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This volume includes papers presented at the Third Annual Computation and Neural Systems meeting (CNS•94) held in Monterey California, July 21 - July 26, 1994. This collection includes 71 of the more than 100 papers presented at this year's meeting. Acceptance for meeting presentation was based on the peer review of preliminary papers by at least two referees. The papers in this volume were submitted in final form after the meeting. As represented by this volume, CNS meetings continue to expand in quality, size and breadth of focus as increasing numbers of neuroscientists are taking a computational approach to understanding nervous system function. The CNS meetings are intended to showcase the best of current research in computational neuroscience. As such the meeting is fundamentally focused on understanding the relationship between the structure of neIVOUS systems and their function. What is clear from the continued expansion of the CNS meetings is that computational approaches are increasingly being applied at all levels of neurobiological analysis. in an ever growing number of experimental preparations. and neural subsystems. Thus. experimental subjects range from crickets to primates; sensory systems range from vision to electroreception; experimental approaches range from realistic models of ion channels to the analysis of the information content of spike trains. For this reason, the eNS meetings represent an opportunity for computational neurobiologists to consider their research results in a much broader context than is usually possible.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perbaps you will find the final question. G. K. Chesterton. The Scandal of Father'The Hermit Clad in Crane Feathers'in R. Brown'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the'tree'of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as'experimental mathematics','CFD','completely integrable systems','chaos, synergetics and large-scale order', which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

One of the driving forces behind much of modern science and technology is the desire to foresee and thereby control the future. In recent years, however, it has become clear that, even in a deterministic world, there is alimit to the accuracy with which we can predict the future. This book details, in a largely nontechnical style, the extent to which we can predict the future development of various physical, biological and socio-economic processes.

Dynamic Neural Field Theory for Motion Perception provides a new theoretical framework that permits a systematic analysis of the dynamic properties of motion perception. This framework uses dynamic neural fields as a key mathematical concept. The author demonstrates how neural fields can be applied for the analysis of perceptual phenomena and its underlying neural processes. Also, similar principles form a basis for the design of computer vision systems as well as the design of artificially behaving systems. The book discusses in detail the application of this theoretical approach to motion perception and will be of great interest to researchers in vision science, psychophysics, and biological visual systems.

Close this book for a moment and look around you. You scan the scene by directing your attention, and gaze, at certain specific objects. Despite the background, you discern them. The process is partially intentional and partially preattentive. How all this can be done is described in the fourth volume of Models of Neural Networks devoted to Early Vision and Atten­ tion that you are holding in your hands. Early vision comprises the first stages of visual information processing. It is as such a scientific challenge whose clarification calls for a penetrating review. Here you see the result. The Heraeus Foundation (Hanau) is to be thanked for its support during the initial phase of this project. John Hertz, who has extensive experience in both computational and ex­ perimental neuroscience, provides in'Neurons, Networks, and Cognition'to neural modeling. John Van Opstal explains in a theoretical introduction'The Gaze Control System'how the eye's gaze control is performed and presents a novel theoretical description incorporating recent experimental results. We then turn to the relay stations thereafter, the lateral genicu­ late nucleus (LGN) and the primary visual cortex. Their anatomy, phys­ iology, functional relations, and ensuing response properties are carefully analyzed by Klaus Funke et al. in'Integrating Anatomy and Physiology of the Primary Visual Pathway: From LGN to Cortex', one of the most comprehensive reviews that is available at the moment.

This monograph presents key method to successfully manage the growing complexity of systems where conventional engineering and scientific methodologies and technologies based on learning and adaptability come to their limits and new ways are nowadays required. The transition from adaptable to evolvable and finally to self-evolvable systems is highlighted, self-properties such as self-organization, self-configuration, and self-repairing are introduced and challenges and limitations of the self-evolvable engineering systems are evaluated.

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.

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different?elds of physics, ranging from quantum?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the?eld-theoretical formulation of the RG idea looks at the?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.

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.

The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints – informational, mechanical, neural, metabolic, and so on – operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music.

This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY'as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the?eld by some of the most important researchers in the area. The?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi's 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso's honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the?eld. So we decided to transcribe it and include it here as the?rst section of the book.

