From the 1 of 8 linked papers with an AI index.
8 papers
Universal topological statistics on triangulated singular spaces
Uzu Lim, Omer Bobrowski, Primoz Skraba
The paper proves that the expected persistent homology of random point clouds on a wide class of triangulable spaces converges to a universal limit that does not depend on the spec…
Sharp Phase Transition for the Formation of Infinite Tubes
Shu Kanazawa, Omer Bobrowski, Primoz Skraba
Classical bond percolation theory studies the conditions for a given point in a random graph to be connected to infinity, or "escape" to infinity, via a sequence of random edges. I…
A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality
Eng-Jon Ong, Omer Bobrowski, Gesine Reinert +1
Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying…
Computing 1-Periodic Persistent Homology with Finite Windows
Adam Onus, Primoz Skraba
Let be a periodic cell complex endowed with a covering where is a finite quotient space of equivalence classes under translations acting on . We assume is…
Wasserstein Stability for Persistence Diagrams
Primoz Skraba, Katharine Turner
The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bot…
Persistent Local Systems of Periodic Spaces
Adam Onus, Primoz Skraba
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as…