Mathematics of Discrete Structures for Computer Science

This book allows students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor. It gives readers a unified

In recent years game theory has had a substantial impact on computer science, especially on Internet- and e-commerce-related issues. Algorithmic Game Theory, first published in 2007, develops the central ideas and results of this exciting area in a clear and succinct manner. More than 40 of the top researchers in this field have written chapters that go from the foundations to the state of the art. Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security. This definitive work will set the tone of research for the next few years and beyond. Students, researchers, and practitioners alike need to learn more about these fascinating theoretical developments and their widespread practical application.

This collection of essays is on the relation between probabilities, especially conditional probabilities, and conditionals. It provides negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work the contributions extend his ideas in directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists.

Polymers exhibit a range of physical characteristics, from rubber-like elasticity to the glassy state. These particular properties are controlled at the molecular level by the mobility of the structural constituents. Remarkable changes in mobility can be witnessed with temperature, over narrow, well defined regions, termed relaxation processes. This is an important, unique phenomenon controlling polymer transition behaviour and is described here at an introductory level. The important types of relaxation processes from amorphous to crystalline polymers and polymeric miscible blends are covered, in conjunction with the broad spectrum of experimental methods used to study them. In-depth discussion of molecular level interpretation, including atomistic level computer simulations and applications to molecular mechanism elucidation, are discussed. The result is a self-contained approach to polymeric interpretation suitable for researchers in materials science, physics and chemistry interest

Iterative processing is an important technique with numerous applications. Exploiting the power of factor graphs, this detailed survey provides a general framework for systematically developing iterative algorithms for digital receivers, and highlights connections between important algorithms. Starting with basic concepts in digital communications, progressively more complex ideas are presented and integrated resulting in the development of cutting-edge algorithms for iterative receivers. Real-world applications are covered in detail, including decoding for turbo and LDPC codes, and detection for multi-antenna and multi-user systems. This accessible framework will allow the reader to apply factor graphs to practical problems, leading to the design of new algorithms in applications beyond digital receivers. With many examples and algorithms in pseudo-code, this book is an invaluable resource for graduate students and researchers in electrical engineering and computer science, and for pr

This book/CD bundle of the greatly expanded third edition of Numerical Recipes now has wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The informal, easy-to-read style that made earlier editions so popular is kept throughout. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support or further licence information please visit www.nr.com

Do you want easy access to the latest methods in scientific computing? This greatly expanded third edition of Numerical Recipes has it, with wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. The executable C++ code, now printed in colour for easy reading, adopts an object-oriented style particularly suited to scientific applications. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior

This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

String matching problems range from the relatively simple task of searching a single text for a string of characters to searching a database for approximate occurrences of a complex pattern. Recent years have witnessed a dramatic increase of interest in sophisticated string matching problems, especially in information retrieval and computational biology. This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice. It covers searching for simple, multiple and extended strings, as well as regular expressions, and exact and approximate searching. It includes all the most significant new developments in complex pattern searching. The clear explanations, step-by-step examples, algorithm pseudocode, and implementation efficiency maps will enable researchers, professionals and students in bioinformatics, computer science, and software engineering to choose the most appropriate algorithms for their applicatio

This book, first published in 2004, describes the application of statistical physics and complex systems theory to the study of the evolution and structure of the Internet. Using a statistical physics approach the Internet is viewed as a growing system that evolves in time through the addition and removal of nodes and links. This perspective permits us to outline the dynamical theory required for a description of the macroscopic evolution of the Internet. The presence of such a theoretical framework appears to be a revolutionary and promising path towards our understanding of the Internet and the various processes taking place on this network, including, for example, the spread of computer viruses or resilience to random or intentional damages. This book will be of interest to graduate students and researchers in statistical physics, computer science and mathematics studying in this subject.

This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used

The simulation of physical systems requires a simplified, hierarchical approach which models each level from the atomistic to the macroscopic scale. From quantum mechanics to fluid dynamics, this book systematically treats the broad scope of computer modeling and simulations, describing the fundamental theory behind each level of approximation. Berendsen evaluates each stage in relation to its applications giving the reader insight into the possibilities and limitations of the models. Practical guidance for applications and sample programs in Python are provided. With a strong emphasis on molecular models in chemistry and biochemistry, this 2007 book will be suitable for advanced undergraduate and graduate courses on molecular modeling and simulation within physics, biophysics, physical chemistry and materials science. It will also be a useful reference to all those working in the field. Additional resources for this title including solutions for instructors and programs are available

