Topology For Computing
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Topology For Computing
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Author : Afra J. Zomorodian
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10
Topology For Computing written by Afra J. Zomorodian 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 2005-01-10 with Computers categories.
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Computational Topology For Data Analysis
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Author : Tamal Krishna Dey
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10
Computational Topology For Data Analysis written by Tamal Krishna Dey 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 2022-03-10 with Computers categories.
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Distributed Computing Through Combinatorial Topology
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Author : Maurice Herlihy
language : en
Publisher: Newnes
Release Date : 2013-11-30
Distributed Computing Through Combinatorial Topology written by Maurice Herlihy and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-30 with Computers categories.
Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises
Computational Topology For Biomedical Image And Data Analysis
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Author : Rodrigo Rojas Moraleda
language : en
Publisher: CRC Press
Release Date : 2019-07-12
Computational Topology For Biomedical Image And Data Analysis written by Rodrigo Rojas Moraleda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Medical categories.
This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data
Computational Topology
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Author : John Harer
language : en
Publisher:
Release Date : 2014-10-13
Computational Topology written by John Harer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with categories.
Computational TopologyBy John Harer
Computational Topology
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Author : Herbert Edelsbrunner
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-31
Computational Topology written by Herbert Edelsbrunner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Mathematics categories.
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Network Topology And Fault Tolerant Consensus
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Author : Dimitris Sakavalas
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Network Topology And Fault Tolerant Consensus written by Dimitris Sakavalas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Computers categories.
As the structure of contemporary communication networks grows more complex, practical networked distributed systems become prone to component failures. Fault-tolerant consensus in message-passing systems allows participants in the system to agree on a common value despite the malfunction or misbehavior of some components. It is a task of fundamental importance for distributed computing, due to its numerous applications. We summarize studies on the topological conditions that determine the feasibility of consensus, mainly focusing on directed networks and the case of restricted topology knowledge at each participant. Recently, significant efforts have been devoted to fully characterize the underlying communication networks in which variations of fault-tolerant consensus can be achieved. Although the deduction of analogous topological conditions for undirected networks of known topology had shortly followed the introduction of the problem, their extension to the directed network case has been proven a highly non-trivial task. Moreover, global knowledge restrictions, inherent in modern large-scale networks, require more elaborate arguments concerning the locality of distributed computations. In this work, we present the techniques and ideas used to resolve these issues. Recent studies indicate a number of parameters that affect the topological conditions under which consensus can be achieved, namely, the fault model, the degree of system synchrony (synchronous vs. asynchronous), the type of agreement (exact vs. approximate), the level of topology knowledge, and the algorithm class used (general vs. iterative). We outline the feasibility and impossibility results for various combinations of the above parameters, extensively illustrating the relation between network topology and consensus.
Topology Via Logic
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Author : Steven Vickers
language : en
Publisher:
Release Date : 1989
Topology Via Logic written by Steven Vickers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.
Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.
Topology Via Logic
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Author : Steven Vickers
language : en
Publisher: Cambridge University Press
Release Date : 1989
Topology Via Logic written by Steven Vickers 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 1989 with Computers categories.
Now in paperback, Topology via Logic is an advanced textbook on topology for computer scientists. Based on a course given by the author to postgraduate students of computer science at Imperial College, it has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the methods of locale theory are freely exploited. Third, there is substantial discussion of some computer science applications. Although books on topology aimed at mathematics exist, no book has been written specifically for computer scientists. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap.
Computational Topology For Data Analysis
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Author : Tamal Krishna Dey
language : en
Publisher:
Release Date : 2022
Computational Topology For Data Analysis written by Tamal Krishna Dey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Topology categories.
"In this chapter, we introduce some of the very basics that are used throughout the book. First, we give the definition of a topological space and related notions of open and closed sets, covers, subspace topology. To connect topology and geometry, we devote a section on metric spaces. Maps such as homeomorphism and homotopy equivalence that play a significant role to relate topological spaces. Certain categories of topological spaces become important for their wide presence in applications. Manifolds are one such category which we introduce in this chapter. Functions on them satisfying certain conditions are presented as Morse functions. The critical points of such functions relate to the topology of the manifold they are defined on. We introduce these concepts in the smooth setting in this chapter, and later adapt them for the piecewise linear domains frequently used for finite computations. Finally, a section on Notes points out to the history and relevant literature for the concepts delineated in the chapter. It ends with a series of exercises that may be used for teaching a class on the subject both at graduate and undergraduate level"--