[{"place":"Cham","alternative_title":["LNCS"],"type":"book_editor","abstract":[{"text":"This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks.","lang":"eng"}],"department":[{"_id":"HeEd"}],"editor":[{"full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","first_name":"Farid"},{"full_name":"Storandt, Sabine","first_name":"Sabine","last_name":"Storandt"}],"intvolume":" 13238","publisher":"Springer Nature","publication_status":"published","title":"Web and Wireless Geographical Information Systems","status":"public","year":"2022","_id":"11429","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":13238,"oa_version":"None","date_updated":"2022-06-02T05:56:22Z","date_created":"2022-06-02T05:40:53Z","edition":"1","article_processing_charge":"No","publication_identifier":{"issn":["0302-9743"],"eisbn":["9783031062452"],"eissn":["1611-3349"],"isbn":["9783031062445"]},"day":"01","month":"05","page":"153","quality_controlled":"1","citation":{"ama":"Karimipour F, Storandt S, eds. Web and Wireless Geographical Information Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2","apa":"Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2","ieee":"F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.","ista":"Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.","short":"F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022.","mla":"Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2.","chicago":"Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2."},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-031-06245-2","date_published":"2022-05-01T00:00:00Z"},{"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2102.11397"}],"oa":1,"external_id":{"arxiv":["2102.11397"]},"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"quality_controlled":"1","doi":"10.1007/978-3-030-95519-9_1","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"month":"01","acknowledgement":"This project started during the Women in Computational Topology workshop held in Canberra in July of 2019. All authors are very grateful for its organisation and the financial support for the workshop from the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics. AG is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860. VR was supported by Australian Research Council Future Fellowship FT140100604 during the early stages of this project.","year":"2022","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"editor":[{"full_name":"Gasparovic, Ellen","last_name":"Gasparovic","first_name":"Ellen"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"},{"full_name":"Turner, Katharine","last_name":"Turner","first_name":"Katharine"}],"publication_status":"published","edition":"1","author":[{"full_name":"Bleile, Bea","first_name":"Bea","last_name":"Bleile"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"full_name":"Robins, Vanessa","first_name":"Vanessa","last_name":"Robins"}],"volume":30,"date_created":"2022-06-07T08:21:11Z","date_updated":"2022-06-07T08:32:42Z","place":"Cham","ec_funded":1,"citation":{"chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In Research in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.","mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” Research in Computational Topology 2, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.","short":"B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.","ista":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology of dual digital image constructions. In: Research in Computational Topology 2. Association for Women in Mathematics Series, vol. 30, 1–26.","ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in Research in Computational Topology 2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1","ama":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:10.1007/978-3-030-95519-9_1"},"publication":"Research in Computational Topology 2","page":"1-26","date_published":"2022-01-27T00:00:00Z","scopus_import":"1","series_title":"AWMS","article_processing_charge":"No","day":"27","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11440","intvolume":" 30","title":"The persistent homology of dual digital image constructions","status":"public","oa_version":"Preprint","type":"book_chapter","alternative_title":["Association for Women in Mathematics Series"],"abstract":[{"text":"To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.","lang":"eng"}]},{"oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12307","title":"Tangible topology through the lens of limits","status":"public","intvolume":" 32","abstract":[{"lang":"eng","text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences."}],"issue":"5","type":"journal_article","date_published":"2022-05-28T00:00:00Z","publication":"PRIMUS","citation":{"chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750.","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.","apa":"Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750"},"article_type":"original","page":"593-609","day":"28","article_processing_charge":"No","scopus_import":"1","keyword":["Education","General Mathematics"],"author":[{"last_name":"Shipman","first_name":"Barbara A.","full_name":"Shipman, Barbara A."},{"full_name":"Stephenson, Elizabeth R","last_name":"Stephenson","first_name":"Elizabeth R","orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2023-01-16T10:07:21Z","date_updated":"2023-01-30T13:02:30Z","volume":32,"year":"2022","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Taylor & Francis","doi":"10.1080/10511970.2021.1872750","language":[{"iso":"eng"}],"quality_controlled":"1","month":"05","publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]}},{"type":"journal_article","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."}],"issue":"2","status":"public","ddc":["000"],"title":"On compatible matchings","intvolume":" 26","_id":"11938","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","file_id":"11940","date_created":"2022-08-22T06:42:42Z","date_updated":"2022-08-22T06:42:42Z","checksum":"dc6e255e3558faff924fd9e370886c11","success":1,"file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","access_level":"open_access","content_type":"application/pdf","file_size":694538,"creator":"dernst"}],"oa_version":"Published Version","scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1","article_type":"original","page":"225-240","publication":"Journal of Graph Algorithms and Applications","citation":{"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.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240."},"date_published":"2022-06-01T00:00:00Z","license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2022-08-22T06:42:42Z","ec_funded":1,"publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"publisher":"Brown University","year":"2022","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).","date_created":"2022-08-21T22:01:56Z","date_updated":"2023-02-23T13:54:21Z","volume":26,"author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara","first_name":"Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Masárová, Zuzana","first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"full_name":"Pilz, Alexander","last_name":"Pilz","first_name":"Alexander"},{"first_name":"Josef","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9296"}]},"month":"06","publication_identifier":{"issn":["1526-1719"]},"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Game Theory"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2101.03928"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.7155/jgaa.00591"},{"date_published":"2022-01-01T00:00:00Z","article_type":"original","page":"967-1012","publication":"Foundations of Computational Mathematics ","citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics , vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0.","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22 (2022) 967–1012.","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics . Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012. doi:10.1007/s10208-021-09520-0","ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . Springer Nature. https://doi.org/10.1007/s10208-021-09520-0","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer Nature, pp. 967–1012, 2022."},"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","oa_version":"Published Version","file":[{"checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","date_updated":"2021-07-14T06:44:36Z","date_created":"2021-07-14T06:44:36Z","relation":"main_file","file_id":"9650","file_size":1455699,"content_type":"application/pdf","creator":"mwintrae","access_level":"open_access","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf"}],"ddc":["516"],"title":"The topological correctness of PL approximations of isomanifolds","status":"public","intvolume":" 22","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9649","abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently\r\nfine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10208-021-09520-0","quality_controlled":"1","isi":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"external_id":{"isi":["000673039600001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"month":"0","publication_identifier":{"eissn":["1615-3383"]},"date_updated":"2023-08-02T06:49:17Z","date_created":"2021-07-14T06:44:53Z","volume":22,"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"7952","relation":"earlier_version","status":"public"}]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2022","acknowledgement":"First and foremost, we acknowledge Siargey Kachanovich for discussions. We thank Herbert Edelsbrunner and all members of his group, all former and current members of the Datashape team (formerly known as Geometrica), and André Lieutier for encouragement. We further thank the reviewers of Foundations of Computational Mathematics and the reviewers and program committee of the Symposium on Computational Geometry for their feedback, which improved the exposition.