Methods of Nonlinear Analysis

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

Advances in experimental methods have resulted in the generation of enormous volumes of data across the life sciences. Hence clustering and classification techniques that were once predominantly the domain of ecologists are now being used more widely. This 2006 book provides an overview of these important data analysis methods, from long-established statistical methods to more recent machine learning techniques. It aims to provide a framework that will enable the reader to recognise the assumptions and constraints that are implicit in all such techniques. Important generic issues are discussed first and then the major families of algorithms are described. Throughout the focus is on explanation and understanding and readers are directed to other resources that provide additional mathematical rigour when it is required. Examples taken from across the whole of biology, including bioinformatics, are provided throughout the book to illustrate the key concepts and each technique's potential.

This book is entirely devoted to the study of children's skeletons from archaeological and forensic contexts. It provides an extensive review of the osteological methods and theoretical concepts of their analysis. Non-adult skeletons provide a wealth of information on the physical and social life of the child from their growth, diet and age at death, to factors that expose them to trauma and disease at different stages of their lives. This book covers the factors that affect non-adult skeletal preservation; the assessment of their age, sex and ancestry; growth and development; infant and child mortality including infanticide; weaning ages and disease of dietary deficiency; skeletal pathology; personal identification and exposure to trauma from birth injuries, accidents and child abuse; providing insights for graduates and postgraduates in osteology, palaeopathology and forensic anthropology.

Computational Molecular Evolution provides an up-to-date and comprehensive coverage of modern statistical and computational methods used in molecular evolutionary analysis, such as maximum likelihood

The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges and high-rise buildings. This 2001 book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The book begins with a review of basic mathematics needed to understand subsequent material. Chapters then cover more recent and valuable developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspec

As the analysis of social networks, or networks of interpersonal and social relationships among social groups, has become an increasingly important method of research in several of the social and behavioural sciences, the gathering of network data has outpaced the development of new methods for its analysis. Addressing the need for analytical tools, Philippa Pattison presents a number of algebraic models for the analysis of network data, explaining in the process the rationale for an algebraic approach. Models are developed for both complete networks, meaning those representing the social ties between all pairs of members in a given group, and local networks, meaning those structured around the social ties of one particular group member. Many applications are presented and the ways that these methods can address a number of important issues confronting network analysis are explained.

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

fMRI is a very popular method for researchers and clinicians to image human brain activity in response to given mental tasks. This book presents a comprehensive review of the methods for computing activity maps, while providing an intuitive and mathematical outline of how each method works. The approaches include statistical parametric maps (SPM), hemodynamic response modeling and deconvolution, Bayesian, Fourier and nonparametric methods. The newest activity maps provide information on regional connectivity and include principal and independent component analysis, crisp and fuzzy clustering, structural equation modeling, and dynamic causal modeling. Preprocessing and experimental design issues are discussed with references made to the software available for implementing the various methods. Aimed at graduate students and researchers, it will appeal to anyone with an interest in fMRI and who is looking to expand their perspectives of this technique.

How do I decide I am ill; how do I decide that my children are ill? How do I learn effective ways of conveying to others that I am ill? This book discusses the languages of illness which we use to present our discomforts to others through an exploration of the child's world of illness. It looks at how illness concepts are introduced to children, how the causes of illness and 'germ' rationales are incorporated into the socialisation of children, and how a particular morality about health and illness is expressed. Besides the analysis of the social context within which the children's views are developing, the book presents the children's own views from three years old up to thirteen. How we talk about illness can have as important consequences as the methods we use to cure it. This book persuades the reader to look more closely at the language of illness, allowing a reappraisal to medical practice, school health programmes and class teaching, health education and even the differences in

Advanced Dynamics is a broad and detailed description of the analytical tools of dynamics as used in mechanical and aerospace engineering. The strengths and weaknesses of various approaches are discussed, and particular emphasis is placed on learning through problem solving. The book begins with a thorough review of vectorial dynamics and goes on to cover Lagrange's and Hamilton's equations as well as less familiar topics such as impulse response, and differential forms and integrability. Techniques are described that provide a considerable improvement in computational efficiency over the standard classical methods, especially when applied to complex dynamical systems. The treatment of numerical analysis includes discussions of numerical stability and constraint stabilization. Many worked examples and homework problems are provided. The book is intended for use on graduate courses on dynamics, and will also appeal to researchers in mechanical and aerospace engineering.

