[{"publication":"Leibniz International Proceedings on Mathematics","date_created":"2022-07-27T09:27:34Z","corr_author":"1","ddc":["510"],"month":"07","oa":1,"oa_version":"Submitted Version","language":[{"iso":"eng"}],"date_updated":"2026-04-07T12:58:48Z","publication_status":"draft","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","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."}],"has_accepted_license":"1","related_material":{"record":[{"id":"15380","status":"public","relation":"later_version"},{"status":"public","relation":"dissertation_contains","id":"15094"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"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.","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.","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>.","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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","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."},"type":"journal_article","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","year":"2022","day":"27","date_published":"2022-07-27T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"11658","author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"}],"article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2022-07-27T09:25:53Z","file":[{"creator":"scultrer","content_type":"application/pdf","file_name":"D-S-E.pdf","checksum":"b2f511e8b1cae5f1892b0cdec341acac","relation":"main_file","file_id":"11659","date_updated":"2022-07-27T09:25:53Z","access_level":"open_access","date_created":"2022-07-27T09:25:53Z","file_size":639266}],"ec_funded":1,"status":"public","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."},{"publication":"arXiv","date_created":"2024-03-08T09:54:20Z","month":"12","corr_author":"1","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"publication_status":"draft","date_updated":"2026-04-07T12:58:47Z","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."}],"title":"On the size of chromatic Delaunay mosaics","external_id":{"arxiv":["2212.03121"]},"OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03121"}],"article_number":"2212.03121","related_material":{"record":[{"id":"20456","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"15094"}]},"citation":{"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.).","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “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>.","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>arXiv</i>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"preprint","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"year":"2022","day":"06","date_published":"2022-12-06T00:00:00Z","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"full_name":"Draganov, Ondrej","last_name":"Draganov","first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"_id":"15090","article_processing_charge":"No","ec_funded":1,"status":"public","arxiv":1},{"oa_version":"Published Version","language":[{"iso":"eng"}],"date_updated":"2026-04-16T09:18:20Z","publication_status":"published","scopus_import":"1","external_id":{"arxiv":["2101.03928"]},"title":"On compatible matchings","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."}],"doi":"10.7155/jgaa.00591","publication":"Journal of Graph Algorithms and Applications","page":"225-240","date_created":"2022-08-21T22:01:56Z","corr_author":"1","ddc":["000"],"month":"06","intvolume":"        26","oa":1,"year":"2022","day":"01","date_published":"2022-06-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"first_name":"Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"last_name":"Pilz","full_name":"Pilz, Alexander","first_name":"Alexander"},{"last_name":"Tkadlec","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef"},{"last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit","first_name":"Birgit"}],"_id":"11938","article_processing_charge":"No","publisher":"Brown University","file_date_updated":"2022-08-22T06:42:42Z","volume":26,"file":[{"date_updated":"2022-08-22T06:42:42Z","access_level":"open_access","date_created":"2022-08-22T06:42:42Z","file_size":694538,"creator":"dernst","success":1,"content_type":"application/pdf","checksum":"dc6e255e3558faff924fd9e370886c11","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","relation":"main_file","file_id":"11940"}],"ec_funded":1,"status":"public","arxiv":1,"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).","publication_identifier":{"issn":["1526-1719"]},"has_accepted_license":"1","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9296"}]},"issue":"2","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"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>.","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>","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.","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>","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."},"type":"journal_article","quality_controlled":"1","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"},{"grant_number":"P 23499-N23","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407"}]},{"page":"2621–2635","publication":"Journal of Ambient Intelligence and Humanized Computing","date_created":"2021-11-02T09:28:55Z","isi":1,"ddc":["000"],"month":"05","intvolume":"        13","oa":1,"oa_version":"Submitted Version","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-04-15T07:16:55Z","scopus_import":"1","external_id":{"isi":["000712198000001"]},"title":"A context-aware dimension reduction framework for trajectory and health signal analyses","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."