Cellular Neural Networks (CNNs) constitute a class of nonlinear, recurrent and locally coupled arrays of identical dynamical cells that operate in parallel. ANALOG chips are being developed for use in applications where sophisticated signal processing at low power consumption is required. Signal processing via CNNs only becomes efficient if the network is implemented in analog hardware. In view of the physical limitations that analog implementations entail, robust operation of a CNN chip with respect to parameter variations has to be insured. By far not all mathematically possible CNN tasks can be carried out reliably on an analog chip; some of them are inherently too sensitive. This book defines a robustness measure to quantify the degree of robustness and proposes an exact and direct analytical design method for the synthesis of optimally robust network parameters. The method is based on a design centering technique which is generally applicable where linear constraints have to be satisfied in an optimum way. Processing speed is always crucial when discussing signal-processing devices. In the case of the CNN, it is shown that the setting time can be specified in closed analytical expressions, which permits, on the one hand, parameter optimization with respect to speed and, on the other hand, efficient numerical integration of CNNs. Interdependence between robustness and speed issues are also addressed. Another goal pursued is the unification of the theory of continuous-time and discrete-time systems. By means of a delta-operator approach, it is proven that the same network parameters can be used for both of these classes, even if their nonlinear output functions differ. More complex CNN optimization problems that cannot be solved analytically necessitate resorting to numerical methods. Among these, stochastic optimization techniques such as genetic algorithms prove their usefulness, for example in image classification problems. Since the inception of the CNN, the problem of finding the network parameters for a desired task has been regarded as a learning or training problem, and computationally expensive methods derived from standard neural networks have been applied. Furthermore, numerous useful parameter sets have been derived by intuition. In this book, a direct and exact analytical design method for the network parameters is presented. The approach yields solutions which are optimum with respect to robustness, an aspect which is crucial for successful implementation of the analog CNN hardware that has often been neglected. `This beautifully rounded work provides many interesting and useful results, for both CNN theorists and circuit designers.' Leon O. Chua

This book examines the testing and modeling of materials and structures under dynamic loading conditions. Readers get an in-depth analysis of the current mathematical modeling and simulation tools available for a variety of materials, alongside discussions of the benefits and limitations of these tools in industrial design. Following a logical and well organized structure, this volume uniquely combines experimental procedures with numerical simulation, and provides many examples.

Systemics of Emergence: Research and Development is a volume devoted to exploring the core theoretical and disciplinary research problems of emergence processes from which systems are established. It focuses on emergence as the key point of any systemic process. This topic is dealt with within different disciplinary approaches, indicated by the organization in sections: 1) Applications; 2) Biology and human care; 3) Cognitive Science; 4) Emergence; 5) General Systems; 6) Learning; 7) Management; 8) Social Systems; 9) Systemic Approach and Information Science; 10) Theoretical issues in Systemics.

The Editors and contributing authors have produced this volume to help, encourage and widen the work in this area of General Systems Research.

The vulnerability of our civilization to earthquakes is rapidly growing, rais ing earthquakes to the ranks of major threats faced by humankind. Earth quake prediction is necessary to reduce that threat by undertaking disaster preparedness measures. This is one of the critically urgent problems whose solution requires fundamental research. At the same time, prediction is a ma jor tool of basic science, a source of heuristic constraints and the final test of theories. This volume summarizes the state-of-the-art in earthquake prediction. Its following aspects are considered: - Existing prediction algorithms and the quality of predictions they pro vide. - Application of such predictions for damage reduction, given their current accuracy, so far limited. - Fundamental understanding of the lithosphere gained in earthquake prediction research. - Emerging possibilities for major improvements of earthquake prediction methods. - Potential implications for predicting other disasters, besides earthquakes. Methodologies. At the heart of the research described here is the inte gration of three methodologies: phenomenological analysis of observations; "universal" models of complex systems such as those considered in statistical physics and nonlinear dynamics; and Earth-specific models of tectonic fault networks. In addition, the theory of optimal control is used to link earthquake prediction with earthquake preparedness."

