This book introduces the novel concept of a fuzzy network whose nodes are rule bases and the connections between the nodes are the interactions between the rule bases in the form of outputs fed as inputs. The concept is presented as a systematic study for improving the feasibility and transparency of fuzzy models by means of modular rule bases whereby the model accuracy and efficiency can be optimised in a flexible way. The study uses an effective approach for fuzzy rule based modelling of complex systems that are characterised by attributes such as nonlinearity, uncertainty, dimensionality and structure.The approach is illustrated by formal models for fuzzy networks, basic and advanced operations on network nodes, properties of operations, feedforward and feedback fuzzy networks as well as evaluation of fuzzy networks. The results are demonstrated by numerous examples, two case studies and software programmes within the Matlab environment that implement some of the theoretical methods from the book. The book shows the novel concept of a fuzzy network with networked rule bases as a bridge between the existing concepts of a standard fuzzy system with a single rule base and a hierarchical fuzzy system with multiple rule bases.

Current companies and communities of practice are involved in intensive networking and collaborative systems by a great variety of electronic relations and collaborative interactions. This has resulted in entangled systems that need to be managed efficiently and in an autonomous way, thus facing many issues and challenges. The extensive research produced in this book will help virtual organizations to exploit latest and powerful technologies based on Grid and Wireless infrastructures as well as Cloud computing in order to alleviate complex issues and challenges arisen in networking and collaborative systems, in terms of collaborative applications, resource management, mobility, and security and system resilience. The ultimate aim of the book is to stimulate research that leads to the creation of responsive environments for networking and, at longer-term, the development of adaptive, secure, mobile, and intuitive intelligent systems for collaborative work and learning. Academic researchers, professionals and practitioners in the field will be inspired and put in practice the ideas and experiences proposed in the book in order to evaluate them for their specific research and work.

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.

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.

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

Modern achievements in the intensively developing field of applied mathematics are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.

There are numerous technological materials - such as metals, polymers, ceramics, concrete, and many others - that vary in properties and serviceability. However, the almost universal common theme to most real materials is that their properties depend on the scale at which the analysis or observation takes place and at each scale "probabilities" play an important role. Here the word "probabilities" is used in a wider than the classical sense. In order to increase the efficiency and serviceability of these materials, researchers from NATO, CP and other countries were brought together to exchange knowledge and develop avenues for progress and applications in the st 21 century. The workshop began by reviewing progress in the subject area over the past few years and by identifying key questions that remain open. One point was how to observe/measure material properties at different scales and whether a probabilistic approach, at each scale, was always applicable and advantageous. The wide range of materials, from wood to advanced metals and from concrete to complex advanced composites, and the diversity of applications, e.g. fatigue, fracture, deformation, etc., were recognized as "obstacles" in identifying a "universal" approach.

This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.

Since the late 1960s, there has been a revolution in robots and industrial automation, from the design of robots with no computing or sensorycapabilities (first-generation), to the design of robots with limited computational power and feedback capabilities (second-generation), and the design of intelligent robots (third-generation), which possess diverse sensing and decision making capabilities. The development of the theory of intelligent machines has been developed in parallel to the advances in robot design. This theory is the natural outcome of research and development in classical control (1950s), adaptive and learning control (1960s), self-organizing control (1970s) and intelligent control systems (1980s). The theory of intelligent machines involves utilization and integration of concepts and ideas from the diverse disciplines of science, engineering and mathematics, and fields like artificial intelligence, system theory and operations research. The main focus and motivation is to bridge the gap between diverse disciplines involved and bring under a common cover several generic methodologies pertaining to what has been defined as machine intelligence. Intelligent robotic systems are a specific application of intelligent machines. They are complex computer controlled robotic systems equipped with a diverse set of visual and non visual sensors and possess decision making and problem solving capabilities within their domain of operation. Their modeling and control is accomplished via analytical and heuristic methodologies and techniques pertaining to generalized system theory and artificial intelligence. Intelligent Robotic Systems: Theory, Design and Applications, presents and justifies the fundamental concepts and ideas associated with the modeling and analysis of intelligent robotic systems. Appropriate for researchers and engineers in the general area of robotics and automation, Intelligent Robotic Systems is both a solid reference as well as a text for a graduate level course in intelligent robotics/machines.

The Fifteenth International Workshop on Maximum Entropy and Bayesian Meth- ods was held July 31-August 4, 1995 in Santa Fe, New Mexico, USA. St. John's College, located in the foothills of the Sangre de Cristo Mountains, provided a congenial setting for the Workshop. The relaxed atmosphere of the College, which was thoroughly enjoyed by all the attendees, stimulated free-flowing and thought- ful discussions. Conversations continued at the social events, which included a reception at the Santa Fe Institute, a New Mexican dinner at Richard Silver's home, and an excursion to Los Alamos that ended with a mixed grill at FUller Lodge, the main hall of the former Los Alamos Ranch School. This volume represents the Proceedings of the Workshop. Articles on the tra- ditional theme of the Workshop, application of the maximum-entropy principle and Bayesian methods for statistical inference in diverse areas of scientific re- search, are contained in these Proceedings. As is tradition, the Workshop opened with a tutorial on Bayesian methods, lucidly presented by Peter Cheeseman and Wray Buntine (NASA AMES, Moffett Field). The lecture notes for their tutorial are available on the World Wide Web at http://bayes .lanl. gov / "'maxent/. In addition, several new thrusts for the Workshop are described below.

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."

Quantum phase transitions, driven by quantum fluctuations, exhibit intriguing features offering the possibility of potentially new applications, e.g. in quantum information sciences. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems.

For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results.

This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area.

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This book contains the lectures given at the NATO ASI 910820 "Cellular Automata and Cooperative Systems" Meeting which was held at the Centre de Physique des Houches, France, from June 22 to July 2, 1992. This workshop brought together mathematical physicists, theoretical physicists and mathe maticians working in fields related to local interacting systems, cellular and probabilistic automata, statistical physics, and complexity theory, as well as applications of these fields. We would like to thank our sponsors and supporters whose interest and help was essential for the success of the meeting: the NATO Scientific Affairs Division, the DRET (Direction des Recherches, Etudes et Techniques), the Ministere des Affaires Etrangeres, the National Science Foundation. We would also like to thank all the secretaries who helped us during the preparation of the meeting, in particular Maryse Cohen-Solal (CPT, Marseille) and Janice Nowinski (Courant Institute, New York). We are grateful for the fine work of Mrs. Gladys Cavallone in preparing this volume."

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

The Dynamics of Digital Excitation provides a fundamental new viewpoint on circuit therapy. It begins with a very real and practical problem and then presents arguments that are set forth for the first time. The most commonly used parameter of digital circuits, the gate delay time, does not exist. This problem emerges most clearly in the high-speed CMOS, above 1 GHz clock frequency. This book explains why that is so and then how to deal with the situation in a practical manner. Most of the large IC companies, and many of the small IC design companies, are now racing to capture above 1 GHz clock CMOS IC markets. A few examples of such companies in the United States are Motorola, Intel and DEC. Numerous new small design-only companies are also interested in this technology. The above 1 GHz circuit design is an extremely difficult concept and, for the designers, the material discussed in this book is indispensable. The Dynamics of Digital Excitation shows that the fastest CMOS circuits can be understood and designed only after understanding their quantum-mechanical nature.The Dynamics of Digital Excitation will help the circuit designer to learn how to deal with the problems of circuit delay when the gate delay is not a valid concept at high switching speeds and how to design the fastest critical paths. This book outlines essential and fundamental guidelines for designing the fastest CMOS circuits. It also explains how to design and structure computer-aided designs to deal with above 1 GHz circuits. The Dynamics of Digital Excitation sets forth exciting new ideas and will be of interest to IC designers and CAD professionals alike.

In recent years, there has been a growing interest in applying neural networks to dynamic systems identification (modelling), prediction and control. Neural networks are computing systems characterised by the ability to learn from examples rather than having to be programmed in a conventional sense. Their use enables the behaviour of complex systems to be modelled and predicted and accurate control to be achieved through training, without a priori information about the systems' structures or parameters. This book describes examples of applications of neural networks In modelling, prediction and control. The topics covered include identification of general linear and non-linear processes, forecasting of river levels, stock market prices and currency exchange rates, and control of a time-delayed plant and a two-joint robot. These applications employ the major types of neural networks and learning algorithms. The neural network types considered in detail are the muhilayer perceptron (MLP), the Elman and Jordan networks and the Group-Method-of-Data-Handling (GMDH) network. In addition, cerebellar-model-articulation-controller (CMAC) networks and neuromorphic fuzzy logic systems are also presented. The main learning algorithm adopted in the applications is the standard backpropagation (BP) algorithm. Widrow-Hoff learning, dynamic BP and evolutionary learning are also described.

One service mathematics has rendered the Et moi, .... si j'avait su comment en revenir, je human race. It has put common sense back n'y serais point aile.' where it belongs, on the topmost shelf next to Jules Verne the dusty canister labelled 'discarded nonsense'. Eric T. Bell The series is divergent; therefore we may be able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer 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."

Computer Simulation in Chemical Physics contains the proceedings of a NATO Advanced Study Institute held at CORISA, Alghero, Sardinia, in September 1992. In the five years that have elapsed since the field was last summarized there have been a number of remarkable advances which have significantly expanded the scope of the methods. Good examples are the Car--Parrinello method, which allows the study of materials with itinerant electrons; the Gibbs technique for the direct simulation of liquid--vapor phase equilibria; the transfer of scaling concepts from simulations of spin models to more complex systems; and the development of the configurational--biased Monte-Carlo methods for studying dense polymers. The field has also been stimulated by an enormous increase in available computing power and the provision of new software. All these exciting developments, an more, are discussed in an accessible way here, making the book indispensable reading for graduate students and research scientists in both academic and industrial settings.

This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

The recentexplosionofactivity inneural modelingseemsto have beendriven more by advances inthe theories and applicationsoflearning paradigms for artificial neural networks than by advances in our knowledge of real nervous systems. In the past few years, major conferences on neural networks and neural modeling have emerged and, appropriately, have focussed on technological exploitation of these advances. Sensingthat the recentleaps in both computational powerand knowledge ofthe nervous system may have setthe stage for a revolution intheoretical neurobiology, neuroscientists have welcomed thenew neural modeling; butmanyofthem would like tosee itdirected as heavily toward understanding of the nervou$ system as it is presently directed toward computertechnology and control-system engineering. Furthermore, some neuroscientists believe thattechnologists shouldnotbe satisfiedonly with exploiting or extending the recent advances in learning paradigms, that emerging knowledge about real nervous systems will suggest other, comparably valuable, paradigms forsignal processingand control. Ourmotive as organizers was to have a conference that focussed on both of these areas -- emerging modeling tools and concepts for neurobiologists, and emerging neurobiological concepts and neurobiological knowledge ofpotential use to technologists. Ourprinciple ofdesign was simple. We attempted to organize aconference withagroup ofspeakers that would be most illuminating and exciting to us and to our students. We succeeded. EdwinR. Lewis INTRODUCTION This volume contains the collected papers of the 1990 Conference on Analysis and ModelingofNeural Systems, held July 25-27, in Berkeley, California. There were 21 invited talks at the meeting, covering aspects ofanalysis and modeling from the subcellularlevel to the networklevel. Inaddition, thirty six posters were accepted forpresentation.

Neural and Synergetic Computers deals with basic aspect of this rapidly developing field. Several contributions are devoted to the application of basic concepts of synergetics and dynamic systems theory to the constructionof neural computers. Further topics include statistical approaches to neural computers and their design (for example by sparse coding), perception motor control, and new types of spatial multistability in lasers.

Non-Destructive Evaluation (NDE) is now playing an increasing role in our modern global economy; in security sensitive industries, for instance. The complexity of the inspection task and either large or limited lot runs now require more operator-assisted or fully- automated signal processing. This book deals with both fields of expertise: NDE and signal processing. On the signal processing side, in the particular context of NDE applications, the following topics are discussed: sensor fusion, signal knowledge representation, artificial intelligence, fuzzy logic, computer vision, integration of numeric and non-numeric informations, parallel decomposition, noise processing and calibration of sensor devices as well as reliability of detection. Some hardware considerations are introduced as well, to discuss platforms on which processing is done. On the NDE side, applications include advances in holographic interferometry, microwave resonance or shearography and also on more traditional NDE techniques such as ultrasonics, infrared techniques, X-ray, computed tomography, Eddy currents. Inverse problems are also discussed. This book is required reading for those who already have some experience in one or both fields (signal processing and/or NDE).

Hybrid Intelligent Systems summarizes the strengths and weaknesses of five intelligent technologies: fuzzy logic, genetic algorithms, case-based reasoning, neural networks and expert systems, reviewing the status and significance of research into their integration. Engineering and scientific examples and case studies are used to illustrate principles and application development techniques. The reader will gain a clear idea of the current status of hybrid intelligent systems and discover how to choose and develop appropriate applications. The book is based on a thorough literature search of recent publications on research and development in hybrid intelligent systems; the resulting 50-page reference section of the book is invaluable. The book starts with a summary of the five major intelligent technologies and of the issues in and current status of research into them. Each subsequent chapter presents a detailed discussion of a different combination of intelligent technologies, along with examples and case studies. Four chapters contain detailed case studies of working hybrid systems.The book enables the reader to: * Describe the important concepts, strengths and limitations of each technology; * Recognize and analyze potential problems with the application of hybrid systems; * Choose appropriate hybrid intelligent solutions; * Understand how applications are designed with any of the approaches covered; * Choose appropriate commercial development shells or tools. An invaluable reference source for those who wish to apply intelligent systems techniques to their own problems.

The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics. The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.

Computation in Neurons and Neural Systems contains the collected papers of the 1993 Conference on Computation and Neural Systems which was held between July 31--August 7, in Washington, DC. These papers represent a cross-section of the state-of-the-art research work in the field of computational neuroscience, and includes coverage of analysis and modeling work as well as results of new biological experimentation.