6 papers
A Universal Law of Large Numbers for Extreme Cycles in Random Čech Complexes
Omer Bobrowski, Primoz Skraba
We study the maximal multiplicative persistence of -cycles in random Čech complexes. Let be a probability density function, let be a Poisso…
Universal topological statistics on triangulated singular spaces
Uzu Lim, Omer Bobrowski, Primoz Skraba
We prove a universality theorem for random persistent homology over a class of triangulable spaces. More precisely, let be a compact -triangulable spa…
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…
Sharp Phase Transitions for k-Fold Coverage Using Morse Theory
Yohai Reani, Omer Bobrowski
We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the numb…
Morse Theory for the k-NN Distance Function
Yohai Reani, Omer Bobrowski
We study the -th nearest neighbor distance function from a finite point-set in . We provide a Morse theoretic framework to analyze the sub-level set topology. In p…