The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

This volume presents the proceedings of the Workshop on Momentum Distributions held on October 24 to 26, 1988 at Argonne National Laboratory. This workshop was motivated by the enormous progress within the past few years in both experimental and theoretical studies of momentum distributions, by the growing recognition of the importance of momentum distributions to the characterization of quantum many-body systems, and especially by the realization that momentum distribution studies have much in common across the entire range of modern physics. Accordingly, the workshop was unique in that it brought together researchers in nuclear physics, electronic systems, quantum fluids and solids, and particle physics to address the common elements of momentum distribution studies. The topics dis cussed in the workshop spanned more than ten orders of magnitude range in charac teristic energy scales. The workshop included an extraordinary variety of interactions from Coulombic to hard core repulsive, from non-relativistic to extreme relativistic."

Polymers are substances made of macromolecules formed by thousands of atoms organized in one (homopolymers) or more (copolymers) groups that repeat themselves to form linear or branched chains, or lattice structures. The concept of polymer traces back to the years 1920's and is one of the most significant ideas of last century. It has given great impulse to indus try but also to fundamental research, including life sciences. Macromolecules are made of sm all molecules known as monomers. The process that brings monomers into polymers is known as polymerization. A fundamental contri bution to the industrial production of polymers, particularly polypropylene and polyethylene, is due to the Nobel prize winners Giulio Natta and Karl Ziegler. The ideas of Ziegler and Natta date back to 1954, and the process has been improved continuously over the years, particularly concerning the design and shaping of the catalysts. Chapter 1 (due to A. Fasano ) is devoted to a review of some results concerning the modelling of the Ziegler- Natta polymerization. The specific ex am pie is the production of polypropilene. The process is extremely complex and all studies with relevant mathematical contents are fairly recent, and several problems are still open.

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk, were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (:::: ) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (:::: ) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

One of the most spectacular consequences of the description of the superfluid condensate in superfluid He or in superconductors as a single macroscopic quantum state is the quantization of circulation, resulting in quantized vortex lines. This book draws no distinction between superfluid He3 and He4 and superconductors. The reader will find the essential introductory chapters and the most recent theoretical and experimental progress in our understanding of the vortex state in both superconductors and superfluids, from lectures given by leading experts in the field, both experimentalists and theoreticians, who gathered in Cargese for a NATO ASI. The peculiar features related to short coherence lengths, 2D geometry, high temperatures, disorder, and pinning are thoroughly discussed. "

Dynamic Neural Field Theory for Motion Perception provides a new theoretical framework that permits a systematic analysis of the dynamic properties of motion perception. This framework uses dynamic neural fields as a key mathematical concept. The author demonstrates how neural fields can be applied for the analysis of perceptual phenomena and its underlying neural processes. Also, similar principles form a basis for the design of computer vision systems as well as the design of artificially behaving systems. The book discusses in detail the application of this theoretical approach to motion perception and will be of great interest to researchers in vision science, psychophysics, and biological visual systems.

In the last few years we have witnessed an upsurge of interest in exactly solvable quantum field theoretical models in many branches of theoretical physics ranging from mathematical physics through high-energy physics to solid states. This book contains six pedagogically written articles meant as an introduction for graduate students to this fascinating area of mathematical physics. It leads them to the front line of present-day research. The topics include conformal field theory and W algebras, the special features of 2d scattering theory as embodied in the exact S matrices and the form factor studies built on them, the Yang--Baxter equations, and the various aspects of the Bethe Ansatz systems.

arise automatically as a result of the recursive structure of the task and the continuous nature of the SRN's state space. Elman also introduces a new graphical technique for study ing network behavior based on principal components analysis. He shows that sentences with multiple levels of embedding produce state space trajectories with an intriguing self similar structure. The development and shape of a recurrent network's state space is the subject of Pollack's paper, the most provocative in this collection. Pollack looks more closely at a connectionist network as a continuous dynamical system. He describes a new type of machine learning phenomenon: induction by phase transition. He then shows that under certain conditions, the state space created by these machines can have a fractal or chaotic structure, with a potentially infinite number of states. This is graphically illustrated using a higher-order recurrent network trained to recognize various regular languages over binary strings. Finally, Pollack suggests that it might be possible to exploit the fractal dynamics of these systems to achieve a generative capacity beyond that of finite-state machines."