}],"doi":"10.1007/s12652-021-03569-z","publication_identifier":{"eissn":["1868-5145"],"issn":["1868-5137"]},"has_accepted_license":"1","keyword":["general computer science"],"article_type":"original","citation":{"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>","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.","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>.","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","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>","ista":"Goudarzi S, Sharif M, Karimipour F. 2022. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 13, 2621–2635.","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” <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>."},"type":"journal_article","project":[{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","year":"2022","day":"01","date_published":"2022-05-01T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Samira","full_name":"Goudarzi, Samira","last_name":"Goudarzi"},{"first_name":"Mohammad","full_name":"Sharif, Mohammad","last_name":"Sharif"},{"first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid","last_name":"Karimipour"}],"_id":"10208","article_processing_charge":"No","publisher":"Springer Nature","file_date_updated":"2022-12-20T23:30:08Z","volume":13,"file":[{"creator":"fkarimip","checksum":"0a8961416a9bb2be5a1cebda65468bcf","content_type":"application/pdf","file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","relation":"main_file","embargo":"2022-11-12","file_id":"10279","date_updated":"2022-12-20T23:30:08Z","access_level":"open_access","file_size":1634958,"date_created":"2021-11-12T19:38:05Z"}],"status":"public","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31."},{"issue":"6","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1912.02342"}],"publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"type":"journal_article","quality_controlled":"1","citation":{"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>.","ista":"Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 41(6), 803–813.","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>","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>","short":"J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.","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>."},"article_type":"original","publisher":"Springer Nature","article_processing_charge":"No","_id":"15275","author":[{"first_name":"Jacob","last_name":"Fox","full_name":"Fox, Jacob"},{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"first_name":"Andrew","last_name":"Suk","full_name":"Suk, Andrew"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"20","year":"2021","date_published":"2021-11-20T00:00:00Z","arxiv":1,"status":"public","volume":41,"month":"11","publication":"Combinatorica","page":"803-813","date_created":"2024-04-03T07:59:57Z","oa":1,"intvolume":"        41","date_updated":"2024-04-09T10:40:08Z","publication_status":"published","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1007/s00493-021-4530-9","abstract":[{"lang":"eng","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."}],"title":"Bounded VC-dimension implies the Schur-Erdős conjecture","external_id":{"arxiv":["1912.02342"]}},{"article_processing_charge":"No","_id":"10071","author":[{"first_name":"Henry","full_name":"Adams, Henry","last_name":"Adams"},{"id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska","full_name":"Kourimska, Hana"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss"},{"last_name":"Percival","full_name":"Percival, Sarah","first_name":"Sarah"},{"last_name":"Ziegelmeier","full_name":"Ziegelmeier, Lori","first_name":"Lori"}],"alternative_title":["Early Career"],"publisher":"American Mathematical Society","date_published":"2021-10-01T00:00:00Z","year":"2021","day":"01","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"volume":68,"status":"public","issue":"9","main_file_link":[{"url":"http://www.ams.org/notices/","open_access":"1"}],"publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"quality_controlled":"1","type":"journal_article","article_type":"letter_note","citation":{"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>.","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>","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.","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>","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.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","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>."},"publication_status":"published","date_updated":"2021-12-03T07:31:26Z","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1090/noti2349","title":"How to tutorial-a-thon","month":"10","date_created":"2021-10-03T22:01:22Z","page":"1511-1514","publication":"Notices of the American Mathematical Society","oa":1,"intvolume":"        68"},{"author":[{"orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","full_name":"Osang, Georg F"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saadatfar","full_name":"Saadatfar, Mohammad","first_name":"Mohammad"}],"_id":"10204","article_processing_charge":"No","publisher":"Royal Society of Chemistry ","day":"20","year":"2021","date_published":"2021-10-20T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"acknowledgement":"MS acknowledges the support by Australian Research Council funding through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour and N. Francois for their input and valuable discussions. 