This work addresses time-delay in complex nonlinear systems and, in particular, its applications in complex networks; its role in control theory and nonlinear optics are also investigated. Delays arise naturally in networks of coupled systems due to finite signal propagation speeds and are thus a key issue in many areas of physics, biology, medicine, and technology. Synchronization phenomena in these networks play an important role, e.g., in the context of learning, cognitive and pathological states in the brain, for secure communication with chaotic lasers or for gene regulation. The thesis includes both novel results on the control of complex dynamics by time-delayed feedback and fundamental new insights into the interplay of delay and synchronization. One of the most interesting results here is a solution to the problem of complete synchronization in general networks with large coupling delay, i.e., large distances between the nodes, by giving a universal classification of networks that has a wide range of interdisciplinary applications.

'Et moi, ..., si j' avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aIle.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'" able 10 do something with it. Eric T. Bell O. Heaviside 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."

Neural Network Simulation Environments describes some of the best examples of neural simulation environments. All current neural simulation tools can be classified into four overlapping categories of increasing sophistication in software engineering. The least sophisticated are undocumented and dedicated programs, developed to solve just one specific problem; these tools cannot easily be used by the larger community and have not been included in this volume. The next category is a collection of custom-made programs, some perhaps borrowed from other application domains, and organized into libraries, sometimes with a rudimentary user interface. More recently, very sophisticated programs started to appear that integrate advanced graphical user interface and other data analysis tools. These are frequently dedicated to just one neural architecture/algorithm as, for example, three layers of interconnected artificial `neurons' learning to generalize input vectors using a backpropagation algorithm. Currently, the most sophisticated simulation tools are complete, system-level environments, incorporating the most advanced concepts in software engineering that can support experimentation and model development of a wide range of neural networks. These environments include sophisticated graphical user interfaces as well as an array of tools for analysis, manipulation and visualization of neural data. Neural Network Simulation Environments is an excellent reference for researchers in both academia and industry, and can be used as a text for advanced courses on the subject.

Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as "system identi?cation" in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit non-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (noise) or by a very high order of equations.

Econophysics is a newborn field of science bridging economics and physics. A special feature of this new science is the data analysis of high-precision market data. In economics arbitrage opportunity is strictly denied; however, by observing high-precision data we can prove the existence of arbitrage opportunity. Also, financial technology neglects the possibility of market prediction; however, in this book you can find many examples of predicted events. There are other surprising findings.

This volume is the proceedings of a workshop on "application of econophysics" at which leading international researchers discussed their most recent results.

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

The aim of this book is to comment on, and clarify, the mathematical aspects of the theory of thermodynamics. The standard presentations of the subject are often beset by a number of obscurities associated with the words "state", "reversible", "irreversible", and "quasi-static". This book is written in the belief that such obscurities are best removed not by the formal axiomatization of thermodynamics, but by setting the theory in the wider context of a genuine field theory which incorporates the effects of heat conduction and intertia, and proving appropriate results about the governing differential equations of this field theory. Even in the simplest one-dimensional case it is a nontrivial task to carry through the details of this program, and many challenging problems remain open.

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."

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.

Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics - CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on theory and applications, and a smaller part on software. The theory part contains fundamental chapters on how to design and/or apply CA for many different areas. In the applications part a number of representative examples of really using CA in a broad range of disciplines is provided - this part will give the reader a good idea of the real strength of this kind of modeling as well as the incentive to apply CA in their own field of study. Finally, we included a smaller section on software, to highlight the important work that has been done to create high quality problem solving environments that allow to quickly and relatively easily implement a CA model and run simulations, both on the desktop and if needed, on High Performance Computing infrastructures.

Adaptive Resonance Theory Microchips describes circuit strategies resulting in efficient and functional adaptive resonance theory (ART) hardware systems. While ART algorithms have been developed in software by their creators, this is the first book that addresses efficient VLSI design of ART systems. All systems described in the book have been designed and fabricated (or are nearing completion) as VLSI microchips in anticipation of the impending proliferation of ART applications to autonomous intelligent systems. To accommodate these systems, the book not only provides circuit design techniques, but also validates them through experimental measurements. The book also includes a chapter tutorially describing four ART architectures (ART1, ARTMAP, Fuzzy-ART and Fuzzy-ARTMAP) while providing easily understandable MATLAB code examples to implement these four algorithms in software. In addition, an entire chapter is devoted to other potential applications for real-time data clustering and category learning.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size."

Contains most of the invited papers of the Second Colloquium and Workshop on 'Random Fields: Rigorous Results in Statistical Mechanics' held in K'oszeg, Hungary between August 26 and September 1, 1984--Pref.

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.

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. "

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.

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.

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.

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.

This volume contains twenty contributions of work, conducted since 1996 in the French- German Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). The main purpose of this publication is to give an overview over the work conducted in this programme, and to make the results obtained available to the pUblic. The reports are grouped under the four headings "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases" and "Turbulent Flows". AIl contributions to this publica- tion were reviewed by a board consisting of T. Alziary de Roquefort (Poitiers, France), P. Bontoux (Marseille, France), JA Desideri (Sophia-Antipolis, France), W. Kordulla (G6t- tingen, Germany), R. Peyret (Nice, France), R. Rannacher (Heidelberg, Germany), G. War- necke (Magdeburg, ,Germany), and the editor. The responsibility for the contents of the reports nevertheless lies with the authors. E. H. Hirschel Editor Preface The Colloquium on "Numerical Simulation of Flows", Marseille, November 21 and 22, th 1997, was the 6 Joint CNRS-DFG Colloquium organized in the frame of the French- German Research Collaboration on Computational Fluid Dynamics. This Collaborative Program was elaborated progressively since 1991, when the two major research groups were brought together: the Priority Program "Flow Simulation with Super Computers" from the DFG in Germany and the Groupement de Recherche de "Mecanique des Fluides NumCrique" (GDR MFN) from the CNRS in France.

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.

First published in 1927 as the second edition of a 1925 original, this book was intended as a general introduction to the principles of thermodynamics for university students involved in the physical sciences. Birtwistle gives a brief overview of the history of science relating to heat and the conservation of energy as well as practical examples to back up salient points in his explanation of key ideas. This book will be of value to anyone with an interest in the history of science.

The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics. Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systems composed by a large enough number of individuals. Examples of such systems are interacting agents in a financial market, potential voters during political elections, or groups of animals with a tendency to flock or herd. Among other possible approaches, this book provides a step-by-step introduction to the mathematical modelling based on a mesoscopic description and the construction of efficient simulation algorithms by Monte Carlo methods. The arguments of the book cover various applications, from the analysis of wealth distributions, the formation of opinions and choices, the price dynamics in a financial market, to the description of cell mutations and the swarming of birds and fishes. By means of methods inspired by the kinetic theory of rarefied gases, a robust approach to mathematical modelling and numerical simulation of multi-agent systems is presented in detail. The content is a useful reference text for applied mathematicians, physicists, biologists and economists who want to learn about modelling and approximation of such challenging phenomena.

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.