--- _id: '14888' abstract: - lang: eng text: 'A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.' acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].' alternative_title: - LNCS article_processing_charge: No author: - first_name: Phoebe full_name: De Nooijer, Phoebe last_name: De Nooijer - first_name: Soeren full_name: Terziadis, Soeren last_name: Terziadis - first_name: Alexandra full_name: Weinberger, Alexandra last_name: Weinberger - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tamara full_name: Mchedlidze, Tamara last_name: Mchedlidze - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2' apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49275-4_2' chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In 31st International Symposium on Graph Drawing and Network Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2. ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33. ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33.' mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2. short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33. conference: end_date: 2023-09-22 location: Isola delle Femmine, Palermo, Italy name: 'GD: Graph Drawing and Network Visualization' start_date: 2023-09-20 date_created: 2024-01-28T23:01:43Z date_published: 2024-01-06T00:00:00Z date_updated: 2024-01-29T09:45:06Z day: '06' department: - _id: UlWa - _id: HeEd doi: 10.1007/978-3-031-49275-4_2 external_id: arxiv: - '2202.12175' intvolume: ' 14466' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2202.12175 month: '01' oa: 1 oa_version: Preprint page: 18-33 publication: 31st International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - 1611-3349 isbn: - '9783031492747' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Removing popular faces in curve arrangements type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14466 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 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 date_created: 2024-02-18T23:01:03Z date_published: 2024-01-01T00:00:00Z date_updated: 2024-02-20T09:13:07Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-031-49272-3_23 ec_funded: 1 external_id: arxiv: - '2306.13201' intvolume: ' 14465' 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: The Wittgenstein Prize publication: 31st International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - '16113349' isbn: - '9783031492716' issn: - '03029743' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Decomposition of geometric graphs into star-forests type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14465 year: '2024' ... --- _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. date_created: 2024-03-08T15:28:10Z date_published: 2024-03-08T00:00:00Z date_updated: 2024-03-20T09:36:57Z day: '08' ddc: - '514' - '500' - '516' degree_awarded: PhD department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:15094 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 has_accepted_license: '1' language: - iso: eng 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: The Wittgenstein Prize - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics - _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: '11660' relation: part_of_dissertation status: public - id: '11658' relation: part_of_dissertation status: public - id: '13182' relation: part_of_dissertation status: public - id: '15090' relation: part_of_dissertation status: public - id: '15091' relation: part_of_dissertation status: public - id: '15093' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- _id: '15093' abstract: - lang: eng text: We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right. acknowledgement: The first and second authors are funded by the European Research Council under the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35. 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 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Lara full_name: Ost, Lara last_name: Ost citation: ama: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11' apa: 'Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M. H., & Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11' chicago: Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika H Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11. ieee: S. Cultrera di Montesano, H. Edelsbrunner, M. H. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria, VA, USA, 2024, pp. 243–295. ista: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorigthms, 243–295.' mla: Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11. short: S. Cultrera di Montesano, H. Edelsbrunner, M.H. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295. conference: end_date: 2024-01-10 location: Alexandria, VA, USA name: 'SODA: Symposium on Discrete Algorigthms' start_date: 2024-01-07 date_created: 2024-03-08T10:27:39Z date_published: 2024-01-04T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '04' department: - _id: HeEd - _id: MoHe doi: 10.1137/1.9781611977912.11 ec_funded: 1 editor: - first_name: David P. full_name: Woodruff, David P. last_name: Woodruff external_id: arxiv: - '2311.01115' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2311.01115 month: '01' oa: 1 oa_version: Preprint page: 243 - 295 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: The Wittgenstein Prize - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Wittgenstein Award - Monika Henzinger - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: 'P33775 ' name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) publication_identifier: eisbn: - '9781611977912' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '15094' relation: dissertation_contains status: public status: public title: Dynamically maintaining the persistent homology of time series type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- _id: '15091' abstract: - lang: eng text: "Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided." article_number: '2212.03128' 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 - first_name: Ondrej full_name: Draganov, Ondrej id: 2B23F01E-F248-11E8-B48F-1D18A9856A87 last_name: Draganov - 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. Chromatic alpha complexes. arXiv. apa: Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). Chromatic alpha complexes. arXiv. chicago: Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” ArXiv, n.d. ieee: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” arXiv. . ista: Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128. mla: Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” ArXiv, 2212.03128. short: S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.). date_created: 2024-03-08T10:13:59Z date_published: 2024-02-07T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '07' department: - _id: HeEd external_id: arxiv: - '2212.03128' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2212.03128 month: '02' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted related_material: record: - id: '15094' relation: dissertation_contains status: public status: public title: Chromatic alpha 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: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- _id: '13048' abstract: - lang: eng text: In this paper we introduce a pruning of the medial axis called the (λ,α)-medial axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff sense under weak assumptions. More formally we prove that if K and K′ are close in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is 1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲ dH(K,K′)1/2. These quantified stability results provide guarantees for practical computations of medial axes from approximations. Moreover, they provide key ingredients for studying the computability of the medial axis in the context of computable analysis. acknowledgement: "We are greatly indebted to Erin Chambers for posing a number of questions that eventually led to this paper. We would also like to thank the other organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted to Tatiana Ezubova for helping with the search for and translation of Russian literature. The second author thanks all members of the Edelsbrunner and Datashape groups for the atmosphere in which the research was conducted.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). 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) M-3073." article_processing_charge: No author: - 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: 'Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In: Proceedings of the 55th Annual ACM Symposium on Theory of Computing. Association for Computing Machinery; 2023:1768-1776. doi:10.1145/3564246.3585113' apa: 'Lieutier, A., & Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (pp. 1768–1776). Orlando, FL, United States: Association for Computing Machinery. https://doi.org/10.1145/3564246.3585113' chicago: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 1768–76. Association for Computing Machinery, 2023. https://doi.org/10.1145/3564246.3585113. ieee: A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets of the medial axis,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Orlando, FL, United States, 2023, pp. 1768–1776. ista: 'Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 1768–1776.' mla: Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–76, doi:10.1145/3564246.3585113. short: A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776. conference: end_date: 2023-06-23 location: Orlando, FL, United States name: 'STOC: Symposium on Theory of Computing' start_date: 2023-06-20 date_created: 2023-05-22T08:02:02Z date_published: 2023-06-02T00:00:00Z date_updated: 2023-05-22T08:15:19Z day: '02' department: - _id: HeEd doi: 10.1145/3564246.3585113 ec_funded: 1 external_id: arxiv: - '2303.04014' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2303.04014 month: '06' oa: 1 oa_version: Preprint page: 1768-1776 project: - _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: Proceedings of the 55th Annual ACM Symposium on Theory of Computing publication_identifier: isbn: - '9781450399135' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: Hausdorff and Gromov-Hausdorff stable subsets of the medial axis type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12086' abstract: - lang: eng text: We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets. 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. article_processing_charge: Yes (via OA deal) 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: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang citation: ama: Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6 apa: Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6 chicago: Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023. https://doi.org/10.1007/s00453-022-01027-6. ieee: H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp. 277–295, 2023. ista: Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295. mla: Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature, 2023, pp. 277–95, doi:10.1007/s00453-022-01027-6. short: H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295. date_created: 2022-09-11T22:01:57Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-06-27T12:53:43Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00453-022-01027-6 ec_funded: 1 external_id: isi: - '000846967100001' file: - access_level: open_access checksum: 71685ca5121f4c837f40c3f8eb50c915 content_type: application/pdf creator: dernst date_created: 2023-01-20T10:02:48Z date_updated: 2023-01-20T10:02:48Z file_id: '12322' file_name: 2023_Algorithmica_Edelsbrunner.pdf file_size: 911017 relation: main_file success: 1 file_date_updated: 2023-01-20T10:02:48Z has_accepted_license: '1' intvolume: ' 85' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 277-295 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: The Wittgenstein Prize - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Algorithmica publication_identifier: eissn: - 1432-0541 issn: - 0178-4617 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A simple algorithm for higher-order Delaunay mosaics and alpha shapes 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: 2EBD1598-F248-11E8-B48F-1D18A9856A87 volume: 85 year: '2023' ... --- _id: '12287' abstract: - lang: eng text: We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use. acknowledgement: "This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF)." article_processing_charge: No article_type: original author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: Ramsay full_name: Dyer, Ramsay last_name: Dyer - first_name: Arijit full_name: Ghosh, Arijit last_name: Ghosh - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 2023;69:156-191. doi:10.1007/s00454-022-00431-7 apa: Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local criteria for triangulating general manifolds. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7 chicago: Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7. ieee: J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” Discrete & Computational Geometry, vol. 69. Springer Nature, pp. 156–191, 2023. ista: Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191. mla: Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry, vol. 69, Springer Nature, 2023, pp. 156–91, doi:10.1007/s00454-022-00431-7. short: J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational Geometry 69 (2023) 156–191. date_created: 2023-01-16T10:04:06Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-08-01T12:47:32Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-022-00431-7 ec_funded: 1 external_id: isi: - '000862193600001' file: - access_level: open_access checksum: 46352e0ee71e460848f88685ca852681 content_type: application/pdf creator: dernst date_created: 2023-02-02T11:01:10Z date_updated: 2023-02-02T11:01:10Z file_id: '12488' file_name: 2023_DiscreteCompGeometry_Boissonnat.pdf file_size: 582850 relation: main_file success: 1 file_date_updated: 2023-02-02T11:01:10Z has_accepted_license: '1' intvolume: ' 69' isi: 1 keyword: - Computational Theory and Mathematics - Discrete Mathematics and Combinatorics - Geometry and Topology - Theoretical Computer Science language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 156-191 project: - _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: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Local criteria for triangulating general 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 69 year: '2023' ... --- _id: '12548' abstract: - lang: eng text: The limited exchange between human communities is a key factor in preventing the spread of COVID-19. This paper introduces a digital framework that combines an integration of real mobility data at the country scale with a series of modeling techniques and visual capabilities that highlight mobility patterns before and during the pandemic. The findings not only significantly exhibit mobility trends and different degrees of similarities at regional and local levels but also provide potential insight into the emergence of a pandemic on human behavior patterns and their likely socio-economic impacts. article_number: '00093' article_processing_charge: No author: - first_name: Mohammad full_name: Forghani, Mohammad last_name: Forghani - first_name: Christophe full_name: Claramunt, Christophe last_name: Claramunt - first_name: Farid full_name: Karimipour, Farid id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425 last_name: Karimipour orcid: 0000-0001-6746-4174 - first_name: Georg full_name: Heiler, Georg last_name: Heiler citation: ama: 'Forghani M, Claramunt C, Karimipour F, Heiler G. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In: 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers; 2023. doi:10.1109/icdmw58026.2022.00093' apa: 'Forghani, M., Claramunt, C., Karimipour, F., & Heiler, G. (2023). Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In 2022 IEEE International Conference on Data Mining Workshops. Orlando, FL, United States: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/icdmw58026.2022.00093' chicago: Forghani, Mohammad, Christophe Claramunt, Farid Karimipour, and Georg Heiler. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers, 2023. https://doi.org/10.1109/icdmw58026.2022.00093. ieee: M. Forghani, C. Claramunt, F. Karimipour, and G. Heiler, “Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic,” in 2022 IEEE International Conference on Data Mining Workshops, Orlando, FL, United States, 2023. ista: 'Forghani M, Claramunt C, Karimipour F, Heiler G. 2023. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. 2022 IEEE International Conference on Data Mining Workshops. ICDMW: Conference on Data Mining Workshops, 00093.' mla: Forghani, Mohammad, et al. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2022 IEEE International Conference on Data Mining Workshops, 00093, Institute of Electrical and Electronics Engineers, 2023, doi:10.1109/icdmw58026.2022.00093. short: M. Forghani, C. Claramunt, F. Karimipour, G. Heiler, in:, 2022 IEEE International Conference on Data Mining Workshops, Institute of Electrical and Electronics Engineers, 2023. conference: end_date: 2022-12-01 location: Orlando, FL, United States name: 'ICDMW: Conference on Data Mining Workshops' start_date: 2022-11-28 date_created: 2023-02-14T07:56:21Z date_published: 2023-02-08T00:00:00Z date_updated: 2023-08-01T13:15:48Z day: '08' ddc: - '600' department: - _id: HeEd doi: 10.1109/icdmw58026.2022.00093 external_id: isi: - '000971492200145' file: - access_level: open_access checksum: c253bee25e6dfe484f96662daa119cb6 content_type: application/pdf creator: fkarimip date_created: 2023-02-14T07:58:26Z date_updated: 2023-02-14T07:58:26Z file_id: '12549' file_name: Visual Analysis_Mobility_COVID19 - SocDM2022.pdf file_size: 1183339 relation: main_file success: 1 file_date_updated: 2023-02-14T07:58:26Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Submitted Version publication: 2022 IEEE International Conference on Data Mining Workshops publication_identifier: eisbn: - '9798350346091' eissn: - 2375-9259 publication_status: published publisher: Institute of Electrical and Electronics Engineers quality_controlled: '1' status: public title: Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2023' ... --- _id: '12544' abstract: - lang: eng text: Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software. acknowledgement: "P.K. acknowledges support from the University of California Multicampus Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant No.1760485). H.E. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, 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.\r\nOpen Access is funded by the Austrian Science Fund (FWF)." article_processing_charge: No article_type: original author: - first_name: Patrice full_name: Koehl, Patrice last_name: Koehl - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 2023;63(3):973-985. doi:10.1021/acs.jcim.2c01346 apa: Koehl, P., Akopyan, A., & Edelsbrunner, H. (2023). Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. American Chemical Society. https://doi.org/10.1021/acs.jcim.2c01346 chicago: Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling. American Chemical Society, 2023. https://doi.org/10.1021/acs.jcim.2c01346. ieee: P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives,” Journal of Chemical Information and Modeling, vol. 63, no. 3. American Chemical Society, pp. 973–985, 2023. ista: Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 63(3), 973–985. mla: Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85, doi:10.1021/acs.jcim.2c01346. short: P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985. date_created: 2023-02-12T23:00:59Z date_published: 2023-02-13T00:00:00Z date_updated: 2023-08-16T12:22:07Z day: '13' ddc: - '510' - '540' department: - _id: HeEd doi: 10.1021/acs.jcim.2c01346 ec_funded: 1 external_id: isi: - '000920370700001' pmid: - '36638318' file: - access_level: open_access checksum: 7d20562269edff1e31b9d6019d4983b0 content_type: application/pdf creator: dernst date_created: 2023-08-16T12:21:13Z date_updated: 2023-08-16T12:21:13Z file_id: '14070' file_name: 2023_JCIM_Koehl.pdf file_size: 8069223 relation: main_file success: 1 file_date_updated: 2023-08-16T12:21:13Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '3' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 973-985 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: The Wittgenstein Prize - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Journal of Chemical Information and Modeling publication_identifier: eissn: - 1549-960X issn: - 1549-9596 publication_status: published publisher: American Chemical Society quality_controlled: '1' scopus_import: '1' status: public title: Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 63 year: '2023' ... --- _id: '12764' abstract: - lang: eng text: We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique. acknowledgement: Open access funding provided by the Austrian Science Fund (FWF). This research was supported by the FWF grant, Project number I4245-N35, and by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Hana full_name: Kourimska, Hana id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E last_name: Kourimska orcid: 0000-0001-7841-0091 citation: ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2 apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2 chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2. ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023. ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153. mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2. short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153. date_created: 2023-03-26T22:01:09Z date_published: 2023-07-01T00:00:00Z date_updated: 2023-10-04T11:46:48Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-023-00484-2 external_id: isi: - '000948148000001' file: - access_level: open_access checksum: cdbf90ba4a7ddcb190d37b9e9d4cb9d3 content_type: application/pdf creator: dernst date_created: 2023-10-04T11:46:24Z date_updated: 2023-10-04T11:46:24Z file_id: '14396' file_name: 2023_DiscreteGeometry_Kourimska.pdf file_size: 1026683 relation: main_file success: 1 file_date_updated: 2023-10-04T11:46:24Z has_accepted_license: '1' intvolume: ' 70' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 123-153 project: - _id: 26AD5D90-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I04245 name: Algebraic Footprints of Geometric Features in Homology publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Discrete yamabe problem for polyhedral surfaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2023' ... --- _id: '12709' abstract: - lang: eng text: Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. acknowledgement: We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: René full_name: Corbet, René last_name: Corbet - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Michael full_name: Lesnick, Michael last_name: Lesnick - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 citation: ama: Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8 apa: Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the multicover bifiltration. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00476-8 chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8. ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 376–405, 2023. ista: Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405. mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8. short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405. date_created: 2023-03-05T23:01:06Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-04T12:03:40Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s00454-022-00476-8 external_id: arxiv: - '2103.07823' isi: - '000936496800001' file: - access_level: open_access checksum: 71ce7e59f7ee4620acc704fecca620c2 content_type: application/pdf creator: cchlebak date_created: 2023-03-07T14:40:14Z date_updated: 2023-03-07T14:40:14Z file_id: '12715' file_name: 2023_DisCompGeo_Corbet.pdf file_size: 1359323 relation: main_file success: 1 file_date_updated: 2023-03-07T14:40:14Z has_accepted_license: '1' intvolume: ' 70' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 376-405 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '9605' relation: earlier_version status: public scopus_import: '1' status: public title: Computing the multicover bifiltration tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2023' ... --- _id: '12763' abstract: - lang: eng text: 'Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert showed that sets of positive reach in Euclidean space and Riemannian manifolds are very similar. In this paper we introduce a slight variant of Kleinjohann’s and Bangert’s extension and quantify the similarity between sets of positive reach in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we bound the local feature size (a local version of the reach) of its lifting to the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated by the importance of the reach and local feature size to manifold learning, topological inference, and triangulating manifolds and the fact that intrinsic approaches circumvent the curse of dimensionality.' acknowledgement: "We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu for encouragement. We further acknowledge the anonymous reviewers whose comments helped improve the exposition.