21 citations · 38 across the 8 of their papers we have counts for
9 papers
The connectivity of Vietoris-Rips complexes of spheres
Henry Adams, Johnathan Bush, Žiga Virk
We survey what is known and unknown about Vietoris-Rips complexes and thickenings of spheres. Afterwards, we show how to control the homotopy connectivity of Vietoris-Rips complexe…
Topological feature selection for time series data
Peter Bubenik, Johnathan Bush
We use tools from applied topology for feature selection on time series data. We develop a method for scoring the variables in a multivariate time series that reflects their contri…
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
Luis Scoccola, Hitesh Gakhar, Johnathan Bush +4
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a -dimensional hole in the…
The topology of projective codes and the distribution of zeros of odd maps
Henry Adams, Johnathan Bush, Florian Frick
We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the to…
Operations on Metric Thickenings
Henry Adams, Johnathan Bush, Joshua Mirth
Many simplicial complexes arising in practice have an associated metric space structure on the vertex set but not on the complex, e.g. the Vietoris-Rips complex in applied topology…