This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

Features recent advances and new applications in graph edge coloring

Reviewing recent advances in the Edge Coloring Problem, "Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture" provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring.

The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as:

Use of Tashkinov trees to obtain an asymptotic positive solution to Goldberg's conjecture

Application of Vizing fans to obtain both known and new results

Kierstead paths as an alternative to Vizing fans

Classification problem of simple graphs

Generalized edge coloring in which a color may appear more than once at a vertex

This book also features first-time English translations of two groundbreaking papers written by Vadim Vizing on an estimate of the chromatic class of a p-graph and the critical graphs within a given chromatic class.

Written by leading experts who have reinvigorated research in the field, "Graph Edge Coloring" is an excellent book for mathematics, optimization, and computer science courses at the graduate level. The book also serves as a valuable reference for researchers interested in discrete mathematics, graph theory, operations research, theoretical computer science, and combinatorial optimization.

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Algorithms from THE BOOK: Incorporates Julia code for easy experimentation. Is written in clear, concise prose consistent with mathematical rigour. Includes a large number of classroom-tested exercises at the end of each chapter. Covers background material, often omitted from undergraduate courses, in the appendices. This textbook is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.

This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: "This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory." Acta Scientiarum Mathematiciarum "Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity." Persi Diaconis & Ron Graham, SIAM Review "The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory." Bulletin of the Institute of Combinatorics and its Applications "Succeeds dramatically ... a hell of a good book." MAA Reviews "A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors." Mathematika " ... like listening to someone explain mathematics." Bulletin of the AMS

Electric power systems have become much more complex in the past years, due to the integration of distributed generation including renewable energy sources and the challenges caused by intermittency of renewables. This complexity makes power systems potentially more vulnerable. However, use of computer-based protection methods (i.e., digital protection relays) supported by communication technology have helped in protecting electrical networks from faults to which they are subjected to. This second edition of the book covers a comprehensive introduction to the protection of electrical power systems using digital protective relays. The new edition offers a thorough revision and update, and comprehensive additional material. Chapters treat the mathematical background of protection algorithms including, sinusoidal-wave-based algorithms, Walsh function and S-Transform-based techniques, least squares and differential equation-based techniques, travelling wave-based protection, protection of transformers, digital line differential protection, a comparison between digital protection algorithms, and importantly, protection of networks with distributed generation including renewable energy resources. The book is written for researchers in electrical engineering and power engineering, in industry, utilities and universities, and for advanced students. The treatment is logically structured, covering mathematics and principles for the development and implementation of the major algorithms underlying different protection techniques. These techniques can be applied to protection of generator transformers, lines, switchgear and cable circuits: the main components of transmission and distribution systems with and without integrated distributed energy sources including renewables.

This volume is the first diverse and comprehensive treatment of algorithms and architectures for the realization of neural network systems. It presents techniques and diverse methods in numerous areas of this broad subject. The book covers major neural network systems structures for achieving effective systems, and illustrates them with examples.
This volume includes Radial Basis Function networks, the Expand-and-Truncate Learning algorithm for the synthesis of Three-Layer Threshold Networks, weight initialization, fast and efficient variants of Hamming and Hopfield neural networks, discrete time synchronous multilevel neural systems with reduced VLSI demands, probabilistic design techniques, time-based techniques, techniques for reducing physical realization requirements, and applications to finite constraint problems.
A unique and comprehensive reference for a broad array of algorithms and architectures, this book will be of use to practitioners, researchers, and students in industrial, manufacturing, electrical, and mechanical engineering, as well as in computer science and engineering.
Key Features
* Radial Basis Function networks
* The Expand-and-Truncate Learning algorithm for the synthesis of Three-Layer Threshold Networks
* Weight initialization
* Fast and efficient variants of Hamming and Hopfield neural networks
* Discrete time synchronous multilevel neural systems with reduced VLSI demands
* Probabilistic design techniques
* Time-based techniques
* Techniques for reducing physical realization requirements
* Applications to finite constraint problems
* Practical realization methods for Hebbian type associative memory systems
*Parallel self-organizing hierarchical neural network systems
* Dynamics of networks of biological neurons for utilization in computational neuroscience
Practitioners, researchers, and students in industrial, manufacturing, electrical, and mechanical engineering, as well as in computer science and engineering, will find this volume a unique and comprehensive reference to a broad array of algorithms and architectures

This text explains how advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers such topics as: the variations of the windowed Fourier transform; constructions of special waveforms suitable for specific tasks; the use of redundant representations in reconstruction and enhancement; applications of efficient numerical compression as a tool for fast numerical analysis; and approximation properties of various waveforms in different contexts.

The memory storage requirements of complex programs are extremely difficult to manage correctly by hand. A single error may lead to indeterminate and inexplicable program crashes. Worse still, failures are often unrepeatable and may surface only long after the program has been delivered to the customer. The eradication of memory errors typically consumes a substantial amount of development time. And yet the answer is relatively easy — garbage collection; removing the clutter of memory management from module interfaces, which then frees the programmer to concentrate on the problem at hand rather than low-level book-keeping details. For this reason, most modern object-oriented languages such as Smalltalk, Eiffel, Java and Dylan, are supported by garbage collection. Garbage collecting, libraries are even available for such uncooperative languages as C and C++. This book considers how dynamic memory can be recycled automatically to guarantee error-free memory management. There is an abundant but disparate literature on the subject, largely confined to research papers. This book sets out to pool this experience in a single accessible and unified framework. Visit this book’s companion Website for updates, revisions, online gc resources, bibliography and links to more gc sites ‘Whatever else Java has accomplished, it has finally brought garbage collection into the mainstream. The efficiency and correctness of garbage collection algorithms is henceforth going to be of concern to hundreds of thousands of programmers; those who really care about this could do no better than to start with Garbage Collection: Algorithms for Automatic Dynamic Memory Management… the sort of comprehensive engineering manual that is so rare in computing.’ Dr Dobb’s Journal

Genetic Algorithms in Molecular Modeling is the first book available on the use of genetic algorithms in molecular design. This volume marks the beginning of an ew series of books, Principles in Qsar and Drug Design, which will be an indispensible reference for students and professionals involved in medicinal chemistry, pharmacology, (eco)toxicology, and agrochemistry. Each comprehensive chapter is written by a distinguished researcher in the field.
Through its up to the minute content, extensive bibliography, and essential information on software availability, this book leads the reader from the theoretical aspects to the practical applications. It enables the uninitiated reader to apply genetic algorithms for modeling the biological activities and properties of chemicals, and provides the trained scientist with the most up to date information on the topic.
. Extremely topical and timely
. Sets the foundations for the development of
computer-aided tools for solving numerous
problems in QSAR and drug design
. Written to be accessible without prior direct
experience in genetic algorithms

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

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

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

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

This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book's software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology's 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography.
The Handbook of Applied Cryptography provides a treatment that is multifunctional:

This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. Matrix Methods in Data Mining and Pattern Recognition, Second Edition is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.

R is a powerful and free software system for data analysis and graphics, with over 5,000 add-on packages available. This book introduces R using SAS and SPSS terms with which you are already familiar. It demonstrates which of the add-on packages are most like SAS and SPSS and compares them to R's built-in functions. It steps through over 30 programs written in all three packages, comparing and contrasting the packages' differing approaches. The programs and practice datasets are available for download. The glossary defines over 50 R terms using SAS/SPSS jargon and again using R jargon. The table of contents and the index allow you to find equivalent R functions by looking up both SAS statements and SPSS commands. When finished, you will be able to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses. This new edition has updated programming, an expanded index, and even more statistical methods covered in over 25 new sections.

Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is Laszlo Lovasz, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovasz's 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.

This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory.

There is no competitor to this book.

The book can be used in classrooms as well as for self-study.

