Computational Tools in Weighted Persistent Homology

Ren, Shiquan; Wu, Chengyuan; Wu, Jie

doi:10.1007/s11401-021-0255-8

Chin. Ann. Math. Ser. B

2021

DOI: 10.1007/s11401-021-0255-8

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Computational Tools in Weighted Persistent Homology

Shiquan Ren

Chengyuan Wu

Jie Wu

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Cited by 4 publications

References 24 publications

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Weighted product of point clouds and simplicial complexes

Babu,

John,

Thankachan

2024

AAECC

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This paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial complexes within a commutative ring with unity. Within an integral domain, the introduction of a weighted product chain group, along with the induced product weighted homomorphism and weighted product boundary maps, leads to significant outcomes and findings. To explore the algebraic characteristics of a weighted product structure, we introduce the concept of weighted product homology. This homology considers the relationship of weights assigned to elements within the structure and their impact on the structure’s underlying algebraic properties.

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Weighted product of point clouds and simplicial complexes

Babu,

John,

Thankachan

2024

AAECC

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The Twisted Homology of Simplicial Set

Zhang

Li²,

2022

Acta. Math. Sin.-English Ser.

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Discrete Differential Calculus on Simplicial Complexes and Constrained Homology

Ren

2023

Chin. Ann. Math. Ser. B

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Computational Tools in Weighted Persistent Homology

Cited by 4 publications

References 24 publications

Weighted product of point clouds and simplicial complexes

Weighted product of point clouds and simplicial complexes

The Twisted Homology of Simplicial Set

Discrete Differential Calculus on Simplicial Complexes and Constrained Homology

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