The science called 'harmonics' was one of the major intellectual enterprises of Greek antiquity. Ptolemy's treatise seeks to invest it with new scientific rigour; its consistently sophisticated procedural self-awareness marks it as a key text in the history of science. This book is a sustained methodological exploration of Ptolemy's project. After an analysis of his explicit pronouncements on the science's aims and the methods appropriate to it, it examines Ptolemy's conduct of his investigation in detail, concluding that despite occasional uncertainties, the declared procedure is followed with remarkable fidelity. Ptolemy pursues tenaciously his novel objective of integrating closely the project's theoretical and empirical phases and shows astonishing mastery of the concept, the design and the conduct of controlled experimental tests. By opening up this neglected text to historians of science, the book aims to provide a point of departure for wider studies of Greek scientific method.

Shakespeare and Social Dialogue deals with Shakespeare's language and the rhetoric of Elizabethan letters. Moving beyond claims about the language of individual Shakespearean characters, Magnusson analyses dialogue, conversation, sonnets and particularly letters of the period, which are normally read as historical documents, as the verbal negotiation of specific social and power relations. Thus, the rhetoric of service or friendship is explored in texts as diverse as Sidney family letters, Shakespearean sonnets and Burghley's state letters. The book draws on ideas from discourse analysis and linguistic pragmatics, especially 'politeness theory', relating these to key ideas in epistolary handbooks of the period, including those by Erasmus and Angel Day and demonstrates that Shakespeare's language is rooted in the everyday language of Elizabethan culture. Magnusson creates a way of reading both literary texts and historical documents which bridges the gap between the methods of new histo

Toru Takemitsu (1930–1996) was the best-known Japanese composer of his generation, bringing aspects of Eastern and Western traditions together, yet he remained something of an elusive figure. The composer's own commentaries about his music, poetic and philosophical in tone, have tended to deepen the mystery and much writing on Takemitsu to date has adopted a similar attitude, leaving many questions about his compositional methods unanswered. This book is the first complete study of the composer's work to appear in English. It is also the first book in this language to offer an in-depth analysis of his music. Takemitsu's works are increasingly popular with Western audiences and Peter Burt attempts for the first time to shed light on the hitherto rather secretive world of his working methods, as well as place him in context as heir to the rich tradition of Japanese composition in the twentieth century.

This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered range from linear algebra, such as inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and non-optimal properties of Gauss-Markov, Bayes, and shrinkage estimators under assumption of normality, the optimal properties of F-test, and the analysis of covariance and missing observa

Laser Induced Breakdown Spectroscopy (LIBS) is an emerging technique for determining elemental composition. With the ability to analyse solids, liquids and gases with little or no sample preparation, it is more versatile than conventional methods and is ideal for on-site analysis. This is a comprehensive reference explaining the fundamentals of the LIBS phenomenon, its history and its fascinating applications across eighteen chapters written by recognized leaders in the field. Over 300 illustrations aid understanding. This book will be of significant interest to researchers in chemical and materials analysis within academia and industry.

Revised and fully updated, the second edition of this graduate textbook offers a comprehensive explanation of the technology and physics of LEDs such as infrared, visible-spectrum, ultraviolet, and white LEDs made from III-V semiconductors. Elementary properties such as electrical and optical characteristics are reviewed, followed by the analysis of advanced device structures. With nine additional chapters, the treatment of LEDs has been vastly expanded, including new material on device packaging, reflectors, UV LEDs, III-V nitride materials, solid-state sources for illumination applications, and junction temperature. Radiative and non-radiative recombination dynamics, methods for improving light extraction, high-efficiency and high-power device designs, white-light emitters with wavelength-converting phosphor materials, optical reflectors, and spontaneous recombination in resonant-cavity structures are discussed in detail. With exercises, solutions, and illustrative examples, this tex

The interdisciplinary nature of bioinformatics presents a research challenge in integrating concepts, methods, software and multiplatform data. Although there have been rapid developments in new technology and an inundation of statistical methods for addressing other types of high-throughput data, such as proteomic profiles that arise from mass spectrometry experiments. This book discusses the development and application of Bayesian methods in the analysis of high-throughput bioinformatics data that arise from medical, in particular, cancer research, as well as molecular and structural biology. The Bayesian approach has the advantage that evidence can be easily and flexibly incorporated into statistical methods. A basic overview of the biological and technical principles behind multi-platform high-throughput experimentation is followed by expert reviews of Bayesian methodology, tools and software for single group inference, group comparisons, classification and clustering, motif discov

A visually intuitive approach to statistical data analysis Visual Statistics brings the most complex and advanced statistical methods within reach of those with little statistical training by

A precise and accessible presentation of linear model theory, illustrated with data examplesStatisticians often use linear models for data analysis and for developing new statistical methods. Most boo

