Nonlinear dynamics is now recognized as playing a crucial role in a wide variety of disciplines. But what is only just beginning is the important process of cross fertilization and transfer of knowledge and expertise from one area to another. This book is intended to promote this process which will undoubtedly contribute greatly to furthering our understanding of complex systems. Contributions are provided by leading experts from the areas of sociology, cognitive science, chemistry, physiology, ecology, economics, neural networks and physics.

In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

A collection of articles on different approaches to the investigation of surface effects on nanosized magnetic materials, with special emphasis on magnetic nanoparticles. The book provides an overview of progress in the field through recent results.

A rich variety of real-life physical problems which are still poorly understood are of a nonlinear nature. Examples include turbulence, granular flows, detonations and flame propagation, fracture dynamics, and a wealth of new biological and chemical phenomena which are being discovered. Particularly interesting among the manifestations of nonlinearity are coherent structures. This book contains reviews and contributions reporting on the state of the art regarding the role of coherent structures and patterns in nonlinear science.

During the last decade there has been a renewed interest in research on supramolecular assemblies in solutions, such as micelles and microemulsions, not only because of their extensive applications in industries dealing with catalysts, detergency, biotechnology, and enhanced oil recovery, but also due to the development of new and more powerful experimental and theoretical tools for probing the microscopic behavior of these systems. Prominent among the array of the newly available experimental techniques are photon correlation spectroscopy, small-angle neutron and X-ray scattering, and neutron spin-echo and nuclear magnetic resonance spectroscopies. On the theoretical side, the traditionally emphasized thermodynamic approach to the study of the phase behavior of self-assembled systems in solutions is gradually being replaced by statistical mechanical studies of semi-micro scopic and microscopic models of the assemblies. Since the statistical mechanical approach demands as its starting point the microscopic struc tural information of the self-assembled system, the experimental determina tion of the structures of micelles and microemulsions becomes of paramount interest. In this regard the scattering techniques mentioned above have played an important role in recent years and will continue to do so in the future. In applying the scattering techniques to the supramolecular species in solution, one cannot often regard the solution to be ideal. This is because the inter-aggregate interaction is often long-ranged since it is coulombic in nature and the interparticle correlations are thus appreciable."

From the reviews:

..".This book is a very useful addition to polymer literature, and it is a pleasure to recommend it to the polymer community." (J.E. Mark, University of Cincinnati, POLYMER NEWS)

One service mathematics has rendered the 'Et moi, ..., si j'avait Sil comment en revenir, je n'y serais point aIle.' human race. It has put common sense back 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 to 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.

In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids. The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics. The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium. Audience: This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena.

Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student.

This book demonstrates the usefulness of tools from statistical mechanics for biology. It includes the new tendencies in topics like membranes, vesicles, microtubules, molecular motors, DNA, protein folding, phase transitions in biological systems, evolution, population dynamics, neural systems and biological oscillators, with special emphasis on the importance of statistical mechanics in their development. The book addresses researchers and graduate students.

This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites.

This book is especially addressed to young researchers in theoretical physics with a basic background in Field Theory and Condensed Matter Physics. The topics were chosen so as to offer the largest possible overlap between the two expertises, selecting a few key problems in Condensed Matter Theory which have been recently revisited within a field-theoretic approach. The presentation of the material is aimed not only at providing the reader with an overview of this exciting frontier area of modern theoretical physics, but also at elucidating most of the tools needed for a technical comprehen sion of the many papers appearing in current issues of physics journals and, hopefully, to enable the reader to tackle research problems in this area of physics. This makes the material a live creature: while not pretending it to be exhaustive, it is tutorial enough to be useful to young researchers as a starting point in anyone of the topics covered in the book."

Speech by Toyosaburo Taniguchi Dr. Kubo, Chairman, Distinguished Guests, and Friends, I am very happy, pleased and honored to be here this evening with so many distinguished guests, friends, and scholars from within this country and from different parts of the world. The Taniguchi Foundation wishes to extend a warm and sincere welcome to the many participants of the Ninth International Symposium on the Theory of Condensed Matter, which se ries was inaugurated eight years ago through the strenuous efforts of Dr. Ryogo Kubo, who is gracing us today with his presence. We are deeply indebted to Dr. Kubo, Dr. Suzuki, and their associates, who havE' spent an enormous amount of time and effort to make this particular symposium possible. We are convinced that the foundation should not be considered as what makes our symposium a success. The success is entirely due, I feel, to the continuous efforts of the Organizing Committee and of all those who have lent their support to this program. In this sense, your words of praise about the symposium, if any, should be directed to all of them. So far, I have met in person a total of 62 participants in this Division from 12 countries: Argentina, Belgium, Canada, Denmark, the Federal Republic of Germany, France, Ireland, Israel, Rumania, Switzerland, the United Kingdom, and the United States of America, with 133 participants from Japan. Those friends I have been privileged to make, I shall always treasure."

Lifelong learning addresses situations in which a learner faces a series of different learning tasks providing the opportunity for synergy among them. Explanation-based neural network learning (EBNN) is a machine learning algorithm that transfers knowledge across multiple learning tasks. When faced with a new learning task, EBNN exploits domain knowledge accumulated in previous learning tasks to guide generalization in the new one. As a result, EBNN generalizes more accurately from less data than comparable methods. Explanation-Based Neural Network Learning: A Lifelong Learning Approach describes the basic EBNN paradigm and investigates it in the context of supervised learning, reinforcement learning, robotics, and chess. The paradigm of lifelong learning - using earlier learned knowledge to improve subsequent learning - is a promising direction for a new generation of machine learning algorithms. Given the need for more accurate learning methods, it is difficult to imagine a future for machine learning that does not include this paradigm.' From the Foreword by Tom M. Mitchell.

A dominant feature of our ordinary experience of the world is a sense of irreversible change: things lose form, people grow old, energy dissipates. On the other hand, a major conceptual scheme we use to describe the natural world, molecular dynamics, has reversibility at its core. The need to harmonize conceptual schemes and experience leads to several questions, one of which is the focus of this book. How does irreversibility at the macroscopic level emerge from the reversibility that prevails at the molecular level? Attempts to explain the emergence have emphasized probability, and assigned different probabilities to the forward and reversed directions of processes so that one direction is far more probable than the other. The conclu sion is promising, but the reasons for it have been obscure. In many cases the aim has been to find an explana tion in the nature of probability itself. Reactions to that have been divided: some think the aim is justified while others think it is absurd."

Applications of Neural Networks gives a detailed description of 13 practical applications of neural networks, selected because the tasks performed by the neural networks are real and significant. The contributions are from leading researchers in neural networks and, as a whole, provide a balanced coverage across a range of application areas and algorithms. The book is divided into three sections. Section A is an introduction to neural networks for nonspecialists. Section B looks at examples of applications using Supervised Training'. Section C presents a number of examples of Unsupervised Training'. For neural network enthusiasts and interested, open-minded sceptics. The book leads the latter through the fundamentals into a convincing and varied series of neural success stories -- described carefully and honestly without over-claiming. Applications of Neural Networks is essential reading for all researchers and designers who are tasked with using neural networks in real life applications.

Dry granular materials, such as sand, sugar and powders, can be poured into a container like a liquid and can also form a pile, resisting gravity like a solid, which is why they can be regarded as a fourth state of matter, neither solid nor liquid. This book focuses on defining the physics of dry granular media in a systematic way, providing a collection of articles written by recognised experts. The physics of this field is new and full of challenges, but many questions (such as kinetic theories, plasticity, continuum and discrete modelling) also require the strong participation of mechanical and chemical engineers, soil mechanists, geologists and astrophysicists. The book gathers into a single volume the relevant concepts from all these disciplines, enabling the reader to gain a rapid understanding of the foundations, as well as the open questions, of the physics of granular materials. The contributors have been chosen particularly for their ability to explain new concepts, making the book attractive to students or researchers contemplating a foray into the field. The breadth of the treatment, on the other hand, makes the book a useful reference for scientists who are already experienced in the subject.

This book has a long history of more than 20 years. The first attempt to write a monograph on information-theoretic approach to thermodynamics was done by one of the authors (RSI) in 1974 when he published, in the preprint form, two volumes of the book "Information Theory and Thermodynamics" concerning classical and quantum information theory, [153] (220 pp.), [154] (185 pp.). In spite of the encouraging remarks by some of the readers, the physical part of this book was never written except for the first chapter. Now this material is written completely anew and in much greater extent. A few years earlier, in 1970, second author of the present book, (AK), a doctoral student and collaborator of RSI in Toruli, published in Polish, also as a preprint, his habilitation dissertation "Information-theoretical decision scheme in quantum statistical mechanics" [196] (96 pp.). This small monograph presented his original results in the physical part of the theory developed in the Torun school. Unfortunately, this preprint was never published in English. The present book contains all these results in a much more modern and developed form.

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I* We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo* These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

1.1 Overview We are living in a decade recently declared as the "Decade of the Brain." Neuroscientists may soon manage to work out a functional map of the brain, thanks to technologies that open windows on the mind. With the average human brain consisting of 15 billion neurons, roughly equal to the number of stars in our milky way, each receiving signals through as many as 10,000 synapses, it is quite a view. "The brain is the last and greatest biological frontier," says James Weston codiscoverer of DNA, considered to be the most complex piece of biological machinery on earth. After many years of research by neuroanatomists and neurophys iologists, the overall organization of the brain is well understood, but many of its detailed neural mechanisms remain to be decoded. In order to understand the functioning of the brain, neurobiologists have taken a bottom-up approach of studying the stimulus-response characteristics of single neurons and networks of neurons, while psy chologists have taken a top-down approach of studying brain func tions from the cognitive and behavioral level. While these two ap proaches are gradually converging, it is generally accepted that it may take another fifty years before we achieve a solid microscopic, intermediate, and macroscopic understanding of brain."

