Discover the benefits of applying algorithms to solve scientific, engineering, and practical problems
Providing a combination of theory, algorithms, and simulations, Handbook of Applied Algorithms presents an all-encompassing treatment of applying algorithms and discrete mathematics to practical problems in "hot" application areas, such as computational biology, computational chemistry, wireless networks, and computer vision.
In eighteen self-contained chapters, this timely book explores:
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Localized algorithms that can be used in topology control for wireless ad-hoc or sensor networks
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Bioinformatics algorithms for analyzing data
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Clustering algorithms and identification of association rules in data mining
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Applications of combinatorial algorithms and graph theory in chemistry and molecular biology
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Optimizing the frequency planning of a GSM network using evolutionary algorithms
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Algorithmic solutions and advances achieved through game theory
Complete with exercises for readers to measure their comprehension of the material presented, Handbook of Applied Algorithms is a much-needed resource for researchers, practitioners, and students within computer science, life science, and engineering.
Amiya Nayak, PhD, has over seventeen years of industrial experience and is Full Professor at the School of Information Technology and Engineering at the University of Ottawa, Canada. He is on the editorial board of several journals. Dr. Nayak's research interests are in the areas of fault tolerance, distributed systems/algorithms, and mobile ad-hoc networks. Ivan StojmenoviC?, PhD, is Professor at the University of Ottawa, Canada (www.site.uottawa.ca/ ivan), and Chair Professor of Applied Computing at the University of Birmingham, United Kingdom. Dr. Stojmenovic? received the Royal Society Wolfson Research Merit Award. His current research interests are mostly in the design and analysis of algorithms for wireless ad-hoc and sensor networks.

HIS book presents a generalized state-space theory for the analysis T and synthesis of finite horizon suboptimal Hoo controllers. We de rive expressions for a suboptimal controller in a general setting and propose an approximate solution to the Hoo performance robustness problem. The material in the book is taken from a collection of research papers written by the author. The book is organized as follows. Chapter 1 treats nonlinear optimal control problems in which the cost functional is of the form of a quotient or a product of powers of definite integrals. The problems considered in Chap ter 1 are very general, and the results are useful for the computation of the actual performance of an Hoo suboptimal controller. Such an application is given in Chapters 4 and 5. Chapter 2 gives a criterion for the evaluation of the infimal Hoc norm in the finite horizon case. Also, a differential equation is derived for the achievable performance as the final time is varied. A general suboptimal control problem is then posed, and an expression for a subopti mal Hoo state feedback controller is derived. Chapter 3 develops expressions for a suboptimal Hoo output feedback controller in a very general case via the solution of two dynamic Riccati equations. Assuming the adequacy of linear expressions, Chapter 4 gives an iterative procedure for the synthesis of a suboptimal Hoo controller that yields the required performance even under parameter variations."

This book presents the multi-criteria approach to decision support, as well as the various multi-criteria tools to help avoid multi-objective optimization. The book is intended as a tool for understanding the multi-criteria tools for decision support and modeling in mathematical programming. It helps to structure models, to easily model complex constraints, to have a basic modeling guide for any multi-criteria system and to better understand models already existing in the literature. The book is structured in the same order as components of the methodology, established in a multi-criteria optimization problem. It introduces the elements of the actors, the decision-making activity under criteria, calculations, specifications and objective criterion.

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent."

This is an introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads. Although this book assumes no previous knowledge of finite element methods, those who do have knowledge will still find the book to be useful. It can be utilised by aeronautical, civil, mechanical, and structural engineers as well as naval architects. This second edition includes information on the many developments that have taken place over the last twenty years. Existing chapters have been expanded where necessary, and three new chapters have been included that discuss the vibration of shells and multi-layered elements and provide an introduction to the hierarchical finite element method.

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.

With the diversification of Internet services and the increase in mobile users, efficient management of network resources has become an extremely important issue in the field of wireless communication networks (WCNs). Adaptive resource management is an effective tool for improving the economic efficiency of WCN systems as well as network design and construction, especially in view of the surge in mobile device demands. This book presents modelling methods based on queueing theory and Markov processes for a wide variety of WCN systems, as well as precise and approximate analytical solution methods for the numerical evaluation of the system performance. This is the first book to provide an overview of the numerical analyses that can be gleaned by applying queueing theory, traffic theory and other analytical methods to various WCN systems. It also discusses the recent advances in the resource management of WCNs, such as broadband wireless access networks, cognitive radio networks, and green cloud computing. It assumes a basic understanding of computer networks and queueing theory, and familiarity with stochastic processes is also recommended. The analysis methods presented in this book are useful for first-year-graduate or senior computer science and communication engineering students. Providing information on network design and management, performance evaluation, queueing theory, game theory, intelligent optimization, and operations research for researchers and engineers, the book is also a valuable reference resource for students, analysts, managers and anyone in the industry interested in WCN system modelling, performance analysis and numerical evaluation.

