Advances in applied and computational topology : AMS Short Course Computational Topology, January 45, 2011, New Orleans, Louisiana
 Corporate Author
 American Mathematical Society. Short Course on Computational Topology (2011 : New Orleans, La.)
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 x, 232 p. : ill ; 26 cm.
 Series

Proceedings of symposia in applied mathematics ; v. 70.
Proceedings of symposia in applied mathematics. AMS short course lecture notes.
Access
Available online

Stacks

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QA1 .S95 V.70

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QA1 .S95 V.70
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Contributors
 Contributor
 Zomorodian, Afra J., 1974
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Topological data analysis / Afra Zomorodian
 Topological dynamics : rigorous numerics via cubical homology / Marian Mrozek
 Euler calculus with applications to signals and sensing / Justin Curry, Robert Ghrist, and Michael Robinson
 On the topology of discrete planning with uncertainty / Michael Erdmann
 Combinatorial optimization of cycles and bases / Jeff Erickson.
 Publisher's Summary
 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 45, 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Algebra, Homological > Congresses.
 Homology theory > Congresses.
 Ergodic theory > Congresses.
 Algebraic topology  Homology and cohomology theories  Other homology theories.
 Algebraic topology  Applied homological algebra and category theory  Abstract complexes.
 Algebraic topology  Explicit machine computation and programs (not the theory of computation or programming)
 Dynamical systems and ergodic theory  Topological dynamics  Index theory, MorseConley indices.
 Dynamical systems and ergodic theory  Approximation methods and numerical treatment of dynamical systems  None of the above, but in this section.
 Dynamical systems and ergodic theory  Dynamical systems with hyperbolic behavior  Strange attractors, chaotic dynamics.
 Algebraic topology  Homology and cohomology theories  Sheaf cohomology.
 Differential geometry  Global differential geometry  Integral geometry.
 Computer science  Artificial intelligence  Reasoning under uncertainty.
 Computer science  Artificial intelligence  Robotics.
 Computer science  Algorithms  Nonnumerical algorithms.
 Computer science  Theory of computing  Analysis of algorithms and problem complexity.
Bibliographic information
 Publication date
 2012
 Responsibility
 Afra Zomorodian, editor.
 Title Variation
 Advances in applied and computational topology : American Mathematical Society Short Course on Computational Topology, January 45, 2011, New Orleans, Louisiana
 Series
 Proceedings of symposia in applied mathematics ; v. 70
 AMS short course lecture notes
 ISBN
 9780821853276 (alk. paper)
 0821853279 (alk. paper)