Independent Component Analysis (ICA) is a signal-processing method to extract independent sources given only observed data that are mixtures of the unknown sources. Recently, blind source separation by ICA has received considerable attention because of its potential signal-processing applications such as speech enhancement systems, telecommunications, medical signal-processing and several data mining issues. This book presents theories and applications of ICA and includes invaluable examples of several real-world applications. Based on theories in probabilistic models, information theory and artificial neural networks, several unsupervised learning algorithms are presented that can perform ICA. The seemingly different theories such as infomax, maximum likelihood estimation, negentropy maximization, nonlinear PCA, Bussgang algorithm and cumulant-based methods are reviewed and put in an information theoretic framework to unify several lines of ICA research. An algorithm is presented that is able to blindly separate mixed signals with sub- and super-Gaussian source distributions. The learning algorithms can be extended to filter systems, which allows the separation of voices recorded in a real environment (cocktail party problem). The ICA algorithm has been successfully applied to many biomedical signal-processing problems such as the analysis of electroencephalographic data and functional magnetic resonance imaging data. ICA applied to images results in independent image components that can be used as features in pattern classification problems such as visual lip-reading and face recognition systems. The ICA algorithm can furthermore be embedded in an expectation maximization framework for unsupervised classification. Independent Component Analysis: Theory and Applications is the first book to successfully address this fairly new and generally applicable method of blind source separation. It is essential reading for researchers and practitioners with an interest in ICA.

Flux quantization experiments indicate that the carriers, Cooper pairs (pairons), in the supercurrent have charge magnitude 2e, and that they move independently. Josephson interference in a Superconducting Quantum Int- ference Device (SQUID) shows that the centers of masses (CM) of pairons move as bosons with a linear dispersion relation. Based on this evidence we develop a theory of superconductivity in conventional and mate- als from a unified point of view. Following Bardeen, Cooper and Schrieffer (BCS) we regard the phonon exchange attraction as the cause of superc- ductivity. For cuprate superconductors, however, we take account of both optical- and acoustic-phonon exchange. BCS started with a Hamiltonian containing "electron" and "hole" kinetic energies and a pairing interaction with the phonon variables eliminated. These "electrons" and "holes" were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define "electrons" and "holes" in terms of the cur- tures of the Fermi surface. "Electrons" (1) and "holes" (2) are different and so they are assigned with different effective masses: Blatt, Schafroth and Butler proposed to explain superconductivity in terms of a Bose-Einstein Condensation (BEC) of electron pairs, each having mass M and a size. The system of free massive bosons, having a quadratic dispersion relation: and moving in three dimensions (3D) undergoes a BEC transition at where is the pair density.

The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden). The main purpose of this book is to present the principles and methods of sprays (path spaces) and Finsler spaces together with examples of applications to physical and life sciences. It is our aim to write an introductory book on Finsler geometry and its applications at a fairly advanced level. It is intended especially for graduate students in pure mathemat ics, science and applied mathematics, but should be also of interest to those pure "Finslerists" who would like to see their subject applied. After more than 70 years of relatively slow development Finsler geometry is now a modern subject with a large body of theorems and techniques and has math ematical content comparable to any field of modern differential geometry. The time has come to say this in full voice, against those who have thought Finsler geometry, because of its computational complexity, is only of marginal interest and with prac tically no interesting applications. Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology, evolution and developmental biology. On the other hand, while the complexity of the subject has not disappeared, the modern bundle theoretic approach has increased greatly its understandability."

Recent Advances in Reinforcement Learning addresses current research in an exciting area that is gaining a great deal of popularity in the Artificial Intelligence and Neural Network communities. Reinforcement learning has become a primary paradigm of machine learning. It applies to problems in which an agent (such as a robot, a process controller, or an information-retrieval engine) has to learn how to behave given only information about the success of its current actions. This book is a collection of important papers that address topics including the theoretical foundations of dynamic programming approaches, the role of prior knowledge, and methods for improving performance of reinforcement-learning techniques. These papers build on previous work and will form an important resource for students and researchers in the area. Recent Advances in Reinforcement Learning is an edited volume of peer-reviewed original research comprising twelve invited contributions by leading researchers. This research work has also been published as a special issue of Machine Learning (Volume 22, Numbers 1, 2 and 3).