Advances in Applied and Computational Topology (Proceedings by Afra Zomorodian

By Afra Zomorodian

What's the form of knowledge? How will we describe flows? will we count number through integrating? How can we plan with uncertainty? what's the so much compact illustration? those questions, whereas unrelated, develop into comparable whilst recast right into a computational environment. Our enter is a suite of finite, discrete, noisy samples that describes an summary house. Our target is to compute qualitative good points of the unknown house. It seems that topology is satisfactorily tolerant to supply us with strong instruments. This quantity relies on lectures added on the 2011 AMS brief path on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. the purpose of the amount is to supply a huge advent to contemporary recommendations from utilized and computational topology. Afra Zomorodian specializes in topological info research through effective building of combinatorial constructions and up to date theories of patience. Marian Mrozek analyzes asymptotic habit of dynamical platforms through effective computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson current Euler Calculus, an quintessential calculus according to the Euler attribute, and use it on sensor and community facts aggregation. Michael Erdmann explores the connection of topology, making plans, and likelihood with the method advanced. Jeff Erickson surveys algorithms and hardness effects for topological optimization difficulties.

Show description

Read Online or Download Advances in Applied and Computational Topology (Proceedings of Symposia in Applied Mathematics) PDF

Similar topology books

Introduction to Topological Manifolds (Graduate Texts in Mathematics)

This booklet is an creation to manifolds at the start graduate point, and obtainable to any scholar who has accomplished an exceptional undergraduate measure in arithmetic. It comprises the fundamental topological rules which are wanted for the extra learn of manifolds, really within the context of differential geometry, algebraic topology, and similar fields.

Braids and Coverings: Selected Topics (London Mathematical Society Student Texts)

This ebook is predicated on a graduate path taught by means of the writer on the college of Maryland. The lecture notes were revised and augmented via examples. the 1st chapters boost the simple idea of Artin Braid teams, either geometrically and through homotopy idea, and talk about the hyperlink among knot concept and the combinatorics of braid teams via Markou's Theorem.

Convergence and Uniformity in Topology. (AM-2) (Annals of Mathematics Studies)

The outline for this booklet, Convergence and Uniformity in Topology. (AM-2), should be imminent.

Additional info for Advances in Applied and Computational Topology (Proceedings of Symposia in Applied Mathematics)

Example text

Below is the labeled β0 barcode. 5, β0 = 3 at that x. The axis unit is filtration grade. 5 in the figure. Persistence barcodes have been quite useful in topological data analysis. Suppose that a geometric process constructs a filtration so that the lifetime of a homology class denotes its significance. Then, we may use barcodes to separate topological noise from features. We have applied barcodes successfully in a number of areas, including shape description [17], biophysics [43], and computer vision [8].

But most of the models take the form of a differential equation which requires the use of numerical approximation schemes and floatingpoint arithmetic. In consequence, the adequateness of approximation depends only on limit theorems. Such theorems, constituting the essence of classical numerical analysis, are often not easy to prove and usually apply only to finite time spans. However, in most problems the asymptotic behaviour of the system is of interest and there are examples of asymptotic behaviour present in numerical schemes which may be proved to be non existent in the system approximated.

ACM Symposium of Computational Geometry, 2010, pp. 257–266. [81] A. Zomorodian and G. Carlsson, Computing persistent homology, Discrete & Computational Geometry 33 (2005), no. 2, 249–274. , Localized homology, Computational Geometry: Theory & Applications 41 (2008), [82] no. 3, 126–148. The D. E. Shaw Group, New York, NY This page intentionally left blank Proceedings of Symposia in Applied Mathematics Volume 70, 2012 Topological Dynamics: Rigorous Numerics via Cubical Homology Marian Mrozek Abstract.

Download PDF sample

Rated 4.45 of 5 – based on 13 votes

About the Author

admin