Ripser: efficient computation of Vietoris–Rips persistence barcodes

U Bauer - Journal of Applied and Computational Topology, 2021 - Springer
We present an algorithm for the computation of Vietoris–Rips persistence barcodes and
describe its implementation in the software Ripser. The method relies on implicit …

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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[图书][B] Combinatorial algebraic topology

D Kozlov - 2007 - books.google.com
Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of
algebraic topology and discrete mathematics. This volume is the first comprehensive …

Matroid filtrations and computational persistent homology

G Henselman, R Ghrist - arXiv preprint arXiv:1606.00199, 2016 - arxiv.org
This technical report introduces a novel approach to efficient computation in homological
algebra over fields, with particular emphasis on computing the persistent homology of a …

Proof of the Lovász conjecture

E Babson, DN Kozlov - Annals of Mathematics, 2007 - JSTOR
To any two graphs G and H one can associate a cell complex Hom (G, H) by taking all graph
multihomomorphisms from G to H as cells. In this paper we prove the Lovász conjecture …

[图书][B] Minimal resolutions via algebraic discrete Morse theory

M Jöllenbeck, V Welker - 2009 - books.google.com
Page 1 MEMOIRSofthe American Mathematical Society Number 923 Minimal Resolutions
via Algebraic Discrete Morse Theory Michael Jollenbeck Volkmar Welker January 2009 • …

[HTML][HTML] Aspects of topological approaches for data science

J Grbić, J Wu, K Xia, GW Wei - Foundations of data science …, 2022 - ncbi.nlm.nih.gov
We establish a new theory which unifies various aspects of topological approaches for data
science, by being applicable both to point cloud data and to graph data, including networks …

Discrete Morse theory for computing cellular sheaf cohomology

J Curry, R Ghrist, V Nanda - Foundations of Computational Mathematics, 2016 - Springer
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly
generalizing persistent homology. We develop an algorithm for simplifying the computation …

Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces

M Lipiński, J Kubica, M Mrozek, T Wanner - Journal of Applied and …, 2023 - Springer
We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector
fields introduced in Mrozek (Found Comput Math 17 (6): 1585–1633, 2017). The …

[图书][B] Organized collapse: an introduction to discrete Morse theory

DN Kozlov - 2021 - books.google.com
Applied topology is a modern subject which emerged in recent years at a crossroads of
many methods, all of them topological in nature, which were used in a wide variety of …