[{"arxiv":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2102.11397"}],"abstract":[{"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.","lang":"eng"}],"year":"2022","oa_version":"Preprint","title":"The persistent homology of dual digital image constructions","publication_status":"published","_id":"11440","oa":1,"ec_funded":1,"intvolume":"        30","series_title":"AWMS","publisher":"Springer Nature","project":[{"call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"alternative_title":["Association for Women in Mathematics Series"],"external_id":{"arxiv":["2102.11397"]},"publication_identifier":{"eisbn":["9783030955199"],"isbn":["9783030955182"]},"author":[{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"last_name":"Garin","first_name":"Adélie","full_name":"Garin, Adélie"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"last_name":"Robins","first_name":"Vanessa","full_name":"Robins, Vanessa"}],"day":"27","language":[{"iso":"eng"}],"date_created":"2022-06-07T08:21:11Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18667"}]},"edition":"1","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.","department":[{"_id":"HeEd"}],"type":"book_chapter","date_updated":"2026-04-07T12:54:09Z","publication":"Research in Computational Topology 2","month":"01","date_published":"2022-01-27T00:00:00Z","page":"1-26","status":"public","volume":30,"quality_controlled":"1","citation":{"ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in <i>Research in Computational Topology 2</i>, 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.","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.","chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">https://doi.org/10.1007/978-3-030-95519-9_1</a>.","mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:<a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">10.1007/978-3-030-95519-9_1</a>.","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. <i>Research in Computational Topology 2</i>. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:<a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">10.1007/978-3-030-95519-9_1</a>","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., &#38; Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, &#38; K. Turner (Eds.), <i>Research in Computational Topology 2</i> (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">https://doi.org/10.1007/978-3-030-95519-9_1</a>"},"place":"Cham","doi":"10.1007/978-3-030-95519-9_1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","editor":[{"full_name":"Gasparovic, Ellen","first_name":"Ellen","last_name":"Gasparovic"},{"full_name":"Robins, Vanessa","first_name":"Vanessa","last_name":"Robins"},{"full_name":"Turner, Katharine","last_name":"Turner","first_name":"Katharine"}],"scopus_import":"1","article_processing_charge":"No"},{"publisher":"Elsevier","license":"https://creativecommons.org/licenses/by/4.0/","publication_identifier":{"issn":["0021-8693"]},"external_id":{"isi":["000861841100004"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"keyword":["Algebra and Number Theory"],"abstract":[{"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 .","lang":"eng"}],"year":"2022","ec_funded":1,"oa":1,"intvolume":"       609","title":"Contravariant pairings between standard Whittaker modules and Verma modules","_id":"11545","publication_status":"published","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1016/j.jalgebra.2022.06.017","volume":609,"quality_controlled":"1","citation":{"ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>.","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. 2022;609(11):145-179. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>","apa":"Brown, A., &#38; Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>","mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>."},"isi":1,"article_processing_charge":"Yes (via OA deal)","file":[{"success":1,"file_name":"2022_JournalAlgebra_Brown.pdf","date_created":"2023-02-02T07:32:48Z","access_level":"open_access","relation":"main_file","file_id":"12473","file_size":582962,"content_type":"application/pdf","creator":"dernst","checksum":"82abaee3d7837f703e499a9ecbb25b7c","date_updated":"2023-02-02T07:32:48Z"}],"scopus_import":"1","article_type":"original","corr_author":"1","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.","file_date_updated":"2023-02-02T07:32:48Z","date_created":"2022-07-08T11:40:07Z","day":"01","language":[{"iso":"eng"}],"author":[{"full_name":"Brown, Adam","first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Romanov","first_name":"Anna","full_name":"Romanov, Anna"}],"page":"145-179","status":"public","publication":"Journal of Algebra","date_published":"2022-11-01T00:00:00Z","month":"11","ddc":["510"],"date_updated":"2025-04-14T07:43:58Z","has_accepted_license":"1","department":[{"_id":"HeEd"}],"issue":"11","type":"journal_article"},{"oa_version":"Submitted Version","_id":"11658","publication_status":"draft","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","ec_funded":1,"oa":1,"year":"2022","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."}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","type":"journal_article","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","date_updated":"2026-04-07T12:58:48Z","ddc":["510"],"date_published":"2022-07-27T00:00:00Z","month":"07","publication":"Leibniz International Proceedings on Mathematics","status":"public","author":[{"last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"language":[{"iso":"eng"}],"date_created":"2022-07-27T09:27:34Z","day":"27","file_date_updated":"2022-07-27T09:25:53Z","related_material":{"record":[{"status":"public","id":"15380","relation":"later_version"},{"id":"15094","status":"public","relation":"dissertation_contains"}]},"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.","corr_author":"1","file":[{"date_created":"2022-07-27T09:25:53Z","access_level":"open_access","relation":"main_file","file_name":"D-S-E.pdf","checksum":"b2f511e8b1cae5f1892b0cdec341acac","creator":"scultrer","date_updated":"2022-07-27T09:25:53Z","file_id":"11659","file_size":639266,"content_type":"application/pdf"}],"article_processing_charge":"No","quality_controlled":"1","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"has_accepted_license":"1","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"type":"journal_article","issue":"2","date_updated":"2026-04-16T09:18:20Z","publication":"Journal