Combinatorial Methods And Models

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Combinatorial Methods and Models

Author : Rudolf Ahlswede
Publisher : Springer
ISBN 13 : 3319531395
Total Pages : 385 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Combinatorial Methods and Models by : Rudolf Ahlswede

Download or read book Combinatorial Methods and Models written by Rudolf Ahlswede and published by Springer. This book was released on 2017-06-30 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

Combinatorial Methods with Computer Applications

Author : Jonathan L. Gross
Publisher : CRC Press
ISBN 13 : 1584887443
Total Pages : 664 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross

Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2016-04-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Combinatorial Physics

Author : Adrian Tanasa
Publisher : Oxford University Press
ISBN 13 : 0192895494
Total Pages : 409 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Combinatorial Physics by : Adrian Tanasa

Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.

Combinatorial Methods in Discrete Mathematics

Author : Vladimir N. Sachkov
Publisher : Cambridge University Press
ISBN 13 : 0521455138
Total Pages : 324 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Combinatorial Methods in Discrete Mathematics by : Vladimir N. Sachkov

Download or read book Combinatorial Methods in Discrete Mathematics written by Vladimir N. Sachkov and published by Cambridge University Press. This book was released on 1996-01-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an attempt to present some complex problems of discrete mathematics in a simple and unified form using a unique, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived.This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.

Combinatorial Methods in Density Estimation

Author : Luc Devroye
Publisher : Springer Science & Business Media
ISBN 13 : 1461301254
Total Pages : 219 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Combinatorial Methods in Density Estimation by : Luc Devroye

Download or read book Combinatorial Methods in Density Estimation written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Introduction to Combinatorial Testing

Author : D. Richard Kuhn
Publisher : CRC Press
ISBN 13 : 1466552301
Total Pages : 341 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Introduction to Combinatorial Testing by : D. Richard Kuhn

Download or read book Introduction to Combinatorial Testing written by D. Richard Kuhn and published by CRC Press. This book was released on 2016-04-19 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial testing of software analyzes interactions among variables using a very small number of tests. This advanced approach has demonstrated success in providing strong, low-cost testing in real-world situations. Introduction to Combinatorial Testing presents a complete self-contained tutorial on advanced combinatorial testing methods for real-world software. The book introduces key concepts and procedures of combinatorial testing, explains how to use software tools for generating combinatorial tests, and shows how this approach can be integrated with existing practice. Detailed explanations and examples clarify how and why to use various techniques. Sections on cost and practical considerations describe tradeoffs and limitations that may impact resources or funding. While the authors introduce some of the theory and mathematics of combinatorial methods, readers can use the methods without in-depth knowledge of the underlying mathematics. Accessible to undergraduate students and researchers in computer science and engineering, this book illustrates the practical application of combinatorial methods in software testing. Giving pointers to freely available tools and offering resources on a supplementary website, the book encourages readers to apply these methods in their own testing projects.

Combinatorial Methods

Author : Jerome K. Percus
Publisher : Springer Science & Business Media
ISBN 13 : 1461264049
Total Pages : 203 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Combinatorial Methods by : Jerome K. Percus

Download or read book Combinatorial Methods written by Jerome K. Percus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not a large overstatement to claim that mathematics has traditionally arisen from attempts to understand quite concrete events in the physical world. The accelerated sophistication of the mathematical community has perhaps obscured this fact, especially during the present century, with the abstract becoming the hallmark of much of respectable mathematics. As a result of the inaccessibility of such work, practicing scientists have often been compelled to fashion their own mathematical tools, blissfully unaware of their prior existence in far too elegant and far too general form. But the mathematical sophistication of scientists has grown rapidly too, as has the scientific sophistication of many mathematicians, and the real worl- suitably defined - is once more serving its traditional role. One of the fields most enriched by this infusion has been that of combinatorics. This book has been written in a way as a tribute to those natural scientists whose breadth of vision has inparted a new vitality to a dormant giant. The present text arose out of a course in Combinatorial Methods given by the writer at the Courant Institute during 1967-68. Its structure has been determined by an attempt to reach an informed but heterogeneous group of students in mathematics, physics, and chemistry. Its lucidity has been enhanced immeasurably by the need to satisfy a very resolute critic, Professor Ora E. Percus, who is responsible for the original lecture notes as well as for their major modifications.

Model Theoretic Methods in Finite Combinatorics

Author : Martin Grohe
Publisher : American Mathematical Soc.
ISBN 13 : 0821849433
Total Pages : 519 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Model Theoretic Methods in Finite Combinatorics by : Martin Grohe

Download or read book Model Theoretic Methods in Finite Combinatorics written by Martin Grohe and published by American Mathematical Soc.. This book was released on 2011-11-28 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC. Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics. This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.