\r\nThis work was funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). This work was also supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411.","file_date_updated":"2021-07-14T06:44:36Z","ec_funded":1},{"quality_controlled":"1","isi":1,"external_id":{"isi":["000791838800012"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.topol.2021.107916","month":"03","publication_identifier":{"issn":["0166-8641"]},"publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","year":"2022","date_updated":"2023-08-02T13:33:24Z","date_created":"2021-12-05T23:01:44Z","volume":309,"author":[{"full_name":"Dikranjan, Dikran","last_name":"Dikranjan","first_name":"Dikran"},{"last_name":"Giordano Bruno","first_name":"Anna","full_name":"Giordano Bruno, Anna"},{"full_name":"Künzi, Hans Peter","last_name":"Künzi","first_name":"Hans Peter"},{"full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"},{"full_name":"Toller, Daniele","first_name":"Daniele","last_name":"Toller"}],"article_number":"107916","article_type":"original","publication":"Topology and its Applications","citation":{"ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier, 2022.","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D. (2022). Generalized quasi-metric semilattices. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2021.107916","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916."},"date_published":"2022-03-15T00:00:00Z","scopus_import":"1","day":"15","article_processing_charge":"No","title":"Generalized quasi-metric semilattices","status":"public","intvolume":" 309","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10413","oa_version":"None","type":"journal_article","abstract":[{"text":"Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces.","lang":"eng"}]},{"_id":"10773","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 67","ddc":["510"],"status":"public","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","file":[{"access_level":"open_access","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","creator":"dernst","file_size":2518111,"content_type":"application/pdf","file_id":"11718","relation":"main_file","success":1,"checksum":"9383d3b70561bacee905e335dc922680","date_updated":"2022-08-02T06:07:55Z","date_created":"2022-08-02T06:07:55Z"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function."}],"citation":{"mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry, vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00371-2.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00371-2","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842, 2022."},"publication":"Discrete and Computational Geometry","page":"811-842","article_type":"original","date_published":"2022-04-01T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","year":"2022","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita"},{"full_name":"Cultrera Di Montesano, Sebastiano","first_name":"Sebastiano","last_name":"Cultrera Di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"volume":67,"date_updated":"2023-08-02T14:31:25Z","date_created":"2022-02-20T23:01:34Z","file_date_updated":"2022-08-02T06:07:55Z","external_id":{"isi":["000752175300002"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","doi":"10.1007/s00454-022-00371-2","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"04"},{"isi":1,"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"language":[{"iso":"eng"}],"doi":"10.1109/BigData52589.2021.9671483","conference":{"name":"Big Data: International Conference on Big Data","end_date":"2021-12-18","start_date":"2021-12-15","location":"Orlando, FL, United States; Virtuell"},"publication_identifier":{"isbn":["9781665439022"]},"month":"01","publisher":"IEEE","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2022","date_updated":"2023-08-02T14:44:21Z","date_created":"2022-03-06T23:01:53Z","author":[{"orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa","full_name":"Heiss, Teresa"},{"first_name":"Sarah","last_name":"Tymochko","full_name":"Tymochko, Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"full_name":"Garin, Adélie","last_name":"Garin","first_name":"Adélie"},{"full_name":"Bui, Hoa","first_name":"Hoa","last_name":"Bui"},{"first_name":"Bea","last_name":"Bleile","full_name":"Bleile, Bea"},{"full_name":"Robins, Vanessa","first_name":"Vanessa","last_name":"Robins"}],"page":"3824-3834","citation":{"ama":"Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: 2021 IEEE International Conference on Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483","apa":"Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483","ieee":"T. Heiss et al., “The impact of changes in resolution on the persistent homology of images,” in 2021 IEEE International Conference on Big Data, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.","ista":"Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The impact of changes in resolution on the persistent homology of images. 2021 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3824–3834.","short":"T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins, in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.","mla":"Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483.","chicago":"Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent Homology of Images.” In 2021 IEEE International Conference on Big Data, 3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483."},"publication":"2021 IEEE International Conference on Big Data","date_published":"2022-01-13T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"13","title":"The impact of changes in resolution on the persistent homology of images","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10828","oa_version":"Preprint","type":"conference","abstract":[{"text":"Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.","lang":"eng"}]},{"date_published":"2022-11-01T00:00:00Z","page":"145-179","article_type":"original","citation":{"ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","apa":"Brown, A., & Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017.","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017."},"publication":"Journal of Algebra","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","keyword":["Algebra and Number Theory"],"scopus_import":"1","oa_version":"Published Version","file":[{"checksum":"82abaee3d7837f703e499a9ecbb25b7c","success":1,"date_created":"2023-02-02T07:32:48Z","date_updated":"2023-02-02T07:32:48Z","relation":"main_file","file_id":"12473","content_type":"application/pdf","file_size":582962,"creator":"dernst","access_level":"open_access","file_name":"2022_JournalAlgebra_Brown.pdf"}],"intvolume":" 609","status":"public","title":"Contravariant pairings between standard Whittaker modules and Verma modules","ddc":["510"],"_id":"11545","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"11","abstract":[{"text":"We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N .","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2022.06.017","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000861841100004"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"issn":["0021-8693"]},"month":"11","volume":609,"date_created":"2022-07-08T11:40:07Z","date_updated":"2023-08-03T11:56:30Z","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Romanov","first_name":"Anna","full_name":"Romanov, Anna"}],"department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","acknowledgement":"We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579.","year":"2022","ec_funded":1,"file_date_updated":"2023-02-02T07:32:48Z"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"10754","status":"public","title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","ddc":["510","576"],"intvolume":" 23","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2022_IJMS_Chang.pdf","file_size":24416183,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"10756","checksum":"8890ad20c54e90dc58ad5ea97c902998","success":1,"date_created":"2022-02-14T07:46:30Z","date_updated":"2022-02-14T07:46:30Z"}],"type":"journal_article","abstract":[{"text":"Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs.","lang":"eng"}],"issue":"3","publication":"International Journal of Molecular Sciences","citation":{"ista":"Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 23(3), 1763.","ieee":"Y. Chang et al., “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” International Journal of Molecular Sciences, vol. 23, no. 3. MDPI, 2022.","apa":"Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V., … Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763","ama":"Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3). doi:10.3390/ijms23031763","chicago":"Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi, Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.","mla":"Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23, no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763.","short":"Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B. Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022)."