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math.AT2022
Computing Persistence Diagram Bundles
Abigail Hickok
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological sp…
math.AT2022
Persistence Diagram Bundles: A Multidimensional Generalization of Vineyards
Abigail Hickok
I introduce the concept of a persistence diagram (PD) bundle, which is the space of PDs for a fibered filtration function (a set o…
cs.CG2022
A Family of Density-Scaled Filtered Complexes
Abigail Hickok
We develop novel methods for using persistent homology to infer the homology of an unknown Riemannian manifold from a point cloud sampled from an arbitrary smooth probabil…