At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entr e to an intriguing and thorny issue at the core of modern physics.

Written for an interdisciplinary readership, this book is a practical guide to the fascinating world of solitons. The author approaches the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. This third edition has been thoroughly revised and updated.

The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

People have always asked what distinguishes the living from the inanimate world and what uni?es the two. The ?elds of biology and physics have a long history of exchange. Milestones at the molecular level were the discoveries of the structure ofDNA, RNA, andproteins. It is not by coincidence that this exchange has intensi?ed in recent years. Laboratory experiments reach down to the level of single molecules. Moreover, thereisnowavastamountofgenomicinformation, whichisstillgrowingex- nentially due to the various sequencing projects. Biologists increasingly feel the need for theoretical models to interpret these data in a quantitative way. At the sametime, theoreticalphysicshasmadesigni?cantprogressinareaslikelyto be relevant for the understanding of biological systems. Some important ex- plesarecooperativephenomena, statisticsfarfromthermodynamicequilibrium, systemswithquencheddisorder, andsoftmatter. Some forms of biological matter have indeed become established areas of - searchwithinphysics, suchasbiomembranes, heteropolymers, molecularmotors, microtubules, neuralsystemsetc.Thisvolumeisfocusedonadi?erentaspect of the living world that can be calledbiologicalinformation, itscoding, rep- duction, andevolution.Biologicalinformationistranslatedintostructuresand patternsoveranenormousrangeofscales, fromsinglebiomoleculestospecies networks coupled over entire continents. Thestatisticaltheory of biological information lives not only in three-dim- sional space. It involves various abstract spaces in which this information is encodedandevolves, suchasnucleotidesequences, genenetworks, ortopologies of the 'tree of life'. The articles collected highlight a few directions of research that may become important parts of this emerging ?eld. The ?rst part of the book, MolecularInformationandEvolution, startswith twoarticlesonsequencesimilarityanalysis, acentralthemeinbioinformatics which has surprisingly deep connections to statistical physics. The genetic code, RNA, andproteinsarethreeexamplesoftheintricateinterplayofsequence, structure, andfunction

Data Mining for Design and Manufacturing: Methods and Applications is the first book that brings together research and applications for data mining within design and manufacturing. The aim of the book is 1) to clarify the integration of data mining in engineering design and manufacturing, 2) to present a wide range of domains to which data mining can be applied, 3) to demonstrate the essential need for symbiotic collaboration of expertise in design and manufacturing, data mining, and information technology, and 4) to illustrate how to overcome central problems in design and manufacturing environments. The book also presents formal tools required to extract valuable information from design and manufacturing data, and facilitates interdisciplinary problem solving for enhanced decision making. Audience: The book is aimed at both academic and practising audiences. It can serve as a reference or textbook for senior or graduate level students in Engineering, Computer, and Management Sciences who are interested in data mining technologies. The book will be useful for practitioners interested in utilizing data mining techniques in design and manufacturing as well as for computer software developers engaged in developing data mining tools.

This book contains the courses given at the Third School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 14th to 18th December 1992. The main idea of this periodic school was to bring together scientists work with recent trends in Statistical Physics. More precisely ing on subjects related related with non linear phenomena, dynamical systems, ergodic theory, cellular au tomata, symbolic dynamics, large deviation theory and neural networks. Scientists working in these subjects come from several areas: mathematics, biology, physics, computer science, electrical engineering and artificial intelligence. Recently, a very important cross-fertilization has taken place with regard to the aforesaid scientific and technological disciplines, so as to give a new approach to the research whose common core remains in statistical physics. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Fran"

Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.

Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field.

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities a la Painleve, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables.
The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved."

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

I am very pleased and privileged to write a short foreword for the monograph of Dean Driebe: Fully Chaotic Maps and Broken Time Symmetry. Despite the technical title this book deals with a problem of fundamental importance. To appreciate its meaning we have to go back to the tragic struggle that was initiated by the work of the great theoretical physicist Ludwig Boltzmann in the second half of the 19th century. Ludwig Boltzmann tried to emulate in physics what Charles Darwin had done in biology and to formulate an evolutionary approach in which past and future would play different roles. Boltzmann's work has lead to innumerable controversies as the laws of classical mechanics (as well as the laws of quan tum mechanics) as traditionally formulated imply symmetry between past and future. As is well known, Albert Einstein often stated that "Time is an illusion." Indeed, as long as dynamics is associated with trajectories satisfy ing the equations of classical mechanics, explaining irreversibility in terms of trajectories appears, as Henri Poincare concluded, as a logical error. After a long struggle, Boltzmann acknowledged his defeat and introduced a probabil ity description in which all microscopic states are supposed to have the same a priori probability. Irreversibility would then be due to the imperfection of our observations associated only with the "macroscopic" state described by temperature, pressure and other similar parameters. Irreversibility then appears devoid of any fundamental significance. However today this position has become untenable."

This book represents a thoroughly comprehensive treatment of computational intelligence from an electrical power system engineer's perspective. Thorough, well-organised and up-to-date, it examines in some detail all the important aspects of this very exciting and rapidly emerging technology, including: expert systems, fuzzy logic, artificial neural networks, genetic algorithms and hybrid systems. Written in a concise and flowing manner, by experts in the area of electrical power systems who have had many years of experience in the application of computational intelligence for solving many complex and onerous power system problems, this book is ideal for professional engineers and postgraduate students entering this exciting field. This book would also provide a good foundation for senior undergraduate students entering into their final year of study.

This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.

Models form the basis of any decision. They are used in di?erent context and for di?erent purposes: for identi?cation, prediction, classi?cation, or control of complex systems. Modeling is done theory-driven by logical-mathematical methods or data-driven based on observational data of the system and some algorithm or software for analyzing this data. Today, this approach is s- marized as Data Mining. There are many Data Mining algorithms known like Arti?cial Neural N- works, Bayesian Networks, Decision Trees, Support Vector Machines. This book focuses on another method: the Group Method of Data Handling. - thoughthismethodologyhasnotyetbeenwellrecognizedintheinternational science community asa verypowerfulmathematicalmodeling andknowledge extraction technology, it has a long history. Developed in 1968bythe Ukrainianscientist A.G. Ivakhnenko it combines the black-box approach and the connectionism of Arti?cial Neural Networks with well-proven Statistical Learning methods and with more behavior- justi?ed elements of inductive self-organization.Over the past 40 years it has been improving and evolving, ?rst by works in the ?eld of what was known in the U.S.A. as Adaptive Learning Networks in the 1970s and 1980s and later by signi? cantcontributions from scientists from Japan,China, Ukraine, Germany. Many papers and books have been published on this modeling technology, the vast majority of them in Ukrainian and Russian language.

The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

The conference Chaos in Astronomy was held in Athens from 17 to 20 September 2007 and was dedicated to the memory of Nikos Voglis, who was directoroftheResearchCenterforAstronomyoftheAcademyofAthensuntil his death on 9 February 2007. It was attended by 73 registered participants coming from 18 di?erent countries. A total of 40 oral papers were delivered including a conference summary. Furthermore 16 posters were presented. The conference was the main event in a series of talks, public lectures and d- cussion meetings about "Chaos in Astronomy" that have taken place at the Research Center for Astronomy. We underline three special talks that have been given by D. Kazanas (NASA-Goddard Space Flight Center), D. Lynden- Bell (Cambridge, UK) and C. Tsallis (Brazilian Academy of Science). The main sponsor of the conference was the "Alexander S. Onassis" Fo- dation. In addition the conference has been supported by the General S- retariat for Research and Technology, the National Observatory of Athens, and the Hellenic Ministry of Culture. We are grateful to all sponsors for their generosity. We also express our gratitude to the Academy of Athens and to the - rectorship of the Biomedical Research Foundation, where the conference took place.

