Hybrid Graph Theory And Network Analysis
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Hybrid Graph Theory And Network Analysis
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Author : Ladislav Novak
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-03
Hybrid Graph Theory And Network Analysis written by Ladislav Novak and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Computers categories.
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.
Hybrid Graph Theory And Network Analysis
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Author : Ladislav Novak
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-02
Hybrid Graph Theory And Network Analysis written by Ladislav Novak and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-02 with Computers categories.
First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved.
Graph Theory And Mobile Communications
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Author : Masakazu Sengoku
language : en
Publisher: World Scientific
Release Date : 2023-01-30
Graph Theory And Mobile Communications written by Masakazu Sengoku and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-30 with Technology & Engineering categories.
This comprehensive compendium discusses the basics of graph theory to its application, focusing on the application of graph theory to mobile communications.A mobile communication connects a mobile terminal and a base station wirelessly, and the base station enables communications all over the world via a wired and satellite communication system. This means that the mobile communication system includes wire and wireless technologies, and also hardware such as analog electric circuits, digital circuits and a software part such as computer algorithms.This useful reference text deeply studies how the network structure influences the performance of the corresponding system.
Algebras Graphs And Their Applications
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Author : Ilwoo Cho
language : en
Publisher: CRC Press
Release Date : 2013-09-11
Algebras Graphs And Their Applications written by Ilwoo Cho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-11 with Mathematics categories.
This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematic
Basic Proof Theory
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Author : A. S. Troelstra
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-27
Basic Proof Theory written by A. S. Troelstra and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-27 with Computers categories.
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Advanced Topics In Bisimulation And Coinduction
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Author : Davide Sangiorgi
language : en
Publisher: Cambridge University Press
Release Date : 2011-10-13
Advanced Topics In Bisimulation And Coinduction written by Davide Sangiorgi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Computers categories.
Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.
Matrix And Operator Equations And Applications
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Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2023-07-29
Matrix And Operator Equations And Applications written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.
This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Derivation And Computation
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Author : H. Simmons
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-18
Derivation And Computation written by H. Simmons and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-18 with Computers categories.
Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises.
Topological Duality For Distributive Lattices
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Author : Mai Gehrke
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-07
Topological Duality For Distributive Lattices written by Mai Gehrke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-07 with Computers categories.
Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory.
Applied Graph Data Science
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Author : Pethuru Raj
language : en
Publisher: Elsevier
Release Date : 2025-01-27
Applied Graph Data Science written by Pethuru Raj and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Computers categories.
Applied Graph Data Science: Graph Algorithms and Platforms, Knowledge Graphs, Neural Networks, and Applied Use Cases delineates how graph data science significantly empowers the application of data science. The book discusses the emerging paradigm of graph data science in detail along with its practical research and real-world applications. Readers will be enriched with the knowledge of graph data science, graph analytics, algorithms, databases, platforms, and use cases across a variety of research and topics and applications. This book also presents how graphs are used as a programming language, especially demonstrating how Sleptsov Net Computing can contribute as an entirely graphical concurrent processing language for supercomputers. Graph data science is emerging as an expressive and illustrative data structure for optimally representing a variety of data types and their insightful relationships. These data structures include graph query languages, databases, algorithms, and platforms. From here, powerful analytics methods and machine learning/deep learning (ML/DL) algorithms are quickly evolving to analyze and make sense out of graph data. As a result, ground-breaking use cases across scientific research topics and industry verticals are being developed using graph data representation and manipulation. A wide range of complex business and scientific research requirements are efficiently represented and solved through graph data analysis, and Applied Graph Data Science: Graph Algorithms and Platforms, Knowledge Graphs, Neural Networks, and Applied Graph Data Science gives readers both the conceptual foundations and technical methods for applying these powerful techniques. - Provides comprehensive coverage of the emerging paradigm of graph data science and its real-world applications - Gives readers practical guidance on how to approach and solve complex data analysis problems using graph data science, with an emphasis on deep analysis techniques including graph neural networks (GNNs), machine learning, algorithms, graph databases, and graph query languages - Covers extended graph models such as bipartite directed graphs of place-transition nets, graphs with dynamical processes defined on them - Petri and Sleptsov nets, and graphs as programming languages - Presents all the key tools and techniques as well as the foundations of graph theory, including mathematical concepts, research, and graph analytics