The theme of 'escape from metastable states', either via noise-assisted hop- ping and/or quantum tunneling, is pivotal to many scientific disciplines. It impacts on suchdiversephysical,chemicalandbiologicalprocessesasdiffu- sion in solids, chemical reactions per se, nucleation phenomenaand transfer ofmatter and information in biologicalcomplexes, to name only a few. With 'New Trends in Kramers' Reaction Rate Theory' this book fills yet another part of the multifaceted scope which underpins the Understanding of Chemical Reactivity. Since the publication of the comprehensive review about reaction rate theory in Rev. Mod. Phys. 52, 251 (1990) the field has witnessed many majordevelopments and extensions both in experiment and theory. In this book the focus will be on the theoretical progress. In doing so, the editorscollected aseries ofauthoritative articles from majorpractitioners in the field which as a whole give a representative- although notcomplete- sample ofthe novel recenttheoretical advances. As an inevitable consequence, the editors recognize that not all readers will wish to digest the volume in its entirety. We trust, however, that the reader will be able to choose from the many methods and techniques which he is interested in, and which he requires to perform his own new research in this area. There is the consistent underlying theme of noise-assisted barrier crossing that is running through all of the book. Nevertheless, each chapter should be considered as self contained. In this spirit the editors share the confident beliefthat the future research on the Kramers problem, and related topics, will be invigorated by the selectedcontributions herein.

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.

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.

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).

E. KONTIZAS Astronomical Institute National Observatory of Athens P. O. Box 20048 Athens GR-1181O GREECE The international conference on "Wide-Field Spectroscopy" and its sub ject matter were agreed during the general assembly of the International Astronomical Union (IAU) in August 1994 by the Working Group of Com mision 9 "Wi de-Field Imaging". This meeting gave an opportunity to world experts on this subject to gather in Athens, in order to discuss the cur rent exploitation and the impending opportunities that exist in the area of multi-object spectroscopy, with particular emphasis on: 1. Astronomical instruments, data acquisition, processing and analysis techniques. 2. Astrophysical problems best tackled through wide-field, multi-object spectroscopy. The new fibre optic technology offers an important tool for the advancement of basic research and the development of industrial applications. Astronom ical spectroscopy is a field of astronomy which has contributed much to the advancement of fundamental physics. The spectra of hot stars have been used to determine the well-known Balmer formula for the wavelength of hydrogen lines, in the late 19th century. Since then, spectroscopy has made enormous progress in stellar atmosphere studies, in kinematics, and in the detection of high redshifts in the Universe. The traditional techniques of obtaining wide-field spectroscopic data are based on slitless spectroscopy (objective prism). Several observations, world wide, make use ofthese tech niques in order to obtain information on the spectral properties of objects in large areas of the sky.

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.

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.

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 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."

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."

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.

Hybrid Neural Network and Expert Systems presents the basics of expert systems and neural networks, and the important characteristics relevant to the integration of these two technologies. Through case studies of actual working systems, the author demonstrates the use of these hybrid systems in practical situations. Guidelines and models are described to help those who want to develop their own hybrid systems. Neural networks and expert systems together represent two major aspects of human intelligence and therefore are appropriate for integration. Neural networks represent the visual, pattern-recognition types of intelligence, while expert systems represent the logical, reasoning processes. Together, these technologies allow applications to be developed that are more powerful than when each technique is used individually. Hybrid Neural Network and Expert Systems provides frameworks for understanding how the combination of neural networks and expert systems can produce useful hybrid systems, and illustrates the issues and opportunities in this dynamic field.

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."

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.

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.

Neural Information Processing and VLSI provides a unified treatment of this important subject for use in classrooms, industry, and research laboratories, in order to develop advanced artificial and biologically-inspired neural networks using compact analog and digital VLSI parallel processing techniques. Neural Information Processing and VLSI systematically presents various neural network paradigms, computing architectures, and the associated electronic/optical implementations using efficient VLSI design methodologies. Conventional digital machines cannot perform computationally-intensive tasks with satisfactory performance in such areas as intelligent perception, including visual and auditory signal processing, recognition, understanding, and logical reasoning (where the human being and even a small living animal can do a superb job). Recent research advances in artificial and biological neural networks have established an important foundation for high-performance information processing with more efficient use of computing resources. The secret lies in the design optimization at various levels of computing and communication of intelligent machines. Each neural network system consists of massively paralleled and distributed signal processors with every processor performing very simple operations, thus consuming little power. Large computational capabilities of these systems in the range of some hundred giga to several tera operations per second are derived from collectively parallel processing and efficient data routing, through well-structured interconnection networks. Deep-submicron very large-scale integration (VLSI) technologies can integrate tens of millions of transistors in a single silicon chip for complex signal processing and information manipulation. The book is suitable for those interested in efficient neurocomputing as well as those curious about neural network system applications. It has been especially prepared for use as a text for advanced undergraduate and first year graduate students, and is an excellent reference book for researchers and scientists working in the fields covered.

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."

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."