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 and from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","volume":17,"file_date_updated":"2023-10-03T09:21:42Z","file":[{"file_id":"14385","relation":"main_file","content_type":"application/pdf","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","checksum":"b4da0c420530295e61b153960f6cb350","creator":"dernst","success":1,"file_size":4678788,"date_created":"2023-10-03T09:21:42Z","access_level":"open_access","date_updated":"2023-10-03T09:21:42Z"}],"ec_funded":1,"status":"public","issue":"40","publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]},"has_accepted_license":"1","pmid":1,"type":"journal_article","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"article_type":"original","citation":{"mla":"Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” <i>Soft Matter</i>, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:<a href=\"https://doi.org/10.1039/d1sm00774b\">10.1039/d1sm00774b</a>.","chicago":"Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” <i>Soft Matter</i>. Royal Society of Chemistry , 2021. <a href=\"https://doi.org/10.1039/d1sm00774b\">https://doi.org/10.1039/d1sm00774b</a>.","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","apa":"Osang, G. F., Edelsbrunner, H., &#38; Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. <i>Soft Matter</i>. Royal Society of Chemistry . <a href=\"https://doi.org/10.1039/d1sm00774b\">https://doi.org/10.1039/d1sm00774b</a>","ieee":"G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” <i>Soft Matter</i>, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.","ista":"Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115.","ama":"Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. <i>Soft Matter</i>. 2021;17(40):9107-9115. doi:<a href=\"https://doi.org/10.1039/d1sm00774b\">10.1039/d1sm00774b</a>"},"date_updated":"2025-04-15T07:16:52Z","publication_status":"published","scopus_import":"1","oa_version":"Submitted Version","language":[{"iso":"eng"}],"doi":"10.1039/d1sm00774b","external_id":{"isi":["000700090000001"],"pmid":["34569592"]},"abstract":[{"text":"Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.","lang":"eng"}],"title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","ddc":["540"],"isi":1,"month":"10","publication":"Soft Matter","page":"9107-9115","date_created":"2021-10-31T23:01:30Z","oa":1,"intvolume":"        17"},{"file_date_updated":"2023-08-14T11:55:10Z","ec_funded":1,"status":"public","file":[{"relation":"main_file","file_id":"14053","success":1,"creator":"dernst","file_name":"2023_ExperimentalMath_Akopyan.pdf","content_type":"application/pdf","checksum":"3514382e3a1eb87fa6c61ad622874415","file_size":1966019,"date_created":"2023-08-14T11:55:10Z","date_updated":"2023-08-14T11:55:10Z","access_level":"open_access"}],"arxiv":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.\r\nWe are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and for directing us to relevant references. We also thank to Anton Mellit for a useful discussion on Bessel functions.","date_published":"2021-10-25T00:00:00Z","day":"25","year":"2021","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10222","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"}],"publisher":"Taylor and Francis","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” <i>Experimental Mathematics</i>. Taylor and Francis, 2021. <a href=\"https://doi.org/10.1080/10586458.2021.1980459\">https://doi.org/10.1080/10586458.2021.1980459</a>.","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","apa":"Akopyan, A., Edelsbrunner, H., &#38; Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. <i>Experimental Mathematics</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/10586458.2021.1980459\">https://doi.org/10.1080/10586458.2021.1980459</a>","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” <i>Experimental Mathematics</i>. Taylor and Francis, pp. 1–15, 2021.","ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15.","ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. <i>Experimental Mathematics</i>. 2021:1-15. doi:<a href=\"https://doi.org/10.1080/10586458.2021.1980459\">10.1080/10586458.2021.1980459</a>","mla":"Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” <i>Experimental Mathematics</i>, Taylor and Francis, 2021, pp. 1–15, doi:<a href=\"https://doi.org/10.1080/10586458.2021.1980459\">10.1080/10586458.2021.1980459</a>."},"project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","type":"journal_article","has_accepted_license":"1","publication_identifier":{"eissn":["1944-950X"],"issn":["1058-6458"]},"external_id":{"isi":["000710893500001"],"arxiv":["2007.07783"]},"title":"The beauty of random polytopes inscribed in the 2-sphere","abstract":[{"text":"Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density.","lang":"eng"}],"doi":"10.1080/10586458.2021.1980459","language":[{"iso":"eng"}],"oa_version":"Published Version","publication_status":"published","date_updated":"2025-04-15T07:45:32Z","scopus_import":"1","oa":1,"date_created":"2021-11-07T23:01:25Z","publication":"Experimental Mathematics","page":"1-15","corr_author":"1","month":"10","ddc":["510"],"isi":1},{"file":[{"date_updated":"2021-11-29T08:41:00Z","access_level":"open_access","file_size":1227703,"date_created":"2021-11-29T08:41:00Z","creator":"cchlebak","success":1,"checksum":"b14052a025a6ecf675bdfe51db98c0d7","file_name":"2021_ACL_Ilharco.pdf","content_type":"application/pdf","relation":"main_file","file_id":"10368"}],"status":"public","file_date_updated":"2021-11-29T08:41:00Z","conference":{"location":"Bangkok, Thailand","end_date":"2021-08-06","name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing","start_date":"2021-08-01"},"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.","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"year":"2021","day":"01","date_published":"2021-08-01T00:00:00Z","publisher":"Association for Computational Linguistics","author":[{"first_name":"Cesar","last_name":"Ilharco","full_name":"Ilharco, Cesar"},{"full_name":"Shirazi, Afsaneh","last_name":"Shirazi","first_name":"Afsaneh"},{"full_name":"Gopalan, Arjun","last_name":"Gopalan","first_name":"Arjun"},{"last_name":"Nagrani","full_name":"Nagrani, Arsha","first_name":"Arsha"},{"first_name":"Blaž","full_name":"Bratanič, Blaž","last_name":"Bratanič"},{"first_name":"Chris","last_name":"Bregler","full_name":"Bregler, Chris"},{"full_name":"Liu, Christina","last_name":"Liu","first_name":"Christina"},{"first_name":"Felipe","last_name":"Ferreira","full_name":"Ferreira, Felipe"},{"full_name":"Barcik, Gabriek","last_name":"Barcik","first_name":"Gabriek"},{"first_name":"Gabriel","full_name":"Ilharco, Gabriel","last_name":"Ilharco"},{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bulian, Jannis","last_name":"Bulian","first_name":"Jannis"},{"full_name":"Frank, Jared","last_name":"Frank","first_name":"Jared"},{"full_name":"Smaira, Lucas","last_name":"Smaira","first_name":"Lucas"},{"first_name":"Qin","last_name":"Cao","full_name":"Cao, Qin"},{"first_name":"Ricardo","full_name":"Marino, Ricardo","last_name":"Marino"},{"last_name":"Patel","full_name":"Patel, Roma","first_name":"Roma"},{"first_name":"Thomas","full_name":"Leung, Thomas","last_name":"Leung"},{"first_name":"Vaiva","last_name":"Imbrasaite","full_name":"Imbrasaite, Vaiva"}],"_id":"10367","article_processing_charge":"No","citation":{"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>.","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.","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>","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.","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.","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>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","quality_controlled":"1","publication_identifier":{"isbn":["9-781-9540-8557-2"]},"has_accepted_license":"1","main_file_link":[{"open_access":"1","url":"https://aclanthology.org/2021.acl-tutorials.6/"}],"title":"Recognizing multimodal entailment","abstract":[{"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.","lang":"eng"}],"doi":"10.18653/v1/2021.acl-tutorials.6","oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2022-01-26T14:26:36Z","oa":1,"page":"29-30","publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","date_created":"2021-11-28T23:01:30Z","ddc":["000"],"month":"08"},{"has_accepted_license":"1","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","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>","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>.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","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>","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>."},"_id":"7905","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","full_name":"Brown, Adam","last_name":"Brown"},{"first_name":"Bei","full_name":"Wang, Bei","last_name":"Wang"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","date_published":"2021-06-01T00:00:00Z","day":"01","year":"2021","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"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.","arxiv":1,"file_date_updated":"2020-11-25T09:06:41Z","volume":65,"status":"public","file":[{"date_created":"2020-11-25T09:06:41Z","file_size":1013730,"access_level":"open_access","date_updated":"2020-11-25T09:06:41Z","file_id":"8803","relation":"main_file","checksum":"487a84ea5841b75f04f66d7ebd71b67e","content_type":"application/pdf","file_name":"2020_DiscreteCompGeometry_Brown.pdf","success":1,"creator":"dernst"}],"corr_author":"1","month":"06","isi":1,"ddc":["510"],"date_created":"2020-05-30T10:26:04Z","publication":"Discrete and Computational Geometry","page":"1166-1198","oa":1,"intvolume":"        65","publication_status":"published","date_updated":"2025-04-15T06:53:15Z","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1007/s00454-020-00206-y","external_id":{"arxiv":["1712.07734"],"isi":["000536324700001"]},"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"}],"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives"},{"ddc":["510"],"isi":1,"month":"09","corr_author":"1","publication":"Discrete and Computational Geometry","page":"666-686","date_created":"2020-08-11T07:11:51Z","oa":1,"intvolume":"        66","scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:44:05Z","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00233-9","title":"Local conditions for triangulating submanifolds of Euclidean space","abstract":[{"text":"We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.","lang":"eng"}],"external_id":{"isi":["000558119300001"]},"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"has_accepted_license":"1","type":"journal_article","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” <i>Discrete and Computational Geometry</i>, vol. 66, Springer Nature, 2021, pp. 666–86, doi:<a href=\"https://doi.org/10.1007/s00454-020-00233-9\">10.1007/s00454-020-00233-9</a>.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. <i>Discrete and Computational Geometry</i>. 2021;66:666-686. doi:<a href=\"https://doi.org/10.1007/s00454-020-00233-9\">10.1007/s00454-020-00233-9</a>","ista":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 66, 666–686.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., &#38; Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00233-9\">https://doi.org/10.1007/s00454-020-00233-9</a>","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” <i>Discrete and Computational Geometry</i>, vol. 66. Springer Nature, pp. 666–686, 2021.