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.

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.

Recent years have witnessed a rapid development of active control of various mechanical systems. With increasingly strict requirements for control speed and system performance, the unavoidable time delays in both controllers and actuators have become a serious problem. For instance, all digital controllers, analogue anti aliasing and reconstruction filters exhibit a certain time delay during operation, and the hydraulic actuators and human being interaction usually show even more significant time delays. These time delays, albeit very short in most cases, often deteriorate the control performance or even cause the instability of the system, be cause the actuators may feed energy at the moment when the system does not need it. Thus, the effect of time delays on the system performance has drawn much at tention in the design of robots, active vehicle suspensions, active tendons for tall buildings, as well as the controlled vibro-impact systems. On the other hand, the properly designed delay control may improve the performance of dynamic sys tems. For instance, the delayed state feedback has found its applications to the design of dynamic absorbers, the linearization of nonlinear systems, the control of chaotic oscillators, etc. Most controlled mechanical systems with time delays can be modeled as the dynamic systems described by a set of ordinary differential equations with time delays."

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

Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network structure and the availability of on- and off-line learning methods for the interconnection weights. However, dynamic models that contain neural network architectures might be highly non-linear and difficult to analyse as a result. Artificial Neural Networks for Modelling and Control of Non-Linear Systems investigates the subject from a system theoretical point of view. However the mathematical theory that is required from the reader is limited to matrix calculus, basic analysis, differential equations and basic linear system theory. No preliminary knowledge of neural networks is explicitly required. The book presents both classical and novel network architectures and learning algorithms for modelling and control. Topics include non-linear system identification, neural optimal control, top-down model based neural control design and stability analysis of neural control systems. A major contribution of this book is to introduce NLq Theory as an extension towards modern control theory, in order to analyze and synthesize non-linear systems that contain linear together with static non-linear operators that satisfy a sector condition: neural state space control systems are an example. Moreover, it turns out that NLq Theory is unifying with respect to many problems arising in neural networks, systems and control. Examples show that complex non-linear systems can be modelled and controlled within NLq theory, including mastering chaos. The didactic flavor of this book makes it suitable for use as a text for a course on Neural Networks. In addition, researchers and designers will find many important new techniques, in particular NLq Theory, that have applications in control theory, system theory, circuit theory and Time Series Analysis.

This book presents a theory for unconventional superconductivity driven by spin excitations. Using the Hubbard Hamiltonian and a self-consistent treatment of the spin excitations, the interplay between magnetism and superconductivity in various unconventional superconductors is discussed. In particular, the monograph applies this theory for Cooper-pairing due to the exchange of spin fluctuations to the case of singlet pairing in hole- and electron-doped high-Tc superconductors, and to triplet pairing in
Sr2RuO4. Within the framework of a generalized Eliashberg-like treatment, calculations of both many normal and superconducting properties as well as elementary excitations are performed. The results are related to the phase diagrams of the materials which reflect
the interaction between magnetism and superconductivity.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each. chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied ( 1-3). A first detailed study of homogeneous turbulent flows follows ( 4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in 5 with the l"Csulting alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms ( 1), their general dynamics ( 2) with the particular case of homogeneous, isotropie turbulence ( 3) whel"C the so-called Kolmogorov's assumptions are discussed at length."

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"

In this monograph, the density ?uctuation theory of transport coe?cients of simple and complex liquids is described together with the kinetic theory of liquids, the generic van der Waals equation of state, and the modi?ed free volume theory. The latter two theories are integral parts of the density ?- tuation theory, which enables us to calculate the density and temperature dependence of transport coe?cients of liquids from intermolecular forces. The terms nanoscience and bioscience are the catch phrases currently in fashion in science. It seems that much of the fundamentals remaining unsolved or poorly understood in the science of condensed matter has been overshadowed by the frenzy over the more glamorous disciplines of the former, shunned by novices, and are on the verge of being forgotten. The transport coe?cients of liquids and gases and related thermophysical properties of matter appear to be one such area in the science of macroscopic properties of molecular systems and statisticalmechanicsofcondensedmatter. Evennano-andbiomaterials, h- ever, cannot be fully and appropriately understood without ?rm grounding and foundations in the macroscopic and molecular theories of transport pr- ertiesandrelatedthermophysicalpropertiesofmatterinthecondensedphase. Oneisstilldealingwithsystemsmadeupofnotafewparticlesbutamultitude of them, often too many to count, to call them few-body problems that can be understoodwithoutthehelpofstatisticalmechanicsandmacroscopicphysics. In the density ?uctuation theory of transport coe?cients, the basic approach taken is quite di?erent from the approaches taken in the conventional kinetic theories of gases and liquids

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

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

In the last two decades remarkable progress has been made in understanding and describing tunneling processes in complex systems in terms of classical trajectories. This book introduces recent concepts and achievements. There is particular emphasis on a dynamical formulation and relations to specific systems in mesoscopic, molecular, atomic and nuclear physics.

