Maximum Betti Numbers of Čech Complexes

Συγγραφείς: Herbert Edelsbrunner, János Pach

Συνεισφορές: Herbert Edelsbrunner and János Pach

Πηγή: Discrete Comput Geom

Θεματικοί όροι: QA Mathematics / matematika, extremal questions, computational topology, Discrete geometry, Delaunay mosaics, Article, 52C45, FOS: Mathematics, Čech complexes, Betti numbers, Combinatorics (math.CO), F.2.2, Alpha complexes

Περιγραφή αρχείου: application/pdf; text

Σύνδεσμος πρόσβασης: https://pmc.ncbi.nlm.nih.gov/articles/PMC12953301/
https://doi.org/10.1007/s00454-025-00796-5
https://pubmed.ncbi.nlm.nih.gov/41783255/
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.53

Sparse Higher Order Čech Filtrations: Sparse higher order Čech filtrations

Συγγραφείς: Mickaël Buchet, Bianca B. Dornelas, Michael Kerber

Συνεισφορές: Mickaël Buchet and Bianca B. Dornelas and Michael Kerber

Πηγή: Journal of the ACM. 71:1-23

Θεματικοί όροι: Computational Geometry (cs.CG), FOS: Computer and information sciences, sparsification, Sparsification, k-fold cover, 0102 computer and information sciences, 01 natural sciences, Higher order Čech complexes, Persistent homology and applications, topological data analysis, Computer graphics, computational geometry (digital and algorithmic aspects), FOS: Mathematics, Algebraic Topology (math.AT), 0101 mathematics, higher-order Čech complexes

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://zbmath.org/8030795
https://doi.org/10.1145/3666085
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20

Maximum persistent Betti numbers of Čech complexes

Συγγραφείς: Edelsbrunner, Herbert^Aff1, Kahle, Matthew^Aff2, Kanazawa, Shu^{Aff3, IDs41468026002333_cor1}

Πηγή: Journal of Applied and Computational Topology. 10(1)

Vietoris thickenings and complexes have isomorphic homotopy groups

Συγγραφείς: Henry Adams, Florian Frick, Ziga Virk

Πηγή: Journal of Applied and Computational Topology. 7:221-241

Θεματικοί όροι: Simplicial sets and complexes in algebraic topology, metric thickenings, nerve lemmas, General Topology (math.GN), Metric Geometry (math.MG), 0102 computer and information sciences, 01 natural sciences, Persistent homology and applications, topological data analysis, Vietoris-Rips complexes, optimal transport, Mathematics - Metric Geometry, Metric spaces, metrizability, homotopy groups, FOS: Mathematics, Čech complexes, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Homotopy equivalences in algebraic topology, 0101 mathematics, Mathematics - General Topology

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2206.08812

Random Čech complexes on manifolds with boundary

Συγγραφείς: Henry-Louis de Kergorlay, Ulrike Tillmann, Oliver Vipond

Πηγή: Random Structures & Algorithms. 61:309-352

Θεματικοί όροι: Probability (math.PR), Combinatorial aspects of simplicial complexes, homology, 0102 computer and information sciences, 01 natural sciences, Persistent homology and applications, topological data analysis, Differential Geometry (math.DG), random geometric complexes, FOS: Mathematics, Čech complexes, Algebraic Topology (math.AT), Geometric probability and stochastic geometry, stochastic topology, Combinatorics (math.CO), 60B99, 60D05, 05E45, 55U10, 53B21, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/rsa.21062
https://zbmath.org/7751079
https://doi.org/10.1002/rsa.21062
https://ora.ox.ac.uk/objects/uuid:9bd00a50-3f99-45e2-8866-af288f65d6ed
https://doi.org/10.1002/rsa.21062

Maximum Betti Numbers of Čech Complexes

Συγγραφείς: Edelsbrunner, Herbert, Pach, János

Συνεισφορές: Herbert Edelsbrunner and János Pach

Θεματικοί όροι: Discrete geometry, computational topology, Čech complexes, Delaunay mosaics, Alpha complexes, Betti numbers, extremal questions

Περιγραφή αρχείου: application/pdf

Relation: Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.53

Διαθεσιμότητα: https://doi.org/10.4230/LIPIcs.SoCG.2024.53
https://nbn-resolving.org/urn:nbn:de:0030-drops-199981
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.53

Čech (Co-) Complexes as Koszul Complexes and Applications: Čech (co-) complexes as Koszul complexes and applications

Συγγραφείς: Schenzel, Peter

Πηγή: Vietnam Journal of Mathematics. 49:1227-1256

Θεματικοί όροι: rimary: 13D25, 13D45, Secondary: 13B35, Local cohomology and commutative rings, Completion of commutative rings, FOS: Mathematics, Čech complexes, Koszul complexes, 0101 mathematics, completion, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, local cohomology, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7425503
https://doi.org/10.1007/s10013-020-00459-3

Sparse Higher Order Čech Filtrations

Συγγραφείς: Buchet, Mickaël, B. Dornelas, Bianca, Kerber, Michael

Συνεισφορές: Mickaël Buchet and Bianca B. Dornelas and Michael Kerber

Θεματικοί όροι: Sparsification, k-fold cover, Higher order Čech complexes

Περιγραφή αρχείου: application/pdf

Relation: Is Part Of LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20

Διαθεσιμότητα: https://doi.org/10.4230/LIPIcs.SoCG.2023.20
https://nbn-resolving.org/urn:nbn:de:0030-drops-178709
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20

