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

Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and "anchorage" realised on semantic grounds. It is the work of "invention" and g- eration (in invariance), linked with the "rooting" of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of "possibles," offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the " le" in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity, whichalsotakes place through the "narration" of the effected construction.

Though the reductionist approachto biology and medicine has led to several imp- tant advances, further progresses with respect to the remaining challenges require integration of representation, characterization and modeling of the studied systems along a wide range of spatial and time scales. Such an approach, intrinsically - lated to systems biology, is poised to ultimately turning biology into a more precise and synthetic discipline, paving the way to extensive preventive and regenerative medicine [1], drug discovery [20] and treatment optimization [24]. A particularly appealing and effective approach to addressing the complexity of interactions inherent to the biological systems is provided by the new area of c- plex networks [34, 30, 8, 13, 12]. Basically, it is an extension of graph theory [10], focusing on the modeling, representation, characterization, analysis and simulation ofcomplexsystemsbyconsideringmanyelementsandtheirinterconnections.C- plex networks concepts and methods have been used to study disease [17], tr- scription networks [5, 6, 4], protein-protein networks [22, 36, 16, 39], metabolic networks [23] and anatomy [40].

This monograph covers phenomena of deformation and machining of granular media: macroscopic particles of different size, shape, and surface properties which typically exhibit behavior similar to fluids, as well as the behavior of solids under deformation. The book analyses the behavior of granular media in soils, rocks and stones, metals and various synthetic materials, presenting a theoretical description, applications and understanding of basic phenomena in granular matter.

The study of cooperative phenomena is one of the dominant features of contem porary physics. Outside physics it has grown to a huge field of interdisciplinary investigation, involving all the natural sciences from physics via biology to socio logy. Yet, during the first few decades following the advent of quantum theory, the pursuit of the single particle or the single atom, as the case may be, has been so fascinating that only a small number of physicists have stressed the importance of collective behaviour. One outstanding personality among these few is Professor HERBERT FROHLICH. He has made an enormous contribution to the modern concept of cooperativity and has stimulated a whole generation of physicists. Therefore, it seemed to the editors very appropriate to dedicate a volume on "cooperative phenomena" to him on the occasion of his official retirement from his university duties. Nevertheless, in the course of carrying out this project, the editors have been somewhat amazed to find that they have covered the essentials of contemporary physics and its im pact on other scientific disciplines. It thus becomes clear how much HERBERT FROHLICH has inspired research workers and has acted as a stimulating discussion partner for others. FROHLICH is one of those exceptional scientists who have wor ked in quite different fields and given them an enormous impetus. Unfortunately, the number of scientists of such distinctive personality has been decreasing in our century."

While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.

The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists of all fields, engineers, physicians, executives, and a host of other professionals to explore common themes and applications of complex system science. With this new volume, Unifying Themes in Complex Systems continues to build common ground between the wide-ranging domains of complex system science.

Thermodynamicsandstatisticalphysicsstudythephysicalproperties(mec- nical, thermal, magnetic, optical, electrical, etc.) of the macroscopic system. The tasks and objects of study in thermodynamics and statistical physics are identical. However, the methods of investigationinto macroscopicsystems are di?erent. Thermodynamics is a phenomenological theory. It studies the properties of bodies, without going into the mechanism of phenomena, i.e., not taking into consideration the relation between the internal structure of substance and phenomena, it generalizes experimental results. As a result of such a g- eralization, postulates and laws of thermodynamics made their appearance. These laws make it possible to ?nd general relations between the di?erent properties of macroscopic systems and the physical events occurring in them. Statisticalphysicsisa microscopic theory.Onthebasisoftheknowledgeof the type of particles a system consists of, the nature of their interaction, and thelawsofmotionoftheseparticlesissuingfromtheconstructionofsubstance, it explains the properties being observedon experiment, and predicts the new properties of systems. Using the laws of classical or quantum mechanics, and alsothe theoryofprobability, itestablishesqualitativelynewstatistical app- priatenesses of the physical properties of macroscopic systems, substantiates the laws of thermodynamics, determines the limits of their applicability, gives the statistical interpretation of thermodynamic parameters, and also works out methods of calculations of their means. The Gibbs method is based on statisticalphysics.Thismethodis themostcanonical.Therefore, inthis book, the exposition of the Gibbs method takes an important pla

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical.

