Methods of Nonlinear Analysis

Computational aeroacoustics (CAA) is a relatively new research area. CAA algorithms have developed rapidly and the methods have been applied in many areas of aeroacoustics. The objective of CAA is not simply to develop computational methods but also to use these methods to solve practical aeroacoustics problems and to perform numerical simulation of aeroacoustic phenomena. By analysing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. This is both a textbook for graduate students and a reference for researchers in CAA and as such is self-contained. No prior knowledge of numerical methods for solving partial differential equations (PDEs) is needed, however, a general understanding of partial differential equations and basic numerical analysis is assumed. Exercises are included and are designed to be an integral part of the chapter content. In addition, sample computer programs are included to illustrate the implementation of

Decision analysis is a prescriptive theory that aids individuals or groups confronted with complex problems in a wide variety of contexts. By framing issues, identifying risks, eliciting stakeholder preferences, and suggesting alternative approaches, decision analysts can offer workable solutions in domains such as the environment, health and medicine, engineering and operations research, and public policy. This book is a mixture of historical and forward-looking essays on key topics in decision analysis. Part I covers the history and foundations of decision analysis. Part II discusses structuring decision problems, including the development of objectives and their attributes, and influence diagrams. Part III discusses probabilities and their elicitation and Bayes nets. Part IV discusses additive and multiplicative utilities, risk preferences, and 'option pricing' methods. Part V discusses risk analysis. Part VI puts decision analysis in a behavioral and organizational context. Part VI

Decision analysis is a prescriptive theory that aids individuals or groups confronted with complex problems in a wide variety of contexts. By framing issues, identifying risks, eliciting stakeholder preferences, and suggesting alternative approaches, decision analysts can offer workable solutions in domains such as the environment, health and medicine, engineering and operations research, and public policy. This book is a mixture of historical and forward-looking essays on key topics in decision analysis. Part I covers the history and foundations of decision analysis. Part II discusses structuring decision problems, including the development of objectives and their attributes, and influence diagrams. Part III discusses probabilities and their elicitation and Bayes nets. Part IV discusses additive and multiplicative utilities, risk preferences, and 'option pricing' methods. Part V discusses risk analysis. Part VI puts decision analysis in a behavioral and organizational context. Part VI

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avante-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this

Discover a modern approach to the analysis, modeling and design of high sensitivity phased arrays. Network theory, numerical methods and computational electromagnetic simulation techniques are uniquely combined to enable full system analysis and design optimization. Beamforming and array signal processing theory are integrated into the treatment from the start. Digital signal processing methods such as polyphase filtering and RFI mitigation are described, along with technologies for real-time hardware implementation. Key concepts from interferometric imaging used in radio telescopes are also considered. A basic development of theory and modeling techniques is accompanied by problem sets that guide readers in developing modeling codes that retain the simplicity of the classical array factor method while incorporating mutual coupling effects and interactions between elements. Combining current research trends with pedagogical material suitable for a first-year graduate course, this is an

Deep learning is revolutionizing how machine translation systems are built today. This book introduces the challenge of machine translation and evaluation - including historical, linguistic, and applied context -- then develops the core deep learning methods used for natural language applications. Code examples in Python give readers a hands-on blueprint for understanding and implementing their own machine translation systems. The book also provides extensive coverage of machine learning tricks, issues involved in handling various forms of data, model enhancements, and current challenges and methods for analysis and visualization. Summaries of the current research in the field make this a state-of-the-art textbook for undergraduate and graduate classes, as well as an essential reference for researchers and developers interested in other applications of neural methods in the broader field of human language processing.

This book provides a comprehensive review of optical pattern recognition, covering theoretical aspects as well as details of practical implementations and signal processing techniques. The first chapter is devoted to pattern recognition performed with optical correlators. Later chapters discuss approaches based on neural networks, wavelet transforms and the fractional Fourier transform. The book also covers nonlinear filter methods and optical-electronic hybrid systems. The final part of the book deals with the devices and materials employed in modern systems, such as photorefractive crystals, microlasers, and liquid crystal spatial light modulators. The book gives many examples of working systems that integrate optics, electronics and computers, and it covers a range of developments from mathematical theories to novel optical materials. It will be of great interest to graduate students and researchers in optical engineering and machine vision.