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). The first author is further supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. The second author is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073." article_processing_charge: No article_type: original author: - first_name: Jean Daniel full_name: Boissonnat, Jean Daniel last_name: Boissonnat - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x apa: Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x chicago: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x. ieee: J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,” Journal of Applied and Computational Topology, vol. 7. Springer Nature, pp. 619–641, 2023. ista: Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641. mla: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x. short: J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641. date_created: 2023-03-26T22:01:08Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-04T12:07:18Z day: '01' department: - _id: HeEd doi: 10.1007/s41468-023-00116-x ec_funded: 1 intvolume: ' 7' language: - iso: eng main_file_link: - open_access: '1' url: https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1 month: '09' oa: 1 oa_version: Submitted Version page: 619-641 project: - _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: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The reach of subsets of manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7 year: '2023' ... --- _id: '12960' abstract: - lang: eng text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M^ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. " acknowledgement: The authors have received funding from the European Research Council under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations of Geometric Un-derstanding in Higher Dimensions). The first author was supported by the French government,through the 3IA C\^ote d'Azur Investments in the Future project managed by the National ResearchAgency (ANR) with the reference ANR-19-P3IA-0002. The third author was supported by the Eu-ropean Union's Horizon 2020 research and innovation programme under the Marie Sk\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science Fund) grant M 3073. article_processing_charge: No article_type: original author: - first_name: Jean Daniel full_name: Boissonnat, Jean Daniel last_name: Boissonnat - first_name: Siargey full_name: Kachanovich, Siargey last_name: Kachanovich - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918 apa: Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918 chicago: Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918. ieee: J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023. ista: Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 52(2), 452–486. mla: Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:10.1137/21M1412918. short: J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486. date_created: 2023-05-14T22:01:00Z date_published: 2023-04-30T00:00:00Z date_updated: 2023-10-10T07:34:35Z day: '30' department: - _id: HeEd doi: 10.1137/21M1412918 ec_funded: 1 external_id: isi: - '001013183000012' intvolume: ' 52' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1 month: '04' oa: 1 oa_version: Submitted Version page: 452-486 project: - _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: SIAM Journal on Computing publication_identifier: eissn: - 1095-7111 issn: - 0097-5397 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '9441' relation: earlier_version status: public scopus_import: '1' status: public title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 52 year: '2023' ... --- _id: '13134' abstract: - lang: eng text: We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line. acknowledgement: The first author has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. article_number: '109693' article_processing_charge: No article_type: original author: - first_name: Lidija full_name: Čomić, Lidija last_name: Čomić - first_name: Gaëlle full_name: Largeteau-Skapin, Gaëlle last_name: Largeteau-Skapin - first_name: Rita full_name: Zrour, Rita last_name: Zrour - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Eric full_name: Andres, Eric last_name: Andres citation: ama: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10). doi:10.1016/j.patcog.2023.109693 apa: Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. Elsevier. https://doi.org/10.1016/j.patcog.2023.109693 chicago: Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693. ieee: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” Pattern Recognition, vol. 142, no. 10. Elsevier, 2023. ista: Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693. mla: Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693. short: L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023). date_created: 2023-06-18T22:00:45Z date_published: 2023-10-01T00:00:00Z date_updated: 2023-10-10T07:37:16Z day: '01' department: - _id: HeEd doi: 10.1016/j.patcog.2023.109693 external_id: isi: - '001013526000001' intvolume: ' 142' isi: 1 issue: '10' language: - iso: eng month: '10' oa_version: None project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics publication: Pattern Recognition publication_identifier: issn: - 0031-3203 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Discrete analytical objects in the body-centered cubic grid type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 142 year: '2023' ... --- _id: '14557' abstract: - lang: eng text: Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem. acknowledgement: "The first and second named authors are members of GNSAGA – INdAM.\r\nThe third named author was supported by the FWF Grant, Project number I4245–N35" article_processing_charge: No article_type: original author: - first_name: D. full_name: Dikranjan, D. last_name: Dikranjan - first_name: A. full_name: Giordano Bruno, A. last_name: Giordano Bruno - first_name: Nicolò full_name: Zava, Nicolò id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad last_name: Zava orcid: 0000-0001-8686-1888 citation: ama: Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221. doi:10.2989/16073606.2023.2247731 apa: Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731 chicago: Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor & Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731. ieee: D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no. S1. Taylor & Francis, pp. 191–221, 2023. ista: Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221. mla: Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor & Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731. short: D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221. date_created: 2023-11-19T23:00:55Z date_published: 2023-11-01T00:00:00Z date_updated: 2023-11-20T09:24:48Z day: '01' department: - _id: HeEd doi: 10.2989/16073606.2023.2247731 intvolume: ' 46' issue: S1 language: - iso: eng month: '11' oa_version: None page: 191-221 project: - _id: 26AD5D90-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I04245 name: Algebraic Footprints of Geometric Features in Homology publication: Quaestiones Mathematicae publication_identifier: eissn: - 1727-933X issn: - 1607-3606 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Epimorphisms and closure operators of categories of semilattices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 46 year: '2023' ... --- _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 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. 2023. doi:10.1007/s00454-023-00566-1 apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2023). 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, 2023. 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. Springer Nature, 2023. ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00566-1. short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023). date_created: 2023-09-17T22:01:10Z date_published: 2023-09-07T00:00:00Z date_updated: 2023-12-13T12:25:06Z day: '07' department: - _id: HeEd doi: 10.1007/s00454-023-00566-1 ec_funded: 1 external_id: arxiv: - '2204.01076' isi: - '001060727600004' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00454-023-00566-1 month: '09' 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: The Wittgenstein Prize - _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: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On angles in higher order Brillouin tessellations and related tilings in the plane type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14464' abstract: - lang: eng text: 'Given a triangle Δ, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ, every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ.' article_processing_charge: No article_type: original author: - first_name: Áron full_name: Ambrus, Áron last_name: Ambrus - first_name: Mónika full_name: Csikós, Mónika last_name: Csikós - first_name: Gergely full_name: Kiss, Gergely last_name: Kiss - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Gábor full_name: Somlai, Gábor last_name: Somlai citation: ama: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 2023;34(7):737-760. doi:10.1142/S012905412342008X apa: Ambrus, Á., Csikós, M., Kiss, G., Pach, J., & Somlai, G. (2023). Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. World Scientific Publishing. https://doi.org/10.1142/S012905412342008X chicago: Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science. World Scientific Publishing, 2023. https://doi.org/10.1142/S012905412342008X. ieee: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and enclosing isosceles triangles,” International Journal of Foundations of Computer Science, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023. ista: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 34(7), 737–760. mla: Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science, vol. 34, no. 7, World Scientific Publishing, 2023, pp. 737–60, doi:10.1142/S012905412342008X. short: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal of Foundations of Computer Science 34 (2023) 737–760. date_created: 2023-10-29T23:01:18Z date_published: 2023-10-05T00:00:00Z date_updated: 2023-12-13T13:04:55Z day: '05' department: - _id: HeEd doi: 10.1142/S012905412342008X external_id: arxiv: - '2205.11637' isi: - '001080874400001' intvolume: ' 34' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2205.11637 month: '10' oa: 1 oa_version: Preprint page: 737-760 publication: International Journal of Foundations of Computer Science publication_identifier: eissn: - 1793-6373 issn: - 0129-0541 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Optimal embedded and enclosing isosceles triangles type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 34 year: '2023' ... --- _id: '12833' abstract: - lang: eng text: 'The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.' acknowledgement: "This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n" article_number: '9' article_processing_charge: No article_type: original author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383 apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383 chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383. ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023. ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9. mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383. short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023). date_created: 2023-04-16T22:01:08Z date_published: 2023-01-18T00:00:00Z date_updated: 2024-01-04T12:42:09Z day: '18' ddc: - '000' department: - _id: KrCh - _id: HeEd - _id: UlWa doi: 10.46298/DMTCS.8383 external_id: arxiv: - '1903.06981' file: - access_level: open_access checksum: 439102ea4f6e2aeefd7107dfb9ccf532 content_type: application/pdf creator: dernst date_created: 2023-04-17T08:10:28Z date_updated: 2023-04-17T08:10:28Z file_id: '12844' file_name: 2022_DMTCS_Biniaz.pdf file_size: 2072197 relation: main_file success: 1 file_date_updated: 2023-04-17T08:10:28Z has_accepted_license: '1' intvolume: ' 24' issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Discrete Mathematics and Theoretical Computer Science publication_identifier: eissn: - 1365-8050 issn: - 1462-7264 publication_status: published publisher: EPI Sciences quality_controlled: '1' related_material: record: - id: '7950' relation: earlier_version status: public scopus_import: '1' status: public title: Token swapping on trees 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '14739' abstract: - lang: eng text: Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods. acknowledgement: "The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions." article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Dashti full_name: Ali, Dashti last_name: Ali - first_name: Aras full_name: Asaad, Aras last_name: Asaad - first_name: Maria-Jose full_name: Jimenez, Maria-Jose last_name: Jimenez - first_name: Vidit full_name: Nanda, Vidit last_name: Nanda - first_name: Eduardo full_name: Paluzo-Hidalgo, Eduardo last_name: Paluzo-Hidalgo - first_name: Manuel full_name: Soriano Trigueros, Manuel id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8 last_name: Soriano Trigueros orcid: 0000-0003-2449-1433 citation: ama: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391 apa: Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391 chicago: Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391. ieee: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023. ista: Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080. mla: Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391. short: D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080. date_created: 2024-01-08T09:59:46Z date_published: 2023-12-01T00:00:00Z date_updated: 2024-01-08T10:11:46Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1109/tpami.2023.3308391 file: - access_level: open_access checksum: 465c28ef0b151b4b1fb47977ed5581ab content_type: application/pdf creator: dernst date_created: 2024-01-08T10:09:14Z date_updated: 2024-01-08T10:09:14Z file_id: '14740' file_name: 2023_IEEEToP_Ali.pdf file_size: 2370988 relation: main_file success: 1 file_date_updated: 2024-01-08T10:09:14Z has_accepted_license: '1' intvolume: ' 45' issue: '12' keyword: - Applied Mathematics - Artificial Intelligence - Computational Theory and Mathematics - Computer Vision and Pattern Recognition - Software language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 14069-14080 publication: IEEE Transactions on Pattern Analysis and Machine Intelligence publication_identifier: eissn: - 1939-3539 issn: - 0162-8828 publication_status: published publisher: IEEE quality_controlled: '1' status: public title: A survey of vectorization methods in topological data analysis tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2023' ... --- _id: '13165' abstract: - lang: eng text: "A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph.\r\nAs an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph.\r\nAs another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small." article_number: '105776' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Lixing full_name: Fang, Lixing last_name: Fang - first_name: Hao full_name: Huang, Hao last_name: Huang - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Gábor full_name: Tardos, Gábor last_name: Tardos - first_name: Junchi full_name: Zuo, Junchi last_name: Zuo citation: ama: Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10). doi:10.1016/j.jcta.2023.105776 apa: Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776 chicago: Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776. ieee: L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol. 199, no. 10. Elsevier, 2023. ista: Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776. mla: Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier, 2023, doi:10.1016/j.jcta.2023.105776. short: L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023). date_created: 2023-06-25T22:00:45Z date_published: 2023-10-01T00:00:00Z date_updated: 2024-01-30T12:03:51Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1016/j.jcta.2023.105776 external_id: arxiv: - '2206.13592' file: - access_level: open_access checksum: 9eebc213b4182a66063a99083ff5bd04 content_type: application/pdf creator: dernst date_created: 2024-01-30T12:03:10Z date_updated: 2024-01-30T12:03:10Z file_id: '14902' file_name: 2023_JourCombinatiorialTheory_Fang.pdf file_size: 352555 relation: main_file success: 1 file_date_updated: 2024-01-30T12:03:10Z has_accepted_license: '1' intvolume: ' 199' issue: '10' language: - iso: eng month: '10' 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' scopus_import: '1' status: public title: Successive vertex orderings of fully regular graphs 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: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 199 year: '2023' ... --- _id: '14362' abstract: - lang: eng text: "Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy." article_number: '114129' article_processing_charge: No article_type: original author: - first_name: Ilaria full_name: Castellano, Ilaria last_name: Castellano - first_name: Anna full_name: Giordano Bruno, Anna last_name: Giordano Bruno - first_name: Nicolò full_name: Zava, Nicolò id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad last_name: Zava orcid: 0000-0001-8686-1888 citation: ama: Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129 apa: Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2023.114129 chicago: Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science. Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129. ieee: I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” Theoretical Computer Science, vol. 977. Elsevier, 2023. ista: Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129. mla: Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier, 2023, doi:10.1016/j.tcs.2023.114129. short: I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023). date_created: 2023-09-24T22:01:11Z date_published: 2023-10-25T00:00:00Z date_updated: 2024-01-30T13:22:04Z day: '25' department: - _id: HeEd doi: 10.1016/j.tcs.2023.114129 external_id: arxiv: - '2212.08424' isi: - '001076934000001' intvolume: ' 977' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: 'https://doi.org/10.48550/arXiv.2212.08424 ' month: '10' oa: 1 oa_version: Preprint publication: Theoretical Computer Science publication_identifier: issn: - 0304-3975 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Weakly weighted generalised quasi-metric spaces and semilattices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 977 year: '2023' ... --- _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. 2023. doi:10.1007/s41468-023-00126-9 apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2023). 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, 2023. 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. Springer Nature, 2023. ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. mla: Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology, Springer Nature, 2023, doi:10.1007/s41468-023-00126-9. short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023). date_created: 2023-07-02T22:00:44Z date_published: 2023-06-17T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '17' ddc: - '000' department: - _id: HeEd doi: 10.1007/s41468-023-00126-9 ec_funded: 1 file: - access_level: open_access checksum: 697249d5d1c61dea4410b9f021b70fce content_type: application/pdf creator: alisjak date_created: 2023-07-03T09:41:05Z date_updated: 2023-07-03T09:41:05Z file_id: '13185' file_name: 2023_Journal of Applied and Computational Topology_Biswas.pdf file_size: 487355 relation: main_file success: 1 file_date_updated: 2023-07-03T09:41:05Z has_accepted_license: '1' 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: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '15094' relation: dissertation_contains status: public scopus_import: '1' status: public 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14226' abstract: - lang: eng text: "We introduce the notion of a Faustian interchange in a 1-parameter family of smooth\r\nfunctions to generalize the medial axis to critical points of index larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating such\r\ngeneralized medial axes." alternative_title: - ISTA Master's Thesis article_processing_charge: No author: - first_name: Elizabeth R full_name: Stephenson, Elizabeth R id: 2D04F932-F248-11E8-B48F-1D18A9856A87 last_name: Stephenson orcid: 0000-0002-6862-208X citation: ama: Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226 apa: Stephenson, E. R. (2023). Generalizing medial axes with homology switches. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226 chicago: Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226. ieee: E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023. ista: Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute of Science and Technology Austria. mla: Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226. short: E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute of Science and Technology Austria, 2023. date_created: 2023-08-24T13:01:18Z date_published: 2023-08-24T00:00:00Z date_updated: 2024-02-26T23:30:04Z day: '24' ddc: - '500' degree_awarded: MS department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:14226 file: - access_level: closed checksum: 453caf851d75c3478c10ed09bd242a91 content_type: application/x-zip-compressed creator: cchlebak date_created: 2023-08-24T13:02:49Z date_updated: 2024-02-26T23:30:03Z embargo_to: open_access file_id: '14227' file_name: documents-export-2023-08-24.zip file_size: 15501411 relation: source_file - access_level: open_access checksum: 7349d29963d6695e555e171748648d9a content_type: application/pdf creator: cchlebak date_created: 2023-08-24T13:03:42Z date_updated: 2024-02-26T23:30:03Z embargo: 2024-02-25 file_id: '14228' file_name: thesis_pdf_a.pdf file_size: 6854783 relation: main_file file_date_updated: 2024-02-26T23:30:03Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: '43' publication_identifier: issn: - 2791-4585 publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Generalizing medial axes with homology switches type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '11428' abstract: - lang: eng text: The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible. acknowledgement: 'Partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics” and the European Research Council (ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported in part by the National Science Foundation through grants DBI-1759807, CCF-1907612, and CCF-2106672. 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) M-3073 Acknowledgements We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing code to generate the examples.' article_processing_charge: No author: - first_name: Erin full_name: Chambers, Erin last_name: Chambers - first_name: Christopher D full_name: Fillmore, Christopher D id: 35638A5C-AAC7-11E9-B0BF-5503E6697425 last_name: Fillmore - 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: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66' apa: 'Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber (Eds.), 38th International Symposium on Computational Geometry (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2022.66' chicago: 'Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.' ieee: 'E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in 38th International Symposium on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.' ista: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary tale: Burning the medial axis is unstable. 38th International Symposium on Computational Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.' mla: 'Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.' short: E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9. conference: end_date: 2022-06-10 location: Berlin, Germany name: 'SoCG: Symposium on Computational Geometry' start_date: 2022-06-07 date_created: 2022-06-01T14:18:04Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-02-21T09:50:52Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2022.66 ec_funded: 1 editor: - first_name: Xavier full_name: Goaoc, Xavier last_name: Goaoc - first_name: Michael full_name: Kerber, Michael last_name: Kerber file: - access_level: open_access checksum: b25ce40fade4ebc0bcaae176db4f5f1f content_type: application/pdf creator: dernst date_created: 2022-06-07T07:58:30Z date_updated: 2022-06-07T07:58:30Z file_id: '11437' file_name: 2022_LIPICs_Chambers.pdf file_size: 17580705 relation: main_file success: 1 file_date_updated: 2022-06-07T07:58:30Z has_accepted_license: '1' intvolume: ' 224' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 66:1-66:9 project: - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 38th International Symposium on Computational Geometry publication_identifier: isbn: - 978-3-95977-227-3 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' series_title: LIPIcs status: public title: 'A cautionary tale: Burning the medial axis is unstable' 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 224 year: '2022' ... --- _id: '11429' abstract: - lang: eng text: "This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. \ The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks." alternative_title: - LNCS article_processing_charge: No citation: ama: 'Karimipour F, Storandt S, eds. Web and Wireless Geographical Information Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2' apa: 'Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2' chicago: 'Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2.' ieee: 'F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.' ista: 'Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.' mla: Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2. short: F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022. date_created: 2022-06-02T05:40:53Z date_published: 2022-05-01T00:00:00Z date_updated: 2022-06-02T05:56:22Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-031-06245-2 edition: '1' editor: - first_name: Farid full_name: Karimipour, Farid id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425 last_name: Karimipour orcid: 0000-0001-6746-4174 - first_name: Sabine