7 papers · 1 filter
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
Stratified Morse Theory for Cell Complexes
Vidit Nanda, Francesca Tombari
We develop a version of discrete Morse theory for finite regular CW complexes equipped with an auxiliary stratification. The key construction is the halo of a cell, which contains…
Gromov-Hausdorff Distance for Directed Spaces
Lisbeth Fajstrup, Brittany Terese Fasy, Wenwen Li +4
The Gromov-Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. We introduce an analogue of this dista…
Realisations of posets and tameness
Wojciech Chacholski, Alvin Jin, Francesca Tombari
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we de…
Matching distance via the extended Pareto grid
Patrizio Frosini, Eloy Mósig GarcÃa, Nicola Quercioli +1
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank inva…