Authors: Bertrand, Gilles, Najman, Laurent
Contributors: Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, S. Brunetti, A. Frosini, S. Rinaldi
Superior Title: International Conference on Discrete Geometry and Mathematical Morphology (DGMM) ; https://hal.science/hal-04217818 ; International Conference on Discrete Geometry and Mathematical Morphology (DGMM), S. Brunetti; A. Frosini; S. Rinaldi, Apr 2024, Florence, Italy
Subject Terms: Homology, Cohomology, Discrete Morse Theory, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Time: Florence, Italy
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2402.02874; hal-04217818; https://hal.science/hal-04217818; https://hal.science/hal-04217818v2/document; https://hal.science/hal-04217818v2/file/lncs_frame_final_DGMM.pdf; ARXIV: 2402.02874
Authors: Bertrand, Gilles, Najman, Laurent
Contributors: Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, S. Brunetti, A. Frosini, S. Rinaldi
Superior Title: International Conference on Discrete Geometry and Mathematical Morphology (DGMM) ; https://hal.science/hal-04217818 ; International Conference on Discrete Geometry and Mathematical Morphology (DGMM), S. Brunetti; A. Frosini; S. Rinaldi, Apr 2024, Florence, Italy
Subject Terms: Homology, Cohomology, Discrete Morse Theory, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Time: Florence, Italy
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2402.02874; hal-04217818; https://hal.science/hal-04217818; https://hal.science/hal-04217818v2/document; https://hal.science/hal-04217818v2/file/lncs_frame_final_DGMM.pdf; ARXIV: 2402.02874
Authors: Bertrand, Gilles, Najman, Laurent
Contributors: Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, S. Brunetti, A. Frosini, S. Rinaldi
Superior Title: International Conference on Discrete Geometry and Mathematical Morphology (DGMM) ; https://hal.science/hal-04217818 ; International Conference on Discrete Geometry and Mathematical Morphology (DGMM), S. Brunetti; A. Frosini; S. Rinaldi, Apr 2024, Florence, Italy
Subject Terms: Homology, Cohomology, Discrete Morse Theory, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Time: Florence, Italy
Relation: hal-04217818; https://hal.science/hal-04217818; https://hal.science/hal-04217818/document; https://hal.science/hal-04217818/file/Morse_Frames-20231010.pdf
Authors: Gaucher, Philippe
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Superior Title: ISSN: 1201-561X ; Theory and Applications of Categories ; https://hal.science/hal-03771404 ; Theory and Applications of Categories, 2024, 41 (7), pp.194-237.
Subject Terms: directed path, generalized Reedy category, Lawvere metric space, pseudometric space, precubical set, accessible model category, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2209.02667; hal-03771404; https://hal.science/hal-03771404; https://hal.science/hal-03771404v3/document; https://hal.science/hal-03771404v3/file/2209.02667.pdf; ARXIV: 2209.02667
Authors: Gaucher, Philippe
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Superior Title: ISSN: 1120-7183.
Subject Terms: directed path, precubical set, directed homotopy, combinatorial model category, accessible category, mixed model structure, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-03741876; https://hal.science/hal-03741876; https://hal.science/hal-03741876v5/document; https://hal.science/hal-03741876v5/file/realisation3top.pdf
Authors: Gaucher, Philippe
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Superior Title: https://hal.science/hal-04563674 ; 2024.
Subject Terms: multipointed d-space, globular subdivision, directed path, natural system, bisimulation, open map, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Relation: hal-04563674; https://hal.science/hal-04563674; https://hal.science/hal-04563674v2/document; https://hal.science/hal-04563674v2/file/GlobularNaturalSystem.pdf
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University of Melbourne, Australian Research Council Future Fellowship FT210100256
Superior Title: https://hal.science/hal-03991861 ; 2024.
Subject Terms: February 15 2023. 2010 Mathematics Subject Classification. Primary 18N20 Secondary 52B11 Categorified operads categorical coherence Seifert-Van Kampen theorem polytopes MacLane coherence theorem rewriting theory Morse theory, February 15, 2023. 2010 Mathematics Subject Classification. Primary 18N20, Secondary 52B11 Categorified operads, categorical coherence, Seifert-Van Kampen theorem, polytopes, MacLane coherence theorem, rewriting theory, Morse theory, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2302.07391; hal-03991861; https://hal.science/hal-03991861; https://hal.science/hal-03991861v2/document; https://hal.science/hal-03991861v2/file/Coherence.pdf; ARXIV: 2302.07391
Authors: Henneuse, Hugo
Contributors: Understanding the Shape of Data (DATASHAPE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-19-CHIA-0001,TopAI,TopAI : Analyse Topologique des Données pour l'apprentissage et l'IA(2019)
Superior Title: https://hal.science/hal-04524998 ; 2024.
Subject Terms: Topological Data Analysis, Persistent Homology, Non-parametric statistics, Minimax, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-04524998; https://hal.science/hal-04524998; https://hal.science/hal-04524998v2/document; https://hal.science/hal-04524998v2/file/2403.19396v2.pdf
Authors: Henneuse, Hugo
Contributors: Understanding the Shape of Data (DATASHAPE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-19-CHIA-0001,TopAI,TopAI : Analyse Topologique des Données pour l'apprentissage et l'IA(2019)
Superior Title: https://hal.science/hal-04524998 ; 2024.
Subject Terms: Topological Data Analysis, Persistent Homology, Non-parametric statistics, Minimax, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-04524998; https://hal.science/hal-04524998; https://hal.science/hal-04524998v2/document; https://hal.science/hal-04524998v2/file/2403.19396v2.pdf
Contributors: Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL), Kalamazoo College, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics Cornell, Cornell University New York
Superior Title: https://hal.science/hal-04465168 ; 2024.
Subject Terms: partitions, Yoneda product, Karoubi envelope, prop, 2024 Mathematics Subject Classification. 18M85, 18G15, 05A17, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2402.12895; hal-04465168; https://hal.science/hal-04465168; https://hal.science/hal-04465168/document; https://hal.science/hal-04465168/file/EHLVZ-WIT.pdf; ARXIV: 2402.12895
Authors: Oulhaj, Ziyad, Carrière, Mathieu, Michel, Bertrand
Contributors: NANTES UNIVERSITÉ - École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Understanding the Shape of Data (DATASHAPE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), ANR-22-CE40-0007,GeoDSIC,Géométrie dans les données : inférence statistique & partitionnement(2022), ANR-23-CE23-0014,TopModel,TopModel: Topologie Multiparamétrée pour les Modèles d'Apprentissage Automatique(2023), ANR-22-PESN-0002,AI4scMED,MultiScale AI for SingleCell-Based Precision Medicine(2022)
Superior Title: https://hal.science/hal-04457645 ; 2024.
Subject Terms: Mapper Graph, Data Visualization, Topological Data Analysis, Persistent Homology, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-04457645; https://hal.science/hal-04457645; https://hal.science/hal-04457645/document; https://hal.science/hal-04457645/file/Mapper_Optimization_Preprint.pdf
Authors: Fresse, Benoit, Guerra, Lorenzo
Contributors: Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-18-CE93-0002,OCHoTop,Opérades, Calcul et méthodes de théorie de l'Homotopie en Topologie(2018)
Superior Title: https://hal.science/hal-04407952 ; 2024.
Subject Terms: 2020 MSC: Primary: 18N70, Secondary: 55U10, 18M70, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2011.11333; hal-04407952; https://hal.science/hal-04407952; https://hal.science/hal-04407952/document; https://hal.science/hal-04407952/file/2011.11333.pdf; ARXIV: 2011.11333
Authors: Oulhaj, Ziyad, Carrière, Mathieu, Michel, Bertrand
Contributors: NANTES UNIVERSITÉ - École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Understanding the Shape of Data (DATASHAPE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), ANR-22-CE40-0007,GeoDSIC,Géométrie dans les données : inférence statistique & partitionnement(2022), ANR-23-CE23-0014,TopModel,TopModel: Topologie Multiparamétrée pour les Modèles d'Apprentissage Automatique(2023), ANR-22-PESN-0002,AI4scMED,MultiScale AI for SingleCell-Based Precision Medicine(2022)
Superior Title: https://hal.science/hal-04457645 ; 2024.
Subject Terms: Mapper Graph, Data Visualization, Topological Data Analysis, Persistent Homology, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-04457645; https://hal.science/hal-04457645; https://hal.science/hal-04457645/document; https://hal.science/hal-04457645/file/Mapper_Optimization_Preprint.pdf
Contributors: Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL), Kalamazoo College, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics Cornell, Cornell University New York
Superior Title: https://hal.science/hal-04465168 ; 2024.
