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Kombinatorik og grafteori

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  • af Jiahu Qin
    1.219,95 - 1.545,95 kr.

    This book aims to work out the distributed economic operation in smart grids in a systematic way, which ranges from model-based to model-free perspectives. The main contributions of this book can be summarized into three folds. First, we investigate the fundamental economic operation problems in smart grids from model-based perspective. Specifically, these problems can be modeled as deterministic optimization models, and we propose some distributed optimization algorithms by integrating the multi-agent consensus theory and optimization techniques to achieve the distributed coordination of various generation units and loads. Second, due to the randomness of the large-scale renewable energies and the flexibility of the loads, we further address these economic operation problems from a model-free perspective, and we propose learning-based approaches to address the uncertainty and randomness. At last, we extend the idea of model-based and model-free algorithms to plug-in electric vehicles (PEVs) charging/discharging scheduling problem, the key challenge of which involves multiple objectives simultaneously while the behavior of PEVs and the electricity price are intrinsically random. This book presents several recent theoretical findings on distributed economic operation in smart grids from model-based and model-free perspectives. By systematically integrating novel ideas, fresh insights, and rigorous results, this book provides a base for further theoretical research on distributed economic operation in smart grids. It can be a reference for graduates and researchers to study the operation and management in smart grids. Some prerequisites for reading this book include optimization theory, matrix theory, game theory, reinforcement learning, etc.

  • af Sandeep Singh
    963,95 kr.

  • af Diogo Pacheco
    1.560,95 - 1.909,95 kr.

  • af Abhishek Kr Singh
    294,95 kr.

    Mathematics can be distinguished among all the sciences due to its precise language and clear rules of reasoning. The notion of proof lies at the heart of mathematics. Typically, proof of any mathematical statement is a logical argument, that can convince anyone of the correctness of the statement. Starting with a set of assumptions a mathematical proof tries to discover new facts using a sequence of logical steps. These logical steps must correspond to the rules of reasoning which are considered correct in mathematics. Ideally, proof should contain all the necessary information so that its veri¿cation becomes a purely mechanical job. However, the contemporary practice of writing mathematical proofs is only an approximation to this ideal, where the task of a reviewer is to use his intelligence to judge whether the proof could be expressed in a way that conforms to the valid rules of reasoning. A reviewer very often comes across inferential gaps, imprecise de¿nitions, and unstated background assumptions. In such circumstances, it is di¿cult to say whether a proof is correct or not. Even if the statement turns out to be true, judging it to be so could take a long time. Mathematical proofs are becoming more and more complex and the length of unusually large proofs has also increased with time. If a proof is short one can check it manually. But if proof is deep and already ¿lls hundreds of journal pages very few people may have the expertise to go through it. The correctness concern of such complex proofs is further enhanced by the fact that some of these proofs rely on extensive computation.

  • af Chuan Shi
    452,95 - 482,95 kr.

    This book provides a comprehensive introduction to the foundations and frontiers of graph neural networks. In addition, the book introduces the basic concepts and definitions in graph representation learning and discusses the development of advanced graph representation learning methods with a focus on graph neural networks. The book providers researchers and practitioners with an understanding of the fundamental issues as well as a launch point for discussing the latest trends in the science. The authors emphasize several frontier aspects of graph neural networks and utilize graph data to describe pairwise relations for real-world data from many different domains, including social science, chemistry, and biology. Several frontiers of graph neural networks are introduced, which enable readers to acquire the needed techniques of advances in graph neural networks via theoretical models and real-world applications. 

  • af Volker Diekert
    486,95 kr.

    This book treats the elements of discrete mathematics that have important applications in computer science, thus providing the necessary tools for the reader to come to a competent mathematical judgement of modern developments in the age of information. Almost all assertions are shown with full proofs. Exercises are provided, with solutions presented in full detail.

  • af Tansel Özyer
    1.304,95 kr.

