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

Hypergraphs capture multi-way relationships in data, and they have consequently seen a
number of applications in higher-order network analysis, computer vision, geometry …

This article presents a computational framework for the Principal Geodesic Analysis of
merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis …

In this paper we introduce a novel family of attributed graphs for the purpose of shape
discrimination. Our graphs typically arise from variations on the Mapper graph construction …

Merge trees, contour trees, and Reeb graphs are graph-based topological descriptors that
capture topological changes of (sub) level sets of scalar fields. Comparing scalar fields …

Morse complexes and Morse-Smale complexes are topological descriptors popular in
topology-based visualization. Comparing these complexes plays an important role in their …

Hypernetworks, sometimes called hypergraphs, generalize the concept of a graph by
allowing edges to join any number of vertices, gaining the ability to capture multi-way …

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial,
geometric, probabilistic and statistical point of view. Computing the persistent homology of a …

The actinide elements are playing larger roles in modern life, finding uses in nuclear energy,
remote power sources, medical uses as radiotherapy isotopes, as well as in geological …