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 …

Comments• page viii, bottom of page: the following names should be added to the
acknowledgements:-Peter Landweber had an invaluable contribution to these notes. First …

We present the main algorithmic and design choices that have been made to represent
complexes and compute persistent homology in the Gudhi library. The Gudhi library …

The increasing amount of data in biomechanics research has greatly increased the
importance of develo** advanced multivariate analysis and machine learning techniques …

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 …

The goal of this work is to extend the standard persistent homology pipeline for exploratory
data analysis to the 2-D persistence setting, in a practical, computationally efficient way. To …

We propose an approach to learning with graph-structured data in the problem domain of
graph classification. In particular, we present a novel type of readout operation to aggregate …

This paper presents the state of the art in the area of topology‐based visualization. It
describes the process and results of an extensive annotation for generating a definition and …

Social and biological contagions are influenced by the spatial embeddedness of networks.
Historically, many epidemics spread as a wave across part of the Earth's surface; however …

We study the problem of learning representations with controllable connectivity properties.
This is beneficial in situations when the imposed structure can be leveraged upstream. In …