Crackle: The Homology of Noise

We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates the vertices, the homology of these complexes can either become trivial as the number n of vertices grows, or can contain...

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Veröffentlicht in:	Discrete & computational geometry 2014-12, Vol.52 (4), p.680-704
Hauptverfasser:	Adler, Robert J., Bobrowski, Omer, Weinberger, Shmuel
Format:	Artikel
Sprache:	eng
Schlagworte:	Analogies Combinatorics Computational Mathematics and Numerical Analysis Gaussian Geometry Homology Learning Manifolds Mathematics Mathematics and Statistics Noise Random variables Signal analysis Temporal logic Texts
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