172 citations · 564 across the 31 of their papers we have counts for
5 papers · 1 filter
Topology Applied to Machine Learning: From Global to Local
Henry Adams, Michael Moy
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology…
Geometric Approaches on Persistent Homology
Henry Adams, Baris Coskunuzer
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence…
The Vietoris-Rips complexes of a circle
Michal Adamaszek, Henry Adams
Given a metric space X and a distance threshold r>0, the Vietoris-Rips simplicial complex has as its simplices the finite subsets of X of diameter less than r. A theorem of Jean-Cl…
Nerve complexes of circular arcs
Michal Adamaszek, Henry Adams, Florian Frick +2
We show that the nerve complex of n arcs in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension. Mo…
Evasion Paths in Mobile Sensor Networks
Henry Adams, Gunnar Carlsson
Suppose that ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists i…