A unique interdisciplinary foundation for real-world problem solving

Stochastic search and optimization techniques are used in a vast number of areas, including aerospace, medicine, transportation, and finance, to name but a few. Whether the goal is refining the design of a missile or aircraft, determining the effectiveness of a new drug, developing the most efficient timing strategies for traffic signals, or making investment decisions in order to increase profits, stochastic algorithms can help researchers and practitioners devise optimal solutions to countless real-world problems.

Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control is a graduate-level introduction to the principles, algorithms, and practical aspects of stochastic optimization, including applications drawn from engineering, statistics, and computer science. The treatment is both rigorous and broadly accessible, distinguishing this text from much of the current literature and providing students, researchers, and practitioners with a strong foundation for the often-daunting task of solving real-world problems.

The text covers a broad range of today’s most widely used stochastic algorithms, including:

• Random search
• Recursive linear estimation
• Stochastic approximation
• Simulated annealing
• Genetic and evolutionary methods
• Machine (reinforcement) learning
• Model selection
• Simulation-based optimization
• Markov chain Monte Carlo
• Optimal experimental design

The book includes over 130 examples, Web links to software and data sets, more than 250 exercises for the reader, and an extensive list of references. These features help make the text an invaluable resource for those interested in the theory or practice of stochastic search and optimization.

Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric).

The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval.

Unique features include:
* The use of graphics to illustrate the fractal view of these spaces;
* Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology;
* A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings;
* Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature.

This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study - the interested reader will find many relevant open problems which will create further research into these topics.

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. In particular, emphasis is placed onlaying the foundationfor solvingproblemsin reliability, insurance, finance, and credit risk.

The material has been carefully selected to cover the basic concepts and techniques on each topic, making this an ideal introductory gateway to more advanced learning. With exercises and solutions to selected problems accompanying each chapter, this textbook is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics."

This second edition sees the light three years after the first one: too short a time to feel seriously concerned to redesign the entire book, but sufficient to be challenged by the prospect of sharpening our investigation on the working of econometric dynamic models and to be inclined to change the title of the new edition by dropping the "Topics in" of the former edition. After considerable soul searching we agreed to include several results related to topics already covered, as well as additional sections devoted to new and sophisticated techniques, which hinge mostly on the latest research work on linear matrix polynomials by the second author. This explains the growth of chapter one and the deeper insight into representation theorems in the last chapter of the book. The role of the second chapter is that of providing a bridge between the mathematical techniques in the backstage and the econometric profiles in the forefront of dynamic modelling. For this purpose, we decided to add a new section where the reader can find the stochastic rationale of vector autoregressive specifications in econometrics. The third (and last) chapter improves on that of the first edition by re- ing the fruits of the thorough analytic equipment previously drawn up."

This book presents the textile-, mathematical and mechanical background for the modelling of fiber based structures such as yarns, braided and knitted textiles. The hierarchical scales of these textiles and the structural elements at the different levels are analysed and the methods for their modelling are presented. The author reports about problems, methods and algorithms and possible solutions from his twenty year experience in the modelling and software development of CAD for textiles.

Over the last decades Discrete Event Simulation has conquered many different application areas. This trend is, on the one hand, driven by an ever wider use of this technology in different fields of science and on the other hand by an incredibly creative use of available software programs through dedicated experts. This book contains articles from scientists and experts from 10 countries. They illuminate the width of application of this technology and the quality of problems solved using Discrete Event Simulation. Practical applications of simulation dominate in the present book. The book is aimed to researchers and students who deal in their work with Discrete Event Simulation and which want to inform them about current applications. By focusing on discrete event simulation, this book can also serve as an inspiration source for practitioners for solving specific problems during their work. Decision makers who deal with the question of the introduction of discrete event simulation for planning support and optimization this book provides a contribution to the orientation, what specific problems could be solved with the help of Discrete Event Simulation within the organization.