This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

The analysis of plates and shells under static and dynamic loads is of greatinterest to scientists and engineers both from the theoretical and the practical viewpoint. The Boun- dary Element Method (BEM) has some distinct advantages over domain techniques such as the Finite Difference Method (FDM) and the Finite Element Method (FEM) for a wide class of structuralanalysis problems. This is the first book to deal specifically with the analysis of plates and shells by the BEM and to cover all aspects of their behaviour, and combi- nes tutorial and state-of-the-art articles on the BEM as ap- plied to plates and shells. It aims to inform scientists and engineers about the use and the advantages of this techni- que, the most recent developments in the field and the per- tinent literature for further study.

This volume contains the invited lectures and a selection of the contributed papers and posters of the workshop on "Fluctuations and Sensitivity in Nonequil ibrium Systems", held at the Joe C. Thompson Conference Center, Un i vers ity of Texas at Austin, March 12-16, 1984. The workshop dealt with stochastic phenomena and sensi- tivity in nonequilibrium systems from a macroscopic point of view. Durin9 the last few years it has been realized that the role of fluctuations is far less trivial in systems far from equilibrium than in systems under thermodynamic equilibrium condi- tions. It was found that random fluctuations often are a determining factor for the state adopted by macroscopic systems and cannot be regarded as secondary effects of minor importance. Further, nonequilibrium systems are also very sensitive to small systematic changes in their environment. The main aims of the workshop were: i) to provide scientists with an occasion to acquaint themselves with the state of the art in fluctuation theory and sensitivity analysis; ii) to provide a forum for the presentation of recent advances in theory and experiment; iii) to bring toge- ther theoreticians and experimentalists in order to delineate the major open problems and to formulate strategies to tackle these problems. The organizing committee of the workshop consisted of W. Horsthemke, O. K. Konde- pudi, G. Dewel, G. Nicolis, I. Prigogine and L. Reichl.

Over the years enormous effort was invested in proving ergodicity, but for a number of reasons, con?dence in the fruitfulness of this approach has waned. - Y. Ben-Menahem and I. Pitowsky [1] Abstract The basic motivation behind the present text is threefold: To give a new explanation for the emergence of thermodynamics, to investigate the interplay between quantum mechanics and thermodynamics, and to explore possible ext- sions of the common validity range of thermodynamics. Originally, thermodynamics has been a purely phenomenological science. Early s- entists (Galileo, Santorio, Celsius, Fahrenheit) tried to give de?nitions for quantities which were intuitively obvious to the observer, like pressure or temperature, and studied their interconnections. The idea that these phenomena might be linked to other ?elds of physics, like classical mechanics, e.g., was not common in those days. Such a connection was basically introduced when Joule calculated the heat equ- alent in 1840 showing that heat was a form of energy, just like kinetic or potential energy in the theory of mechanics. At the end of the 19th century, when the atomic theory became popular, researchers began to think of a gas as a huge amount of bouncing balls inside a box.

In May 2002 a number of about 20 scientists from various disciplines were invited by the Berlin-Brandenburg Academy of Sciences and Humanities to participate in an interdisciplinary workshop on structures and structure generating processes. The site was the beautiful little castle of Blankensee, south of Berlin. The disciplines represented ranged from mathematics and information theory, over various ?elds of engineering, biochemistry and biology, to the economic and social sciences. All participants presented talks explaining the nature of structures considered in their ?elds and the associated procedures of analysis. It soon became evident that the study of structures is indeed a common c- cern of virtually all disciplines. The motivation as well as the methods of analysis, however, differ considerably. In engineering, the generation of artifacts, such as infrastructures or technological processes, are of primary interest. Frequently, the analysis aims there at de?ning a simpli?ed mathematical model for the optimization of the structures and the structure generating processes. Mathematical or heuristic methods are applied, the latter preferably of the type of biology based evolutionary algorithms. On the other hand, setting up complex technical structures is not pos- ble by such simpli?ed model calculations but requires a different and less model but rather knowledge-based type of approach, using empirical rules rather than formal equations. In biochemistry, interest is frequently focussed on the structures of molecules, such as proteins or ribonucleic acids. Again, optimal structures can usually be de?ned.

Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties are not directly deducible from the lower-level motion of that system. Emergent properties are properties of the "whole'' that are not possessed by any of the individual parts making up that whole. Such phenomena exist in various domains and can be described, using complexity concepts and thematic knowledges. This book highlights complexity modelling through dynamical or behavioral systems. The pluridisciplinary purposes, developed along the chapters, are able to design links between a wide-range of fundamental and applicative Sciences. Developing such links - instead of focusing on specific and narrow researches - is characteristic of the Science of Complexity that we try to promote by this contribution.

The paradigm of complexity is pervading both science and engineering, le- ing to the emergence of novel approaches oriented at the development of a systemic view of the phenomena under study; the de?nition of powerful tools for modelling, estimation, and control; and the cross-fertilization of di?erent disciplines and approaches. One of the most promising paradigms to cope with complexity is that of networked systems. Complex, dynamical networks are powerful tools to model, estimate, and control many interesting phenomena, like agent coordination, synch- nization, social and economics events, networks of critical infrastructures, resourcesallocation, informationprocessing, controlovercommunicationn- works, etc. Advances in this ?eld are highlighting approaches that are more and more oftenbasedondynamicalandtime-varyingnetworks, i.e.networksconsisting of dynamical nodes with links that can change over time. Moreover, recent technological advances in wireless communication and decreasing cost and size of electronic devices are promoting the appearance of large inexpensive interconnected systems, each with computational, sensing and mobile ca- bilities. This is fostering the development of many engineering applications, which exploit the availability of these systems of systems to monitor and control very large-scale phenomena with ?ne resoluti

Thisvolumeexploresabductivecognition, animportantbut, atleastuntilthe third quarter of the last century, neglected topic in cognition. It integrates and further develops ideas already introduced in a previous book, which I published in 2001 (Abduction, Reason, and Science. Processes of Discovery and Explanation, Kluwer Academic/Plenum Publishers, New York). Thestatusofabductionisverycontroversial. Whendealingwithabductive reasoning misinterpretations and equivocations are common. What are the di?erences between abduction and induction? What are the di?erences - tween abduction and the well-known hypothetico-deductive method? What did Peircemeanwhen heconsideredabductionboth a kindofinferenceanda kind of instinct or when he considered perception a kind of abduction? Does abduction involve only the generation of hypotheses or their evaluation too? Are the criteria for the best explanation in abductive reasoning epistemic, or pragmatic, or both? Does abduction preserve ignorance or extend truth or both? How many kinds of abduction are there? Is abduction merely a kind of "explanatory" inference or does it involve other non-explanatory ways of guessing hypotheses? The book aims at increasing knowledge about creative and expert inf- ences. The study of these high-level methods of abductive reasoning is s- uated at the crossroads of philosophy, logic, epistemology, arti?cial intel- gence, neuroscience, cognitive psychology, animal cognition and evolutionary theories; that is, at the heart of cognitive science. Philosophers of science in thetwentiethcenturyhavetraditionallydistinguishedbetweentheinferential processesactiveinthelogicofdiscoveryandtheonesactiveinthelogicofj- ti?cation. Most have concluded that no logic of creative processes exists and, moreover, that a rational model of discovery is impossible. In short, scienti?c creative inferences are irrational and there is no "reasoning" to hypotheses.

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 Kung, Hakwan C. Lau, Dean Mobbs, Nancey Murphy, William Newsome, Timothy O'Connor, Sean A.. Spence, and Evan Thompson.