    This book includes chapters which discuss effective and efficient approaches in dealing with various aspects of social media analysis by using machine learning techniques from clustering to deep learning. A variety of theoretical aspects, application domains and case studies are covered to highlight how it is affordable to maximize the benefit of various applications from postings on social media platforms. Social media platforms have significantly influenced and reshaped various social aspects. They have set new means of communication and interaction between people, turning the whole world into a small village where people with internet connect can easily communicate without feeling any barriers. This has attracted the attention of researchers who have developed techniques and tools capable of studying various aspects of posts on social media platforms with main concentration on Twitter. This book addresses challenging applications in this dynamic domain where it is not possible to continue applying conventional techniques in studying social media postings. The content of this book helps the reader in developing own perspective about how to benefit from machine learning techniques in dealing with social media postings and how social media postings may directly influence various applications.

  • af Yusheng Li
    878,95 - 987,95 kr.

    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.

  • af Frederick Hoffman
    1.304,95 - 1.428,95 kr.

    This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world - many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.

  • af Sunil Mathew
    1.304,95 kr.

    One of the most preeminent ways of applying mathematics in real-world scenario modeling involves graph theory. A graph can be undirected or directed depending on whether the pairwise relationships among objects are symmetric or not. Nevertheless, in many real-world situations, representing a set of complex relational objects as directed or undirected is not su¢ cient. Weighted graphs o§er a framework that helps to over come certain conceptual limitations. We show using the concept of an isomorphism that weighted graphs have a natural connection to fuzzy graphs. As we show in the book, this allows results to be carried back and forth between weighted graphs and fuzzy graphs. This idea is in keeping with the important paper by Klement and Mesiar that shows that many families of fuzzy sets are lattice isomorphic to each other. We also outline the important work of Head and Weinberger that show how results from ordinary mathematics can be carried over to fuzzy mathematics. We focus on the concepts connectivity, degree sequences and saturation, and intervals and gates in weighted graphs.

  • af Song Yang
    878,95 - 987,95 kr.

    Network Function Virtualization (NFV) has recently attracted considerable attention from both research and industrial communities. Numerous papers have been published regarding solving the resource- allocation problems in NFV, from various perspectives, considering different constraints, and adopting a range of techniques. However, it is difficult to get a clear impression of how to understand and classify different kinds of resource allocation problems in NFV and how to design solutions to solve these problems efficiently.This book addresses these concerns by offering a comprehensive overview and explanation of different resource allocation problems in NFV and presenting efficient solutions to solve them. It covers resource allocation problems in NFV, including an introduction to NFV and QoS parameters modelling as well as related problem definition, formulation and the respective state-of-the-art algorithms.This book allows readers to gain a comprehensive understanding of and deep insights into the resource allocation problems in NFV. It does so by exploring (1) the working principle and architecture of NFV, (2) how to model the Quality of Service (QoS) parameters in NFV services, (3) definition, formulation and analysis of different kinds of resource allocation problems in various NFV scenarios, (4) solutions for solving the resource allocation problem in NFV, and (5) possible future work in the respective area.

  • af José M. Mazón
    1.390,95 kr.

    This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research.Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.

  • af M. Ram Murty & Sebastian M. Cioab¿
    407,95 - 622,95 kr.

    This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

  • af Santosh Kumar Yadav
    939,95 kr.

    This book is designed to meet the requirement of undergraduate and postgraduate students pursuing computer science, information technology, mathematical science, and physical science course. No formal prerequisites are needed to understand the text matter except a very reasonable background in college algebra. The text contains in-depth coverage of all major topics proposed by professional institutions and universities for a discrete mathematics course. It emphasizes on problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof technique, algorithmic development, algorithm correctness, and numeric computations. A sufficient amount of theory is included for those who enjoy the beauty in development of the subject and a wealth of applications as well as for those who enjoy the power of problem-solving techniques.Biographical sketches of nearly 25 mathematicians and computer scientists who have played a significant role in the development of the field are threaded into the text to provide a human dimension and attach a human face to major discoveries. Each section of the book contains a generous selection of carefully tailored examples to classify and illuminate various concepts and facts. Theorems are backbone of mathematics. Consequently, this book contains the various proof techniques, explained and illustrated in details. Most of the concepts, definitions, and theorems in the book are illustrated with appropriate examples. Proofs shed additional light on the topic and enable students to sharpen thin problem-solving skills. Each chapter ends with a summary of important vocabulary, formulae, properties developed in the chapter, and list of selected references for further exploration and enrichment.

