54 citations · 227 across the 23 of their papers we have counts for
3 papers · 2 filters
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…
Probabilistic Convergence and Stability of Random Mapper Graphs
Adam Brown, Omer Bobrowski, Elizabeth Munch +1
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space equipped with a continuous function $f: \mathbb{X} \rightarro…
Local Versus Global Distances for Zigzag Persistence Modules
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottlen…