88 citations · 227 across the 22 of their papers we have counts for
29 papers
On Vietoris--Rips complexes of hypercube graphs
Michał Adamaszek, Henry Adams
We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale parameters. In more detail, let be the vertex set of the hypercube graph with $2^…
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…
Metric reconstruction via optimal transport
Michal Adamaszek, Henry Adams, Florian Frick
Given a sample of points in a metric space and a scale , the Vietoris-Rips simplicial complex is a standard construction to attempt to recover f…
On Vietoris-Rips complexes of ellipses
Michal Adamaszek, Henry Adams, Samadwara Reddy
For a metric space and a scale parameter, the Vietoris-Rips complex (resp. ) has as its vertex set, and a finite subset as a…
On homotopy types of Euclidean Rips complexes
Michal Adamaszek, Florian Frick, Adrien Vakili
The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We…
Random cyclic dynamical systems
Michał Adamaszek, Henry Adams, Francis Motta
For X a finite subset of the circle and for 0 < r <= 1 fixed, consider the function f_r : X -> X which maps each point to the clockwise furthest element of X within angular distanc…