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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory

Ramsey Theory for Discrete Structures (Hardcover, 2013 ed.): Hans Jurgen Proemel Ramsey Theory for Discrete Structures (Hardcover, 2013 ed.)
Hans Jurgen Proemel
R1,557 Discovery Miles 15 570 Ships in 10 - 15 working days

This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century.

The book first presents a detailed discussion of the roots of Ramsey theory before offering a thorough discussion of the role of parameter sets. It presents several examples of structures that can be interpreted in terms of parameter sets and features the most fundamental Ramsey-type results for parameter sets: Hales-Jewett's theorem and Graham-Rothschild s Ramsey theorem as well as their canonical versions and several applications. Next, the book steps back to the most basic structure, to sets. It reviews classic results as well as recent progress on Ramsey numbers and the asymptotic behavior of classical Ramsey functions. In addition, it presents product versions of Ramsey's theorem, a combinatorial proof of the incompleteness of Peano arithmetic, provides a digression to discrepancy theory and examines extensions of Ramsey's theorem to larger cardinals. The next part of the book features an in-depth treatment of the Ramsey problem for graphs and hypergraphs. It gives an account on the existence of sparse and restricted Ramsey theorem's using sophisticated constructions as well as probabilistic methods. Among others it contains a proof of the induced Graham-Rothschild theorem and the random Ramsey theorem. The book closes with a chapter on one of the recent highlights of Ramsey theory: a combinatorial proof of the density Hales-Jewett theorem.

This book provides graduate students as well as advanced researchers with a solid introduction and reference to the field."

Graph Theory for Programmers - Algorithms for Processing Trees (Hardcover, 2000 ed.): Victor N. Kasyanov, Vladimir A. Evstigneev Graph Theory for Programmers - Algorithms for Processing Trees (Hardcover, 2000 ed.)
Victor N. Kasyanov, Vladimir A. Evstigneev
R3,195 Discovery Miles 31 950 Ships in 10 - 15 working days

In delivering lectures and writing books, we were most often forced to pay absolutely no attention to a great body of interesting results and useful algorithms appearing in numerous sources and occasionally encountered. It was absolutely that most of these re sults would finally be forgotten because it is impossible to run through the entire variety of sources where these materials could be published. Therefore, we decided to do what we can to correct this situation. We discussed this problem with Ershov and came to an idea to write an encyclopedia of algorithms on graphs focusing our main attention on the algorithms already used in programming and their generalizations or modifications. We thought that it is reasonable to group all graphs into certain classes and place the algo rithms developed for each class into a separate book. The existence of trees, i. e., a class of graphs especially important for programming, also supported this decision. This monograph is the first but, as we hope, not the last book written as part of our project. It was preceded by two books "Algorithms on Trees" (1984) and "Algorithms of Processing of Trees" (1990) small editions of which were published at the Computer Center of the Siberian Division of the Russian Academy of Sciences. The books were distributed immediately and this made out our decision to prepare a combined mono graph on the basis of these books even stronger."

Erdos on Graphs - His Legacy of Unsolved Problems (Paperback, 2 Rev Ed): Fan Chung, Ron Graham, At&T Labs Erdos on Graphs - His Legacy of Unsolved Problems (Paperback, 2 Rev Ed)
Fan Chung, Ron Graham, At&T Labs
R974 Discovery Miles 9 740 Ships in 12 - 17 working days

This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch or problem posers". It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erdos never had a home and never held a job. His "home" was a bag or two containing all his belongings and a record of the collective activities of the mathematical community. His "job" was one at which he excelled: identifying a fundamental roadblock in some particular line of approach and capturing it in a well-chosen, often innocent-looking problem, whose solution would likewise provide insight into the underlying theory. By cataloguing the unsolved problems of Erdos in a comprehensive and well-documented volume, the authors hope to continue the work of an unusual and special man who fundamentally influenced the field of mathematics.