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

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

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

Condensed-matter physics plays an ever increasing role in photonics, electronic and atomic collisions research. Dispersion (Dynamics and Relaxation) includes scattering/collisions in the gaseous phase. It also includes thermal agitation, tunneling and relaxation in the liquid and solid phases. Classical mechanics, classical statistical mechanics, classical relativity and quantum mechanics are all implicated. 'Semiclassical' essentially means that there is a large or asymptotic real parameter. 'Semiclassical' can also mean 'classical with first-order quantal correction', based on an exponentiated Liouville series commencing with a simple pole in the -plane, being Planck's reduced constant and coming with all the attendant connection problems associated with the singularity at the turning or transition point and with the Stokes phenomenon. Equally, ' semiclassical' can mean 'electrons described quantally and the heavy particles classically'. This latter gives rise to the so-called impact parameter method based on a pre-assigned classical trajectory.

With evermore sophisticated experiments, it has become equally more important to test theory over a wider range of parameters. For instance, at low impact energies in heavy-particle collisions, the inverse velocity is a large parameter; in single-domain ferromagnetism, thermal agitation (including Brownian motion and continuous-time random walks) is faced with a barrier of height 'sigma', a possibly large parameter. Methods of solution include phase-integral analysis, integral transforms and change-of-dependent variable. We shall consider the Schrodinger time-independent and time-dependent equations, the Dirac equation, the Fokker Planck equation, the Langevin equation and the equations of Einstein's classical general relativity equations.

There is an increasing tendency among physicists to decry applied mathematics and theoretical physics in favour of computational blackboxes. One may say applied mathematics concerns hard sums and products (and their inverses) but unless one can simplify and sum infinite series of products of infinite series, can one believe the results of a computer program? The era of the polymath has passed; this book proposal aims to show the relevance to, and impact of theory on, laboratory scientists."

In this book, we approach neurophysiology at the interface of neurology and clinical neurophysiology. The medical disciplines of the nervous system, n- rology and clinical neurophysiology, rest heavily on other sciences, notably cellular biology, neuro-anatomy, neuro-physiology, applied physics and ma- ematical biology. Existing medical textbooks on neurophysiology, neurology and clinical neurophysiology are an excellent source of the phenomenology of various principles and diseases. Here, we choose to elucidate some of the under- ing physiological, physical processes and experimental methods, intended for a broad audience - medical residents and students, as well as students in the emerging area of medical technical sciences. We feel that a good understanding of fundamentals may signi?cantly - hance insight into various aspects of clinical neurology and clinical neu- physiology. This book, therefore, is focused on a selection of clinical signs and symptoms to highlight basic principles of neurology, (neuro-)physiology and neuroanatomy. While we believe this text to be of interest to medical students or residents in neurology or clinical neurophysiology, we speci?cally aim at students - terested in contributing to new developments and innovations in neurology and clinical neurophysiology. These students are involved with patients, even though they are not trained for routine patient care.

Computational Mechanics of the Classical Guitar describes a new dynamic paradigm in instrument acoustics based on time-dependent transient analysis and simulation of complete musical instruments. It describes the current state of theoretical and experimental research into the guitar for engineers, instrument makers and musicians. This includes a summary of the basic equations for the mechanics of vibrating bodies and a presentation of the FDM (finite difference method) model with which the true vibrational behaviour of the instrument as an entire system can be understood for the first time. This monograph presents various new theoretical and experimental results and insights into guitar playing such as the coupling between the strings and the top plate or a description of the finger noise made when the fingers slide over the strings before plucking.

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

In the modern world of gigantic datasets, which scientists and practioners of all fields of learning are confronted with, the availability of robust, scalable and easy-to-use methods for pattern recognition and data mining are of paramount importance, so as to be able to cope with the avalanche of data in a meaningful way. This concise and pedagogical research monograph introduces the reader to two specific aspects - clustering techniques and dimensionality reduction - in the context of complex network analysis. The first chapter provides a short introduction into relevant graph theoretical notation; chapter 2 then reviews and compares a number of cluster definitions from different fields of science. In the subsequent chapters, a first-principles approach to graph clustering in complex networks is developed using methods from statistical physics and the reader will learn, that even today, this field significantly contributes to the understanding and resolution of the related statistical inference issues. Finally, an application chapter examines real-world networks from the economic realm to show how the network clustering process can be used to deal with large, sparse datasets where conventional analyses fail.

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 system

By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.

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

This lecture notes in physics volume mainly focuses on the semi classical and qu- tum aspects of percolation and breakdown in disordered, composite or granular s- tems. The main reason for this undertaking has been the fact that, of late, there have been a lot of (theoretical) work on quantum percolation, but there is not even a (single) published review on the topic (and, of course, no book). Also, there are many theoretical and experimental studies on the nonlinear current-voltage characteristics both away from, as well as one approaches, an electrical breakdown in composite materials. Some of the results are quite intriguing and may broadly be explained utilising a semi classical (if not, fully quantum mechanical) tunnelling between - cron or nano-sized metallic islands dispersed separated by thin insulating layers, or in other words, between the dangling ends of small percolation clusters. There have also been several (theoretical) studies of Zener breakdown in Mott or Anderson in- lators. Again, there is no review available, connecting them in any coherent fashion. A compendium volume connecting these experimental and theoretical studies should be unique and very timely, and hence this volume. The book is organised as follows. For completeness, we have started with a short and concise introduction on classical percolation. In the ?rst chapter, D. Stauffer reviews the scaling theory of classical percolation emphasizing (biased) diffusion, without any quantum effects. The next chapter by A. K.

The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks' As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital.