**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

Share this page *Edited by *
*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.