Efficient Algorithms for Listing Combinatorial Structures (Hardcover): Leslie Ann Goldberg Efficient Algorithms for Listing Combinatorial Structures (Hardcover)
Leslie Ann Goldberg
R3,118 R2,855 Discovery Miles 28 550 Save R263 (8%) Ships in 12 - 17 working days

First published in 1993, this thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members? What general methods are useful for listing combinatorial structures? How can these be applied to those families which are of interest to theoretical computer scientists and combinatorialists? Amongst those families considered are unlabelled graphs, first order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colourable graphs. Some related work is also included, which compares the listing problem with the difficulty of solving the existence problem, the construction problem, the random sampling problem, and the counting problem. In particular, the difficulty of evaluating Polya's cycle polynomial is demonstrated.

Extremal Combinatorial Problems and Their Applications (Hardcover, 1995 ed.): B. S Stechkin, V.I. Baranov Extremal Combinatorial Problems and Their Applications (Hardcover, 1995 ed.)
B. S Stechkin, V.I. Baranov
R1,657 Discovery Miles 16 570 Ships in 12 - 17 working days

Combinatorial research has proceeded vigorously in Russia over the last few decades, based on both translated Western sources and original Russian material. The present volume extends the extremal approach to the solution of a large class of problems, including some that were hitherto regarded as exclusively algorithmic, and broadens the choice of theoretical bases for modelling real phenomena in order to solve practical problems. Audience: Graduate students of mathematics and engineering interested in the thematics of extremal problems and in the field of combinatorics in general. Can be used both as a textbook and as a reference handbook.

Combinatorial and Additive Number Theory III - CANT, New York, USA, 2017 and 2018 (Hardcover, 1st ed. 2020): Melvyn B Nathanson Combinatorial and Additive Number Theory III - CANT, New York, USA, 2017 and 2018 (Hardcover, 1st ed. 2020)
Melvyn B Nathanson
R3,700 Discovery Miles 37 000 Ships in 10 - 15 working days

Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Game Theory, Alive (Hardcover): Anna R. Karlin, Yuval Peres Game Theory, Alive (Hardcover)
Anna R. Karlin, Yuval Peres
R2,150 R2,039 Discovery Miles 20 390 Save R111 (5%) Ships in 12 - 17 working days

We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, engineering, or statistics. The importance of game-theoretic thinking transcends the academic setting-for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

Counting: The Art of Enumerative Combinatorics (Hardcover, 2001 ed.): George E. Martin Counting: The Art of Enumerative Combinatorics (Hardcover, 2001 ed.)
George E. Martin
R2,439 Discovery Miles 24 390 Ships in 10 - 15 working days

Counting: The Art of Enumerative Combinatorics provides an introduction to discrete mathematics that addresses questions that begin, How many ways are there to...For example, ¿How many ways are there to order a collection of 12 ice cream cones if 8 flavors are available?¿ At the end of the book the reader should be able to answer such nontrivial counting questions as, ¿How many ways are there to color the faces of a cube if ¿k¿ colors are available with each face having exactly one color?¿ or ¿How many ways are there to stack ¿n¿ poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip?¿ Since there are no prerequisites, this book can be used for college courses in combinatorics at the sophomore level for either computer science or mathematics students. The first five chapters have served as the basis for a graduate course for in-service teachers. Chapter 8 introduces graph theory.

Graphical Models - Methods for Data Analysis and Mining (Hardcover): Christian Borgelt, Rudolf Kruse Graphical Models - Methods for Data Analysis and Mining (Hardcover)
Christian Borgelt, Rudolf Kruse
R3,519 R2,814 Discovery Miles 28 140 Save R705 (20%) Out of stock

The use of graphical models in applied statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides a self-contained introduction to the learning of graphical models from data, and includes detailed coverage of possibilistic networks - a tool that allows the user to infer results from problems with imprecise data.

One of the most important applications of graphical modelling today is data mining - the data-driven discovery and modelling of hidden patterns in large data sets. The techniques described have a wide range of industrial applications, and a quality testing programme at a major car manufacturer is included as a real-life example.

  • Provides a self-contained introduction to learning relational, probabilistic and possibilistic networks from data.

  • Each concept is carefully explained and illustrated by examples.

  • Contains all necessary background material, including modelling under uncertainty, decomposition of distributions, and graphical representation of decompositions.

  • Features applications of learning graphical models from data, and problems for further research.

  • Includes a comprehensive bibliography.
Graphical Models: Methods for Data Analysis and Mining will be invaluable to researchers and practitioners who use graphical models in their work. Graduate students of applied statistics, computer science and engineering will find this book provides an excellent introduction to the subject.
Bayesian Heuristic Approach to Discrete and Global Optimization - Algorithms, Visualization, Software, and Applications... Bayesian Heuristic Approach to Discrete and Global Optimization - Algorithms, Visualization, Software, and Applications (Hardcover, 1997 ed.)
Jonas Mockus, William Eddy, Gintaras Reklaitis
R7,465 Discovery Miles 74 650 Ships in 10 - 15 working days

Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.

Cooperative Control of Multi-agent Systems - Distributed-Observer and Distributed-Internal-Model Approaches (Hardcover, 1st ed.... Cooperative Control of Multi-agent Systems - Distributed-Observer and Distributed-Internal-Model Approaches (Hardcover, 1st ed. 2022)
He Cai, Youfeng Su, Jie Huang
R4,491 Discovery Miles 44 910 Ships in 12 - 17 working days

The main focus of this book is a pair of cooperative control problems: consensus and cooperative output regulation. Its emphasis is on complex multi-agent systems characterized by strong nonlinearity, large uncertainty, heterogeneity, external disturbances and jointly connected switching communication topologies. The cooperative output regulation problem is a generalization of the classical output regulation problem to multi-agent systems and it offers a general framework for handling a variety of cooperative control problems such as consensus, formation, tracking and disturbance rejection. The book strikes a balance between rigorous mathematical proof and engineering practicality. Every design method is systematically presented together with illustrative examples and all the designs are validated by computer simulation. The methods presented are applied to several practical problems, among them the leader-following consensus problem of multiple Euler-Lagrange systems, attitude synchronization of multiple rigid-body systems, and power regulation of microgrids. The book gives a detailed exposition of two approaches to the design of distributed control laws for complex multi-agent systems-the distributed-observer and distributed-internal-model approaches. Mastering both will enhance a reader's ability to deal with a variety of complex real-world problems. Cooperative Control of Multi-agent Systems can be used as a textbook for graduate students in engineering, sciences, and mathematics, and can also serve as a reference book for practitioners and theorists in both industry and academia. Some knowledge of the fundamentals of linear algebra, calculus, and linear systems are needed to gain maximum benefit from this book. Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Approximation Algorithms and Semidefinite Programming (Hardcover, 2012): Bernd Gartner, Jiri Matousek Approximation Algorithms and Semidefinite Programming (Hardcover, 2012)
Bernd Gartner, Jiri Matousek
R2,445 Discovery Miles 24 450 Ships in 10 - 15 working days

Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.

There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms.

This book follows the "semidefinite side" of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms."

Modern Survey Analysis - Using Python for Deeper Insights (Hardcover, 1st ed. 2022): Walter R Paczkowski Modern Survey Analysis - Using Python for Deeper Insights (Hardcover, 1st ed. 2022)
Walter R Paczkowski
R2,982 Discovery Miles 29 820 Ships in 10 - 15 working days

This book develops survey data analysis tools in Python, to create and analyze cross-tab tables and data visuals, weight data, perform hypothesis tests, and handle special survey questions such as Check-all-that-Apply. In addition, the basics of Bayesian data analysis and its Python implementation are presented. Since surveys are widely used as the primary method to collect data, and ultimately information, on attitudes, interests, and opinions of customers and constituents, these tools are vital for private or public sector policy decisions. As a compact volume, this book uses case studies to illustrate methods of analysis essential for those who work with survey data in either sector. It focuses on two overarching objectives: Demonstrate how to extract actionable, insightful, and useful information from survey data; and Introduce Python and Pandas for analyzing survey data.

