Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

A great success of solid state physics comes from the characterization of crystal structures in
the reciprocal (wave vector) space. The power of structural characterization in Fourier space …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

This article proposes a topological method that extracts hierarchical structures of various
amorphous solids. The method is based on the persistence diagram (PD), a mathematical …

A thoroughly revised and updated edition of this introduction to modern statistical methods
for shape analysis Shape analysis is an important tool in the many disciplines where objects …

Topological data analysis (TDA) is an emerging mathematical concept for characterizing
shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …

The broken symmetry in the atomic-scale ordering of glassy versus crystalline solids leads to
a daunting challenge to provide suitable metrics for describing the order within disorder …

Uncovering grain-scale mechanisms that underlie the disorder–order transition in
assemblies of dissipative, athermal particles is a fundamental problem with technological …

Optimal transport (\OT) theory defines a powerful set of tools to compare probability
distributions.\OT~ suffers however from a few drawbacks, computational and statistical …