4 citations · 11 across the 9 of their papers we have counts for
9 papers
Convergence of persistence diagrams for discrete time stationary processes
Andrew M. Thomas
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law o…
Dynamic Atomic Column Detection in Transmission Electron Microscopy Videos via Ridge Estimation
Yuchen Xu, Andrew M. Thomas, Peter A. Crozier +1
Ridge detection is a classical tool to extract curvilinear features in image processing. As such, it has great promise in applications to material science problems; specifically, f…
Fractal dimension, approximation and data sets
L. Betti, I. Chio, J. Fleischman +13
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Princi…
Feature detection and hypothesis testing for extremely noisy nanoparticle images using topological data analysis
Andrew M. Thomas, Peter A. Crozier, Yuchen Xu +1
We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra low signal-to-noise ratio using cubical persistent homology. Our main application…
The VC-dimension of a class of multiples of the primes, and a connection to AdaBoost
Andrew M. Thomas
We discuss the VC-dimension of a class of multiples of integers and primes (equivalently indicator functions) and demonstrate connections to prime counting functions. Additionally,…
Central limit theorems and asymptotic independence for local -statistics on diverging halfspaces
Andrew M. Thomas
We consider the stochastic behavior of a class of local -statistics of Poisson processeswhich include subgraph and simplex counts as special cases, and amounts to quantifying…
Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds
Andrew M. Thomas, Takashi Owada
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric complexes whose points lie in t…
Functional limit theorems for the Euler characteristic process in the critical regime
Andrew M. Thomas, Takashi Owada
This study presents functional limit theorems for the Euler characteristic of Vietoris-Rips complexes. The points are drawn from a non-homogeneous Poisson process on …
Limit theorems for process-level Betti numbers for sparse, critical, and Poisson regimes
Takashi Owada, Andrew Thomas
The objective of this study is to examine the asymptotic behavior of Betti numbers of Čech complexes treated as stochastic processes and formed from random points in the -dimens…