Morse theory for filtrations and efficient computation of persistent homology

K Mischaikow, V Nanda - Discrete & Computational Geometry, 2013 - Springer
Morse Theory for Filtrations and Efficient Computation of Persistent Homology |
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[HTML][HTML] Phat–persistent homology algorithms toolbox

U Bauer, M Kerber, J Reininghaus, H Wagner - Journal of symbolic …, 2017 - Elsevier
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 …

Parallel computation of 2D Morse-Smale complexes

N Shivashankar, M Senthilnathan… - IEEE Transactions on …, 2011 - ieeexplore.ieee.org
The Morse-Smale complex is a useful topological data structure for the analysis and
visualization of scalar data. This paper describes an algorithm that processes all mesh …

Towards personalized diagnosis of glioblastoma in fluid-attenuated inversion recovery (FLAIR) by topological interpretable machine learning

M Rucco, G Viticchi, L Falsetti - Mathematics, 2020 - mdpi.com
Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which
tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all …

Efficient computation of 3D Morse–Smale complexes and persistent homology using discrete Morse theory

D Günther, J Reininghaus, H Wagner, I Hotz - The Visual Computer, 2012 - Springer
We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-
scale images. This complex allows for an efficient computation of persistent homology since …

Persistent homology of unweighted complex networks via discrete Morse theory

H Kannan, E Saucan, I Roy, A Samal - Scientific reports, 2019 - nature.com
Topological data analysis can reveal higher-order structure beyond pairwise connections
between vertices in complex networks. We present a new method based on discrete Morse …

Computational topology in text mining

H Wagner, P Dłotko, M Mrozek - … , CTIC 2012, Bertinoro, Italy, May 28-30 …, 2012 - Springer
In this paper we present our ongoing research on applying computational topology to
analysis of structure of similarities within a collection of text documents. Our work is on the …

Discrete morse theory for computing zigzag persistence

C Maria, H Schreiber - Discrete & Computational Geometry, 2024 - Springer
We introduce a theoretical and computational framework to use discrete Morse theory as an
efficient preprocessing in order to compute zigzag persistent homology. From a zigzag …

[PDF][PDF] Discrete Morse theory for filtrations

V Nanda - 2012 - rucore.libraries.rutgers.edu
We provide a brief synopsis of definitions and results from homological algebra in Section
2.2 and combinatorial topology in Section 2.5 while referring the reader to the excellent …

Forman-Ricci curvature and persistent homology of unweighted complex networks

I Roy, S Vijayaraghavan, SJ Ramaia, A Samal - Chaos, Solitons & Fractals, 2020 - Elsevier
We present the application of topological data analysis (TDA) to study unweighted complex
networks via their persistent homology. By endowing appropriate weights that capture the …