Geographical Information Systems has moved from the domain of the computer specialist into the wider archaeological community, providing it with an exciting new research method. This clearly written but rigorous book provides a comprehensive guide to that use. Topics covered include: the theoretical context and the basics of GIS; data acquisition including database design; interpolation of elevation models; exploratory data analysis including spatial queries; statistical spatial analysis; map algebra; spatial operations including the calculation of slope and aspect, filtering and erosion modeling; methods for analysing regions; visibility analysis; network analysis including hydrological modeling; the production of high quality output for paper and electronic publication; and the use and production of metadata. Offering an extensive range of archaeological examples, it is an invaluable source of practical information for all archaeologists, whether engaged in cultural resource manageme

This second volume of Brahms studies contains twelve contributions by leading international authorities on various music. Like the preceding volume of the same title (edited by Robert Pascall), Michael Musgrave's volume aims to provide original scholarly material on different facets of a major composer still inadequately discussed in book form and employs more precise methods of analysis and more critical approaches to materials then generally available in writings on Brahms in English. Half of the volume takes the music itself as focus, though from very different vantage points. There are two studies of a single opus (the two String Quartets Op. 51 Nos, 1 and 2), discussions of the Fourth Symphony and the motet 'Warum', and a view of Brahms's harmony. The underlying historical theme emerges more openly in an account of Brahms's interest in German Renaissance music. The remaining essays give details of the state of Brahms's unpublished compositions and arrangements at his death and the

This 2006 book presents a systematic introduction to the theory of parametric stability of structures under both deterministic and stochastic loadings. A comprehensive range of theories are presented and various application problems are formulated and solved, often using more than one approach. Investigation of an elastic system's dynamic stability frequently leads to the study of dynamic behaviour of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterised by exponential growth of the response amplitudes even in the presence of damping. The emphasis in this book is on the applications and various analytical and numerical methods for solving engineering problems. The materials presented are as self-contained as possible, with all of the important steps of analysis provided in order to make the book suitable as a graduate-level textbook and especially for self-study.

The Navier-Stokes equations were firmly established in the 19th Century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been sought by scientists. Collectively these solutions allow a clear insight into the behavior of fluids, providing a vehicle for novel mathematical methods and a useful check for computations in fluid dynamics, a field in which theoretical research is now dominated by computational methods. This 2006 book draws together exact solutions from widely differing sources and presents them in a coherent manner, in part by classifying solutions via their temporal and geometric constraints. It will prove to be a valuable resource to all who have an interest in the subject of fluid mechanics, and in particular to those who are learning or teaching the subject at the senior undergraduate and graduate levels.

Just as each person develops from infancy to adulthood, all interpersonal relationships have a life history that encompasses the changes in how people communicate with each other. This book is about how a relationship transforms itself from one pattern of communication to another. The authors present a unique research method called 'relational-historical research', based on advances in dynamic systems theory in developmental psychology, and qualitative methods in life history research. It rests on three premises: that the developing relationship (not the individual) is the unit of analysis; that change emerges from, but is not entirely constrained by, the patterns of the past; and that the developmental process is best revealed by making frequent observations within a particular case before, during, and after a key developmental transition. Looking specifically at the mother–infant relationship, this is a compelling piece of research that will appeal to an international audience of int

Solitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose–Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general p

The last twenty years have seen a resurgence of interest in human evolution in many aspects. A distinction can be made between 'narrow' (general acceptance that human evolution occurred, historically) and 'broad' (evolutionary ideas that stretch much further into all aspects of humanity, past and present) human evolution. The broad perspective is beginning to make its presence felt, for example, through the developments in evolutionary genetics, evolutionary psychology and behavioural ecology. There must, therefore, be, among the variety of human adaptations, natures and behaviours, phenomena which are not susceptible to an evolutionary analysis, which are beyond the bounds of evolution. The problem is, though, that we do not really know where that boundary lies. Here, the limits of human evolution are explored, using two approaches - first, finding where humans 'fit' the expectations of evolutionary principles; and second, applying evolutionary methods to particular human contexts, wh

This is the first book devoted to the Queen's Men, one of the major acting companies of the age of Shakespeare. In describing the troupe's position in the general political situation and the London theatre scene of the 1580s, the authors break new ground by showing how Elizabethan theatre history can be refocused by concentrating on the company which produced the plays rather than on the authors who wrote them. The book combines a thorough examination of documentary evidence with textual and critical analysis, to provide a full account of the characteristics which gave the company its identity: its acting style, staging methods, touring patterns and repertoire. The conclusions will interest Elizabethan historians as well as students and scholars of early modern theatre.

This book draws on key theories and methods from the social sciences to develop a framework for the systematic study of human rights problems. It argues that solid empirical analysis of human rights p

Completely updated, this new edition explains the major methods of experimental design and evaluation such as multivariate, sequential, and principal components analysis. It offers new sections on ne

Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

What came before 'postmodernism' in historical studies? By thinking through the assumptions, methods and cast of mind of English historians writing between about 1870 and 1970, this book reveals the intellectual world of the modernists and offers a full analysis of English historiography in this crucial period. Modernist historiography set itself the objective of going beyond the colourful narratives of 'whigs' and 'popularizers' in order to establish history as the queen of the humanities and as a rival to the sciences as a vehicle of knowledge. Professor Bentley does not follow those who deride modernism as 'positivist' or 'empiricist' but instead shows how it set in train brilliant new styles of investigation that transformed how historians understood the English past. But he shows how these strengths were eventually outweighed by inherent confusions and misapprehensions that threatened to kill the very subject that the modernists had intended to sustain.

What came before 'postmodernism' in historical studies? By thinking through the assumptions, methods and cast of mind of English historians writing between about 1870 and 1970, this book reveals the intellectual world of the modernists and offers a full analysis of English historiography in this crucial period. Modernist historiography set itself the objective of going beyond the colourful narratives of 'whigs' and 'popularizers' in order to establish history as the queen of the humanities and as a rival to the sciences as a vehicle of knowledge. Professor Bentley does not follow those who deride modernism as 'positivist' or 'empiricist' but instead shows how it set in train brilliant new styles of investigation that transformed how historians understood the English past. But he shows how these strengths were eventually outweighed by inherent confusions and misapprehensions that threatened to kill the very subject that the modernists had intended to sustain.

Self-contained text covering practical image processing methods and theory for image texture analysis. Techniques for the analysis of texture in digital images are essential to a range of application

Fundamentals of Critical Argumentation presents the basic tools for the identification, analysis, and evaluation of common arguments for beginners. The book teaches by using examples of arguments in dialogues, both in the text itself and in the exercises. Examples of controversial legal, political, and ethical arguments are analyzed. Illustrating the most common kinds of arguments, the book also explains how to evaluate each kind by critical questioning. Douglas Walton shows how arguments can be reasonable under the right dialogue conditions by using critical questions to evaluate them. The book teaches by example, both in the text itself and in exercises, but it is based on methods that have been developed through the author's thirty years of research in argumentation studies.

The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Lévy–Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy–Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang–Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory.

The contents of this volume comprise the proceedings of the International Symposia in Economic Theory and Econometrics conference held in 1987 at the IC^T2 (Innovation, Creativity, and Capital) Institute at the University of Texas at Austin. The essays present fundamental new research on the analysis of complicated outcomes in relatively simple macroeconomic models. The book covers econometric modelling and time series analysis techniques in five parts. Part I focuses on sunspot equilibria, the study of uncertainty generated by nonstochastic economic models. Part II examines the more traditional examples of deterministic chaos: bubbles, instability, and hyperinflation. Part III contains the most current literature dealing with empirical tests for chaos and strange attractors. Part IV deals with chaos and informational complexity. Part V, Nonlinear Econometric Modelling, includes tests for and applications of nonlinearity.

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.

Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition. The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing. This book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises. It shows both digital and optical implementations. It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition. Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical

In this 1999 book, Karl Gunnar Persson surveys a broad sweep of economic history, examining one of the most crucial markets - grain. His analysis allows him to draw more general lessons, for example that liberalization of markets was linked to political authoritarianism. Grain Markets in Europe traces the markets' early regulation, their poor performance and the frequent market failures. Price volatility caused by harvest shocks was of major concern for central and local government because of the unrest it caused. Regulation became obsolete when markets became more integrated and performed better through trade triggered by falling transport costs. Persson, a specialist in economic history, uses insights from development economics, explores contemporary economic thought on the advantages of free trade, and measures the extent of market integration using the latest econometric methods. Grain Markets in Europe will be of value to scholars and students in economic history, social history a

This book describes the most reliable methods available for evaluating the transport properties, such as viscosity, thermal conductivity and diffusion, of pure gases and fluid mixtures. Particular emphasis is placed on recent theoretical advances in our understanding of fluid transport properties in all the different regions of temperature and pressure. In addition to the important theoretical tools, the different methods of data representation are also covered, followed by a section which demonstrates the application of selected models in a range of circumstances. Case studies of transport property analysis for real fluids are then given, and the book concludes with a discussion of various international data banks and prediction packages. Advanced students of kinetic theory, as well as engineers and scientists involved with the design of process equipment or the interpretation of measurements of fluid transport properties, will find this book indispensable.