Persistence and Sheaves
Karthik Yegnesh
TL;DR
This paper explores a variation of persistent homology and applies it to analyze the cohomology of network coding sheaves on networks that are deteriorating over time.
Contribution
It introduces a new variation of persistent homology and applies it to the study of cellular sheaf cohomology in deteriorating networks.
Findings
Analysis of persistent cellular sheaf cohomology on deteriorating networks
New variation of persistent homology introduced
Application to network coding sheaves
Abstract
We study a variation of Carlsson and Zomorodian's persistent homology. As an application, we analyze the persistent cellular sheaf cohomology of network coding sheaves on deteriorating networks.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Neuroimaging Techniques and Applications · Homotopy and Cohomology in Algebraic Topology