These Proceedings of a NATO-ARW (HTECH ARW 96 00 52) held at the International Center for Theoretical Physics, Trieste, Italy from Aug 5 till Aug 9, 1996 resulted from many discussions between various workers, concerning the need for a gathering of all (if possible) who were concerned about the subject of superconductivity fluctuations in High critical Temperature Superconductors (HTS). It appeared to many that the Skocpol-Tinkham work of 1975 had to be revitalized in view of the discovery of the new superconducting ceramics and the enormous amount of work having already taken place. The study of HTS is one of the most prominent research subject in solid state sciences. The understanding of the role of fluctuations is also thought to be necessary before technological applications since the fluctuations may destroy the superconducting state. The workshop discussions have touched upon (i) Superconducting fluctuations in the vicinity of the critical transition, (ii) Superconductivity fluctuations near the percolation transition, and (iii) Fluctuations of the vortex lattice at the lattice melting temperature. These topics served as initiators for a very great amount of discussions with many comments from the audience. More than forty "long lectures" and two "poster sessions" were held. Private discussions going unrecorded but obviously took place at many locations : lecture halls, staircases, cafetaria, bedrooms, bars, beach, . . .

This understandable and inspiring book brings together both theorists and experimentalists working on the properties of nuclear and hadronic matter produced in heavy-ion collisions in various energy ranges. The main focus is on experimental signals revealing the possible phase changes of the matter.

Fuzzy logic is `a recent revolutionary technology' which has brought together researchers from mathematics, engineering, computer science, cognitive and behavioral sciences, etc. The work in fuzzy technology at the Laboratory for International Fuzzy Engineering (LIFE) has been specifically applied to engineering problems. This book reflects the results of the work that has been undertaken at LIFE with chapters treating the following topical areas: Decision Support Systems, Intelligent Plant Operations Support, Fuzzy Modeling and Process Control, System Design, Image Understanding, Behavior Decisions for Mobile Robots, the Fuzzy Computer, and Fuzzy Neuro Systems. The book is a thorough analysis of research which has been implemented in the areas of fuzzy engineering technology. The analysis can be used to improve these specific applications or, perhaps more importantly, to investigate more sophisticated fuzzy control applications.

Neural Networks in Robotics is the first book to present an integrated view of both the application of artificial neural networks to robot control and the neuromuscular models from which robots were created. The behavior of biological systems provides both the inspiration and the challenge for robotics. The goal is to build robots which can emulate the ability of living organisms to integrate perceptual inputs smoothly with motor responses, even in the presence of novel stimuli and changes in the environment. The ability of living systems to learn and to adapt provides the standard against which robotic systems are judged. In order to emulate these abilities, a number of investigators have attempted to create robot controllers which are modelled on known processes in the brain and musculo-skeletal system. Several of these models are described in this book. On the other hand, connectionist (artificial neural network) formulations are attractive for the computation of inverse kinematics and dynamics of robots, because they can be trained for this purpose without explicit programming. Some of the computational advantages and problems of this approach are also presented. For any serious student of robotics, Neural Networks in Robotics provides an indispensable reference to the work of major researchers in the field. Similarly, since robotics is an outstanding application area for artificial neural networks, Neural Networks in Robotics is equally important to workers in connectionism and to students for sensormonitor control in living systems.

The FIRST MEXICAN MEETING ON MATHEMATICAL AND EXPERI MENTAL PHYSICS was held at EL COLEGIO N ACIONAL in Mexico Cit y, Mexico, from September 10 to 14, 2001. This event consisted of the LEOPOLDO GARciA-COLiN SCHERER Medal Lecture, delivered by Prof. Nicholas G. van Kampen, a series of plenary talks by Leopoldo Garcia-Colin, Giinter Nimtz, Luis F. Rodriguez, Ruoon Barrera, and Donald Saari, and of three parallel symposia, namely, Cosmology and Gravitation, Statistical Physics and Beyond, and Hydrodynamics and Dynamical Systems. The response from the Physics community was enthusiastic, with over 200 participants and around 80 speakers, from allover the world: USA, Canada, Mexico, Germany, France, Holland, United Kingdom, Switzerland, Spain, and Hungary. The main aim of the conference is to provide a scenario to Mexican researchers on the topics of Mathematical and Experimental Physics in order to keep them in contact with work going on in other parts of the world and at the same time to motivate and support the young and mid career researchers from our country. To achieve this goal, we decided to the most distinguished experts in the subjects of the invite as lecturers conference and to give the opportunity to young scientist to communi cate the results of their work. The plan is to celebrate this international endeavor every three years.

