--- _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' ...