Multi-Valued and Universal Binary Neurons deals with two new types of neurons: multi-valued neurons and universal binary neurons. These neurons are based on complex number arithmetic and are hence much more powerful than the typical neurons used in artificial neural networks. Therefore, networks with such neurons exhibit a broad functionality. They can not only realise threshold input/output maps but can also implement any arbitrary Boolean function. Two learning methods are presented whereby these networks can be trained easily. The broad applicability of these networks is proven by several case studies in different fields of application: image processing, edge detection, image enhancement, super resolution, pattern recognition, face recognition, and prediction. The book is hence partitioned into three almost equally sized parts: a mathematical study of the unique features of these new neurons, learning of networks of such neurons, and application of such neural networks. Most of this work was developed by the first two authors over a period of more than 10 years and was only available in the Russian literature. With this book we present the first comprehensive treatment of this important class of neural networks in the open Western literature. Multi-Valued and Universal Binary Neurons is intended for anyone with a scholarly interest in neural network theory, applications and learning. It will also be of interest to researchers and practitioners in the fields of image processing, pattern recognition, control and robotics.

Evolutionary algorithms, such as evolution strategies, genetic algorithms, or evolutionary programming, have found broad acceptance in the last ten years. In contrast to its broad propagation, theoretical analysis in this subject has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is deriving a qualitative understanding of why and how these ES algorithms work.

This monograph presents an introduction into basic mechanical aspects of mechatronic systems for students, researchers and engineers from industrial practice. An overview over the theoretical background of rigid body mechanics is given as well as a systematic approach for deriving and solving model equations of general rigid body mechanisms in the form of differential-algebraic equations (DAE). The objective of this book is to prepare the reader for being capable of efficiently handling and applying general purpose rigid body programs to complex mechanisms. The reader will be able to set up symbolic mathematical models of planar and spatial mechanisms in DAE-form for computer simulations, often required in dynamic analysis and in control design.

This completely revised edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications.

Most of the specialists working in this interdisciplinary field of physics, biology, biophysics and medicine are associated with "The International Institute of Biophysics" (IIB), in Neuss, Germany, where basic research and possibilities for applications are coordinated. The growth in this field is indicated by the increase in financial support, interest from the scientific community and frequency of publications.

Audience: The scientists of IIB have presented the most essential background and applications of biophotonics in these lecture notes in biophysics, based on the summer school lectures by this group. This book is devoted to questions of elementary biophysics, as well as current developments and applications. It will be of interest to graduate and postgraduate students, life scientists, and the responsible officials of industries and governments looking for non-invasive methods of investigating biological tissues.

Intended for self-study, this second volume presents a systematic approach for deriving model equations of planar and spatial mechanisms. The necessary theoretical foundations have been laid in the first volume. The focus is on the application of the modeling methodology to various examples of rigid-body mechanisms, simple planar ones as well as more challenging spatial problems. A rich variety of joint models, active constraints, as well as active and passive force elements is treated. The book is intended for self-study by working engineers and students concerned with the control of mechanical systems, i.e. robotics, mechatronics, vehicles, and machine tools. Its examples can be used as models for university lectures.

The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such as closed curves and surfaces and other domain contours.

The first part of the book introduces the mathematical concept required for treating the manifolds considered. An introduction to the theory of motion of curves and surfaces is given. The second and third parts discuss the modeling of various physical solitons on compact systems.

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

The basic principles guiding sensing, perception and action in bio systems seem to rely on highly organised spatial-temporal dynamics. In fact, all biological senses, (visual, hearing, tactile, etc.) process signals coming from different parts distributed in space and also show a complex time evolution. As an example, mammalian retina performs a parallel representation of the visual world embodied into layers, each of which r- resents a particular detail of the scene. These results clearly state that visual perception starts at the level of the retina, and is not related uniquely to the higher brain centres. Although vision remains the most useful sense guiding usual actions, the other senses, ?rst of all hearing but also touch, become essential particularly in cluttered conditions, where visual percepts are somehow obscured by environment conditions. Ef?cient use of hearing can be learnt from acoustic perception in animals/insects, like crickets, that use this ancient sense more than all the others, to perform a vital function, like mating.

