Topological methods for data modelling

G Carlsson - Nature Reviews Physics, 2020 - nature.com
The analysis of large and complex data sets is one of the most important problems facing the
scientific community, and physics in particular. One response to this challenge has been the …

The DIRAC code for relativistic molecular calculations

T Saue, R Bast, ASP Gomes, HJA Jensen… - The Journal of …, 2020 - pubs.aip.org
DIRAC is a freely distributed general-purpose program system for one-, two-, and four-
component relativistic molecular calculations at the level of Hartree–Fock, Kohn–Sham …

Wasserstein distances, geodesics and barycenters of merge trees

M Pont, J Vidal, J Delon, J Tierny - IEEE Transactions on …, 2021 - ieeexplore.ieee.org
This paper presents a unified computational framework for the estimation of distances,
geodesics and barycenters of merge trees. We extend recent work on the edit distance 104 …

Principal geodesic analysis of merge trees (and persistence diagrams)

M Pont, J Vidal, J Tierny - IEEE Transactions on Visualization …, 2022 - ieeexplore.ieee.org
This article presents a computational framework for the Principal Geodesic Analysis of
merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis …

Discrete morse sandwich: Fast computation of persistence diagrams for scalar data–an algorithm and a benchmark

P Guillou, J Vidal, J Tierny - IEEE Transactions on Visualization …, 2023 - ieeexplore.ieee.org
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 …

Localized topological simplification of scalar data

J Lukasczyk, C Garth, R Maciejewski… - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
This paper describes a localized algorithm for the topological simplification of scalar data, an
essential pre-processing step of topological data analysis (TDA). Given a scalar field f and a …

Topological analysis of interaction patterns in cancer-specific gene regulatory network: Persistent homology approach

H Masoomy, B Askari, S Tajik, AK Rizi, GR Jafari - Scientific Reports, 2021 - nature.com
In this study, we investigated cancer cellular networks in the context of gene interactions and
their associated patterns in order to recognize the structural features underlying this disease …

Parallel Computation of Piecewise Linear Morse-Smale Segmentations

RGC Maack, J Lukasczyk, J Tierny… - … on Visualization and …, 2023 - ieeexplore.ieee.org
This article presents a well-scaling parallel algorithm for the computation of Morse-Smale
(MS) segmentations, including the region separators and region boundaries. The …

Topomap: A 0-dimensional homology preserving projection of high-dimensional data

H Doraiswamy, J Tierny, PJS Silva… - … on Visualization and …, 2020 - ieeexplore.ieee.org
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and
visualization. With very few exceptions, projection techniques are designed to map data from …

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

M Olejniczak, J Tierny - Physical Chemistry Chemical Physics, 2023 - pubs.rsc.org
A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-
induced current density (MICD) in molecular systems is introduced, and its pilot application …