Title: Further Properties and Applications of Weighted Persistent Homology
Abstract:In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weigh...In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology. For applications, we show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. We also prove a theorem that allows us to calculate the mod $p^2$ weighted persistent homology given some information on the mod $p$ weighted persistent homology. In the paper, we include many examples to illustrate the concepts.Read More
Publication Year: 2017
Publication Date: 2017-11-25
Language: en
Type: article
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Cited By Count: 1
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