},"article_type":"original","date_published":"2022-02-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes","has_accepted_license":"1","year":"2022","acknowledgement":"This work was partially supported by grants from National Institutes of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary Research Program (to B.C., H.V.K. and Z.P.). ","publication_status":"published","publisher":"MDPI","department":[{"_id":"HeEd"}],"author":[{"full_name":"Chang, Yan","first_name":"Yan","last_name":"Chang"},{"full_name":"Funk, Marah","last_name":"Funk","first_name":"Marah"},{"full_name":"Roy, Souvik","first_name":"Souvik","last_name":"Roy"},{"orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson","first_name":"Elizabeth R","full_name":"Stephenson, Elizabeth R"},{"first_name":"Sangyong","last_name":"Choi","full_name":"Choi, Sangyong"},{"first_name":"Hristo V.","last_name":"Kojouharov","full_name":"Kojouharov, Hristo V."},{"last_name":"Chen","first_name":"Benito","full_name":"Chen, Benito"},{"last_name":"Pan","first_name":"Zui","full_name":"Pan, Zui"}],"date_updated":"2023-08-09T10:17:07Z","date_created":"2022-02-13T23:01:35Z","volume":23,"article_number":"1763","file_date_updated":"2022-02-14T07:46:30Z","external_id":{"isi":["000754773500001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"doi":"10.3390/ijms23031763","language":[{"iso":"eng"}],"month":"02","publication_identifier":{"issn":["16616596"],"eissn":["14220067"]}},{"doi":"10.1007/s40879-020-00405-0","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1912.12685"]},"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"month":"12","publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"date_created":"2020-05-03T22:00:48Z","date_updated":"2024-02-22T15:58:42Z","volume":8,"year":"2022","acknowledgement":"AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:48:03Z","ec_funded":1,"date_published":"2022-12-01T00:00:00Z","publication":"European Journal of Mathematics","citation":{"ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312.","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","apa":"Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0","mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics. Springer Nature, 2022. https://doi.org/10.1007/s40879-020-00405-0."},"article_type":"original","page":"1309 - 1312","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","file":[{"creator":"dernst","content_type":"application/pdf","file_size":263926,"file_name":"2020_EuropMathematics_Akopyan.pdf","access_level":"open_access","date_created":"2020-05-04T10:33:42Z","date_updated":"2020-07-14T12:48:03Z","checksum":"f53e71fd03744075adcd0b8fc1b8423d","file_id":"7796","relation":"main_file"}],"oa_version":"Published Version","_id":"7791","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"When different norms lead to same billiard trajectories?","intvolume":" 8","abstract":[{"lang":"eng","text":"Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law."}],"issue":"4","type":"journal_article"},{"publication":"LIPIcs","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “A Window to the Persistence of 1D Maps. 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I: Geometric characterization of critical point pairs. LIPIcs.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs."},"date_published":"2022-07-25T00:00:00Z","day":"25","has_accepted_license":"1","article_processing_charge":"No","status":"public","ddc":["510"],"title":"A window to the persistence of 1D maps. 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Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. "}],"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"The Wittgenstein Prize"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"month":"07","publication_status":"submitted","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2022","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. ","date_updated":"2024-03-20T09:36:56Z","date_created":"2022-07-27T09:31:15Z","author":[{"last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita"},{"full_name":"Cultrera di Montesano, Sebastiano","first_name":"Sebastiano","last_name":"Cultrera di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian"}],"related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"file_date_updated":"2022-07-27T09:30:30Z","ec_funded":1},{"publication":"Leibniz International Proceedings on Mathematics","citation":{"apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik, n.d.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics, Schloss Dagstuhl - Leibniz Zentrum für Informatik."},"date_published":"2022-07-27T00:00:00Z","day":"27","article_processing_charge":"No","has_accepted_license":"1","_id":"11658","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","ddc":["510"],"status":"public","oa_version":"Submitted Version","file":[{"checksum":"b2f511e8b1cae5f1892b0cdec341acac","date_created":"2022-07-27T09:25:53Z","date_updated":"2022-07-27T09:25:53Z","file_id":"11659","relation":"main_file","creator":"scultrer","file_size":639266,"content_type":"application/pdf","access_level":"open_access","file_name":"D-S-E.pdf"}],"type":"journal_article","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."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"language":[{"iso":"eng"}],"month":"07","year":"2022","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_status":"submitted","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"15094"}]},"date_created":"2022-07-27T09:27:34Z","date_updated":"2024-03-20T09:36:56Z","file_date_updated":"2022-07-27T09:25:53Z","ec_funded":1},{"type":"preprint","article_number":"2212.03121","ec_funded":1,"abstract":[{"lang":"eng","text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications."}],"department":[{"_id":"HeEd"}],"title":"On the size of chromatic Delaunay mosaics","publication_status":"submitted","status":"public","_id":"15090","year":"2022","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Preprint","date_created":"2024-03-08T09:54:20Z","date_updated":"2024-03-20T09:36:56Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"15094"}]},"author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita"},{"last_name":"Cultrera di Montesano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","last_name":"Draganov","first_name":"Ondrej","full_name":"Draganov, Ondrej"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"article_processing_charge":"No","month":"12","day":"06","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, n.d.","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, 2212.03121.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. .","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03121"}],"external_id":{"arxiv":["2212.03121"]},"oa":1,"publication":"arXiv","language":[{"iso":"eng"}],"date_published":"2022-12-06T00:00:00Z"},{"month":"05","publication_identifier":{"eissn":["1868-5145"],"issn":["1868-5137"]},"language":[{"iso":"eng"}],"doi":"10.1007/s12652-021-03569-z","isi":1,"quality_controlled":"1","project":[{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"external_id":{"isi":["000712198000001"]},"oa":1,"file_date_updated":"2022-12-20T23:30:08Z","date_created":"2021-11-02T09:28:55Z","date_updated":"2023-08-02T13:31:48Z","volume":13,"author":[{"last_name":"Goudarzi","first_name":"Samira","full_name":"Goudarzi, Samira"},{"first_name":"Mohammad","last_name":"Sharif","full_name":"Sharif, Mohammad"},{"full_name":"Karimipour, Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","orcid":"0000-0001-6746-4174","first_name":"Farid","last_name":"Karimipour"}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2022","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","day":"01","article_processing_charge":"No","has_accepted_license":"1","keyword":["general computer science"],"scopus_import":"1","date_published":"2022-05-01T00:00:00Z","article_type":"original","page":"2621–2635","publication":"Journal of Ambient Intelligence and Humanized Computing","citation":{"chicago":"Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing. Springer Nature, 2022. https://doi.org/10.1007/s12652-021-03569-z.","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:10.1007/s12652-021-03569-z.","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","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.","apa":"Goudarzi, S., Sharif, M., & Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z","ieee":"S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” Journal of Ambient Intelligence and Humanized Computing, vol. 13. Springer Nature, pp. 2621–2635, 2022.","ama":"Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z"},"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."}],"type":"journal_article","file":[{"content_type":"application/pdf","file_size":1634958,"creator":"fkarimip","file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","access_level":"open_access","date_updated":"2022-12-20T23:30:08Z","date_created":"2021-11-12T19:38:05Z","checksum":"0a8961416a9bb2be5a1cebda65468bcf","relation":"main_file","file_id":"10279","embargo":"2022-11-12"}],"oa_version":"Submitted Version","status":"public","ddc":["000"],"title":"A context-aware dimension reduction framework for trajectory and health signal analyses","intvolume":" 13","_id":"10208","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"month":"10","publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"doi":"10.1090/noti2349","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"http://www.ams.org/notices/","open_access":"1"}],"quality_controlled":"1","author":[{"full_name":"Adams, Henry","first_name":"Henry","last_name":"Adams"},{"id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska","full_name":"Kourimska, Hana"},{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"first_name":"Sarah","last_name":"Percival","full_name":"Percival, Sarah"},{"last_name":"Ziegelmeier","first_name":"Lori","full_name":"Ziegelmeier, Lori"}],"date_updated":"2021-12-03T07:31:26Z","date_created":"2021-10-03T22:01:22Z","volume":68,"year":"2021","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2021-10-01T00:00:00Z","publication":"Notices of the American Mathematical Society","citation":{"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.","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021.","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021). How to tutorial-a-thon. Notices of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/noti2349","ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.","mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:10.1090/noti2349.