Random Čech complexes on Riemannian manifolds

Συγγραφείς: Omer Bobrowski, Gonçalo Oliveira

Πηγή: Random Structures & Algorithms. 54:373-412

Θεματικοί όροι: random topology, Probability (math.PR), Combinatorial aspects of simplicial complexes, 01 natural sciences, homological connectivity, Riemannian manifolds, Differential Geometry (math.DG), FOS: Mathematics, Čech complexes, Algebraic Topology (math.AT), Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Geometric probability and stochastic geometry, Combinatorics (math.CO), Primary: 60B99, 60D05, 05E45. Secondary: 55U10 53B21, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7063912
https://doi.org/10.1002/rsa.20800

On homotopy types of Vietoris–Rips complexes of metric gluings

Συγγραφείς: Adamaszek, Michał^Aff1, Adams, Henry^Aff2, Gasparovic, Ellen^{Aff3, IDs4146802000054y_cor3}, Gommel, Maria^Aff4, Purvine, Emilie^Aff5, Sazdanovic, Radmila^Aff6, Wang, Bei^Aff7, Wang, Yusu^Aff8, Ziegelmeier, Lori^Aff9

Πηγή: Journal of Applied and Computational Topology. 4(3):425-454

Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes

Συγγραφείς: Attali, Dominique, Lieutier, André, Salinas, David

Συνεισφορές: GIPSA - Architecture, Géométrie, Perception, Images, Gestes (GIPSA-AGPIG), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS), Dassault Systèmes

Πηγή: Proceedings of the twenty-seventh annual symposium on Computational geometry. :491-500

Θεματικοί όροι: high dimensions, Shape reconstruction, homotopy equivalence, Čech complexes, collapses, 0102 computer and information sciences, 0101 mathematics, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Rips complexes, clique complexes

Σύνδεσμος πρόσβασης: https://hal.archives-ouvertes.fr/hal-00579864/file/2010-socg-Rips.pdf

Vietoris-Rips and Cech Complexes of Metric Gluings

Συγγραφείς: Adamaszek, Michal, Adams, Henry, Gasparovic, Ellen, Gommel, Maria, Purvine, Emilie, Sazdanovic, Radmila, Wang, Bei, Wang, Yusu, Ziegelmeier, Lori

Συνεισφορές: Michal Adamaszek and Henry Adams and Ellen Gasparovic and Maria Gommel and Emilie Purvine and Radmila Sazdanovic and Bei Wang and Yusu Wang and Lori Ziegelmeier

Θεματικοί όροι: Vietoris-Rips and Cech complexes, metric space gluings and wedge sums, metric graphs, persistent homology

Περιγραφή αρχείου: application/pdf

Relation: Is Part Of LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.3

Διαθεσιμότητα: https://doi.org/10.4230/LIPIcs.SoCG.2018.3
https://nbn-resolving.org/urn:nbn:de:0030-drops-87162
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.3

Geometric reconstruction and persistence methods

Συγγραφείς: Garcia Pascual, Belen

Διαθεσιμότητα: https://hdl.handle.net/1956/23118

Vietoris–Rips complexes also provide topologically correct reconstructions of sampled shapes

Συγγραφείς: Attali, Dominique ^{a, ⁎}, Lieutier, André ^{b, ⁎}, Salinas, David ^{a, ⁎}

Πηγή: In Computational Geometry: Theory and Applications May 2013 46(4):448-465

On the topology of random complexes built over stationary point processes

Συγγραφείς: D. Yogeshwaran, Robert J. Adler

Πηγή: Ann. Appl. Probab. 25, no. 6 (2015), 3338-3380
Annals of Applied Probability

Θεματικοί όροι: stationary point processes, Combinatorial aspects of simplicial complexes, Čech, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory, Vietoris-Rips complexes, 05E45, Stationary stochastic processes, Morse critical points, 58K05, FOS: Mathematics, Čech complexes, Mathematics - Combinatorics, Algebraic Topology (math.AT), 55U10, Betti numbers, Mathematics - Algebraic Topology, 60D05, 0101 mathematics, Point process, Simplicial sets and complexes in algebraic topology, Probability (math.PR), 16. Peace & justice, random geometric complex, negative association, Critical points of functions and mappings on manifolds, component counts, Vietoris–Rips, 13. Climate action, random geometric complexes, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), Geometric probability and stochastic geometry, Combinatorics (math.CO), Mathematics - Probability, 05C10

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1211.0061
http://projecteuclid.org/euclid.aoap/1443703776

Local Cohomology and Čech Complexes

Συγγραφείς: 陳韋達

Συνεισφορές: 劉容真

Θεματικοί όροι: Local Cohomology, Čech Complexes

Περιγραφή αρχείου: application/pdf

Relation: GN0696400179; http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101777

Διαθεσιμότητα: http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101777
https://hdl.handle.net/20.500.12235/101777
http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN0696400179%22.&%22.id.&

Sparse Higher Order Čech Filtrations

Συγγραφείς: Mickaël Buchet and Bianca B. Dornelas and Michael Kerber, Buchet, Mickaël, B. Dornelas, Bianca, Kerber, Michael

Όροι ευρετηρίου: Sparsification, k-fold cover, Higher order Čech complexes, InProceedings, Text, doc-type:ResearchArticle, publishedVersion

Σύνδεσμος: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20
Is Part Of LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)