Primary Audience for the Book * Specialists in numerical computations who are interested in algorithms with automatic result verification. * Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. * Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.

This book analyses quantitative open source software (OSS) reliability assessment and its applications, focusing on three major topic areas: the Fundamentals of OSS Quality/Reliability Measurement and Assessment; the Practical Applications of OSS Reliability Modelling; and Recent Developments in OSS Reliability Modelling. Offering an ideal reference guide for graduate students and researchers in reliability for open source software (OSS) and modelling, the book introduces several methods of reliability assessment for OSS including component-oriented reliability analysis based on analytic hierarchy process (AHP), analytic network process (ANP), and non-homogeneous Poisson process (NHPP) models, the stochastic differential equation models and hazard rate models. These measurement and management technologies are essential to producing and maintaining quality/reliable systems using OSS.

This is the 9th volume in Avner Friedman's collection of Mathematics in Industrial problems. This book aims to foster interaction between industry and mathematics at the "grass roots" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The topics explored in this volume include diffusion in porous media and in rubber/glass transition, coating flows, solvation of molecules, semiconductor processing, optoelectronics, photographic images, density-functional theory, sphere packing, performance evaluation, causal networks, electrical well logging, general positioning system, sensor management, pursuit-evasion algorithms, and nonlinear viscoelasticity. Open problems and references are incorporated into most of the chapters. The final chapter contains some solutions to problems raised in earlier volumes.

Over the past 25 years, Harold and Darren Franck have investigated hundreds of accidents involving vehicles of almost every shape, size, and type imaginable. In Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, these seasoned experts demonstrate the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.

The book is anchored on basic principles of physics that may be applied to any of the above-named vehicles or equipment. Topics covered include the foundations of measurement, the various energy methods used in reconstruction, momentum methods, vehicle specifications, failure analysis, geometrical characteristics of highways, and softer scientific issues such as visibility, perception, and reaction.

The authors examine the fundamental characteristics of different vehicles, discuss the retrieval of data from crash data recorders, and review low speed impacts with an analysis of staged collisions. Finally, the book details standards and protocols for accident reconstruction.

Exploring a broad range of accident scenarios and also acknowledging the limits of applicability of the various physical methods employed, the breadth and depth of the book s coverage makes it a critical reference for engineers and scientists who perform vehicular accident reconstructions.

This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications. Key features: * An introductory chapter including a historical account of the growth of queueing theory in more than 100 years. * A modeling-based approach with emphasis on identification of models * Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics. * A chapter on matrix-analytic method as an alternative to the traditional methods of analysis of queueing systems. * A comprehensive treatment of statistical inference for queueing systems. * Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. "...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition

The primary goal of this book is to present the research findings and conclusions of physicists, economists, mathematicians and financial engineers working in the field of "Econophysics" who have undertaken agent-based modelling, comparison with empirical studies and related investigations.
Most standard economic models assume the existence of the representative agent, who is "perfectly rational" and applies the utility maximization principle when taking action. One reason for this is the desire to keep models mathematically tractable: no tools are available to economists for solving non-linear models of heterogeneous adaptive agents without explicit optimization. In contrast, multi-agent models, which originated from statistical physics considerations, allow us to go beyond the prototype theories of traditional economics involving the representative agent. This book is based on the Econophys-Kolkata VII Workshop, at which many such modelling efforts were presented. In the book, leading researchers in their fields report on their latest work, consider recent developments and review the contemporary literature.

This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 18-20, 2010. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

These proceedings contain research papers presented at the 5th International Conference on Dynamics in Logistics, held in Bremen, Germany, February 2016. The conference is concerned with dynamic aspects of logistic processes and networks. The spectrum of topics reaches from modeling, planning and control of processes over supply chain management and maritime logistics to innovative technologies and robotic applications for cyber-physical production and logistic systems. The growing dynamic confronts the area of logistics with completely new challenges: it must become possible to describe, identify and analyze the process changes. Moreover, logistic processes and networks must be redevised to be rapidly and flexibly adaptable to continuously changing conditions. The book primarily addresses researchers and practitioners from the field of industrial engineering and logistics, but it may also be beneficial for graduate students.