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514."},"article_type":"letter_note","page":"1511-1514","issue":"9","type":"journal_article","alternative_title":["Early Career"],"oa_version":"Published Version","_id":"10071","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","title":"How to tutorial-a-thon","intvolume":" 68"},{"_id":"10367","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Recognizing multimodal entailment","status":"public","ddc":["000"],"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"10368","date_created":"2021-11-29T08:41:00Z","date_updated":"2021-11-29T08:41:00Z","checksum":"b14052a025a6ecf675bdfe51db98c0d7","success":1,"file_name":"2021_ACL_Ilharco.pdf","access_level":"open_access","content_type":"application/pdf","file_size":1227703,"creator":"cchlebak"}],"type":"conference","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"}],"publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","citation":{"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.","apa":"Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6","ieee":"C. Ilharco et al., “Recognizing multimodal entailment,” in 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok, Thailand, 2021, pp. 29–30.","ama":"Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6","chicago":"Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30. Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6.","mla":"Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6.","short":"C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler, C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L. Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30."},"page":"29-30","date_published":"2021-08-01T00:00:00Z","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"No","year":"2021","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.","publication_status":"published","department":[{"_id":"HeEd"}],"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"},{"first_name":"Arjun","last_name":"Gopalan","full_name":"Gopalan, Arjun"},{"full_name":"Nagrani, Arsha","last_name":"Nagrani","first_name":"Arsha"},{"last_name":"Bratanič","first_name":"Blaž","full_name":"Bratanič, Blaž"},{"first_name":"Chris","last_name":"Bregler","full_name":"Bregler, Chris"},{"full_name":"Liu, Christina","first_name":"Christina","last_name":"Liu"},{"full_name":"Ferreira, Felipe","last_name":"Ferreira","first_name":"Felipe"},{"first_name":"Gabriek","last_name":"Barcik","full_name":"Barcik, Gabriek"},{"last_name":"Ilharco","first_name":"Gabriel","full_name":"Ilharco, Gabriel"},{"last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"},{"full_name":"Bulian, Jannis","last_name":"Bulian","first_name":"Jannis"},{"full_name":"Frank, Jared","last_name":"Frank","first_name":"Jared"},{"last_name":"Smaira","first_name":"Lucas","full_name":"Smaira, Lucas"},{"last_name":"Cao","first_name":"Qin","full_name":"Cao, Qin"},{"full_name":"Marino, Ricardo","last_name":"Marino","first_name":"Ricardo"},{"full_name":"Patel, Roma","last_name":"Patel","first_name":"Roma"},{"first_name":"Thomas","last_name":"Leung","full_name":"Leung, Thomas"},{"full_name":"Imbrasaite, Vaiva","first_name":"Vaiva","last_name":"Imbrasaite"}],"date_updated":"2022-01-26T14:26:36Z","date_created":"2021-11-28T23:01:30Z","file_date_updated":"2021-11-29T08:41:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"main_file_link":[{"open_access":"1","url":"https://aclanthology.org/2021.acl-tutorials.6/"}],"oa":1,"quality_controlled":"1","conference":{"name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing","start_date":"2021-08-01","location":"Bangkok, Thailand","end_date":"2021-08-06"},"doi":"10.18653/v1/2021.acl-tutorials.6","language":[{"iso":"eng"}],"month":"08","publication_identifier":{"isbn":["9-781-9540-8557-2"]}},{"doi":"10.1007/s40879-021-00515-3","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","month":"12","publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"author":[{"full_name":"Weighill, Thomas","last_name":"Weighill","first_name":"Thomas"},{"last_name":"Yamauchi","first_name":"Takamitsu","full_name":"Yamauchi, Takamitsu"},{"full_name":"Zava, Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","last_name":"Zava","first_name":"Nicolò"}],"date_created":"2022-01-09T23:01:27Z","date_updated":"2022-01-10T08:36:55Z","acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria).","year":"2021","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"file_date_updated":"2022-01-10T08:33:22Z","date_published":"2021-12-30T00:00:00Z","publication":"European Journal of Mathematics","citation":{"ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” European Journal of Mathematics. Springer Nature, 2021.","apa":"Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-021-00515-3","ista":"Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021, doi:10.1007/s40879-021-00515-3.","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3."},"article_type":"original","day":"30","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","file":[{"access_level":"open_access","file_name":"2021_EuJournalMath_Weighill.pdf","creator":"cchlebak","file_size":384908,"content_type":"application/pdf","file_id":"10610","relation":"main_file","success":1,"checksum":"c435dcfa1ad3aadc5cdd7366bc7f4e98","date_updated":"2022-01-10T08:33:22Z","date_created":"2022-01-10T08:33:22Z"}],"oa_version":"Published Version","_id":"10608","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","ddc":["500"],"abstract":[{"text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.","lang":"eng"}],"type":"journal_article"},{"month":"02","publication_identifier":{"issn":["03029743"],"isbn":["9783030682101"],"eissn":["16113349"]},"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"call_identifier":"FWF","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407"}],"external_id":{"arxiv":["2101.03928"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"language":[{"iso":"eng"}],"conference":{"end_date":"2021-03-02","location":"Yangon, Myanmar","start_date":"2021-02-28","name":"WALCOM: Algorithms and Computation"},"doi":"10.1007/978-3-030-68211-8_18","ec_funded":1,"publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"publisher":"Springer Nature","year":"2021","acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","date_updated":"2023-02-21T16:33:44Z","date_created":"2021-03-28T22:01:41Z","volume":12635,"author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2401-8670","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"last_name":"Parada","first_name":"Irene","full_name":"Parada, Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"full_name":"Tkadlec, Josef","last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"related_material":{"record":[{"id":"11938","relation":"later_version","status":"public"}]},"scopus_import":"1","day":"16","article_processing_charge":"No","page":"221-233","publication":"15th International Conference on Algorithms and Computation","citation":{"short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233."},"date_published":"2021-02-16T00:00:00Z","alternative_title":["LNCS"],"type":"conference","abstract":[{"lang":"eng","text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge."}],"title":"On compatible matchings","status":"public","intvolume":" 12635","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9296","oa_version":"Preprint"},{"oa_version":"Published Version","file":[{"file_id":"9544","relation":"main_file","date_updated":"2021-06-11T13:16:26Z","date_created":"2021-06-11T13:16:26Z","success":1,"checksum":"e52a832f1def52a2b23d21bcc09e646f","file_name":"2021_Geometry_Edelsbrunner.pdf","access_level":"open_access","creator":"kschuh","content_type":"application/pdf","file_size":694706}],"_id":"9465","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 112","ddc":["510"],"title":"A step in the Delaunay mosaic of order k","status":"public","issue":"1","abstract":[{"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.","lang":"eng"}],"type":"journal_article","date_published":"2021-04-01T00:00:00Z","citation":{"short":"H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).","mla":"Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4.","ama":"Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4","ieee":"H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.","apa":"Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4","ista":"Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15."