For an introductory or one or two semester courses in Probability and Statistics or Applied Statistics for engineering, physical science, and mathematics students. An Applications-Focused Introduction to Probability and Statistics Miller & Freund's Probability and Statistics for Engineers is rich in exercises and examples, and explores both elementary probability and basic statistics, with an emphasis on engineering and science applications. Much of the data has been collected from the author's own consulting experience and from discussions with scientists and engineers about the use of statistics in their fields. In later chapters, the text emphasises designed experiments, especially two-level factorial design. The Ninth Edition includes several new datasets and examples showing application of statistics in scientific investigations, familiarising students with the latest methods, and readying them to become real-world engineers and scientists.

This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in engineering and applied mathematics.

This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

Information and dynamics are key terms in many contemporary directions of research in numerous fields. Basic frarneworks in this regard are information theory and the theory of dynamical systems. The origin of both areas essentially dates back into the 20s of this century. An excellent presentation of the history of information theory from its early days (e.g, Nyquist, Hartley) until to the 70s has been given by J.R. Pierce et al. in the IEEE Transactions on Information Theory IT-19 (1973). System theory, the other branch mentioned above, also started with first publications in the 20s (e.g., Kohler, Lotka). A historical sketch can be found in 1. v. Bertalanffy's General Systems Theory (Braziller, Ncw York, 1968), the main body ofwhich presents a proper introduction into the main concepts and applications. At present, both branches, information theory and system theory, are hardly sepa- rable any more. Aspects of both appcar in cybernetics, contral theory, communication theory, computer science, game theory, cognitive science, and related fields. Combin- ing knowledge of various individual scientific disciplines, they are particularly useful to deal with problems of basically intcrdisciplinary character.

This book presents the Statistical Learning Theory in a detailed and easy to understand way, by using practical examples, algorithms and source codes. It can be used as a textbook in graduation or undergraduation courses, for self-learners, or as reference with respect to the main theoretical concepts of Machine Learning. Fundamental concepts of Linear Algebra and Optimization applied to Machine Learning are provided, as well as source codes in R, making the book as self-contained as possible. It starts with an introduction to Machine Learning concepts and algorithms such as the Perceptron, Multilayer Perceptron and the Distance-Weighted Nearest Neighbors with examples, in order to provide the necessary foundation so the reader is able to understand the Bias-Variance Dilemma, which is the central point of the Statistical Learning Theory. Afterwards, we introduce all assumptions and formalize the Statistical Learning Theory, allowing the practical study of different classification algorithms. Then, we proceed with concentration inequalities until arriving to the Generalization and the Large-Margin bounds, providing the main motivations for the Support Vector Machines. From that, we introduce all necessary optimization concepts related to the implementation of Support Vector Machines. To provide a next stage of development, the book finishes with a discussion on SVM kernels as a way and motivation to study data spaces and improve classification results.

This book is one of the first to include an extensive discussion of integrated public transport planning. In times of growing urban populations and increasing environmental awareness, the importance of optimizing public transport systems is ever-developing. Three different aspects are presented: line planning, timetabling, and vehicle scheduling. Classically, challenges concerning these three aspects of planning are solved sequentially. Due to their high interdependence, the author presents a clear and detailed analysis of innovative, integrated models with accompanied numerical experiments performed to assess, and often support, the benefits of integration. The book will appeal to a wide readership ranging from graduate students to researchers.

This book offers comprehensive coverage of all the mathematical tools needed by engineers in the field of processing and transport of all forms of information, data and images - as well as many other engineering disciplines. It provides essential theories, equations and results in probability theory and statistics, which constitute the basis for the presentation of signal processing, information theory, traffic and queueing theory, and reliability. The mathematical foundations of simulation are also covered.

The book's accessible style will enable students, engineers and researches new to this area to advance their knowledge of communication and other engineering technologies; however, it will also serve as a useful reference guide to anyone wishing to further explore this field.

Fundamentals of Artificial Intelligence introduces the foundations of present day AI and provides coverage to recent developments in AI such as Constraint Satisfaction Problems, Adversarial Search and Game Theory, Statistical Learning Theory, Automated Planning, Intelligent Agents, Information Retrieval, Natural Language & Speech Processing, and Machine Vision. The book features a wealth of examples and illustrations, and practical approaches along with the theoretical concepts. It covers all major areas of AI in the domain of recent developments. The book is intended primarily for students who major in computer science at undergraduate and graduate level but will also be of interest as a foundation to researchers in the area of AI.

