Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented. Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertainty and nu merical approaches are often distinguished. Although this distinction is somewhat misleading, it is used as a means to structure the present volume. This is even to some degree reflected in the two first chapters, which treat fundamental, general methods of computation in systems designed to represent uncertainty. It has been noted early by Shenoy and Shafer, that computations in different domains have an underlying common structure. Essentially pieces of knowledge or information are to be combined together and then focused on some particular question or domain. This can be captured in an algebraic structure called valuation algebra which is described in the first chapter. Here the basic operations of combination and focus ing (marginalization) of knowledge and information is modeled abstractly subject to simple axioms."

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new "hands on" didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. "The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory." (John Casti, Santa Fe Institute)

Updated for Excel 2021 and based on the bestselling editions from previous versions, Excel 2021 / Microsoft 365 Programming by Example is a practical, how-to book on Excel programming, suitable for readers already proficient with the Excel user interface. If you are looking to automate Excel routine tasks, this book will progressively introduce you to programming concepts via numerous illustrated hands-on exercises. More advanced topics are demonstrated via custom projects. From recording and editing a macro and writing VBA code from scratch to programming the Ribbon interface and working with XML documents, this book takes you on a programming journey that will change the way you work with Excel. The book provides information on performing automatic operations on files, folders, and other Microsoft Office applications. It also covers proper use of event procedures, testing and debugging, and guides you through programming more advanced Excel features, such as working with VBA classes and raising your own events in standalone class modules. Includes companion files with source code, hands-on projects, and figures.

It is, indeed, widely acceptable today that nowhere is it more important to focus on the improvement of software quality than in the case of systems with requirements in the areas of safety and reliability - especially for distributed, real-time and embedded systems. Thus, much research work is under progress in these fields, since software process improvement impinges directly on achieved levels of quality, and many application experiments aim to show quantitative results demonstrating the efficacy of particular approaches. Requirements for safety and reliability - like other so-called non-functional requirements for computer-based systems - are often stated in imprecise and ambiguous terms, or not at all. Specifications focus on functional and technical aspects, with issues like safety covered only implicitly, or not addressed directly because they are felt to be obvious; unfortunately what is obvious to an end user or system user is progressively less so to others, to the extend that a software developer may not even be aware that safety is an issue. Therefore, there is a growing evidence for encouraging greater understanding of safety and reliability requirements issues, right across the spectrum from end user to software developer; not just in traditional safety-critical areas (e.g. nuclear, aerospace) but also acknowledging the need for such things as heart pacemakers and other medical and robotic systems to be highly dependable.

This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations. Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised... There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)

This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms. Richard Karp,University Professor, University of California at Berkeley Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer. It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic. I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms. László Lovász, Senior Researcher, Microsoft Research

The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.

Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances, especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume, cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decade

Effective compilers allow for a more efficient execution of application programs for a given computer architecture, while well-conceived architectural features can support more effective compiler optimization techniques. A well thought-out strategy of trade-offs between compilers and computer architectures is the key to the successful designing of highly efficient and effective computer systems. From embedded micro-controllers to large-scale multiprocessor systems, it is important to understand the interaction between compilers and computer architectures. The goal of the Annual Workshop on Interaction between Compilers and Computer Architectures (INTERACT) is to promote new ideas and to present recent developments in compiler techniques and computer architectures that enhance each other's capabilities and performance. Interaction Between Compilers and Computer Architectures is an updated and revised volume consisting of seven papers originally presented at the Fifth Workshop on Interaction between Compilers and Computer Architectures (INTERACT-5), which was held in conjunction with the IEEE HPCA-7 in Monterrey, Mexico in 2001. This volume explores recent developments and ideas for better integration of the interaction between compilers and computer architectures in designing modern processors and computer systems. Interaction Between Compilers and Computer Architectures is suitable as a secondary text for a graduate level course, and as a reference for researchers and practitioners in industry.

Software Process Modeling brings together experts to discuss relevant results in software process modeling, and expresses their personal view of this field. This book focuses on new aspects of software process modeling. Specifically, it deals with socio-technological aspects, process modeling for new development types (open source software, dependability applications, etc.) and organization change management.

The computer audience is placing growing demands on the software industry today. Consumers are looking for more complex products that are, at the same time, easier to use. Software developer organizations are expected to produce higher quality products and deliver them to the public faster. In so doing, however, globally distributed development teams have to cope with understaffing and changing technologies. The challenges for the software industry are apparently mounting.

Over the years, a variety of software process models have been designed to structure, describe and prescribe the software systems construction process. Most recently, software process modeling is increasingly dealing with new challenges raised by the tests that the software industry has to stand.

Software Process Modeling is designed for a professional audience of researchers and practitioners in industry. The book is also suitable for graduate-level students in computer science.

Algorithmic discrete mathematics plays a key role in the development of information and communication technologies, and methods that arise in computer science, mathematics and operations research in particular in algorithms, computational complexity, distributed computing and optimization are vital to modern services such as mobile telephony, online banking and VoIP.

