This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

In "Distributed Algorithms," Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers.

"Distributed Algorithms" contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others.

The material is organized according to the system model first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference.

The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures."

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche's method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.

Professor Fenner's definitive text is now back in print, with added corrections. It serves as an introduction to finite element methods for engineering undergraduates and other students at an equivalent level. Postgraduate and practising engineers will also find it useful if they are comparatively new to finite element methods.The main emphasis is on the simplest methods suitable for solving two-dimensional continuum mechanics problems, particularly those encountered in the fields of stress analysis, fluid mechanics and heat transfer. Complete FORTRAN programs are presented, described and discussed in detail, and several practical case studies serve to illustrate the methods developed in the book.Finite element methods are compared and contrasted with finite difference methods, and throughout the level of computer programming, continuum mechanics, numerical analysis, matrix algebra and other mathematics employed corresponds to that normally covered in undergraduate engineering courses.

The main purpose of the present volume is to advance our understanding of the notions of knowledge and context, the connections between them and the ways in which they can be modeled, in particular formalized a question of prime importance and utmost relevance to such diverse disciplines as philosophy, linguistics, computer science and artificial intelligence and cognitive science.

Bringing together essays written by world-leading experts and emerging researchers in epistemology, logic, philosophy of language, linguistics and theoretical computer science, the book examines the formal modeling of knowledge and the knowledge-context link at one or more of three intersections - context and epistemology, epistemology and formalism, formalism and context and presents a novel range of approaches to the current discussions that the connections between knowledge, language, action, reasoning and context continually enlivens. It develops powerful ideas that will push the relevant fields forward and give a sense of the new directions in which mainstream and formal research on knowledge and context is heading."

This contributed volume offers a collection of papers presented at the 2016 Network Games, Control, and Optimization conference (NETGCOOP), held at the University of Avignon in France, November 23-25, 2016. These papers highlight the increasing importance of network control and optimization in many networking application domains, such as mobile and fixed access networks, computer networks, social networks, transportation networks, and, more recently, electricity grids and biological networks. Covering a wide variety of both theoretical and applied topics in the areas listed above, the authors explore several conceptual and algorithmic tools that are needed for efficient and robust control operation, performance optimization, and better understanding the relationships between entities that may be acting cooperatively or selfishly in uncertain and possibly adversarial environments. As such, this volume will be of interest to applied mathematicians, computer scientists, engineers, and researchers in other related fields.

The aim of this book is to present the mathematical theory and the know-how to make computer programs for the numerical approximation of Optimal Control of PDE's. The computer programs are presented in a straightforward generic language. As a consequence they are well structured, clearly explained and can be translated easily into any high level programming language. Applications and corresponding numerical tests are also given and discussed. To our knowledge, this is the first book to put together mathematics and computer programs for Optimal Control in order to bridge the gap between mathematical abstract algorithms and concrete numerical ones. The text is addressed to students and graduates in Mathematics, Mechanics, Applied Mathematics, Numerical Software, Information Technology and Engineering. It can also be used for Master and Ph.D. programs.

This book presents recent research on Advanced Computing in Industrial Mathematics, which is one of the most prominent interdisciplinary areas, bringing together mathematics, computer science, scientific computations, engineering, physics, chemistry, medicine, etc. Further, the book presents the major tools used in Industrial Mathematics, which are based on mathematical models, and the corresponding computer codes, which are used to perform virtual experiments to obtain new data or to better understand previous experimental findings. The book gathers the peer-reviewed papers presented at the 11th Annual Meeting of the Bulgarian Section of SIAM (BGSIAM), from December 20 to 22, 2016 in Sofia, Bulgaria.

The book contains the methods and bases of functional analysis that are directly adjacent to the problems of numerical mathematics and its applications; they are what one needs for the understand ing from a general viewpoint of ideas and methods of computational mathematics and of optimization problems for numerical algorithms. Functional analysis in mathematics is now just the small visible part of the iceberg. Its relief and summit were formed under the influence of this author's personal experience and tastes. This edition in English contains some additions and changes as compared to the second edition in Russian; discovered errors and misprints had been corrected again here; to the author's distress, they jump incomprehensibly from one edition to another as fleas. The list of literature is far from being complete; just a number of textbooks and monographs published in Russian have been included. The author is grateful to S. Gerasimova for her help and patience in the complex process of typing the mathematical manuscript while the author corrected, rearranged, supplemented, simplified, general ized, and improved as it seemed to him the book's contents. The author thanks G. Kontarev for the difficult job of translation and V. Klyachin for the excellent figures."

