Search Results - "Bobrowski, Omer"

A universal null-distribution for topological data analysis by Bobrowski, Omer, Skraba, Primoz

“…One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams arising from data…”
Get full text

Topology of random geometric complexes: a survey by Bobrowski, Omer, Kahle, Matthew

“…In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes. Random geometric complexes may be viewed as…”
Get full text

The topology of probability distributions on manifolds by Bobrowski, Omer, Mukherjee, Sayan

“…Let P be a set of n random points in R d , generated from a probability measure on a m -dimensional manifold M ⊂ R d . In this paper we study the homology of U…”
Get full text

Cluster Persistence for Weighted Graphs by Bobrowski, Omer, Skraba, Primoz

“…Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology…”
Get full text

Random Čech complexes on Riemannian manifolds by Bobrowski, Omer, Oliveira, Goncalo

“…In this paper we study the homology of a random Čech complex generated by a homogeneous Poisson process in a compact Riemannian manifold M. In particular, we…”
Get full text

Homological connectivity in random Čech complexes by Bobrowski, Omer

“…We study the homology of random Čech complexes generated by a homogeneous Poisson process. We focus on ‘homological connectivity’—the stage where the random…”
Get full text

Homological Percolation: The Formation of Giant k-Cycles by Bobrowski, Omer, Skraba, Primoz

“…Abstract In this paper we introduce and study a higher dimensional analogue of the giant component in continuum percolation. Using the language of algebraic…”
Get full text

Cycle Registration in Persistent Homology With Applications in Topological Bootstrap by Reani, Yohai, Bobrowski, Omer

“…We propose a novel approach for comparing the persistent homology representations of two spaces (or filtrations). Commonly used methods are based on numerical…”
Get full text

MAXIMALLY PERSISTENT CYCLES IN RANDOM GEOMETRIC COMPLEXES by Bobrowski, Omer, Kahle, Matthew, Skraba, Primoz

“…We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-k in…”
Get full text

Advances in random topology by Bobrowski, Omer, Yogeshwaran, D.

Get full text

On the vanishing of homology in random Čech complexes by Bobrowski, Omer, Weinberger, Shmuel

“…ABSTRACT 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…”
Get full text

Topological consistency via kernel estimation by BOBROWSKI, OMER, MUKHERJEE, SAYAN, TAYLOR, JONATHAN E.

“…We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and…”
Get full text

Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime by Onaran, Efe, Bobrowski, Omer, Adler, Robert J.

“…We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are…”
Get full text

Poisson process approximation under stabilization and Palm coupling by Bobrowski, Omer, Schulte, Matthias, Yogeshwaran, D.

Get full text

Probabilistic convergence and stability of random mapper graphs by Brown, Adam, Bobrowski, Omer, Munch, Elizabeth, Wang, Bei

“…We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f : X → R . We…”
Get full text

Alarm Sound Detection Using Topological Signal Processing by Fireaizen, Tomer, Ron, Saar, Bobrowski, Omer

“…We present a novel approach to alarm sound detection using topological data analysis. Our main focus is on proposing a new set of robust features, based on…”
Get full text

Crackle: The Homology of Noise by Adler, Robert J., Bobrowski, Omer, Weinberger, Shmuel

“…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…”
Get full text

On the spectrum of dense random geometric graphs by Adhikari, Kartick, Adler, Robert J., Bobrowski, Omer, Rosenthal, Ron

“…In this paper we study the spectrum of the random geometric graph G(n,r), in a regime where the graph is dense and highly connected. In the Erdős–Rényi G(n,p)…”
Get full text

Universality in Random Persistent Homology and Scale-Invariant Functionals by Bobrowski, Omer, Skraba, Primoz

“…In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point…”
Get full text

Morse Theory for the k-NN Distance Function by Reani, Yohai, Bobrowski, Omer

“…We study the $k$-th nearest neighbor distance function from a finite point-set in $\mathbb{R}^d$. We provide a Morse theoretic framework to analyze the…”
Get full text