47 citations · 177 across the 25 of their papers we have counts for
33 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…
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…
Persistent (Co)Homology in Matrix Multiplication Time
Dmitriy Morozov, Primoz Skraba
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found d…
Approximating Metric Magnitude of Point Sets
Rayna Andreeva, James Ward, Primoz Skraba +2
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests…
Universality in Random Persistent Homology and Scale-Invariant Functionals
Omer Bobrowski, Primoz Skraba
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we…
Probabilistic Analysis of Multiparameter Persistence Decompositions
Ángel Javier Alonso, Michael Kerber, Primoz Skraba
Multiparameter persistence modules can be uniquely decomposed into indecomposable summands. Among these indecomposables, intervals stand out for their simplicity, making them prefe…
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…
Cluster-Persistence for Weighted Graphs
Omer Bobrowski, Primoz Skraba
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their -dimensional homology. While this area has be…
Möbius Homology
Amit Patel, Primoz Skraba
This paper introduces and develops Möbius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology a…
On the Universality of Random Persistence Diagrams
Omer Bobrowski, Primoz Skraba
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largel…
Central Limit Theorem for Euclidean Minimal Spanning Acycles
Primoz Skraba, D. Yogeshwaran
We investigate asymptotics for the minimal spanning acycles of the (Alpha)-Delaunay complex on a stationary Poisson process on . Minimal spanning acycles ar…
Notes on an Elementary Proof for the Stability of Persistence Diagrams
Primoz Skraba, Katharine Turner
These notes are a self-contained short proof of the stability of persistence diagrams.
Euler Characteristic Surfaces
Gabriele Beltramo, Rayna Andreeva, Ylenia Giarratano +3
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appea…
Persistent Homology in Metric
Gabriele Beltramo, Primoz Skraba
Proximity complexes and filtrations are central constructions in topological data analysis. Built using distance functions, or more generally metrics, they are often used to infer…
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…
Homological Percolation: The Formation of Giant k-Cycles
Omer Bobrowski, Primoz Skraba
In this paper we introduce and study a higher-dimensional analogue of the giant component in continuum percolation. Using the language of algebraic topology, we define the notion o…
Homological Percolation and the Euler Characteristic
Omer Bobrowski, Primoz Skraba
In this paper we study the connection between the phenomenon of homological percolation (the formation of "giant" cycles in persistent homology), and the zeros of the expected Eule…
A Topology Layer for Machine Learning
Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath +3
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topolog…
Topology-Aware Surface Reconstruction for Point Clouds
Rickard Brüel-Gabrielsson, Vignesh Ganapathi-Subramanian, Primoz Skraba +1
We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to…
Randomly Weighted complexes: Minimal Spanning Acycles and Persistence Diagrams
Primoz Skraba, Gugan Thoppe, D. Yogeshwaran
A weighted complex is a simplicial complex of dimension in which each face is assigned a real-valued weight. We derive three key results here concerning persistence diagram…
An Approximate Nerve Theorem
Dejan Govc, Primoz Skraba
The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and n…