This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.

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.

A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.

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.

The expression 'Neural Networks' refers traditionally to a class of mathematical algorithms that obtain their proper performance while they 'learn' from examples or from experience. As a consequence, they are suitable for performing straightforward and relatively simple tasks like classification, pattern recognition and prediction, as well as more sophisticated tasks like the processing of temporal sequences and the context dependent processing of complex problems. Also, a wide variety of control tasks can be executed by them, and the suggestion is relatively obvious that neural networks perform adequately in such cases because they are thought to mimic the biological nervous system which is also devoted to such tasks. As we shall see, this suggestion is false but does not do any harm as long as it is only the final performance of the algorithm which counts. Neural networks are also used in the modelling of the functioning of (sub systems in) the biological nervous system. It will be clear that in such cases it is certainly not irrelevant how similar their algorithm is to what is precisely going on in the nervous system. Standard artificial neural networks are constructed from 'units' (roughly similar to neurons) that transmit their 'activity' (similar to membrane potentials or to mean firing rates) to other units via 'weight factors' (similar to synaptic coupling efficacies)."

The subject of this book is predictive modular neural networks and their ap plication to time series problems: classification, prediction and identification. The intended audience is researchers and graduate students in the fields of neural networks, computer science, statistical pattern recognition, statistics, control theory and econometrics. Biologists, neurophysiologists and medical engineers may also find this book interesting. In the last decade the neural networks community has shown intense interest in both modular methods and time series problems. Similar interest has been expressed for many years in other fields as well, most notably in statistics, control theory, econometrics etc. There is a considerable overlap (not always recognized) of ideas and methods between these fields. Modular neural networks come by many other names, for instance multiple models, local models and mixtures of experts. The basic idea is to independently develop several "subnetworks" (modules), which may perform the same or re lated tasks, and then use an "appropriate" method for combining the outputs of the subnetworks. Some of the expected advantages of this approach (when compared with the use of "lumped" or "monolithic" networks) are: superior performance, reduced development time and greater flexibility. For instance, if a module is removed from the network and replaced by a new module (which may perform the same task more efficiently), it should not be necessary to retrain the aggregate network."

This is the eighth volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chapters usually provide references to the mathematical literature and a list of open problems that are of interest to industrial scientists. For some problems, a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the previous volume, as well as references to papers in which such solutions have been published."

VLSI-Compatible Implementations for Artificial Neural Networks introduces the basic premise of the authors' approach to biologically-inspired and VLSI-compatible definition, simulation, and implementation of artificial neural networks. In addition, the book develops a set of guidelines for general hardware implementation of ANNs. These guidelines are then used to find solutions for the usual difficulties encountered in any potential work, and as guidelines by which to reach the best compromise when several options exist. Furthermore, system-level consequences of using the proposed techniques in future submicron technologies with almost-linear MOS devices are discussed. While the major emphasis in this book is to develop neural networks optimized for compatibility with their implementation media, the work has also been extended to the design and implementation of a fully-quadratic ANN based on the desire to have network definitions epitomized for both efficient discrimination of closed-boundary circular areas and ease of implementation in a CMOS technology.VLSI-Compatible Implementations for Artificial Neural Networks implements a comprehensive approach which starts with an analytical evaluation of specific artificial networks. This provides a clear geometrical interpretation of the behavior of different variants of these networks. In combination with the guidelines developed towards a better final implementation, these concepts have allowed the authors to conquer various problems encountered and to make effective compromises. Then, to facilitate the investigation of the models needed when more difficult problems must be faced, a custom simulating program for various cases is developed. Finally, in order to demonstrate the authors' findings and expectations, several VLSI integrated circuits have been designed, fabricated, and tested. VLSI-Compatible Implementations for Artificial Neural Networksm> serves as an excellent reference source and may be used as a text for advanced courses on the subject.