of Graph Algorithms and Applications","month":"06","date_published":"2022-06-01T00:00:00Z","ddc":["000"],"page":"225-240","status":"public","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","first_name":"Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","last_name":"Arroyo Guevara"},{"first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"last_name":"Parada","first_name":"Irene","full_name":"Parada, Irene"},{"full_name":"Perz, Daniel","last_name":"Perz","first_name":"Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684"},{"full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber","first_name":"Birgit"}],"file_date_updated":"2022-08-22T06:42:42Z","language":[{"iso":"eng"}],"date_created":"2022-08-21T22:01:56Z","day":"01","related_material":{"record":[{"status":"public","id":"9296","relation":"earlier_version"}]},"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).","corr_author":"1","article_type":"original","scopus_import":"1","article_processing_charge":"No","file":[{"file_id":"11940","file_size":694538,"content_type":"application/pdf","creator":"dernst","checksum":"dc6e255e3558faff924fd9e370886c11","date_updated":"2022-08-22T06:42:42Z","success":1,"file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","relation":"main_file","date_created":"2022-08-22T06:42:42Z","access_level":"open_access"}],"volume":26,"citation":{"ieee":"O. Aichholzer <i>et al.</i>, “On compatible matchings,” <i>Journal of Graph Algorithms and Applications</i>, 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.","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.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2022. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. 2022;26(2):225-240. doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>."},"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.7155/jgaa.00591","oa_version":"Published Version","title":"On compatible matchings","_id":"11938","publication_status":"published","oa":1,"ec_funded":1,"intvolume":"        26","arxiv":1,"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."}],"year":"2022","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"},{"name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"279307"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","call_identifier":"FWF"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF","grant_number":"S11407"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2101.03928"]},"publication_identifier":{"issn":["1526-1719"]},"publisher":"Brown University"},{"issue":"5","type":"journal_article","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"date_updated":"2024-10-09T21:03:58Z","date_published":"2022-05-28T00:00:00Z","month":"05","publication":"PRIMUS","status":"public","page":"593-609","author":[{"last_name":"Shipman","first_name":"Barbara A.","full_name":"Shipman, Barbara A."},{"orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson"}],"date_created":"2023-01-16T10:07:21Z","day":"28","language":[{"iso":"eng"}],"corr_author":"1","article_type":"original","scopus_import":"1","article_processing_charge":"No","quality_controlled":"1","citation":{"ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” <i>PRIMUS</i>, vol. 32, no. 5. Taylor &#38; Francis, pp. 593–609, 2022.","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>.","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>, vol. 32, no. 5, Taylor &#38; Francis, 2022, pp. 593–609, doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>.","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. <i>PRIMUS</i>. 2022;32(5):593-609. doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>","apa":"Shipman, B. A., &#38; Stephenson, E. R. (2022). Tangible topology through the lens of limits. <i>PRIMUS</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>"},"volume":32,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1080/10511970.2021.1872750","oa_version":"None","publication_status":"published","_id":"12307","title":"Tangible topology through the lens of limits","intvolume":"        32","year":"2022","keyword":["Education","General Mathematics"],"abstract":[{"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.","lang":"eng"}],"publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]},"publisher":"Taylor & Francis"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"external_id":{"arxiv":["2212.03121"]},"article_number":"2212.03121","title":"On the size of chromatic Delaunay mosaics","_id":"15090","publication_status":"draft","oa_version":"Preprint","ec_funded":1,"oa":1,"arxiv":1,"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."}],"year":"2022","main_file_link":[{"url":"https://arxiv.org/abs/2212.03121","open_access":"1"}],"article_processing_charge":"No","citation":{"ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, 2212.03121.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, n.d.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” <i>arXiv</i>. ."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-04-07T12:58:47Z","department":[{"_id":"HeEd"}],"type":"preprint","status":"public","publication":"arXiv","month":"12","date_published":"2022-12-06T00:00:00Z","date_created":"2024-03-08T09:54:20Z","language":[{"iso":"eng"}],"day":"06","author":[{"orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"orcid":"0000-0003-0464-3823","full_name":"Draganov, Ondrej","first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","last_name":"Draganov"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"corr_author":"1","OA_place":"repository","related_material":{"record":[{"status":"public","id":"20456","relation":"later_version"},{"id":"15094","status":"public","relation":"dissertation_contains"}]}},{"volume":244,"citation":{"mla":"Aichholzer, Oswin, et al. “Hardness of Token Swapping on Trees.” <i>30th Annual European Symposium on Algorithms</i>, vol. 244, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">10.4230/LIPIcs.ESA.2022.3</a>.","apa":"Aichholzer, O., Demaine, E. D., Korman, M., Lubiw, A., Lynch, J., Masárová, Z., … Wein, N. (2022). Hardness of token swapping on trees. In <i>30th Annual European Symposium on Algorithms</i> (Vol. 244). Berlin/Potsdam, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">https://doi.org/10.4230/LIPIcs.ESA.2022.3</a>","ama":"Aichholzer O, Demaine ED, Korman M, et al. Hardness of token swapping on trees. In: <i>30th Annual European Symposium on Algorithms</i>. Vol 244. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">10.4230/LIPIcs.ESA.2022.3</a>","chicago":"Aichholzer, Oswin, Erik D. Demaine, Matias Korman, Anna Lubiw, Jayson Lynch, Zuzana Masárová, Mikhail Rudoy, Virginia Vassilevska Williams, and Nicole Wein. “Hardness of Token Swapping on Trees.” In <i>30th Annual European Symposium on Algorithms</i>, Vol. 244. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">https://doi.org/10.4230/LIPIcs.ESA.2022.3</a>.","short":"O. Aichholzer, E.D. Demaine, M. Korman, A. Lubiw, J. Lynch, Z. Masárová, M. Rudoy, V. Vassilevska Williams, N. Wein, in:, 30th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","ista":"Aichholzer O, Demaine ED, Korman M, Lubiw A, Lynch J, Masárová Z, Rudoy M, Vassilevska Williams V, Wein N. 2022. Hardness of token swapping on trees. 30th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 244, 3.","ieee":"O. Aichholzer <i>et al.</i>, “Hardness of token swapping on trees,” in <i>30th Annual European Symposium on Algorithms</i>, Berlin/Potsdam, Germany, 2022, vol. 244."},"quality_controlled":"1","doi":"10.4230/LIPIcs.ESA.2022.3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","article_processing_charge":"Yes","file":[{"file_id":"17420","content_type":"application/pdf","file_size":1406071,"checksum":"a1fbd3e7baad510fbcb998cf4a7d9f7f","creator":"dernst","date_updated":"2024-08-12T08:51:44Z","success":1,"file_name":"2022_LIPIcS_Aichholzer.pdf","relation":"main_file","access_level":"open_access","date_created":"2024-08-12T08:51:44Z"}],"file_date_updated":"2024-08-12T08:51:44Z","language":[{"iso":"eng"}],"date_created":"2024-05-29T06:27:16Z","day":"01","author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"full_name":"Demaine, Erik D.","first_name":"Erik D.","last_name":"Demaine"},{"full_name":"Korman, Matias","last_name":"Korman","first_name":"Matias"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"first_name":"Jayson","last_name":"Lynch","full_name":"Lynch, Jayson"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"full_name":"Rudoy, Mikhail","last_name":"Rudoy","first_name":"Mikhail"},{"first_name":"Virginia","last_name":"Vassilevska Williams","full_name":"Vassilevska Williams, Virginia"},{"last_name":"Wein","first_name":"Nicole","full_name":"Wein, Nicole"}],"acknowledgement":"g Anna Lubiw: Supported by the Natural Sciences and Engineering Research Council of\r\nCanada (NSERC). Jayson Lynch: Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Zuzana Masárová: Supported by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. Virginia Vassilevska Williams: Supported by an NSF CAREER Award, NSF Grants CCF-1528078, CCF-1514339 and CCF-1909429, a BSF Grant BSF:2012338, a Google Research Fellowship and a Sloan Research Fellowship.\r\nNicole Wein: Supported by a grant to DIMACS from the Simons Foundation (820931). This work was done while the author was at MIT.\r\nThis research was initiated at the 34th Bellairs Winter Workshop on Computational Geometry, co-organized by Erik Demaine and Godfried Toussaint, held on March 22–29,\r\n2019 in Holetown, Barbados. We thank the other participants of that workshop for providing a\r\nstimulating research environment.","corr_author":"1","date_updated":"2025-04-15T07:16:56Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"has_accepted_license":"1","type":"conference","status":"public","publication":"30th Annual European Symposium on Algorithms","month":"09","date_published":"2022-09-01T00:00:00Z","ddc":["510"],"article_number":"3","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"alternative_title":["LIPIcs"],"external_id":{"arxiv":["2103.06707"]},"conference":{"name":"ESA: European Symposium on Algorithms","end_date":"2022-09-09","location":"Berlin/Potsdam, Germany","start_date":"2022-09-05"},"arxiv":1,"abstract":[{"text":"Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which exchanges the tokens at the two endpoints of an edge of the graph. In parallel token swapping, the goal is to use the fewest rounds, each of which consists of one or more swaps on the edges of a matching. We prove that both of these problems remain NP-hard when the graph is restricted to be a tree. These token swapping problems have been studied by disparate groups of researchers in discrete mathematics, theoretical computer science, robot motion planning, game theory, and engineering. Previous work establishes NP-completeness on general graphs (for both problems), constant-factor approximation algorithms, and some poly-time exact algorithms for simple graph classes such as cliques, stars, paths, and cycles. Sequential and parallel token swapping on trees were first studied over thirty years ago (as \"sorting with a transposition tree\") and over twenty-five years ago (as \"routing permutations via matchings\"), yet their complexities were previously unknown. We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is 2) and show that no such algorithm can achieve an approximation factor less than 2.","lang":"eng"}],"year":"2022","title":"Hardness of token swapping on trees","_id":"17084","publication_status":"published","oa_version":"Published Version","oa":1,"intvolume":"       244"},{"article_number":"107916","publisher":"Elsevier","external_id":{"isi":["000791838800012"]},"publication_identifier":{"issn":["0166-8641"]},"abstract":[{"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.","lang":"eng"}],"year":"2022","oa_version":"None","title":"Generalized quasi-metric semilattices","_id":"10413","publication_status":"published","intvolume":"       309","volume":309,"quality_controlled":"1","citation":{"ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. <i>Topology and its Applications</i>. 2022;309. doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., &#38; Toller, D. (2022). Generalized quasi-metric semilattices. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>, vol. 309, 107916, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>.","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” <i>Topology and its Applications</i>, vol. 309. Elsevier, 2022."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1016/j.topol.2021.107916","scopus_import":"1","article_processing_charge":"No","isi":1,"author":[{"full_name":"Dikranjan, Dikran","last_name":"Dikranjan","first_name":"Dikran"},{"full_name":"Giordano Bruno, Anna","last_name":"Giordano Bruno","first_name":"Anna"},{"first_name":"Hans Peter","last_name":"Künzi","full_name":"Künzi, Hans Peter"},{"last_name":"Zava","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888"},{"full_name":"Toller, Daniele","first_name":"Daniele","last_name":"Toller"}],"date_created":"2021-12-05T23:01:44Z","language":[{"iso":"eng"}],"day":"15","article_type":"original","corr_author":"1","acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","department":[{"_id":"HeEd"}],"type":"journal_article","date_updated":"2024-10-09T21:01:16Z","publication":"Topology and its Applications","date_published":"2022-03-15T00:00:00Z","month":"03","status":"public"},{"citation":{"apa":"Weighill, T., Yamauchi, T., &#38; Zava, N. (2022). Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. 2022;8(1):335-355. doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>, vol. 8, no. 1, Springer Nature, 2022, pp. 335–55, doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>.","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>.","ista":"Weighill T, Yamauchi T, Zava N. 2022. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 8(1), 335–355.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics 8 (2022) 335–355.","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” <i>European Journal of Mathematics</i>, vol. 8, no. 1. Springer Nature, pp. 335–355, 2022."},"quality_controlled":"1","volume":8,"doi":"10.1007/s40879-021-00515-3","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","file":[{"relation":"main_file","date_created":"2024-05-22T11:10:10Z","access_level":"open_access","success":1,"file_name":"2022_EuJournalMath_Weighill.pdf","checksum":"ce35cbb2d8c889dc7750719972634ed4","creator":"kschuh","date_updated":"2024-05-22T11:10:10Z","file_id":"17036","file_size":371515,"content_type":"application/pdf"}],"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Weighill","first_name":"Thomas","full_name":"Weighill, Thomas"},{"full_name":"Yamauchi, Takamitsu","first_name":"Takamitsu","last_name":"Yamauchi"},{"first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","last_name":"Zava","orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò"}],"language":[{"iso":"eng"}],"day":"01","date_created":"2022-01-09T23:01:27Z","file_date_updated":"2024-05-22T11:10:10Z","article_type":"original","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).","type":"journal_article","issue":"1","has_accepted_license":"1","department":[{"_id":"HeEd"}],"date_updated":"2024-05-22T11:10:22Z","ddc":["500"],"month":"03","date_published":"2022-03-01T00:00:00Z","publication":"European Journal of Mathematics","status":"public","page":"335-355","publisher":"Springer Nature","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"year":"2022","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","publication_status":"published","_id":"10608","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","intvolume":"         8","oa":1},{"abstract":[{"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.","lang":"eng"}],"year":"2022","oa_version":"Published Version","title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","_id":"10754","publication_status":"published","oa":1,"intvolume":"        23","pmid":1,"article_number":"1763","publisher":"MDPI","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"pmid":["35163685"],"isi":["000754773500001"]},"publication_identifier":{"eissn":["1422-0067"],"issn":["1661-6596"]},"author":[{"first_name":"Yan","last_name":"Chang","full_name":"Chang, Yan"},{"full_name":"Funk, Marah","first_name":"Marah","last_name":"Funk"},{"full_name":"Roy, Souvik","first_name":"Souvik","last_name":"Roy"},{"orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson"},{"full_name":"Choi, Sangyong","last_name":"Choi","first_name":"Sangyong"},{"first_name":"Hristo V.","last_name":"Kojouharov","full_name":"Kojouharov, Hristo V."},{"full_name":"Chen, Benito","last_name":"Chen","first_name":"Benito"},{"full_name":"Pan, Zui","last_name":"Pan","first_name":"Zui"}],"file_date_updated":"2022-02-14T07:46:30Z","date_created":"2022-02-13T23:01:35Z","day":"01","language":[{"iso":"eng"}],"article_type":"original","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.). ","department":[{"_id":"HeEd"}],"has_accepted_license":"1","issue":"3","type":"journal_article","date_updated":"2025-06-11T13:46:46Z","publication":"International Journal of Molecular Sciences","month":"02","date_published":"2022-02-01T00:00:00Z","ddc":["510","576"],"status":"public","volume":23,"quality_controlled":"1","citation":{"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. <i>International Journal of Molecular Sciences</i>. MDPI. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>","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. <i>International Journal of Molecular Sciences</i>. 2022;23(3). doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>","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.” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3, 1763, MDPI, 2022, doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>.","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.” <i>International Journal of Molecular Sciences</i>. MDPI, 2022. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>.","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.","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).","ieee":"Y. Chang <i>et al.</i>, “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3. MDPI, 2022."},"doi":"10.3390/ijms23031763","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","article_processing_charge":"Yes","file":[{"file_name":"2022_IJMS_Chang.pdf","success":1,"relation":"main_file","access_level":"open_access","date_created":"2022-02-14T07:46:30Z","file_id":"10756","content_type":"application/pdf","file_size":24416183,"checksum":"8890ad20c54e90dc58ad5ea97c902998","creator":"dernst","date_updated":"2022-02-14T07:46:30Z"}],"isi":1},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"external_id":{"isi":["000752175300002"]},"publisher":"Springer Nature","publication_status":"published","_id":"10773","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","oa_version":"Published Version","intvolume":"        67","oa":1,"year":"2022","abstract":[{"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.","lang":"eng"}],"scopus_import":"1","isi":1,"file":[{"file_id":"11718","file_size":2518111,"content_type":"application/pdf","checksum":"9383d3b70561bacee905e335dc922680","creator":"dernst","date_updated":"2022-08-02T06:07:55Z","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","success":1,"access_level":"open_access","date_created":"2022-08-02T06:07:55Z","relation":"main_file"}],"article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>.","mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 67, Springer Nature, 2022, pp. 811–42, doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. 2022;67:811-842. doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, 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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842."},"volume":67,"doi":"10.1007/s00454-022-00371-2","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2024-10-09T21:01:38Z","type":"journal_article","has_accepted_license":"1","department":[{"_id":"HeEd"}],"status":"public","page":"811-842","ddc":["510"],"date_published":"2022-04-01T00:00:00Z","month":"04","publication":"Discrete and Computational Geometry","day":"01","language":[{"iso":"eng"}],"date_created":"2022-02-20T23:01:34Z","file_date_updated":"2022-08-02T06:07:55Z","author":[{"orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano","first_name":"Sebastiano","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","corr_author":"1","article_type":"original"},{"oa_version":"Published Version","title":"When different norms lead to same billiard trajectories?","publication_status":"published","_id":"7791","oa":1,"ec_funded":1,"intvolume":"         8","arxiv":1,"abstract":[{"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.","lang":"eng"}],"year":"2022","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["1912.12685"]},"publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"publisher":"Springer Nature","has_accepted_license":"1","department":[{"_id":"HeEd"}],"issue":"4","type":"journal_article","date_updated":"2025-04-14T07:48:36Z","publication":"European Journal of Mathematics","ddc":["510"],"month":"12","date_published":"2022-12-01T00:00:00Z","page":"1309 - 1312","status":"public","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"file_date_updated":"2020-07-14T12:48:03Z","date_created":"2020-05-03T22:00:48Z","day":"01","language":[{"iso":"eng"}],"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_type":"original","corr_author":"1","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","file":[{"date_updated":"2020-07-14T12:48:03Z","creator":"dernst","checksum":"f53e71fd03744075adcd0b8fc1b8423d","file_size":263926,"content_type":"application/pdf","file_id":"7796","relation":"main_file","access_level":"open_access","date_created":"2020-05-04T10:33:42Z","file_name":"2020_EuropMathematics_Akopyan.pdf"}],"volume":8,"citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>.","mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>.","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. 2022;8(4):1309-1312. doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>","apa":"Akopyan, A., &#38; Karasev, R. (2022). When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” <i>European Journal of Mathematics</i>, 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.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312."},"quality_controlled":"1","doi":"10.1007/s40879-020-00405-0","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"ec_funded":1,"oa":1,"intvolume":"         8","title":"Billiards in ellipses revisited","publication_status":"published","_id":"8538","oa_version":"Preprint","abstract":[{"text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.","lang":"eng"}],"year":"2022","main_file_link":[{"url":"https://arxiv.org/abs/2001.02934","open_access":"1"}],"arxiv":1,"publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"external_id":{"arxiv":["2001.02934"]},"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"}],"publisher":"Springer Nature","page":"1313-1327","status":"public","publication":"European Journal of Mathematics","month":"12","date_published":"2022-12-01T00:00:00Z","date_updated":"2025-04-14T07:48:34Z","department":[{"_id":"HeEd"}],"issue":"4","type":"journal_article","acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","article_type":"original","day":"01","language":[{"iso":"eng"}],"date_created":"2020-09-20T22:01:38Z","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan"},{"first_name":"Richard","last_name":"Schwartz","full_name":"Schwartz, Richard"},{"first_name":"Serge","last_name":"Tabachnikov","full_name":"Tabachnikov, Serge"}],"article_processing_charge":"No","scopus_import":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s40879-020-00426-9","volume":8,"quality_controlled":"1","citation":{"ista":"Akopyan A, Schwartz R, Tabachnikov S. 2022. Billiards in ellipses revisited. European Journal of Mathematics. 8(4), 1313–1327.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics 8 (2022) 1313–1327.","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1313–1327, 2022.","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1313–27, doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>.","apa":"Akopyan, A., Schwartz, R., &#38; Tabachnikov, S. (2022). Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. 2022;8(4):1313-1327. doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>."}},{"isi":1,"file":[{"date_created":"2021-07-14T06:44:36Z","access_level":"open_access","relation":"main_file","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf","checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","creator":"mwintrae","date_updated":"2021-07-14T06:44:36Z","file_id":"9650","file_size":1455699,"content_type":"application/pdf"}],"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s10208-021-09520-0","quality_controlled":"1","citation":{"chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>, vol. 22, Springer Nature, 2022, pp. 967–1012, doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>.","apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. 2022;22:967-1012. doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” <i>Foundations of Computational Mathematics </i>, 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.","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics  22 (2022) 967–1012."},"volume":22,"status":"public","page":"967-1012","date_published":"2022-01-01T00:00:00Z","ddc":["516"],"month":"01","publication":"Foundations of Computational Mathematics ","date_updated":"2025-04-22T13:45:18Z","type":"journal_article","has_accepted_license":"1","department":[{"_id":"HeEd"}],"corr_author":"1","article_type":"original","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.","related_material":{"record":[{"id":"7952","status":"public","relation":"earlier_version"}]},"day":"01","date_created":"2021-07-14T06:44:53Z","language":[{"iso":"eng"}],"file_date_updated":"2021-07-14T06:44:36Z","author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publication_identifier":{"eissn":["1615-3383"]},"external_id":{"isi":["000673039600001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"publisher":"Springer Nature","intvolume":"        22","oa":1,"ec_funded":1,"_id":"9649","publication_status":"published","title":"The topological correctness of PL approximations of isomanifolds","oa_version":"Published Version","year":"2022","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."}]},{"date_updated":"2026-08-13T09:41:58Z","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"type":"journal_article","status":"public","publication":"LIPIcs","ddc":["510"],"date_published":"2022-07-25T00:00:00Z","month":"07","file_date_updated":"2022-07-27T09:30:30Z","language":[{"iso":"eng"}],"day":"25","date_created":"2022-07-27T09:31:15Z","author":[{"last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"corr_author":"1","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. ","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"},{"relation":"later_version","status":"public","id":"13182"}]},"article_processing_charge":"No","file":[{"date_updated":"2022-07-27T09:30:30Z","creator":"scultrer","checksum":"95903f9d1649e8e437a967b6f2f64730","file_size":564836,"content_type":"application/pdf","file_id":"11661","access_level":"open_access","date_created":"2022-07-27T09:30:30Z","relation":"main_file","file_name":"window 1.pdf"}],"citation":{"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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (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,” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","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. <i>LIPIcs</i>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>, 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.” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d."},"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","publication_status":"submitted","_id":"11660","oa_version":"Submitted Version","oa":1,"ec_funded":1,"abstract":[{"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. ","lang":"eng"}],"year":"2022","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik"},{"project":[{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"external_id":{"isi":["000712198000001"]},"publication_identifier":{"eissn":["1868-5145"],"issn":["1868-5137"]},"publisher":"Springer Nature","oa_version":"Submitted Version","title":"A context-aware dimension reduction framework for trajectory and health signal analyses","publication_status":"published","_id":"10208","oa":1,"intvolume":"        13","keyword":["general computer science"],"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."}],"year":"2022","scopus_import":"1","article_processing_charge":"No","file":[{"creator":"fkarimip","checksum":"0a8961416a9bb2be5a1cebda65468bcf","date_updated":"2022-12-20T23:30:08Z","file_id":"10279","content_type":"application/pdf","file_size":1634958,"relation":"main_file","access_level":"open_access","date_created":"2021-11-12T19:38:05Z","file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","embargo":"2022-11-12"}],"isi":1,"volume":13,"quality_controlled":"1","citation":{"ama":"Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. <i>Journal of Ambient Intelligence and Humanized Computing</i>. 2022;13:2621–2635. doi:<a href=\"https://doi.org/10.1007/s12652-021-03569-z\">10.1007/s12652-021-03569-z</a>","apa":"Goudarzi, S., Sharif, M., &#38; Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. <i>Journal of Ambient Intelligence and Humanized Computing</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s12652-021-03569-z\">https://doi.org/10.1007/s12652-021-03569-z</a>","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” <i>Journal of Ambient Intelligence and Humanized Computing</i>, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:<a href=\"https://doi.org/10.1007/s12652-021-03569-z\">10.1007/s12652-021-03569-z</a>.","chicago":"Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” <i>Journal of Ambient Intelligence and Humanized Computing</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s12652-021-03569-z\">https://doi.org/10.1007/s12652-021-03569-z</a>.","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.","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","ieee":"S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” <i>Journal of Ambient Intelligence and Humanized Computing</i>, vol. 13. Springer Nature, pp. 2621–2635, 2022."