This book examines communication networking from a mathematical viewpoint. The contributing authors took part in the European COST action 293 a four-year program of multidisciplinary research on this subject. In this book they offer introductory overviews and state-of-the-art assessments of current and future research in the fields of broadband, optical, wireless and ad hoc networks. Particular topics of interest are design, optimization, robustness and energy consumption.

The book will be of interest to graduate students, researchers and practitioners in the areas of networking, theoretical computer science, operations research, distributed computing and mathematics."

In recent years there has been a remarkable convergence of interest in programming languages based on ALGOL 60. Researchers interested in the theory of procedural and object-oriented languages discovered that ALGOL 60 shows how to add procedures and object classes to simple imperative languages in a general and clean way. And, on the other hand, researchers interested in purely functional languages discovered that ALGOL 60 shows how to add imperative mechanisms to functional languages in a way that does not compromise their desirable properties. Unfortunately, many of the key works in this field have been rather hard to obtain. The primary purpose of this collection is to make the most significant material on ALGoL-like languages conveniently available to graduate students and researchers. Contents Introduction to Volume 1 1 Part I Historical Background 1 Part n Basic Principles 3 Part III Language Design 5 Introduction to Volume 2 6 Part IV Functor-Category Semantics 7 Part V Specification Logic 7 Part VI Procedures and Local Variables 8 Part vn Interference, Irreversibility and Concurrency 9 Acknowledgements 11 Bibliography 11 Introduction to Volume 1 This volume contains historical and foundational material, and works on lan guage design. All of the material should be accessible to beginning graduate students in programming languages and theoretical Computer Science."

C++/CLI is Microsofts latest extension to C++ that targets the heart of .NET 2.0, the common language runtime. "Expert Visual C++/CLI" is written by visual C++ MVP -->Marcus Heege-->, who examines the core of the C++/CLI language. He explains both how the language elements work and how Microsoft intends them to be used.

Even if you're new to C++/CLI and are planning to migrate to it from another language, this book will ground you in the core language elements and give you the confidence to explore further and migrate effectively. It provides concise, yet in-depth coverage of all major C++/CLI features; short code examples succinctly illustrate syntax and concepts, and more elaborate examples show how C++/CLI should be used.

In any software design project, the analysis stage - documenting and designing technical requirements for the needs of users - is vital to the success of the project.This book provides a thorough introduction & survey to all aspects of analysis. This new edition provides new features including: additional chapters on system Development Life Cycle & Data Element Naming Conventions & Standards; more coverage on converting logical models to physical models, how to generate DDL & testing database functionalities; expansion of database section with concepts such as denormalization, security & change control; developments on new design & technologies, particularly in the area of web analysis and design; a revised Web/Commerce chapter, which addresses component middleware for complex systems design; and, new case studies. This book is a valuable resource and guide for all information systems students, practitioners and professionals who need an in-depth understanding of the principles of the analysis and design process.

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

2. The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3. Convergence Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., . . . . 60 4. Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A Simple Proof for a Result of Ollerenshaw on Steiner Trees . . . . . . . . . . 68 Xiufeng Du, Ding-Zhu Du, Biao Gao, and Lixue Qii 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2. In the Euclidean Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3. In the Rectilinear Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4. Discussion . . . . . . . . . . . . -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Optimization Algorithms for the Satisfiability (SAT) Problem . . . . . . . . . 72 Jun Gu 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2. A Classification of SAT Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7:3 3. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV 4. Complete Algorithms and Incomplete Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5. Optimization: An Iterative Refinement Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6. Local Search Algorithms for SAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7. Global Optimization Algorithms for SAT Problem . . . . . . . . . . . . . . . . . . . . . . . . 106 8. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 10. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Ergodic Convergence in Proximal Point Algorithms with Bregman Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Osman Guier 1. Introduction . . .: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 2. Convergence for Function Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 3. Convergence for Arbitrary Maximal Monotone Operators . . . . . . . . . . . .

'Subdivision' is a way of representing smooth shapes in a computer. A curve or surface (both of which contain an in?nite number of points) is described in terms of two objects. One object is a sequence of vertices, which we visualise as a polygon, for curves, or a network of vertices, which we visualise by drawing the edges or faces of the network, for surfaces. The other object is a set of rules for making denser sequences or networks. When applied repeatedly, the denser and denser sequences are claimed to converge to a limit, which is the curve or surface that we want to represent. This book focusses on curves, because the theory for that is complete enough that a book claiming that our understanding is complete is exactly what is needed to stimulate research proving that claim wrong. Also because there are already a number of good books on subdivision surfaces. The way in which the limit curve relates to the polygon, and a lot of interesting properties of the limit curve, depend on the set of rules, and this book is about how one can deduce those properties from the set of rules, and how one can then use that understanding to construct rules which give the properties that one wants.

Modern methods of filter design and controller design often yield systems of very high order, posing a problem for their implementation. Over the past two decades or so, sophisticated methods have been developed to achieve simplification of filters and controllers. Such methods often come with easy-to-use error bounds, and in the case of controller simplification methods, such error bounds will usually be related to closed-loop properties.This book is the first comprehensive treatment of approximation methods for filters and controllers. It is fully up to date, and it is authored by two leading researchers who have personally contributed to the development of some of the methods. Balanced truncation, Hankel norm reduction, multiplicative reduction, weighted methods and coprime factorization methods are all discussed.The book is amply illustrated with examples, and will equip practising control engineers and graduates for intelligent use of commercial software modules for model and controller reduction.

The new multimedia standards (for example, MPEG-21) facilitate the seamless integration of multiple modalities into interoperable multimedia frameworks, transforming the way people work and interact with multimedia data. These key technologies and multimedia solutions interact and collaborate with each other in increasingly effective ways, contributing to the multimedia revolution and having a significant impact across a wide spectrum of consumer, business, healthcare, education and governmental domains. This book aims to provide a complete coverage of the areas outlined and to bring together the researchers from academic and industry as well as practitioners to share ideas, challenges and solutions relating to the multifaceted aspects of this field.

There are increasing opportunities to consider the application of semantic technologies for business information systems. Semantic technologies are expected to improve business processes and information systems, and lead to savings in cost and time as well as improved efficiency. Semantic Technologies for Business and Information Systems Engineering: Concepts and Applications investigates the application of semantic technologies to business and information systems engineering. This reference work assists researchers in academia and industry, students, business process analysts, information management professionals, software engineers, and other practitioners in gaining knowledge on applying semantic technologies for advanced business information systems, in annotating semantics to business processes, and in semantically integrating advanced business information systems.

Genetic and evolutionary algorithms (GEAs) have often achieved an enviable success in solving optimization problems in a wide range of disciplines. This book provides effective optimization algorithms for solving a broad class of problems quickly, accurately, and reliably by employing evolutionary mechanisms.

System Modeling and Optimization XX deals with new developments in the areas of optimization, optimal control and system modeling. The themes range across various areas of optimization: continuous and discrete, numerical and analytical, finite and infinite dimensional, deterministic and stochastic, static and dynamic, theory and applications, foundations and case studies. Besides some classical topics, modern areas are also presented in the contributions, including robust optimization, filter methods, optimization of power networks, data mining and risk control.
This volume contains invited and selected papers from presentations at the 20th IFIP TC7 Conference on System Modeling and Optimization, which took place at the University of Trier, Germany from July 23 to 27, 2001, and which was sponsored by the International Federation for Information Processing (IFIP).

This book introduces the parallel and distributed approach to logic programming, examining existing models of distributed logic programming, and proposing an alternative framework for distributed logic programming using extended Petri nets. The hardwired realization of the Petri net based framework is presented in detail, and principles of mapping of a logic program on to the proposed framework are outlined. Finally, the book explores the scope of Petri net models in designing next-generation deductive database machines.

The connected dominating set has been a classic subject studied in graph theory since 1975. Since the 1990s, it has been found to have important applications in communication networks, especially in wireless networks, as a virtual backbone. Motivated from those applications, many papers have been published in the literature during last 15 years. Now, the connected dominating set has become a hot research topic in computer science. In this book, we are going to collect recent developments on the connected dominating set, which presents the state of the art in the study of connected dominating sets. The book consists of 16 chapters. Except the 1st one, each chapter is devoted to one problem, and consists of three parts, motivation and overview, problem complexity analysis, and approximation algorithm designs, which will lead the reader to see clearly about the background, formulation, existing important research results, and open problems. Therefore, this would be a very valuable reference book for researchers in computer science and operations research, especially in areas of theoretical computer science, computer communication networks, combinatorial optimization, and discrete mathematics.

Mathematical Programming has been of significant interest and relevance in engineering, an area that is very rich in challenging optimization problems. In particular, many design and operational problems give rise to nonlinear and mixed-integer nonlinear optimization problems whose modeling and solu tion is often nontrivial. Furthermore, with the increased computational power and development of advanced analysis (e. g. , process simulators, finite element packages) and modeling systems (e. g. , GAMS, AMPL, SPEEDUP, ASCEND, gPROMS), the size and complexity of engineering optimization models is rapidly increasing. While the application of efficient local solvers (nonlinear program ming algorithms) has become widespread, a major limitation is that there is often no guarantee that the solutions that are generated correspond to global optima. In some cases finding a local solution might be adequate, but in others it might mean incurring a significant cost penalty, or even worse, getting an incorrect solution to a physical problem. Thus, the need for finding global optima in engineering is a very real one. It is the purpose of this monograph to present recent developments of tech niques and applications of deterministic approaches to global optimization in engineering. The present monograph is heavily represented by chemical engi neers; and to a large extent this is no accident. The reason is that mathematical programming is an active and vibrant area of research in chemical engineering. This trend has existed for about 15 years.