This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

In this text, we introduce the basic concepts for the numerical modeling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

This book contains the main results of the talks given at the workshop "Recent Advances in PDEs: Analysis, Numerics and Control", which took place in Sevilla (Spain) on January 25-27, 2017. The work comprises 12 contributions given by high-level researchers in the partial differential equation (PDE) area to celebrate the 60th anniversary of Enrique Fernandez-Cara (University of Sevilla). The main topics covered here are: Control and inverse problems, Analysis of Fluid mechanics and Numerical Analysis. The work is devoted to researchers in these fields.

In 1965 Juris Hartmanis and Richard E. Stearns published a paper "On the Computational Complexity of Algorithms." The field of complexity theory takes its name from this seminal paper and many of the major concepts and issues of complexity theory were introduced by Hartmanis in subsequent work. In honor of the contribution of Juris Hartmanis to the field of complexity theory, a special session of invited talks by Richard E. Stearns, Allan Borodin and Paul Young was held at the third annual meeting of the Structure in Complexity conference, and the first three chapters of this book are the final versions of these talks. They recall intellectual and professional trends in Hartmanis' contributions. All but one of the remainder of the chapters in this volume originated as a presentation at one of the recent meetings of the Structure in Complexity Theory Conference and appeared in preliminary form in the conference proceedings. In all, these expositions form an excellent description of much of contemporary complexity theory.

No more than about 10 years ago, it seemed to be unrealistic to simulate the com plex flow, transport, and transformation processes of organic compounds in multi-phase systems of water-unsaturated soils (Schwille Sch84]). Numerical solutions of compre hensive models consisting, for instance, of a system of three partial differential equations and chemical reactions based on local thermodynamic equilibrium assumption (Abriola and Pinder AP85a]), were at that time regarded as far too computational expensive; optimizations seemed to be by far not practicable using such numerical models. How ever, even more complex mathematical models have been developed since then, like, for example, by considering the temperature-dependency of processes and non-equilibrium phase-transfers, or the increase of the number of components and spatial dimensions in volved (e. g., Bear and Nitao BN92]). Those models require efficient numerical solution algorithms adopted to the possibilities of the latest computer developments. The book describes the work of a three years research project funded by the The Federal Ministry for Education, Science, Research and Technology (BMBF), Grant Number 03-H07BWM. The idea for the project was developed by Prof. Dr. Ulrich Hornung, Dr. Dirk Stegemann, and Dr. Horst H. Gerke in late 1992 after intensive discussions about the BMBF-opened program (Die anwendungsorientierte Verbundprojekte auf dem Ge biet der Mathematik des Bundesministerium fur Bildung, WissenschaJt, Forschung und Technologie) on applied mathematics in industrial areas. Dr. Stegemann worked at that time for the company GEO-data, Garbsen near Hannover."

'Et moi, ..., si j"avait su comment en revenir, One service mathematics bas rendered the je n'y seWs point alit: human race. It bas put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

Visualization technology is becoming increasingly important for medical and biomedical data processing and analysis. The interaction between visualization and medicine is one of the fastest expanding fields, both scientifically and commercially. This book discusses some of the latest visualization techniques and systems for effective analysis of such diverse, large, complex, and multi-source data.

Based on both theoretical investigations and industrial experience, this book provides an extensive approach to support the planning and optimization process for modern communication networks. The book contains a thorough survey and a detailed comparison of state-of-the-art numerical algorithms in the matrix-geometric field.

This book offers a concise introduction to morphogenetic computing, showing that its use makes global and local relations, defects in crystal non-Euclidean geometry databases with source and sink, genetic algorithms, and neural networks more stable and efficient. It also presents applications to database, language, nanotechnology with defects, biological genetic structure, electrical circuit, and big data structure. In Turing machines, input and output states form a system - when the system is in one state, the input is transformed into output. This computation is always deterministic and without any possible contradiction or defects. In natural computation there are defects and contradictions that have to be solved to give a coherent and effective computation. The new computation generates the morphology of the system that assumes different forms in time. Genetic process is the prototype of the morphogenetic computing. At the Boolean logic truth value, we substitute a set of truth (active sets) values with possible contradictions. The value of a proposition is a set of true and false values. The aim of morphogenetic computing is to use and solve the contradictions in order to transform systems to allow classical computation.

I ?rst met Jingqiao when he had just commenced his PhD research in evolutionary algorithms with Arthur Sanderson at Rensselaer. Jingqiao's goals then were the investigation and development of a novel class of se- adaptivedi?erentialevolutionalgorithms, later calledJADE. I had remarked to Jingqiao then that Arthur always appreciated strong theoretical foun- tions in his research, so Jingqiao's prior mathematically rigorous work in communications systems would be very useful experience. Later in 2007, whenJingqiaohadcompletedmostofthetheoreticalandinitialexperimental work on JADE, I invited him to spend a year at GE Global Research where he applied his developments to several interesting and important real-world problems. Most evolutionary algorithm conferences usually have their share of in- vative algorithm oriented papers which seek to best the state of the art - gorithms. The best algorithms of a time-frame create a foundation for a new generationof innovativealgorithms, and so on, fostering a meta-evolutionary search for superior evolutionary algorithms. In the past two decades, during whichinterest andresearchin evolutionaryalgorithmshavegrownworldwide by leaps and bounds, engaging the curiosity of researchers and practitioners frommanydiversescienceandtechnologycommunities, developingstand-out algorithms is getting progressively harder.

Dynamical models on graphs or random graphs are increasingly used in applied sciences as mathematical tools to study complex systems whose exact structure is too complicated to be known in detail. Besides its importance in applied sciences, the field is increasingly attracting the interest of mathematicians and theoretical physicists also because of the fundamental phenomena (synchronization, phase transitions etc.) that can be studied in the relatively simple framework of dynamical models of random graphs. This volume was developed from the Mathematical Technology of Networks conference held in Bielefeld, Germany in December 2013. The conference was designed to bring together functional analysts, mathematical physicists, and experts in dynamical systems. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs. Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures.

This volume gives a survey on mathematical and computational methods in image registration. During the last year sophisticated numerical models for registration and efficient numerical methods have been proposed. Many of them are contained in this volume. The book also summarizes the state-of-the-art in mathematical and computational methods in image registration. In addition, it covers some practical applications and new directions with industrial relevance in data processing.

Environmental science (ecology, conservation, and resource management) is an increasingly quantitative field. A well-trained ecologist now needs to evaluate evidence generated from complex quantitative methods, and to apply these methods in their own research. Yet the existing books and academic coursework are not adequately serving most of the potential audience - instead they cater to the specialists who wish to focus on either mathematical or statistical aspects, and overwhelmingly appeal to those who already have confidence in their quantitative skills. At the same time, many texts lack an explicit emphasis on the epistemology of quantitative techniques. That is, how do we gain understanding about the real world from models that are so vastly simplified? This accessible textbook introduces quantitative ecology in a manner that aims to confront these limitations and thereby appeal to a far wider audience. It presents material in an informal, approachable, and encouraging manner that welcomes readers with any degree of confidence and prior training. It covers foundational topics in both mathematical and statistical ecology before describing how to implement these concepts to choose, use, and analyse models, providing guidance and worked examples in both spreadsheet format and R. The emphasis throughout is on the skilful interpretation of models to answer questions about the natural world. Introduction to Quantitative Ecology is suitable for advanced undergraduate students and incoming graduate students, seeking to strengthen their understanding of quantitative methods and to apply them successfully to real world ecology, conservation, and resource management scenarios.

This book highlights relevant studies and applications in the area of robotics, which reflect the latest research, from interdisciplinary theoretical studies and computational algorithm development, to representative applications. It presents chapters on advanced control, such as fuzzy, neural, backstepping, sliding mode, adaptive, predictive, diagnosis and fault tolerant control etc. and addresses topics including cloud robotics, cable-driven robots, two-wheeled robots, mobile robots, swarm robots, hybrid vehicle, and drones. Each chapter employs a uniform structure: background, motivation, quantitative development (equations), case studies/illustration/tutorial (simulations, experiences, curves, tables, etc.), allowing readers to easily tailor the techniques to their own applications.

This monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.

Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black-Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.