This textbook introduces students to mass and energy balances and focuses on basic principles for calculation, design, and optimization as they are applied in industrial processes and equipment. While written primarily for undergraduate programs in chemical, energy, mechanical, and environmental engineering, the book can also be used as a reference by technical staff and design engineers interested who are in, and/or need to have basic knowledge of process engineering calculation. Concepts and techniques presented in this volume are highly relevant within many industrial sectors including manufacturing, oil/gas, green and sustainable energy, and power plant design. Drawing on 15 years of teaching experiences, and with a clear understanding of students' interests, the authors have adopted a very accessible writing style that includes many examples and additional citations to research resources from the literature, referenced at the ends of chapters.

This hands-on textbook/reference presents an introduction to the fundamental aspects of modelling and simulation, both for those wishing to learn about this methodology and also for those who have a need to apply it in their work. The text is supported by illustrative examples, drawn from projects formulated within the domains of discrete-event dynamic systems (DEDS) and continuous-time dynamic systems (CTDS). This updated new edition has been enhanced with new illustrative case studies, and additional examples demonstrating some new features and the effectiveness of the ABCmod conceptual modelling framework. Changes that facilitate the development of simulation models with ABSmod/J are illustrated. New material includes a presentation of the experimentation strategy called "design of experiments" and three new chapters that explore the optimization-simulation interface. Topics and features: presents a goal-based and project-oriented perspective of modelling and simulation; describes the ABCmod framework, an activity-based conceptual modelling framework for DEDS; examines the simulation-optimization interface in both the CTDS and DEDS domains; provides numerous illustrative examples, case studies and useful algorithms, as well as exercises and projects at the end of most chapters; includes appendices on probability and statistics, the GPSS programming environment, and relevant MATLAB features; provides supplementary software and teaching support material at an associated website, including lecture slides and a methodology for organizing student projects. Serving as an essential guide to the foundations of modelling and simulation, this practical primer is ideal for senior undergraduate and junior graduate-level students. Also suitable for self-study, the book will be of great benefit to professionals seeking insight into the vast potential of this rapidly evolving problem-solving paradigm.

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed.The book contains material on:- Linear Vector Space Analysis and the Approximation of a Function;- Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature;- Differential Quadrature Weighting Coefficient Matrices;- Solution of Differential Quadrature-resultant Equations;- The Solution of Incompressible Navier-Stokes and Helmholtz Equations;- Structural and Vibrational Analysis Applications;- Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations.Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.

Overview Scilab is a scientific software package that provides a powerful open com- puting environment for engineering and scientific applications. Distributed freely via the Internet since 1994, Scilab is currently being used in educa- tional and industrial environments around the world. This book contains all the information needed to master Scilab: how to use it interactively as a super calculator, how to write programs, how to de- velop complex applications, and more. The authors, Carey Bunks (BBN1), Jean-Philippe Chancelier (ENPC2), Fran~ois Delebecque, Claude Gomez, 3 Maurice Goursat, Ramine Nikoukhah, and Serge Steer (INRlA ), have not only been involved in the development of Scilab, but have used it for teach- ing and industrial applications for many years. A CD-ROM, containing the entire Scilab soUrce code as well as a set of precompiled binary executables for a variety of computing platforms, is included with this book. The objective here is to give a thorough description of Scilab's use, in- cluding how to master its environment and programming language, the use of the integrated graphics, the incorporation of user-provided func- tions, and a tour of the numerous application toolboxes. The purpose is to provide students and professionals with an introduction to Scilab and its use in engineering and scientific problem solving. The numerous practical examples serve as a framework that can be used as a basis for developing other applications.

Optimization methods have been considered in many articles, monographs, and handbooks. However, experts continue to experience difficulties in correctly stating optimization problems in engineering. These troubles typically emerge when trying to define the set of feasible solutions, i.e. the constraints imposed on the design variables, functional relationships, and criteria. The Parameter Space Investigation (PSI) method was developed specifically for the correct statement and solution of engineering optimization problems. It is implemented in the MOVI 1.0 software package, a tutorial version of which is included in this book. The PSI method and MOVI 1.0 software package have a wide range of applications. The PSI method can be successfully used for the statement and solution of the following multicriteria problems: design, identification, design with control, the optional development of prototypes, finite element models, and the decomposition and aggregation of large-scale systems.

Audience: The PSI method will be of interest to researchers, graduate students, and engineers who work in engineering, mathematical modelling and industrial mathematics, and in computer and information science.

This book uses Ludwig Wittgenstein's philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein's writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein's philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein's philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including: Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.