12 citations · 12 across the 4 of their papers we have counts for
5 papers
How a Change to Topology's Union Axiom Affects Continuity
Rachel Bergjord, Matthew Zabka
The most general definition of a continuous function requires that the preimage of any open set be open. Thus, to discuss continuity in the abstract, it is necessary to first defin…
MVF Designer: Design and Visualization of Morse Vector Fields
Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro +2
Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field de…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…
A Model for Random Chain Complexes
Michael J. Catanzaro, Matthew J. Zabka
We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps…
A Random Bockstein Operator
Matthew Zabka
As more of topology's tools become popular in analyzing high dimensional data sets, the goal of understanding the underlying probabilistic properties of these tools becomes even mo…