This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.

This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges - its effervescence with respect to fields ranging from metaphysics to computer programming - provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise remain hidden. More concretely, the book identifies and discusses a host of cases in which analytic implication can play an important role in revealing distinct problems to be facets of a larger, cross-disciplinary problem. It introduces an element of constancy and cohesion that has previously been absent in a regrettably fractured field, shoring up those who are sympathetic to the worth of mereological analogy. Moreover, it generates new interest in the field by illustrating a wide range of interesting features present in such logics - and highlighting these features to appeal to researchers in many fields.

This book is devoted to a novel conceptual theoretical framework of neuro science and is an attempt to show that we can postulate a very small number of assumptions and utilize their heuristics to explain a very large spectrum of brain phenomena. The major assumption made in this book is that inborn and acquired neural automatisms are generated according to the same func tional principles. Accordingly, the principles that have been revealed experi mentally to govern inborn motor automatisms, such as locomotion and scratching, are used to elucidate the nature of acquired or learned automat isms. This approach allowed me to apply the language of control theory to describe functions of biological neural networks. You, the reader, can judge the logic of the conclusions regarding brain phenomena that the book derives from these assumptions. If you find the argument flawless, one can call it common sense and consider that to be the best praise for a chain of logical conclusions. For the sake of clarity, I have attempted to make this monograph as readable as possible. Special attention has been given to describing some of the concepts of optimal control theory in such a way that it will be under standable to a biologist or physician. I have also included plenty of illustra tive examples and references designed to demonstrate the appropriateness and applicability of these conceptual theoretical notions for the neurosciences."

This introduction to random variables and signals provides engineering students with the analytical and computational tools for processing random signals using linear systems. It presents the underlying theory as well as examples and applications using computational aids throughout, in particular, computer-based symbolic computation programs are used for performing the analytical manipulations and the numerical calculations. The accompanying CD-ROM provides MathcadTM and MatlabTM notebooks and sheets to develop processing methods. Intended for a one-semester course for advanced undergraduate or beginning graduate students, the book covers such topics as: set theory and probability; random variables, distributions, and processes; deterministic signals, spectral properties, and transformations; and filtering, and detection theory. The large number of worked examples together with the programming aids make the book eminently suited for self study as well as classroom use.

Genetic programming (GP), one of the most advanced forms of evolutionary computation, has been highly successful as a technique for getting computers to automatically solve problems without having to tell them explicitly how. Since its inceptions more than ten years ago, GP has been used to solve practical problems in a variety of application fields. Along with this ad-hoc engineering approaches interest increased in how and why GP works. This book provides a coherent consolidation of recent work on the theoretical foundations of GP. A concise introduction to GP and genetic algorithms (GA) is followed by a discussion of fitness landscapes and other theoretical approaches to natural and artificial evolution. Having surveyed early approaches to GP theory it presents new exact schema analysis, showing that it applies to GP as well as to the simpler GAs. New results on the potentially infinite number of possible programs are followed by two chapters applying these new techniques.

This monograph studies the logical aspects of domains as used in de notational semantics of programming languages. Frameworks of domain logics are introduced; these serve as foundations for systematic derivations of proof systems from denotational semantics of programming languages. Any proof system so derived is guaranteed to agree with denotational se mantics in the sense that the denotation of any program coincides with the set of assertions true of it. The study focuses on two categories for dena tational semantics: SFP domains, and the less standard, but important, category of stable domains. The intended readership of this monograph includes researchers and graduate students interested in the relation between semantics of program ming languages and formal means of reasoning about programs. A basic knowledge of denotational semantics, mathematical logic, general topology, and category theory is helpful for a full understanding of the material. Part I SFP Domains Chapter 1 Introduction This chapter provides a brief exposition to domain theory, denotational se mantics, program logics, and proof systems. It discusses the importance of ideas and results on logic and topology to the understanding of the relation between denotational semantics and program logics. It also describes the motivation for the work presented by this monograph, and how that work fits into a more general program. Finally, it gives a short summary of the results of each chapter. 1. 1 Domain Theory Programming languages are languages with which to perform computa tion."

The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory."

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: fully worked-out examples; many carefully selected and formulated problems; fast Fourier transform methods; a thorough discussion of some important minimization methods; solution of stiff or implicit ordinary differential equations and of differential algebraic systems; modern shooting techniques for solving two-point boundary value problems; and basics of multigrid methods. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. New material on differential equations and the iterative solution of linear equations include: solving differential equations in the presence of discontinuities whose locations are not known at the outset; techniques for sensitivity analyses of differential equations dependent on additional parameters; new advanced techniques in multiple shooting; and Krylov space methods for non-symmetric systems of linear equations.

This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.

