76 citations · 213 across the 18 of their papers we have counts for
14 papers · 1 filter
-Stability of Weighted Persistence Diagrams
Aziz Burak Gülen, Facundo Mémoli, Amit Patel
We introduce the concept of weighted persistence diagrams and develop a functorial pipeline for constructing them from finite metric measure spaces. This builds upon an existing fu…
A Categorical Approach to Möbius Inversion via Derived Functors
Alex Elchesen, Amit Patel
We develop a cohomological approach to Möbius inversion using derived functors in the enriched categorical setting. For a poset and a closed symmetric monoidal abelian category…
Möbius Homology
Amit Patel, Primoz Skraba
This paper introduces and develops Möbius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology a…
Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
Amit Patel, Tatum Rask
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincaré dualit…
Combinatorial Persistent Homology Transform
Brittany Terese Fasy, Amit Patel
The combinatorial interpretation of the persistence diagram as a Möbius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Tr…
Edit Distance and Persistence Diagrams Over Lattices
Alexander McCleary, Amit Patel
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persist…