Networks And Chaos Statistical And Probabilistic Aspects

This volume consists of a collection of tutorial papers by leading experts on statistical and probabilistic aspects of chaos and networks, in particular neural networks. While written for the non-expert, they are intended to bring the reader up to the forefront of knowledge and research in the subject areas concerned. The papers, which contain extensive references to the literature, can separately or in various combinations serve as bases for short- or full-length courses, at graduate or more advanced levels. The papers are directed not only to mathematical statisticians but also to students and researchers in related fields of biology, engineering, geology, physics and probability.

This volume consists of the revised versions of most of the main papers given at the first Seminaire Europeen de Statistique on Chaos and Neural Networks and at the subsequent Study Institute on other types ofnetworks, held at Sandbjerg/Aarhus University from 25 April to 7 May 1992. The aim of the Seminaire Europeen de Statistique and the Study Institute, in which about 35 young statisticians from all over Europe participated, was to provide talented young researchers in statistics with an opportunity to get quickly to the forefront of knowledge and research in the statistical aspects of chaos and networks. Accordingly the papers in this volume all have a tutorial character and it is hoped that they will be found broadly useful. The first Seminaire Europeen de Statistique was organized by O.E. Barndorff-Nielsen, Aarbus University; D.R. Cox, Nuffield College, Oxford; Jens Ledet Jensen, Aarbus University; Wilfrid S. Kendall, University of Warwick; and Gerard Letac, Universite Paul Sabatier, Toulouse. It is hoped in the future to arrange further Seminaires Europeens de Statistique, each one devoted to one or two research topics of great current interest and activity. The Seminaire Europeen de Statistique and Study Institute was supported by the Directorate General for Science and Development of the European Communities and by the Danish Research Acad emy, and their support is gratefully acknowledged.

This book contains the proceedings of the conference ANNIMAB-l, held 13-16 May 2000 in Goteborg, Sweden. The conference was organized by the Society for Artificial Neural Networks in Medicine and Biology (ANNIMAB-S), which was established to promote research within a new and genuinely cross-disciplinary field. Forty-two contributions were accepted for presentation; in addition to these, S invited papers are also included. Research within medicine and biology has often been characterised by application of statistical methods for evaluating domain specific data. The growing interest in Artificial Neural Networks has not only introduced new methods for data analysis, but also opened up for development of new models of biological and ecological systems. The ANNIMAB-l conference is focusing on some of the many uses of artificial neural networks with relevance for medicine and biology, specifically: • Medical applications of artificial neural networks: for better diagnoses and outcome predictions from clinical and laboratory data, in the processing of ECG and EEG signals, in medical image analysis, etc. More than half of the contributions address such clinically oriented issues. • Uses of ANNs in biology outside clinical medicine: for example, in models of ecology and evolution, for data analysis in molecular biology, and (of course) in models of animal and human nervous systems and their capabilities. • Theoretical aspects: recent developments in learning algorithms, ANNs in relation to expert systems and to traditional statistical procedures, hybrid systems and integrative approaches.

The NATO Advanced Study Institute From Statistics to Neural Networks, Theory and Pattern Recognition Applications took place in Les Arcs, Bourg Saint Maurice, France, from June 21 through July 2, 1993. The meeting brought to gether over 100 participants (including 19 invited lecturers) from 20 countries. The invited lecturers whose contributions appear in this volume are: L. Almeida (INESC, Portugal), G. Carpenter (Boston, USA), V. Cherkassky (Minnesota, USA), F. Fogelman Soulie (LRI, France), W. Freeman (Berkeley, USA), J. Friedman (Stanford, USA), F. Girosi (MIT, USA and IRST, Italy), S. Grossberg (Boston, USA), T. Hastie (AT&T, USA), J. Kittler (Surrey, UK), R. Lippmann (MIT Lincoln Lab, USA), J. Moody (OGI, USA), G. Palm (U1m, Germany), B. Ripley (Oxford, UK), R. Tibshirani (Toronto, Canada), H. Wechsler (GMU, USA), C. Wellekens (Eurecom, France) and H. White (San Diego, USA). The ASI consisted of lectures overviewing major aspects of statistical and neural network learning, their links to biological learning and non-linear dynamics (chaos), and real-life examples of pattern recognition applications. As a result of lively interactions between the participants, the following topics emerged as major themes of the meeting: (1) Unified framework for the study of Predictive Learning in Statistics and Artificial Neural Networks (ANNs); (2) Differences and similarities between statistical and ANN methods for non parametric estimation from examples (learning); (3) Fundamental connections between artificial learning systems and biological learning systems.

Will provide a more elementary introduction to these topics than other books available; Gentle is the author of two other Springer books

This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.

This 1996 book explains the statistical framework for pattern recognition and machine learning, now in paperback.

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It isremarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This editionincludes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these threenew chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. This book is a collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics (in the physiological and biological sciences) and statistics. It presents theproceedings of a four-day workshop entitled ''Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences'' held at the Centre de Recherches Mathematiques (CRM) in Montreal in July 1995. The goal of the workshop was to provide an exchange forum and to create a link between two diverse groups with a common interest in the analysis of nonlinear time series data. The editors and peer reviewers of this work have attempted to minimize the problems ofmaintaining communication between the different scientific fields. The result is a collection of interrelated papers that highlight current areas of research in statistics that might have particular applicability to nonlinear dynamics and new methodology and open data analysis problems in nonlinear dynamicsthat might find their way into the toolkits and research interests of statisticians. Features: A survey of state-of-the-art developments in nonlinear dynamics time series analysis with open statistical problems and areas for further research. Contributions by statisticians to understanding and improving modern techniques commonly associated with nonlinear time series analysis, such as surrogate data methods and estimation of local Lyapunov exponents. Starting point for both scientists andstatisticians who want to explore the field. Expositions that are readable to scientists outside the featured fields of specialization. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario,Canada).