1. ON ζ APPROXIMATIONS OF PERSISTENCE DIAGRAMS.
- Author
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JAQUETTE, JONATHAN and KRAMÁR, MIROSLAV
- Subjects
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APPROXIMATION theory , *SPATIOTEMPORAL processes , *HOMOLOGY theory , *LATTICE theory , *ALGORITHMS - Abstract
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently observed in nature. In this paper a theoretical framework for the algorithmic computation of an arbitrarily good approximation of the persistent homology is developed. We study the filtrations generated by sub-level sets of a function f : X → R, where X is a CW-complex. In the special case X = [0, 1]N, N ∈ N, we discuss implementation of the proposed algorithms. We also investigate a priori and a posteriori bounds of the approximation error introduced by our method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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