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s12652-021-03569-z","department":[{"_id":"HeEd"}],"has_accepted_license":"1","type":"journal_article","date_updated":"2025-04-15T07:16:55Z","publication":"Journal of Ambient Intelligence and Humanized Computing","date_published":"2022-05-01T00:00:00Z","ddc":["000"],"month":"05","page":"2621–2635","status":"public","author":[{"full_name":"Goudarzi, Samira","last_name":"Goudarzi","first_name":"Samira"},{"last_name":"Sharif","first_name":"Mohammad","full_name":"Sharif, Mohammad"},{"last_name":"Karimipour","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174"}],"file_date_updated":"2022-12-20T23:30:08Z","language":[{"iso":"eng"}],"day":"01","date_created":"2021-11-02T09:28:55Z","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","article_type":"original"},{"publication_status":"published","_id":"15275","title":"Bounded VC-dimension implies the Schur-Erdős conjecture","oa_version":"Preprint","intvolume":"        41","oa":1,"arxiv":1,"year":"2021","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"abstract":[{"text":"In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.02342","open_access":"1"}],"publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"external_id":{"arxiv":["1912.02342"]},"publisher":"Springer Nature","date_updated":"2024-04-09T10:40:08Z","issue":"6","type":"journal_article","department":[{"_id":"HeEd"}],"status":"public","page":"803-813","date_published":"2021-11-20T00:00:00Z","month":"11","publication":"Combinatorica","language":[{"iso":"eng"}],"date_created":"2024-04-03T07:59:57Z","day":"20","author":[{"full_name":"Fox, Jacob","last_name":"Fox","first_name":"Jacob"},{"full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach"},{"first_name":"Andrew","last_name":"Suk","full_name":"Suk, Andrew"}],"article_type":"original","article_processing_charge":"No","citation":{"ista":"Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 41(6), 803–813.","short":"J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.","ieee":"J. Fox, J. Pach, and A. Suk, “Bounded VC-dimension implies the Schur-Erdős conjecture,” <i>Combinatorica</i>, vol. 41, no. 6. Springer Nature, pp. 803–813, 2021.","apa":"Fox, J., Pach, J., &#38; Suk, A. (2021). Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>","ama":"Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. 2021;41(6):803-813. doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>","mla":"Fox, Jacob, et al. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>, vol. 41, no. 6, Springer Nature, 2021, pp. 803–13, doi:<a href=\"https://doi.org/10.1007/s00493-021-4530-9\">10.1007/s00493-021-4530-9</a>.","chicago":"Fox, Jacob, János Pach, and Andrew Suk. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” <i>Combinatorica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00493-021-4530-9\">https://doi.org/10.1007/s00493-021-4530-9</a>."},"quality_controlled":"1","volume":41,"doi":"10.1007/s00493-021-4530-9","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_updated":"2026-06-18T08:36:13Z","department":[{"_id":"HeEd"}],"issue":"9","type":"journal_article","page":"1511-1514","status":"public","publication":"Notices of the American Mathematical Society","date_published":"2021-10-01T00:00:00Z","month":"10","ddc":["500"],"language":[{"iso":"eng"}],"day":"01","date_created":"2021-10-03T22:01:22Z","author":[{"full_name":"Adams, Henry","first_name":"Henry","last_name":"Adams"},{"first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","last_name":"Kourimska","orcid":"0000-0001-7841-0091","full_name":"Kourimska, Hana"},{"orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss"},{"full_name":"Percival, Sarah","last_name":"Percival","first_name":"Sarah"},{"last_name":"Ziegelmeier","first_name":"Lori","full_name":"Ziegelmeier, Lori"}],"article_type":"letter_note","scopus_import":"1","article_processing_charge":"No","volume":68,"citation":{"ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. 2021;68(9):1511-1514. doi:<a href=\"https://doi.org/10.1090/noti2349\">10.1090/noti2349</a>","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., &#38; Ziegelmeier, L. (2021). How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/noti2349\">https://doi.org/10.1090/noti2349</a>","mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:<a href=\"https://doi.org/10.1090/noti2349\">10.1090/noti2349</a>.","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/noti2349\">https://doi.org/10.1090/noti2349</a>.","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.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” <i>Notices of the American Mathematical Society</i>, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021."},"quality_controlled":"1","doi":"10.1090/noti2349","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"How to tutorial-a-thon","publication_status":"published","_id":"10071","oa_version":"Published Version","oa":1,"intvolume":"        68","year":"2021","main_file_link":[{"open_access":"1","url":"http://www.ams.org/notices/"}],"publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"alternative_title":["Early Career"],"publisher":"American Mathematical