Graphs Dioids And Semirings
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Graphs Dioids And Semirings
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Author : Michel Gondran
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-14
Graphs Dioids And Semirings written by Michel Gondran 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 2008-05-14 with Business & Economics categories.
The primary objective of this essential text is to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties. It does so at the same time as demonstrating the modeling and problem-solving flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures which either extend usual algebra or form a new branch of it.
Algebraic Methodology And Software Technology
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Author : Michael Johnson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-14
Algebraic Methodology And Software Technology written by Michael Johnson 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 2011-01-14 with Computers categories.
This book constitutes the refereed proceedings of the 13th International Conference on Algebraic Methodology and Software Technology, AMAST 2010, held in Lac-Beauport, QC, Canada, in June 2010. The 14 revised full papers presented were carefully reviewed and selected from 33 submissions. The papers are organized in 1 invited paper, 10 contributed research papers, and 4 system demonstrations.
Semirings As Building Blocks In Cryptography
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Author : Mariana Durcheva
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2019-11-12
Semirings As Building Blocks In Cryptography written by Mariana Durcheva and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-12 with Mathematics categories.
Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.
Generalized Fuzzy Matrices And Relations
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Author : Herbert Toth
language : en
Publisher: World Scientific
Release Date : 2025-02-25
Generalized Fuzzy Matrices And Relations written by Herbert Toth and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-25 with Mathematics categories.
The book provides an overview of the main concepts and results related to fuzzy matrices and fuzzy relations, using 'fuzzy' in a general sense to mean many-valued. This overview, along with numerous references to original contributions dispersed across various journals, serves as a comprehensive guide for further exploration.This volume can be viewed in two ways: (i) as a companion to the author's previous work, 'Relations: Concrete, Abstract, and Applied' (published by WSPC, 2020), but with a distinct emphasis on many-valued concepts; or (ii) as a standalone volume that can be read independently, which necessarily includes some repetition of material from the earlier book as preliminary or reference content.Similar to the previous book, this one does not present new findings but offers a self-contained compilation of known results selected from the extensive research conducted over the past five decades, arranged in a systematic manner.The topics covered in this text have been the subject of intensive research over the last two decades, yet there has been no book publication on this subject for over 15 years. This book aims to bridge that gap.
Path Problems In Networks
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Author : John Baras
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Path Problems In Networks written by John Baras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Computers categories.
The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path problem, and an exposition of a broad range of applications. First of all, the shortest path problem is presented so as to fix terminology and concepts: existence and uniqueness of solutions, robustness to parameter changes, and centralized and distributed computation algorithms. Then, these concepts are generalized to the algebraic context of semirings. Methods for creating new semirings, useful for modeling new problems, are provided. A large part of the book is then devoted to numerous applications of the algebraic path problem, ranging from mobile network routing to BGP routing to social networks. These applications show what kind of problems can be modeled as algebraic path problems; they also serve as examples on how to go about modeling new problems. This monograph will be useful to network researchers, engineers, and graduate students. It can be used either as an introduction to the topic, or as a quick reference to the theoretical facts, algorithms, and application examples. The theoretical background assumed for the reader is that of a graduate or advanced undergraduate student in computer science or engineering. Some familiarity with algebra and algorithms is helpful, but not necessary. Algebra, in particular, is used as a convenient and concise language to describe problems that are essentially combinatorial. Table of Contents: Classical Shortest Path / The Algebraic Path Problem / Properties and Computation of Solutions / Applications / Related Areas / List of Semirings and Applications
Tropical And Idempotent Mathematics
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Author : Grigoriĭ Lazarevich Litvinov
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Tropical And Idempotent Mathematics written by Grigoriĭ Lazarevich Litvinov 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 2009 with Mathematics categories.
This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade. Tropical mathematics can be viewed as a result of the Maslov dequantization applied to 'traditional' mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks. Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.
Tropical Mathematics And Applications To Theoretical Physics And Scientific Computing
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Author : Abdel O. Kenoufi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-01-27
Tropical Mathematics And Applications To Theoretical Physics And Scientific Computing written by Abdel O. Kenoufi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Mathematics categories.
Tropical Mathematics built on Idempotent Semi-Rings and Dioids permits an extension of the usual Linear methods to Non-Linear problems and provides powerful analyzing and computing in Theoretical Physics and Applied Mathematics. Until recently, solutions in mathematics and physics were organized around algebraic structures such as groups, rings, and fields. These techniques are not well-suited to modeling and solving non-linear problems.
Generic Inference
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Author : Marc Pouly
language : en
Publisher: John Wiley & Sons
Release Date : 2012-01-10
Generic Inference written by Marc Pouly and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-10 with Technology & Engineering categories.
This book provides a rigorous algebraic study of the most popular inference formalisms with a special focus on their wide application area, showing that all these tasks can be performed by a single generic inference algorithm. Written by the leading international authority on the topic, it includes an algebraic perspective (study of the valuation algebra framework), an algorithmic perspective (study of the generic inference schemes) and a "practical" perspective (formalisms and applications). Researchers in a number of fields including artificial intelligence, operational research, databases and other areas of computer science; graduate students; and professional programmers of inference methods will benefit from this work.
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Soft Computing State Of The Art Theory And Novel Applications
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Author : Ronald R Yager
language : en
Publisher: Springer
Release Date : 2012-10-31
Soft Computing State Of The Art Theory And Novel Applications written by Ronald R Yager and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-31 with Technology & Engineering categories.
This book is a tribute to Lotfi A. Zadeh, the father of fuzzy logic, on the occasion of his 90th Birthday. The book gathers original scientific contributions written by top scientists and presenting the latest theories, applications and new trends in the fascinating and challenging field of soft computing.