By combining metal nodes with organic linkers we can potentially synthesize millions of
possible metal–organic frameworks (MOFs). The fact that we have so many materials opens …

We introduce giotto-tda, a Python library that integrates high-performance topological data
analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ …

Many and varied methods currently exist for featurization, which is the process of mapping
persistence diagrams to Euclidean space, with the goal of maximally preserving structure …

In this paper we develop an alternative topological data analysis (TDA) approach for
studying graph representations of time series of dynamical systems. Specifically, we show …

Experimental measurements of physical systems often have a limited number of
independent channels, causing essential dynamical variables to remain unobserved …

In numerical optimization, the characterization of optimization problems and their properties
has been a long-standing issue. Overcoming it is a crucial prerequisite for many optimization …

Topological data analysis is a new theoretical trend using topological techniques to mine
data. This approach helps determine topological data structures. It focuses on investigating …

Research has found that the vividness of conscious experience is related to brain dynamics.
Despite both being anaesthetics, propofol and ketamine produce different subjective states …

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 …

This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent
spaces. DMTs combine both π 0 and H n information into a single data structure that …