In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are intr...In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are introduced. For applications, the authors show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. They also prove a theorem to calculate the mod p^(2) weighted persistent homology provided with some information on the mod p weighted persistent homology.展开更多
基金This work was supported by the Singapore Ministry of Education Research Grant(AcRF Tier 1 WBS No.R-146-000-222-112)the Postdoctoral International Exchange Program of China 2019 Project from the Office of China Postdoctoral Council+4 种基金China Postdoctoral Science Foundationthe President’s Graduate Fellowship of National University of Singaporethe Natural Science Foundation of China(Nos.11971144,12001310)High-Level Scientific Research Foundation of Hebei ProvinceChina Postdoctoral Science Foundation(No.2019-2021)。
文摘In this paper, the authors study further properties and applications of weighted homology and persistent homology. The Mayer-Vietoris sequence and generalized Bockstein spectral sequence for weighted homology are introduced. For applications, the authors show an algorithm to construct a filtration of weighted simplicial complexes from a weighted network. They also prove a theorem to calculate the mod p^(2) weighted persistent homology provided with some information on the mod p weighted persistent homology.