full_name: Storandt, Sabine last_name: Storandt intvolume: ' 13238' language: - iso: eng month: '05' oa_version: None page: '153' place: Cham publication_identifier: eisbn: - '9783031062452' eissn: - 1611-3349 isbn: - '9783031062445' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Web and Wireless Geographical Information Systems type: book_editor user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 13238 year: '2022' ... --- _id: '11440' abstract: - lang: eng text: To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation. acknowledgement: This project started during the Women in Computational Topology workshop held in Canberra in July of 2019. All authors are very grateful for its organisation and the financial support for the workshop from the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics. AG is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860. VR was supported by Australian Research Council Future Fellowship FT140100604 during the early stages of this project. alternative_title: - Association for Women in Mathematics Series article_processing_charge: No author: - first_name: Bea full_name: Bleile, Bea last_name: Bleile - first_name: Adélie full_name: Garin, Adélie last_name: Garin - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Kelly full_name: Maggs, Kelly last_name: Maggs - first_name: Vanessa full_name: Robins, Vanessa last_name: Robins citation: ama: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:10.1007/978-3-030-95519-9_1' apa: 'Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1' chicago: 'Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In Research in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.' ieee: 'B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in Research in Computational Topology 2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.' ista: 'Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology of dual digital image constructions. In: Research in Computational Topology 2. Association for Women in Mathematics Series, vol. 30, 1–26.' mla: Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” Research in Computational Topology 2, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1. short: B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26. date_created: 2022-06-07T08:21:11Z date_published: 2022-01-27T00:00:00Z date_updated: 2022-06-07T08:32:42Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-030-95519-9_1 ec_funded: 1 edition: '1' editor: - first_name: Ellen full_name: Gasparovic, Ellen last_name: Gasparovic - first_name: Vanessa full_name: Robins, Vanessa last_name: Robins - first_name: Katharine full_name: Turner, Katharine last_name: Turner external_id: arxiv: - '2102.11397' intvolume: ' 30' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2102.11397' month: '01' oa: 1 oa_version: Preprint page: 1-26 place: Cham project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication: Research in Computational Topology 2 publication_identifier: eisbn: - '9783030955199' isbn: - '9783030955182' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: AWMS status: public title: The persistent homology of dual digital image constructions type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2022' ... --- _id: '12307' abstract: - lang: eng text: Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences. article_processing_charge: No article_type: original author: - first_name: Barbara A. full_name: Shipman, Barbara A. last_name: Shipman - first_name: Elizabeth R full_name: Stephenson, Elizabeth R id: 2D04F932-F248-11E8-B48F-1D18A9856A87 last_name: Stephenson orcid: 0000-0002-6862-208X citation: ama: Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750 apa: Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750 chicago: Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750. ieee: B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022. ista: Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609. mla: Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750. short: B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609. date_created: 2023-01-16T10:07:21Z date_published: 2022-05-28T00:00:00Z date_updated: 2023-01-30T13:02:30Z day: '28' department: - _id: HeEd - _id: GradSch doi: 10.1080/10511970.2021.1872750 intvolume: ' 32' issue: '5' keyword: - Education - General Mathematics language: - iso: eng month: '05' oa_version: None page: 593-609 publication: PRIMUS publication_identifier: eissn: - 1935-4053 issn: - 1051-1970 publication_status: published publisher: Taylor & Francis quality_controlled: '1' scopus_import: '1' status: public title: Tangible topology through the lens of limits type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 32 year: '2022' ... --- _id: '11938' abstract: - lang: eng text: A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge. acknowledgement: 'A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).' article_processing_charge: No article_type: original author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Alexander full_name: Pilz, Alexander last_name: Pilz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591 apa: Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591 chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591. ieee: O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022. ista: Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240. mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591. short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240. date_created: 2022-08-21T22:01:56Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-02-23T13:54:21Z day: '01' ddc: - '000' department: - _id: UlWa - _id: HeEd - _id: KrCh doi: 10.7155/jgaa.00591 ec_funded: 1 external_id: arxiv: - '2101.03928' file: - access_level: open_access checksum: dc6e255e3558faff924fd9e370886c11 content_type: application/pdf creator: dernst date_created: 2022-08-22T06:42:42Z date_updated: 2022-08-22T06:42:42Z file_id: '11940' file_name: 2022_JourGraphAlgorithmsApplic_Aichholzer.pdf file_size: 694538 relation: main_file success: 1 file_date_updated: 2022-08-22T06:42:42Z has_accepted_license: '1' intvolume: ' 26' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 225-240 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: Journal of Graph Algorithms and Applications publication_identifier: issn: - 1526-1719 publication_status: published publisher: Brown University quality_controlled: '1' related_material: record: - id: '9296' relation: earlier_version status: public scopus_import: '1' status: public title: On compatible matchings tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2022' ... --- _id: '9649' abstract: - lang: eng text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently\r\nfine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary." acknowledgement: "First and foremost, we acknowledge Siargey Kachanovich for discussions. We thank Herbert Edelsbrunner and all members of his group, all former and current members of the Datashape team (formerly known as Geometrica), and André Lieutier for encouragement. We further thank the reviewers of Foundations of Computational Mathematics and the reviewers and program committee of the Symposium on Computational Geometry for their feedback, which improved the exposition.\r\nThis work was funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). This work was also supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012. doi:10.1007/s10208-021-09520-0 apa: Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . Springer Nature. https://doi.org/10.1007/s10208-021-09520-0 chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics . Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0. ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer Nature, pp. 967–1012, 2022. ista: Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012. mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics , vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0. short: J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22 (2022) 967–1012. date_created: 2021-07-14T06:44:53Z date_published: 2022-01-01T00:00:00Z date_updated: 2023-08-02T06:49:17Z day: '01' ddc: - '516' department: - _id: HeEd doi: 10.1007/s10208-021-09520-0 ec_funded: 1 external_id: isi: - '000673039600001' file: - access_level: open_access checksum: f1d372ec3c08ec22e84f8e93e1126b8c content_type: application/pdf creator: mwintrae date_created: 2021-07-14T06:44:36Z date_updated: 2021-07-14T06:44:36Z file_id: '9650' file_name: Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf file_size: 1455699 relation: main_file file_date_updated: 2021-07-14T06:44:36Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '0' oa: 1 oa_version: Published Version page: 967-1012 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'Foundations of Computational Mathematics ' publication_identifier: eissn: - 1615-3383 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '7952' relation: earlier_version status: public scopus_import: '1' status: public title: The topological correctness of PL approximations of isomanifolds 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2022' ... --- _id: '10413' abstract: - lang: eng text: Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces. acknowledgement: Dedicated to the memory of Hans-Peter Künzi. article_number: '107916' article_processing_charge: No article_type: original author: - first_name: Dikran full_name: Dikranjan, Dikran last_name: Dikranjan - first_name: Anna full_name: Giordano Bruno, Anna last_name: Giordano Bruno - first_name: Hans Peter full_name: Künzi, Hans Peter last_name: Künzi - first_name: Nicolò full_name: Zava, Nicolò id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad last_name: Zava orcid: 0000-0001-8686-1888 - first_name: Daniele full_name: Toller, Daniele last_name: Toller citation: ama: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916 apa: Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D. (2022). Generalized quasi-metric semilattices. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2021.107916 chicago: Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916. ieee: D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier, 2022. ista: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916. mla: Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916. short: D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022). date_created: 2021-12-05T23:01:44Z date_published: 2022-03-15T00:00:00Z date_updated: 2023-08-02T13:33:24Z day: '15' department: - _id: HeEd doi: 10.1016/j.topol.2021.107916 external_id: isi: - '000791838800012' intvolume: ' 309' isi: 1 language: - iso: eng month: '03' oa_version: None publication: Topology and its Applications publication_identifier: issn: - 0166-8641 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Generalized quasi-metric semilattices type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 309 year: '2022' ... --- _id: '10773' abstract: - lang: eng text: The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function. acknowledgement: Open access funding provided by the Institute of Science and Technology (IST Austria). 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 last_name: Saghafian citation: ama: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2 apa: Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00371-2 chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00371-2. ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842, 2022. ista: Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842. mla: Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry, vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2. short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842. date_created: 2022-02-20T23:01:34Z date_published: 2022-04-01T00:00:00Z date_updated: 2023-08-02T14:31:25Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-022-00371-2 external_id: isi: - '000752175300002' file: - access_level: open_access checksum: 9383d3b70561bacee905e335dc922680 content_type: application/pdf creator: dernst date_created: 2022-08-02T06:07:55Z date_updated: 2022-08-02T06:07:55Z file_id: '11718' file_name: 2022_DiscreteCompGeometry_Biswas.pdf file_size: 2518111 relation: main_file success: 1 file_date_updated: 2022-08-02T06:07:55Z has_accepted_license: '1' intvolume: ' 67' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 811-842 publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 67 year: '2022' ... --- _id: '10828' abstract: - lang: eng text: Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown. 