5 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…
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 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 categor…
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…
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 T…