This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computing are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. In current research, modeling and simulation, making decisions under uncertainty and pattern recognition have become very common. Professionals across different educational levels and disciplines need exposure to advances in mathematics and computing. In this context, this book presents research papers on applicable areas of current interest. It also includes papers in which experts summarize research findings, such as signal processing and analysis and low-rank-matrix approximation for solving large systems, which will emerge as powerful tools for further research. These new advances and cutting-edge research in the fields of mathematics and their applications to computing are of paramount importance for young researchers.

The past decades have seen significant improvements in 3D imaging where the related techniques and technologies have advanced to a mature state. These exciting developments have sparked increasing interest in the challenges and opportunities afforded by 3D sensing. As a consequence, the emerging area of safety and security related imaging incorporates these important new technologies beyond the limitations of 2D image processing.This book presents the thoroughly revised versions of lectures given by leading researchers during the Workshop on Advanced 3D Imaging for Safety and Security in conjunction with the International Conference on Computer Vision and Pattern Recognition CVPR 2005, held in San Diego, CA, USA in June 2005.It covers the current state of the art in 3D imaging for safety and security.

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool environment. Finally the appendix covers the basics of category theory, signatures and algebras. The book addresses both research scientists and graduate students in computer science, mathematics and engineering.

The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.

This bookisan outgrowthoften yearsof researchatthe Universityof Florida Computational NeuroEngineering Laboratory (CNEL) in the general area of statistical signal processing and machine learning. One of the goals of writing the book is exactly to bridge the two ?elds that share so many common problems and techniques but are not yet e?ectively collaborating. Unlikeotherbooks thatcoverthe state ofthe artinagiven?eld, this book cuts across engineering (signal processing) and statistics (machine learning) withacommontheme: learningseenfromthepointofviewofinformationt- orywithanemphasisonRenyi'sde?nitionofinformation.Thebasicapproach is to utilize the information theory descriptors of entropy and divergence as nonparametric cost functions for the design of adaptive systems in unsup- vised or supervised training modes. Hence the title: Information-Theoretic Learning (ITL). In the course of these studies, we discovered that the main idea enabling a synergistic view as well as algorithmic implementations, does not involve the conventional central moments of the data (mean and covariance). Rather, the core concept is the ?-norm of the PDF, in part- ular its expected value (? = 2), which we call the information potential. This operator and related nonparametric estimators link information theory, optimization of adaptive systems, and reproducing kernel Hilbert spaces in a simple and unconventional way.

When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, control, and finance.

Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic.
Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs.
-Guides readers to develop sound solutions, avoid known mistakes, and repeat successful design decisions.
-Presents comprehensive coverage3/4from fundamental theories to current research trends.
-Written in a clear and engaging style by two masters of the field.
-Concludes each chapter with in-depth discussions of the key literature.
-Includes a full set of over 250 exercises, an on-line appendix with solutions to one-third of the exercises and 600 lecture slides

This book discusses major milestones in Rohit Jivanlal Parikh's scholarly work. Highlighting the transition in Parikh's interest from formal languages to natural languages, and how he approached Wittgenstein's philosophy of language, it traces the academic trajectory of a brilliant scholar whose work opened up various new avenues in research. This volume is part of Springer's book series Outstanding Contributions to Logic, and honours Rohit Parikh and his works in many ways. Parikh is a leader in the realm of ideas, offering concepts and definitions that enrich the field and lead to new research directions. Parikh has contributed to a variety of areas in logic, computer science and game theory. In mathematical logic his contributions have been in recursive function theory, proof theory and non-standard analysis; in computer science, in the areas of modal, temporal and dynamic logics of programs and semantics of programs, as well as logics of knowledge; in artificial intelligence in the area of belief revision; and in game theory in the formal analysis of social procedures, with a strong undercurrent of philosophy running through all his work.This is not a collection of articles limited to one theme, or even directly connected to specific works by Parikh, but instead all papers are inspired and influenced by Parikh in some way, adding structures to and enriching "Parikh-land". The book presents a brochure-like overview of Parikh-land before providing an "introductory video" on the sights and sounds that you experience when reading the book.

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines.

Future Data and Knowledge Base Systems will require new functionalities: richer data modelling capabilities, more powerful query languages, and new concepts of query answers. Future query languages will include functionalities such as hypothetical reasoning, abductive reasoning, modal reasoning, and metareasoning, involving knowledge and belief. Intentional answers will lead to cooperative query answering in which the answer to a query takes into consideration user's expectations. Non-classical logic plays an important role in this book for the formalization of new queries and new answers. It is shown how logic permits precise definitions for concepts like cooperative answers, subjective queries, or reliable sources of information, and gives a precise framework for reasoning about these complex concepts. It is worth noting that advances in knowledge management are not just an application domain for existing results in logic, but also require new developments in logic. The book is organized into 10 chapters which cover the areas of cooperative query answering (in the first three chapters), metareasoning and abductive reasoning (chapters 5 to 7), and, finally, hypothetical and subjunctive reasoning (last three chapters).

Refinement is one of the cornerstones of the formal approach to software engineering, and its use in various domains has led to research on new applications and generalisation. This book brings together this important research in one volume, with the addition of examples drawn from different application areas. It covers four main themes: Data refinement and its application to Z Generalisations of refinement that change the interface and atomicity of operations Refinement in Object-Z Modelling state and behaviour by combining Object-Z with CSP Refinement in Z and Object-Z: Foundations and Advanced Applications provides an invaluable overview of recent research for academic and industrial researchers, lecturers teaching formal specification and development, industrial practitioners using formal methods in their work, and postgraduate and advanced undergraduate students. This second edition is a comprehensive update to the first and includes the following new material: Early chapters have been extended to also include trace refinement, based directly on partial relations rather than through totalisation Provides an updated discussion on divergence, non-atomic refinements and approximate refinement Includes a discussion of the differing semantics of operations and outputs and how they affect the abstraction of models written using Object-Z and CSP Presents a fuller account of the relationship between relational refinement and various models of refinement in CSP Bibliographic notes at the end of each chapter have been extended with the most up to date citations and research

"Set Theory for Computing" provides a comprehensive account of set-oriented symbolic manipulation methods suitable for automated reasoning. Its main objective is twofold: 1) to provide a flexible formalization for a variety of set languages, and 2) to clarify the semantics of set constructs firmly established in modern specification languages and in the programming practice. Topics include: semantic unification, decision algorithms, modal logics, declarative programming, tableau-based proof techniques, and theory-based theorem proving. The style of presentation is self-contained, rigorous and accurate. Some familiarity with symbolic logic is helpful but not a requirement. This book is a useful resource for all advanced students, professionals, and researchers in computing sciences, artificial intelligence, automated reasoning, logic, and computational mathematics. It will serve to complement their intuitive understanding of set concepts with the ability to master them by symbolic and logically based algorithmic methods and deductive techniques.

This book presents the theory of continuum mechanics for mechanical, thermodynamical, and electrodynamical systems. It shows how to obtain governing equations and it applies them by computing the reality. It uses only open-source codes developed under the FEniCS project and includes codes for 20 engineering applications from mechanics, fluid dynamics, applied thermodynamics, and electromagnetism. Moreover, it derives and utilizes the constitutive equations including coupling terms, which allow to compute multiphysics problems by incorporating interactions between primitive variables, namely, motion, temperature, and electromagnetic fields. An engineering system is described by the primitive variables satisfying field equations that are partial differential equations in space and time. The field equations are mostly coupled and nonlinear, in other words, difficult to solve. In order to solve the coupled, nonlinear system of partial differential equations, the book uses a novel collection of open-source packages developed under the FEniCS project. All primitive variables are solved at once in a fully coupled fashion by using finite difference method in time and finite element method in space.

This volume, the 6th volume in the DRUMS Handbook series, is part of the after math of the successful ESPRIT project DRUMS (Defeasible Reasoning and Un certainty Management Systems) which took place in two stages from 1989-1996. In the second stage (1993-1996) a work package was introduced devoted to the topics Reasoning and Dynamics, covering both the topics of 'Dynamics of Rea soning', where reasoning is viewed as a process, and 'Reasoning about Dynamics', which must be understood as pertaining to how both designers of and agents within dynamic systems may reason about these systems. The present volume presents work done in this context. This work has an emphasis on modelling and formal techniques in the investigation of the topic "Reasoning and Dynamics," but it is not mere theory that occupied us. Rather research was aimed at bridging the gap between theory and practice. Therefore also real-life applications of the modelling techniques were considered, and we hope this also shows in this volume, which is focused on the dynamics of reasoning processes. In order to give the book a broader perspective, we have invited a number of well-known researchers outside the project but working on similar topics to contribute as well. We have very pleasant recollections of the project, with its lively workshops and other meetings, with the many sites and researchers involved, both within and outside our own work package."

Integral equations have wide applications in various fields, including continuum mechanics, potential theory, geophysics, electricity and magnetism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control systems, communication theory, mathematical economics, population genetics, queueing theory, and medicine.

Computational Methods for Linear Integral Equations presents basic theoretical material that deals with numerical analysis, convergence, error estimates, and accuracy. The unique computational aspect leads the reader from theoretical and practical problems all the way through to computation with hands-on guidance for input files and the execution of computer programs.

Features:

* Offers all supporting MathematicaA(R) files related to the book via the Internet at the authors' Web sites: www.math.uno.edu/fac/pkythe.html or www.math.uno.edu/fac/ppuri.html

* Contains identification codes for problems, related methods, and computer programs that are cross-referenced throughout the book to make the connections easy to understand

* Illustrates a how-to approach to computational work in the development of algorithms, construction of input files, timing, and accuracy analysis

* Covers linear integral equations of Fredholm and Volterra types of the first and second kinds as well as associated singular integral equations, integro-differential equations, and eigenvalue problems

* Provides clear, step-by-step guidelines for solving difficult and complex computational problems

This book is an essential reference and authoritative resource for all professionals, graduate students, and researchers in mathematics, physical sciences, and engineering. Researchers interested in the numerical solution of integral equations will find its practical problem-solving style both accessible and useful for their work.

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+e)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial optimization.

The topic of level sets is currently very timely and useful for creating realistic 3-D images and animations. They are powerful numerical techniques for analyzing and computing interface motion in a host of application settings. In computer vision, it has been applied to stereo and segmentation, whereas in graphics it has been applied to the postproduction process of in-painting and 3-D model construction. Osher is co-inventor of the Level Set Methods, a pioneering framework introduced jointly with James Sethian from the University of Berkeley in 1998. This methodology has been used up to now to provide solutions to a wide application range not limited to image processing, computer vision, robotics, fluid mechanics, crystallography, lithography, and computer graphics. The topic is of great interest to advanced students, professors, and R&D professionals working in the areas of graphics (post-production), video-based surveillance, visual inspection, augmented reality, document image processing, and medical image processing. These techniques are already employed to provide solutions and products in the industry (Cognitech, Siemens, Philips, Focus Imaging). An essential compilation of survey chapters from the leading researchers in the field, emphasizing the applications of the methods. This book can be suitable for a short professional course related with the processing of visual information.

All over the world sport plays a prominent role in society: as a leisure activity for many, as an ingredient of culture, as a business and as a matter of national prestige in such major events as the World Cup in soccer or the Olympic Games. Hence, it is not surprising that science has entered the realm of sports, and, in particular, that computer simulation has become highly relevant in recent years. This is explored in this book by choosing five different sports as examples, demonstrating that computational science and engineering (CSE) can make essential contributions to research on sports topics on both the fundamental level and, eventually, by supporting athletes performance."

This book describes a novel methodology for studying algorithmic skills, intended as cognitive activities related to rule-based symbolic transformation, and argues that some human computational abilities may be interpreted and analyzed as genuine examples of extended cognition. It shows that the performance of these abilities relies not only on innate neurocognitive systems or language-related skills, but also on external tools and general agent-environment interactions. Further, it asserts that a low-level analysis, based on a set of core neurocognitive systems linking numbers and language, is not sufficient to explain some specific forms of high-level numerical skills, like those involved in algorithm execution. To this end, it reports on the design of a cognitive architecture for modeling all the relevant features involved in the execution of algorithmic strategies, including external tools, such as paper and pencils. The first part of the book discusses the philosophical premises for endorsing and justifying a position in philosophy of mind that links a modified form of computationalism with some recent theoretical and scientific developments, like those introduced by the so-called dynamical approach to cognition. The second part is dedicated to the description of a Turing-machine-inspired cognitive architecture, expressly designed to formalize all kinds of algorithmic strategies.

The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields.
The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications.

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. The style is friendly and approachable and cartoon characters guide the way. Inside this book, readers will find detailed descriptions of algorithms, implementations in Julia that illustrate concepts and allow readers to explore methods on their own, and illustrations and graphics that emphasize core concepts and demonstrate algorithms. Numerical Linear Algebra with Julia is a textbook for undergraduate and graduate students. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. The book may also serve as a reference for researchers in various fields such as computational engineering, statistics, data-science, and machine learning, who depend on numerical solvers in linear algebra.

In a world of almost permanent and rapidly increasing electronic data availability, techniques of filtering, compressing, and interpreting this data to transform it into valuable and easily comprehensible information is of utmost importance. One key topic in this area is the capability to deduce future system behavior from a given data input. This book brings together for the first time the complete theory of data-based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data-based modelling, new concepts including extended additive and multiplicative submodels are developed and their extensions to state estimation and data fusion are derived. All these algorithms are illustrated with benchmark and real-life examples to demonstrate their efficiency. Chris Harris and his group have carried out pioneering work which has tied together the fields of neural networks and linguistic rule-based algortihms. This book is aimed at researchers and scientists in time series modeling, empirical data modeling, knowledge discovery, data mining, and data fusion.

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.

Automatic Graph Drawing is concerned with the layout of relational structures as they occur in Computer Science (Data Base Design, Data Mining, Web Mining), Bioinformatics (Metabolic Networks), Businessinformatics (Organization Diagrams, Event Driven Process Chains), or the Social Sciences (Social Networks). In mathematical terms, such relational structures are modeled as graphs or more general objects such as hypergraphs, clustered graphs, or compound graphs. A variety of layout algorithms that are based on graph theoretical foundations have been developed in the last two decades and implemented in software systems. After an introduction to the subject area and a concise treatment of the technical foundations for the subsequent chapters, this book features 14 chapters on state-of-the-art graph drawing software systems, ranging from general "tool boxes'' to customized software for various applications. These chapters are written by leading experts, they follow a uniform scheme and can be read independently from each other.

New Approaches to Circle Packing into the Square is devoted to the most recent results on the densest packing of equal circles in a square. In the last few decades, many articles have considered this question, which has been an object of interest since it is a hard challenge both in discrete geometry and in mathematical programming. The authors have studied this geometrical optimization problem for a long time, and they developed several new algorithms to solve it. The book completely covers the investigations on this topic.