},"publication":"Journal of Geometry","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko"},{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"}],"volume":112,"date_updated":"2022-05-12T11:41:45Z","date_created":"2021-06-06T22:01:29Z","year":"2021","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","file_date_updated":"2021-06-11T13:16:26Z","article_number":"15","doi":"10.1007/s00022-021-00577-4","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","publication_identifier":{"eissn":["14208997"],"issn":["00472468"]},"month":"04"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"25C5A090-B435-11E9-9278-68D0E5697425","grant_number":"Z00312"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2021.32","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Virtual"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"]},"month":"06","acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","year":"2021","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa"},{"first_name":"Vitaliy","last_name":" Kurlin ","full_name":" Kurlin , Vitaliy"},{"first_name":"Philip","last_name":"Smith","full_name":"Smith, Philip"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"volume":189,"date_updated":"2023-02-23T13:55:40Z","date_created":"2021-04-22T08:09:58Z","ec_funded":1,"file_date_updated":"2021-04-22T08:08:14Z","citation":{"ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16."},"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"32:1-32:16","date_published":"2021-06-02T00:00:00Z","has_accepted_license":"1","article_processing_charge":"No","day":"02","_id":"9345","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 189","title":"The density fingerprint of a periodic point set","status":"public","ddc":["004","516"],"oa_version":"Published Version","file":[{"date_created":"2021-04-22T08:08:14Z","date_updated":"2021-04-22T08:08:14Z","checksum":"1787baef1523d6d93753b90d0c109a6d","success":1,"relation":"main_file","file_id":"9346","content_type":"application/pdf","file_size":3117435,"creator":"mwintrae","file_name":"df_socg_final_version.pdf","access_level":"open_access"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction."}]},{"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"year":"2021","date_updated":"2023-02-23T14:02:28Z","date_created":"2021-06-27T22:01:48Z","volume":189,"author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"article_number":"16","file_date_updated":"2021-06-28T13:11:39Z","ec_funded":1,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"conference":{"name":"SoCG: International Symposium on Computational Geometry","end_date":"2021-06-11","start_date":"2021-06-07","location":"Online"},"doi":"10.4230/LIPIcs.SoCG.2021.16","month":"06","publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"status":"public","title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","ddc":["516"],"intvolume":" 189","_id":"9604","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"9611","checksum":"22b11a719018b22ecba2471b51f2eb40","success":1,"date_updated":"2021-06-28T13:11:39Z","date_created":"2021-06-28T13:11:39Z","access_level":"open_access","file_name":"2021_LIPIcs_Biswas.pdf","file_size":727817,"content_type":"application/pdf","creator":"asandaue"}],"alternative_title":["LIPIcs"],"type":"conference","abstract":[{"lang":"eng","text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation."}],"publication":"Leibniz International Proceedings in Informatics","citation":{"ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16."},"date_published":"2021-06-02T00:00:00Z","scopus_import":"1","day":"02","has_accepted_license":"1","article_processing_charge":"No"},{"acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","year":"2021","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"full_name":"Čomić, Lidija","first_name":"Lidija","last_name":"Čomić"},{"full_name":"Zrour, Rita","first_name":"Rita","last_name":"Zrour"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"date_created":"2021-08-08T22:01:29Z","date_updated":"2022-05-31T06:58:21Z","volume":12708,"ec_funded":1,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"conference":{"end_date":"2021-05-27","location":"Uppsala, Sweden","start_date":"2021-05-24","name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology"},"doi":"10.1007/978-3-030-76657-3_10","language":[{"iso":"eng"}],"month":"05","publication_identifier":{"issn":["03029743"],"isbn":["9783030766566"],"eissn":["16113349"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9824","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","status":"public","intvolume":" 12708","oa_version":"None","type":"conference","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain."}],"publication":"Discrete Geometry and Mathematical Morphology","citation":{"short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163."},"page":"152-163","date_published":"2021-05-16T00:00:00Z","scopus_import":"1","day":"16","article_processing_charge":"No"},{"intvolume":" 93","status":"public","title":"Folding polyominoes with holes into a cube","_id":"8317","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.","lang":"eng"}],"article_type":"original","citation":{"ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700."},"publication":"Computational Geometry: Theory and Applications","date_published":"2021-02-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2021","acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","volume":93,"date_created":"2020-08-30T22:01:09Z","date_updated":"2023-08-04T10:57:42Z","related_material":{"record":[{"id":"6989","relation":"shorter_version","status":"public"}]},"author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"full_name":"Akitaya, Hugo A.","last_name":"Akitaya","first_name":"Hugo A."},{"full_name":"Cheung, Kenneth C.","first_name":"Kenneth C.","last_name":"Cheung"},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"last_name":"Demaine","first_name":"Martin L.","full_name":"Demaine, Martin L."},{"first_name":"Sándor P.","last_name":"Fekete","full_name":"Fekete, Sándor P."},{"full_name":"Kleist, Linda","last_name":"Kleist","first_name":"Linda"},{"last_name":"Kostitsyna","first_name":"Irina","full_name":"Kostitsyna, Irina"},{"last_name":"Löffler","first_name":"Maarten","full_name":"Löffler, Maarten"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"article_number":"101700","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2020.101700","publication_identifier":{"issn":["09257721"]},"month":"02"},{"oa_version":"Preprint","_id":"8773","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Contravariant forms on Whittaker modules","intvolume":" 149","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."}],"issue":"1","type":"journal_article","date_published":"2021-01-01T00:00:00Z","publication":"Proceedings of the American Mathematical Society","citation":{"ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52."},"article_type":"original","page":"37-52","day":"01","article_processing_charge":"No","keyword":["Applied Mathematics","General Mathematics"],"author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam"},{"last_name":"Romanov","first_name":"Anna","full_name":"Romanov, Anna"}],"date_updated":"2023-08-04T11:11:47Z","date_created":"2020-11-19T10:17:40Z","volume":149,"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.","year":"2021","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","ec_funded":1,"doi":"10.1090/proc/15205","language":[{"iso":"eng"}],"external_id":{"arxiv":["1910.08286"],"isi":["000600416300004"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.08286"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"month":"01","publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]}},{"author":[{"full_name":"Heiler, Georg","last_name":"Heiler","first_name":"Georg"},{"last_name":"Reisch","first_name":"Tobias","full_name":"Reisch, Tobias"},{"full_name":"Hurt, Jan","first_name":"Jan","last_name":"Hurt"},{"full_name":"Forghani, Mohammad","first_name":"Mohammad","last_name":"Forghani"},{"full_name":"Omani, Aida","first_name":"Aida","last_name":"Omani"},{"last_name":"Hanbury","first_name":"Allan","full_name":"Hanbury, Allan"},{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","orcid":"0000-0001-6746-4174","first_name":"Farid","last_name":"Karimipour","full_name":"Karimipour, Farid"}],"date_updated":"2023-08-07T14:00:13Z","date_created":"2021-03-21T11:34:07Z","year":"2021","publisher":"IEEE","department":[{"_id":"HeEd"}],"publication_status":"published","publication_identifier":{"isbn":["9781728162515"]},"month":"03","doi":"10.1109/bigdata50022.2020.9378374","conference":{"name":"Big Data: International Conference on Big Data","end_date":"2020-12-13","start_date":"2020-12-10","location":"Atlanta, GA, United States"},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.10064"}],"external_id":{"arxiv":["2008.10064"],"isi":["000662554703032"]},"oa":1,"quality_controlled":"1","isi":1,"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."}],"type":"conference","oa_version":"Preprint","_id":"9253","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","status":"public","article_processing_charge":"No","day":"19","scopus_import":"1","date_published":"2021-03-19T00:00:00Z","citation":{"ama":"Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374","apa":"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. In 2020 IEEE International Conference on Big Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374","ieee":"G. Heiler et al., “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in 2020 IEEE International Conference on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132.","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.","mla":"Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.","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 2020 IEEE International Conference on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374."},"publication":"2020 IEEE International Conference on Big Data","page":"3123-3132"},{"publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2021","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).","volume":65,"date_updated":"2023-08-07T14:35:44Z","date_created":"2021-04-11T22:01:15Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"187"}]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"}],"ec_funded":1,"file_date_updated":"2021-12-01T10:56:53Z","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000635460400001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00454-021-00281-9","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"03","intvolume":" 65","ddc":["516"],"title":"The multi-cover persistence of Euclidean balls","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9317","file":[{"file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","access_level":"open_access","creator":"cchlebak","file_size":677704,"content_type":"application/pdf","file_id":"10394","relation":"main_file","date_created":"2021-12-01T10:56:53Z","date_updated":"2021-12-01T10:56:53Z","success":1,"checksum":"59b4e1e827e494209bcb4aae22e1d347"}],"oa_version":"Published Version","type":"journal_article","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"}],"page":"1296–1313","article_type":"original","citation":{"ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1296–1313, 2021.","apa":"Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00281-9","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00281-9.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313."},"publication":"Discrete and Computational Geometry","date_published":"2021-03-31T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"31"},{"volume":151,"date_updated":"2023-08-10T13:38:00Z","date_created":"2021-06-27T22:01:47Z","author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","first_name":"János","full_name":"Pach, János"},{"full_name":"Tomon, István","first_name":"István","last_name":"Tomon"}],"publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","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.","year":"2021","file_date_updated":"2021-06-28T13:33:23Z","language":[{"iso":"eng"}],"doi":"10.1016/j.jctb.2021.05.004","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"quality_controlled":"1","isi":1,"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000702280800002"]},"publication_identifier":{"issn":["0095-8956"]},"month":"06","oa_version":"Published Version","file":[{"file_size":418168,"content_type":"application/pdf","creator":"asandaue","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","access_level":"open_access","date_updated":"2021-06-28T13:33:23Z","date_created":"2021-06-28T13:33:23Z","checksum":"15fbc9064cd9d1c777ac0043b78c8f12","success":1,"relation":"main_file","file_id":"9612"}],"intvolume":" 151","title":"Erdős-Hajnal-type results for monotone paths","ddc":["510"],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9602","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."}],"type":"journal_article","date_published":"2021-06-09T00:00:00Z","page":"21-37","article_type":"original","citation":{"chicago":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","mla":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp. 21–37, doi:10.1016/j.jctb.2021.05.004.","apa":"Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004","ieee":"J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.","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. Journal of Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004"},"publication":"Journal of Combinatorial Theory. Series B","has_accepted_license":"1","article_processing_charge":"No","day":"09","scopus_import":"1"},{"type":"journal_article","issue":"7","abstract":[{"text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.","lang":"eng"}],"intvolume":" 16","ddc":["006"],"status":"public","title":"Persistent homology as a new method of the assessment of heart rate variability","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9821","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"9832","date_updated":"2021-08-09T09:25:41Z","date_created":"2021-08-09T09:25:41Z","checksum":"0277aa155d5db1febd2cb384768bba5f","success":1,"file_name":"2021_PLoSONE_Graff.pdf","access_level":"open_access","content_type":"application/pdf","file_size":2706919,"creator":"asandaue"}],"scopus_import":"1","article_processing_charge":"Yes","has_accepted_license":"1","day":"01","article_type":"original","citation":{"ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 2021;16(7). doi:10.1371/journal.pone.0253851","ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851","ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:10.1371/journal.pone.0253851.","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science, 2021. https://doi.org/10.1371/journal.pone.0253851."},"publication":"PLoS ONE","date_published":"2021-07-01T00:00:00Z","article_number":"e0253851","file_date_updated":"2021-08-09T09:25:41Z","publisher":"Public Library of Science","department":[{"_id":"HeEd"}],"publication_status":"published","pmid":1,"acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","year":"2021","volume":16,"date_updated":"2023-08-10T14:21:42Z","date_created":"2021-08-08T22:01:28Z","author":[{"first_name":"Grzegorz","last_name":"Graff","full_name":"Graff, Grzegorz"},{"last_name":"Graff","first_name":"Beata","full_name":"Graff, Beata"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","first_name":"Pawel","full_name":"Pilarczyk, Pawel"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","last_name":"Jablonski","full_name":"Jablonski, Grzegorz"},{"first_name":"Dariusz","last_name":"Gąsecki","full_name":"Gąsecki, Dariusz"},{"last_name":"Narkiewicz","first_name":"Krzysztof","full_name":"Narkiewicz, Krzysztof"}],"publication_identifier":{"eissn":["19326203"]},"month":"07","quality_controlled":"1","isi":1,"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000678124900050"],"pmid":["34292957"]},"language":[{"iso":"eng"}],"doi":"10.1371/journal.pone.0253851"},{"citation":{"ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459","ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15.","apa":"Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2021.1980459","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis, pp. 1–15, 2021.","mla":"Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459.","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics. Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459."},"publication":"Experimental Mathematics","page":"1-15","article_type":"original","date_published":"2021-10-25T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"25","_id":"10222","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The beauty of random polytopes inscribed in the 2-sphere","status":"public","ddc":["510"],"oa_version":"Published Version","file":[{"file_size":1966019,"content_type":"application/pdf","creator":"dernst","file_name":"2023_ExperimentalMath_Akopyan.pdf","access_level":"open_access","date_updated":"2023-08-14T11:55:10Z","date_created":"2023-08-14T11:55:10Z","checksum":"3514382e3a1eb87fa6c61ad622874415","success":1,"relation":"main_file","file_id":"14053"}],"type":"journal_article","abstract":[{"lang":"eng","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."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000710893500001"],"arxiv":["2007.07783"]},"oa":1,"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"isi":1,"quality_controlled":"1","doi":"10.1080/10586458.2021.1980459","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"month":"10","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.","year":"2021","department":[{"_id":"HeEd"}],"publisher":"Taylor and Francis","publication_status":"published","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Nikitenko","first_name":"Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"}],"date_created":"2021-11-07T23:01:25Z","date_updated":"2023-08-14T11:57:07Z","ec_funded":1,"file_date_updated":"2023-08-14T11:55:10Z"},{"doi":"10.1007/s00454-020-00250-8","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000597770300001"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"month":"07","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"last_name":"Kachanovich","first_name":"Siargey","full_name":"Kachanovich, Siargey"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"date_created":"2020-12-12T11:07:02Z","date_updated":"2023-09-05T15:02:40Z","volume":66,"year":"2021","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).","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"file_date_updated":"2021-08-06T09:52:29Z","ec_funded":1,"date_published":"2021-07-01T00:00:00Z","publication":"Discrete & Computational Geometry","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8"},"article_type":"original","page":"386-434","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"file":[{"access_level":"open_access","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","creator":"kschuh","file_size":983307,"content_type":"application/pdf","file_id":"9795","relation":"main_file","success":1,"checksum":"c848986091e56699dc12de85adb1e39c","date_updated":"2021-08-06T09:52:29Z","date_created":"2021-08-06T09:52:29Z"}],"oa_version":"Published Version","_id":"8940","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["516"],"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","status":"public","intvolume":" 66","abstract":[{"lang":"eng","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."}],"issue":"1","type":"journal_article"},{"month":"03","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"external_id":{"arxiv":["1909.03488"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"doi":"10.1007/s41468-020-00063-x","language":[{"iso":"eng"}],"file_date_updated":"2021-02-11T14:43:59Z","ec_funded":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","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam"},{"full_name":"Bobrowski, Omer","first_name":"Omer","last_name":"Bobrowski"},{"full_name":"Munch, Elizabeth","last_name":"Munch","first_name":"Elizabeth"},{"full_name":"Wang, Bei","last_name":"Wang","first_name":"Bei"}],"date_updated":"2023-09-05T15:37:56Z","date_created":"2021-02-11T14:41:02Z","volume":5,"scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publication":"Journal of Applied and Computational Topology","citation":{"apa":"Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.","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.","ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x","chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.","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.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x."},"article_type":"original","page":"99-140","date_published":"2021-03-01T00:00:00Z","type":"journal_article","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."}],"issue":"1","_id":"9111","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Probabilistic convergence and stability of random mapper graphs","ddc":["510"],"status":"public","intvolume":" 5","oa_version":"Published Version","file":[{"success":1,"checksum":"3f02e9d47c428484733da0f588a3c069","date_updated":"2021-02-11T14:43:59Z","date_created":"2021-02-11T14:43:59Z","file_id":"9112","relation":"main_file","creator":"dernst","file_size":2090265,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_JourApplCompTopology_Brown.pdf"}]},{"type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.","lang":"eng"}],"_id":"9056","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Multi-cover persistence and Delaunay mosaics","ddc":["006","514","516"],"file":[{"access_level":"closed","file_name":"thesis_source.zip","creator":"patrickd","content_type":"application/zip","file_size":13446994,"file_id":"9063","relation":"source_file","checksum":"bcf27986147cab0533b6abadd74e7629","date_created":"2021-02-02T14:09:25Z","date_updated":"2021-02-03T10:37:28Z"},{"success":1,"checksum":"9cc8af266579a464385bbe2aff6af606","date_created":"2021-02-02T14:09:18Z","date_updated":"2021-02-02T14:09:18Z","file_id":"9064","relation":"main_file","creator":"patrickd","file_size":5210329,"content_type":"application/pdf","access_level":"open_access","file_name":"thesis_pdfA2b.pdf"}],"oa_version":"Published Version","day":"01","article_processing_charge":"No","has_accepted_license":"1","citation":{"ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056."},"page":"134","date_published":"2021-02-01T00:00:00Z","place":"Klosterneuburg","file_date_updated":"2021-02-03T10:37:28Z","year":"2021","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Institute of Science and Technology Austria","author":[{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116"}],"related_material":{"record":[{"id":"187","status":"public","relation":"part_of_dissertation"},{"id":"8703","relation":"part_of_dissertation","status":"public"}]},"date_created":"2021-02-02T14:11:06Z","date_updated":"2023-09-07T13:29:01Z","month":"02","publication_identifier":{"issn":["2663-337X"]},"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"doi":"10.15479/AT:ISTA:9056","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"degree_awarded":"PhD","language":[{"iso":"eng"}]},{"volume":17,"date_updated":"2023-10-03T09:24:27Z","date_created":"2021-10-31T23:01:30Z","author":[{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saadatfar, Mohammad","first_name":"Mohammad","last_name":"Saadatfar"}],"publisher":"Royal Society of Chemistry ","department":[{"_id":"HeEd"}],"publication_status":"published","pmid":1,"year":"2021","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.","ec_funded":1,"file_date_updated":"2023-10-03T09:21:42Z","language":[{"iso":"eng"}],"doi":"10.1039/d1sm00774b","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"external_id":{"pmid":["34569592"],"isi":["000700090000001"]},"oa":1,"publication_identifier":{"issn":["1744-683X"],"eissn":["1744-6848"]},"month":"10","oa_version":"Submitted Version","file":[{"relation":"main_file","file_id":"14385","checksum":"b4da0c420530295e61b153960f6cb350","success":1,"date_created":"2023-10-03T09:21:42Z","date_updated":"2023-10-03T09:21:42Z","access_level":"open_access","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","file_size":4678788,"content_type":"application/pdf","creator":"dernst"}],"intvolume":" 17","ddc":["540"],"status":"public","title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","_id":"10204","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"40","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"}],"type":"journal_article","date_published":"2021-10-20T00:00:00Z","page":"9107-9115","article_type":"original","citation":{"short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","mla":"Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.","chicago":"Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b.","ama":"Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115. doi:10.1039/d1sm00774b","ieee":"G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” Soft Matter, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.","apa":"Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b","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."},"publication":"Soft Matter","article_processing_charge":"No","has_accepted_license":"1","day":"20","scopus_import":"1"},{"month":"06","publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"quality_controlled":"1","external_id":{"arxiv":["2103.07823"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"conference":{"end_date":"2021-06-11","location":"Online","start_date":"2021-06-07","name":"SoCG: International Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2021.27","article_number":"27","file_date_updated":"2021-06-28T12:40:47Z","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","year":"2021","date_created":"2021-06-27T22:01:49Z","date_updated":"2023-10-04T12:03:39Z","volume":189,"author":[{"last_name":"Corbet","first_name":"René","full_name":"Corbet, René"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","first_name":"Georg F","last_name":"Osang","full_name":"Osang, Georg F"}],"related_material":{"link":[{"relation":"extended_version","url":"https://arxiv.org/abs/2103.07823"}],"record":[{"id":"12709","relation":"later_version","status":"public"}]},"scopus_import":"1","day":"02","has_accepted_license":"1","article_processing_charge":"No","publication":"Leibniz International Proceedings in Informatics","citation":{"apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing the multicover bifiltration. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27."},"date_published":"2021-06-02T00:00:00Z","alternative_title":["LIPIcs"],"type":"conference","abstract":[{"lang":"eng","text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. "}],"ddc":["516"],"status":"public","title":"Computing the multicover bifiltration","intvolume":" 189","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","_id":"9605","oa_version":"Published Version","file":[{"creator":"cziletti","content_type":"application/pdf","file_size":"1367983","file_name":"2021_LIPIcs_Corbet.pdf","access_level":"open_access","date_updated":"2021-06-28T12:40:47Z","date_created":"2021-06-28T12:40:47Z","success":1,"checksum":"0de217501e7ba8b267d58deed0d51761","file_id":"9610","relation":"main_file"}]},{"has_accepted_license":"1","article_processing_charge":"No","day":"02","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","date_published":"2021-06-02T00:00:00Z","citation":{"ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 17:1-17:16.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17","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.","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.","mla":"Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17.","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17."},"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"17:1-17:16","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"}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"file_name":"LIPIcs-SoCG-2021-17.pdf","access_level":"open_access","creator":"mwintrae","file_size":1972902,"content_type":"application/pdf","file_id":"9442","relation":"main_file","date_created":"2021-06-02T10:22:33Z","date_updated":"2021-06-02T10:22:33Z","success":1,"checksum":"c322aa48d5d35a35877896cc565705b6"}],"oa_version":"Published Version","_id":"9441","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 189","ddc":["005","516","514"],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","status":"public","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-184-9"]},"month":"06","doi":"10.4230/LIPIcs.SoCG.2021.17","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Virtual","start_date":"2021-06-07","end_date":"2021-06-11"},"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","ec_funded":1,"file_date_updated":"2021-06-02T10:22:33Z","place":"Dagstuhl, Germany","related_material":{"record":[{"id":"12960","status":"public","relation":"later_version"}]},"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"volume":189,"date_updated":"2023-10-10T07:34:34Z","date_created":"2021-06-02T10:10:55Z","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.","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published"},{"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Bobenko","first_name":"Alexander I.","full_name":"Bobenko, Alexander I."