Analysis, Control and Optimization of Complex Dynamic Systems gathers in a single volume a spectrum of complex dynamic systems related papers written by experts in their fields, and strongly representative of current research trends. Complex systems present important challenges, in great part due to their sheer size which makes it difficult to grasp their dynamic behavior, optimize their operations, or study their reliability. Yet, we live in a world where, due to increasing inter-dependencies and networking of systems, complexity has become the norm. With this in mind, the volume comprises two parts. The first part is dedicated to a spectrum of complex problems of decision and control encountered in the area of production and inventory systems. The second part is dedicated to large scale or multi-agent system problems occurring in other areas of engineering such as telecommunication and electric power networks, as well as more generic context.

This present book provides an alternative approach to study the pre-kernel solution of transferable utility games based on a generalized conjugation theory from convex analysis. Although the pre-kernel solution possesses an appealing axiomatic foundation that lets one consider this solution concept as a standard of fairness, the pre-kernel and its related solutions are regarded as obscure and too technically complex to be treated as a real alternative to the Shapley value. Comprehensible and efficient computability is widely regarded as a desirable feature to qualify a solution concept apart from its axiomatic foundation as a standard of fairness. We review and then improve an approach to compute the pre-kernel of a cooperative game by the indirect function. The indirect function is known as the Fenchel-Moreau conjugation of the characteristic function. Extending the approach with the indirect function, we are able to characterize the pre-kernel of the grand coalition simply by the solution sets of a family of quadratic objective functions.

The emphasis of this textbook is on industrial applications of Statistical Measurement Theory. It deals with the principal issues of measurement theory, is concise and intelligibly written, and to a wide extent self-contained. Difficult theoretical issues are separated from the mainstream presentation. Each topic starts with an informal introduction followed by an example, the rigorous problem formulation, solution method, and a detailed numerical solution. Each chapter concludes with a set of exercises of increasing difficulty, mostly with solutions. The book is meant as a text for graduate students and a reference for researchers and industrial experts specializing in measurement and measurement data analysis for quality control, quality engineering and industrial process improvement using statistical methods. Knowledge of calculus and fundamental probability and statistics is required for the understanding of its contents.

The 1996 NATO Advanced Study Institute (ASI) followed the international tradi tion of the schools held in Cargese in 1976, 1979, 1983, 1987 and 1991. Impressive progress in quantum field theory had been made since the last school in 1991. Much of it is connected with the interplay of quantum theory and the structure of space time, including canonical gravity, black holes, string theory, application of noncommutative differential geometry, and quantum symmetries. In addition there had recently been important advances in quantum field theory which exploited the electromagnetic duality in certain supersymmetric gauge theories. The school reviewed these developments. Lectures were included to explain how the "monopole equations" of Seiberg and Witten can be exploited. They were presented by E. Rabinovici, and supplemented by an extra 2 hours of lectures by A. Bilal. Both the N = 1 and N = 2 supersymmetric Yang Mills theory and resulting equivalences between field theories with different gauge group were discussed in detail. There are several roads to quantum space time and a unification of quantum theory and gravity. There is increasing evidence that canonical gravity might be a consistent theory after all when treated in. a nonperturbative fashion. H. Nicolai presented a series of introductory lectures. He dealt in detail with an integrable model which is obtained by dimensional reduction in the presence of a symmetry."

The book presents the state of the art in high performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and software development in general and specifically the future of high performance systems and heterogeneous architectures. The application contributions cover computational fluid dynamics, material science, medical applications and climate research. Innovative fields like coupled multi-physics or multi-scale simulations are presented. All papers were chosen from presentations given at the 14th Teraflop Workshop held in December 2011 at HLRS, University of Stuttgart, Germany and the Workshop on Sustained Simulation Performance at Tohoku University in March 2012.

The text of the Persian poet Rum - - ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the 'big picture'. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even 'bare' turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.

The complexity of biological systems has intrigued scientists from many disciplines and has given birth to the highly influential field of systems biology wherein a wide array of mathematical techniques, such as flux balance analysis, and technology platforms, such as next generation sequencing, is used to understand, elucidate, and predict the functions of complex biological systems. More recently, the field of synthetic biology, i.e., de novo engineering of biological systems, has emerged. Scientists from various fields are focusing on how to render this engineering process more predictable, reliable, scalable, affordable, and easy. Systems and control theory is a branch of engineering and applied sciences that rigorously deals with the complexities and uncertainties of interconnected systems with the objective of characterising fundamental systemic properties such as stability, robustness, communication capacity, and other performance metrics. Systems and control theory also strives to offer concepts and methods that facilitate the design of systems with rigorous guarantees on these properties. Over the last 100 years, it has made stellar theoretical and technological contributions in diverse fields such as aerospace, telecommunication, storage, automotive, power systems, and others. Can it have, or evolve to have, a similar impact in biology? The chapters in this book demonstrate that, indeed, systems and control theoretic concepts and techniques can have a significant impact in systems and synthetic biology. Volume II contains chapters contributed by leading researchers in the field of systems and synthetic biology that concern modeling physiological processes and bottom-up constructions of scalable biological systems. The modeling problems include characterisation and synthesis of memory, understanding how homoeostasis is maintained in the face of shocks and relatively gradual perturbations, understanding the functioning and robustness of biological clocks such as those at the core of circadian rhythms, and understanding how the cell cycles can be regulated, among others. Some of the bottom-up construction problems investigated in Volume II are as follows: How should biomacromolecules, platforms, and scalable architectures be chosen and synthesised in order to build programmable de novo biological systems? What are the types of constrained optimisation problems encountered in this process and how can these be solved efficiently? As the eminent computer scientist Donald Knuth put it, "biology easily has 500 years of exciting problems to work on". This edited book presents but a small fraction of those for the benefit of (1) systems and control theorists interested in molecular and cellular biology and (2) biologists interested in rigorous modelling, analysis and control of biological systems.

This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to reusable, adaptable and scalable code fragments. This book also serves as a GPU implementation manual for many numerical algorithms, sharing tips on GPUs that can increase application efficiency. The valuable insights into parallelization strategies for GPUs are supplemented by ready-to-use code fragments. Numerical Computations with GPUs targets professionals and researchers working in high performance computing and GPU programming. Advanced-level students focused on computer science and mathematics will also find this book useful as secondary text book or reference.

This is the first book to present a comprehensive treatment of the mathematical physics of quantum wires and devices. The focus is on the recent results in the area of the spectral theory of bent and deformed quantum wires, simple quantum devices, Anderson localization, the quantum Hall effect and graphical models for quantum wire systems. The Selberg trace formula for finite volume graphical models is reviewed. Examples and relationships to recent work on acoustic and fluid flow, trapped states and spectral resonances, quantum chaos, random matrix theory, spectral statistics, point interactions, photonic crystals, Landau models, quantum transistors, edge states and metal-insulator transitions are developed. Problems related to modeling open quantum devices are discussed. The research of Exner and co-workers in quantum wires, Stollmann, Figotin, Bellissard et al. in the area of Anderson localization and the quantum Hall effect, and Bird, Ferry, Berggren and others in the area of quantum devices and their modeling is surveyed. The work on finite volume graphical models is interconnected to recent work on Ramanujan graphs and diagrams, the Phillips-Sarnak conjectures, L-functions and scattering theory. Audience: This book will be of use to physicists, mathematicians and engineers interested in quantum wires, quantum devices and related mesoscopic systems.

This book is a comprehensive presentation of recent results and developments on several widely used transforms and their fast algorithms. In many cases, new options are provided for improved or new fast algorithms, some of which are not well known in the digital signal processing community. The book is suitable as a textbook for senior undergraduate and graduate courses in digital signal processing. It may also serve as an excellent self-study reference for electrical engineers and applied mathematicians whose work is related to the fields of electronics, signal processing, image and speech processing, or digital design and communication.

This is the second volume of a comprehensive two-volume treatment of mechanics intended for students of civil and mechanical engineering. Used for several years in courses at Bradley university, the text presents dynamics in a clear and straightforward way and emphasizes problem solving. More than 350 examples clarify the discussion. The diskette included with the book contains EnSolve, a program written by the authors for solving problems in engineering mechanics. The program runs on Macintosh and PC-DOS computers and includes the following: - a unit converter for SI to US units and vice versa - a graphics program for plotting functions and data - a set of numerical subroutines The graphics module will, among other features, fit smooth splines between data, plot regression lines and curves, and change scales ß including from arithmetic to log and log-log. The numerical routines will, for example, find roots of polynomials, solve systems of equations, invert matrices, differentiate and integrate, and solve boundary-value problems.

This edition of the invaluable text Modern Differential Geometry for Physicists contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made.These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Quantum Fields and Fundamental Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory.The volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry.

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved."

This textbook on computational statistics presents tools and concepts of univariate and multivariate statistical data analysis with a strong focus on applications and implementations in the statistical software R. It covers mathematical, statistical as well as programming problems in computational statistics and contains a wide variety of practical examples. In addition to the numerous R sniplets presented in the text, all computer programs (quantlets) and data sets to the book are available on GitHub and referred to in the book. This enables the reader to fully reproduce as well as modify and adjust all examples to their needs. The book is intended for advanced undergraduate and first-year graduate students as well as for data analysts new to the job who would like a tour of the various statistical tools in a data analysis workshop. The experienced reader with a good knowledge of statistics and programming might skip some sections on univariate models and enjoy the various ma thematical roots of multivariate techniques. The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allows readers to reproduce the tables, pictures and calculations inside this Springer book.

This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.

