54 citations · 82 across the 11 of their papers we have counts for
12 papers
A survey of simplicial, relative, and chain complex homology theories for hypergraphs
Ellen Gasparovic, Emilie Purvine, Radmila Sazdanovic +3
Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hype…
A Structural Average of Labeled Merge Trees for Uncertainty Visualization
Lin Yan, Yusu Wang, Elizabeth Munch +2
Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour…
Intrinsic Interleaving Distance for Merge Trees
Ellen Gasparovic, Elizabeth Munch, Steve Oudot +3
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applicat…
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…
On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings
Michal Adamaszek, Henry Adams, Ellen Gasparovic +6
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equival…