Monte Carlo computer simulations are now a standard tool in scientific fields such as condensed-matter physics, including surface-physics and applied-physics problems (metallurgy, diffusion, and segregation, etc. ), chemical physics, including studies of solutions, chemical reactions, polymer statistics, etc., and field theory. With the increasing ability of this method to deal with quantum-mechanical problems such as quantum spin systems or many-fermion problems, it will become useful for other questions in the fields of elementary-particle and nuclear physics as well. The large number of recent publications dealing either with applications or further development of some aspects of this method is a clear indication that the scientific community has realized the power and versatility of Monte Carlo simula tions, as well as of related simulation techniques such as "molecular dynamics" and "Langevin dynamics," which are only briefly mentioned in the present book. With the increasing availability of recent very-high-speed general-purpose computers, many problems become tractable which have so far escaped satisfactory treatment due to prac tical limitations (too small systems had to be chosen, or too short averaging times had to be used). While this approach is admittedly rather expensive, two cheaper alternatives have become available, too: (i) array or vector processors specifical ly suited for wide classes of simulation purposes; (ii) special purpose processors, which are built for a more specific class of problems or, in the extreme case, for the simulation of one single model system."

This work arises from our teaching this subject during many years. The vast majority of these exercises are the exams we gave to our students in this period. We carefully selected the subjects of the exercises to cover all the material which is most needed and which is treated in the most well known texts on these subjects. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that, from our experience, are found most difficult from the average student. Indeed, several exercises are designed to throw light on aspects of the theory that, for one reason or another, are usually neglected with the result to make the students feel uneasy about them. In fact most students get acquainted just with the more common manipulations, which are illustrated by many examples in textbooks. Our exercises never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from the principles, rather than by analogy with some previously solved exercise."

It is increasingly being recognized that the experimental and theoretical study of the complex system brain requires the cooperation of many disciplines, in cluding biology, medicine, physics, chemistry, mathematics, computer science, linguistics, and others. In this way brain research has become a truly interdis ciplinary endeavor. Indeed, the most important progress is quite often made when different disciplines cooperate. Thus it becomes necessary for scientists to look across the fence surrounding their disciplines. The present book is written precisely in this spirit. It addresses graduate students, professors and scientists in a variety of fields, such as biology, medicine and physics. Be yond its mathematical representation the book gives ample space to verbal and pictorial descriptions of the main and, as I believe, fundamental new insights, so that it will be of interest to a general readership, too. I use this opportunity to thank my former students, some of whom are my present co-workers, for their cooperation over many years. Among them I wish to mention in particular M. Bestehorn, L. Borland, H. Bunz, A. Daf fertshofer, T. Ditzinger, E. Fischer, A. Fuchs, R. Haas, R. Honlinger, V. Jirsa, M. Neufeld, M. Ossig, D. Reimann, M. Schanz, G. Schoner, P. Tass, C. Uhl. My particular thanks go to R. Friedrich and A. Wunderlin for their constant help in many respects. Stimulating discussions with a number of colleagues from a variety of fields are also highly appreciated.

In recent years, the study of neutron stars and black holes has become increasingly important, and rigorous mathematical analysis needs to be applied in order to understand their basic physics. This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9780521863834.

This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.

One of the great intellectual challenges for the next few decades is the question of brain organization. What is the basic mechanism for storage of memory? What are the processes that serve as the interphase between the basically chemical processes of the body and the very specific and nonstatistical operations in the brain? Above all, how is concept formation achieved in the human brain? I wonder whether the spirit of the physics that will be involved in these studies will not be akin to that which moved the founders of the "rational foundation of thermodynamics". C. N. Yang! 10 The human brain is said to have roughly 10 neurons connected through about 14 10 synapses. Each neuron is itself a complex device which compares and integrates incoming electrical signals and relays a nonlinear response to other neurons. The brain certainly exceeds in complexity any system which physicists have studied in the past. Nevertheless, there do exist many analogies of the brain to simpler physical systems. We have witnessed during the last decade some surprising contributions of physics to the study of the brain. The most significant parallel between biological brains and many physical systems is that both are made of many tightly interacting components.

Computer Simulation Studies in Condensed-Matter Physics VIII covers recent developments in this field presented at the 1995 workshop, such as new algorithms, methods of analysis, and conceptual developments. This volume is composed of three parts. The first part contains invited papers that deal with simulational studies of classical systems. The second part is devoted to invited papers on quantum systems, including new results for strongly correlated electron and quantum spin models. The final part comprises contributed presentations.