Pattern Classification Using Ensemble Methods

Historically, naturalists who proposed theories of evolution, including Darwin and Wallace, did so in order to explain the apparent relationship of natural classification. This book begins by exploring the intimate historical relationship between patterns of classification and patterns of phylogeny. However, it is a circular argument to use the data for classification. Alec Panchen presents other evidence for evolution in the form of a historically based but rigorously logical argument. This is followed by a history of methods of classification and phylogeny reconstruction including current mathematical and molecular techniques. The author makes the important claim that if the hierarchical pattern of classification is a real phenomenon, then biology is unique as a science in making taxonomic statements. This conclusion is reached by way of historical reviews of theories of evolutionary mechanism and the philosophy of science as applied to biology. The book is addressed to biologists, p

From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena has been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyse and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another. Suitable as an upper-undergraduate textbook for mathematics students or as a fascinating, engaging, and fully illustrated resource for readers in physics and biology, Rebecca Hoyle's book, using a non-partisan approach, unifies a range of techniques used by active researchers in this growing field.

Functional magnetic resonance imaging (fMRI) has become the most popular method for imaging brain function. Handbook of Functional MRI Data Analysis provides a comprehensive and practical introduction to the methods used for fMRI data analysis. Using minimal jargon, this book explains the concepts behind processing fMRI data, focusing on the techniques that are most commonly used in the field. This book provides background about the methods employed by common data analysis packages including FSL, SPM and AFNI. Some of the newest cutting-edge techniques, including pattern classification analysis, connectivity modeling and resting state network analysis, are also discussed. Readers of this book, whether newcomers to the field or experienced researchers, will obtain a deep and effective knowledge of how to employ fMRI analysis to ask scientific questions and become more sophisticated users of fMRI analysis software.

Kernel methods provide a powerful and unified framework for pattern discovery, motivating algorithms that can act on general types of data (e.g. strings, vectors or text) and look for general types of relations (e.g. rankings, classifications, regressions, clusters). The application areas range from neural networks and pattern recognition to machine learning and data mining. This book, developed from lectures and tutorials, fulfils two major roles: firstly it provides practitioners with a large toolkit of algorithms, kernels and solutions ready to use for standard pattern discovery problems in fields such as bioinformatics, text analysis, image analysis. Secondly it provides an easy introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.

The classification of stars into their various types is one of the fundamental areas of astronomy. This book is a comprehensive handbook on the tools, methods and results of stellar taxonomy. Although this subject is firmly rooted in classical astronomy, vast improvements in observational techniques have transformed the subject and greatly broadened the wavelength regions available for study. The first six chapters describe modern methods of spectroscopic and photometric classification. The remaining nine chapters describe particular families of stars, progressing from the hottest to the coolest. Within each category a description is given of the normal type and all the peculiar stars. Throughout the emphasis is on the phenomenology of classification, rather than the underlying astrophysics. Both authors have devoted themselves to developing the international centre for stellar data at Strasbourg, which uniquely qualifies them to write this definitive handbook for professional astronom

The fundamental algorithms in data mining and machine learning form the basis of data science, utilizing automated methods to analyze patterns and models for all kinds of data in applications ranging from scientific discovery to business analytics. This textbook for senior undergraduate and graduate courses provides a comprehensive, in-depth overview of data mining, machine learning and statistics, offering solid guidance for students, researchers, and practitioners. The book lays the foundations of data analysis, pattern mining, clustering, classification and regression, with a focus on the algorithms and the underlying algebraic, geometric, and probabilistic concepts. New to this second edition is an entire part devoted to regression methods, including neural networks and deep learning.

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.

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

This revised and updated edition focuses on constrained ordination (RDA, CCA), variation partitioning and the use of permutation tests of statistical hypotheses about multivariate data. Both classification and modern regression methods (GLM, GAM, loess) are reviewed and species functional traits and spatial structures analysed. Nine case studies of varying difficulty help to illustrate the suggested analytical methods, using the latest version of Canoco 5. All studies utilise descriptive and manipulative approaches, and are supported by data sets and project files available from the book website: http://regent.prf.jcu.cz/maed2/. Written primarily for community ecologists needing to analyse data resulting from field observations and experiments, this book is a valuable resource to students and researchers dealing with both simple and complex ecological problems, such as the variation of biotic communities with environmental conditions or their response to experimental manipulation.

In recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make

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 recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make

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

The Berliner Ensemble was founded by Bertolt Brecht and his wife Helene Weigel in 1949. The company soon gained international prominence, and its productions and philosophy influenced the work of theatre-makers around the world. David Barnett's book is the first study of the company in any language. Based on extensive archival research, it uncovers Brecht's working methods and those of the company's most important directors after his death. The book considers the boon and burden of Brecht's legacy, and provides new insights into battles waged behind the scenes for the preservation of the Brechtian tradition. The Berliner Ensemble was also the German Democratic Republic's most prestigious cultural export, attracting attention from the highest circles of government, and from the Stasi, before it privatised itself after German reunification in 1990. Barnett pieces together a complex history that sheds light on both the company's groundbreaking productions and their turbulent times.

Modern biological classification is based on the system developed by Linnaeus, and interpreted by Darwin as representing the tree of life. But despite its widespread acceptance, the evolutionary interpretation has some problems and limitations. This comprehensive book provides a single resource for understanding all the main philosophical issues and controversies about biological classification. It surveys the history of biological classification from Aristotle to contemporary phylogenetics and shows how modern biological classification has developed and changed over time. Readers will also be able to see how biological classification is in part a consequence of human psychology, language development and culture. The book will be valuable for student readers and others interested in a range of topics in philosophy and biology.

Modern biological classification is based on the system developed by Linnaeus, and interpreted by Darwin as representing the tree of life. But despite its widespread acceptance, the evolutionary interpretation has some problems and limitations. This comprehensive book provides a single resource for understanding all the main philosophical issues and controversies about biological classification. It surveys the history of biological classification from Aristotle to contemporary phylogenetics and shows how modern biological classification has developed and changed over time. Readers will also be able to see how biological classification is in part a consequence of human psychology, language development and culture. The book will be valuable for student readers and others interested in a range of topics in philosophy and biology.

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

The Berliner Ensemble was founded by Bertolt Brecht and his wife Helene Weigel in 1949. The company soon gained international prominence, and its productions and philosophy influenced the work of theatre-makers around the world. David Barnett's book is the first study of the company in any language. Based on extensive archival research, it uncovers Brecht's working methods and those of the company's most important directors after his death. The book considers the boon and burden of Brecht's legacy, and provides new insights into battles waged behind the scenes for the preservation of the Brechtian tradition. The Berliner Ensemble was also the German Democratic Republic's most prestigious cultural export, attracting attention from the highest circles of government, and from the Stasi, before it privatised itself after German reunification in 1990. Barnett pieces together a complex history that sheds light on both the company's groundbreaking productions and their turbulent times.

Nonlinear Structural Dynamics Using FE Methods emphasises fundamental mechanics principles and outlines a modern approach to understanding structural dynamics. This will be useful to practising engineers but also students who will find advanced topics presented in an accessible manner. The book successfully presents the fundamentals of structural dynamics and infuses them with finite element (FE) methods. First, the author establishes and develops mechanics principles that are basic enough to form the foundations of FE methods. Second, the book presents specific computer procedures to implement FE methods so that general problems can be 'solved' - that is, responses can be produced given the loads, initial conditions and so on. Finally, the book introduces methods of analyses to leverage and expand the FE solutions.

Modern astronomical research is beset with a vast range of statistical challenges, ranging from reducing data from megadatasets to characterizing an amazing variety of variable celestial objects or testing astrophysical theory. Linking astronomy to the world of modern statistics, this volume is a unique resource, introducing astronomers to advanced statistics through ready-to-use code in the public domain R statistical software environment. The book presents fundamental results of probability theory and statistical inference, before exploring several fields of applied statistics, such as data smoothing, regression, multivariate analysis and classification, treatment of nondetections, time series analysis, and spatial point processes. It applies the methods discussed to contemporary astronomical research datasets using the R statistical software, making it invaluable for graduate students and researchers facing complex data analysis tasks. A link to the author's website for this book ca

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and gradua

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.

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.

The predictability of the physical arrangement of plants, at whatever scale it is viewed, is referred to as their spatial pattern. Spatial pattern is a crucial aspect of vegetation which has important implications not only for the plants themselves, but also for other organisms which interact with plants, such as herbivores and pollinators, or those animals for which plants provide a habitat. This book describes and evaluates methods for detecting and quantifying a variety of characteristics of spatial pattern. As well as discussing the concepts on which these techniques are based, examples from real field studies and worked examples are included, which, together with numerous line figures, help guide the reader through the text. The result is a book that will be of value to graduate students and research workers in the fields of vegetation science, conservation biology and applied ecology.

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and gradua

The predictability of the physical arrangement of plants, at whatever scale it is viewed, is referred to as their spatial pattern. Spatial pattern is a crucial aspect of vegetation which has important implications not only for the plants themselves, but also for other organisms which interact with plants, such as herbivores and pollinators, or those animals for which plants provide a habitat. This book describes and evaluates methods for detecting and quantifying a variety of characteristics of spatial pattern. As well as discussing the concepts on which these techniques are based, examples from real field studies and worked examples are included, which, together with numerous line figures, help guide the reader through the text. The result is a book that will be of value to graduate students and research workers in the fields of vegetation science, conservation biology and applied ecology.

Bootstrap methods are computer-intensive methods of statistical analysis, which use simulation to calculate standard errors, confidence intervals, and significance tests. The methods apply for any level of modelling, and so can be used for fully parametric, semiparametric, and completely nonparametric analysis. This 1997 book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. S-Plus programs for implementing the

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric conve

Quantitative Methods in Archaeology Using R is the first hands-on guide to using the R statistical computing system written specifically for archaeologists. It shows how to use the system to analyze many types of archaeological data. Part I includes tutorials on R, with applications to real archaeological data showing how to compute descriptive statistics, create tables, and produce a wide variety of charts and graphs. Part II addresses the major multivariate approaches used by archaeologists, including multiple regression (and the generalized linear model); multiple analysis of variance and discriminant analysis; principal components analysis; correspondence analysis; distances and scaling; and cluster analysis. Part III covers specialized topics in archaeology, including intra-site spatial analysis, seriation, and assemblage diversity.

Quantitative Methods in Archaeology Using R is the first hands-on guide to using the R statistical computing system written specifically for archaeologists. It shows how to use the system to analyze many types of archaeological data. Part I includes tutorials on R, with applications to real archaeological data showing how to compute descriptive statistics, create tables, and produce a wide variety of charts and graphs. Part II addresses the major multivariate approaches used by archaeologists, including multiple regression (and the generalized linear model); multiple analysis of variance and discriminant analysis; principal components analysis; correspondence analysis; distances and scaling; and cluster analysis. Part III covers specialized topics in archaeology, including intra-site spatial analysis, seriation, and assemblage diversity.

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.

There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.

Qualitative Comparative Analysis (QCA) and other set-theoretic methods distinguish themselves from other approaches to the study of social phenomena by using sets and the search for set relations. In virtually all social science fields, statements about social phenomena can be framed in terms of set relations, and using set-theoretic methods to investigate these statements is therefore highly valuable. This book guides readers through the basic principles of set theory and then on to the applied practices of QCA. It provides a thorough understanding of basic and advanced issues in set-theoretic methods together with tricks of the trade, software handling and exercises. Most arguments are introduced using examples from existing research. The use of QCA is increasing rapidly and the application of set-theory is both fruitful and still widely misunderstood in current empirical comparative social research. This book provides the comprehensive guide to these methods for researchers across t

Qualitative Comparative Analysis (QCA) and other set-theoretic methods distinguish themselves from other approaches to the study of social phenomena by using sets and the search for set relations. In virtually all social science fields, statements about social phenomena can be framed in terms of set relations, and using set-theoretic methods to investigate these statements is therefore highly valuable. This book guides readers through the basic principles of set theory and then on to the applied practices of QCA. It provides a thorough understanding of basic and advanced issues in set-theoretic methods together with tricks of the trade, software handling and exercises. Most arguments are introduced using examples from existing research. The use of QCA is increasing rapidly and the application of set-theory is both fruitful and still widely misunderstood in current empirical comparative social research. This book provides the comprehensive guide to these methods for researchers across t

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric conve

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.

This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This was an important book, describing many ideas not previously available in English; the author has taken the chance to rewrite parts of the text and refresh the references where appropriate.

Where does the particular form or configuration of a pattern come from, and how is it propagated from pattern to pattern? Templets and the Explanation of Complex Patterns provides a natural language for analysing such questions. Using it, the organisational forces that underlie the fabrication of any pattern can be divided into two classes. First, there are the 'universal laws' of pattern assembly, the configurational rules and constraints inherent within the fabric of the pattern elements themselves. Second, there are the 'templets' - external, situational constraints imposed on the pattern elements. From the perspective of templeting, simple patterns can be directly contrasted with complex patterns: the former are completely determined by their universal laws, whereas the latter also require extensive templets. Natural patterns range along the entire spectrum from simple to complex, and the most complex of these include both random patterns and many biological patterns.