Showing math.ATShow all
3 papers · 1 filter
math.AT2024
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…
math.AT2021
Topological data analysis of C. elegans locomotion and behavior
Ashleigh Thomas, Kathleen Bates, Alex Elchesen +3
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of co…
math.AT2018
The reflection distance between zigzag persistence modules
Alexander Elchesen, Facundo Mémoli
By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length,…