The book provides a generalized theoretical technique for solving the fewbody Schroedinger equation. Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles. The introduction of Jacobi vectors, hyperspherical variables and hyperspherical harmonics as an expansion basis is an elegant way to tackle systematically the problem of an increasing number of interacting particles. Analytic expressions for hyperspherical harmonics, appropriate symmetrisation of the wave function under exchange of identical particles and calculation of matrix elements of the interaction have been presented. Applications of this technique to various problems of physics have been discussed. In spite of straight forward generalization of the mathematical tools for increasing number of particles, the method becomes computationally difficult for more than a few particles. Hence various approximation methods have also been discussed. Chapters on the potential harmonics and its application to Bose-Einstein condensates (BEC) have been included to tackle dilute system of a large number of particles. A chapter on special numerical algorithms has also been provided. This monograph is a reference material for theoretical research in the few-body problems for research workers starting from advanced graduate level students to senior scientists.

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in od, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative study of a dissipative system; chaos of postural sway in humans; oscillators with fractional derivatives; controlling chaos via bifurcation diagrams; theories relating to optical choppers with rotating wheels; dynamics in expert systems; shooting methods for non-standard boundary value problems; automatic sleep scoring governed by delay differential equations; isochronous oscillations; the aerodynamics pendulum and its limit cycles; constrained N-body problems; nano-fractal oscillators and dynamically-coupled dry friction."

The spectral theory of linear operators in Hilbert spaces is the most important tool in the mathematical formulation of quantum mechanics; in fact, linear ope- tors and quantum mechanics have had a symbiotic relationship. However, typical physicstextbooks on quantum mechanics givejust a roughsketch of operator t- ory, occasionallytreating linear operatorsas matricesin ?nite-dimensional spaces; the implicit justi?cation is that the details of the theory of unbounded operators are involved and those texts are most interested in applications. Further, it is also assumed that mathematical intricacies do not show up in the models to be d- cussedorareskippedby"heuristicarguments. "Inmanyoccasionssomequestions, such as the very de?nition of the hamiltonian domain, are not touched, leaving an open door for controversies, ambiguities and choices guided by personal tastes and ad hoc prescriptions. All in all, sometimes a blank is left in the mathematical background of people interested in nonrelativistic quantum mechanics. Quantum mechanics was the most profound revolution in physics; it is not natural to our common sense (check, for instance, the wave-particle duality) and the mathematics may become crucial when intuition fails. Even some very simple systemspresentnontrivialquestionswhoseanswersneedamathematicalapproach. For example, the Hamiltonian of a quantum particle con?ned to a box involves a choice of boundary conditions at the box ends; since di?erent choices imply di?erentphysicalmodels, studentsshouldbeawareofthebasicdi?cultiesintrinsic tothis(inprinciple)verysimple model, aswellasinmoresophisticatedsituations. The theory of linear operators and their spectra constitute a wide ?eld and it is expected that the selection of topics in this book will help to ?ll this theoretical gap. Ofcoursethisselectionisgreatlybiasedtowardthepreferencesofthe author.

This book gives a wide-ranging description of the many facets of complex dynamic networks and systems within an infrastructure provided by integrated control and supervision: envisioning, design, experimental exploration, and implementation. The theoretical contributions and the case studies presented can reach control goals beyond those of stabilization and output regulation or even of adaptive control. Reporting on work of the Control of Complex Systems (COSY) research program, Complex Systems follows from and expands upon an earlier collection: Control of Complex Systems by introducing novel theoretical techniques for hard-to-control networks and systems. The major common feature of all the superficially diverse contributions encompassed by this book is that of spotting and exploiting possible areas of mutual reinforcement between control, computing and communications. These help readers to achieve not only robust stable plant system operation but also properties such as collective adaptivity, integrity and survivability at the same time retaining desired performance quality. Applications in the individual chapters are drawn from: * the general implementation of model-based diagnosis and systems engineering in medical technology, in communication, and in power and airport networks; * the creation of biologically inspired control brains and safety-critical human-machine systems, * process-industrial uses; * biped robots; * large space structures and unmanned aerial vehicles; and * precision servomechanisms and other advanced technologies. Complex Systems provides researchers from engineering, applied mathematics and computer science backgrounds with innovative theoretical and practical insights into the state-of-the-art of complex networks and systems research. It employs physical implementations and extensive computer simulations. Graduate students specializing in complex-systems

This monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.

This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference "Optimization and Its Applications in Control and Data Science" dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015. This book reflects developments in theory and applications rooted by Professor Polyak's fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each paper focuses on techniques for solving complex optimization problems in different application areas and recent developments in optimization theory and methods. Open problems in optimization, game theory and control theory are included in this collection which will interest engineers and researchers working with efficient algorithms and software for solving optimization problems in market and data analysis. Theoreticians in operations research, applied mathematics, algorithm design, artificial intelligence, machine learning, and software engineering will find this book useful and graduate students will find the state-of-the-art research valuable.

This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11-14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

The papers in this volume present rules for mechanical models in a general systematic way, always in combination with small and large examples, many from industry, illustrating the most important features of modeling. The best way to reach a good solution is discussed. The papers address researchers and engineers from academia and from industry, doctoral students and postdocs, working in the fields of mechanical, civil and electrical engineering as well as in fields like applied physics or applied mathematics.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year's special focus is on Voronoi diagrams and their applications, celebrating the 150th birthday of G.F. Voronoi. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

This volume features key contributions from the International Conference on Pattern Recognition Applications and Methods, (ICPRAM 2012,) held in Vilamoura, Algarve, Portugal from February 6th-8th, 2012. The conference provided a major point of collaboration between researchers, engineers and practitioners in the areas of Pattern Recognition, both from theoretical and applied perspectives, with a focus on mathematical methodologies. Contributions describe applications of pattern recognition techniques to real-world problems, interdisciplinary research, and experimental and theoretical studies which yield new insights that provide key advances in the field. This book will be suitable for scientists and researchers in optimization, numerical methods, computer science, statistics and for differential geometers and mathematical physicists.

Cognitive Informatics (CI) is the science of cognitive information processing and its applications in cognitive computing. CI is a transdisciplinary enquiry of computer science, information science, cognitive science, and intelligence science that investigates into the internal information processing mechanisms and processes of the brain. Advances and engineering applications of CI have led to the emergence of cognitive computing and the development of Cognitive Computers (CCs) that reason and learn. As initiated by Yingxu Wang and his colleagues, CC has emerged and developed based on the transdisciplinary research in CI, abstract intelligence (aI), and denotational mathematics after the inauguration of the series of IEEE International Conference on Cognitive Informatics since 2002 at Univ. of Calgary, Stanford Univ., and Tsinghua Univ., etc. This volume in LNCS (subseries of Computational Intelligence), LNCI 323, edited by Y. Wang, D. Zhang, and W. Kinsner, presents the latest development in cognitive informatics and cognitive computing. The book focuses on the explanation of cognitive models of the brain, the layered reference model of the brain, the fundamental mechanisms of abstract intelligence, and the implementation of computational intelligence by autonomous inference and learning engines based on CCs.

A guide to stochastic calculus as the basis behind mathematical finance An increasingly popular field of study at universities and an essential skill for investment bank employees, mathematical finance has changed dramatically in recent years, but its roots remain in stochastic calculus. Problems and Solutions in Mathematical Finance: Volume 1 provides a comprehensive explanation of stochastic calculus and probability theory focusing on their relationship with mathematical finance. Quantitative analysts Dr. Eric Chin and Dian Nel and Professor Sverrir Olafsson portray stochastic calculus' role in generating partial differentiation equations for pricing options and constructing probability measures in conjunction with martingale theory. Mathematical and computational finance rely on computational intelligence, numerical methods, and computer simulations to make trading, hedging, and investment decisions, to determine the risk of those decisions, and to define price derivatives. -Includes chapter-by-chapter introduction of the fundamental tenets, essential definitions, and detailed explanations needed to solve financial problems -Offers advice from experts in price testing methodologies, model calibration, energy markets, hedging in incomplete markets, and risk management Problems and Solutions in Mathematical Finance: Volume 1 functions as either an independent information text or a study supplement for students and practitioners eager to recover the basics of mathematical finance.

The analysis of experimental data is at heart of science from its beginnings.
But it was the advent of digital computers that allowed the execution of highly non-linear and increasingly complex data analysis procedures - methods that were completely unfeasible before. Non-linear curve fitting, clustering and machine learning belong to these modern techniques which are a further step towards computational intelligence.

The goal of this book is to provide an interactive and illustrative guide to these topics. It concentrates on the road from two dimensional curve fitting to multidimensional clustering and machine learning with neural networks or support vector machines. Along the way topics like mathematical optimization or evolutionary algorithms are touched. All concepts and ideas are outlined in a clear cut manner with graphically depicted plausibility arguments and a little elementary mathematics. The major topics are extensively outlined with
exploratory examples and applications. The primary goal is to be as illustrative as possible without hiding problems and pitfalls but to address them. The character of an illustrative cookbook is complemented with specific sections that address more fundamental questions like the relation between machine learning and human intelligence. These sections may be skipped without affecting
the main road but they will open up possibly interesting insights beyond the mere data massage.

