--- _id: '18107' abstract: - lang: eng text: We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and ρ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260). acknowledgement: 'Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.' article_number: e78 article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 2024;12. doi:10.1017/fms.2024.56' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2024.56' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma. Cambridge University Press, 2024. https://doi.org/10.1017/fms.2024.56.' ieee: 'A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” Forum of Mathematics, Sigma, vol. 12. Cambridge University Press, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma, vol. 12, e78, Cambridge University Press, 2024, doi:10.1017/fms.2024.56.' short: A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024). corr_author: '1' das_tickbox: '0' date_created: 2024-09-20T12:25:25Z date_published: 2024-09-09T00:00:00Z date_updated: 2026-10-02T11:43:00Z day: '09' ddc: - '510' department: - _id: GradSch - _id: RoSe doi: 10.1017/fms.2024.56 external_id: arxiv: - '2407.05990' isi: - '001307817400001' file: - access_level: open_access checksum: 330b881240013213a8e08538fec13d29 content_type: application/pdf creator: dernst date_created: 2024-09-23T09:56:17Z date_updated: 2024-09-23T09:56:17Z file_id: '18126' file_name: 2024_ForumMath_Lauritsen.pdf file_size: 599886 relation: main_file success: 1 file_date_updated: 2024-09-23T09:56:17Z fulldoi: https://doi.org/10.1017/fms.2024.56 has_accepted_license: '1' intvolume: ' 12' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'Pressure of a dilute spin-polarized Fermi gas: Lower bound' 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 12 year: '2024' ... --- OA_place: publisher OA_type: free access _id: '18443' abstract: - lang: eng text: "In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Maria A full_name: Sisak, Maria A id: 44A03D04-AEA4-11E9-B225-EA2DE6697425 last_name: Sisak citation: ama: Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443 apa: Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443 chicago: Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443. ieee: M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024. ista: Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. mla: Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18443. short: M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-10-19T12:00:37Z date_published: 2024-10-24T00:00:00Z date_updated: 2026-10-02T11:43:57Z day: '24' ddc: - '516' degree_awarded: PhD department: - _id: GradSch - _id: TaHa doi: 10.15479/at:ista:18443 doi_confirm: '1' file: - access_level: open_access checksum: 8c4893e726aaa4b3efb82758da9b6851 content_type: application/pdf creator: msisak date_created: 2024-10-23T14:42:45Z date_updated: 2024-10-23T14:42:45Z file_id: '18467' file_name: MASisak_dissertation.pdf file_size: 1672547 relation: main_file success: 1 - access_level: closed checksum: 1831b072e861a1e5481024ca9d02b036 content_type: application/x-zip-compressed creator: msisak date_created: 2024-10-23T14:43:56Z date_updated: 2024-10-24T08:09:13Z file_id: '18468' file_name: MASisak_source.zip file_size: 617913 relation: source_file file_date_updated: 2024-10-24T08:09:13Z fulldoi: https://doi.org/10.15479/at:ista:18443 has_accepted_license: '1' keyword: - hyperkaehler geometry - branes - mirror symmetry - T-duality language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '178' project: - _id: 6286e8c4-2b32-11ec-9570-f5297902f67f grant_number: '26069' name: Branes on hyperkähler manifolds publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria researchdata_availability: no status: public supervisor: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel orcid: 0000-0002-9582-2634 supplementarymaterial: no title: T-dual branes on hyperkähler manifolds 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: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- APC_amount: 2748 EUR OA_place: publisher OA_type: hybrid _id: '17634' abstract: - lang: eng text: System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems. acknowledgement: This work was supported in part by the ERC-2020-AdG 101020093. N. Mazzocchi was affiliated with ISTA when his collaboration started. alternative_title: - LNCS article_processing_charge: Yes (in subscription journal) arxiv: 1 author: - first_name: Marek full_name: Chalupa, Marek id: 87e34708-d6c6-11ec-9f5b-9391e7be2463 last_name: Chalupa - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000-0002-2985-7724 - first_name: Nicolas Adrien full_name: Mazzocchi, Nicolas Adrien id: b26baa86-3308-11ec-87b0-8990f34baa85 last_name: Mazzocchi - first_name: Naci E full_name: Sarac, Naci E id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425 last_name: Sarac citation: ama: 'Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. QuAK: Quantitative Automata Kit. In: 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation. Vol 15222. Springer Nature; 2024:3-20. doi:10.1007/978-3-031-75387-9_1' apa: 'Chalupa, M., Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2024). QuAK: Quantitative Automata Kit. In 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation (Vol. 15222, pp. 3–20). Crete, Greece: Springer Nature. https://doi.org/10.1007/978-3-031-75387-9_1' chicago: 'Chalupa, Marek, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac. “QuAK: Quantitative Automata Kit.” In 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, 15222:3–20. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-75387-9_1.' ieee: 'M. Chalupa, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “QuAK: Quantitative Automata Kit,” in 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Crete, Greece, 2024, vol. 15222, pp. 3–20.' ista: 'Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. 2024. QuAK: Quantitative Automata Kit. 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation. ISoLA: International Symposium on Leveraging Applications, LNCS, vol. 15222, 3–20.' mla: 'Chalupa, Marek, et al. “QuAK: Quantitative Automata Kit.” 