For over two decades, this comprehensive manual has been the standard introduction and complete reference for writing articles and books containing mathematical formulas. If the reader requires a streamlined approach to learning LaTeX for composing everyday documents, Gratzer's (c) 2014 Practical LaTeX may also be a good choice. In this carefully revised fifth edition, the Short Course has been brought up to date and reflects a modern and practical approach to LaTeX usage. New chapters have been added on illustrations and how to use LaTeX on an iPad. Key features: An example-based, visual approach and a gentle introduction with the Short Course A detailed exposition of multiline math formulas with a Visual Guide A unified approach to TeX, LaTeX, and the AMS enhancements A quick introduction to creating presentations with formulas From earlier reviews: Gratzer's book is a solution. -European Mathematical Society Newsletter There are several LaTeX guides, but this one wins hands down for the elegance of its approach and breadth of coverage. -Amazon.com, Best of 2000, Editor's choice A novice reader will be able to learn the most essential features of LaTeX sufficient to begin typesetting papers within a few hours of time... An experienced TeX user, on the other hand, will find a systematic and detailed discussion of LaTeX fea tures. -Report on Mathematical Physics A very helpful and useful tool for all scientists and engineers. -Review of Astronomical Tools

Written to appeal to a wide field of engineers and scientists who work on multiscale and multiphysics analysis, Multiphysics and Multiscale Modeling: Techniques and Applications is dedicated to the many computational techniques and methods used to develop man-made systems as well as understand living systems that exist in nature. Presenting a body of research on multiscale and multiphysics analysis collected by the author over the years, this book provides an assessment of multiple computational techniques that include the finite element method, lattice Boltzmann method, cellular automata, and the molecular dynamics technique. The author also presents a number of example problems relevant to multiphysics and multiscale analyses, and introduces the proper coupling techniques that can be used in conjunction with computational methods to solve a multitude of multiscale and multiphysics problems. In addition, this detailed book: Provides a simplified analysis for crystalline structures using the finite element method and molecular dynamics Discusses multiscale analysis of biomaterials using human bones as an example Presents multiphysics problems for composite structures Includes fluidstructure interaction for composite structures surrounded by water Contains an example of the multiphysics analysis of electromechanical problems Introduces a multiphysics analysis of biomechanics using the example of blood vessels (for which there is fluid-structure interaction) Multiphysics and Multiscale Modeling: Techniques and Applications emphasizes the use of multiphysics and multiscale techniques to aid in the understanding and development of complex physical behaviors and systems. This book serves as a resource in mechanical engineering, bioengineering, and materials engineering study, practice, and research.

Expert coverage of the design and implementation of state estimation algorithms for tracking and navigation

Estimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations. It explains state estimator design using a balanced combination of linear systems, probability, and statistics.

The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimation with a focus on applying these techniques to real systems. Other features include:

• Problems that apply theoretical material to real-world applications
• In-depth coverage of the Interacting Multiple Model (IMM) estimator
• Companion DynaEst™ software for MATLAB™ implementation of Kalman filters and IMM estimators
• Design guidelines for tracking filters

Suitable for graduate engineering students and engineers working in remote sensors and tracking, Estimation with Applications to Tracking and Navigation provides expert coverage of this important area.

This book states that blockchain technology provides a secure distributed, peer-to-peer, and decentralized network with advanced cryptography primitives and protocols. The important question that arises in the quantum computing world is to test the existing blockchain networks against quantum attacks and design quantum computing enabled secure blockchain solutions. This book encourages professionals from different fields to provide blockchain and quantum technology-integrated solutions that incorporate low-cost, effective QoS, fast, secure, and futuristic demands. This book has surveyed and proposed approaches that improve quantum computing and cryptography protocols. Quantum computing and quantum science are not just helpful in software but the hardware world as well. To design networks with quantum science, quantum-enabled devices like quantum memories and quantum repeaters can be useful to demonstrate for organizations. For example, designing a single quantum repeater for long-distance quantum communication is useful in reducing the network cost, and ensuring better security levels. This book has introduced the quantum computing and blockchain technology aspects, their integration approaches and future directions.

Comprehensive presentation of both analytic and probabilistic techniques

As a comprehensive survey of the major techniques of average case analysis, this work presents, in detail, both analytic methods used for well-structured algorithms and probabilistic methods used for more structurally complex algorithms. In particular, the applications in the book use algorithms that focus on data structures on sequences, also called strings, which are widely used in computer science, computational biology, and information theory. Specific techniques covered include the inclusion-exclusion principle, the first and second moment methods, the random coding technique, the subadditive ergodic theorem, large deviations, generating functions, complex asymptotic methods, the Mellin transform, and analytic poissonization and depoissonization. Each method is clearly explained and accompanied by related applications and problems involving algorithms on sequences.

