--- _id: '8323' article_processing_charge: No article_type: letter_note author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach citation: ama: Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5 apa: Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5 chicago: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5. ieee: J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020. ista: Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574. mla: Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5. short: J. Pach, Discrete and Computational Geometry 64 (2020) 571–574. date_created: 2020-08-30T22:01:12Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T09:05:04Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-020-00237-5 external_id: isi: - '000561483500001' intvolume: ' 64' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00454-020-00237-5 month: '10' oa: 1 oa_version: None page: 571-574 publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer Nature scopus_import: '1' status: public title: A farewell to Ricky Pollack type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 64 year: '2020' ... --- _id: '8580' abstract: - lang: eng text: We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients. article_number: '9158054' article_processing_charge: No author: - first_name: Grzegorz full_name: Graff, Grzegorz last_name: Graff - first_name: Beata full_name: Graff, Beata last_name: Graff - first_name: Grzegorz full_name: Jablonski, Grzegorz id: 4483EF78-F248-11E8-B48F-1D18A9856A87 last_name: Jablonski orcid: 0000-0002-3536-9866 - first_name: Krzysztof full_name: Narkiewicz, Krzysztof last_name: Narkiewicz citation: ama: 'Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054' apa: 'Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054' chicago: 'Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.' ieee: 'G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.' ista: 'Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054.' mla: 'Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.' short: 'G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.' conference: end_date: 2020-07-15 location: Pisa, Italy name: 'ESGCO: European Study Group on Cardiovascular Oscillations' start_date: 2020-07-15 date_created: 2020-09-28T08:59:27Z date_published: 2020-08-01T00:00:00Z date_updated: 2023-08-22T09:33:34Z day: '01' department: - _id: HeEd doi: 10.1109/ESGCO49734.2020.9158054 external_id: isi: - '000621172600045' isi: 1 language: - iso: eng month: '08' oa_version: None publication: '11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ' publication_identifier: isbn: - '9781728157511' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: The application of persistent homology in the analysis of heart rate variability type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2020' ... --- _id: '10867' abstract: - lang: eng text: In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces. acknowledgement: ' Supported by the Russian Foundation for Basic Research grant 18-01-00036.' 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: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037 apa: Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037 chicago: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037. ieee: A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020. ista: Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697. mla: Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037. short: A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697. date_created: 2022-03-18T11:39:30Z date_published: 2020-02-01T00:00:00Z date_updated: 2023-08-24T14:19:55Z day: '01' department: - _id: HeEd doi: 10.1093/imrn/rny037 external_id: arxiv: - '1702.07513' isi: - '000522852700002' intvolume: ' 2020' isi: 1 issue: '3' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1702.07513 month: '02' oa: 1 oa_version: Preprint page: 669-697 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: Waist of balls in hyperbolic and spherical spaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 2020 year: '2020' ... --- _id: '7460' abstract: - lang: eng text: "Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Katharina full_name: Ölsböck, Katharina id: 4D4AA390-F248-11E8-B48F-1D18A9856A87 last_name: Ölsböck orcid: 0000-0002-4672-8297 citation: ama: Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460 apa: Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460 chicago: Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460. ieee: K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020. ista: Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria. mla: Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460. short: K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020. date_created: 2020-02-06T14:56:53Z date_published: 2020-02-10T00:00:00Z date_updated: 2023-09-07T13:15:30Z day: '10' ddc: - '514' degree_awarded: PhD department: - _id: HeEd - _id: GradSch doi: 10.15479/AT:ISTA:7460 file: - access_level: open_access checksum: 1df9f8c530b443c0e63a3f2e4fde412e content_type: application/pdf creator: koelsboe date_created: 2020-02-06T14:43:54Z date_updated: 2020-07-14T12:47:58Z file_id: '7461' file_name: thesis_ist-final_noack.pdf file_size: 76195184 relation: main_file - access_level: closed checksum: 7a52383c812b0be64d3826546509e5a4 content_type: application/x-zip-compressed creator: koelsboe date_created: 2020-02-06T14:52:45Z date_updated: 2020-07-14T12:47:58Z description: latex source files, figures file_id: '7462' file_name: latex-files.zip file_size: 122103715 relation: source_file file_date_updated: 2020-07-14T12:47:58Z has_accepted_license: '1' keyword: - shape reconstruction - hole manipulation - ordered complexes - Alpha complex - Wrap complex - computational topology - Bregman geometry language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '02' oa: 1 oa_version: Published Version page: '155' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '6608' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: The hole system of triangulated shapes tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '7944' abstract: - lang: eng text: "This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 citation: ama: Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944 apa: Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944 chicago: Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944. ieee: Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020. ista: Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria. mla: Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944. short: Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020. date_created: 2020-06-08T00:49:46Z date_published: 2020-06-09T00:00:00Z date_updated: 2023-09-07T13:17:37Z day: '09' ddc: - '516' - '514' degree_awarded: PhD department: - _id: HeEd - _id: UlWa doi: 10.15479/AT:ISTA:7944 file: - access_level: open_access checksum: df688bc5a82b50baee0b99d25fc7b7f0 content_type: application/pdf creator: zmasarov date_created: 2020-06-08T00:34:00Z date_updated: 2020-07-14T12:48:05Z file_id: '7945' file_name: THESIS_Zuzka_Masarova.pdf file_size: 13661779 relation: main_file - access_level: closed checksum: 45341a35b8f5529c74010b7af43ac188 content_type: application/zip creator: zmasarov date_created: 2020-06-08T00:35:30Z date_updated: 2020-07-14T12:48:05Z file_id: '7946' file_name: THESIS_Zuzka_Masarova_SOURCE_FILES.zip file_size: 32184006 relation: source_file file_date_updated: 2020-07-14T12:48:05Z has_accepted_license: '1' keyword: - reconfiguration - reconfiguration graph - triangulations - flip - constrained triangulations - shellability - piecewise-linear balls - token swapping - trees - coloured weighted token swapping language: - iso: eng license: https://creativecommons.org/licenses/by-sa/4.0/ month: '06' oa: 1 oa_version: Published Version page: '160' publication_identifier: isbn: - 978-3-99078-005-3 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '7950' relation: part_of_dissertation status: public - id: '5986' relation: part_of_dissertation status: public status: public supervisor: - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Reconfiguration problems tmp: image: /images/cc_by_sa.png legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) short: CC BY-SA (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _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 license: https://creativecommons.org/licenses/by/4.0/ 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' ...