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, vol. 15222, Springer Nature, 2024, pp. 3–20, doi:10.1007/978-3-031-75387-9_1.' short: M. Chalupa, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Springer Nature, 2024, pp. 3–20. conference: end_date: 2024-10-31 location: Crete, Greece name: 'ISoLA: International Symposium on Leveraging Applications' start_date: 2024-10-27 corr_author: '1' das_tickbox: '0' date_created: 2024-09-05T14:27:08Z date_published: 2024-10-26T00:00:00Z date_updated: 2026-10-02T11:44:52Z day: '26' ddc: - '000' department: - _id: GradSch - _id: ToHe doi: 10.1007/978-3-031-75387-9_1 ec_funded: 1 external_id: arxiv: - '2409.03569' isi: - '001419008700001' file: - access_level: open_access checksum: 43e432f82be376434b358f3dd7a94b71 content_type: application/pdf creator: esarac date_created: 2024-09-05T14:26:02Z date_updated: 2024-09-05T14:26:02Z file_id: '17635' file_name: isola24.pdf file_size: 847422 relation: main_file success: 1 - access_level: open_access checksum: 6bc04f07bb5612c0e7ea00ac121a69b6 content_type: application/pdf creator: dernst date_created: 2025-01-21T14:39:49Z date_updated: 2025-01-21T14:39:49Z file_id: '18865' file_name: 2024_LNCS_Chalupa.pdf file_size: 1358706 relation: main_file success: 1 file_date_updated: 2025-01-21T14:39:49Z fulldoi: https://doi.org/10.1007/978-3-031-75387-9_1 has_accepted_license: '1' intvolume: ' 15222' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 3-20 project: - _id: 62781420-2b32-11ec-9570-8d9b63373d4d call_identifier: H2020 grant_number: '101020093' name: Vigilant Algorithmic Monitoring of Software publication: 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation publication_identifier: eissn: - 1611-3349 isbn: - '9783031753862' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '20147' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'QuAK: Quantitative Automata Kit' 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 15222 year: '2024' ... --- _id: '14345' abstract: - lang: eng text: For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)). acknowledgement: Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Garber, Alexey last_name: Garber - first_name: Mohadese full_name: Ghafari, Mohadese last_name: Ghafari - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 2024;72:29-48. doi:10.1007/s00454-023-00566-1 apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1 chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature, 2024. https://doi.org/10.1007/s00454-023-00566-1. ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” Discrete and Computational Geometry, vol. 72. Springer Nature, pp. 29–48, 2024. ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48. mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, vol. 72, Springer Nature, 2024, pp. 29–48, doi:10.1007/s00454-023-00566-1. short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48. corr_author: '1' das_tickbox: '0' date_created: 2023-09-17T22:01:10Z date_published: 2024-07-01T00:00:00Z date_updated: 2026-10-02T11:45:50Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-023-00566-1 ec_funded: 1 external_id: arxiv: - '2204.01076' isi: - '001060727600004' pmid: - '39610762' file: - access_level: open_access checksum: b207b4e00f904e8ea8a30e24f0251f79 content_type: application/pdf creator: dernst date_created: 2024-07-22T09:43:19Z date_updated: 2024-07-22T09:43:19Z file_id: '17301' file_name: 2024_DiscreteComputGeom_Edelsbrunner.pdf file_size: 892019 relation: main_file success: 1 file_date_updated: 2024-07-22T09:43:19Z fulldoi: https://doi.org/10.1007/s00454-023-00566-1 has_accepted_license: '1' intvolume: ' 72' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 29-48 pmid: 1 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: yes title: On angles in higher order Brillouin tessellations and related tilings in the plane 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 72 year: '2024' ... --- OA_place: publisher _id: '18132' abstract: - lang: eng text: "In this thesis, we are dealing with both arithmetic and geometric problems coming from the\r\nstudy of rational points with a particular focus on function fields over finite fields:\r\n(1) Using the circle method we produce upper bounds for the number of rational points of\r\nbounded height on diagonal cubic surfaces and fourfolds over Fq(t). This is based on\r\njoint work with Leonhard Hochfilzer.\r\n(2) We study rational points on smooth complete intersections X defined by cubic and\r\nquadratic hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square”\r\ndeveloped by Vishe [202] and use the circle method with a Kloosterman refinement to\r\nestablish an asymptotic formula for the number of rational points of bounded height on\r\nX when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation.\r\n(3) In joint work with Hochfilzer, we obtain upper bounds for the number of rational points of\r\nbounded height on del Pezzo surfaces of low degree over any global field. Our approach\r\nis to take hyperplane sections, which reduces the problem to uniform estimates for the\r\nnumber of rational points on curves.\r\n(4) We develop a version of the circle method capable of counting Fq-points on jet schemes\r\nof moduli spaces of rational curves on hypersurfaces. Combining this with a spreading\r\nout argument and a result of Mustaţă [150], this allows us to show that these moduli\r\nspaces only have canonical singularities under suitable assumptions on the degree and the\r\ndimension.\r\nIn addition, we give an overview of guiding questions and conjectures in the field of rational\r\npoints and explain the basic mechanism underlying the circle method.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Counting rational points over function fields. 2024. doi:10.15479/at:ista:18132 apa: Glas, J. (2024). Counting rational points over function fields. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18132 chicago: Glas, Jakob. “Counting Rational Points over Function Fields.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18132. ieee: J. Glas, “Counting rational points over function fields,” Institute of Science and Technology Austria, 2024. ista: Glas J. 2024. Counting rational points over function fields. Institute of Science and Technology Austria. mla: Glas, Jakob. Counting Rational Points over Function Fields. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18132. short: J. Glas, Counting Rational Points over Function Fields, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-09-23T18:58:08Z date_published: 2024-09-23T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '23' ddc: - '512' degree_awarded: PhD department: - _id: GradSch - _id: TiBr doi: 10.15479/at:ista:18132 doi_confirm: '1' file: - access_level: closed checksum: 2f8cf5cefdab108b1979caa8146cae9a content_type: application/x-zip-compressed creator: jglas date_created: 2024-09-23T18:49:22Z date_updated: 2024-09-23T18:49:22Z file_id: '18133' file_name: PhDthesis (3).zip file_size: 5382106 relation: source_file - access_level: open_access checksum: 08bb6f14c42b47ff25882a2ce3ea0d8a content_type: application/pdf creator: jglas date_created: 2024-09-25T14:08:57Z date_updated: 2024-09-25T14:08:57Z file_id: '18140' file_name: example-phd.pdf file_size: 2380127 relation: main_file success: 1 file_date_updated: 2024-09-25T14:08:57Z fulldoi: https://doi.org/10.15479/at:ista:18132 has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc/4.0/ month: '09' oa: 1 oa_version: Published Version page: '195' project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '18173' relation: part_of_dissertation status: public - id: '18295' relation: part_of_dissertation status: public - id: '18294' relation: part_of_dissertation status: public - id: '18293' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 supplementarymaterial: no title: Counting rational points over function fields 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: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- _id: '18173' abstract: - lang: eng text: Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation. acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and Pankaj Vishe for useful comments. Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise in exponential sums and geometry. While working on this paper, the author was supported by FWF grant (DOI 10.55776/P36278). article_number: e12991 article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991 apa: Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.12991 chicago: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991. ieee: J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” Journal of the London Mathematical Society, vol. 110, no. 4. London Mathematical Society, 2024. ista: Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991. mla: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991. short: J. Glas, Journal of the London Mathematical Society 110 (2024). corr_author: '1' das_tickbox: '0' date_created: 2024-10-06T22:01:11Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1112/jlms.12991 external_id: arxiv: - '2306.02718' file: - access_level: open_access checksum: 11ebf690363151026ce81f91f2220855 content_type: application/pdf creator: dernst date_created: 2024-10-07T08:51:01Z date_updated: 2024-10-07T08:51:01Z file_id: '18181' file_name: 2024_JLondonMathSoc_Glas.pdf file_size: 579601 relation: main_file success: 1 file_date_updated: 2024-10-07T08:51:01Z fulldoi: https://doi.org/10.1112/jlms.12991 has_accepted_license: '1' intvolume: ' 110' issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: London Mathematical Society quality_controlled: '1' related_material: record: - id: '18132' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t) 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 110 year: '2024' ... --- OA_place: repository _id: '18295' abstract: - lang: eng text: By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d. article_processing_charge: No arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. doi:10.48550/arXiv.2405.16648 apa: Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. https://doi.org/10.48550/arXiv.2405.16648 chicago: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.16648. ieee: J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” arXiv. . ista: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, 10.48550/arXiv.2405.16648. mla: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, doi:10.48550/arXiv.2405.16648. short: J. Glas, ArXiv (n.d.). corr_author: '1' das_tickbox: '0' date_created: 2024-10-10T13:15:43Z date_published: 2024-05-26T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '26' department: - _id: TiBr doi: 10.48550/arXiv.2405.16648 external_id: arxiv: - '2405.16648' fulldoi: https://doi.org/10.48550/arXiv.2405.16648 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.16648 month: '05' oa: 1 oa_version: Preprint project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: arXiv publication_status: submitted related_material: record: - id: '19013' relation: later_version status: public - id: '18132' relation: dissertation_contains status: public researchdata_availability: no status: public supplementarymaterial: no title: Canonical singularities on moduli spaces of rational curves via the circle method 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: preprint user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- _id: '17144' abstract: - lang: eng text: "We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let \U0001D4AE ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set \U0001D4AE. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(\U0001D4AE), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms." acknowledgement: "This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I 02979-N35.\r\nSupported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher Fillmore, and Elizabeth Stephenson for early discussions and all members of the Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape team (Inria) for the atmosphere in which this research was conducted." alternative_title: - LIPIcs article_number: '69' article_processing_charge: No arxiv: 1 author: - first_name: Hana full_name: Kourimska, Hana id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E last_name: Kourimska orcid: 0000-0001-7841-0091 - first_name: André full_name: Lieutier, André last_name: Lieutier - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: 'Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.69' apa: 'Kourimska, H., Lieutier, A., & Wintraecken, M. (2024). The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.69' chicago: Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.69. ieee: H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69.' mla: Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” 40th International Symposium on Computational Geometry, vol. 293, 69, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.69. short: H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:46:39Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.69 ec_funded: 1 external_id: arxiv: - '2212.01118' file: - access_level: open_access checksum: b40ff456c19294adb5d9613fcfd751c6 content_type: application/pdf creator: dernst date_created: 2024-06-17T08:33:40Z date_updated: 2024-06-17T08:33:40Z file_id: '17150' file_name: 2024_LIPICS_Kourimska.pdf file_size: 1612558 relation: main_file success: 1 file_date_updated: 2024-06-17T08:33:40Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.69 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- _id: '17146' abstract: - lang: eng text: The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry. acknowledgement: "The first author is supported by the European Research Council (ERC), grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart for early discussions on the linked circles construction in three dimensions, and Gábor Tardos for helpful remarks and suggestions." alternative_title: - LIPIcs article_number: '53' article_processing_charge: No arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach citation: ama: 'Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.53' apa: 'Edelsbrunner, H., & Pach, J. (2024). Maximum Betti numbers of Čech complexes. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.53' chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.53. ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 53.' mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” 40th International Symposium on Computational Geometry, vol. 293, 53, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.53. short: H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' start_date: 2024-06-11 das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:48:01Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.53 ec_funded: 1 external_id: arxiv: - '2310.14801' file: - access_level: open_access checksum: 5442d44fb89d77477a87668d6e61aac9 content_type: application/pdf creator: dernst date_created: 2024-06-17T08:46:33Z date_updated: 2024-06-17T08:46:33Z file_id: '17152' file_name: 2024_LIPICS_Edelsbrunner.pdf file_size: 766562 relation: main_file success: 1 file_date_updated: 2024-06-17T08:46:33Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.53 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version 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 - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '20657' relation: later_version status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Maximum Betti numbers of Čech complexes 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- _id: '17145' abstract: - lang: eng text: Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes. acknowledgement: Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23. alternative_title: - LIPIcs article_number: '76' article_processing_charge: No arxiv: 1 author: - first_name: Günter full_name: Rote, Günter last_name: Rote - first_name: Moritz full_name: Rüber, Moritz last_name: Rüber - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: 'Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.76' apa: 'Rote, G., Rüber, M., & Saghafian, M. (2024). Grid peeling of parabolas. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.76' chicago: Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.76. ieee: G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76.' mla: Rote, Günter, et al. “Grid Peeling of Parabolas.” 40th International Symposium on Computational Geometry, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.76. short: G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' start_date: 2024-06-11 das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:47:18Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.76 external_id: arxiv: - '2402.15787' file: - access_level: open_access checksum: fbad1de06383a6b7e8a1cb3e8c7205ce content_type: application/pdf creator: dernst date_created: 2024-06-17T08:40:04Z date_updated: 2024-06-17T08:40:04Z file_id: '17151' file_name: 2024_LIPICS_Rote.pdf file_size: 1430896 relation: main_file success: 1 file_date_updated: 2024-06-17T08:40:04Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.76 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Grid peeling of parabolas 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- _id: '17891' abstract: - lang: eng text: "Abstract\r\nMethods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics." acknowledgement: We thank Anton Nikitenko for first observing that the Wrap complex can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej Draganov for correcting a critical mistake in one of our formulas in Section 2. article_number: '637' article_processing_charge: Yes article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Katharina full_name: Ölsböck, Katharina id: 4D4AA390-F248-11E8-B48F-1D18A9856A87 last_name: Ölsböck orcid: 0000-0002-4672-8297 - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0009-0009-9111-8429 citation: ama: Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions in information space. Entropy. 2024;26(8). doi:10.3390/e26080637 apa: Edelsbrunner, H., Ölsböck, K., & Wagner, H. (2024). Understanding higher-order interactions in information space. Entropy. MDPI. https://doi.org/10.3390/e26080637 chicago: Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding Higher-Order Interactions in Information Space.” Entropy. MDPI, 2024. https://doi.org/10.3390/e26080637. ieee: H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions in information space,” Entropy, vol. 26, no. 8. MDPI, 2024. ista: Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions in information space. Entropy. 26(8), 637. mla: Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information Space.” Entropy, vol. 26, no. 8, 637, MDPI, 2024, doi:10.3390/e26080637. short: H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024). das_tickbox: '1' dataavailabilitystatement: 'The software and data used for this study is available at: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/ (accessed on 19 July 2024).' date_created: 2024-09-08T22:01:11Z date_published: 2024-08-01T00:00:00Z date_updated: 2026-10-02T11:50:23Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.3390/e26080637 external_id: isi: - '001305543500001' pmid: - '39202107' file: - access_level: open_access checksum: 624a9e2c5b49d6c38b88b0f675467ba3 content_type: application/pdf creator: dernst date_created: 2024-09-09T09:01:12Z date_updated: 2024-09-09T09:01:12Z file_id: '17948' file_name: 2024_Entropy_Edelsbrunner.pdf file_size: 8025139 relation: main_file success: 1 file_date_updated: 2024-09-09T09:01:12Z fulldoi: https://doi.org/10.3390/e26080637 has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '8' language: - iso: eng month: '08' oa: 1 oa_version: Published Version pmid: 1 publication: Entropy publication_identifier: eissn: - 1099-4300 publication_status: published publisher: MDPI quality_controlled: '1' related_material: link: - relation: software url: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/ researchdata_availability: yes scopus_import: '1' status: public supplementarymaterial: yes title: Understanding higher-order interactions in information space 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 26 year: '2024' ... --- _id: '15012' abstract: - lang: eng text: We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs. acknowledgement: János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31. alternative_title: - LNCS article_processing_charge: No arxiv: 1 author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian - first_name: Patrick full_name: Schnider, Patrick last_name: Schnider citation: ama: 'Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14465. Springer Nature; 2024:339-346. doi:10.1007/978-3-031-49272-3_23' apa: 'Pach, J., Saghafian, M., & Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49272-3_23' chicago: Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In 31st International Symposium on Graph Drawing and Network Visualization, 14465:339–46. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49272-3_23. ieee: J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346. ista: 'Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.' mla: Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:10.1007/978-3-031-49272-3_23. short: J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346. conference: end_date: 2023-09-22 location: Isola delle Femmine, Palermo, Italy name: 'GD: Graph Drawing and Network Visualization' start_date: 2023-09-20 das_tickbox: '0' date_created: 2024-02-18T23:01:03Z date_published: 2024-01-01T00:00:00Z date_updated: 2026-10-02T11:50:59Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-031-49272-3_23 ec_funded: 1 external_id: arxiv: - '2306.13201' isi: - '001207939600023' fulldoi: https://doi.org/10.1007/978-3-031-49272-3_23 intvolume: ' 14465' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2306.13201 month: '01' oa: 1 oa_version: Preprint page: 339-346 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science publication: 31st International Symposium on Graph Drawing and Network Visualization publication_identifier: eisbn: - '9783031492723' eissn: - 1611-3349 isbn: - '9783031492716' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '21253' relation: later_version status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Decomposition of geometric graphs into star-forests type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 14465 year: '2024' ... --- _id: '17190' abstract: - lang: eng text: "For a locally finite set, \U0001D434⊆ℝ\U0001D451\r\n, the \U0001D458\r\nth Brillouin zone of \U0001D44E∈\U0001D434\r\n is the region of points \U0001D465∈ℝ\U0001D451\r\n for which ‖\U0001D465−\U0001D44E‖\r\n is the \U0001D458\r\nth smallest among the Euclidean distances between \U0001D465\r\n and the points in \U0001D434\r\n. If \U0001D434\r\n is a lattice, the \U0001D458\r\nth Brillouin zones of the points in \U0001D434\r\n are translates of each other, and together they tile space. Depending on the value of \U0001D458\r\n, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of the maximum volume of a chamber to zero for the integer lattice." acknowledgement: The second author is partially supported by the Alexander von Humboldt Foundation. The sixth author is supported by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF) grant I 02979-N35. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Garber, Alexey last_name: Garber - first_name: Mohadese full_name: Ghafaris, Mohadese last_name: Ghafaris - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Morteza full_name: Saghafiant, Morteza last_name: Saghafiant - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 2024;38(2):1784-1807. doi:10.1137/22M1489071 apa: Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., & Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/22M1489071 chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss, Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices and Their Perturbations.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/22M1489071. ieee: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken, “Brillouin zones of integer lattices and their perturbations,” SIAM Journal on Discrete Mathematics, vol. 38, no. 2. Society for Industrial and Applied Mathematics, pp. 1784–1807, 2024. ista: Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807. mla: Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their Perturbations.” SIAM Journal on Discrete Mathematics, vol. 38, no. 2, Society for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:10.1137/22M1489071. short: H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807. corr_author: '1' das_tickbox: '0' date_created: 2024-06-30T22:01:05Z date_published: 2024-06-07T00:00:00Z date_updated: 2026-10-02T11:49:10Z day: '07' department: - _id: HeEd doi: 10.1137/22M1489071 ec_funded: 1 external_id: arxiv: - '2204.01077' isi: - '001292728600001' fulldoi: https://doi.org/10.1137/22M1489071 intvolume: ' 38' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2204.01077 month: '06' oa: 1 oa_version: Preprint page: 