Operator Calculus On Graphs Theory And Applications In Computer Science

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Operator Calculus On Graphs Theory And Applications In Computer Science

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Author : George Stacey Staples
language : en
Publisher: World Scientific
Release Date : 2012-02-23

Operator Calculus On Graphs Theory And Applications In Computer Science written by George Stacey Staples and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-23 with Mathematics categories.

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

Discrete Calculus

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Author : Leo J. Grady
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23

Discrete Calculus written by Leo J. Grady and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Computers categories.

This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.

The Mathematics Of Finite Networks

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Author : Michael Rudolph
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-12

The Mathematics Of Finite Networks written by Michael Rudolph 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 2022-05-12 with Computers categories.

Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory.

Graph Theory Combinatorics And Algorithms

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Author : Martin Charles Golumbic
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Graph Theory Combinatorics And Algorithms written by Martin Charles Golumbic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Clifford Algebras And Zeons Geometry To Combinatorics And Beyond

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Author : George Stacey Staples
language : en
Publisher: World Scientific
Release Date : 2019-09-24

Clifford Algebras And Zeons Geometry To Combinatorics And Beyond written by George Stacey Staples and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Mathematics categories.

Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.

Probability On Algebraic And Geometric Structures

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Author : Gregory Budzban
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-29

Probability On Algebraic And Geometric Structures written by Gregory Budzban and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-29 with Mathematics categories.

This volume contains the proceedings of the International Research Conference “Probability on Algebraic and Geometric Structures”, held from June 5–7, 2014, at Southern Illinois University, Carbondale, IL, celebrating the careers of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea. These proceedings include survey papers and new research on a variety of topics such as probability measures and the behavior of stochastic processes on groups, semigroups, and Clifford algebras; algebraic methods for analyzing Markov chains and products of random matrices; stochastic integrals and stochastic ordinary, partial, and functional differential equations.

Commutation Relations Normal Ordering And Stirling Numbers

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Author : Toufik Mansour
language : en
Publisher: CRC Press
Release Date : 2015-09-18

Commutation Relations Normal Ordering And Stirling Numbers written by Toufik Mansour and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.

Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

Graph Theory With Applications To Algorithms And

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Author : Y. Alavi
language : en
Publisher:
Release Date : 1985

Graph Theory With Applications To Algorithms And written by Y. Alavi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.

Systems Approximation Singular Integral Operators And Related Topics

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Author : Alexander A. Borichev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Systems Approximation Singular Integral Operators And Related Topics written by Alexander A. Borichev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

Algebraic Structures And Operator Calculus Special Functions And Computer Science

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Author : Philip Joel Feinsilver
language : en
Publisher: Springer
Release Date : 1993

Algebraic Structures And Operator Calculus Special Functions And Computer Science written by Philip Joel Feinsilver and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Algebra categories.

This is the second of three volumes which present, in an original way, some of the most important tools of applied mathematics in areas such as probability theory, operator calculus, representation theory, and special functions, used in solving problems in mathematics, physics and computer science. This second volume - Special Functions and Computer Science - presents some applications of special functions in computer science. It largely consists of adaptations of articles that have appeared in the literature, but here they are presented in a format made accessible for the non-expert by providing some context. The material on group representation and Young tableaux is introductory in nature. The algebraic approach of Chapter 2 is original to the authors and has not appeared previously. Similarly, the material and approach based on Appell states, so formulated, is presented here for the first time. The solutions are tackled with the help of various analytical techniques, such as generating functions and probabilistic methods and insights appear regularly. For pure and applied mathematicians and theoretical computer scientists. It is suitable for selfstudy by researchers, as well as being appropriate as a text for a course or advanced seminar.