Multi-Objective Combinatorial Optimization Problems and Solution Methods

Author : Mehdi Toloo
Publisher : Academic Press
ISBN 13 : 0128238003
Total Pages : 316 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Multi-Objective Combinatorial Optimization Problems and Solution Methods by : Mehdi Toloo

Download or read book Multi-Objective Combinatorial Optimization Problems and Solution Methods written by Mehdi Toloo and published by Academic Press. This book was released on 2022-02-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Combinatorial Methods in Topology and Algebra

Author : Bruno Benedetti
Publisher : Springer
ISBN 13 : 3319201557
Total Pages : 227 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Combinatorial Methods in Topology and Algebra by : Bruno Benedetti

Download or read book Combinatorial Methods in Topology and Algebra written by Bruno Benedetti and published by Springer. This book was released on 2015-10-31 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

Combinatorial Methods in Discrete Distributions

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 0471733172
Total Pages : 440 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Combinatorial Methods in Discrete Distributions by : Charalambos A. Charalambides

Download or read book Combinatorial Methods in Discrete Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.

Probability, Combinatorics and Control

Author : Andrey Kostogryzov
Publisher : BoD – Books on Demand
ISBN 13 : 1838801030
Total Pages : 336 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Probability, Combinatorics and Control by : Andrey Kostogryzov

Download or read book Probability, Combinatorics and Control written by Andrey Kostogryzov and published by BoD – Books on Demand. This book was released on 2020-04-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic and combinatorial techniques are often used for solving advanced problems. This book describes different probabilistic modeling methods and their applications in various areas, such as artificial intelligence, offshore platforms, social networks, and others. It aims to educate how modern probabilistic and combinatorial models may be created to formalize uncertainties; to train how new probabilistic models can be generated for the systems of complex structures; to describe the correct use of the presented models for rational control in systems creation and operation; and to demonstrate analytical possibilities and practical effects for solving different system problems on each life cycle stage.

Monte Carlo Methods and Applications

Author : Karl K. Sabelfeld
Publisher : Walter de Gruyter
ISBN 13 : 3110293587
Total Pages : 248 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Monte Carlo Methods and Applications by : Karl K. Sabelfeld

Download or read book Monte Carlo Methods and Applications written by Karl K. Sabelfeld and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the "8th IMACS Seminar on Monte Carlo Methods" held from August 29 to September 2, 2011 in Borovets, Bulgaria, and organized by the Institute of Information and Communication Technologies of the Bulgarian Academy of Sciences in cooperation with the International Association for Mathematics and Computers in Simulation (IMACS). Included are 24 papers which cover all topics presented in the sessions of the seminar: stochastic computation and complexity of high dimensional problems, sensitivity analysis, high-performance computations for Monte Carlo applications, stochastic metaheuristics for optimization problems, sequential Monte Carlo methods for large-scale problems, semiconductor devices and nanostructures. The history of the IMACS Seminar on Monte Carlo Methods goes back to April 1997 when the first MCM Seminar was organized in Brussels: 1st IMACS Seminar, 1997, Brussels, Belgium 2nd IMACS Seminar, 1999, Varna, Bulgaria 3rd IMACS Seminar, 2001, Salzburg, Austria 4th IMACS Seminar, 2003, Berlin, Germany 5th IMACS Seminar, 2005, Tallahassee, USA 6th IMACS Seminar, 2007, Reading, UK 7th IMACS Seminar, 2009, Brussels, Belgium 8th IMACS Seminar, 2011, Borovets, Bulgaria

Combinatorial Methods for Chemical and Biological Sensors

Author : Radislav A. Potyrailo
Publisher : Springer Science & Business Media
ISBN 13 : 0387737138
Total Pages : 495 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorial Methods for Chemical and Biological Sensors by : Radislav A. Potyrailo

Download or read book Combinatorial Methods for Chemical and Biological Sensors written by Radislav A. Potyrailo and published by Springer Science & Business Media. This book was released on 2009-03-21 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chemical sensors are in high demand for applications as varied as water pollution detection, medical diagnostics, and battlefield air analysis. Designing the next generation of sensors requires an interdisciplinary approach. The book provides a critical analysis of new opportunities in sensor materials research that have been opened up with the use of combinatorial and high-throughput technologies, with emphasis on experimental techniques. For a view of component selection with a more computational perspective, readers may refer to the complementary volume of Integrated Analytical Systems edited by M. Ryan et al., entitled “Computational Methods for Sensor Material Selection”.

Combinatorial Physics

Author : Adrian Tanasa
Publisher : Oxford University Press
ISBN 13 : 0192648063
Total Pages : 420 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Combinatorial Physics by : Adrian Tanasa

Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021-04-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between combinatorics and theoretical physics is a recent trend which appears to us as particularly natural, since the unfolding of new ideas in physics is often tied to the development of combinatorial methods, and, conversely, problems in combinatorics have been successfully tackled using methods inspired by theoretical physics. We can thus speak nowadays of an emerging domain of Combinatorial Physics. The interference between these two disciplines is moreover an interference of multiple facets. Its best known manifestation (both to combinatorialists and theoretical physicists) has so far been the one between combinatorics and statistical physics, as statistical physics relies on an accurate counting of the various states or configurations of a physical system. But combinatorics and theoretical physics interact in various other ways. This book is mainly dedicated to the interactions of combinatorics (algebraic, enumerative, analytic) with (commutative and non-commutative) quantum field theory and tensor models, the latter being seen as a quantum field theoretical generalisation of matrix models.

Handbook of Combinatorial Optimization

Author : Ding-Zhu Du
Publisher : Springer Science & Business Media
ISBN 13 : 0387238301
Total Pages : 395 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Handbook of Combinatorial Optimization by : Ding-Zhu Du

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.