Over the past five de-:: ades researchers have sought to develop a new framework that would resolve the anomalies attributable to a patchwork formulation of relativistic quantum mechanics. This book chronicles the development of a new paradigm for describing relativistic quantum phenomena. What makes the new paradigm unique is its inclusion of a physically measurable, invariant evolution parameter. The resulting theory has been sufficiently well developed in the refereed literature that it is now possible to present a synthesis of its ideas and techniques. My synthesis is intended to encourage and enhance future research, and is presented in six parts. The environment within which the conventional paradigm exists is described in the Introduction. Part I eases the mainstream reader into the ideas of the new paradigm by providing the reader with a discussion that should look very familiar, but contains subtle nuances. Indeed, I try to provide the mainstream reader with familiar "landmarks" throughout the text. This is possible because the new paradigm contains the conventional paradigm as a subset. The foundation of the new paradigm is presented in Part II, fol owed by numerous applications in the remaining three parts. The reader should notice that the new paradigm handles not only the broad class of problems typically dealt with in conventional relativistic quantum theory, but also contains fertile research areas for both experimentalists and theorists. To avoid developing a theoretical framework without physical validity, numerous comparisons between theory and experiment are provided, and several predictions are made.

Neural Networks in Telecommunications consists of a carefully edited collection of chapters that provides an overview of a wide range of telecommunications tasks being addressed with neural networks. These tasks range from the design and control of the underlying transport network to the filtering, interpretation and manipulation of the transported media. The chapters focus on specific applications, describe specific solutions and demonstrate the benefits that neural networks can provide. By doing this, the authors demonstrate that neural networks should be another tool in the telecommunications engineer's toolbox. Neural networks offer the computational power of nonlinear techniques, while providing a natural path to efficient massively-parallel hardware implementations. In addition, the ability of neural networks to learn allows them to be used on problems where straightforward heuristic or rule-based solutions do not exist. Together these capabilities mean that neural networks offer unique solutions to problems in telecommunications. For engineers and managers in telecommunications, Neural Networks in Telecommunications provides a single point of access to the work being done by leading researchers in this field, and furnishes an in-depth description of neural network applications.

An Analog VLSI System for Stereoscopic Vision investigates the interaction of the physical medium and the computation in both biological and analog VLSI systems by synthesizing a functional neuromorphic system in silicon. In both the synthesis and analysis of the system, a point of view from within the system is adopted rather than that of an omniscient designer drawing a blueprint. This perspective projects the design and the designer into a living landscape. The motivation for a machine-centered perspective is explained in the first chapter. The second chapter describes the evolution of the silicon retina. The retina accurately encodes visual information over orders of magnitude of ambient illumination, using mismatched components that are calibrated as part of the encoding process. The visual abstraction created by the retina is suitable for transmission through a limited bandwidth channel. The third chapter introduces a general method for interchip communication, the address-event representation, which is used for transmission of retinal data. The address-event representation takes advantage of the speed of CMOS relative to biological neurons to preserve the information of biological action potentials using digital circuitry in place of axons. The fourth chapter describes a collective circuit that computes stereodisparity. In this circuit, the processing that corrects for imperfections in the hardware compensates for inherent ambiguity in the environment. The fifth chapter demonstrates a primitive working stereovision system. An Analog VLSI System for Stereoscopic Vision contributes to both computer engineering and neuroscience at a concrete level. Through the construction of a working analog of biological vision subsystems, new circuits for building brain-style analog computers have been developed. Specific neuropysiological and psychophysical results in terms of underlying electronic mechanisms are explained. These examples demonstrate the utility of using biological principles for building brain-style computers and the significance of building brain-style computers for understanding the nervous system.