Graph-Based Social Media Analysis (Paperback): Ioannis Pitas Graph-Based Social Media Analysis (Paperback)
Ioannis Pitas
R1,389 Discovery Miles 13 890 Ships in 12 - 17 working days

Focused on the mathematical foundations of social media analysis, Graph-Based Social Media Analysis provides a comprehensive introduction to the use of graph analysis in the study of social and digital media. It addresses an important scientific and technological challenge, namely the confluence of graph analysis and network theory with linear algebra, digital media, machine learning, big data analysis, and signal processing. Supplying an overview of graph-based social media analysis, the book provides readers with a clear understanding of social media structure. It uses graph theory, particularly the algebraic description and analysis of graphs, in social media studies. The book emphasizes the big data aspects of social and digital media. It presents various approaches to storing vast amounts of data online and retrieving that data in real-time. It demystifies complex social media phenomena, such as information diffusion, marketing and recommendation systems in social media, and evolving systems. It also covers emerging trends, such as big data analysis and social media evolution. Describing how to conduct proper analysis of the social and digital media markets, the book provides insights into processing, storing, and visualizing big social media data and social graphs. It includes coverage of graphs in social and digital media, graph and hyper-graph fundamentals, mathematical foundations coming from linear algebra, algebraic graph analysis, graph clustering, community detection, graph matching, web search based on ranking, label propagation and diffusion in social media, graph-based pattern recognition and machine learning, graph-based pattern classification and dimensionality reduction, and much more. This book is an ideal reference for scientists and engineers working in social media and digital media production and distribution. It is also suitable for use as a textbook in undergraduate or graduate courses on digital media, social media, or social networks.

Emerging Applications of Number Theory (Hardcover, 1999 ed.): Dennis A. Hejhal, Joel Friedman, Martin C. Gutzwiller, Andrew M.... Emerging Applications of Number Theory (Hardcover, 1999 ed.)
Dennis A. Hejhal, Joel Friedman, Martin C. Gutzwiller, Andrew M. Odlyzko
R3,282 Discovery Miles 32 820 Ships in 12 - 17 working days

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Hybrid Graph Theory and Network Analysis (Hardcover): Ladislav Novak, Alan Gibbons Hybrid Graph Theory and Network Analysis (Hardcover)
Ladislav Novak, Alan Gibbons
R3,109 R2,846 Discovery Miles 28 460 Save R263 (8%) Ships in 12 - 17 working days

This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors examine in detail two dual structures associated with a graph, namely circuits and cutsets. These are strongly dependent on one another and together constitute a third, hybrid, vertex-independent structure called a graphoid, whose study is here termed hybrid graph theory. This approach has particular relevance for network analysis. The first account of the subject in book form, the text includes many new results as well as the synthesizing and reworking of much research done over the past thirty years (historically, the study of hybrid aspects of graphs owes much to the foundational work of Japanese researchers). This work will be regarded as the definitive account of the subject, suitable for all working in theoretical network analysis: mathematicians, computer scientists or electrical engineers.

Matrices and Matroids for Systems Analysis (Hardcover, 2000 ed.): Kazuo Murota Matrices and Matroids for Systems Analysis (Hardcover, 2000 ed.)
Kazuo Murota
R5,495 Discovery Miles 54 950 Ships in 10 - 15 working days

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis.This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the last decade. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems.This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science.

Handbook of Combinatorial Optimization - Supplement Volume A (Hardcover, 1999 ed.): Dingzhu Du, Panos M. Pardalos Handbook of Combinatorial Optimization - Supplement Volume A (Hardcover, 1999 ed.)
Dingzhu Du, Panos M. Pardalos
R4,616 Discovery Miles 46 160 Ships in 12 - 17 working days

Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics)."

Combinatorics and Reasoning - Representing, Justifying and Building Isomorphisms (Hardcover, 2011 ed.): Carolyn A. Maher,... Combinatorics and Reasoning - Representing, Justifying and Building Isomorphisms (Hardcover, 2011 ed.)
Carolyn A. Maher, Arthur B. Powell, Elizabeth B. Uptegrove
R3,067 Discovery Miles 30 670 Ships in 10 - 15 working days

Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.