This is an up-to-date review of developments in the field of bifurcations and instabilities in geomechanics from some of the world 's leading experts. Leading international researchers and practitioners of the topics debate the developments and applications which have occurred over the last few decades. Beside fundamental research findings, applications in geotechnical, petroleum, mining, and bulk materials engineering are emphasised.

It is with pleasure that I write the foreword to this excellent book. A wide range of observations in geology and solid-earth geophysics can be - plained in terms of fractal distributions. In this volume a collection of - pers considers the fractal behavior of the Earth's continental crust. The book begins with an excellent introductory chapter by the editor Dr. V.P. Dimri. Surface gravity anomalies are known to exhibit power-law spectral behavior under a wide range of conditions and scales. This is self-affine fractal behavior. Explanations of this behavior remain controversial. In chapter 2 V.P. Dimri and R.P. Srivastava model this behavior using Voronoi tessellations. Another approach to understanding the structure of the continental crust is to use electromagnetic induction experiments. Again the results often exhibit power law spectral behavior. In chapter 3 K. Bahr uses a fractal based random resister network model to explain the observations. Other examples of power-law spectral observations come from a wide range of well logs using various logging tools. In chapter 4 M. Fedi, D. Fiore, and M. La Manna utilize multifractal models to explain the behavior of well logs from the main KTB borehole in Germany. In chapter 5 V.V. Surkov and H. Tanaka model the electrokinetic currents that may be as- ciated with seismic electric signals using a fractal porous media. In chapter 6 M. Pervukhina, Y. Kuwahara, and H. Ito use fractal n- works to correlate the elastic and electrical properties of porous media.

This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. Readers will learn the basic concepts and methods of complex system research. The book is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory, making the book useful for students of science majors and graduate courses.

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions.

It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution).

The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions.

Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.

This book provides a unified framework that describes how genetic learning can be used to design pattern recognition and learning systems. It examines how a search technique, the genetic algorithm, can be used for pattern classification mainly through approximating decision boundaries. Coverage also demonstrates the effectiveness of the genetic classifiers vis-a-vis several widely used classifiers, including neural networks. "

This book provides a summary of the research conducted at UCLA, Stanford University, and UCSD over the last ?ve years in the area of nonlinear dyn- ics and chaos as applied to digital communications. At ?rst blush, the term "chaotic communications" seems like an oxymoron; how could something as precise and deterministic as digital communications be chaotic? But as this book will demonstrate, the application of chaos and nonlinear dynamicstocommunicationsprovidesmanypromisingnewdirectionsinareas of coding, nonlinear optical communications, and ultra-wideband commu- cations. The eleven chapters of the book summarize many of the promising new approaches that have been developed, and point the way to new research directions in this ?eld. Digital communications techniques have been continuously developed and re?ned for the past ?fty years to the point where today they form the heart of a multi-hundred billion dollar per year industry employing hundreds of thousands of people on a worldwide basis. There is a continuing need for transmission and reception of digital signals at higher and higher data rates. There are a variety of physical limits that place an upper limit on these data rates, and so the question naturally arises: are there alternative communi- tion techniques that can overcome some of these limitations? Most digital communications today is carried out using electronic devices that are essentially "linear," and linear system theory has been used to c- tinually re?ne their performance. In many cases, inherently nonlinear devices are linearized in order to achieve a certain level of linear system performance.

This book is devoted to applications of complex nonlinear dynamic phenomena to real systems and device applications. In recent decades there has been significant progress in the theory of nonlinear phenomena, but there are comparatively few devices that actually take this rich behavior into account. The text applies and exploits this knowledge to propose devices which operate more efficiently and cheaply, while affording the promise of much better performance.

Until the 1980s, a tacit agreement among many physical oceanographers was that nothing deserving attention could be found in the upper few meters of the ocean. The lack of adequete knowledge about the near-surface layer of the ocean was mainly due to the fact that the widely used oceanographic instruments (such as bathythermographs, CTDs, current meters, etc.) were practically useless in the upper few meters of the ocean. Interest in the ne- surface layer of the ocean rapidly increased along with the development of remote sensing techniques. The interpretation of ocean surface signals sensed from satellites demanded thorough knowledge of upper ocean processes and their connection to the ocean interior. Despite its accessibility to the investigator, the near-surface layer of the ocean is not a simple subject of experimental study. Random, sometimes huge, vertical motions of the ocean surface due to surface waves are a serious complication for collecting quality data close to the ocean surface. The supposedly minor problem of avoiding disturbances from ships' wakes has frustrated several generations of oceanographers attempting to take reliable data from the upper few meters of the ocean. Important practical applications nevertheless demanded action, and as a result several pioneering works in the 1970s and 1980s laid the foundation for the new subject of oceanography - the near-surface layer of the ocean.

This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.

This book examines life not from the reductionist point of view, but rather asks the questions: what are the universal properties of living systems, and how can one construct from there a phenomenological theory of life that leads naturally to complex processes such as reproductive cellular systems, evolution and differentiation? The presentation is relatively non-technical to appeal to a broad spectrum of students and researchers.

Clouds affect the climate of the Earth, and they are an important factor in the weather. Therefore, their radiative properties must be understood in great detail. This book summarizes current knowledge on cloud optical properties, for example their ability to absorb, transmit, and reflect light, which depends on the clouds geometrical and microphysical characteristics such as sizes of droplets and crystals, their shapes, and structures. In addition, problems related to the image transfer through clouds and cloud remote sensing are addressed in this book in great detail.

This book can serve as a major introductory text in cloud optics for students; it can also be an important source of information on theoretical cloud optics for cloud physicists, meteorologists and optical engineers.

All basic ideas of optics as related to scattering of light in clouds (e.g. Mie theory and radiative transfer) are considered in a self consistent way. Consequently, the book can also be a useful textbook to newcomers to the field."

This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.

Complexity science has been a source of new insight in physical and social systems and has demonstrated that unpredictability and surprise are fundamental aspects of the world around us. This book is the outcome of a discussion meeting of leading scholars and critical thinkers with expertise in complex systems sciences and leaders from a variety of organizations, sponsored by the Prigogine Center at The University of Texas at Austin and the Plexus Institute, to explore strategies for understanding uncertainty and surprise. Besides contributions to the conference, it includes a key digest by the editors as well as a commentary by the late nobel laureate Ilya Prigogine, "Surprises in half of a century." The book is intended for researchers and scientists in complexity science, as well as for a broad interdisciplinary audience of both practitioners and scholars. It will well serve those interested in the research issues and in the application of complexity science to physical and social systems.

social network analysis has been an established eld since the 1950s; in computer and information sciences, in biology, and of course in mathematics (graph theory) networks are central representations of objects and methods (De Nooy, forthc- ing). More detailed bibliometric studies have examined the individual, cognitive, and institutional composition of complex network theory (Morris and Yen 2004), and social network theory (Otte and Rousseau 2002). Among the more impor- .. tant pieces of literature are Borner et al. (2007), Bornholdt and Schuster (2003), Buchanan (2002), Dorogovtsev and Mendes (2003), Otte and Rousseau (2002), Newman (2003), and Watts (1999, 2004). Of these, Borner .. et al. (2007) stand out because they have most recently re-examined network science, considering it as a possible innovation in information science. All the reviews mentioned include efforts to build bridges between different scienti c disciplines and specialties. In this book we draw particular attention to the link between evolutionary economics and statistical physics. Despite this impressive development, claims that an entirely new science has been created (Barabasi ' 2002) have nevertheless been the subject of criticism. - depth analyses of a subset of "complex networks" contributions (1991-2003) have shown that the notion of "complex networks" was already prevalent in a number of different elds before it became practically a "brand name" or the popular label for a new specialty area in physics, or a new cross-disciplinary paradigm.

This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan. The Symposium was proposed in 1996, aiming at organizing concen trated discussions on current understanding of fluid turbulence with empha sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation. There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others."