A formal method is not the main engine of a development process, its contribution is to improve system dependability by motivating formalisation where useful. This book summarizes the results of the DEPLOY research project on engineering methods for dependable systems through the industrial deployment of formal methods in software development. The applications considered were in automotive, aerospace, railway, and enterprise information systems, and microprocessor design. The project introduced a formal method, Event-B, into several industrial organisations and built on the lessons learned to provide an ecosystem of better tools, documentation and support to help others to select and introduce rigorous systems engineering methods. The contributing authors report on these projects and the lessons learned. For the academic and research partners and the tool vendors, the project identified improvements required in the methods and supporting tools, while the industrial partners learned about the value of formal methods in general. A particular feature of the book is the frank assessment of the managerial and organisational challenges, the weaknesses in some current methods and supporting tools, and the ways in which they can be successfully overcome. The book will be of value to academic researchers, systems and software engineers developing critical systems, industrial managers, policymakers, and regulators.

This Volume discusses the underlying principles and analysis of the different concepts associated with an emerging socio-inspired optimization tool referred to as Cohort Intelligence (CI). CI algorithms have been coded in Matlab and are freely available from the link provided inside the book. The book demonstrates the ability of CI methodology for solving combinatorial problems such as Traveling Salesman Problem and Knapsack Problem in addition to real world applications from the healthcare, inventory, supply chain optimization and Cross-Border transportation. The inherent ability of handling constraints based on probability distribution is also revealed and proved using these problems.

This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors' past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Goedel's theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.

Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Godel-Lob provability logic GL. One chapter scrutinizes Esakia s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues."

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.

"Computational Analysis of Terrorist Groups: Lashkar-e-Taiba "provides an in-depth look at Web intelligence, and how advanced mathematics and modern computing technology can influence the insights we have on terrorist groups. This book primarily focuses on one famous terrorist group known as Lashkar-e-Taiba (or LeT), and how it operates.After 10 years of counter Al Qaeda operations, LeT is considered by many in the counter-terrorism community to be an even greater threat to the US and world peace than Al Qaeda.

"Computational Analysis of Terrorist Groups: Lashkar-e-Taiba "is the first book that demonstrates how to use modern computational analysis techniques including methods for "big data" analysis. This book presents how to quantify both the environment in which LeT operate, and the actions it took over a 20-year period, and represent it as a relational database table. This table is then mined using sophisticated data mining algorithms in order to gain detailed, mathematical, computational and statistical insights into LeT and its operations.This book also provides a detailed history of Lashkar-e-Taiba based on extensive analysis conducted by using open source information and public statements. Each chapter includes a case study, as well as a slide describing the key results which are available on the authors' web sites.

"Computational Analysis of Terrorist Groups: Lashkar-e-Taiba "is designed for a professional market composed of government or military workers, researchers and computer scientists working in the web intelligence field. Advanced-level students in computer science will also find this valuable as a reference book."

This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication.

Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.

This book is devoted to the state-of-the-art in all aspects of fireworks algorithm (FWA), with particular emphasis on the efficient improved versions of FWA. It describes the most substantial theoretical analysis including basic principle and implementation of FWA and modeling and theoretical analysis of FWA. It covers exhaustively the key recent significant research into the improvements of FWA so far. In addition, the book describes a few advanced topics in the research of FWA, including multi-objective optimization (MOO), discrete FWA (DFWA) for combinatorial optimization, and GPU-based FWA for parallel implementation. In sequels, several successful applications of FWA on non-negative matrix factorization (NMF), text clustering, pattern recognition, and seismic inversion problem, and swarm robotics, are illustrated in details, which might shed new light on more real-world applications in future. Addressing a multidisciplinary topic, it will appeal to researchers and professionals in the areas of metahuristics, swarm intelligence, evolutionary computation, complex optimization solving, etc.

