4 papers
Sharp Phase Transitions for k-Fold Coverage Using Morse Theory
Yohai Reani, Omer Bobrowski
We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the numb…
Morse Theory for the k-NN Distance Function
Yohai Reani, Omer Bobrowski
We study the -th nearest neighbor distance function from a finite point-set in . We provide a Morse theoretic framework to analyze the sub-level set topology. In p…
A Coupled Alpha Complex
Yohai Reani, Omer Bobrowski
The alpha complex is a subset of the Delaunay triangulation and is often used in computational geometry and topology. One of the main drawbacks of using the alpha complex is that i…
Cycle Registration in Persistent Homology with Applications in Topological Bootstrap
Yohai Reani, Omer Bobrowski
In this article we propose a novel approach for comparing the persistent homology representations of two spaces (filtrations). Commonly used methods are based on numerical summarie…