Advances in applied and computational topology : AMS Short Course Computational Topology, January 4-5, 2011, New Orleans, Louisiana
- Corporate Author
- American Mathematical Society. Short Course on Computational Topology (2011 : New Orleans, La.)
- Providence, R.I. : American Mathematical Society, c2012.
- Physical description
- x, 232 p. : ill ; 26 cm.
Proceedings of symposia in applied mathematics ; v. 70.
Proceedings of symposia in applied mathematics. AMS short course lecture notes.
QA1 .S95 V.70
- Unknown QA1 .S95 V.70
- Zomorodian, Afra J., 1974-
- Includes bibliographical references and index.
- 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 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.
(source: Nielsen Book Data)
- 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, Morse-Conley 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.
- Publication date
- Afra Zomorodian, editor.
- Title Variation
- Advances in applied and computational topology : American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana
- Proceedings of symposia in applied mathematics ; v. 70
- AMS short course lecture notes