Electrical neuroimaging is based on the analysis of brain electrical activity recorded from the human scalp with multichannel EEG. It offers enormous potential for the dynamic mapping of brain functions, and for the non-invasive diagnosis of neurological and psychiatric conditions. This authoritative reference gives a systematic overview of new electrical imaging methods, with a sound introduction to the basics of multichannel recording of EEG and event-related potential (ERP) data, as well as spatio-temporal analysis of the potential fields. The book enables researchers to measure valid data, select and apply appropriate analysis strategies, and avoid the most common mistakes when analyzing and interpreting EEG/ERP data. Importantly, it informs the research communities of the possibilities opened by these space-domain oriented approaches to the analysis of brain electrical activity, and of their potential to offer even more powerful diagnostic techniques when integrated with other cli

Bayesian methods are being increasingly employed in many different areas of research in the physical sciences. In astrophysics, models are used to make predictions to be compared to observations. These observations offer information that is incomplete and uncertain, so the comparison has to be pursued by following a probabilistic approach. With contributions from leading experts, this volume covers the foundations of Bayesian inference, a description of computational methods, and recent results from their application to areas such as exoplanet detection and characterisation, image reconstruction, and cosmology. It appeals to both young researchers seeking to learn about Bayesian methods as well as to astronomers wishing to incorporate these approaches in their research areas. It provides the next generation of researchers with the tools of modern data analysis that are already becoming standard in current astrophysical research.

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

In 1989, Michael Rabin proposed a fundamentally new approach to the problems of fault-tolerant routing and memory management in parallel computation, based on the idea of information dispersal. Yuh-Dauh Lyuu developed this idea in a number of new and exciting ways in his PhD thesis. Further work has led to extensions of these methods to other applications such as shared memory emulations. This volume presents an extended and updated printing of Lyuu's thesis. It gives a detailed treatment of the information dispersal approach to the problems of fault-tolerance and distributed representations of information which have resisted rigorous analysis by previous methods.

The masses of neutron stars are limited by an instability to gravitational collapse and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume includes more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamen

Configural Frequency Analysis (CFA) is a method for analysis of groups of individuals in cross-classifications. Individuals belong to a type if their particular pattern of characteristics occurs more often than expected, and to an antityte if their particular pattern of characteristics occurs less often than expected. The author's original contribution is his linking of CFA to log-linear modeling and the General Linear Model, enabling the reader to relate CFA to a well-known statistical background. It is shown that CFA and log-linear modeling are methods that complement each other. Introduction to Configural Frequency Analysis covers the latest developments in CFA, and it will be easy to read even for those with only an elementary statistics course as a background.

Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-cl

Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

Disrupting Dark Networks focuses on how social network analysis can be used to craft strategies to track, destabilize and disrupt covert and illegal networks. The book begins with an overview of the key terms and assumptions of social network analysis and various counterinsurgency strategies. The next several chapters introduce readers to algorithms and metrics commonly used by social network analysts. They provide worked examples from four different social network analysis software packages (UCINET, NetDraw, Pajek and ORA) using standard network data sets as well as data from an actual terrorist network that serves as a running example throughout the book. The book concludes by considering the ethics of and various ways that social network analysis can inform counterinsurgency strategizing. By contextualizing these methods in a larger counterinsurgency framework, this book offers scholars and analysts an array of approaches for disrupting dark networks.

Disrupting Dark Networks focuses on how social network analysis can be used to craft strategies to track, destabilize and disrupt covert and illegal networks. The book begins with an overview of the key terms and assumptions of social network analysis and various counterinsurgency strategies. The next several chapters introduce readers to algorithms and metrics commonly used by social network analysts. They provide worked examples from four different social network analysis software packages (UCINET, NetDraw, Pajek and ORA) using standard network data sets as well as data from an actual terrorist network that serves as a running example throughout the book. The book concludes by considering the ethics of and various ways that social network analysis can inform counterinsurgency strategizing. By contextualizing these methods in a larger counterinsurgency framework, this book offers scholars and analysts an array of approaches for disrupting dark networks.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited papers by leaders in their respective fields allow researchers and graduate students alike quickly to grasp the then current trends and developments of 1994. Highlights of the year's issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited papers by leaders in their respective fields allow researchers and graduate students alike quickly to grasp the then current trends and developments of 1994. Highlights of the year's issue are articles on domain decomposition, mesh adaption, pseudospectral methods and neural networks.

Morphometrics is the statistical study of biological shape and shape change. Its richest data are landmarks, points such as 'the bridge of the nose' that have biological names as well as geometric locations. This book is the first systematic survey of morphometric methods for landmark data. The methods presented here combine conventional multivariate statistical analysis with themes from plane and solid geometry and from biomathematics to support biological insights into the features of many different organs and organisms. This book will be of value to applied statisticians and geometers, as well as to all biological and biomedical researchers who need quantitative analyses of information from biomedical images.

Ethnoprimatology, the combining of primatological and anthropological practice and the viewing of humans and other primates as living in integrated and shared ecological and social spaces, has become an increasingly popular approach to primate studies in the twenty-first century. Offering an insight into the investigation and documentation of human-nonhuman primate relations in the Anthropocene, this book guides the reader through the preparation, design, implementation, and analysis of an ethnoprimatological research project, offering practical examples of the vast array of methods and techniques at chapter level. With contributions from the world's leading experts in the field, Ethnoprimatology critically analyses current primate conservation efforts, outlines their major research questions, theoretical bases and methods, and tackles the challenges and complexities involved in mixed-methods research. Documenting the spectrum of current research in the field, it is an ideal volume for

This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.

This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.

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.

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.

Valuation and Risk Management in Energy Markets surveys the mechanics of energy markets and the valuation of structures commonly arising in practice. The presentation balances quantitative issues and practicalities facing portfolio managers, with substantial attention paid to the ways in which common methods fail in practice and to alternative methods when they exist. The material spans basic fundamentals of markets, statistical analysis of price dynamics, and a sequence of increasingly challenging structures, concluding with issues arising at the enterprise level. In totality, the material has been selected to provide readers with the analytical foundation required to function in modern energy trading and risk management groups.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.

Originally published in 1939, this book presents a comprehensive study of hydrophthalmia, also known as buphthalmia, incorporating information on causes, treatment and outlook as they were understood at the time of publication. An approach based on comparative anatomy and pathology is used, with analysis of Australian fauna such as ornithorhyncus, echidna, pseudochirus and dasyurus incorporated into the study. The text also provides descriptions of all the different methods of operative treatment which had been tried, with a thorough analysis of the results obtained by various surgeons. Numerous illustrative figures are included throughout. This book will be of interest to anyone with an interest in the history of medicine and ophthalmology.

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

The aim of the book is to introduce the reader to the kinetic analysis of a wide range of biological processes at the molecular level. It is intended to show that the same approach can be used to resolve the number of steps in enzyme reactions, muscle contraction, visual perception and ligand binding receptors that trigger other physiological processes. Attention is also given to methods for characterizing these steps in chemical terms. Although the treatment is mainly theoretical, a wide range of examples and experimental techniques are also introduced and an historical approach is used to demonstrate the development of the theory and experimental techniques of kinetic analysis in biology.

The aim of the book is to introduce the reader to the kinetic analysis of a wide range of biological processes at the molecular level. It is intended to show that the same approach can be used to resolve the number of steps in enzyme reactions, muscle contraction, visual perception and ligand binding receptors that trigger other physiological processes. Attention is also given to methods for characterizing these steps in chemical terms. Although the treatment is mainly theoretical, a wide range of examples and experimental techniques are also introduced and an historical approach is used to demonstrate the development of the theory and experimental techniques of kinetic analysis in biology.

The book provides an extensive theoretical treatment of whistler-mode propagation, instabilities and damping in a collisionless plasma. This book fills a gap between oversimplified analytical studies of these waves, based on the cold plasma approximation, and studies based on numerical methods. Although the book is primarily addressed to space plasma physicists and radio physicists, it will also prove useful to laboratory plasma physicists. Mathematical methods described in the book can be applied in a straightforward way to the analysis of other types of plasma waves. Problems included in this book, along with their solutions, allow it to be used as a textbook for postgraduate students.

Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications in discrete approximation and statistics. The general approach considered in this text, first published in 2001, has permitted the development of finite algorithms for the rank regression problem. The key ideas are those of developing a general format for specifying the polyhedral function and the application of this to derive multiplier conditions to characterize optimality. Also considered is the application of the general approach to the development of active se

This book describes the full range of mass spectrometry techniques and applications. This versatile technique is in ubiquitous use in universities and industry laboratories because of its ability to identify and quantify materials quickly and, if necessary, in minute amounts, and solve analytical problems in a huge variety of fields. The authors adopt an instructional approach and make use of recent examples to illustrate important points. This second edition includes new methods and applications that have developed in the last ten years. Powerful methods combining mass spectrometry with newer separation techniques, the increased use of computers, and analysis of once difficult polar and large-mass compounds such as proteins using new ionisation methods are all discussed. Requiring no previous knowledge of mass spectrometry, this is an ideal teaching text at both undergraduate and postgraduate level, and will also be of considerable interest to research workers.

The optical fiber based supercontinuum source has recently become a significant scientific and commercial success, with applications ranging from frequency comb production to advanced medical imaging. This one-of-a-kind book explains the theory of fiber supercontinuum broadening, describes the diverse operational regimes and indicates principal areas of applications, making it a very important guide for researchers and graduate students. With contributions from major figures and groups who have pioneered research in this field, the book describes the historical development of the subject, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers to confidently predict and model supercontinuum generation characteristics under realistic conditio