All topics are completely demonstrated with the aid of the commercial computing platform Mathematica and the Computational Intelligence Packages (CIP), a high-level function library developed with Mathematica's programming language on top of Mathematica's algorithms. CIP is open-source so the detailed code of every method is freely accessible. All examples and applications shown throughout the book may be used and customized by the reader without any
restrictions.

The target readerships are students of (computer) science and engineering as well as scientific practitioners in industry and academia who deserve an illustrative introduction to these topics. Readers with programming skills may easily port and customize the provided code.
"

With this book, distinguished and notable contributors wish to honor Professor Charles S. Tapiero s scientific achievements. Although it covers only a few of the directions Professor Tapiero has taken in his work, it presents important modern developments in theory and in diverse applications, as studied by his colleagues and followers, further advancing the topics Tapiero has been investigating. The book is divided into three parts featuring original contributions covering the following areas: general modeling and analysis; applications to marketing, economy and finance; and applications to operations and manufacturing.

Professor Tapiero is among the most active researchers in control theory; in the late sixties, he started to enthusiastically promote optimal control theory along with differential games, successfully applying it to diverse problems ranging from classical operations research models to finance, risk and insurance, marketing, transportation and operations management, conflict management and game theory, engineering, regional and urban sciences, environmental economics, and organizational behavior. Over the years, Professor Tapiero has produced over 300 papers and communications and 14 books, which have had a major impact on modern theoretical and applied research. Notable among his numerous pioneering scientific contributions are the use of graph theory in the behavioral sciences, the modeling of advertising as a random walk, the resolution of stochastic zero-sum differential games, the modeling of quality control as a stochastic competitive game, and the development of impulsive control methods in management. Charles Tapiero s creativity applies both in formulating original issues, modeling complex phenomena and solving complex mathematical problems."

This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schroedinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved.The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schroedinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schroedinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method.This book consists of two parts. Part I is the main part. The time slicing method is performed step by step in detail in Part I. The time interval is divided into small pieces. Corresponding to each division a finite-dimensional integral is constructed following Feynman's famous paper. This finite-dimensional integral is not absolutely convergent. Owing to the assumption of the potential, it is an oscillatory integral. The oscillatory integral techniques developed in the theory of partial differential equations are applied to it. It turns out that the finite-dimensional integral gives a finite definite value. The stationary phase method is applied to it. Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail.Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer. A careful discussion is required to prove the convergence of the approximate sequence as the length of each of the small subintervals tends to 0. For that purpose the book uses the stationary phase method of oscillatory integrals over a space of large dimension, of which the detailed proof is given in Part II of the book. By virtue of this method, the approximate sequence converges to the limit. This proves that the Feynman path integral converges. It turns out that the convergence occurs in a very strong topology. The fact that the limit is the fundamental solution of the Schroedinger equation is proved also by the stationary phase method. The semi-classical asymptotic formula naturally follows from the above discussion.A prerequisite for readers of this book is standard knowledge of functional analysis. Mathematical techniques required here are explained and proved from scratch in Part II, which occupies a large part of the book, because they are considerably different from techniques usually used in treating the Schroedinger equation.

Stochastic global optimization is a very important subject, that has applications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the reader's intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA is able to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

This book contains the proceedings of the 17th European Conference on Mathematics for Industry, ECMI2012, held in Lund, Sweden, July 2012, at whichECMI celebrated its 25th anniversary. It covers mathematics in a wide range of applications and methods, from circuit and electromagnetic devices, environment, fibers, flow, medicine, robotics and automotive industry, further applications to methods and education.

The book includes contributions from leading figures in business, science and academiathat promote the application of mathematics to industry and emphasize industrial sectors that offer the most exciting opportunities. The contributions reinforce the role of mathematics as being a catalyst for innovation as well as an overarching resource for industry and business.

The book features an accessible presentation of real-world problems in industry and finance, provides insight and tools for engineers and scientistswho will help them to solve similar problems and offers modeling and simulation techniques that will provide mathematicians with a source of fresh ideas and inspiration."