54 citations · 227 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vess…
A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road…