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00233-9\">https://doi.org/10.1007/s00454-020-00233-9</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","publisher":"Springer Nature","author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Dyer","full_name":"Dyer, Ramsay","first_name":"Ramsay"},{"last_name":"Ghosh","full_name":"Ghosh, Arijit","first_name":"Arijit"},{"first_name":"Andre","full_name":"Lieutier, Andre","last_name":"Lieutier"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"_id":"8248","article_processing_charge":"Yes (via OA deal)","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"year":"2021","day":"01","date_published":"2021-09-01T00:00:00Z","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India.\r\nThis work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","ec_funded":1,"status":"public","volume":66},{"isi":1,"month":"10","page":"938-976","publication":"Discrete and Computational Geometry","date_created":"2020-09-06T22:01:13Z","oa":1,"intvolume":"        66","scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:48:36Z","oa_version":"Preprint","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00240-w","abstract":[{"lang":"eng","text":"Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory."}],"title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1908.00856"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"type":"journal_article","quality_controlled":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. 2021;66:938-976. doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>","ista":"Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 66, 938–976.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>.","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” <i>Discrete and Computational Geometry</i>, vol. 66. Springer Nature, pp. 938–976, 2021.","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., &#38; Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>, vol. 66, Springer Nature, 2021, pp. 938–76, doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>."},"article_type":"original","publisher":"Springer Nature","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Alexander I.","full_name":"Bobenko, Alexander I.","last_name":"Bobenko"},{"first_name":"Wolfgang K.","full_name":"Schief, Wolfgang K.","last_name":"Schief"},{"last_name":"Techter","full_name":"Techter, Jan","first_name":"Jan"}],"_id":"8338","article_processing_charge":"No","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"year":"2021","day":"01","date_published":"2021-10-01T00:00:00Z","acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by the Australian Research Council (DP1401000851). A.V.A. was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha).","arxiv":1,"status":"public","ec_funded":1,"volume":66},{"doi":"10.1090/proc/15205","abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"title":"Contravariant forms on Whittaker modules","external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:43:50Z","oa_version":"Preprint","language":[{"iso":"eng"}],"oa":1,"intvolume":"       149","isi":1,"month":"01","publication":"Proceedings of the American Mathematical Society","page":"37-52","date_created":"2020-11-19T10:17:40Z","arxiv":1,"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","ec_funded":1,"status":"public","volume":149,"publisher":"American Mathematical Society","author":[{"full_name":"Brown, Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"_id":"8773","article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2021","day":"01","date_published":"2021-01-01T00:00:00Z","type":"journal_article","quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>.","apa":"Brown, A., &#38; Romanov, A. (2021). Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. 2021;149(1):37-52. doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52."},"article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"issue":"1","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"keyword":["Applied Mathematics","General Mathematics"]},{"acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","ec_funded":1,"status":"public","file":[{"relation":"main_file","file_id":"9795","success":1,"creator":"kschuh","checksum":"c848986091e56699dc12de85adb1e39c","content_type":"application/pdf","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","file_size":983307,"date_created":"2021-08-06T09:52:29Z","date_updated":"2021-08-06T09:52:29Z","access_level":"open_access"}],"volume":66,"file_date_updated":"2021-08-06T09:52:29Z","publisher":"Springer Nature","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"_id":"8940","article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"date_published":"2021-07-01T00:00:00Z","year":"2021","day":"01","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","type":"journal_article","citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00250-8\">https://doi.org/10.1007/s00454-020-00250-8</a>.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete &#38; Computational Geometry 66 (2021) 386–434.","apa":"Boissonnat, J.-D., Kachanovich, S., &#38; Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00250-8\">https://doi.org/10.1007/s00454-020-00250-8</a>","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. <i>Discrete &#38; Computational Geometry</i>. 2021;66(1):386-434. doi:<a href=\"https://doi.org/10.1007/s00454-020-00250-8\">10.1007/s00454-020-00250-8</a>","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete &#38; Computational Geometry. 66(1), 386–434.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” <i>Discrete &#38; Computational Geometry</i>, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:<a href=\"https://doi.org/10.1007/s00454-020-00250-8\">10.1007/s00454-020-00250-8</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","issue":"1","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"has_accepted_license":"1","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"doi":"10.1007/s00454-020-00250-8","title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","abstract":[{"text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.","lang":"eng"}],"external_id":{"isi":["000597770300001"]},"scopus_import":"1","date_updated":"2025-04-14T07:43:50Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"intvolume":"        66","month":"07","ddc":["516"],"isi":1,"corr_author":"1","date_created":"2020-12-12T11:07:02Z","page":"386-434","publication":"Discrete & Computational Geometry"},{"page":"99-140","publication":"Journal of Applied and Computational Topology","date_created":"2021-02-11T14:41:02Z","ddc":["510"],"month":"03","intvolume":"         5","oa":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:43:51Z","abstract":[{"lang":"eng","text":"We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data."}],"title":"Probabilistic convergence and stability of random mapper graphs","external_id":{"arxiv":["1909.03488"]},"doi":"10.1007/s41468-020-00063-x","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"has_accepted_license":"1","issue":"1","citation":{"ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. <i>Journal of Applied and Computational Topology</i>. 2021;5(1):99-140. doi:<a href=\"https://doi.org/10.1007/s41468-020-00063-x\">10.1007/s41468-020-00063-x</a>","ista":"Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140.","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” <i>Journal of Applied and Computational Topology</i>, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.","apa":"Brown, A., Bobrowski, O., Munch, E., &#38; Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-020-00063-x\">https://doi.org/10.1007/s41468-020-00063-x</a>","chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s41468-020-00063-x\">https://doi.org/10.1007/s41468-020-00063-x</a>.","short":"A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140.","mla":"Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” <i>Journal of Applied and Computational Topology</i>, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:<a href=\"https://doi.org/10.1007/s41468-020-00063-x\">10.1007/s41468-020-00063-x</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"day":"01","year":"2021","date_published":"2021-03-01T00:00:00Z","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","_id":"9111","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Bobrowski","full_name":"Bobrowski, Omer","first_name":"Omer"},{"full_name":"Munch, Elizabeth","last_name":"Munch","first_name":"Elizabeth"},{"first_name":"Bei","full_name":"Wang, Bei","last_name":"Wang"}],"file":[{"file_id":"9112","relation":"main_file","content_type":"application/pdf","file_name":"2020_JourApplCompTopology_Brown.pdf","checksum":"3f02e9d47c428484733da0f588a3c069","creator":"dernst","success":1,"date_created":"2021-02-11T14:43:59Z","file_size":2090265,"access_level":"open_access","date_updated":"2021-02-11T14:43:59Z"}],"ec_funded":1,"status":"public","volume":5,"file_date_updated":"2021-02-11T14:43:59Z","arxiv":1,"acknowledgement":"AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria)."},{"year":"2021","day":"19","date_published":"2021-03-19T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"article_processing_charge":"No","_id":"9253","author":[{"first_name":"Georg","last_name":"Heiler","full_name":"Heiler, Georg"},{"last_name":"Reisch","full_name":"Reisch, Tobias","first_name":"Tobias"},{"full_name":"Hurt, Jan","last_name":"Hurt","first_name":"Jan"},{"first_name":"Mohammad","last_name":"Forghani","full_name":"Forghani, Mohammad"},{"last_name":"Omani","full_name":"Omani, Aida","first_name":"Aida"},{"first_name":"Allan","full_name":"Hanbury, Allan","last_name":"Hanbury"},{"full_name":"Karimipour, Farid","last_name":"Karimipour","first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","orcid":"0000-0001-6746-4174"}],"publisher":"IEEE","status":"public","conference":{"start_date":"2020-12-10","name":"Big Data: International Conference on Big Data","location":"Atlanta, GA, United States","end_date":"2020-12-13"},"arxiv":1,"publication_identifier":{"isbn":["9781728162515"]},"main_file_link":[{"url":"https://arxiv.org/abs/2008.10064","open_access":"1"}],"citation":{"mla":"Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” <i>2020 IEEE International Conference on Big Data</i>, IEEE, 2021, pp. 3123–32, doi:<a href=\"https://doi.org/10.1109/bigdata50022.2020.9378374\">10.1109/bigdata50022.2020.9378374</a>.","ama":"Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: <i>2020 IEEE International Conference on Big Data</i>. IEEE; 2021:3123-3132. doi:<a href=\"https://doi.org/10.1109/bigdata50022.2020.9378374\">10.1109/bigdata50022.2020.9378374</a>","ista":"Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F. 2021. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. 2020 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3123–3132.","short":"G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour, in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132.","chicago":"Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani, Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In <i>2020 IEEE International Conference on Big Data</i>, 3123–32. IEEE, 2021. <a href=\"https://doi.org/10.1109/bigdata50022.2020.9378374\">https://doi.org/10.1109/bigdata50022.2020.9378374</a>.","apa":"Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., &#38; Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In <i>2020 IEEE International Conference on Big Data</i> (pp. 3123–3132). Atlanta, GA, United States: IEEE. <a href=\"https://doi.org/10.1109/bigdata50022.2020.9378374\">https://doi.org/10.1109/bigdata50022.2020.9378374</a>","ieee":"G. Heiler <i>et al.