No-one who took part in the NATO Advanced Studies Institute from which this book emerges will have forgotten the experience. True, the necessary conditions for a very successful workshop were satisfied: a field of physics bursting with new power and new puzzles, a matchless team of lecturers, an international gathering of students many of whom had themselves contributed at the forefront of their subject, an admirable overlap of experiment and theory, a good mix of experimenters and theorists, an enviable environment. But who could have foreseen the way the workshop became a focus for future directions, how fresh scientific ideas tumbled out of the discussion periods, how the context of teaching the field produced such fruitfulness of research at the highest level? The organisers did have some specific aims in mind. Perhaps foremost was the desire to compare notes among different areas within the sub field of soft condensed matter physics fast becoming known as "complex fluids." For readers seeking a definition, the prosaic "fluids with bits in" can be passed rapidly over in favour of the elegant discussion of slow variables by Scott Milner in his chapter. The uniting goals of the subject are to model the essential molecular or mesoscopic structure theoretically, and to probe this structure as well as the bulk response of the system experimentally. Our famous examples were: colloids, polymers, liquid crystals, block co-polymers and self-assembling surfactant systems.

Engineers have long been fascinated by how efficient and how fast biological neural networks are capable of performing such complex tasks as recognition. Such networks are capable of recognizing input data from any of the five senses with the necessary accuracy and speed to allow living creatures to survive. Machines which perform such complex tasks as recognition, with similar ac curacy and speed, were difficult to implement until the technological advances of VLSI circuits and systems in the late 1980's. Since then, the field of VLSI Artificial Neural Networks (ANNs) have witnessed an exponential growth and a new engineering discipline was born. Today, many engineering curriculums have included a course or more on the subject at the graduate or senior under graduate levels. Since the pioneering book by Carver Mead; "Analog VLSI and Neural Sys tems," Addison-Wesley, 1989; there were a number of excellent text and ref erence books on the subject, each dealing with one or two topics. This book attempts to present an integrated approach of a single research team to VLSI ANNs Engineering."

We present here the lectures and a selection of the seminars given at the Ninth International Workshop on Instabilities and Nonequilibrium Structures which took place in Vifiadel Mar, Chile, in December 2001. The Workshop was organized by Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Instituto de Fisica of Universidad Cat6lica de Valparaiso, Centro de Fisica No Lineal y Sistemas Complejos de Santiago and Facultad de Ingenieria, Universidad de los Andes, which starting from this year joins the other institutions in the coorganization ofthe Workshop. The organizers would like to express their gratitude to the following sponsors: Facultad de Ciencias Fisicas y Matematicas de la Universidad de Chile, Instituto de Fisica de la Universidad Cat6lica de Valparaiso, Facultad de Ingenieria de la Universidad de los Andes, Centro de Fisica No Lineal y Sistemas Complejos de Santiago, Academia Chilena de Ciencias, Ministere Francais des Affaires Etrangeres, CONICYT (Comisi6n Nacional de Investigaci6n Cientifica y Tecno16gicade Chile) and Departamento Tecnico de Investigaci6n y de Relaciones Internacionales de la Universidad de Chile. Enrique Tirapegui PREFACE This book consists of two parts, the first one has three lectures written by Professors H. R. Brand, M. Moreau and L. S. Tuckerman. H. R. Brand gives an overview about reorientation and undulation instabilities in liquid crystals, M. Moreau presents recent results on biased tracer diffusion in lattice gases, finally, L. S. Tuckerman summarizes some numerical methods used in bifurcation problems.

Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms is an organized edited collection of contributed chapters covering basic principles, methodologies, and applications of fuzzy systems, neural networks and genetic algorithms. All chapters are original contributions by leading researchers written exclusively for this volume. This book reviews important concepts and models, and focuses on specific methodologies common to fuzzy systems, neural networks and evolutionary computation. The emphasis is on development of cooperative models of hybrid systems. Included are applications related to intelligent data analysis, process analysis, intelligent adaptive information systems, systems identification, nonlinear systems, power and water system design, and many others. Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms provides researchers and engineers with up-to-date coverage of new results, methodologies and applications for building intelligent systems capable of solving large-scale problems.