Important features of the book include:

• A foreword by well-known expert Dr. Philippe Flajolet, INRIA, France
• Presentation of complex analysis used to solve discrete and probabilistic problems on sequences
• Discussions of Lempel-Ziv data compression-schemes, the string edit problem, pattern matching algorithms, many variations of digital trees, the leader election algorithm, and more
• A chapter devoted to tools used in information theory, particularly the random coding technique and pattern matching approach to data compression
• Application sections in each chapter that illustrate the methods covered
• An extensive bibliography

A modern approach to statistical learning and its applications through visualization methods

With a unique and innovative presentation, "Multivariate Nonparametric Regression and Visualization "provides readers with the core statistical concepts to obtain complete and accurate predictions when given a set of data. Focusing on nonparametric methods to adapt to the multiple types of data generatingmechanisms, the book begins with an overview of classification and regression.

The book then introduces and examines various tested and proven visualization techniques for learning samples and functions. "Multivariate Nonparametric Regression and Visualization "identifies risk management, portfolio selection, and option pricing as the main areas in which statistical methods may be implemented in quantitative finance. The book provides coverage of key statistical areas including linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods. Exploring the additional applications of nonparametric and semiparametric methods, "Multivariate" "Nonparametric Regression and Visualization "features: An extensive appendix with R-package training material to encourage duplication and modification of the presented computations and researchMultiple examples to demonstrate the applications in the field of financeSections with formal definitions of the various applied methods for readers to utilize throughout the book

"Multivariate Nonparametric Regression and Visualization "is an ideal textbook for upper-undergraduate and graduate-level courses on nonparametric function estimation, advanced topics in statistics, and quantitative finance. The book is also an excellent reference for practitioners who apply statistical methods in quantitative finance.

This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms. Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

A survey of the philosophical implications and practical applications of fuzzy systems

Fuzzy mathematical concepts such as fuzzy sets, fuzzy logic, and similarity relations represent one of the most exciting currents in modern engineering and have great potential in applications ranging from control theory to bioinformatics. Data Engineering guides the reader through a number of concepts interconnected by fuzzy mathematics and discusses these concepts from a systems engineering perspective to showcase the continuing vitality, attractiveness, and applicability of fuzzy mathematics.

The author discusses the fundamental aspects of data analysis, systems modeling, and uncertainty calculi. He avoids a narrow discussion of specialized methodologies and takes a holistic view of the nature and application of fuzzy systems, considering principles, paradigms, and methodologies along the way. This broad coverage includes:

• Fundamentals of modeling, identification, and clustering
• System analysis
• Uncertainty techniques
• Random-set modeling and identification
• Fuzzy inference engines
• Fuzzy classification, control, and mathematics

In the important emerging field of bioinformatics, the book sets out how to encode a natural system in mathematical models, describes methods to identify interrelationships and interactions from data, and thereby helps the practitioner to decide which variables to measure and why.

Data Engineering serves as an up-to-date and informative survey of the theoretical and practical tools for analyzing complex systems. It offers a unique treatment of complex issues that is accessible to students and researchers from a variety of backgrounds.

Iterative Computer Algorithms with Applications in Engineering describes in-depth the five main iterative algorithms for solving hard combinatorial optimization problems: Simulated Annealing, Genetic Algorithms, Tabu Search, Simulated Evolution, and Stochastic Evolution. The authors present various iterative techniques and illustrate how they can be applied to solve several NP-hard problems.

For each algorithm, the authors present the procedures of the algorithm, parameter selection criteria, convergence property analysis, and parallelization. There are also several real-world examples that illustrate various aspects of the algorithms. The book includes an introduction to fuzzy logic and its application in the formulation of multi-objective optimization problems, a discussion on hybrid techniques that combine features of heuristics, a survey of recent research work, and examples that illustrate required mathematical concepts.

The unique features of this book are: An integrated and up-to-date description of iterative non-deterministic algorithms; Detailed descriptions of Simulated Evolution and Stochastic Evolution; A level of treatment suitable for first year graduate student and practicing engineers; Parallelization aspects and particular parallel implementations; A brief survey of recent research work; Graded exercises and an annotated bibliography in each chapter