This 2007 volume contains survey articles based on the invited lectures given at the Twenty-first British Combinatorial Conference, held in July 2007 at the University of Reading. This biennial conference is a well-established international event and the articles are of the high quality that befits the event. By its nature this volume provides an overview of current research activity in several areas of combinatorics, ranging from graph theory to current applications of combinatorial mathematics, including efficient approximability of NP-hard optimization problems and cryptographic key management. The authors are some of the world's foremost researchers in their fields, and here they summarize existing results, and give a unique preview of work currently being written up. The book provides a valuable survey of the state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics a

Students of evolutionary and behavioural ecology are often unfamiliar with mathematical techniques, though much of biology relies on mathematics. Evolutionary ideas are often complex, meaning that the logic of hypotheses proposed should not only be tested empirically but also mathematically. There are numerous different modelling tools used by ecologists, ranging from population genetic 'bookkeeping', to game theory and individual-based computer simulations. Due to the many different modelling options available, it is often difficult to know where to start. Hanna Kokko has designed this 2007 book to help with these decisions. Each method described is illustrated with one or two biologically interesting examples that have been chosen to help overcome fears of many biologists when faced with mathematical work, whilst also providing the programming code (Matlab) for each problem. Aimed primarily at students of evolutionary and behavioural ecology, this book will be of interest to any biol

Students of evolutionary and behavioural ecology are often unfamiliar with mathematical techniques, though much of biology relies on mathematics. Evolutionary ideas are often complex, meaning that the logic of hypotheses proposed should not only be tested empirically but also mathematically. There are numerous different modelling tools used by ecologists, ranging from population genetic 'bookkeeping', to game theory and individual-based computer simulations. Due to the many different modelling options available, it is often difficult to know where to start. Hanna Kokko has designed this 2007 book to help with these decisions. Each method described is illustrated with one or two biologically interesting examples that have been chosen to help overcome fears of many biologists when faced with mathematical work, whilst also providing the programming code (Matlab) for each problem. Aimed primarily at students of evolutionary and behavioural ecology, this book will be of interest to any biol

Offers fifteen activities in language arts and literacy, visual arts, mathematics, science, and performing art, along with guidelines for implementing, interpreting, and "bridging" observations of chi

This accessible volume offers a unique set of research exemplars for science, mathematics and technology educators. The volume explores the important challenge of how to translate leading-edge methodo

Model order reduction (MOR) techniques reduce the complexity of VLSI designs, paving the way to higher operating speeds and smaller feature sizes. This book presents a systematic introduction to, and treatment of, the key MOR methods employed in general linear circuits, using real-world examples to illustrate the advantages and disadvantages of each algorithm. Following a review of traditional projection-based techniques, coverage progresses to more advanced MOR methods for VLSI design, including HMOR, passive truncated balanced realization (TBR) methods, efficient inductance modeling via the VPEC model, and structure-preserving MOR techniques. Where possible, numerical methods are approached from the CAD engineer's perspective, avoiding complex mathematics and allowing the reader to take on real design problems and develop more effective tools. With practical examples and over 100 illustrations, this book is suitable for researchers and graduate students of electrical and computer eng

Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.

Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.

Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer

A unique overview of Portuguese oceanic expansion between 1400 and 1800, the essays in this volume treat a wide range of subjects - economy and society, politics and institutions, cultural configurations and comparative dimensions - and radically update data and interpretations on the economic and financial trends of the Portuguese Empire. Interregional networks are analysed in a substantial way. Patterns of settlement, political configurations, ecclesiastical structures, and local powers are put in global context. Language and literature, the arts, and science and technology are revisited with refreshing and innovative approaches. The interaction between Portuguese and local people is studied in different contexts, while the entire imperial and colonial culture of the Portuguese world is looked at synthetically for the first time. In short, this book provides a broad understanding of the Portuguese Empire in its first four centuries as a factor in world history and as a major componen

The book is intended for lectures on string processes and pattern matching in Master's courses of computer science and software engineering curricula. The details of algorithms are given with correctness proofs and complexity analysis, which make them ready to implement. Algorithms are described in a C-like language. The book is also a reference for students in computational linguistics or computational biology. It presents examples of questions related to the automatic processing of natural language, to the analysis of molecular sequences, and to the management of textual databases.

Distributed systems are fast becoming the norm in computer science. Formal mathematical models and theories of distributed behaviour are needed in order to understand them. This book proposes a distributed pi-calculus called Dpi, for describing the behaviour of mobile agents in a distributed world. It is based on an existing formal language, the pi-calculus, to which it adds a network layer and a primitive migration construct. A mathematical theory of the behaviour of these distributed systems is developed, in which the presence of types plays a major role. It is also shown how in principle this theory can be used to develop verification techniques for guaranteeing the behavior of distributed agents. The text is accessible to computer scientists with a minimal background in discrete mathematics. It contains an elementary account of the pi-calculus, and the associated theory of bisimulations. It also develops the type theory required by Dpi from first principles.

CD and DVD Forensics will take the reader through all facets of handling, examining, and processing CD and DVD evidence for computer forensics. At a time where data forensics is becoming a major part

An introductory textbook for advanced students of physics, chemistry and computer science, covering an area of physics that has lately witnessed rapid expansion. The topics treated here include quantu

The great popularity of fantasy and science fiction themes in films, books, graphic novels, and computer games has created a continuing demand for artists who can conceptualize and draw convincing sp

The book is an introductory textbook mainly for students of computer science and mathematics. Its guiding phrase is "what every theoretical computer scientist should know about linear programming". A

This is a major new survey of the social and cultural history of sexuality in early modern Europe. Within a frame that includes the Renaissance, the Reformation, the Scientific Revolution, and the Enlightenment, it weaves together statistical findings, discussions of changing sexual ideology, and evidence of belief structures regarding family, religion, science, crime, and deviance. While broad in overall scope and coverage, the transformations are framed to highlight the narrative of change over time within each domain. By emphasizing the interrelationship between practices and ideological change - in family form, religious organization, medical logic, legal structures, and notions of deviancy - Katherine Crawford's accessible survey reveals how these changes produced the conditions in which our modern notions of sexuality were developed. This book will be essential reading for students of early modern European history and the history of sexuality.

Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-d

Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-d

Elements of Quantum Information' introduces the reader to the fascinating field of quantum information processing, which lives on the interface between computer science, physics, mathematics, and engi

Peak signal power is an important factor in the implementation of multicarrier (MC) modulation schemes, like OFDM, in wireless and wireline communication systems. This 2007 book describes tools necessary for analyzing and controlling the peak-to-average power ratio in MC systems, and how these techniques are applied in practical designs. The author starts with an overview of multicarrier signals and basic tools and algorithms, before discussing properties of MC signals in detail: discrete and continuous maxima; statistical distribution of peak power; codes with constant peak-to-average power ratio are all covered, concluding with methods to decrease peak power in MC systems. Current knowledge, problems, methods and definitions are summarized using rigorous mathematics, with an overview of the tools for the engineer. The book is aimed at graduate students and researchers in electrical engineering, computer science and applied mathematics, and practitioners in the telecommunications indu

The reconnection of magnetic fields is one of the most fascinating processes in plasma physics, responsible for phenomena such as solar flares and magnetospheric substorms. The concept of reconnection has developed through recent advances in exploring the magnetospheres of the Sun and Earth through theory, computer simulations and spacecraft observations. The great challenge in understanding it stems from balancing the large volumes of plasma and magnetic fields involved with the energy release with the physical mechanism which relies on the strongly localized behavior of charged particles. This book, edited by and with contributions from leading scientists in the field, provides a comprehensive overview of recent theoretical and observational findings concerning the physics of reconnection and the complex structures that may give rise to, or develop from, reconnection. It is intended for researchers and graduate students interested in the dynamics of plasmas.

Quantum Information Processing is a young and rapidly growing field of research at the intersection of physics, mathematics, and computer science. Its ultimate goal is to harness quantum physics to co

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

Text mining is a new and exciting area of computer science research that tries to solve the crisis of information overload by combining techniques from data mining, machine learning, natural language processing, information retrieval, and knowledge management. Similarly, link detection – a rapidly evolving approach to the analysis of text that shares and builds upon many of the key elements of text mining – also provides new tools for people to better leverage their burgeoning textual data resources. The Text Mining Handbook presents a comprehensive discussion of the state-of-the-art in text mining and link detection. In addition to providing an in-depth examination of core text mining and link detection algorithms and operations, the book examines advanced pre-processing techniques, knowledge representation considerations, and visualization approaches. Finally, the book explores current real-world, mission-critical applications of text mining and link detection in such varied fields a

The metaphor of the adaptive landscape - that evolution via the process of natural selection can be visualized as a journey across adaptive hills and valleys, mountains and ravines - permeates both evolutionary biology and the philosophy of science. The focus of this 2006 book is to demonstrate to the reader that the adaptive landscape concept can be put into actual analytical practice through the usage of theoretical morphospaces - geometric spaces of both existent and non-existent biological form - and to demonstrate the power of the adaptive landscape concept in understanding the process of evolution. The adaptive landscape concept further allows us to take a spatial approach to the concepts of natural selection, evolutionary constraint and evolutionary development. For that reason, this book relies heavily on spatial graphics to convey the concepts developed within these pages, and less so on formal mathematics.