How is free will possible in the light of the physical and chemical underpinnings of brain activity and recent neurobiological experiments? How can the emergence of complexity in hierarchical systems such as the brain, based at the lower levels in physical interactions, lead to something like genuine free will? The nature of our understanding of free will in the light of present-day neuroscience is becoming increasingly important because of remarkable discoveries on the topic being made by neuroscientists at the present time, on the one hand, and its crucial importance for the way we view ourselves as human beings, on the other. A key tool in understanding how free will may arise in this context is the idea of downward causation in complex systems, happening coterminously with bottom up causation, to form an integral whole. Top-down causation is usually neglected, and is therefore emphasized in the other part of the book's title. The concept is explored in depth, as are the ethical and legal implications of our understanding of free will. This book arises out of a workshop held in California in April of 2007, which was chaired by Dr. Christof Koch. It was unusual in terms of the breadth of people involved: they included physicists, neuroscientists, psychiatrists, philosophers, and theologians. This enabled the meeting, and hence the resulting book, to attain a rather broader perspective on the issue than is often attained at academic symposia. The book includes contributions by Sarah-Jayne Blakemore, George F. R. Ellis, Christopher D. Frith, Mark Hallett, David Hodgson, Owen D. Jones, Alicia Juarrero, J. A. Scott Kelso, Christof Koch, Hans Küng, Hakwan C. Lau, Dean Mobbs, Nancey Murphy, William Newsome, Timothy O'Connor, Sean A.. Spence, and Evan Thompson.

Synchronization: From Simple to Complex is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from human heart to neural networks. The authors study this phenomenon as applied to oscillations of different nature such as those with periodic, chaotic, noisy and noise-induced nature, reveal the general mechanisms behind synchronization, and bring to light other important effects that accompany synchronization such as phase multistability, dephasing and multimode interaction. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating system can be described in the framework of the general approach.

The?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics,?uidization processes, applied optics, stochastic resonance,?ocking and?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.

Interest in the control and optimization of multiscale process systems has been triggered by the need to achieve tight feedback control and optimal operation of complex processes, such as deposition and sputtering of thin films in semiconductor manufacturing, which are characterized by highly coupled macroscopic and microscopic phenomena. Drawing from recent advances in the dynamics and control of distributed parameter processes for which continuum laws are applicable as well as stochastic modeling of phenomena at mesoscopic/microscopic length scales, control and optimization of multiscale process systems has evolved into a very active research area of systems and control engineering. This book—the first of its kind—presents general methods for feedback controller synthesis and optimization of multiscale systems, illustrating their application to thin-film growth, sputtering processes, and catalytic systems of industrial interest. Beginning with an introduction to general issues on control and optimization of multiscale systems and a review of previous work in this area, the book discusses detailed modeling approaches for multiscale processes with emphasis on the theory and implementation of kinetic Monte Carlo simulation, methods for feedback control using kinetic Monte Carlo models, stochastic model construction and parameter estimation, predictive and covariance control using stochastic partial differential equation models, and both steady-state and dynamic optimization algorithms that efficiently address coupled macroscopic and microscopic objectives. Key features of the work: • Demonstrates the advantages of the methods presented for control and optimization through extensive simulations. • Includes new techniques for feedback controller design and optimization of multiscale process systems that are not included in other books. • Illustrates the application of controller design and optimization methods to complexmultiscale processes of industrial interest. • Contains a rich collection of new research topics and references to significant recent work. The book requires basic knowledge of differential equations, probability theory, and control theory, and is intended for researchers, graduate students, and process control engineers. Throughout the book, practical implementation issues are addressed to help researchers and engineers understand the development and application of the methods presented in greater depth.

recently discovered advantages of amorphous forms of medicines/pharmaceutical products which focused a significant part of industry-related efforts on the GFA (Glass Forming Ability) and the glass temperature (T) versus pressure g dependences. 1 b? 0?? o? P? Pg P? Pg 0???? T (P) = F (P)D (P) =T 1 + exp? g g? 0???? c + Pg???? 400 1 b 0 o???? P? P P? P g g 0???? T (P) = F (P)D (P) =T 1 + exp? g g 0???? c? + P max g???? T ~7 GPa g max P ~ 304 K Liquid g 300 1 HS glass 0 200 -1 mSG?=0. 044 Liquid -2 100 -3 glass?=0. 12 -1. 2 -0. 9 -0. 6 -0. 3 0. 0 log T 10 scaled -1 0 1 2 3 4 5 6 7 8 9 10 11 12 P (GPa) g 19 Figure 1. T he pressure evolution of the glass temperature in gl Th ye s cerol ol. id curve shows the parameterization of experimental data via the novel, modifie d Glat Sizm elon type equation, given in the Figure.

Hydroinformatics is an emerging subject that is expected to gather speed, momentum and critical mass throughout the forthcoming decades of the 21st century. This book provides a broad account of numerous advances in that field - a rapidly developing discipline covering the application of information and communication technologies, modelling and computational intelligence in aquatic environments. A systematic survey, classified according to the methods used (neural networks, fuzzy logic and evolutionary optimization, in particular) is offered, together with illustrated practical applications for solving various water-related issues....

Unmanned Aerial Vehicles (UAVs) have seen unprecedented levels of growth in military and civilian application domains. Fixed-wing aircraft, heavier or lighter than air, rotary-wing (rotorcraft, helicopters), vertical take-off and landing (VTOL) unmanned vehicles are being increasingly used in military and civilian domains for surveillance, reconnaissance, mapping, cartography, border patrol, inspection, homeland security, search and rescue, fire detection, agricultural imaging, traffic monitoring, to name just a few application domains. When initially introduced during World War I, UAVs were criticized heavily as being unreliable and inaccurate, and only a handful of people recognized at that early stage their potential and (future) impact on cha- ing the battlefield. To nobody's surprise, about a century later, the total market for UAVs will reach within a few years more than $16 billion, with the US Depa- ment of Defense (DOD) being the champion in funding initiatives, - search and development, as well as procurement. Europe, as a continent, is a very distant second player, expected to spend about €2 billion in research and development, and procurement.

Computational Neurosciences is a burgeoning field of research where only the combined effort of neuroscientists, biologists, psychologists, physicists, mathematicians, computer scientists, engineers and other specialists, e.g. from linguistics and medicine, seem to be able to expand the limits of our knowledge. The present volume is an introduction, largely from the physicists'perspective, to the subject matter with in-depth contributions by system neuroscientists. A conceptual model for complex networks of neurons is introduced that incorporates many important features of the real brain, such as various types of neurons, various brain areas, inhibitory and excitatory coupling and the plasticity of the network. The computational implementation on supercomputers, which is introduced and discussed in detail in this book, will enable the readers to modify and adapt the algortihm for their own research. Worked-out examples of applications are presented for networks of Morris-Lecar neurons to model the cortical connections of a cat's brain, supported with data from experimental studies. This book is particularly suited for graduate students and nonspecialists from related fields with a general science background, looking for a substantial but “hands-on” introduction to the subject matter.

This book is a tribute to Prof. Alberto Isidori on the occasion of his 65th birthday. Prof. Isidori's proli?c, pioneering and high-impact research activity has spanned over 35 years. Throughout his career, Prof. Isidori has developed ground-breaking results, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his dedication to explain intricate issues and di?cult concepts in a simple and rigorous way and to motivate young researchers has been instrumental to the intellectual growth of the nonlinear control community worldwide. The volume collects 27 contributions written by a total of 52 researchers. The principal author of each contribution has been selected among the - searchers who have worked with Prof. Isidori, have in?uenced his research activity, or have had the privilege and honour of being his PhD students. The contributions address a signi?cant number of control topics, including th- retical issues, advanced applications, emerging control directions and tutorial works. The diversity of the areas covered, the number of contributors and their international standing provide evidence of the impact of Prof. Isidori in the control and systems theory communities. The book has been divided into six parts: System Analysis, Optimization Methods, Feedback Design, Regulation, Geometric Methods and Asymptotic Analysis, re?ecting important control areas which have been strongly in- enced and, in some cases, pioneered by Prof. Isidori.

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word'instability'in day-to-day language is associated with some­ thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about'good'instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi­ bility in thermodynamics, the phenomena of chaos and turbulence in clas­ sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de­ scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or'errors'in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al­ ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.

One of the most striking features of Coordination Dynamics is its interdisciplinary character. The problems we are trying to solve in this field range from behavioral phenomena of interlimb coordination and coordination between stimuli and movements (perception-action tasks) through neural activation patterns that can be observed during these tasks to clinical applications and social behavior. It is not surprising that close collaboration among scientists from different fields as psychology, kinesiology, neurology and even physics are imperative to deal with the enormous difficulties we are facing when we try to understand a system as complex as the human brain. The chapters in this volume are not simply write-ups of the lectures given by the experts at the meeting but are written in a way that they give sufficient introductory information to be comprehensible and useful for all interested scientists and students.

Nonlinear Dynamics in Geosciences is comprised of the proceedings of'20 Years of Nonlinear Dynamics in Geosciences', held June 11-16, 2006 in Rhodes, Greece as part of the Aegean Conferences. The volume brings together the most up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences, and discusses the advances made and the future directions of nonlinear dynamics. Topics covered include predictability, ensemble prediction, nonlinear prediction, nonlinear time series analysis, low-dimensional chaos, nonlinear modeling, fractals and multifractals, bifurcation, and other aspects of nonlinear science.

Our contemporary understanding of brain function is deeply rooted in the ideas of the nonlinear dynamics of distributed networks. Cognition and motor coordination seem to arise from the interactions of local neuronal networks, which themselves are connected in large scales across the entire brain. The spatial architectures between various scales inevitably influence the dynamics of the brain and thereby its function. But how can we integrate brain connectivity amongst these structural and functional domains? Our Handbook provides an account of the current knowledge on the measurement, analysis and theory of the anatomical and functional connectivity of the brain. All contributors are leading experts in various fields concerning structural and functional brain connectivity. In the first part of the Handbook, the chapters focus on an introduction and discussion of the principles underlying connected neural systems. The second part introduces the currently available non-invasive technologies for measuring structural and functional connectivity in the brain. Part three provides an overview of the analysis techniques currently available and highlights new developments. Part four introduces the application and translation of the concepts of brain connectivity to behavior, cognition and the clinical domain.

If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard', we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book. In our previous book, Geometrical - namics of Complex Systems, Vol. 31 in Springer book series Microprocessor– Based and Intelligent Systems Engineering, we developed the most powerful mathematical machinery to deal with high–dimensional nonlinear dynamics. In the present text, we consider the extreme cases of nonlinear dynamics, the high–dimensional chaotic and other attractor systems. Although they might look as examples of complete disorder – they still represent control systems, with their inputs, outputs, states, feedbacks, and stability. Today, we can see a number of nice books devoted to nonlinear dyn- ics and chaos theory (see our reference list). However, all these books are only undergraduate, introductory texts, that are concerned exclusively with oversimpli?ed low–dimensional chaos, thus providing only an inspiration for the readers to actually throw themselves into the real–life chaotic dynamics.

The formation of collective behavior in large ensembles or networks of coupled oscillatory elements is one of the oldest and most fundamental aspects of dynamical systems theory. Potential and present applications span a vast spectrum of fields ranging from physics, chemistry, geoscience, through life- and neurosciences to engineering, the economic and the social sciences. 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 the heart muscle - to name but a few. This 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.

Synchronization processes are of great interest and importance in biology, medicine and physics. In particular, for the comprehension of brain function­ ing it appears inevitable that one should analyze neuronal synchronization processes. This book presents a new understanding of how a stimulus in­ fluences synchronization patterns of a population of oscillators. On the one hand, a variety of stimulation-induced dynamical phenomena will be pre­ sented; on the other hand, new data analysis tools will be developed which will serve as a link between theory and experiment. In this way it will be possible to use the theory presented here as a basis for the design and evalu­ and ation of stimulation experiments and stimulation techniques in medicine biology. We shall focus particularly on applications concerning the analysis of magnetoencephalography (MEG) and electroencephalography (EEG) data as well as deep brain stimulation techniques used in Parkinsonian patients. This book addresses graduate students, professors and scientists in vari­ ous fields including biology, mathematics, medicine, neuroscience, physiology and physics. Besides mathematically involved parts, the book also provides the reader with numerous illustrations and explications of the deep dynamical principles governing stimulation-induced desynchronization and synchroniza­ tion processes. Therefore this book will be of interest to a general readership, and those who are not familiar with mathematics should not be deterred by the formulas.

Computational Mind: A Complex Dynamics Perspective is a graduate–level monographic textbook in the field of Computational Intelligence. It presents a modern dynamical theory of the computational mind, combining cognitive psychology, artificial and computational intelligence, and chaos theory with quantum consciousness and computation. The book introduces to human and computational mind, comparing and contrasting main themes of cognitive psychology, artificial and computational intelligence. It presents brain/mind dynamics from the chaos theory perspective, including sections on chaos in human EEG, basics of nonlinear dynamics and chaos, techniques of chaos control, synchronization in chaotic systems and complexity in humanoid robots. This book presents modern theory of quantum computational mind, including sections on Dirac–Feynman quantum dynamics, quantum consciousness, and quantum computation using Josephson junctions. The book is designed as a one–semester course for computer scientists, engineers, physicists and applied mathematicians, both in industry and academia. It includes a strong bibliography on the subject and detailed index.

Higher cognition and consciousness became the objective of intensive scienti?c studiesandoftenspiriteddebatesinthe pastdecades.Thebrainhasimmenselyc- plex structure and functionality,while our understandingof its operationis yet in its infancy. Some investigators declare that higher-level cognition and consciousness are ultimately beyond the realms of human scienti?c understanding and reasoning, and research into these areas is a futile exercise. Yet, the knowledge instinct deeply rootedinhumanactivitydrivesresearcherstowardexploringthemysteriesofhuman thought. These efforts lead to the development of increasingly sophisticated sci- ti?c methods of understanding the operation of brains and the very nature of c- sciousness. The studies rely on the immense amountof experimentaldata becoming available as the result of advanced brain monitoring techniques. The experimental techniquesrequire,in turn,the developmentofnovelmethodsoftheoreticalanalysis and interpretation tools. Our work is part of these endeavors. This volume presents an in-depth overview of theoretical and experimental - proaches to cognitive dynamics and applications in designing intelligent devices. The research efforts leading to this book have started about 2 years ago when we embarked on organizing a series of special and invited sessions which took place in July 2006 at the World Congress of Computational Intelligence WCCI2006, in beautiful Vancouver, Canada. The talks covered various aspects of neurodynamics of higher-level cognitive behavior, consciousness, and modeling emotions. The main theme of this volume is the dynamics of higher cognitive functions.

An updated guide to GNSS and INS, and solutions to real-world GPS/INS problems with Kalman filtering Written by recognized authorities in the field, this second edition of a landmark work provides engineers, computer scientists, and others with a working familiarity with the theory and contemporary applications of Global Navigation Satellite Systems (GNSS), Inertial Navigational Systems (INS), and Kalman filters. Throughout, the focus is on solving real-world problems, with an emphasis on the effective use of state-of-the-art integration techniques for those systems, especially the application of Kalman filtering. To that end, the authors explore the various subtleties, common failures, and inherent limitations of the theory as it applies to real-world situations, and provide numerous detailed application examples and practice problems, including GNSS-aided INS, modeling of gyros and accelerometers, and SBAS and GBAS. Drawing upon their many years of experience with GNSS, INS, and the Kalman filter, the authors present numerous design and implementation techniques not found in other professional references. This Second Edition has been updated to include: GNSS signal integrity with SBAS Mitigation of multipath, including results Ionospheric delay estimation with Kalman filters New MATLAB programs for satellite position determination using almanac and ephemeris data and ionospheric delay calculations from single and dual frequency data New algorithms for GEO with L1 /L5 frequencies and clock steering Implementation of mechanization equations in numerically stable algorithms To enhance comprehension of the subjects covered, the authors have included software in MATLAB, demonstrating the working of the GNSS, INS, and filter algorithms. In addition to showing the Kalman filter in action, the software also demonstrates various practical aspects of finite word length arithmetic and the need for alternative algorithms to preserve result accuracy.

We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kineticequations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

As soon as we (AS and PS) completed writing the book on H Optimal Con- 2 trol, another task of equal magnitude was laid to our charge. This task was to work on?ltering and related topics. This book releases us from this charge. In this endeavor, we are fortunate to have found a capable person in our friend and colleague (AAS) who helped us release our burden. The subject of?ltering is indeed vast and immense, much more so than the subject of H Optimal Control. In this work, we have tried to present what we 2 believe to be the fundamental issues of?ltering. The book is not intended to give a chronological development of?ltering from a historical point of view. A vast number of books already do so. Our intent here is to develop from our perspective the complete theory of?ltering and various design methodologies associated with it along with their practical implementations. In this respect, we present here a state-of-the-art view of exact and almost input-decoupled?ltering, H,and H 2 1?ltering and inverse?ltering issues, and include an application of?ltering and inverse?ltering to fault detection, isolation, and estimation. Most of the work reported here arose out of the research conducted by one or more of us and so- times in collaboration with our students and colleagues. Supposedly, young F.

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems. It is encountered in a great variety of settings, both in nature and technology, and has numerous applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. Nature creates its variety of forms through spontaneous pattern formation and self-assembly, and this strategy is likely to be imitated by future biomorphic technologies. This book is a first-hand account by one of the leading players in this field, which gives in-depth descriptions of analytical methods elucidating the complex evolution of nonlinear dissipative systems, and brings the reader to the forefront of current research. The introductory chapter on the theory of dynamical systems is written with a view to applications of its powerful methods to spatial and spatio-temporal patterns. It is followed by two chapters treating moving interfaces, based largely on reaction-diffusion and phase-separating systems. The following two chapters on amplitude equations for patterns and waves describe universal phenomena generated by representative equations which can be derived for a variety of non-equilibrium systems originating in fluid mechanics, physical chemistry or nonlinear optics. This book addresses graduate students and non-specialists from the many related areas of applied mathematics, physical chemistry, chemical engineering and biology, as well as the seasoned scientist in search of a modern source of reference.

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains. In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed.

'Nonlinear Oscillations in Mechanical Engineering'explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused by dry friction and collisions. Another important source of nonlinearity which is covered is that caused by rotating unbalanced parts common in various machines as well as variable inertias occurring in all kinds of crank mechanisms. This book is written for advanced undergraduate and postgraduate students, but it may be also helpful and interesting for both theoreticians and practitioners working in the area of mechanical engineering at universities, in research labs or institutes and especially in the R and D departments within industrial firms.

Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

Recent developments in constrained control and estimation have created a need for this comprehensive introduction to the underlying fundamental principles. These advances have significantly broadened the realm of application of constrained control. - Using the principal tools of prediction and optimisation, examples of how to deal with constraints are given, placing emphasis on model predictive control. - New results combine a number of methods in a unique way, enabling you to build on your background in estimation theory, linear control, stability theory and state-space methods. - Companion web site, continually updated by the authors. Easy to read and at the same time containing a high level of technical detail, this self-contained, new approach to methods for constrained control in design will give you a full understanding of the subject.

Mesoscopic physics deals with effects at submicron and nanoscales where the conventional wisdom of macroscopic averaging is no longer applicable. A wide variety of new devices have recently evolved, all extremely promising for major novel directions in technology, including carbon nanotubes, ballistic quantum dots, hybrid mesoscopic junctions made of different type of normal, superconducting and ferromagnetic materials. This, in turn, demands a profound understanding of fundamental physical phenomena on mesoscopic scales. As a result, the forefront of fundamental research in condensed matter has been moved to the areas where the interplay between electron-electron interactions and quantum interference of phase-coherent electrons scattered by impurities and/or boundaries is the key to such understanding. An understanding of decoherence as well as other effects of the interactions is crucial for developing future electronic, photonic and spintronic devices, including the element base for quantum computation.

In 1995, the Deutsche Forschungsgemeinschaft (DFG), the largest public research funding organization in Germany, decided to launch a priority program (Schw- punktprogramm in German) calledKondisk– Dynamics and Control of Systems with Mixed Continuous and Discrete Dynamics. Such a priority program is usually sponsored for six years and supports about twenty scientists at a time, in engineering andcomputersciencemostlyyoungresearchersworkingforadoctoraldegree. There is a yearly competition across all disciplines of arts and sciences for the funding of such programs, and the group of proposers was the happy winner of a slot in that year. The program started in 1996 after an open call for proposals; the successful projects were presented and re-evaluated periodically, and new projects could be submitted simultaneously. During the course of the focused research program, 25 different projects were funded in 19 participating university institutes, some of the projects were collaborative efforts of two groups with different backgrounds, mostly one from engineering and one from computer science. There were two main motivations for establishingKondisk. The rst was the fact that technical systems nowadays are composed of physical components with (mostly) continuous dynamics and computerized control systems where the reaction to discrete events plays a major role, implemented in Programmable Logic Contr- lers (PLCs), Distributed Control Systems (DCSs) or real-time computer systems.