Intheworldweliveinconcurrencyisthenorm.Forexample,thehumanbody isamassivelyconcurrentsystem,comprisingahugenumberofcells,allsim- taneously evolving and independently engaging in their individual biological processing.Inaddition,inthebiologicalworld,trulysequentialsystemsrarely arise. However, they are more common when manmade artefacts are cons- ered. In particular, computer systems are often developed from a sequential perspective. Why is this? The simple reason is that it is easier for us to think about sequential, rather than concurrent, systems. Thus, we use sequentiality as a device to simplify the design process. However, the need for increasingly powerful, ?exible and usable computer systems mitigates against simplifying sequentiality assumptions. A good - ample of this is the all-powerful position held by the Internet, which is highly concurrent at many di?erent levels of decomposition. Thus, the modern c- puter scientist (and indeed the modern scientist in general) is forced to think aboutconcurrentsystemsandthesubtleandintricatebehaviourthatemerges from the interaction of simultaneously evolving components. Over a period of 25 years, or so, the ?eld of concurrency theory has been involved in the development of a set of mathematical techniques that can help system developers to think about and build concurrent systems. These theories are the subject matter of this book.

The Third Conference on Applied Mathematics and Scienti?c Computing took place June 23-27, 2003 on island of Brijuni, Croatia. The main goal of the conference was to interchange ideas among applied mathematicians in the broadest sense both from and outside academia, as well as experts from other areas who apply different mathematical techniques. During the meeting there were invited and contributed talksand software presentations. Invited presentations were given by active researchers from the ?eldsof approximation theory, numerical methods for differential equations and numericallinear algebra. These proceedings contain research and review papers by invited speakers and selected contributed papers from the ?elds of applied and numerical mathematics. A particular aim of the conference was to encourage young scientists to present results of their research. Traditionally, the best presentation given by PhD student was rewarded. This year awardee was Luka Grubisi ? c ' (University of Hagen, Hagen, Germany) and we congratulate him for this achievement. It would be hard to organize the conference without generous support of the Croatian Ministry of Science and Technology and we acknowledge it. We are also indebted to themainorganizer, Department of Mathematics, University of Zagreb.Motivating beautiful nature should bealso mentioned.And,attheend, we are thankful to Drs. JosipTambaca ? and Ivica Nakic ' for giving this book its ?nal shape.

This is the first text and monograph about DNA computing, a molecular approach that might revolutionize our thinking and ideas about computing. Although it is too soon to predict whether computer hardware to change from silicon to carbon and from microchips to DNA molecules, the theoretical premises have already been studied extensively. The book starts with an introduction to DNA-related matters, the basics of biochemistry and language and computation theory, and progresses to the most advanced mathematical theory developed so far in the area. All three authors are pioneers in the theory of DNA computing. Apart from being well-known scientists, they are known for their lucid writing. Many of their previous books have become classics in their field, and this book too is sure to follow their example.

In recent years there has been an explosion of research into linear programming, as well as further steady advances in integer programming. This research has been reported in the research literature but there has been little done from the view of a "combined whole". This book aims to overcome this. With an international authorship of contributors from acknowledged experts in their field, this book provides a clear exposition on such topics as simplex algorithms, and interior point algorithms, both from a theoretical and a computational viewpoint. Surveying recent research that is currently only available in journals this topical book will be of interest not only in the field of mathematics, but also in computer science and operations research as well.

Evolutionary algorithms (EAs) is now a mature problem-solving family of heuristics that has found its way into many important real-life problems and into leading-edge scientific research. Spatially structured EAs have different properties than standard, mixing EAs. By virtue of the structured disposition of the population members they bring about new dynamical features that can be harnessed to solve difficult problems faster and more efficiently. This book describes the state of the art in spatially structured EAs by using graph concepts as a unifying theme. The models, their analysis, and their empirical behavior are presented in detail. Moreover, there is new material on non-standard networked population structures such as small-world networks.

The book should be of interest to advanced undergraduate and graduate students working in evolutionary computation, machine learning, and optimization. It should also be useful to researchers and professionals working in fields where the topological structures of populations and their evolution plays a role.

Action theory is the object of growing attention in a variety of scientific disciplines and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence and automata theory to jurisprudence, deontology and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology. The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic and its key applications in algorithmic and programming theory. The coverage thus fills a notable lacuna in the literary corpus and offers solid formal underpinning in cognitive science by approaching the problem of cognition as a composite action of mind.

