Phat is an open-source C++ library for the computation of persistent homology by matrix
reduction, targeted towards developers of software for topological data analysis. We aim for …

We show how discrete Morse theory provides a rigorous and unifying foundation for defining
skeletons and partitions of grayscale digital images. We model a grayscale image as a …

Interactions between atoms have a major influence on the chemical properties of molecular
systems. While covalent interactions impose the structural integrity of molecules …

We present a parallel algorithm for computing the persistent homology of a filtered chain
complex. Our approach differs from the commonly used reduction algorithm by first …

Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

In persistent homology, the persistence barcode encodes pairs of simplices meaning birth
and death of homology classes. Persistence barcodes depend on the ordering of the …

A primary hypothesis that drives scientific and engineering studies is that data has structure.
The dominant paradigms for describing such structure are statistics (eg, moments …

This paper introduces an efficient algorithm for persistence diagram computation, given an
input piecewise linear scalar field defined on a-dimensional simplicial complex, with. Our …

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in
complex data. Standard methods in TDA such as persistent homology (PH) are typically …

Pore-scale modeling based on the 3D structural information of porous materials has
enormous potential in assessing physical properties beyond the capabilities of laboratory …