**Proceedings of Symposia in Applied Mathematics**

Volume: 70;
2012;
232 pp;
Hardcover

MSC: Primary 55; 37; 53; 68;

Print ISBN: 978-0-8218-5327-6

Product Code: PSAPM/70

List Price: $60.00

Individual Member Price: $48.00

**Electronic ISBN: 978-0-8218-8997-8
Product Code: PSAPM/70.E**

List Price: $60.00

Individual Member Price: $48.00

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# Advances in Applied and Computational Topology

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*Afra Zomorodian*

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.

#### Table of Contents

# Table of Contents

## Advances in Applied and Computational Topology

- Contents vii8 free
- Preface ix10 free
- Topological Data Analysis 112 free
- Topological Dynamics: Rigorous Numerics via Cubical Homology 4152
- Euler Calculus with Applications to Signals and Sensing Justin Curry, Robert Ghrist, and Michael Robinson 7586
- On the Topology of Discrete Planning with Uncertainty 147158
- Combinatorial Optimization of Cycles and Bases 195206
- Index 229240

#### Readership

Graduate students and research mathematicians interested in applied and computational topology.