1784-1807 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science publication: SIAM Journal on Discrete Mathematics publication_identifier: issn: - 0895-4801 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Brillouin zones of integer lattices and their perturbations type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 38 year: '2024' ... --- OA_place: publisher OA_type: gold _id: '18556' abstract: - lang: eng text: Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25. acknowledgement: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, "Discretization in Geometry and Dynamics", Austrian Science Fund (FWF), grant no. I 02979-N35. alternative_title: - LIPIcs article_number: '3' article_processing_charge: Yes arxiv: 1 author: - first_name: Sebastiano full_name: Cultrera di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera di Montesano orcid: 0000-0001-6249-0832 - first_name: Ondrej full_name: Draganov, Ondrej id: 2B23F01E-F248-11E8-B48F-1D18A9856A87 last_name: Draganov orcid: 0000-0003-0464-3823 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean MST-ratio for bi-colored lattices. In: 32nd International Symposium on Graph Drawing and Network Visualization. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.GD.2024.3' apa: 'Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (2024). The Euclidean MST-ratio for bi-colored lattices. In 32nd International Symposium on Graph Drawing and Network Visualization (Vol. 320). Vienna, Austria: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.GD.2024.3' chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In 32nd International Symposium on Graph Drawing and Network Visualization, Vol. 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.GD.2024.3. ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “The Euclidean MST-ratio for bi-colored lattices,” in 32nd International Symposium on Graph Drawing and Network Visualization, Vienna, Austria, 2024, vol. 320. ista: 'Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LIPIcs, vol. 320, 3.' mla: Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored Lattices.” 32nd International Symposium on Graph Drawing and Network Visualization, vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.GD.2024.3. short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-09-20 location: Vienna, Austria name: 'GD: Graph Drawing and Network Visualization' start_date: 2024-09-18 corr_author: '1' das_tickbox: '0' date_created: 2024-11-17T23:01:47Z date_published: 2024-10-28T00:00:00Z date_updated: 2026-10-02T11:52:23Z day: '28' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.GD.2024.3 ec_funded: 1 external_id: arxiv: - '2403.10204' isi: - '001540278400001' file: - access_level: open_access checksum: 5f9b35e115c3d375e99be78da9054cb4 content_type: application/pdf creator: dernst date_created: 2024-11-18T07:49:25Z date_updated: 2024-11-18T07:49:25Z file_id: '18560' file_name: 2024_LIPIcs_CultreradiMontesano.pdf file_size: 908541 relation: main_file success: 1 file_date_updated: 2024-11-18T07:49:25Z fulldoi: https://doi.org/10.4230/LIPIcs.GD.2024.3 has_accepted_license: '1' intvolume: ' 320' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: 32nd International Symposium on Graph Drawing and Network Visualization publication_identifier: isbn: - '9783959773430' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: The Euclidean MST-ratio for bi-colored lattices 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 320 year: '2024' ... --- _id: '18097' abstract: - lang: eng text: "In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape \U0001D4AE (either manifold or general set with positive reach) such that one can infer the homotopy of \U0001D4AE from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting." acknowledgement: "This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I02979-N35. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion." alternative_title: - LIPIcs article_number: '87' article_processing_charge: Yes author: - first_name: Dominique full_name: Attali, Dominique last_name: Attali - first_name: Hana full_name: Kourimska, Hana id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E last_name: Kourimska orcid: 0000-0001-7841-0091 - first_name: Christopher D full_name: Fillmore, Christopher D id: 35638A5C-AAC7-11E9-B0BF-5503E6697425 last_name: Fillmore - first_name: Ishika full_name: Ghosh, Ishika id: ee449b28-344d-11ef-a6d5-9ca430e9e9ff last_name: Ghosh - first_name: Andre full_name: Lieutier, Andre last_name: Lieutier - first_name: Elizabeth R full_name: Stephenson, Elizabeth R id: 2D04F932-F248-11E8-B48F-1D18A9856A87 last_name: Stephenson orcid: 0000-0002-6862-208X - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: 'Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality construction for homotopy inference (media exposition). In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.87' apa: 'Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson, E. R., & Wintraecken, M. (2024). The ultimate frontier: An optimality construction for homotopy inference (media exposition). In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.87' chicago: 'Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh, Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.87.' ieee: 'D. Attali et al., “The ultimate frontier: An optimality construction for homotopy inference (media exposition),” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293.' ista: 'Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. The ultimate frontier: An optimality construction for homotopy inference (media exposition). 