Subject Terms: partitions, Yoneda product, Karoubi envelope, prop, 2024 Mathematics Subject Classification. 18M85, 18G15, 05A17, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2402.12895; hal-04465168; https://hal.science/hal-04465168; https://hal.science/hal-04465168/document; https://hal.science/hal-04465168/file/EHLVZ-WIT.pdf; ARXIV: 2402.12895
Authors: David, Claire, Lapidus, Michel, L
Contributors: Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University of California Riverside (UC Riverside), University of California (UC)
Superior Title: https://hal.science/hal-03797595 ; 2024.
Subject Terms: Weierstrass Curve, best Hölder exponent, reverse Hölder continuity, Complex Dimensions of an iterated fractal drum, box-counting (or Minkowski) dimension, fractal tube formula, tube zeta function, distance zeta function, (upper, lower and average) Minkowski contents, Minkowski non-measurability, Minkowski nondegeneracy, nowhere differentiability, differential operators, differentials, fractal cohomology, cohomology groups, topological invariants, fractal expansions, cohomology infinitesimal, MSC Classification: 11M41, 28A12, 28A75, 28A80, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]
Relation: hal-03797595; https://hal.science/hal-03797595; https://hal.science/hal-03797595v3/document; https://hal.science/hal-03797595v3/file/FractalComplexDimensionsAndCohomologyWHAL.pdf
Authors: Fresse, Benoit, Turchin, Victor, Willwacher, Thomas
Contributors: Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics (University of Kansas), University of Kansas Lawrence (KU), Institut für Mathematik Zürich, Universität Zürich Zürich = University of Zurich (UZH), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-18-CE93-0002,OCHoTop,Opérades, Calcul et méthodes de théorie de l'Homotopie en Topologie(2018)
Superior Title: https://hal.science/hal-04407953 ; 2024.
Relation: info:eu-repo/semantics/altIdentifier/arxiv/1703.06123; hal-04407953; https://hal.science/hal-04407953; https://hal.science/hal-04407953/document; https://hal.science/hal-04407953/file/1703.06123.pdf; ARXIV: 1703.06123
Authors: Fresse, Benoit, Turchin, Victor, Willwacher, Thomas
Contributors: Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics (University of Kansas), University of Kansas Lawrence (KU), Institut für Mathematik Zürich, Universität Zürich Zürich = University of Zurich (UZH), ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011), ANR-18-CE93-0002,OCHoTop,Opérades, Calcul et méthodes de théorie de l'Homotopie en Topologie(2018)
Superior Title: https://hal.science/hal-04407946 ; 2024.
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2008.08146; hal-04407946; https://hal.science/hal-04407946; https://hal.science/hal-04407946/document; https://hal.science/hal-04407946/file/2008.08146.pdf; ARXIV: 2008.08146
Contributors: Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL), Kalamazoo College, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics Cornell, Cornell University New York
Superior Title: https://hal.science/hal-04465168 ; 2024.
Subject Terms: partitions, Yoneda product, Karoubi envelope, prop, 2024 Mathematics Subject Classification. 18M85, 18G15, 05A17, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2402.12895; hal-04465168; https://hal.science/hal-04465168; https://hal.science/hal-04465168/document; https://hal.science/hal-04465168/file/EHLVZ-WIT.pdf; ARXIV: 2402.12895
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), School of Mathematics and Statistics Melbourne, Faculty of Science Melbourne, University of Melbourne-University of Melbourne, Andrew Sisson Fund, Australian Research Council Future Fellowship FT210100256
Superior Title: https://hal.science/hal-04520995 ; 2024.
Subject Terms: Term rewriting, nestohedra, hypergraph polytopes, categorified operads, categorical coherence, MacLane coherence theorem, Primary 68Q42, Secondary 18N20, 52B11, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2403.15987; hal-04520995; https://hal.science/hal-04520995; https://hal.science/hal-04520995v2/document; https://hal.science/hal-04520995v2/file/Coherence2_HAL.pdf; ARXIV: 2403.15987
Authors: Gaucher, Philippe
Contributors: Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Superior Title: https://hal.science/hal-04118042 ; 2024.
Subject Terms: precubical set, directed path, presheaf, Reedy category, Lawvere metric space, process algebra, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
Relation: hal-04118042; https://hal.science/hal-04118042; https://hal.science/hal-04118042v3/document; https://hal.science/hal-04118042v3/file/ThickCategoryCubes.pdf