The expansion of digital data has transformed various sectors of business such as healthcare, industrial manufacturing, and transportation. A new way of solving business problems has emerged through the use of machine learning techniques in conjunction with big data analytics. Deep Learning Innovations and Their Convergence With Big Data is a pivotal reference for the latest scholarly research on upcoming trends in data analytics and potential technologies that will facilitate insight in various domains of science, industry, business, and consumer applications. Featuring extensive coverage on a broad range of topics and perspectives such as deep neural network, domain adaptation modeling, and threat detection, this book is ideally designed for researchers, professionals, and students seeking current research on the latest trends in the field of deep learning techniques in big data analytics. Contents include: Deep Auto-Encoders Deep Neural Network Domain Adaptation Modeling Multilayer Perceptron (MLP) Natural Language Processing (NLP) Restricted Boltzmann Machines (RBM) Threat Detection

This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches. It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on September 18-20, 2000. The colloquium was a meeting place for researchers in mathematics and computer science and thus an important opportunity to exchange ideas and points of view, and to present new approaches and new results in the common areas such as algorithms analysis, trees, combinatorics, optimization, performance evaluation and probabilities. The book is intended for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and related modern mathematical methods. The range of applications is very wide and reaches beyond computer science.

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra.

This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyperelliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

The resilience of computing systems includes their dependability as well as their fault tolerance and security. It defines the ability of a computing system to perform properly in the presence of various kinds of disturbances and to recover from any service degradation. These properties are immensely important in a world where many aspects of our daily life depend on the correct, reliable and secure operation of often large-scale distributed computing systems. Wolter and her co-editors grouped the 20 chapters from leading researchers into seven parts: an introduction and motivating examples, modeling techniques, model-driven prediction, measurement and metrics, testing techniques, case studies, and conclusions. The core is formed by 12 technical papers, which are framed by motivating real-world examples and case studies, thus illustrating the necessity and the application of the presented methods. While the technical chapters are independent of each other and can be read in any order, the reader will benefit more from the case studies if he or she reads them together with the related techniques. The papers combine topics like modeling, benchmarking, testing, performance evaluation, and dependability, and aim at academic and industrial researchers in these areas as well as graduate students and lecturers in related fields. In this volume, they will find a comprehensive overview of the state of the art in a field of continuously growing practical importance.

The Formal Aspects of Computing Science (FACS) Specialist Group of the British Computer Society set up a seriesof evening seminarsin 2005to report on advances in the application of formal design and analysis techniques in all the stages of software development. The seminars attracted an audience fromboth academiaand industry, andgavethem the opportunity to hear and meet pioneers andkeyresearchersin computing science.Normally it wouldbe necessaryto travelabroadand attend an internationalconference to be in the presence of such respected ?gures; instead, the evening seminar programme, overa period of threeyears, broughtthe keynotespeakers of the conference to theBritishComputerSocietyheadquarters, fortheconvenienceofanaudience basedinLondon.Severalspeakersfromtheperiod2005-2007kindlydeveloped their talks into full papers, which form the basis of this volume. Iamdelightedtowelcomethepublicationofsuchanexcellentandcomp- hensiveseriesofcontributions.Theyarenowavailableinbookformtoaneven wider audience, including developers interested in solutions already available, and researchers interested in problems which remain for future solution. Sir Tony Hoare Preface They envy the distinction I have won; let them therefore, envy my toils, my honesty, and the methods by which I gained it. - Sallust (86-34 BC) Formalmethods area powerfultechniqueforhelping toensure the correctness of software. The growth in their use has been slow but steady and they are typically applied in critical systems where safety or security is paramoun

"Complex Intelligent Systems and Applications" presents the most up-to-date advances in complex, software intensive and intelligent systems. Each self-contained chapter is the contribution of distinguished experts in areas of research relevant to the study of complex, intelligent, and software intensive systems. These contributions focus on the resolution of complex problems from areas of networking, optimization and artificial intelligence. The book is divided into three parts focusing on complex intelligent network systems, efficient resource management in complex systems, and artificial data mining systems. Through the presentation of these diverse areas of application, the volume provides insights into the multidisciplinary nature of complex problems. Throughout the entire book, special emphasis is placed on optimization and efficiency in resource management, network interaction, and intelligent system design. This book presents the most recent interdisciplinary results in this area of research and can serve as a valuable tool for researchers interested in defining and resolving the types of complex problems that arise in networking, optimization, and artificial intelligence.

The project of writing this monograph was conceived in August 2006. It is a m- ter of delight and satisfaction that this monograph would be published during the centenary year (May 27, 2008 - May 26, 2009) of our dear alma mater, the Indian Institute of Science, which is truly a magni cent temple and an eternal source of inspiration, with a splendid ambiance for research. Studying the rational behavior of entities interacting with each other in or- nized or ad-hoc marketplaces has been the bread and butter of our research group here at the Electronic Commerce Laboratory, Department of Computer Science and Automation, Indian Institute of Science. Speci cally, the application of game th- retic modeling and mechanism design principles to the area of network economics was an area of special interest to the authors. In fact, the dissertations of the s- ond, third, and fourth authors (Dinesh Garg, Ramasuri Narayanam, and Hastagiri Prakash) were all in this area. Dinesh Garg's Doctoral Thesis, which later won the Best Dissertation Award at the Department of Computer Science and Automation, Indian Institute of Science for the academic year 2006-07, included an interesting chapter on applying the brilliant work of Roger Myerson (Nobel laureate in E- nomic Sciences in 2007) to the topical problem of sponsored search auctions on the web. Ramasuri's Master's work applied mechanism design to develop robust broadcastprotocolsin wireless adhoc networkswhile Hastagiri's Master's work - veloped resource allocation mechanisms for computational grids.

Timing issues are of growing importance for the conceptualization and design of computer-based systems. Timing may simply be essential for the correct behaviour of a system, e.g. of a controller. Even if timing is not essential for the correct behaviour of a system, there may be good reasons to introduce it in such a way that suitable timing becomes relevant for the correct behaviour of a complex system. This book is unique in presenting four algebraic theories about processes, each dealing with timing from a different point of view, in a coherent and systematic way. The timing of actions is either relative or absolute and the underlying time scale is either discrete or continuous. All presented theories are extensions of the algebra of communicating processes. The book is essential reading for researchers and advanced students interested in timing issues in the context of the design and analysis of concurrent and communicating processes.

Distributed Computing is rapidly becoming the principal computing paradigm in diverse areas of computing, communication, and control. Processor clusters, local and wide area networks, and the information highway evolved a new kind of problems which can be solved with distributed algorithms.In this textbook a variety of distributed algorithms are presented independently of particular programming languages or hardware, using the graphically suggestive technique of Petri nets which is both easy to comprehend intuitively and formally rigorous. By means of temporal logic the author provides surprisingly simple yet powerful correctness proofs for the algorithms.The scope of the book ranges from distributed control and synchronization of two sites up to algorithms on any kind of networks. Numerous examples show that description and analysis of distributed algorithms in this framework are intuitive and technically transparent.

This textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modeling. The author's aim is to derive probability theory in a way that highlights the complementary nature of its formal, intuitive, and applicative aspects while illustrating how the theory is applied in a variety of settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including being conversant with limits, but otherwise, this book provides a self-contained approach suitable for graduate or advanced undergraduate students. The first half of the book covers the basic concepts of probability, including combinatorics, expectation, random variables, and fundamental theorems. In the second half of the book, the reader is introduced to stochastic processes. Subjects covered include renewal processes, queueing theory, Markov processes, matrix geometric techniques, reversibility, and networks of queues. Examples and applications are drawn from problems in computer performance modeling. Throughout, large numbers of exercises of varying degrees of difficulty will help to secure a reader's understanding of these important and fascinating subjects.

This book explores alternative ways of accomplishing secure information transfer with incoherent multi-photon pulses in contrast to conventional Quantum Key Distribution techniques. Most of the techniques presented in this book do not need conventional encryption. Furthermore, the book presents a technique whereby any symmetric key can be securely transferred using the polarization channel of an optical fiber for conventional data encryption. The work presented in this book has largely been practically realized, albeit in a laboratory environment, to offer proof of concept rather than building a rugged instrument that can withstand the rigors of a commercial environment.

This new edition includes the latest advances and developments in computational probability involving A Probability Programming Language (APPL). The book examines and presents, in a systematic manner, computational probability methods that encompass data structures and algorithms. The developed techniques address problems that require exact probability calculations, many of which have been considered intractable in the past. The book addresses the plight of the probabilist by providing algorithms to perform calculations associated with random variables. Computational Probability: Algorithms and Applications in the Mathematical Sciences, 2nd Edition begins with an introductory chapter that contains short examples involving the elementary use of APPL. Chapter 2 reviews the Maple data structures and functions necessary to implement APPL. This is followed by a discussion of the development of the data structures and algorithms (Chapters 3-6 for continuous random variables and Chapters 7-9 for discrete random variables) used in APPL. The book concludes with Chapters 10-15 introducing a sampling of various applications in the mathematical sciences. This book should appeal to researchers in the mathematical sciences with an interest in applied probability and instructors using the book for a special topics course in computational probability taught in a mathematics, statistics, operations research, management science, or industrial engineering department.

The application of modern methods in numerical mathematics on problems in chemical engineering is essential for designing, analyzing and running chemical processes and even entire plants. Scientific Computing in Chemical Engineering II gives the state of the art from the point of view of numerical mathematicians as well as that of engineers.
The present volume as part of a two-volume edition covers topics such as computer-aided process design, combustion and flame, image processing, optimization, control, and neural networks. The volume is aimed at scientists, practitioners and graduate students in chemical engineering, industrial engineering and numerical mathematics.