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 87.' mla: 'Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” 40th International Symposium on Computational Geometry, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.87.' short: D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' start_date: 2024-06-11 corr_author: '1' das_tickbox: '0' date_created: 2024-09-19T10:29:48Z date_published: 2024-06-06T00:00:00Z date_updated: 2026-10-02T11:51:50Z day: '06' ddc: - '000' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.87 ec_funded: 1 file: - access_level: open_access checksum: 9355c2e60b8ec285e1b22719c5b73f1a content_type: application/pdf creator: dernst date_created: 2024-09-19T10:30:37Z date_updated: 2024-09-19T10:30:37Z file_id: '18098' file_name: 2024_LIPICs_Attali.pdf file_size: 3507177 relation: main_file success: 1 file_date_updated: 2024-09-19T10:30:37Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.87 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: yes title: 'The ultimate frontier: An optimality construction for homotopy inference (media exposition)' 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: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '13182' abstract: - lang: eng text: "We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram." acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Sebastiano full_name: Cultrera Di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera Di Montesano orcid: 0000-0001-6249-0832 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 2024;8:1101-1119. doi:10.1007/s41468-023-00126-9 apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2024). Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9 chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology. Springer Nature, 2024. https://doi.org/10.1007/s41468-023-00126-9. ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” Journal of Applied and Computational Topology, vol. 8. Springer Nature, pp. 1101–1119, 2024. ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119. mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:10.1007/s41468-023-00126-9. short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119. corr_author: '1' das_tickbox: '0' date_created: 2023-07-02T22:00:44Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-10-02T11:52:56Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s41468-023-00126-9 ec_funded: 1 external_id: pmid: - '39678706' file: - access_level: open_access checksum: d493df5088c222b88d9ca46b623ad0ee content_type: application/pdf creator: dernst date_created: 2025-01-09T07:39:41Z date_updated: 2025-01-09T07:39:41Z file_id: '18783' file_name: 2024_JourApplCompTopo_Biswas.pdf file_size: 476896 relation: main_file success: 1 file_date_updated: 2025-01-09T07:39:41Z fulldoi: https://doi.org/10.1007/s41468-023-00126-9 has_accepted_license: '1' intvolume: ' 8' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1101-1119 pmid: 1 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Persistent Homology, Algorithms and Stochastic Geometry - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '11660' relation: earlier_version status: public - id: '15094' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Geometric characterization of the persistence of 1D 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 8 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15380' abstract: - lang: eng text: The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements. acknowledgement: "The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Sebastiano full_name: Cultrera Di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera Di Montesano orcid: 0000-0001-6249-0832 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 2024;8:557-578. doi:10.1007/s41468-024-00173-w' apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-024-00173-w' chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Journal of Applied and Computational Topology. Springer Nature, 2024. https://doi.org/10.1007/s41468-024-00173-w.' ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Journal of Applied and Computational Topology, vol. 8. Springer Nature, pp. 557–578, 2024.' ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578.' mla: 'Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Journal of Applied and Computational Topology, vol. 8, Springer Nature, 2024, pp. 557–78, doi:10.1007/s41468-024-00173-w.' short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578. corr_author: '1' das_tickbox: '0' date_created: 2024-05-12T22:01:03Z date_published: 2024-09-01T00:00:00Z date_updated: 2026-10-02T11:55:12Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s41468-024-00173-w ec_funded: 1 external_id: pmid: - '39308789' file: - access_level: open_access checksum: 0ee15c1493a6413cf356ab2f32c81a9e content_type: application/pdf creator: dernst date_created: 2025-04-23T08:01:36Z date_updated: 2025-04-23T08:01:36Z file_id: '19612' file_name: 2024_JourApplCompTopo_BiswasRa.pdf file_size: 522831 relation: main_file success: 1 file_date_updated: 2025-04-23T08:01:36Z fulldoi: https://doi.org/10.1007/s41468-024-00173-w has_accepted_license: '1' intvolume: ' 8' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 557-578 pmid: 1 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '11658' relation: earlier_version status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'Depth in arrangements: Dehn–Sommerville–Euler relations with applications' 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 8 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15247' abstract: - lang: eng text: Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples. acknowledgement: We are grateful to Balázs Keszegh, and to the members of the Miklós Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib for pointing out several important mathematical typos. article_number: '105889' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Peter full_name: Frankl, Peter last_name: Frankl - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Dömötör full_name: Pálvölgyi, Dömötör last_name: Pálvölgyi citation: ama: Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 2024;206(8). doi:10.1016/j.jcta.2024.105889 apa: Frankl, P., Pach, J., & Pálvölgyi, D. (2024). Odd-sunflowers. Journal of Combinatorial Theory, Series A. Elsevier. https://doi.org/10.1016/j.jcta.2024.105889 chicago: Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” Journal of Combinatorial Theory, Series A. Elsevier, 2024. https://doi.org/10.1016/j.jcta.2024.105889. ieee: P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” Journal of Combinatorial Theory, Series A, vol. 206, no. 8. Elsevier, 2024. ista: Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889. mla: Frankl, Peter, et al. “Odd-Sunflowers.” Journal of Combinatorial Theory, Series A, vol. 206, no. 8, 105889, Elsevier, 2024, doi:10.1016/j.jcta.2024.105889. short: P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024). corr_author: '1' das_tickbox: '1' dataavailabilitystatement: No data was used for the research described in the article. date_created: 2024-03-31T22:01:11Z date_published: 2024-08-01T00:00:00Z date_updated: 2026-10-02T11:54:47Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1016/j.jcta.2024.105889 external_id: arxiv: - '2310.16701' isi: - '001217739200001' file: - access_level: open_access checksum: ffc29d65e712849f0d31009271e06a63 content_type: application/pdf creator: dernst date_created: 2025-01-09T08:37:20Z date_updated: 2025-01-09T08:37:20Z file_id: '18791' file_name: 2024_JourCombiTheoryA_Frankl.pdf file_size: 366029 relation: main_file success: 1 file_date_updated: 2025-01-09T08:37:20Z fulldoi: https://doi.org/10.1016/j.jcta.2024.105889 has_accepted_license: '1' intvolume: ' 206' isi: 1 issue: '8' language: - iso: eng month: '08' oa: 1 oa_version: Published Version publication: Journal of Combinatorial Theory, Series A publication_identifier: eissn: - 1096-0899 issn: - 0097-3165 publication_status: published publisher: Elsevier quality_controlled: '1' researchdata_availability: not applicable scopus_import: '1' status: public supplementarymaterial: yes title: Odd-sunflowers 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 206 year: '2024' ... --- OA_place: publisher _id: '18667' abstract: - lang: eng text: "Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability." acknowledgement: "I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 citation: ama: Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:10.15479/at:ista:18667 apa: Heiss, T. (2024). New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18667 chicago: Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18667. ieee: T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024. ista: Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria. mla: Heiss, Teresa. New Methods for Applying Topological Data Analysis to Materials Science. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18667. short: T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-12-17T16:17:55Z date_published: 2024-12-17T00:00:00Z date_updated: 2026-10-02T11:55:42Z day: '17' ddc: - '514' - '516' - '004' degree_awarded: PhD department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:18667 doi_confirm: '1' ec_funded: 1 file: - access_level: open_access checksum: 247bb057aed2fba1cd4711917aaa2d77 content_type: application/pdf creator: theiss date_created: 2024-12-19T10:24:46Z date_updated: 2024-12-19T10:24:46Z file_id: '18686' file_name: Teresa_Heiss_PhD_Thesis_final.pdf file_size: 7752253 relation: main_file success: 1 - access_level: closed checksum: 9648b45c07a008ee11a07f99856a139d content_type: application/zip creator: theiss date_created: 2024-12-19T10:24:50Z date_updated: 2024-12-19T10:24:50Z file_id: '18687' file_name: PhD_Thesis.zip file_size: 17197731 relation: source_file file_date_updated: 2024-12-19T10:24:50Z fulldoi: https://doi.org/10.15479/at:ista:18667 has_accepted_license: '1' keyword: - persistent homology - topological data analysis - periodic - crystalline materials - images - fingerprint language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: '111' project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication_identifier: isbn: - 978-3-99078-052-7 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10828' relation: part_of_dissertation status: public - id: '11440' relation: part_of_dissertation status: public - id: '9345' relation: part_of_dissertation status: public - id: '18673' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 supplementarymaterial: no title: New methods for applying topological data analysis to materials science 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: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- OA_place: publisher _id: '15094' abstract: - lang: eng text: "Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sebastiano full_name: Cultrera di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera di Montesano orcid: 0000-0001-6249-0832 citation: ama: Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:10.15479/at:ista:15094 apa: Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094 chicago: Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094. ieee: S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024. ista: Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. mla: Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094. short: S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-03-08T15:28:10Z date_published: 2024-03-08T00:00:00Z date_updated: 2026-10-02T11:57:31Z day: '08' ddc: - '514' - '500' - '516' degree_awarded: PhD department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:15094 doi_confirm: '1' ec_funded: 1 file: - access_level: open_access checksum: 1e468bfa42a7dcf04d89f4dadc621c87 content_type: application/pdf creator: scultrer date_created: 2024-03-14T08:55:07Z date_updated: 2024-03-14T08:55:07Z file_id: '15112' file_name: Thesis Sebastiano.pdf file_size: 4106872 relation: main_file success: 1 - access_level: closed checksum: bcbd213490f5a7e68855a092bbce93f1 content_type: application/zip creator: scultrer date_created: 2024-03-14T08:56:24Z date_updated: 2024-03-14T14:14:35Z file_id: '15113' file_name: Thesis (1).zip file_size: 4746234 relation: source_file file_date_updated: 2024-03-14T14:14:35Z fulldoi: https://doi.org/10.15479/at:ista:15094 has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '03' oa: 1 oa_version: Published Version page: '108' project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Persistent Homology, Algorithms and Stochastic Geometry - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '15090' relation: part_of_dissertation status: public - id: '11658' relation: part_of_dissertation status: public - id: '11660' relation: part_of_dissertation status: public - id: '13182' relation: part_of_dissertation status: public - id: '15091' relation: part_of_dissertation status: public - id: '15093' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 supplementarymaterial: no title: Persistence and Morse theory for discrete geometric structures 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ...