Journal of Applied and Computational Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Journal of Applied and Computational Topology write by . This book was released on . Journal of Applied and Computational Topology available in PDF, EPUB and Kindle.
Computational Topology
Computational Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Topology write by Herbert Edelsbrunner. This book was released on 2022-01-31. Computational Topology available in PDF, EPUB and Kindle. 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.
Advances in Applied and Computational Topology
Advances in Applied and Computational Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Applied and Computational Topology write by American Mathematical Society. Short Course on Computational Topology. This book was released on 2012-07-05. Advances in Applied and Computational Topology available in PDF, EPUB and Kindle. What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.
Distributed Computing Through Combinatorial Topology
Distributed Computing Through Combinatorial Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distributed Computing Through Combinatorial Topology write by Maurice Herlihy. This book was released on 2013-11-30. Distributed Computing Through Combinatorial Topology available in PDF, EPUB and Kindle. 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
A Short Course in Computational Geometry and Topology
A Short Course in Computational Geometry and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Short Course in Computational Geometry and Topology write by Herbert Edelsbrunner. This book was released on 2014-04-28. A Short Course in Computational Geometry and Topology available in PDF, EPUB and Kindle. This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
