Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and
structure in data in order to answer questions from the data's domain. This is done by …

In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …

Transcriptional programs control cellular lineage commitment and differentiation during
development. Understanding of cell fate has been advanced by studying single-cell RNA …

In this article, we study the question of the statistical convergence of the 1-dimensional
Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal …

Given a continuous function f: X → R f: X→ R and a cover II of its image by intervals, the
Mapper is the nerve of a refinement of the pullback cover f^-1 (I) f-1 (I). Despite its success in …

This paper presents an efficient algorithm for the computation of the Reeb space of an input
bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and …

Deep neural networks such as GoogLeNet, ResNet, and BERT have achieved impressive
performance in tasks such as image and text classification. To understand how such …

A merge tree is a type of graph-based topological summary that tracks the evolution of
connected components in the sublevel sets of scalar functions. Merge trees enjoy …

The mapper algorithm is a popular tool from topological data analysis for extracting
topological summaries of high-dimensional datasets. In this paper, we present Mapper …