Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differenti...Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differential calculus on V.Moreover,he defines an independence hyper graph to be the complement of a simplicial complex in the complete hypergraph on V.Let L be an independence hypergraph with its vertices in V.He constructs some constrained cohomology groups of L by using the differential calculus on V.展开更多
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
In this paper,the authors define the homology of sets,which comes from and contains the ideas of path homology and embedded homology.Moreover,A Kunneth formula for sets associated to the homology of sets is given.
基金supported by China Postdoctoral Science Foundation(No.2022M721023)。
文摘Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differential calculus on V.Moreover,he defines an independence hyper graph to be the complement of a simplicial complex in the complete hypergraph on V.Let L be an independence hypergraph with its vertices in V.He constructs some constrained cohomology groups of L by using the differential calculus on V.
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.
基金supported by the National Natural Science Foundation of China(No.12001310)Science and Technology Project of Hebei Education Department(No.QN2019333)+2 种基金the Natural Fund of Cangzhou Science and Technology Bureau(No.197000002)a Project of Cangzhou Normal University(No.xnjjl1902)China Postdoctoral Science Foundation(No.2020M680494)。
文摘In this paper,the authors define the homology of sets,which comes from and contains the ideas of path homology and embedded homology.Moreover,A Kunneth formula for sets associated to the homology of sets is given.