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 - first_name: Sarah full_name: Tymochko, Sarah last_name: Tymochko - first_name: Brittany full_name: Story, Brittany last_name: Story - first_name: Adélie full_name: Garin, Adélie last_name: Garin - first_name: Hoa full_name: Bui, Hoa last_name: Bui - first_name: Bea full_name: Bleile, Bea last_name: Bleile - first_name: Vanessa full_name: Robins, Vanessa last_name: Robins citation: ama: 'Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: 2021 IEEE International Conference on Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483' apa: 'Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483' chicago: Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent Homology of Images.” In 2021 IEEE International Conference on Big Data, 3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483. ieee: T. Heiss et al., “The impact of changes in resolution on the persistent homology of images,” in 2021 IEEE International Conference on Big Data, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834. ista: 'Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The impact of changes in resolution on the persistent homology of images. 2021 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3824–3834.' mla: Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483. short: T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins, in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834. conference: end_date: 2021-12-18 location: Orlando, FL, United States; Virtuell name: 'Big Data: International Conference on Big Data' start_date: 2021-12-15 date_created: 2022-03-06T23:01:53Z date_published: 2022-01-13T00:00:00Z date_updated: 2023-08-02T14:44:21Z day: '13' department: - _id: HeEd doi: 10.1109/BigData52589.2021.9671483 external_id: arxiv: - '2111.05663' isi: - '000800559503126' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2111.05663 month: '01' oa: 1 oa_version: Preprint page: 3824-3834 publication: 2021 IEEE International Conference on Big Data publication_identifier: isbn: - '9781665439022' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: The impact of changes in resolution on the persistent homology of images type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2022' ... --- _id: '11545' abstract: - lang: eng text: "We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N ." acknowledgement: We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Adam full_name: Brown, Adam id: 70B7FDF6-608D-11E9-9333-8535E6697425 last_name: Brown - first_name: Anna full_name: Romanov, Anna last_name: Romanov citation: ama: Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017 apa: Brown, A., & Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017 chicago: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017. ieee: A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier, pp. 145–179, 2022. ista: Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179. mla: Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017. short: A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179. date_created: 2022-07-08T11:40:07Z date_published: 2022-11-01T00:00:00Z date_updated: 2023-08-03T11:56:30Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1016/j.jalgebra.2022.06.017 ec_funded: 1 external_id: isi: - '000861841100004' file: - access_level: open_access checksum: 82abaee3d7837f703e499a9ecbb25b7c content_type: application/pdf creator: dernst date_created: 2023-02-02T07:32:48Z date_updated: 2023-02-02T07:32:48Z file_id: '12473' file_name: 2022_JournalAlgebra_Brown.pdf file_size: 582962 relation: main_file success: 1 file_date_updated: 2023-02-02T07:32:48Z has_accepted_license: '1' intvolume: ' 609' isi: 1 issue: '11' keyword: - Algebra and Number Theory language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 145-179 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Algebra publication_identifier: issn: - 0021-8693 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Contravariant pairings between standard Whittaker modules and Verma modules 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 609 year: '2022' ... --- _id: '10754' abstract: - lang: eng text: Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs. acknowledgement: "This work was partially supported by grants from National Institutes of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary Research Program (to B.C., H.V.K. and Z.P.). " article_number: '1763' article_processing_charge: Yes article_type: original author: - first_name: Yan full_name: Chang, Yan last_name: Chang - first_name: Marah full_name: Funk, Marah last_name: Funk - first_name: Souvik full_name: Roy, Souvik last_name: Roy - 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: Sangyong full_name: Choi, Sangyong last_name: Choi - first_name: Hristo V. full_name: Kojouharov, Hristo V. last_name: Kojouharov - first_name: Benito full_name: Chen, Benito last_name: Chen - first_name: Zui full_name: Pan, Zui last_name: Pan citation: ama: Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3). doi:10.3390/ijms23031763 apa: Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V., … Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763 chicago: Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi, Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763. ieee: Y. Chang et al., “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” International Journal of Molecular Sciences, vol. 23, no. 3. MDPI, 2022. ista: Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 23(3), 1763. mla: Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23, no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763. short: Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B. Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022). date_created: 2022-02-13T23:01:35Z date_published: 2022-02-01T00:00:00Z date_updated: 2023-08-09T10:17:07Z day: '01' ddc: - '510' - '576' department: - _id: HeEd doi: 10.3390/ijms23031763 external_id: isi: - '000754773500001' file: - access_level: open_access checksum: 8890ad20c54e90dc58ad5ea97c902998 content_type: application/pdf creator: dernst date_created: 2022-02-14T07:46:30Z date_updated: 2022-02-14T07:46:30Z file_id: '10756' file_name: 2022_IJMS_Chang.pdf file_size: 24416183 relation: main_file success: 1 file_date_updated: 2022-02-14T07:46:30Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '3' language: - iso: eng month: '02' oa: 1 oa_version: Published Version publication: International Journal of Molecular Sciences publication_identifier: eissn: - '14220067' issn: - '16616596' publication_status: published publisher: MDPI quality_controlled: '1' scopus_import: '1' status: public title: Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 23 year: '2022' ... --- _id: '7791' abstract: - lang: eng text: Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law. acknowledgement: AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Karasev R. When different norms lead to same billiard trajectories? European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0 apa: Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0 chicago: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics. Springer Nature, 2022. https://doi.org/10.1007/s40879-020-00405-0. ieee: A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022. ista: Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312. mla: Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0. short: A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312. date_created: 2020-05-03T22:00:48Z date_published: 2022-12-01T00:00:00Z date_updated: 2024-02-22T15:58:42Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s40879-020-00405-0 ec_funded: 1 external_id: arxiv: - '1912.12685' file: - access_level: open_access checksum: f53e71fd03744075adcd0b8fc1b8423d content_type: application/pdf creator: dernst date_created: 2020-05-04T10:33:42Z date_updated: 2020-07-14T12:48:03Z file_id: '7796' file_name: 2020_EuropMathematics_Akopyan.pdf file_size: 263926 relation: main_file file_date_updated: 2020-07-14T12:48:03Z has_accepted_license: '1' intvolume: ' 8' issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 1309 - 1312 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: European Journal of Mathematics publication_identifier: eissn: - 2199-6768 issn: - 2199-675X publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: When different norms lead to same billiard trajectories? 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2022' ... --- _id: '11660' abstract: - lang: eng text: 'We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. ' 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_processing_charge: No 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 last_name: Saghafian citation: ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.' apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.' chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.' ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs,” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.' ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.' mla: 'Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.' short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.). date_created: 2022-07-27T09:31:15Z date_published: 2022-07-25T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '25' ddc: - '510' department: - _id: GradSch - _id: HeEd ec_funded: 1 file: - access_level: open_access checksum: 95903f9d1649e8e437a967b6f2f64730 content_type: application/pdf creator: scultrer date_created: 2022-07-27T09:30:30Z date_updated: 2022-07-27T09:30:30Z file_id: '11661' file_name: window 1.pdf file_size: 564836 relation: main_file file_date_updated: 2022-07-27T09:30:30Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Submitted 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: The Wittgenstein Prize - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: LIPIcs publication_status: submitted publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '15094' relation: dissertation_contains status: public status: public title: 'A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2022' ... --- _id: '11658' 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: 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: No 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. Leibniz International Proceedings on Mathematics.' apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.' chicago: 'Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik, n.d.' ieee: 'R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.' ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.' mla: 'Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics, Schloss Dagstuhl - Leibniz Zentrum für Informatik.' short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.). date_created: 2022-07-27T09:27:34Z date_published: 2022-07-27T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '27' ddc: - '510' department: - _id: GradSch - _id: HeEd ec_funded: 1 file: - access_level: open_access checksum: b2f511e8b1cae5f1892b0cdec341acac content_type: application/pdf creator: scultrer date_created: 2022-07-27T09:25:53Z date_updated: 2022-07-27T09:25:53Z file_id: '11659' file_name: D-S-E.pdf file_size: 639266 relation: main_file file_date_updated: 2022-07-27T09:25:53Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Submitted 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: The Wittgenstein Prize - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Leibniz International Proceedings on Mathematics publication_status: submitted publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '15094' relation: dissertation_contains status: public status: public 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2022' ... --- _id: '15090' abstract: - lang: eng text: Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications. article_number: '2212.03121' article_processing_charge: No 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: Ondrej full_name: Draganov, Ondrej id: 2B23F01E-F248-11E8-B48F-1D18A9856A87 last_name: Draganov - 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, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv. apa: Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv. chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, n.d. ieee: R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. . ista: Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121. mla: Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, 2212.03121. short: R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.). date_created: 2024-03-08T09:54:20Z date_published: 2022-12-06T00:00:00Z date_updated: 2024-03-20T09:36:56Z day: '06' department: - _id: HeEd ec_funded: 1 external_id: arxiv: - '2212.03121' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2212.03121 month: '12' oa: 1 oa_version: Preprint 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: Discretization in Geometry and Dynamics - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: arXiv publication_status: submitted related_material: record: - id: '15094' relation: dissertation_contains status: public status: public title: On the size of chromatic Delaunay mosaics 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '10208' abstract: - lang: eng text: It is practical to collect a huge amount of movement data and environmental context information along with the health signals of individuals because there is the emergence of new generations of positioning and tracking technologies and rapid advancements of health sensors. The study of the relations between these datasets and their sequence similarity analysis is of interest to many applications such as health monitoring and recommender systems. However, entering all movement parameters and health signals can lead to the complexity of the problem and an increase in its computational load. In this situation, dimension reduction techniques can be used to avoid consideration of simultaneous dependent parameters in the process of similarity measurement of the trajectories. The present study provides a framework, named CaDRAW, to use spatial–temporal data and movement parameters along with independent context information in the process of measuring the similarity of trajectories. In this regard, the omission of dependent movement characteristic signals is conducted by using an unsupervised feature selection dimension reduction technique. To evaluate the effectiveness of the proposed framework, it was applied to a real contextualized movement and related health signal datasets of individuals. The results indicated the capability of the proposed framework in measuring the similarity and in decreasing the characteristic signals in such a way that the similarity results -before and after reduction of dependent characteristic signals- have small differences. The mean differences between the obtained results before and after reducing the dimension were 0.029 and 0.023 for the round path, respectively. acknowledgement: The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. article_processing_charge: No article_type: original author: - first_name: Samira full_name: Goudarzi, Samira last_name: Goudarzi - first_name: Mohammad full_name: Sharif, Mohammad last_name: Sharif - first_name: Farid full_name: Karimipour, Farid id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425 last_name: Karimipour orcid: 0000-0001-6746-4174 citation: ama: Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z apa: Goudarzi, S., Sharif, M., & Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z chicago: Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing. Springer Nature, 2022. https://doi.org/10.1007/s12652-021-03569-z. ieee: S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” Journal of Ambient Intelligence and Humanized Computing, vol. 13. Springer Nature, pp. 2621–2635, 2022. ista: Goudarzi S, Sharif M, Karimipour F. 2022. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 13, 2621–2635. mla: Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:10.1007/s12652-021-03569-z. short: S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635. date_created: 2021-11-02T09:28:55Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-02T13:31:48Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s12652-021-03569-z external_id: isi: - '000712198000001' file: - access_level: open_access checksum: 0a8961416a9bb2be5a1cebda65468bcf content_type: application/pdf creator: fkarimip date_created: 2021-11-12T19:38:05Z date_updated: 2022-12-20T23:30:08Z embargo: 2022-11-12 file_id: '10279' file_name: A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf file_size: 1634958 relation: main_file file_date_updated: 2022-12-20T23:30:08Z has_accepted_license: '1' intvolume: ' 13' isi: 1 keyword: - general computer science language: - iso: eng month: '05' oa: 1 oa_version: Submitted Version page: 2621–2635 project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: Journal of Ambient Intelligence and Humanized Computing publication_identifier: eissn: - 1868-5145 issn: - 1868-5137 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A context-aware dimension reduction framework for trajectory and health signal analyses type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 13 year: '2022' ... --- _id: '10071' alternative_title: - Early Career article_processing_charge: No article_type: letter_note author: - first_name: Henry full_name: Adams, Henry last_name: Adams - first_name: Hana full_name: Kourimska, Hana id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E last_name: Kourimska - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Sarah full_name: Percival, Sarah last_name: Percival - first_name: Lori full_name: Ziegelmeier, Lori last_name: Ziegelmeier citation: ama: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349 apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021). How to tutorial-a-thon. Notices of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/noti2349 chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349. ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021. ista: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon. Notices of the American Mathematical Society. 68(9), 1511–1514. mla: Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:10.1090/noti2349. short: H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514. date_created: 2021-10-03T22:01:22Z date_published: 2021-10-01T00:00:00Z date_updated: 2021-12-03T07:31:26Z day: '01' department: - _id: HeEd doi: 10.1090/noti2349 intvolume: ' 68' issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ams.org/notices/ month: '10' oa: 1 oa_version: Published Version page: 1511-1514 publication: Notices of the American Mathematical Society publication_identifier: eissn: - 1088-9477 issn: - 0002-9920 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: How to tutorial-a-thon type: journal_article user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 68 year: '2021' ... --- _id: '10367' abstract: - lang: eng text: How information is created, shared and consumed has changed rapidly in recent decades, in part thanks to new social platforms and technologies on the web. With ever-larger amounts of unstructured and limited labels, organizing and reconciling information from different sources and modalities is a central challenge in machine learning. This cutting-edge tutorial aims to introduce the multimodal entailment task, which can be useful for detecting semantic alignments when a single modality alone does not suffice for a whole content understanding. Starting with a brief overview of natural language processing, computer vision, structured data and neural graph learning, we lay the foundations for the multimodal sections to follow. We then discuss recent multimodal learning literature covering visual, audio and language streams, and explore case studies focusing on tasks which require fine-grained understanding of visual and linguistic semantics question answering, veracity and hatred classification. Finally, we introduce a new dataset for recognizing multimodal entailment, exploring it in a hands-on collaborative section. Overall, this tutorial gives an overview of multimodal learning, introduces a multimodal entailment dataset, and encourages future research in the topic. acknowledgement: "We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn, Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina, Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell, John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar, Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao, Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes." article_processing_charge: No author: - first_name: Cesar full_name: Ilharco, Cesar last_name: Ilharco - first_name: Afsaneh full_name: Shirazi, Afsaneh last_name: Shirazi - first_name: Arjun full_name: Gopalan, Arjun last_name: Gopalan - first_name: Arsha full_name: Nagrani, Arsha last_name: Nagrani - first_name: Blaž full_name: Bratanič, Blaž last_name: Bratanič - first_name: Chris full_name: Bregler, Chris last_name: Bregler - first_name: Christina full_name: Liu, Christina last_name: Liu - first_name: Felipe full_name: Ferreira, Felipe last_name: Ferreira - first_name: Gabriek full_name: Barcik, Gabriek last_name: Barcik - first_name: Gabriel full_name: Ilharco, Gabriel last_name: Ilharco - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang - first_name: Jannis full_name: Bulian, Jannis last_name: Bulian - first_name: Jared full_name: Frank, Jared last_name: Frank - first_name: Lucas full_name: Smaira, Lucas last_name: Smaira - first_name: Qin full_name: Cao, Qin last_name: Cao - first_name: Ricardo full_name: Marino, Ricardo last_name: Marino - first_name: Roma full_name: Patel, Roma last_name: Patel - first_name: Thomas full_name: Leung, Thomas last_name: Leung - first_name: Vaiva full_name: Imbrasaite, Vaiva last_name: Imbrasaite citation: ama: 'Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6' apa: 'Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6' chicago: Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30. Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6. ieee: C. Ilharco et al., “Recognizing multimodal entailment,” in 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok, Thailand, 2021, pp. 29–30. ista: 'Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C, Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q, Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment. 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing, 29–30.' mla: Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6. short: C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler, C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L. Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30. conference: end_date: 2021-08-06 location: Bangkok, Thailand name: 'ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing' start_date: 2021-08-01 date_created: 2021-11-28T23:01:30Z date_published: 2021-08-01T00:00:00Z date_updated: 2022-01-26T14:26:36Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.18653/v1/2021.acl-tutorials.6 file: - access_level: open_access checksum: b14052a025a6ecf675bdfe51db98c0d7 content_type: application/pdf creator: cchlebak date_created: 2021-11-29T08:41:00Z date_updated: 2021-11-29T08:41:00Z file_id: '10368' file_name: 2021_ACL_Ilharco.pdf file_size: 1227703 relation: main_file success: 1 file_date_updated: 2021-11-29T08:41:00Z has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://aclanthology.org/2021.acl-tutorials.6/ month: '08' oa: 1 oa_version: Published Version page: 29-30 publication: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts publication_identifier: isbn: - 9-781-9540-8557-2 publication_status: published publisher: Association for Computational Linguistics quality_controlled: '1' scopus_import: '1' status: public title: Recognizing multimodal entailment 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2021' ... --- _id: '10608' abstract: - lang: eng text: We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property. acknowledgement: We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Thomas full_name: Weighill, Thomas last_name: Weighill - first_name: Takamitsu full_name: Yamauchi, Takamitsu last_name: Yamauchi - first_name: Nicolò full_name: Zava, Nicolò id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad last_name: Zava citation: ama: Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3 apa: Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-021-00515-3 chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3. ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” European Journal of Mathematics. Springer Nature, 2021. ista: Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. mla: Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021, doi:10.1007/s40879-021-00515-3. short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021). date_created: 2022-01-09T23:01:27Z date_published: 2021-12-30T00:00:00Z date_updated: 2022-01-10T08:36:55Z day: '30' ddc: - '500' department: - _id: HeEd doi: 10.1007/s40879-021-00515-3 file: - access_level: open_access checksum: c435dcfa1ad3aadc5cdd7366bc7f4e98 content_type: application/pdf creator: cchlebak date_created: 2022-01-10T08:33:22Z date_updated: 2022-01-10T08:33:22Z file_id: '10610' file_name: 2021_EuJournalMath_Weighill.pdf file_size: 384908 relation: main_file success: 1 file_date_updated: 2022-01-10T08:33:22Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: European Journal of Mathematics publication_identifier: eissn: - 2199-6768 issn: - 2199-675X publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Coarse infinite-dimensionality of hyperspaces of finite subsets 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2021' ... --- _id: '9296' abstract: - lang: eng text: ' matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge.' acknowledgement: 'A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Irene full_name: Parada, Irene last_name: Parada - first_name: Daniel full_name: Perz, Daniel last_name: Perz - first_name: Alexander full_name: Pilz, Alexander last_name: Pilz - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18' apa: 'Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18' chicago: Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18. ieee: O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233. ista: 'Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233.' mla: Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18. short: O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233. conference: end_date: 2021-03-02 location: Yangon, Myanmar name: 'WALCOM: Algorithms and Computation' start_date: 2021-02-28 date_created: 2021-03-28T22:01:41Z date_published: 2021-02-16T00:00:00Z date_updated: 2023-02-21T16:33:44Z day: '16' department: - _id: UlWa - _id: HeEd - _id: KrCh doi: 10.1007/978-3-030-68211-8_18 ec_funded: 1 external_id: arxiv: - '2101.03928' intvolume: ' 12635' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.03928 month: '02' oa: 1 oa_version: Preprint page: 221-233 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: 15th International Conference on Algorithms and Computation publication_identifier: eissn: - '16113349' isbn: - '9783030682101' issn: - '03029743' publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '11938' relation: later_version status: public scopus_import: '1' status: public title: On compatible matchings type: conference user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 12635 year: '2021' ... --- _id: '9465' abstract: - lang: eng text: "Given a locally finite set \U0001D44B⊆ℝ\U0001D451 and an integer \U0001D458≥0, we consider the function \U0001D430\U0001D458:Del\U0001D458(\U0001D44B)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space." article_number: '15' article_processing_charge: Yes (via OA deal) 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: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang citation: ama: Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4 apa: Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4 chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4. ieee: H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021. ista: Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15. mla: Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4. short: H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021). date_created: 2021-06-06T22:01:29Z date_published: 2021-04-01T00:00:00Z date_updated: 2022-05-12T11:41:45Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00022-021-00577-4 file: - access_level: open_access checksum: e52a832f1def52a2b23d21bcc09e646f content_type: application/pdf creator: kschuh date_created: 2021-06-11T13:16:26Z date_updated: 2021-06-11T13:16:26Z file_id: '9544' file_name: 2021_Geometry_Edelsbrunner.pdf file_size: 694706 relation: main_file success: 1 file_date_updated: 2021-06-11T13:16:26Z has_accepted_license: '1' intvolume: ' 112' issue: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Journal of Geometry publication_identifier: eissn: - '14208997' issn: - '00472468' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A step in the Delaunay mosaic of order k tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 112 year: '2021' ... --- _id: '9345' abstract: - lang: eng text: Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction. acknowledgement: The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective. alternative_title: - LIPIcs article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Vitaliy full_name: ' Kurlin , Vitaliy' last_name: ' Kurlin ' - first_name: Philip full_name: Smith, Philip last_name: Smith - 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, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32' apa: 'Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32' chicago: Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32. ieee: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16. ista: 'Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.' mla: Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32. short: H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16. conference: end_date: 2021-06-11 location: Virtual name: 'SoCG: Symposium on Computational Geometry' start_date: 2021-06-07 date_created: 2021-04-22T08:09:58Z date_published: 2021-06-02T00:00:00Z date_updated: 2023-02-23T13:55:40Z day: '02' ddc: - '004' - '516' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2021.32 ec_funded: 1 file: - access_level: open_access checksum: 1787baef1523d6d93753b90d0c109a6d content_type: application/pdf creator: mwintrae date_created: 2021-04-22T08:08:14Z date_updated: 2021-04-22T08:08:14Z file_id: '9346' file_name: df_socg_final_version.pdf file_size: 3117435 relation: main_file success: 1 file_date_updated: 2021-04-22T08:08:14Z has_accepted_license: '1' intvolume: ' 189' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 32:1-32:16 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: Discretization in Geometry and Dynamics - _id: 25C5A090-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00312 name: The Wittgenstein Prize - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 37th International Symposium on Computational Geometry (SoCG 2021) publication_identifier: issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' status: public title: The density fingerprint of a periodic point set 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: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 189 year: '2021' ... --- _id: '9604' abstract: - lang: eng text: Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation. alternative_title: - LIPIcs article_number: '16' article_processing_charge: No 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 last_name: Saghafian citation: ama: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16' apa: 'Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16' chicago: Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16. ieee: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189. ista: 'Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.' mla: Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16. short: R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. conference: end_date: 2021-06-11 location: Online name: 'SoCG: International Symposium on Computational Geometry' start_date: 2021-06-07 date_created: 2021-06-27T22:01:48Z date_published: 2021-06-02T00:00:00Z date_updated: 2023-02-23T14:02:28Z day: '02' ddc: - '516' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2021.16 ec_funded: 1 file: - access_level: open_access checksum: 22b11a719018b22ecba2471b51f2eb40 content_type: application/pdf creator: asandaue date_created: 2021-06-28T13:11:39Z date_updated: 2021-06-28T13:11:39Z file_id: '9611' file_name: 2021_LIPIcs_Biswas.pdf file_size: 727817 relation: main_file success: 1 file_date_updated: 2021-06-28T13:11:39Z has_accepted_license: '1' intvolume: ' 189' 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: The Wittgenstein Prize - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics publication: Leibniz International Proceedings in Informatics publication_identifier: isbn: - '9783959771849' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Counting cells of order-k voronoi tessellations in ℝ3 with morse theory 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: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 189 year: '2021' ... --- _id: '9824' abstract: - lang: eng text: We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain. acknowledgement: 'This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).' alternative_title: - LNCS article_processing_charge: No author: - first_name: Lidija full_name: Čomić, Lidija last_name: Čomić - first_name: Rita full_name: Zrour, Rita last_name: Zrour - first_name: Gaëlle full_name: Largeteau-Skapin, Gaëlle last_name: Largeteau-Skapin - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Eric full_name: Andres, Eric last_name: Andres citation: ama: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10' apa: 'Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10' chicago: Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10. ieee: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163. ista: 'Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.' mla: Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10. short: L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163. conference: end_date: 2021-05-27 location: Uppsala, Sweden name: 'DGMM: International Conference on Discrete Geometry and Mathematical Morphology' start_date: 2021-05-24 date_created: 2021-08-08T22:01:29Z date_published: 2021-05-16T00:00:00Z date_updated: 2022-05-31T06:58:21Z day: '16' department: - _id: HeEd doi: 10.1007/978-3-030-76657-3_10 ec_funded: 1 intvolume: ' 12708' language: - iso: eng month: '05' oa_version: None page: 152-163 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Discrete Geometry and Mathematical Morphology publication_identifier: eissn: - '16113349' isbn: - '9783030766566' issn: - '03029743' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Body centered cubic grid - coordinate system and discrete analytical plane definition type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 12708 year: '2021' ... --- _id: '8317' abstract: - lang: eng text: When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability. acknowledgement: This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. article_number: '101700' article_processing_charge: No article_type: original author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Hugo A. full_name: Akitaya, Hugo A. last_name: Akitaya - first_name: Kenneth C. full_name: Cheung, Kenneth C. last_name: Cheung - first_name: Erik D. full_name: Demaine, Erik D. last_name: Demaine - first_name: Martin L. full_name: Demaine, Martin L. last_name: Demaine - first_name: Sándor P. full_name: Fekete, Sándor P. last_name: Fekete - first_name: Linda full_name: Kleist, Linda last_name: Kleist - first_name: Irina full_name: Kostitsyna, Irina last_name: Kostitsyna - first_name: Maarten full_name: Löffler, Maarten last_name: Löffler - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Klara full_name: Mundilova, Klara last_name: Mundilova - first_name: Christiane full_name: Schmidt, Christiane last_name: Schmidt citation: ama: 'Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700' apa: 'Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700' chicago: 'Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.' ieee: 'O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.' ista: 'Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.' mla: 'Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.' short: 'O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).' date_created: 2020-08-30T22:01:09Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-08-04T10:57:42Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2020.101700 external_id: arxiv: - '1910.09917' isi: - '000579185100004' intvolume: ' 93' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.09917v3 month: '02' oa: 1 oa_version: Preprint project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: 'Computational Geometry: Theory and Applications' publication_identifier: issn: - '09257721' publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '6989' relation: shorter_version status: public scopus_import: '1' status: public title: Folding polyominoes with holes into a cube type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 93 year: '2021' ... --- _id: '8773' abstract: - lang: eng text: Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell. acknowledgement: "We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059." article_processing_charge: No article_type: original author: - first_name: Adam full_name: Brown, Adam id: 70B7FDF6-608D-11E9-9333-8535E6697425 last_name: Brown - first_name: Anna full_name: Romanov, Anna last_name: Romanov citation: ama: Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205 apa: Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205 chicago: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205. ieee: A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021. ista: Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52. mla: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205. short: A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52. date_created: 2020-11-19T10:17:40Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-08-04T11:11:47Z day: '01' department: - _id: HeEd doi: 10.1090/proc/15205 ec_funded: 1 external_id: arxiv: - '1910.08286' isi: - '000600416300004' intvolume: ' 149' isi: 1 issue: '1' keyword: - Applied Mathematics - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.08286 month: '01' oa: 1 oa_version: Preprint page: 37-52 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: American Mathematical Society quality_controlled: '1' status: public title: Contravariant forms on Whittaker modules type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 149 year: '2021' ...