This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be possible in Computational Science and Engineering due to recent advances in algorithms, hardware, and networks, and what can actually be achieved in practice; they also examine novel computing architectures, where computation itself is a multifaceted process, with hardware awareness or ubiquitous parallelism due to many-core systems being just two of the challenges faced. Topics cover both the methodological aspects of advanced computing (algorithms, parallel computing, data exploration, software engineering) and cutting-edge applications from the fields of chemistry, the geosciences, civil and mechanical engineering, etc., reflecting the highly interdisciplinary nature of the Munich Centre of Advanced Computing.

This invaluable reference offers the most comprehensive introduction available to the concepts of multisensor data fusion. It introduces key algorithms, provides advice on their utilization, and raises issues associated with their implementation. With a diverse set of mathematical and heuristic techniques for combining data from multiple sources, the book shows how to implement a data fusion system, describes the process for algorithm selection, functional architectures and requirements for ancillary software, and illustrates man-machine interface requirements an database issues.

Computer simulation and mathematical modelling are the most important approaches in the quantitative analysis of the diffusive processes fundamental to many physical, chemical, biological, and geological systems.

This comprehensive text/reference addresses the key issues in the "Modelling and Simulation of Diffusive Processes" from a broad range of different application areas. Applying an holistic approach, the book presents illuminating viewpoints drawn from an international selection of experts across a wide spectrum of disciplines, from computer science, mathematics and engineering, to natural resource management, environmental sciences, applied geo-sciences, agricultural sciences, and theoretical medicine.

Topics and features: presents a detailed introduction to diffusive processes and modelling; discusses diffusion and molecular transport in living cells, and suspended sediment in open channels; examines the mathematical modelling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media, and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modelling of nitrogen fate and transport at the sediment-water interface, and groundwater flow in unconfined aquifers; investigates two-dimensional solute transport from a varying pulse type point source, and futile cycles in metabolic flux modelling; studies contaminant concentration prediction along unsteady groundwater flow, and modelling synovial fluid flow in human joints; explores the modelling of soil organic carbon, and crop growth simulation.

This interdisciplinary volume will be invaluable to researchers, lecturers and graduate students from such diverse fields as computer science, mathematics, hydrology, agriculture and biology.

This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.

This book brings together historical notes, reviews of research developments, fresh ideas on how to make VC (Vapnik-Chervonenkis) guarantees tighter, and new technical contributions in the areas of machine learning, statistical inference, classification, algorithmic statistics, and pattern recognition. The contributors are leading scientists in domains such as statistics, mathematics, and theoretical computer science, and the book will be of interest to researchers and graduate students in these domains.

This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Epistemic Logic. 'Formal epistemology' is a term coined in the late 1990s for a new constellation of interests in philosophy, the origins of which are found in earlier works of epistemologists, philosophers of science and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty, rationality, deliberation, decision, strategy, action and agent interaction - and it does so using methods from logic, probability, computability, decision and game theory. The volume also includes a thorough index and suggestions for further reading, and thus offers a complete teaching and research package for students as well as research scholars of formal epistemology, philosophy, logic, computer science, theoretical economics and cognitive psychology.

Symbolic Integration I is destined to become the standard reference work in the field. Manuel Bronstein is a leading expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

This second edition offers a new chapter on parallel integration, a number of other improvements and a couple of additional exercises.

From the reviews of the first edition: ..". The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions " F. Winkler, Computing Reviews 1997 "

This book gives senior undergraduate and beginning graduate students and researchers in computer vision, applied mathematics, computer graphics, and robotics a self-contained introduction to the geometry of 3D vision; that is the reconstruction of 3D models of objects from a collection of 2D images. Following a brief introduction, Part I provides background materials for the rest of the book. The two fundamental transformations, namely rigid body motion and perspective projection are introduced and image formation and feature extraction discussed. Part II covers the classic theory of two view geometry based on the so-called epipolar constraint. Part III shows that a more proper tool for studying the geometry of multiple views is the so- called rank considtion on the multiple view matrix. Part IV develops practical reconstruction algorithms step by step as well as discusses possible extensions of the theory. Exercises are provided at the end of each chapter. Software for examples and algorithms are available on the author's website.

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation. The book will be of value to researchers and graduate students in logic and theoretical computer science.

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.