Society"},{"date_published":"2021-08-01T00:00:00Z","ddc":["000"],"month":"08","publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","status":"public","page":"29-30","type":"conference","department":[{"_id":"HeEd"}],"has_accepted_license":"1","date_updated":"2022-01-26T14:26:36Z","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.","author":[{"full_name":"Ilharco, Cesar","last_name":"Ilharco","first_name":"Cesar"},{"full_name":"Shirazi, Afsaneh","last_name":"Shirazi","first_name":"Afsaneh"},{"last_name":"Gopalan","first_name":"Arjun","full_name":"Gopalan, Arjun"},{"full_name":"Nagrani, Arsha","last_name":"Nagrani","first_name":"Arsha"},{"last_name":"Bratanič","first_name":"Blaž","full_name":"Bratanič, Blaž"},{"last_name":"Bregler","first_name":"Chris","full_name":"Bregler, Chris"},{"full_name":"Liu, Christina","last_name":"Liu","first_name":"Christina"},{"full_name":"Ferreira, Felipe","first_name":"Felipe","last_name":"Ferreira"},{"full_name":"Barcik, Gabriek","first_name":"Gabriek","last_name":"Barcik"},{"full_name":"Ilharco, Gabriel","first_name":"Gabriel","last_name":"Ilharco"},{"last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F"},{"full_name":"Bulian, Jannis","first_name":"Jannis","last_name":"Bulian"},{"first_name":"Jared","last_name":"Frank","full_name":"Frank, Jared"},{"full_name":"Smaira, Lucas","first_name":"Lucas","last_name":"Smaira"},{"full_name":"Cao, Qin","last_name":"Cao","first_name":"Qin"},{"last_name":"Marino","first_name":"Ricardo","full_name":"Marino, Ricardo"},{"full_name":"Patel, Roma","first_name":"Roma","last_name":"Patel"},{"last_name":"Leung","first_name":"Thomas","full_name":"Leung, Thomas"},{"full_name":"Imbrasaite, Vaiva","last_name":"Imbrasaite","first_name":"Vaiva"}],"day":"01","date_created":"2021-11-28T23:01:30Z","language":[{"iso":"eng"}],"file_date_updated":"2021-11-29T08:41:00Z","file":[{"access_level":"open_access","date_created":"2021-11-29T08:41:00Z","relation":"main_file","success":1,"file_name":"2021_ACL_Ilharco.pdf","checksum":"b14052a025a6ecf675bdfe51db98c0d7","creator":"cchlebak","date_updated":"2021-11-29T08:41:00Z","file_id":"10368","file_size":1227703,"content_type":"application/pdf"}],"article_processing_charge":"No","scopus_import":"1","doi":"10.18653/v1/2021.acl-tutorials.6","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","quality_controlled":"1","citation":{"ama":"Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: <i>59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts</i>. Association for Computational Linguistics; 2021:29-30. doi:<a href=\"https://doi.org/10.18653/v1/2021.acl-tutorials.6\">10.18653/v1/2021.acl-tutorials.6</a>","apa":"Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In <i>59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts</i> (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. <a href=\"https://doi.org/10.18653/v1/2021.acl-tutorials.6\">https://doi.org/10.18653/v1/2021.acl-tutorials.6</a>","mla":"Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” <i>59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts</i>, Association for Computational Linguistics, 2021, pp. 29–30, doi:<a href=\"https://doi.org/10.18653/v1/2021.acl-tutorials.6\">10.18653/v1/2021.acl-tutorials.6</a>.","chicago":"Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In <i>59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts</i>, 29–30. Association for Computational Linguistics, 2021. <a href=\"https://doi.org/10.18653/v1/2021.acl-tutorials.6\">https://doi.org/10.18653/v1/2021.acl-tutorials.6</a>.","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.","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.","ieee":"C. Ilharco <i>et al.</i>, “Recognizing multimodal entailment,” in <i>59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts</i>, Bangkok, Thailand, 2021, pp. 29–30."},"oa":1,"oa_version":"Published Version","publication_status":"published","_id":"10367","title":"Recognizing multimodal entailment","main_file_link":[{"open_access":"1","url":"https://aclanthology.org/2021.acl-tutorials.6/"}],"year":"2021","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."}],"conference":{"end_date":"2021-08-06","name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing","location":"Bangkok, Thailand","start_date":"2021-08-01"},"publication_identifier":{"isbn":["9-781-9540-8557-2"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Association for Computational Linguistics"},{"oa":1,"intvolume":"        65","oa_version":"Published Version","title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","_id":"7905","publication_status":"published","abstract":[{"text":"We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.","lang":"eng"}],"year":"2021","arxiv":1,"external_id":{"isi":["000536324700001"],"arxiv":["1712.07734"]},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Springer Nature","publication":"Discrete and Computational Geometry","ddc":["510"],"date_published":"2021-06-01T00:00:00Z","month":"06","page":"1166-1198","status":"public","department":[{"_id":"HeEd"}],"has_accepted_license":"1","type":"journal_article","date_updated":"2025-04-15T06:53:15Z","corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375. The authors would like to thank the anonymous referees for their insightful comments.","article_type":"original","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam"},{"last_name":"Wang","first_name":"Bei","full_name":"Wang, Bei"}],"file_date_updated":"2020-11-25T09:06:41Z","language":[{"iso":"eng"}],"date_created":"2020-05-30T10:26:04Z","day":"01","article_processing_charge":"Yes (via OA deal)","file":[{"file_name":"2020_DiscreteCompGeometry_Brown.pdf","success":1,"date_created":"2020-11-25T09:06:41Z","access_level":"open_access","relation":"main_file","file_size":1013730,"content_type":"application/pdf","file_id":"8803","date_updated":"2020-11-25T09:06:41Z","checksum":"487a84ea5841b75f04f66d7ebd71b67e","creator":"dernst"}],"isi":1,"scopus_import":"1","doi":"10.1007/s00454-020-00206-y","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":65,"citation":{"ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” <i>Discrete and Computational Geometry</i>, vol. 65. Springer Nature, pp. 1166–1198, 2021.","mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” <i>Discrete and Computational Geometry</i>, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:<a href=\"https://doi.org/10.1007/s00454-020-00206-y\">10.1007/s00454-020-00206-y</a>.","ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. <i>Discrete and Computational Geometry</i>. 2021;65:1166-1198. doi:<a href=\"https://doi.org/10.1007/s00454-020-00206-y\">10.1007/s00454-020-00206-y</a>","apa":"Brown, A., &#38; Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00206-y\">https://doi.org/10.1007/s00454-020-00206-y</a>","chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00206-y\">https://doi.org/10.1007/s00454-020-00206-y</a>."},"quality_controlled":"1"}]