  • af Jesse Sakari Hyttinen
    691,95 kr.

    Tree successor algebra: A new branch in mathematics is a book about a formal theory of tree generation with an axiomatic basis for a new object called collection space. The elements of this space, in other words collections, have a clear connection to rooted trees and are treated as variables in sum form equations, the application area of tree successor algebra. With connections to different branches of mathematics such as number theory, linear algebra and algebra, tree successor algebra shows a fundamental link between rooted tree generation and partition generation, establishing a well-defined order in which rooted trees are generated. This in turn makes it possible to define a successor operator, the unit of least action in tree generation, and generalize it in order to create a concept of tree sequences. Due to this, the concept of the infinite sequence of all rooted trees can be formed, and the notion of a rooted tree line, and thus the need for tools to solve sum form equations rises. The axiomatic system answers to this need.

  • af Santosh Kumar Yadav
    998,95 kr.

    The present book is based on the curriculum of undergraduate and postgraduate courses of universities in India and abroad. Every effort is made to present the various topics in the theory of graphs in a logical manner with adequate historical background and include suitable figures to illustrate concepts and results ideally. The formidable exercises, neither easy nor straightforward, are bold faced and highlighted. The theory portion of each chapter is studied thoroughly as it helps solve many of the problems with comparative ease. Selected material from this book is used for a semester course on graph theory, while the entire book serves for a whole session course.

  • af Julien Riposo
    1.049,95 kr.

    This book provides a foundation for the mathematics of blockchain. It is inspired by a general analysis and synthesis of the current knowledge of blockchain technology and starts by laying a foundation for the mathematics of blockchain. The aim is for research in the area of blockchain to lead their study from the construction highlighted in this book.First, the basis of a blockchain is set: block, transaction contents, block header, Merkle tree, nonce, Proof-of-Work. Connections with elliptic curves and cryptographic signatures are made.Second, the book ties this with a Graph and Matrix Theories approach and models the peer-to-peer relationship through the Bitcoin Network.Third, it is proposed further modelling, notably around halving, optimal storing, or diffusion of information, which are consequences of the mathematical foundation. The notion of Entropy of Privacy and the Particles model are introduced.Finally, the mathematical statements therein are proven and essential reminders can be found before each section, so the content can be accessible from a graduate level.

  • af He Cai
    1.430,95 - 1.649,95 kr.

    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.

  • af Mark R. Budden
    409,95 kr.

    This text is a comprehensive survey of the literature surrounding star-critical Ramsey numbers. First defined by Jonelle Hook in her 2010 dissertation, these numbers aim to measure the sharpness of the corresponding Ramsey numbers by determining the minimum number of edges needed to be added to a critical graph for the Ramsey property to hold. Despite being in its infancy, the topic has gained significant attention among Ramsey theorists.This work provides researchers and students with a resource for studying known results and their complete proofs. It covers typical results, including multicolor star-critical Ramsey numbers for complete graphs, trees, cycles, wheels, and n-good graphs, among others. The proofs are streamlined and, in some cases, simplified, with a few new results included. The book also explores the connection between star-critical Ramsey numbers and deleted edge numbers, which focus on destroying the Ramsey property by removing edges.The book concludes with open problems and conjectures for researchers to consider, making it a valuable resource for those studying the field of star-critical Ramsey numbers.

  • af Elena Deza
    1.587,95 kr.

    Stirling numbers are one of the most known classes of special numbers in Mathematics, especially in Combinatorics and Algebra. They were introduced by Scottish mathematician James Stirling (1692-1770) in his most important work, Differential Method with a Tract on Summation and Interpolation of Infinite Series (1730). Stirling numbers have a rich history; many arithmetic, number-theoretical, analytical and combinatorial connections; numerous classical properties; as well as many modern applications.This book collects much of the scattered material on the two subclasses of Stirling numbers to provide a holistic overview of the topic. From the combinatorial point of view, Stirling numbers of the second kind, S(n, k), count the number of ways to partition a set of n different objects (i.e., a given n-set) into k non-empty subsets. Stirling numbers of the first kind, s(n, k), give the number of permutations of n elements with k disjoint cycles. Both subclasses of Stirling numbers play an important role in Algebra: they form the coefficients, connecting well-known sets of polynomials.This book is suitable for students and professionals, providing a broad perspective of the theory of this class of special numbers, and many generalisations and relatives of Stirling numbers, including Bell numbers and Lah numbers. Throughout the book, readers are provided exercises to test and cement their understanding.

  • af Miklós Bóna
    1.210,95 kr.

    The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises - more than a hundred in total - which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.

  • af Teresa W. Haynes
    1.538,95 kr.

    This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity.The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they¿ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.

  • af Christin Schmidt
    405,95 kr.

    Dieses Lehrbuch bietet eine kompakte Einführung in die Grundlagen der Graphentheorie und die Methoden der Netzwerkanalyse. Zahlreiche praktische Beispiele und Übungsaufgaben mit Lösungsvorschlägen helfen Leser:innen dabei, die theoretischen Konzepte besser zu verstehen und anzuwenden. Dabei werden unterschiedliche Technologien und Programmiersprachen verwendet, um ein breites Spektrum an Anwendungen abzudecken. Darüber hinaus beleuchten spezielle Kapitel die Methodik mit Blick auf die Planung und Durchführung eigener Netzwerkanalyseprojekte sowie ethische und datenschutzrechtliche Aspekte. So liefert das Buch nicht nur einen theoretischen Überblick, sondern auch praktische Tipps und Anleitungen für die Untersuchung eigener netzwerkanalytischer Fragestellungen. Dieses Buch eignet sich nicht nur als Nachschlagewerk für Studierende und Dozierende vielfältiger Fachdisziplinen mit curricularem Bezug zum Thema, sondern auch als Ergänzung des Repertoires von Praktiker:innen im Bereich Data Science mit Interesse an der Untersuchung von Netzwerken. Ob als theoretischer Einstieg oder als praktischer Ratgeber - dieses Buch leistet einen Beitrag für die Untersuchung und Analyse von Netzwerken und bietet eine Grundlage für weiterführende Studien und Projekte.

  • af Ravindra B. Bapat, Stephen J. Kirkland, Simo Puntanen, mfl.
    1.219,95 kr.

    This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

  • af Andreia Sofia Teixeira
    1.758,95 kr.

    This book contains contributions in the area of Network Science, presented at the 14th International Conference on Complex Networks (CompleNet), 24-28 April, 2023 in Aveiro, Portugal. CompleNet is an international conference on complex networks that brings together researchers and practitioners from diverse disciplines¿from sociology, biology, physics, and computer science¿who share a passion to better understand the interdependencies within and across systems. CompleNet is a venue to discuss ideas and findings about all types networks, from biological, to technological, to informational and social. It is this interdisciplinary nature of complex networks that CompleNet aims to explore and celebrate.The audience of the work are professionals and academics working in Network Science, a highly-multidisciplinary field.

  • af Amaury Freslon
    485,95 - 1.121,95 kr.

  • af Massih-Reza Amini, Grigorios Tsoumakas, Petra Kralj Novak, mfl.
    877,95 kr.

  • af Parthiban A
    317,95 kr.

    The theoretical foundations of graph theory are insightfully explored in "A Study on Prime Distance Labeling of Graphs" by Parthiban A. The book gives a thorough explanation of prime distance labelling in graphs, including its uses and advantages. Both students and math professionals can easily understand the subject because to the author's clear and succinct writing style.In-depth discussion of prime distance labeling's foundational ideas and how it might be applied to enhance computing algorithms is provided in this book. The author also offers insightful explanations of the main difficulties and restrictions related to prime distance labelling in graphs. Anyone wishing to gain a deeper understanding of graph theory and its applications should consult this book as a vital resource.A Study on Prime Distance Labeling of Graphs is a must-read for anybody interested in mathematics, whether they are a student, researcher, or professional. It is an excellent addition to any library and offers a distinctive viewpoint on the intricate world of graph theory. This book is for you if you're seeking for an interesting and educational read that investigates the theoretical foundations of computational mathematics.

  • af József Beck
    1.582,95 kr.

    The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.

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