--- _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 license: https://creativecommons.org/licenses/by/4.0/ 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' ...