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pro vyhledávání: '"Boissonnat, P"'
The \emph{strong collapse} of a simplicial complex, proposed by Barmak and Minian (\emph{Disc. Comp. Geom. 2012}), is a combinatorial collapse of a complex onto its sub-complex. Recently, it has received attention from computational topology research
Externí odkaz:
http://arxiv.org/abs/2301.03514
Autor:
Boissonnat, Jean-Daniel, Dutta, Kunal
Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning as shown by Phillips, Wang and Zheng [SoCG 2015]. However, contrary to the case of computing persistent homology using the
Externí odkaz:
http://arxiv.org/abs/2301.03321
Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Cech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for this problem, answering an open quest
Externí odkaz:
http://arxiv.org/abs/2110.05897
Publikováno v:
Journal of Applied and Computational Topology, Springer, 2019, 3 (1-2), pp.16
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent homological featu
Externí odkaz:
http://arxiv.org/abs/2001.02960
Publikováno v:
Algorithmica, Springer Verlag, 2014, 70 (3), pp.20
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex.
Externí odkaz:
http://arxiv.org/abs/2001.02581
Autor:
Marijke De Saint-Hubert, Guillaume Boissonnat, Uwe Schneider, Christian Bäumer, Nico Verbeek, Johannes Esser, Jörg Wulff, Florian Stuckmann, Finja Suesselbeck, Racell Nabha, Jérémie Dabin, Fabiano Vasi, Stephan Radonic, Miguel Rodriguez, Anne Catherine Simon, Neige Journy, Beate Timmermann, Isabelle Thierry-Chef, Lorenzo Brualla
Publikováno v:
Frontiers in Oncology, Vol 13 (2023)
BackgroundIn radiotherapy, especially when treating children, minimising exposure of healthy tissue can prevent the development of adverse outcomes, including second cancers. In this study we propose a validated Monte Carlo framework to evaluate the
Externí odkaz:
https://doaj.org/article/e255b0da705e4a23b3ffba2c6a280d1e
Akademický článek
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We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak a
Externí odkaz:
http://arxiv.org/abs/1809.10945
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeo
Externí odkaz:
http://arxiv.org/abs/1803.07642
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a pra
Externí odkaz:
http://arxiv.org/abs/1703.06487