Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

The cosmological principle (CP)—the notion that the Universe is spatially isotropic and
homogeneous on large scales—underlies a century of progress in cosmology. It is …

Networks, as efficient representations of complex systems, have appealed to scientists for a
long time and now permeate many areas of science, including neuroimaging (Bullmore and …

In this paper we discuss the adaptation of the methods of homology from algebraic topology
to the problem of pattern recognition in point cloud data sets. The method is referred to as …

Introduction: For the past decade, the focus of complex disease research has been the
genotype. From technological advancements to the development of analysis methods, great …

The statistical mechanical approach to complex networks is the dominant paradigm in
describing natural and societal complex systems. The study of network properties, and their …

Let P be a distribution with support S. The salient features of S can be quantified with
persistent homology, which summarizes topological features of the sublevel sets of the …

We introduce a multiscale topological description of the Megaparsec web-like cosmic matter
distribution. Betti numbers and topological persistence offer a powerful means of describing …

The purpose of this study is to evaluate the accuracy for classification of hepatic tumors by
characterization of T1-weighted magnetic resonance (MR) images using two radiomics …

We develop an analysis pipeline for characterizing the topology of large scale structure and
extracting cosmological constraints based on persistent homology. Persistent homology is a …