91 citations · 276 across the 48 of their papers we have counts for
4 papers · 1 filter
On the Vanishing of Homology in Random Čech Complexes
Omer Bobrowski, Shmuel Weinberger
We compute the homology of random Čech complexes over a homogeneous Poisson process on the d-dimensional torus, and show that there are, coarsely, two phase transitions. The first…
Convergence of the Reach for a Sequence of Gaussian-Embedded Manifolds
Robert J. Adler, Sunder Ram Krishnan, Jonathan E. Taylor +1
Motivated by questions of manifold learning, we study a sequence of random manifolds, generated by embedding a fixed, compact manifold into Euclidean spheres of increasing dime…
Crackle: The Persistent Homology of Noise
Robert J. Adler, Omer Bobrowski, Shmuel Weinberger
We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates t…
Persistent Homology for Random Fields and Complexes
Robert J. Adler, Omer Bobrowski, Matthew S. Borman +2
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to un…