to cover user instruction set design, including RISC architecture. A unique feature of the book is its memory-centric approach - memory systems are discussed before processor implementations. The author also deals with pipelined processors, input/output techniques, queuing modes, and extended instruction set architectures. Each topic is illustrated with reference to actual IBM and Intel architectures. The book contains many worked examples and over 130 homework exer

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.

This textbook provides a general overview of realistic mathematical models in life sciences, considering both deterministic and stochastic models and covering dynamical systems, game theory, stochasti

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

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

This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.

Electronic Concepts provides a detailed introduction to modern microelectronics. Equal emphasis is placed on analog and digital circuits, and the applications of particular devices and circuits are described within the context of actual electronic systems. The author begins with an overview of several important electronic systems, discussing in detail the types of signals that circuits are used to process. In the following chapters, he deals with individual devices. For each device he presents a brief physical description and demonstrates the use of different models in describing the device's behaviour in a particular circuit application. SPICE computer simulations are used throughout the text to supplement analytic descriptions. The book contains over 500 circuit diagrams and figures, over 400 homework problems, and over 100 simulation and design exercises. It includes many worked examples and is an ideal textbook for introductory courses in electronics. Laboratory experiments are ava

This book is an introduction to the physics of highly excited, easily perturbed or interacting atoms. The book begins with a brief introduction to the traditional view of electron shells and their properties, and then goes on to discuss Rydberg states, quantum defect theory, atomic f-values, centrifugal barrier effects, autoionisation, inner shell and double excitation spectra, K-matrix theory, atoms in high laser fields, statistical methods, quantum chaos, and atomic effects in solids. The emphasis is throughout on radial properties, orbital collapse, many body effects, the breakdown of the independent particle approach, the emergence of chaos, and the behaviour of atoms inside clusters and solids. A very full account of autoionisation includes not only the standard treatment for isolated resonances, but also several alternative approaches. The book discusses many experimental examples and has many diagrams and a comprehensive reference list.

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review articles at an advanced research level, describing results for one-dimensional models of dynamical processes such as chemical reactions and catalysis, kinetic ising models, phase separation and cluster growth, monolayer and multilayer adsorption with added relaxation, surface and hard-core particle dynamics, diffusional transport, random systems and experimental results. It also covers experimental results for systems ranging from chemical reactions to adsorption and reactions on polymer chains, steps on crystalline surfaces, and DNA. All chapters are written by leading scientists in the field. They present a self-contained review of this subject that will guide a reader from basic concepts, ideas, methods and models to the forefront o

Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical rigor. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling - game theory, statistics, and computational methods - and proposes a new framework for modeling. Unlike previous treatments which view each field separately, the treatment provides a framework that spans and incorporates the different methodological approaches. The goal is to arrive at a new vision of modeling that allows researchers to solve more complex problems in the social sciences. Additionally, a special emphasis is placed upon the role of computational modeling in the social sciences.

Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical rigor. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling - game theory, statistics, and computational methods - and proposes a new framework for modeling. Unlike previous treatments which view each field separately, the treatment provides a framework that spans and incorporates the different methodological approaches. The goal is to arrive at a new vision of modeling that allows researchers to solve more complex problems in the social sciences. Additionally, a special emphasis is placed upon the role of computational modeling in the social sciences.

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulatio

Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for stude

Human Demography and Disease offers an interdisciplinary and integrated perspective on the relationship between historical populations and the dynamics of epidemiological processes. It brings the techniques of time-series analysis and computer matrix modelling to historical demography and geography to extract detailed information concerning the oscillations in births, deaths, migrations and epidemics from parish registers and other data series and to build mathematical models of the population cycles. This book presents a new way of studying pre-industrial communities and explores the subtle, and hitherto undetected effects of fluctuating nutritional levels on mortality patterns and the dynamics of infectious diseases. It will be of interest to researchers, teachers and students in the fields of demography, anthropology, historical geography, social history, population biology and epidemiology.

In recent years the application of random matrix techniques to analytic number theory has been responsible for major advances in this area of mathematics. As a consequence it has created a new and rapidly developing area of research. The aim of this book is to provide the necessary grounding both in relevant aspects of number theory and techniques of random matrix theory, as well as to inform the reader of what progress has been made when these two apparently disparate subjects meet. This volume of proceedings is addressed to graduate students and other researchers in both pure mathematics and theoretical physics. The contributing authors, who are among the world leading experts in this area, have taken care to write self-contained lectures on subjects chosen to produce a coherent volume.

This text provides a new approach to the subject, including a comprehensive survey of novel theoretical approaches, methods, and models used in macroeconomics and macroeconometrics. The book gives ext

Acid-base cements have been known since the mid-nineteenth century and offer an alternative to polymerization as a route for forming solid substances. They are quick setting materials and some have unusual properties for cements, such as adhesion and translucency. They find diverse applications ranging from the biomedical to the industrial. Despite this there has been a failure to recognize them as constituting a single, well defined class of material. This book attempts to remedy this situation by unifying the subject and treating this range of materials as a single class. Following a brief historical overview, an introductory chapter defines these cements as materials that are formed by reacting a basic powder with an acidic liquid to yield a salt-like matrix. The nature of the cementation process and the cement-forming acids and bases are discussed. Other chapters are devoted to the methods of study, the structure of water and simple polyelectrolyte theory. In the remaining chapter

The Lund model, inspired by quantum chromodynamics, has provided a very promising approach to the dynamics of quark and gluon interactions. Starting with a brief reprise of basic concepts in relativity, quantum mechanics of fields and particle physics, this 1998 book discusses: the dynamics of the massless relativistic string; confinement; causality and relativistic covariance; Lund fragmentation processes; QED and QCD Bremsstrahlung; multiplicities and particle-parton distributions. Throughout the book, theory is confronted with current experimental data, and implications for future experiments are also considered. The book also explores the relationships between the Lund model and other models based on field theory (the Schwinger model, S-matrix models, light-cone algebra physics and variations of the parton model), and models based on statistical mechanics (the Feynman-Wilson gas, scaling, iterative cascade models).

This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemic

This authoritative volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example, 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory.

This is the first book presenting a stochastic extension of process algebra, PEPA; this is shown to be suitable for specifying a Markov process, which can then be applied to performance modelling. The method, which is illustrated with case studies taken from the area of communication systems, can readily be used to construct a variety of models that can be analysed using standard numerical techniques. One of the major advantages of PEPA over the standard methods for specifying stochastic performance models is the inherent apparatus for reasoning about the structure and behaviour of models. In the later chapters this apparatus is exploited to define four equivalence relations over PEPA components. Each of these notions of equivalence has intrinsic interest from a process algebra perspective. However, they are also demonstrated to be useful in a performance modelling context. To conclude the book, a section has been added surveying recent results in the area and discussing open questions

The 26 chapters in this graduate text examine the recognized methods for quantifying each of the major components at the five body composition levels, body composition models for estimating specific c

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.

Personality is now understood to be a function of both biological and environmental influences. This revised and updated edition of Psychobiology of Personality describes what is currently known about the biological basis of the primary personality traits, including genetic, neurological, biochemical, physiological, and behavioral influences. Emphasis is placed on understanding the connections between phenomena at these levels. The research discussed makes use of animal models, based on experimental brain research, as well as human clinical and normal personality research. Chapters are devoted to temperament and personality trait structure, psychobiological methods, and each of four major personality traits: extraversion, impulsive, sensation seeking, and aggression. Recent advances in psychobiological methods, such as molecular genetics and brain imaging have enabled us to begin to unravel the genetic and neurological sources of behavior and personality. These advances are discussed i

Personality is now understood to be a function of both biological and environmental influences. This revised and updated edition of Psychobiology of Personality describes what is currently known about the biological basis of the primary personality traits, including genetic, neurological, biochemical, physiological, and behavioral influences. Emphasis is placed on understanding the connections between phenomena at these levels. The research discussed makes use of animal models, based on experimental brain research, as well as human clinical and normal personality research. Chapters are devoted to temperament and personality trait structure, psychobiological methods, and each of four major personality traits: extraversion, impulsive, sensation seeking, and aggression. Recent advances in psychobiological methods, such as molecular genetics and brain imaging have enabled us to begin to unravel the genetic and neurological sources of behavior and personality. These advances are discussed i

This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

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

Two professors at Indiana University walk through the process of constructing mathematical models, and illustrate the use of stochastic processes to model several situations arising in biology, ecolog

This book studies the formation of complex societies in prehistoric China during the Neolithic and early state periods, c. 7000–1500 BC. Archaeological materials are interpreted through anthropological perspectives, using systematic analytic methods in settlement and burial patterns. Both agency and process are considered in the development of chiefdoms and in the emergence of early states in the Yellow River region. Interrelationships between factors such as mortuary practice, craft specialization, ritual activities, warfare, exchange of elite goods, climatic fluctuations, and environmental changes are emphasized. This study offers a critical evaluation of current archaeological data from Chinese sources, and argues that, although some general tendencies are noted, social changes were affected by multiple factors in no pre-determined sequence. In this most comprehensive study to date, Li Liu attempts to reconstruct developmental trajectories toward early states in Chinese civilization

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and

Inelastic Analysis of Solids and Structures presents in a unified manner the physical and theoretical background of inelastic material models and computational methods, and illustrates the behavior of

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

Knowledge Management in the Construction Industry: A Socio-Technical Perspective presents a portfolio of concepts, methods, models, and tools supported by real life case studies from various corners o