A modern information retrieval system must have the capability to find, organize and present very different manifestations of information - such as text, pictures, videos or database records - any of which may be of relevance to the user. However, the concept of relevance, while seemingly intuitive, is actually hard to define, and it's even harder to model in a formal way.

Lavrenko does not attempt to bring forth a new definition of relevance, nor provide arguments as to why any particular definition might be theoretically superior or more complete. Instead, he takes a widely accepted, albeit somewhat conservative definition, makes several assumptions, and from them develops a new probabilistic model that explicitly captures that notion of relevance. With this book, he makes two major contributions to the field of information retrieval: first, a new way to look at topical relevance, complementing the two dominant models, i.e., the classical probabilistic model and the language modeling approach, and which explicitly combines documents, queries, and relevance in a single formalism; second, a new method for modeling exchangeable sequences of discrete random variables which does not make any structural assumptions about the data and which can also handle rare events.

Thus his book is of major interest to researchers and graduate students in information retrieval who specialize in relevance modeling, ranking algorithms, and language modeling.

Many large-scale projects for detecting gravitational radiation are currently being developed, all with the aim of opening a new window onto the observable Universe. As a result, numerical relativity has recently become a major field of research, and Elements of Numerical Relativity and Relativistic Hydrodynamics is a valuable primer for both graduate students and non-specialist researchers wishing to enter the field.

A revised and significantly enlarged edition of LNP 673 Elements of Numerical Relativity, this book starts with the most basic insights and aspects of numerical relativity before it develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism; gauge, initial, and boundary conditions; and various numerical algorithms. And in addition to many revisions, it includes new, convenient damping terms for numerical implementations, a presentation of the recently-developed harmonic formalism, and an extensive, new chapter on matter space-times, containing a thorough introduction to relativistic hydrodynamics.

While proper reference is given to advanced applications requiring large computational resources, most tests and applications in this book can be performed on a standard PC.

Bayesian networks currently provide one of the most rapidly growing areas of research in computer science and statistics. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. Each of the twelve chapters is self-contained.

Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Graduate students since it shows the direction of current research.

"Paradox" conjures up arrows and tortoises. But it has a speculative, gedanken ring: no one would dream of really conjuring up Achilles to confirm that he catches the tortoise. The paradox of Einstein, Podolsky, and Rosen, however, is capable of empirical test. Attempted experimental resolutions have involved photons, but these are not detected often enough to settle the matter. Kaons are easier to detect and will soon be used to discriminate between quantum mechanics and local realism. The existence ofan objective physical reality, which had disappeared behind the impressive formalism of quantum mechanics, was originally intended to be the central issue of the paradox; locality, like the mathematics used, was just assumed to hold. Quantum mechanics, with its incompatible measurements, was born rather by chance in an atmosphere of great positivistic zeal, in which only the obviously measurable had scientific respectability. Speculation about occult "unobservable" quantities was viewed as vacuous metaphysics, which should surely form no part of a mature scientific attitude. Soon the "unmeasurable, " once only disreputable, vanished altogether. One had first been told not to worry about it; then, as dogma got more carefully defined, one was assured that the unobserved was just not there. This made it easier not to think about it and to avoid hazardous metaphysical temptation.

This book presents a first attempt to systematically collect, classify and solve various continuous-time scheduling problems. The classes of problems distinguish scheduling by the number of machines and products, production constraints and performance measures. Although such classes are usually considered to be a prerogative of only combinatorial scheduling literature, the scheduling methodology suggested in this book is based on two mathematical tools - optimal control and combinatorics. Generally considered as belonging to two totally different areas of research and application, these seemingly irreconcilable tools can be integrated in a unique solution approach with the advantages of both. This new approach provides the possibility of developing effective polynomial-time algorithms to solve the generic scheduling problems. This book is aimed at a student audience - final year undergraduates as well as master and Ph.D. students, primarily in Operations Research, Management, Industrial Engineering and Control Systems. Indeed, some of the material in the book has formed part of the content of undergraduate and graduate courses taught at the Industrial Engineering Department of Tel-Aviv University, the Logistics Department of Bar-Ilan University and the Technology Management Department of Rolon Center for Technological Education, Israel. The book is also useful for practicing engineers interested in planning, scheduling and optimization methods. Since the book addresses the theory and design of computer-based scheduling algorithms, applied mathematicians and computer software specialists engaged in developing scheduling software for industrial engineering and management problems will find that the methods developed here can be embedded very efficiently in large applications.

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.

Nonsmoothness and nonconvexity arise in numerous applications of mechan- ics and modeling due to the need for studying more and more complicated phe- nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap- plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon- vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex- pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size."

This text explains how advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers such topics as: the variations of the windowed Fourier transform; constructions of special waveforms suitable for specific tasks; the use of redundant representations in reconstruction and enhancement; applications of efficient numerical compression as a tool for fast numerical analysis; and approximation properties of various waveforms in different contexts.

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three "M's" Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.