This volume is published as the proceedings of the third Russian-German - vanced Research Workshop on Computational Science and High Performance Computing in Novosibirsk, Russia, in July 2007. The contributions of these proceedings were provided and edited by the - thors, chosen after a careful selection and reviewing. The workshop was organized by the High Performance Computing Center Stuttgart(Stuttgart,Germany)andtheInstituteofComputationalTechnologies SBRAS(Novosibirsk,Russia)intheframeworkofactivitiesoftheGerman-Russian CenterforComputationalTechnologiesandHighPerformanceComputing. Thee event is held biannually and has already become a good tradition for German and Russian scientists. The ?rst Workshop took place in September 2003 in Novosibirskand the second Workshopwas hosted by Stuttgart in March 2005. Both workshops gave the possibility of sharing and discussing the latest results and developing further scienti?c contacts in the ?eld of computational science and high performance computing. The topics of the current workshop include software and hardware for high performancecomputation,numericalmodellingingeophysicsandcomputational ?uid dynamics, mathematical modelling of tsunami waves, simulation of fuel cellsandmodern? breopticsdevices,numericalmodellingincryptographypr- lems andaeroacoustics,interval analysis,toolsfor Gridapplications,researchon service-oriented architecture (SOA) and telemedicine technologies. Theparticipationofrepresentativesofmajorresearchorganizationsengagedin the solution of the most complex problems of mathematical modelling, devel- ment of new algorithms,programsandkey elementsof informationtechnologies, elaboration and implementation of software and hardware for high performance computing systems,provideda highlevelof competenceofthe workshop. Among the German participants were the heads and leading specialists of the HighPerformanceComputingCenterStuttgart(HLRS)(UniversityofStuttgart), NECHighPerformanceComputingEuropeGmbH,SectionofAppliedMathem- ics(UniversityofFreiburgi.Br.),InstituteofAerodynamics(RWTHAachen),- gionalComputingCenterErlangen(RRZE(UniversityofErlangen-Nuremberg), Center for High Performance Computing (ZHR) (Dresden University of Technology).

Intelligent Multimedia Multi-Agent Systems focuses on building intelligent successful systems. The book adopts a human-centered approach and considers various pragmatic issues and problems in areas like intelligent systems, software engineering, multimedia databases, electronic commerce, data mining, enterprise modeling and human-computer interaction for developing a human-centered virtual machine. The authors describe an ontology of the human-centered virtual machine which includes four components: activity-centered analysis component, problem solving adapter component, transformation agent component, and multimedia based interpretation component. These four components capture the external and internal planes of the system development spectrum. They integrate the physical, social and organizational reality on the external plane with stakeholder goals, tasks and incentives, and organization culture on the internal plane. The human-centered virtual machine and its four components are used for developing intelligent multimedia multi-agent systems in areas like medical decision support and health informatics, medical image retrieval, e-commerce, face detection and annotation, internet games and sales recruitment. The applications in these areas help to expound various aspects of the human-centered virtual machine including, human-centered domain modeling, distributed intelligence and communication, perceptual and cognitive task modeling, component based software development, and multimedia based data modeling. Further, the applications described in the book employ various intelligent technologies like neural networks, fuzzy logic and knowledge based systems, software engineering artifacts like agents and objects, internet technologies like XML and multimedia artifacts like image, audio, video and text.

Fully Tuned Radial Basis Function Neural Networks for Flight Control presents the use of the Radial Basis Function (RBF) neural networks for adaptive control of nonlinear systems with emphasis on flight control applications. A Lyapunov synthesis approach is used to derive the tuning rules for the RBF controller parameters in order to guarantee the stability of the closed loop system. Unlike previous methods that tune only the weights of the RBF network, this book presents the derivation of the tuning law for tuning the centers, widths, and weights of the RBF network, and compares the results with existing algorithms. It also includes a detailed review of system identification, including indirect and direct adaptive control of nonlinear systems using neural networks. Fully Tuned Radial Basis Function Neural Networks for Flight Control is an excellent resource for professionals using neural adaptive controllers for flight control applications.

TheconferenceChanceinPhysics: FoundationsandPerspectiveswasheldfrom 29thNovemberto3rdDecember1999inIschia, Italy. Itwassponsoredbythe IstitutoItalianoPerGliStudiFiloso?ciinNaples, bytheDeutscheForschun- gemeinschaft(DFG), andbytheSocietaItalianaDiFondamentiDellaFisica. SponsoringbytheInternationalSchoolforAdvancedStudies(ISAS)ofTrieste, Italy, madethecompilationofthisvolumepossible;thefundingbytheIs- tutoItalianoPerGliStudiFiloso?ciwascrucialfortheconferenceandisvery gratefullyacknowledged. TheIstitutomanagedtoprovideauniqueatmosphere foraninterdisciplinarymeeting, andtheseproceedingsre?ectindeedthevery friendlybutneverthelessintenseandneverendingdiscussionsononeofthemost debatedissuesofscience: probability, andinparticularprobabilityinphysics. Wegratefullyacknowlegdetheorganisationalworkaswellastheeditorialwork donebyoursecretaryofthemeetingPhDstudentRoderichTumulka. Themeetingwasintendedtostimulaterenewedre?ectiononthefundam- talandpracticalaspectsofprobabilityinphysics, inparticularthefoundations ofstatisticalsechanics, theprobabilityinthefoundationsofquantummech- ics, thealgebraicviewofprobabilityandthephilosophyofprobabilityinits interrelationwithphysics. Questionslikewhatprobabilityis, orwhatitisabout, orhowprobability entersphysicsareofasubtlekind. Theyaredi?cultinvariousways, often mixedupwiththeenormouscomplexityandtheinescapablelackofmat- maticalrigorinthephysicalapplication, orwiththefoundationalproblemsof quantummechanics, wheretheprobabilisticignoranceconcerningthevaluesof certainphysicalquantitieshasevenbeenelevatedtoamatterofprinciple. At present, theunderstandingofprobabilityinphysicsisalmostaspersonalasthe understandingofquantumtheory. Theaimoftheconferencewasthustofocusonideasaboutprobabilityin physics, itsmeaninganditsphilosophicalimplications, byreviewingthedi?erent facetsofprobabilityinphysicsinitsmodernsettingsandbytakingintoaccount modernquantumtheorieswithoutobservers, wheretheoriginofprobabilityis notmysti?edbydogmatism. Thereviewsweregiveninone-hourtalks, andthediscussionswereheldin theformofroundtables, whereshortercontributionswerealsogiven. Thespeakerswereaskednottodilutethemainthemesoftheconference withtechnicalitiesandtofocussharplyontheissueofprobability. Thiswas VI Preface takentoheartbyallspeakersandthemeetingthusprovedverysuccessful. The contributionsinthisvolumeconsequentlyfocusonconceptualissues, andthey makeworthwhilereadingforspecialistsinthe?eldoffoundationsaswellasfor nonspecialists, becauseextensivetechnicalpriorknowledgeisnotrequired. The contributionshavebeenleftintheordertheywerediscussedinthemeeting, whichprovedtobeaverynaturalone: 1. ClassicalStatisticalMechanics, whereBoltzmann'sunderstandingofstat- ticalmechnanicsasarisingfromkineticgastheoryisreviewedandputinto modernperspectives, withanoutlookonrelativisticstatisticalmechanics. Therelativelackofemphasisonthee?ectofchaoticbehaviouronthefo- dationsofprobabilityisnoteworthy. 2. QuantumMechanics, wherewereviewthoseontologicalquantumtheories, thathavebeenmostseriouslydiscussedintherecentyears. Amongthese areadeterministictheory(Bohmianmechanics)andboththeintrinsically randomtheoriesofwavepacketreductionandtheoperator-basedconsistent (decoherent)histories. Itstartswiththe"orthodox"view, againwith- phasisontheprobabilisticaspectsofthesetheories. 3. Chaoticsystems, wherethedynamicalaspectsforthefoundationsofpro- bilityinphysicsareadressed. 4. PhilosophyofProbability, wheretheissuesoftheearliersectionsarefurther scrutinizedonphilosophicalgrounds. Thesecontributionshavenoabstracts. T

The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.