The present volume is a tribute to Gian-Carlo Rota. It is an anthology of the production of a unique collaboration among leading researchers who were greatly influenced by Gian-Carlo Rota's mathematical thought.The book begins with an essay in mathematical biography by H. Crapo in which the prospects for research opened up by Rota's work are outlined. The subsequent section is devoted to the prestigious Fubini lectures delivered by Gian-Carlo Rota at the Institute for scientific Interchange in 1998, with a preface by E. Vesentini. These lectures provide the only published documentation of Rota's plans for a fundamental reform of probability theory, a program interrupted by his untimely demise.The lectures by M. Aigner and D. Perrin specially conceived for this volume, provide self-contained surveys of central topics in combinatorics and theoretical computer science; they will also be of great use to both undergraduate and graduate students.The essays and research papers that appear in the final section present recent developments of some of the mathematical themes promoted by Gian-Carlo Rota. These will be of particular interest as they propose many new problems for research.

Energy Power Risk: Derivatives, Computation and Optimization is a comprehensive guide presenting the latest mathematical and computational tools required for the quantification and management of energy power risk. Written by a practitioner with many years' experience in the field, it provides readers with valuable insights in to the latest practices and methodologies used in today's markets, showing readers how to create innovative quantitative models for energy and power risk and derivative valuation. The book begins with an introduction to the mathematics of Brownian motion and stochastic processes, covering Geometric Brownian motion, Ito's lemma, Ito's Isometry, the Ornstein Uhlenbeck process and more. It then moves on to the simulation of power prices and the valuation of energy derivatives, before considering software engineering techniques for energy risk and portfolio optimization. The book also covers additional topics including wind and solar generation, intraday storage, generation and demand optionality. Written in a highly practical manner and with example C++ and VBA code provided throughout, Energy Power Risk: Derivatives, Computation and Optimization will be an essential reference for quantitative analysts, financial engineers and other practitioners in the field of energy risk management, as well as researchers and students interested in the industry and how it works.

Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This trend will continue as many new signal processing applications are opening up in consumer products and communications systems.
In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. This volume gives particular emphasis to exposing broader contexts of the signal processing problems so that the impact of algorithms and hardware can be better understood; it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques. This volume will be of interest to both applied mathematicians and engineers.

This long-awaited revision offers a comprehensive introduction to natural language understanding with developments and research in the field today. Building on the effective framework of the first edition, the new edition gives the same balanced coverage of syntax, semantics, and discourse, and offers a uniform framework based on feature-based context-free grammars and chart parsers used for syntactic and semantic processing. Thorough treatment of issues in discourse and context-dependent interpretation is also provided.

In addition, this title offers coverage of two entirely new subject areas. First, the text features a new chapter on statistically-based methods using large corpora. Second, it includes an appendix on speech recognition and spoken language understanding. Also, the information on semantics that was covered in the first edition has been largely expanded in this edition to include an emphasis on compositional interpretation.
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Strategies for Quasi-Monte Carlo builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC). One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension, while the other variables collectively are relatively insignificant. Another is smoothing. The book provides many illustrations of both keys, in particular for problems involving Poisson processes or Gaussian processes. RQMC beats grids by a huge margin. With low effective dimension, RQMC is an order-of-magnitude more efficient than standard Monte Carlo. With, in addition, certain smoothness - perhaps induced - RQMC is an order-of-magnitude more efficient than deterministic QMC. Unlike the latter, RQMC permits error estimation via the central limit theorem. For random-dimensional problems, such as occur with discrete-event simulation, RQMC gets judiciously combined with standard Monte Carlo to keep memory requirements bounded. This monograph has been designed to appeal to a diverse audience, including those with applications in queueing, operations research, computational finance, mathematical programming, partial differential equations (both deterministic and stochastic), and particle transport, as well as to probabilists and statisticians wanting to know how to apply effectively a powerful tool, and to those interested in numerical integration or optimization in their own right. It recognizes that the heart of practical application is algorithms, so pseudocodes appear throughout the book. While not primarily a textbook, it is suitable as a supplementary text for certain graduate courses. As a reference, it belongs on the shelf of everyone with a serious interest in improving simulation efficiency. Moreover, it will be a valuable reference to all those individuals interested in improving simulation efficiency with more than incremental increases.

The Bia owie a workshops on Geometric Methods in Physics, taking place in the unique environment of the Bia owie a natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938 2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking "k-slices" of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Automated and semi-automated manipulation of so-called labelled transition systems has become an important means in discovering flaws in software and hardware systems. Process algebra has been developed to express such labelled transition systems algebraically, which enhances the ways of manipulation by means of equational logic and term rewriting.The theory of process algebra has developed rapidly over the last twenty years, and verification tools have been developed on the basis of process algebra, often in cooperation with techniques related to model checking. This textbook gives a thorough introduction into the basics of process algebra and its applications.

Advances in microelectronic technology have made massively parallel computing a reality and triggered an outburst of research activity in parallel processing architectures and algorithms. Distributed memory multiprocessors - parallel computers that consist of microprocessors connected in a regular topology - are increasingly being used to solve large problems in many application areas. In order to use these computers for a specific application, existing algorithms need to be restructured for the architecture and new algorithms developed. The performance of a computation on a distributed memory multiprocessor is affected by the node and communication architecture, the interconnection network topology, the I/O subsystem, and the parallel algorithm and communication protocols. Each of these parametersis a complex problem, and solutions require an understanding of the interactions among them. This book is based on the papers presented at the NATO Advanced Study Institute held at Bilkent University, Turkey, in July 1991. The book is organized in five parts: Parallel computing structures and communication, Parallel numerical algorithms, Parallel programming, Fault tolerance, and Applications and algorithms.

Identifying the input-output relationship of a system or discovering the evolutionary law of a signal on the basis of observation data, and applying the constructed mathematical model to predicting, controlling or extracting other useful information constitute a problem that has been drawing a lot of attention from engineering and gaining more and more importance in econo metrics, biology, environmental science and other related areas. Over the last 30-odd years, research on this problem has rapidly developed in various areas under different terms, such as time series analysis, signal processing and system identification. Since the randomness almost always exists in real systems and in observation data, and since the random process is sometimes used to model the uncertainty in systems, it is reasonable to consider the object as a stochastic system. In some applications identification can be carried out off line, but in other cases this is impossible, for example, when the structure or the parameter of the system depends on the sample, or when the system is time-varying. In these cases we have to identify the system on line and to adjust the control in accordance with the model which is supposed to be approaching the true system during the process of identification. This is why there has been an increasing interest in identification and adaptive control for stochastic systems from both theorists and practitioners."

This book is for researchers in computer science, mathematical logic, and philosophical logic. It shows the state of the art in current investigations of process calculi with mainly two major paradigms at work: linear logic and modal logic. The combination of approaches and pointers for further integration also suggests a grander vision for the field.

Contents: The Possibility of Using Computer to Study the Equation of Gravitation (Q K Lu); Solving Polynomial Systems by Homotopy Continuation Methods (T Y Li); Sketch of a New Discipline of Modeling (E Engeler); The Symmetry Groups of Computer Programs and Program Equivalence (J R Gabriel); Computations with Rational Parametric Equations (S C Chou et al.); Computer Versus Paper and Pencil (M Mignotte); The Finite Basis of an Irreducible Ascending Set (H Shi); A Note on Wu Wen-Tsun's Non-Degenerate Condition (J Z Zhang et al.); Mechanical Theorem Proving in Riemann Geometry Using Wu's Method (S C Chou & X S Gao); and other papers;

When we learn from books or daily experience, we make associations and draw inferences on the basis of information that is insufficient for under standing. One example of insufficient information may be a small sample derived from observing experiments. With this perspective, the need for de veloping a better understanding of the behavior of a small sample presents a problem that is far beyond purely academic importance. During the past 15 years considerable progress has been achieved in the study of this issue in China. One distinguished result is the principle of in formation diffusion. According to this principle, it is possible to partly fill gaps caused by incomplete information by changing crisp observations into fuzzy sets so that one can improve the recognition of relationships between input and output. The principle of information diffusion has been proven suc cessful for the estimation of a probability density function. Many successful applications reflect the advantages of this new approach. It also supports an argument that fuzzy set theory can be used not only in "soft" science where some subjective adjustment is necessary, but also in "hard" science where all data are recorded."

There are many surprising connections between the theory of numbers, which is one of the oldest branches of mathematics, and computing and information theory. Number theory has important applications in computer organization and security, coding and cryptography, random number generation, hash functions, and graphics. Conversely, number theorists use computers in factoring large integers, determining primes, testing conjectures, and solving other problems. This book takes the reader from elementary number theory, via algorithmic number theory, to applied number theory in computer science. It introduces basic concepts, results, and methods, and discusses their applications in the design of hardware and software, cryptography, and security. It is aimed at undergraduates in computing and information technology, but will also be valuable to mathematics students interested in applications. In this 2nd edition full proofs of many theorems are added and some corrections are made.

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. These include: * the setting of learning problems based on the model of minimizing the risk functional from empirical data * a comprehensive analysis of the empirical risk minimization principle including necessary and sufficient conditions for its consistency * non-asymptotic bounds for the risk achieved using the empirical risk minimization principle * principles for controlling the generalization ability of learning machines using small sample sizes based on these bounds * the Support Vector methods that control the generalization ability when estimating function using small sample size. The second edition of the book contains three new chapters devoted to further development of the learning theory and SVM techniques. These include: * the theory of direct method of learning based on solving multidimensional integral equations for density, conditional probability, and conditional density estimation * a new inductive principle of learning. Written in a readable and concise style, the book is intended for statisticians, mathematicians, physicists, and computer scientists. Vladimir N. Vapnik is Technology Leader AT&T Labs-Research and Professor of London University. He is one of the founders of statistical learning theory, and the author of seven books published in English, Russian, German, and Chinese.