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.

Dr. Ganti has introduced Chemoton Theory to explain the origin of life. Theoretical Foundations of Fluid Machineries is a discussion of the theoretical foundations of fluid automata. It introduces quantitative methods - cycle stoichiometry and stoichiokinetics - in order to describe fluid automata with the methods of algebra, as well as their construction, starting from elementary chemical reactions up to the complex, program-directed, proliferating fluid automata, the chemotons. Chemoton Theory outlines the development of a theoretical biology, based on exact quantitative considerations and the consequences of its application on biotechnology and on the artificial synthesis of living systems.

One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu ment since has been shown to be rather susceptible to generalization."

One high-level ability of the human brain is to understand what it has learned. This seems to be the crucial advantage in comparison to the brain activity of other primates. At present we are technologically almost ready to artificially reproduce human brain tissue, but we still do not fully understand the information processing and the related biological mechanisms underlying this ability. Thus an electronic clone of the human brain is still far from being realizable. At the same time, around twenty years after the revival of the connectionist paradigm, we are not yet satisfied with the typical subsymbolic attitude of devices like neural networks: we can make them learn to solve even difficult problems, but without a clear explanation of why a solution works. Indeed, to widely use these devices in a reliable and non elementary way we need formal and understandable expressions of the learnt functions. of being tested, manipulated and composed with These must be susceptible other similar expressions to build more structured functions as a solution of complex problems via the usual deductive methods of the Artificial Intelligence. Many effort have been steered in this directions in the last years, constructing artificial hybrid systems where a cooperation between the sub symbolic processing of the neural networks merges in various modes with symbolic algorithms. In parallel, neurobiology research keeps on supplying more and more detailed explanations of the low-level phenomena responsible for mental processes.

Nervous System Actions and Interactions: Concepts in Neurophysiology approaches the nervous system from a functional, rather than structural, point of view.

While all of the central topics of functional neuroscience are covered, these topics are organized from a neurophysiological perspective yielding chapters on subjects such as information storage and effector actions. Each chapter is organized around general concepts that then are further developed in the text. The authors attempt to establish a dialogue with the reader by means of proposed experiments and open ended questions that are designed to both reinforce and question the text. This volume is intended to be a book of ideas for the novice or seasoned researcher in neuroscience.

A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry.

Originally published in 1991, "Intersections of Random Walks" focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections.

The presentsoftcover reprint includes corrections andaddenda fromthe1996 printing, andmakesthis classic monographavailable to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks."

Connection science is a new information-processing paradigm which attempts to imitate the architecture and process of the brain, and brings together researchers from disciplines as diverse as computer science, physics, psychology, philosophy, linguistics, biology, engineering, neuroscience and AI. Work in Connectionist Natural Language Processing (CNLP) is now expanding rapidly, yet much of the work is still only available in journals, some of them quite obscure. To make this research more accessible this book brings together an important and comprehensive set of articles from the journal CONNECTION SCIENCE which represent the state of the art in Connectionist natural language processing; from speech recognition to discourse comprehension. While it is quintessentially Connectionist, it also deals with hybrid systems, and will be of interest to both theoreticians as well as computer modellers. Range of topics covered: Connectionism and Cognitive Linguistics Motion, Chomsky's Government-binding Theory Syntactic Transformations on Distributed Representations Syntactic Neural Networks A Hybrid Symbolic/Connectionist Model for Understanding of Nouns Connectionism and Determinism in a Syntactic Parser Context Free Grammar Recognition Script Recognition with Hierarchical Feature Maps Attention Mechanisms in Language Script-Based Story Processing A Connectionist Account of Similarity in Vowel Harmony Learning Distributed Representations Connectionist Language Users Representation and Recognition of Temporal Patterns A Hybrid Model of Script Generation Networks that Learn about Phonological Features Pronunciation in Text-to-Speech Systems

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an swers are needed to important fundamental questions such as (a) what can neu ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines."