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

Design happens everywhere, whether in animate objects (e.g., dendritic lung structures, bacterial colonies, and corals), inanimate patterns (river basins, beach slope, and dendritic crystals), social dynamics (pedestrian traffic flows), or engineered systems (heat dissipation in electronic circuitry). This design in nature often takes on remarkably similar patterns, which can be explained under one unifying Constructal Law. This book explores the unifying power of the Constructal Law and its applications in all domains of design generation and evolution, ranging from biology and geophysics to globalization, energy, sustainability, and security.
The Constructal Law accounts for the universal tendency of flow systems to morph into evolving configurations that provide greater and easier access over time. The Constructal Law resolves the many and contradictory ad hoc statements of optimality, end design, and destiny in nature, such as minimum and maximum entropy production and minimum and maximum flow resistance, and also explains the designs that are observed and copied in biomimetics.
"Constructal Law and the Unifying Principle of Design" covers the fundamentals of Constructal Theory and Design, as well as presenting a variety ofstate-of-the-art applications. Experts from the biological, physical and social sciences demonstrate the unification of all design phenomena in nature, and apply this knowledge to novel designs in modern engineering, such as vascularization for self-healing and self-cooling materials for aircraft, and tree fins and cavities for heat transfer enhancement.

Thermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data.
This book has the twofold aim to present coherently the relevant results coming from the recent scientific literature and to guide the readers through the process of deriving results, enabling them to explore the limits of the mathematical approximations and test the power of the method. The book is focused on the fundamental properties of nanosystems in the gas phase. For this reason there is a strong emphasis on microcanonical physics. Each chapter is enrichedwith exercises and 3 Appendices provide additional useful materials."

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.

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.

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

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.

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.

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.

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.

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.

Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

also in: THE KLUWER INTERNATIONAL SERIES ON ASIAN STUDIES IN COMPUTER AND INFORMATION SCIENCE, Volume 2

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.

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.

Nonlinear Modeling: Advanced Black-Box Techniques discusses methods on Neural nets and related model structures for nonlinear system identification; Enhanced multi-stream Kalman filter training for recurrent networks; The support vector method of function estimation; Parametric density estimation for the classification of acoustic feature vectors in speech recognition; Wavelet-based modeling of nonlinear systems; Nonlinear identification based on fuzzy models; Statistical learning in control and matrix theory; Nonlinear time-series analysis. It also contains the results of the K.U. Leuven time series prediction competition, held within the framework of an international workshop at the K.U. Leuven, Belgium in July 1998.

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.

This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run."

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.

Neural nets offer a fascinating new strategy for spatial analysis, and their application holds enormous potential for the geographic sciences. However, the number of studies that have utilized these techniques is limited. This lack of interest can be attributed, in part, to lack of exposure, to the use of extensive and often confusing jargon, and to the misapprehension that, without an underlying statistical model, the explanatory power of the neural net is very low. Neural Nets: Applications for Geography attacks all three issues; the text demonstrates a wide variety of neural net applications in geography in a simple manner, with minimal jargon. The volume presents an introduction to neural nets that describes some of the basic concepts, as well as providing a more mathematical treatise for those wishing further details on neural net architecture. The bulk of the text, however, is devoted to descriptions of neural net applications in such broad-ranging fields as census analysis, predicting the spread of AIDS, describing synoptic controls on mountain snowfall, examining the relationships between atmospheric circulation and tropical rainfall, and the remote sensing of polar cloud and sea ice characteristics. The text illustrates neural nets employed in modes analogous to multiple regression analysis, cluster analysis, and maximum likelihood classification. Not only are the neural nets shown to be equal or superior to these more conventional methods, particularly where the relationships have a strong nonlinear component, but they are also shown to contain significant explanatory power. Several chapters demonstrate that the nets themselves can be decomposed to illuminate causative linkages between different events in both the physical and human environments.

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.

In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.

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."