Investigations in Algebraic Theory of Combinatorial Objects (Hardcover, 1994 ed.): I.A. Faradzev, A. A. Ivanov, M. Klin, A.J.... Investigations in Algebraic Theory of Combinatorial Objects (Hardcover, 1994 ed.)
I.A. Faradzev, A. A. Ivanov, M. Klin, A.J. Woldar
R3,912 Discovery Miles 39 120 Ships in 12 - 17 working days

X Kochendorffer, L.A. Kalu: lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed."

Opinion Dynamics and the Evolution of Social Power in Social Networks (Hardcover, 1st ed. 2019): Mengbin Ye Opinion Dynamics and the Evolution of Social Power in Social Networks (Hardcover, 1st ed. 2019)
Mengbin Ye
R2,941 Discovery Miles 29 410 Ships in 10 - 15 working days

This book uses rigorous mathematical analysis to advance opinion dynamics models for social networks in three major directions. First, a novel model is proposed to capture how a discrepancy between an individual's private and expressed opinions can develop due to social pressures that arise in group situations or through extremists deliberately shaping public opinion. Detailed theoretical analysis of the final opinion distribution is followed by use of the model to study Asch's seminal experiments on conformity, and the phenomenon of pluralistic ignorance. Second, the DeGroot-Friedkin model for evolution of an individual's social power (self-confidence) is developed in a number of directions. The key result establishes that an individual's initial social power is forgotten exponentially fast, even when the network changes over time; eventually, an individual's social power depends only on the (changing) network structure. Last, a model for the simultaneous discussion of multiple logically interdependent topics is proposed. To ensure that a consensus across the opinions of all individuals is achieved, it turns out that the interpersonal interactions must be weaker than an individual's introspective cognitive process for establishing logical consistency among the topics. Otherwise, the individual may experience cognitive overload and the opinion system becomes unstable. Conclusions of interest to control engineers, social scientists, and researchers from other relevant disciplines are discussed throughout the thesis with support from both social science and control literature.

Elementary Methods of  Graph Ramsey Theory (Hardcover, 1st ed. 2022): Yu-Sheng Li, Qizhong Lin Elementary Methods of Graph Ramsey Theory (Hardcover, 1st ed. 2022)
Yu-Sheng Li, Qizhong Lin
R2,978 Discovery Miles 29 780 Ships in 10 - 15 working days

This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turan numbers and communication channels, etc.

Fuzzy Graph Theory (Hardcover, 1st ed. 2018): Sunil Mathew, John N. Mordeson, Davender S. Malik Fuzzy Graph Theory (Hardcover, 1st ed. 2018)
Sunil Mathew, John N. Mordeson, Davender S. Malik
R4,819 Discovery Miles 48 190 Ships in 12 - 17 working days

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine's work on fuzzy interval graphs, fuzzy analogs of Marczewski's theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger's theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

Topological Methods in Data Analysis and Visualization - Theory, Algorithms, and Applications (Hardcover, Edition.): Valerio... Topological Methods in Data Analysis and Visualization - Theory, Algorithms, and Applications (Hardcover, Edition.)
Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny
R2,975 Discovery Miles 29 750 Ships in 10 - 15 working days

Topology-based methods are of increasing importance in the analysis and visualization of dataset from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. (see also below for a list of selected issues). While there is an increasing number of high-quality publications in this field, many fundamental questions remain unsolved. New focused efforts are needed in a variety of techniques ranging from the theoretical foundations of topological models, algorithmic issues related to the representation power of computer-based implementations as well as their computational efficiency, user interfaces for presentation of quantitative topological information, and the development of new techniques for systematic mapping of science problems in topological constructs that can be solved computationally. In this forum the editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. The 2009 workshop in Snowbird, Utah, follows the two successful workshops in 2005 (Budmerice, Slovakia) and 2007 (Leipzig, Germany).

An Invitation to Combinatorics (Hardcover): Shahriar Shahriari An Invitation to Combinatorics (Hardcover)
Shahriar Shahriari
R1,300 Discovery Miles 13 000 Ships in 9 - 15 working days

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author - an award-winning teacher - writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

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Monther Alfuraidan, Qamrul Ansari Hardcover R2,030 R1,915 Discovery Miles 19 150

 

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