6 citations · 6 across the 2 of their papers we have counts for
4 papers
Adaptive Metrics for Adaptive Samples
Nicholas J. Cavanna, Donald R. Sheehy
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the…
The Generalized Persistent Nerve Theorem
Nicholas J. Cavanna, Donald R. Sheehy
In this paper a parameterized generalization of a good cover filtration is introduced called an ε-good cover, defined as a cover filtration in which the reduced homology groups of…
Supporting Ruled Polygons
Nicholas J. Cavanna, Marc Khoury, Donald R. Sheehy
We explore several problems related to ruled polygons. Given a ruling of a polygon , we consider the Reeb graph of induced by the ruling. We define the Reeb complexity of $P…
A Geometric Perspective on Sparse Filtrations
Nicholas J. Cavanna, Mahmoodreza Jahanseir, Donald R. Sheehy
We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applyi…