Synchronization is a universal phenomenon that is encountered in nature, science and engineering. The book presents a broad view of modern theoretical and experimental approaches to synchronization, especially in complex and chaotic systems, and its applications in life sciences and engineering. Contributors include applied mathematicians, physicists, biologists, and specialists in communications and control theory. The study of synchronization is presented in its many aspects: basic mathematical theory, numerical simulation of complex systems, applications of methods in theoretical physics, experimental implementation, and applications in engineering and life sciences.

In March 1997, we launched the Japan Association for Evolutionary Economics {JAFEE) to gather the academic minds that, out of dissatisfaction with established dynamic approaches, were separately searching for new approaches to economics. To our surprise and joy,as many as 500members, including graduate students,joined us. Later that year Prof. Horst Hanusch, then President of the International [oseph A. Schumpeter Society, remarked that such a start would take a couple of decades in Europe to prepare for. Since then we have been developing our activities incessantly not only in terms of the number of members, but also in terms of the intensity of international academic exchange. Originally the planning of this book came about as the successful outcome of our fourth annual conference organized as an international one, JAFEE 2000.Incorporat­ ing other international contributions related to our preceding conferences, this book has eventually turned out to be one of the most enterprising anthologies on evolu­ tionary economics ever published. Specifically, it contains excellent papers on such topics as streams of evolutionary economics, evolutionary nonlinear dynamics, experimental economics and evolution, multiagent systems and complexity, new frontiers for evolutionary economics, and economic heresies. In short, this book will provide a vivid and full-fledged picture of up-to-date evolutionary economics.

First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is outlined. The remainder of the book presents the main effects of synchronization in a rigorous and systematic manner, describing classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering and natural sciences.

This collection of articles introduces the idea of a hierarchical order in chaotic systems and natural phenomena. To understand nature, nonlinear sciences use a multidisciplinary perspective. Therefore the book integrates research work of different fields: experimental evidence for the theory drawn from physics, biology and chemistry; theoretical progress in mathematical treatment, numerical techniques and graphical methods of nonlinear sciences; and to not-yet-understood philosophical and fundamental problems related to chaos and cosmos, chaos and quantum mechanics or evolutionary dynamics. Featuring the most recent advances in nonlinear dynamics this collection should provide an indispensable reference source and starting point for further research concerning dynamical and hierarchical chaotic systems. Besides this book is in honor of Professor O E Rössler, one of the pioneers of Chaos Theory, who celebrated his 50th birthday in May 1990.

ICANN, the International Conference on Artificial Neural Networks, is the official conference series of the European Neural Network Society which started in Helsinki in 1991. Since then ICANN has taken place in Brighton, Amsterdam, Sorrento, Paris, Bochum and Lausanne, and has become Europe's major meeting in the field of neural networks. This book contains the proceedings of ICANN 98, held 2-4 September 1998 in Skovde, Sweden. Of 340 submissions to ICANN 98, 180 were accepted for publication and presentation at the conference. In addition, this book contains seven invited papers presented at the conference. A conference of this size is obviously not organized by three individuals alone. We therefore would like to thank the following people and organizations for supporting ICANN 98 in one way or another: • the European Neural Network Society and the Swedish Neural Network Society for their active support in the organization of this conference, • the Programme Committee and all reviewers for the hard and timely work that was required to produce more than 900 reviews during April 1998, • the Steering Committee which met in Skovde in May 1998 for the final selection of papers and the preparation of the conference program, • the other Module Chairs: Bengt Asker (Industry and Research), Harald Brandt (Applications), Anders Lansner (Computational Neuroscience and Brain Theory), Thorsteinn Rognvaldsson (Theory), Noel Sharkey (co­ chair Autonomous Robotics and Adaptive Behavior), Bertil Svensson (Hardware and Implementations), • the conference secretary, Leila Khammari, and the rest of the