</i>, “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in <i>2020 IEEE International Conference on Big Data</i>, Atlanta, GA, United States, 2021, pp. 3123–3132."},"type":"conference","quality_controlled":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-08-07T14:00:13Z","scopus_import":"1","external_id":{"isi":["000662554703032"],"arxiv":["2008.10064"]},"title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","abstract":[{"lang":"eng","text":"In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics."}],"doi":"10.1109/bigdata50022.2020.9378374","publication":"2020 IEEE International Conference on Big Data","page":"3123-3132","date_created":"2021-03-21T11:34:07Z","isi":1,"month":"03","oa":1},{"oa":1,"intvolume":"        65","month":"03","isi":1,"ddc":["516"],"corr_author":"1","date_created":"2021-04-11T22:01:15Z","publication":"Discrete and Computational Geometry","page":"1296–1313","doi":"10.1007/s00454-021-00281-9","abstract":[{"text":"Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.","lang":"eng"}],"title":"The multi-cover persistence of Euclidean balls","external_id":{"isi":["000635460400001"],"pmid":["34720303"]},"scopus_import":"1","publication_status":"published","date_updated":"2025-06-12T06:36:54Z","language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","type":"journal_article","pmid":1,"citation":{"ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. <i>Discrete and Computational Geometry</i>. 2021;65:1296–1313. doi:<a href=\"https://doi.org/10.1007/s00454-021-00281-9\">10.1007/s00454-021-00281-9</a>","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","apa":"Edelsbrunner, H., &#38; Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-021-00281-9\">https://doi.org/10.1007/s00454-021-00281-9</a>","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” <i>Discrete and Computational Geometry</i>, vol. 65. Springer Nature, pp. 1296–1313, 2021.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-021-00281-9\">https://doi.org/10.1007/s00454-021-00281-9</a>.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” <i>Discrete and Computational Geometry</i>, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:<a href=\"https://doi.org/10.1007/s00454-021-00281-9\">10.1007/s00454-021-00281-9</a>."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"187"}]},"has_accepted_license":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria).","ec_funded":1,"status":"public","file":[{"file_id":"10394","relation":"main_file","content_type":"application/pdf","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","checksum":"59b4e1e827e494209bcb4aae22e1d347","success":1,"creator":"cchlebak","file_size":677704,"date_created":"2021-12-01T10:56:53Z","access_level":"open_access","date_updated":"2021-12-01T10:56:53Z"}],"volume":65,"file_date_updated":"2021-12-01T10:56:53Z","publisher":"Springer Nature","_id":"9317","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Osang, Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","orcid":"0000-0002-8882-5116"}],"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-03-31T00:00:00Z","year":"2021","day":"31"},{"scopus_import":"1","date_updated":"2025-04-15T07:09:18Z","publication_status":"published","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.4230/LIPIcs.SoCG.2021.17","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","month":"06","ddc":["005","516","514"],"date_created":"2021-06-02T10:10:55Z","page":"17:1-17:16","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","oa":1,"intvolume":"       189","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"9441","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","department":[{"_id":"HeEd"}],"place":"Dagstuhl, Germany","date_published":"2021-06-02T00:00:00Z","day":"02","year":"2021","acknowledgement":"We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge the reviewers.","conference":{"location":"Virtual","end_date":"2021-06-11","name":"SoCG: Symposium on Computational Geometry","start_date":"2021-06-07"},"status":"public","ec_funded":1,"file":[{"relation":"main_file","file_id":"9442","creator":"mwintrae","success":1,"content_type":"application/pdf","file_name":"LIPIcs-SoCG-2021-17.pdf","checksum":"c322aa48d5d35a35877896cc565705b6","date_created":"2021-06-02T10:22:33Z","file_size":1972902,"date_updated":"2021-06-02T10:22:33Z","access_level":"open_access"}],"file_date_updated":"2021-06-02T10:22:33Z","volume":189,"related_material":{"record":[{"status":"public","relation":"later_version","id":"12960"}]},"has_accepted_license":"1","publication_identifier":{"isbn":["978-3-95977-184-9"],"issn":["1868-8969"]},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","type":"conference","citation":{"ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,” in <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, Virtual, 2021, vol. 189, p. 17:1-17:16.","apa":"Boissonnat, J.-D., Kachanovich, S., &#38; Wintraecken, M. (2021). Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i> (Vol. 189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.17\">https://doi.org/10.4230/LIPIcs.SoCG.2021.17</a>","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” In <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, 189:17:1-17:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.17\">https://doi.org/10.4230/LIPIcs.SoCG.2021.17</a>.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs), LIPIcs, vol. 189, 17:1-17:16.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>. Vol 189. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.17\">10.4230/LIPIcs.SoCG.2021.17</a>","mla":"Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” <i>37th International Symposium on Computational Geometry (SoCG 2021)</i>, vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 17:1-17:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.17\">10.4230/LIPIcs.SoCG.2021.17</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"}},{"_id":"9465","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton"},{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","year":"2021","day":"01","date_published":"2021-04-01T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":112,"file_date_updated":"2021-06-11T13:16:26Z","file":[{"creator":"kschuh","success":1,"content_type":"application/pdf","checksum":"e52a832f1def52a2b23d21bcc09e646f","file_name":"2021_Geometry_Edelsbrunner.pdf","relation":"main_file","file_id":"9544","date_updated":"2021-06-11T13:16:26Z","access_level":"open_access","file_size":694706,"date_created":"2021-06-11T13:16:26Z"}],"status":"public","issue":"1","article_number":"15","publication_identifier":{"issn":["0047-2468"],"eissn":["1420-8997"]},"has_accepted_license":"1","type":"journal_article","quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"mla":"Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” <i>Journal of Geometry</i>, vol. 112, no. 1, 15, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00022-021-00577-4\">10.1007/s00022-021-00577-4</a>.","short":"H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” <i>Journal of Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00022-021-00577-4\">https://doi.org/10.1007/s00022-021-00577-4</a>.","ieee":"H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” <i>Journal of Geometry</i>, vol. 112, no. 1. Springer Nature, 2021.","apa":"Edelsbrunner, H., Nikitenko, A., &#38; Osang, G. F. (2021). A step in the Delaunay mosaic of order k. <i>Journal of Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00022-021-00577-4\">https://doi.org/10.1007/s00022-021-00577-4</a>","ista":"Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15.","ama":"Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. <i>Journal of Geometry</i>. 2021;112(1). doi:<a href=\"https://doi.org/10.1007/s00022-021-00577-4\">10.1007/s00022-021-00577-4</a>"},"date_updated":"2025-07-10T12:01:46Z","publication_status":"published","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1007/s00022-021-00577-4","abstract":[{"lang":"eng","text":"Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space."}],"title":"A step in the Delaunay mosaic of order k","corr_author":"1","ddc":["510"],"month":"04","publication":"Journal of Geometry","date_created":"2021-06-06T22:01:29Z","oa":1,"intvolume":"       112"},{"month":"06","isi":1,"ddc":["510"],"corr_author":"1","date_created":"2021-06-27T22:01:47Z","page":"21-37","publication":"Journal of Combinatorial Theory. Series B","oa":1,"intvolume":"       151","scopus_import":"1","date_updated":"2025-04-15T07:16:52Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1016/j.jctb.2021.05.004","title":"Erdős-Hajnal-type results for monotone paths","abstract":[{"lang":"eng","text":"An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees."}],"external_id":{"isi":["000702280800002"]},"has_accepted_license":"1","publication_identifier":{"issn":["0095-8956"]},"project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"quality_controlled":"1","type":"journal_article","citation":{"mla":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” <i>Journal of Combinatorial Theory. Series B</i>, vol. 151, Elsevier, 2021, pp. 21–37, doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.05.004\">10.1016/j.jctb.2021.05.004</a>.","ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37.","ama":"Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. <i>Journal of Combinatorial Theory Series B</i>. 2021;151:21-37. doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.05.004\">10.1016/j.jctb.2021.05.004</a>","chicago":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” <i>Journal of Combinatorial Theory. Series B</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jctb.2021.05.004\">https://doi.org/10.1016/j.jctb.2021.05.004</a>.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","apa":"Pach, J., &#38; Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. <i>Journal of Combinatorial Theory. Series B</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jctb.2021.05.004\">https://doi.org/10.1016/j.jctb.2021.05.004</a>","ieee":"J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” <i>Journal of Combinatorial Theory. Series B</i>, vol. 151. Elsevier, pp. 21–37, 2021."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publisher":"Elsevier","author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"István","full_name":"Tomon, István","last_name":"Tomon"}],"_id":"9602","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"date_published":"2021-06-09T00:00:00Z","year":"2021","day":"09","acknowledgement":"We would like to thank the anonymous referees for their useful comments and suggestions. János Pach is partially supported by Austrian Science Fund (FWF) grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially supported by Swiss National Science Foundation grant no. 200021_196965, and thanks the support of MIPT Moscow. Both authors are partially supported by The Russian Government in the framework of MegaGrant no. 075-15-2019-1926.","status":"public","file":[{"relation":"main_file","file_id":"9612","success":1,"creator":"asandaue","checksum":"15fbc9064cd9d1c777ac0043b78c8f12","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","content_type":"application/pdf","date_created":"2021-06-28T13:33:23Z","file_size":418168,"date_updated":"2021-06-28T13:33:23Z","access_level":"open_access"}],"file_date_updated":"2021-06-28T13:33:23Z","volume":151}]