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math.AT2026
Essential Simplices Dominate in Harmonic Representatives of One-Dimensional Persistent Classes
Saugata Basu, Aldo Guzmán-Sáenz, Laxmi Parida
Persistent homology summarizes the birth and death of topological features, but it does not by itself specify where a feature is located in the underlying complex. Harmonic persist…
math.AT2022
Sequents, barcodes, and homology
Saugata Basu, Negin Karisani, Laxmi Parida
We consider the problem of generating hypothesis from data based on ideas from logic. We introduce a notion of barcodes, which we call sequent barcodes, that mirrors the barcodes i…
math.AT2013
Spectral Sequences, Exact Couples and Persistent Homology of filtrations
Saugata Basu, Laxmi Parida
In this paper we study the relationship between a very classical algebraic object associated to a filtration of spaces, namely a spectral sequence introduced by Leray in the 1940's…