--- _id: '8703' abstract: - lang: eng text: 'Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ' alternative_title: - LIPIcs article_number: '75' article_processing_charge: No author: - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 - first_name: Mael full_name: Rouxel-Labbé, Mael last_name: Rouxel-Labbé - first_name: Monique full_name: Teillaud, Monique last_name: Teillaud citation: ama: 'Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75' apa: 'Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75' chicago: Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75. ieee: G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173. ista: 'Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75.' mla: Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75. short: G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-09-09 location: Virtual, Online; Pisa, Italy name: 'ESA: Annual European Symposium on Algorithms' start_date: 2020-09-07 date_created: 2020-10-25T23:01:18Z date_published: 2020-08-26T00:00:00Z date_updated: 2023-09-07T13:29:00Z day: '26' ddc: - '000' department: - _id: HeEd doi: 10.4230/LIPIcs.ESA.2020.75 ec_funded: 1 file: - access_level: open_access checksum: fe0f7c49a99ed870c671b911e10d5496 content_type: application/pdf creator: cziletti date_created: 2020-10-27T14:31:52Z date_updated: 2020-10-27T14:31:52Z file_id: '8712' file_name: 2020_LIPIcs_Osang.pdf file_size: 733291 relation: main_file success: 1 file_date_updated: 2020-10-27T14:31:52Z has_accepted_license: '1' intvolume: ' 173' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '08' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication: 28th Annual European Symposium on Algorithms publication_identifier: isbn: - '9783959771627' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '9056' relation: dissertation_contains status: public scopus_import: '1' status: public title: Generalizing CGAL periodic Delaunay triangulations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 173 year: '2020' ... --- _id: '8163' abstract: - lang: eng text: Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces. acknowledgement: "The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31." article_processing_charge: No article_type: original author: - first_name: Gert full_name: Vegter, Gert last_name: Vegter - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454 apa: Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454 chicago: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454. ieee: G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020. ista: Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199. mla: Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454. short: G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199. date_created: 2020-07-24T07:09:18Z date_published: 2020-07-24T00:00:00Z date_updated: 2023-10-10T13:05:27Z day: '24' ddc: - '510' department: - _id: HeEd doi: 10.1556/012.2020.57.2.1454 ec_funded: 1 external_id: isi: - '000570978400005' file: - access_level: open_access content_type: application/pdf creator: mwintrae date_created: 2020-07-24T07:09:06Z date_updated: 2020-07-24T07:09:06Z file_id: '8164' file_name: 57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf file_size: 1476072 relation: main_file file_date_updated: 2020-07-24T07:09:06Z has_accepted_license: '1' intvolume: ' 57' isi: 1 issue: '2' language: - iso: eng license: https://creativecommons.org/licenses/by-nc/4.0/ month: '07' oa: 1 oa_version: Published Version page: 193-199 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: Studia Scientiarum Mathematicarum Hungarica publication_identifier: eissn: - 1588-2896 issn: - 0081-6906 publication_status: published publisher: Akadémiai Kiadó quality_controlled: '1' scopus_import: '1' status: public title: Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 57 year: '2020' ... --- _id: '9157' abstract: - lang: eng text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy. acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)." article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100 apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100 chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100. ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020. ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67. mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100. short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67. date_created: 2021-02-17T15:13:01Z date_published: 2020-06-20T00:00:00Z date_updated: 2023-10-17T12:34:51Z day: '20' ddc: - '510' department: - _id: HeEd doi: 10.1515/cmb-2020-0100 ec_funded: 1 file: - access_level: open_access checksum: cea41de9937d07a3b927d71ee8b4e432 content_type: application/pdf creator: dernst date_created: 2021-02-19T13:56:24Z date_updated: 2021-02-19T13:56:24Z file_id: '9171' file_name: 2020_CompMathBiophysics_Akopyan2.pdf file_size: 562359 relation: main_file success: 1 file_date_updated: 2021-02-19T13:56:24Z has_accepted_license: '1' intvolume: ' 8' issue: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 51-67 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Computational and Mathematical Biophysics publication_identifier: issn: - 2544-7297 publication_status: published publisher: De Gruyter quality_controlled: '1' status: public title: The weighted mean curvature derivative of a space-filling diagram tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2020' ... --- _id: '9156' abstract: - lang: eng text: The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy. acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)." article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101 apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101 chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101. ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020. ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88. mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101. short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88. date_created: 2021-02-17T15:12:44Z date_published: 2020-07-21T00:00:00Z date_updated: 2023-10-17T12:35:10Z day: '21' ddc: - '510' department: - _id: HeEd doi: 10.1515/cmb-2020-0101 ec_funded: 1 external_id: arxiv: - '1908.06777' file: - access_level: open_access checksum: ca43a7440834eab6bbea29c59b56ef3a content_type: application/pdf creator: dernst date_created: 2021-02-19T13:33:19Z date_updated: 2021-02-19T13:33:19Z file_id: '9170' file_name: 2020_CompMathBiophysics_Akopyan.pdf file_size: 707452 relation: main_file success: 1 file_date_updated: 2021-02-19T13:33:19Z has_accepted_license: '1' intvolume: ' 8' issue: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 74-88 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Computational and Mathematical Biophysics publication_identifier: issn: - 2544-7297 publication_status: published publisher: De Gruyter quality_controlled: '1' status: public title: The weighted Gaussian curvature derivative of a space-filling diagram tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2020' ... --- _id: '15064' abstract: - lang: eng text: We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems. acknowledgement: This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: U. full_name: Bauer, U. last_name: Bauer - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Grzegorz full_name: Jablonski, Grzegorz id: 4483EF78-F248-11E8-B48F-1D18A9856A87 last_name: Jablonski orcid: 0000-0002-3536-9866 - first_name: M. full_name: Mrozek, M. last_name: Mrozek citation: ama: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8 apa: Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8 chicago: Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8. ieee: U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020. ista: Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480. mla: Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8. short: U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480. date_created: 2024-03-04T10:47:49Z date_published: 2020-12-01T00:00:00Z date_updated: 2024-03-04T10:54:04Z day: '01' ddc: - '500' department: - _id: HeEd doi: 10.1007/s41468-020-00058-8 file: - access_level: open_access checksum: eed1168b6e66cd55272c19bb7fca8a1c content_type: application/pdf creator: dernst date_created: 2024-03-04T10:52:42Z date_updated: 2024-03-04T10:52:42Z file_id: '15065' file_name: 2020_JourApplCompTopology_Bauer.pdf file_size: 851190 relation: main_file success: 1 file_date_updated: 2024-03-04T10:52:42Z has_accepted_license: '1' intvolume: ' 4' issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 455-480 publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Čech-Delaunay gradient flow and homology inference for self-maps tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 4 year: '2020' ...