Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior.

Thetopics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful referencetext forapplied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems."

Knowledge acquisition is one of the most important aspects influencing the quality of methods used in artificial intelligence and the reliability of expert systems. The various issues dealt with in this volume concern many different approaches to the handling of partial knowledge and to the ensuing methods for reasoning and decision making under uncertainty, as applied to problems in artificial intelligence. The volume is composed of the invited and contributed papers presented at the Workshop on Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, held at the Ettore Majorana Center for Scientific Culture of Erice (Sicily, Italy) on June 19-25, 1994, in the framework of the International School of Mathematics "G.Stampacchia." It includes also a transcription of the roundtable held during the workshop to promote discussions on fundamental issues, since in the choice of invited speakers we have tried to maintain a balance between the various schools of knowl edge and uncertainty modeling. Choquet expected utility models are discussed in the paper by Alain Chateauneuf: they allow the separation of perception of uncertainty or risk from the valuation of outcomes, and can be of help in decision mak ing. Petr Hajek shows that reasoning in fuzzy logic may be put on a strict logical (formal) basis, so contributing to our understanding of what fuzzy logic is and what one is doing when applying fuzzy reasoning."

The correlations between physical systems provide significant information about their collective behaviour - information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated 'resource' is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.

Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design.

After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks.

In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids.

In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures.

This book is part of a series on Mathematics for Industry and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications."

This book is addressed to scientists, engineers and students of engineering departments, who make use of modelling and computer simulation. Since more and more physical experiments are being replaced by computer simulations the use of mathematical models of various engineering systems has become an especially important area of research. The book is devoted to selected problems of various engineering domains, such as control, electrical engineering or electrical metrology. They are based on different mathematical fields such as matrix theory, differential equations, function approximation with applications in dynamic modelling, methods of simplifying high-order models, determining mapping errors of simplified models, their optimization and the synthesis of suitable input signals. The book is easy to read and understand because all the needed mathematical transformations and formula are derived and explained by means of the examples enclosed.

This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework. This book presents the first treatment of optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution.It is also the first to make use of the concepts of epi-convergence and optimality functions in the construction of consistent approximations to infinite dimensional problems.

Presenting techniques, case-studies and methodologies that combine the use of simulation approaches with optimization techniques for facing problems in manufacturing, logistics, or aeronautical problems, this book provides solutions to common industrial problems in several fields, which range from manufacturing to aviation problems, where the common denominator is the combination of simulation's flexibility with optimization techniques' robustness. Providing readers with a comprehensive guide to tackle similar issues in industrial environments, this text explores novel ways to face industrial problems through hybrid approaches (simulation-optimization) that benefit from the advantages of both paradigms, in order to give solutions to important problems in service industry, production processes, or supply chains, such as scheduling, routing problems and resource allocations, among others.

This book gives an overview of the state of the art in five different approaches to social science simulation on the individual level. The volume contains microanalytical simulation models designed for policy implementation and evaluation, multilevel simulation methods designed for detecting emergent phenomena, dynamical game theory applications, the use of cellular automata to explain the emergence of structure in social systems, and multi-agent models using the experience from distributed artificial intelligence applied to special phenomena. The book collects the results of an international conference which brought together social scientists and computer scientists both engaged in a wide range of simulation approaches for the first time.

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be usefulfor not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science.

Accelerated degradation of soils and surface waters produce increasing problems in many parts of the world. Within this context, the book addresses the topic Application of Physically Based Soil Erosion Models in order to present some essential tools for improving land-use strategies and conservation measures. Over the last 20 years, the need for more accurate assessments of soil losses and sediment yields has led to the development of some highly complex, process-based soil erosion models. In 14 papers, specialists from 5 European countries, the USA and Brazil report on practical applications of these models and give insight into the latest developments. This book will help to implement state-of-the-art soil erosion prediction technologies within soil and water conservation planning and assessment. Hence, the book should be of special interest to agricultural and environmental engineers, hydrologists, soil scientists and geoscientists.

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research. The tools covered in this book allow the reader to develop physics-based mathematical models for a variety of flows, including attached and separated flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book covers all of the ingredients of these models: the solution of potential flows about arbitrary body shapes in two- and three-dimensional contexts, with a particular focus on conformal mapping in the plane; the decomposition of the flow into contributions from ambient vorticity and body motion; generalized edge conditions, of which the Kutta condition is a special case; and the calculation of force and moment, with extensive treatments of added mass and the influence of fluid vorticity. The book also contains an extensive primer with all of the necessary mathematical tools. The concepts are demonstrated on several example problems, both classical and modern.

This award-winning thesis investigates the mechanisms underlying cardiac arrhythmia development and termination from an entirely new perspective. By viewing the heart as a complex system, the author uses theoretical tools from nonlinear dynamics combined with numerical simulations and experiments to achieve insights into the relationship between its structure and dynamics, thereby paving the way towards innovative low-energy defibrillation strategies. The work tackles, among other things: the effect of substrate heterogeneity on the spatial-temporal dynamics of cardiac arrhythmias and ways in which weak pulsed electric fields can be used to control these dynamics in heterogeneous cardiac tissue. The long-term vision of this research is to replace the current strategy of applying painful and sometimes tissue damaging electric shock - currently the only reliable way to terminate life-threatening fibrillation - by a more subtle but equally effective intervention. The book maps out a number of promising research directions for biophysicists and medical researchers working on the origins and treatment of cardiac arrhythmias.

This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author's original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

This book reports on advanced theories and cutting-edge applications in the field of soft computing. The individual chapters, written by leading researchers, are based on contributions presented during the 4th World Conference on Soft Computing, held May 25-27, 2014, in Berkeley. The book covers a wealth of key topics in soft computing, focusing on both fundamental aspects and applications. The former include fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation and neural networks, while the latter include soft computing in data analysis, image processing, decision-making, classification, series prediction, economics, control, and modeling. By providing readers with a timely, authoritative view on the field, and by discussing thought-provoking developments and challenges, the book will foster new research directions in the diverse areas of soft computing.

In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.

Self-organizing maps (SOM) have proven to be of significant economic value in the areas of finance, economic and marketing applications. As a result, this area is rapidly becoming a non-academic technology. This book looks at near state-of-the-art SOM applications in the above areas, and is a multi-authored volume, edited by Guido Deboeck, a leading exponent in the use of computational methods in financial and economic forecasting, and by the originator of SOM, Teuvo Kohonen. The book contains chapters on applications of unsupervised neural networks using Kohonen's self-organizing map approach.

The book examines the performance and optimization of systems where queueing and congestion are important constructs. Both finite and infinite queueing systems are examined. Many examples and case studies are utilized to indicate the breadth and depth of the queueing systems and their range of applicability. Blocking of these processes is very important and the book shows how to deal with this problem in an effective way and not only compute the performance measures of throughput, cycle times, and WIP but also to optimize the resources within these systems. The book is aimed at advanced undergraduate, graduate, and professionals and academics interested in network design, queueing performance models and their optimization. It assumes that the audience is fairly sophisticated in their mathematical understanding, although the explanations of the topics within the book are fairly detailed.

... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/: " "Oil CO/lll , IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple .... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX."

The present book fmds its roots in the International Conference on Methods and Applications of Multiple Criteria Decision Making held in Mons in May 1997. A small number of contributions to that conference were selected via a refereeing procedure and retained authors were requested to include in their final version their more recent results. This explains why some papers differ significantly from the original presentation. The introductory paper of Raynaud addresses the long range forecasts in Multiple Criteria Decision Making on the basis of a Delphi process that was run before and during the congress. In a second part, the French author explains how he and some of his partners could find the proof of an important conjecture : the iteration of a strongly monotonic choice function is not a strongly monotonic ranking function. The second part of the book covers methodological aspects of decision theory. The contribution of Bouyssou and Pirlot concerns the reformulation of classical conjoint measurement models that induce a complete and transitive preference binary relation on the set of alternatives which seem to be unrealistic when decision makers are asked to compare objects evaluated on several attributes. The authors propose to consider non transitive, non complete and non additive decomposable conjoint models. They define properties that characterize such models.

The book surveys the state-of-the-art methods that are currently available to model and simulate the presence of rigid particles in a fluid flow. For particles that are very small relative to the characteristic flow scales and move without interaction with other particles, effective equations of motion for particle tracking are formulated and applied (e.g. in gas-solid flows). For larger particles, for particles in liquid-solid flows and for particles that interact with each other or possibly modify the overall flow detailed model are presented. Special attention is given to the description of the approximate force coupling method (FCM) as a more general treatment for small particles, and derivations in the context of low Reynolds numbers for the particle motion as well as application at finite Reynolds numbers are provided. Other topics discussed in the book are the relation to higher resolution immersed boundary methods, possible extensions to non-spherical particles and examples of applications of such methods to dispersed multiphase flows.

This book contains revised and extended research articles written by prominent researchers participating in the international conference on Advances in Engineering Technologies and Physical Science ("London, U.K., 3-5 July, 2013)." Topics covered include mechanical engineering, bioengineering, internet engineering, image engineering, wireless networks, knowledge engineering, manufacturing engineering, and industrial applications. The book offers state of art of tremendous advances in engineering technologies and physical science and applications, and also serves as an excellent reference work for researchers and graduate students working with/on engineering technologies and physical science.

The aim of this book is to present a rigorous phenomenological and mathematical formulation of sedimentation processes and to show how this theory can be applied to the design and control of continuous thickeners. The book is directed to stu dents and researchers in applied mathematics and engineering sciences, especially in metallurgical, chemical, mechanical and civil engineering, and to practicing en gineers in the process industries. Such a vast and diverse audience should read this book differently. For this reason we have organized the chapters in such a way that the book can be read in two ways. Engineers and engineering students will find a rigorous formulation of the mathematical model of sedimentation and the exact and approximate solutions for the most important problems encountered in the laboratory and in industry in Chapters 1 to 3, 7 and 8, and 10 to 12, which form a self-contained subject. They can skip Chapters 4 to 6 and 9, which are most important to applied mathematicians, without losing the main features of sedimentation processes. On the other hand, applied mathematicians will find special interest in Chapters 4 to 6 and 9 which show some known but many recent results in the field of conservation laws of quasilinear hyperbolic and degenerate parabolic equations of great interest today. These two approaches to the theory keep their own styles: the mathematical approach with theorems and proofs, and the phenomenological approach with its deductive technique."

This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications.