In this article, we study Euler characteristic techniques in topological data analysis.
Pointwise computing the Euler characteristic of a family of simplicial complexes built from …

The spatial distribution of galaxies at sufficiently small scales will encode information about
the identity of the dark matter. We develop a novel description of the halo distribution using …

This study presents functional limit theorems for the Euler characteristic of Vietoris–Rips
complexes. The points are drawn from a nonhomogeneous Poisson process on, and the …

The persistent Betti numbers are used in topological data analysis (TDA) to infer the scales
at which topological features appear and disappear in the filtration of a topological space …

We study functional central limit theorems for persistent Betti numbers obtained from
networks defined on a Poisson point process. The limit is formed in large volumes of …

We consider a binary supervised learning classification problem where instead of having
data in a finite-dimensional Euclidean space, we observe measures on a compact space …

We establish a functional central limit theorem for the empirical Ripley's K-function of Gibbs
point processes and point processes with fast decay of correlations. Our theorem greatly …

This paper adopts a tool from computational topology, the Euler characteristic curve (ECC)
of a sample, to perform one-and two-sample goodness of fit tests. We call our procedure …

We study topological and geometric functionals of l∞-random geometric graphs on the high-
dimensional torus in a sparse regime, where the expected number of neighbors decays …

We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech
filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical …