Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Mathematics of computing → Topology"'
Autor:
Alonso, Ángel Javier, Kerber, Michael
We study the decomposition of zero-dimensional persistence modules, viewed as functors valued in the category of vector spaces factorizing through sets. Instead of working directly at the level of vector spaces, we take a step back and first study th
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http://arxiv.org/abs/2303.06118
http://arxiv.org/abs/2303.06118
We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter persistence modul
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0fd059db70b7aa1ebeaf39bd917067a1
Autor:
Burton, Benjamin A., He, Alexander
We often rely on censuses of triangulations to guide our intuition in $3$-manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexamples are too large to appear in our census. Since the number of triangula
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Computability and continuity are closely linked - in fact, continuity can be seen as computability relative to an arbitrary oracle. As such, concepts from topology and descriptive set theory feature heavily in the foundations of computable analysis.
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https://explore.openaire.eu/search/publication?articleId=doi_________::019267836dd997199f50dc762b308ded
Autor:
Mémoli, Facundo, Zhou, Ling
We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of filtered chain complexes. The information present at the level of fil
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Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at cohomology level
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http://arxiv.org/abs/2107.01553
http://arxiv.org/abs/2107.01553
Autor:
de Brecht, Matthew
We construct the space of valuations on a quasi-Polish space in terms of the characterization of quasi-Polish spaces as spaces of ideals of a countable transitive relation. Our construction is closely related to domain theoretical work on the probabi
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http://arxiv.org/abs/2106.15780
http://arxiv.org/abs/2106.15780
The notion of generalized rank invariant in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as generalized persistence diagrams. Naturally, computing these rank invaria
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Front Matter, Table of Contents, Preface, Conference Organization
LIPIcs, Vol. 204, 29th Annual European Symposium on Algorithms (ESA 2021), pages 0:i-0:xx
LIPIcs, Vol. 204, 29th Annual European Symposium on Algorithms (ESA 2021), pages 0:i-0:xx
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Publikováno v:
European Symposium on Algorithms
European Symposium on Algorithms, Sep 2021, Lisbon, Portugal. ⟨10.4230/LIPIcs.ESA.2021.32⟩
European Symposium on Algorithms, Sep 2021, Lisbon, Portugal. ⟨10.4230/LIPIcs.ESA.2021.32⟩
We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is homeomorphic to a su
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