Deng Feng Wang was born February 8, 1965 in Chongqing City, China and died August 15, 1999 while swimming with friends in the Atlantic Ocean off Island Beach State Park, New Jersey. In his brief life, he was to have an influence far beyond his years. On August 12th 2000, The Deng Feng Wang Memorial Conference was held at his alma mater, Princeton University, during which Deng Feng's mentors, collaborators and friends presented scientific talks in a testimonial to his tremendous influence on their work and careers. The first part of this volume contains proceedings contributions from the conference, with plenary talks by Nobel Laureate Professor Phil Anderson of Princeton University and leading Condensed Matter Theorists Professor Piers Coleman of Rutgers University and Professor Christian Gruber of the University of Lausanne. Other talks, given by collaborators, friends and classmates testify to the great breadth of Deng Feng Wang's influence, with remarkable connections shown between seemingly unrelated areas in physics such as Condensed Matter Physics, Superconductivity, One-Dimensional Models, Statistical Physics, Mathematical Physics, Quantum Field Theory, High Energy Theory, Nuclear Magnetic Resonance, Supersymmetry, M-Theory and String Theory, in addition to such varied fields outside of physics such as Oil Drilling, Mixed Signal Circuits and Neurology. The second part of the volume consists of reprints of some of Deng Feng Wang's most important papers in the areas of Condensed Matter Physics, Statistical Physics, Magnetism, Mathematical Physics and Mathematical Finance. This volume represents a fascinating synthesis of a wide variety of topics, and ultimately points to the universality of physics and of science as a whole. As such, it represents a fitting tribute to a remarkable individual, whose tragic death will never erase his enduring influence.

Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

One SCI\'ice mathematics bas rendered the 'Et moi, ...si j'avait su comment en revcnir. je n'y serais point aile: human race. It bas put common sc:nsc back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

The contents of this book correspond to Sessions VII and VIII of the International Workshop on Instabilities and Nonequilibrium Structures which took place in Vifia del Mar, Chile, in December 1997 and December 1999, respectively. We were not able to publish this book before and we apologize for this fact to the authors and participants of the meeting. We have made an effort to actualize the courses and articles which have been reviewed by the authors. Both Workshops were organized by Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Instituto de Fisica of Universidad Cat61ica de Valparaiso and Centro de Fisica No Lineal y Sistemas Complejos de Santiago. We are glad to acknowledge here the support of the Facultad de Ingenieria of Universidad de los Andes of Santiago which also be from now on one of the organizing Institutions of future Workshops. Enrique Tirapegui PREFACE This book is divided in two parts. In Part I we have collected the courses given in Sessions VII and VIII of the Workshop and in Part II we include a selection of the invited Conferences and Seminars presented at both meetings.

Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stephane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Levy fields. The Levy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'etre of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

It is our pleasure to contribute the forewordto this book on symbiotic mul- robot organisms, which is largely based on the scienti?c ?ndings and exp- rations of two major EU research projects, Symbrion and Replicator, funded under the Seventh Framework Programme for Research and Technological 1 development (FP7) . FP7 emphasises consortia of European partners, tra- national collaboration, open coordination, ?exibility and excellence of - search and plays a leading role in multidisciplinary research and cooperative activities in Europe and beyond. Its impact is major in terms of integrating and structuring research communities across national borders to achieve a critical mass, providing the leverage for high-potential ?elds to take o?, and encouraging healthy competition at European level while avoiding unn- essary duplication of research capacities. Research proposals are evaluated through a demanding peer-review process and only the best are selected to be funded bythe EuropeanCommission(EC). The InformationandCom- nication Technologies(ICT) theme has set out a number of challengeswithin this context, which cover topics such as cognitive systems, modular robotics, adaptive systems and societies of artefacts. * Symbrion was selected following the Call "Pervasive Adaptation" of the 2 "Future and Emerging Technologies (FET)" programme area. Itstarted on 1 February 2008 and will run for 5 years. FET Proactive addresses evolutionary and revolutionary approaches through multidisciplinary - operation and investigates new future technology options in response to emerging societal and industrial needs and identi?es new drivers for - search.

Computational intelligence encompasses a wide variety of techniques that allow computation to learn, to adapt, and to seek. That is, they may be designed to learn information without explicit programming regarding the nature of the content to be retained, they may be imbued with the functionality to adapt to maintain their course within a complex and unpredictably changing environment, and they may help us seek out truths about our own dynamics and lives through their inclusion in complex system modeling. These capabilities place our ability to compute in a category apart from our ability to erect suspension bridges, although both are products of technological advancement and reflect an increased understanding of our world. In this book, we show how to unify aspects of learning and adaptation within the computational intelligence framework. While a number of algorithms exist that fall under the umbrella of computational intelligence, with new ones added every year, all of them focus on the capabilities of learning, adapting, and helping us seek. So, the term unified computational intelligence relates not to the individual algorithms but to the underlying goals driving them. This book focuses on the computational intelligence areas of neural networks and dynamic programming, showing how to unify aspects of these areas to create new, more powerful, computational intelligence architectures to apply to new problem domains.

Modern astronomy has been characterized by an enormous growth in data acquisition - from new technologies in telescopes, detectors, and computation. One can now compile catalogs of tens or hundreds of millions of stars or galaxies and databases from satellite-based observations are reaching terabit proportions. This wealth of data gives rise to statistical challenges not previously encountered in astronomy. This book is the result of a workshop held at Pennsylvania State University in August 1991 that brought together leading astronomers and statisticians to consider statistical challenges encountered in modern astronomical research. The chapters have all been thoroughly revised in the light of the discussions at the conference, and some of the lively discussion is recorded here as well.

In this book, the authors deal with basic concepts and models, with methodologies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition between order and chaos is crucial for synergetic behavior and evolution.

Computational Architectures Integrating Neural and Symbolic Processes: A Perspective on the State of the Art focuses on a currently emerging body of research. With the reemergence of neural networks in the 1980s with their emphasis on overcoming some of the limitations of symbolic AI, there is clearly a need to support some form of high-level symbolic processing in connectionist networks. As argued by many researchers, on both the symbolic AI and connectionist sides, many cognitive tasks, e.g. language understanding and common sense reasoning, seem to require high-level symbolic capabilities. How these capabilities are realized in connectionist networks is a difficult question and it constitutes the focus of this book. Computational Architectures Integrating Neural and Symbolic Processes addresses the underlying architectural aspects of the integration of neural and symbolic processes. In order to provide a basis for a deeper understanding of existing divergent approaches and provide insight for further developments in this field, this book presents: (1) an examination of specific architectures (grouped together according to their approaches), their strengths and weaknesses, why they work, and what they predict, and (2) a critique/comparison of these approaches. Computational Architectures Integrating Neural and Symbolic Processes is of interest to researchers, graduate students, and interested laymen, in areas such as cognitive science, artificial intelligence, computer science, cognitive psychology, and neurocomputing, in keeping up-to-date with the newest research trends. It is a comprehensive, in-depth introduction to this new emerging field.

Data analysis lies at the heart of every experimental science. Providing a modern introduction to statistics, this book is ideal for undergraduates in physics. It introduces the necessary tools required to analyse data from experiments across a range of areas, making it a valuable resource for students. In addition to covering the basic topics, the book also takes in advanced and modern subjects, such as neural networks, decision trees, fitting techniques and issues concerning limit or interval setting. Worked examples and case studies illustrate the techniques presented, and end-of-chapter exercises help test the reader's understanding of the material.

Stochastic Resonance: Theory and Applications deals with the theory of noise-added systems and in particular with Stochastic Resonance, a quite novel theory that was introduced in the 1980s to provide better understanding of some natural phenomena (e.g. ice age recurrence). Following the very first works, a number of different applications to both natural and human-produced phenomena were proposed. The book aims to improve the understanding of noise-based techniques and to focus on practical applications of this class of phenomena (an aspect that has been very poorly investigated up to now). Based on this objective, the book is roughly divided into two parts. The first part deals with the essential theory of noise-added systems and in particular a new approach to noise-added techniques that allows a number of strategies proposed in previous years to be unified. The proposed approach also allows real-time control of the noise characteristics, assuring optimal system performance. In the second part a large number of applications are described in detail in the field of electric and electronic devices, with the aim of allowing readers to build their own experimental set. The book comes with a diskette of educational software that the authors developed. Stochastic Resonance: Theory and Applications is an invaluable reference for students, researchers and engineering professionals working in the fields of electric and electronic measurements, electronics and signal theory.