},{"full_name":"Schief, Wolfgang K.","first_name":"Wolfgang K.","last_name":"Schief"},{"full_name":"Techter, Jan","first_name":"Jan","last_name":"Techter"}],"date_created":"2020-09-06T22:01:13Z","date_updated":"2024-03-07T14:51:11Z","volume":66,"year":"2021","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).","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"ec_funded":1,"doi":"10.1007/s00454-020-00240-w","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1908.00856","open_access":"1"}],"external_id":{"isi":["000564488500002"],"arxiv":["1908.00856"]},"quality_controlled":"1","isi":1,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"month":"10","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"oa_version":"Preprint","_id":"8338","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","intvolume":" 66","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."}],"type":"journal_article","date_published":"2021-10-01T00:00:00Z","publication":"Discrete and Computational Geometry","citation":{"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.","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.","ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976. doi:10.1007/s00454-020-00240-w","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976."},"article_type":"original","page":"938-976","day":"01","article_processing_charge":"No","scopus_import":"1"},{"isi":1,"quality_controlled":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"oa":1,"external_id":{"isi":["000558119300001"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00233-9","month":"09","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"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.","year":"2021","date_created":"2020-08-11T07:11:51Z","date_updated":"2024-03-07T14:54:59Z","volume":66,"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"full_name":"Ghosh, Arijit","first_name":"Arijit","last_name":"Ghosh"},{"full_name":"Lieutier, Andre","last_name":"Lieutier","first_name":"Andre"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"ec_funded":1,"article_type":"original","page":"666-686","publication":"Discrete and Computational Geometry","citation":{"apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.","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.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9."},"date_published":"2021-09-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","ddc":["510"],"status":"public","title":"Local conditions for triangulating submanifolds of Euclidean space","intvolume":" 66","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"8248","oa_version":"Published Version","type":"journal_article","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"}]},{"abstract":[{"lang":"eng","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."}],"type":"journal_article","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_DiscreteCompGeometry_Brown.pdf","creator":"dernst","content_type":"application/pdf","file_size":1013730,"file_id":"8803","relation":"main_file","success":1,"checksum":"487a84ea5841b75f04f66d7ebd71b67e","date_updated":"2020-11-25T09:06:41Z","date_created":"2020-11-25T09:06:41Z"}],"intvolume":" 65","ddc":["510"],"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"7905","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2021-06-01T00:00:00Z","page":"1166-1198","article_type":"original","citation":{"ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198. doi:10.1007/s00454-020-00206-y","ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1166–1198, 2021.","apa":"Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00206-y","mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y."},"publication":"Discrete and Computational Geometry","file_date_updated":"2020-11-25T09:06:41Z","volume":65,"date_created":"2020-05-30T10:26:04Z","date_updated":"2024-03-07T15:01:58Z","author":[{"full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","last_name":"Brown"},{"full_name":"Wang, Bei","last_name":"Wang","first_name":"Bei"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2021","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.","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00206-y","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000536324700001"],"arxiv":["1712.07734"]}},{"publication_identifier":{"eissn":["1661-8289"],"issn":["1661-8270"]},"month":"03","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"doi":"10.1007/s11786-020-00461-5","ec_funded":1,"file_date_updated":"2020-11-20T10:18:02Z","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2020","volume":14,"date_updated":"2021-01-12T08:14:13Z","date_created":"2020-03-05T13:30:18Z","author":[{"full_name":"Choudhary, Aruni","first_name":"Aruni","last_name":"Choudhary"},{"full_name":"Kachanovich, Siargey","first_name":"Siargey","last_name":"Kachanovich"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","page":"141-176","article_type":"original","citation":{"mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science. Springer Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176.","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” Mathematics in Computer Science, vol. 14. Springer Nature, pp. 141–176, 2020.","apa":"Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5"},"publication":"Mathematics in Computer Science","date_published":"2020-03-01T00:00:00Z","type":"journal_article","abstract":[{"text":"Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space.","lang":"eng"}],"intvolume":" 14","status":"public","ddc":["510"],"title":"Coxeter triangulations have good quality","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"7567","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_MathCompScie_Choudhary.pdf","file_size":872275,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"8783","checksum":"1d145f3ab50ccee735983cb89236e609","success":1,"date_updated":"2020-11-20T10:18:02Z","date_created":"2020-11-20T10:18:02Z"}]},{"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha and No 638176). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","date_updated":"2021-01-12T08:17:06Z","date_created":"2020-07-19T22:00:59Z","volume":15,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"},{"full_name":"Ölsböck, Katharina","first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"},{"id":"331776E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Synak","full_name":"Synak, Peter"}],"file_date_updated":"2020-10-08T08:56:14Z","ec_funded":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"638176","_id":"2533E772-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-43408-3_8","month":"06","publication_identifier":{"isbn":["9783030434076"],"eissn":["21978549"],"issn":["21932808"]},"ddc":["510"],"status":"public","title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","intvolume":" 15","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8135","oa_version":"Submitted Version","file":[{"file_id":"8628","relation":"main_file","date_updated":"2020-10-08T08:56:14Z","date_created":"2020-10-08T08:56:14Z","success":1,"checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":2207071}],"alternative_title":["Abel Symposia"],"type":"conference","abstract":[{"text":"Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results obtained with this new approach, and discusses some of its shortcomings. It uses simulations to illustrate the results and to form conjectures, getting numerical estimates for combinatorial, topological, and geometric properties of weighted and unweighted Delaunay mosaics, their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in the mosaics.","lang":"eng"}],"page":"181-218","publication":"Topological Data Analysis","citation":{"ama":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: Topological Data Analysis. Vol 15. Springer Nature; 2020:181-218. doi:10.1007/978-3-030-43408-3_8","apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In Topological Data Analysis (Vol. 15, pp. 181–218). Springer Nature. https://doi.org/10.1007/978-3-030-43408-3_8","ieee":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in Topological Data Analysis, 2020, vol. 15, pp. 181–218.","ista":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. 2020. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. Topological Data Analysis. , Abel Symposia, vol. 15, 181–218.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” Topological Data Analysis, vol. 15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In Topological Data Analysis, 15:181–218. 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De Gruyter. https://doi.org/10.1515/mathm-2020-0106"},"article_type":"original","page":"143-158","date_published":"2020-11-17T00:00:00Z","type":"journal_article","abstract":[{"text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.","lang":"eng"}],"issue":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9249","status":"public","ddc":["510"],"title":"Digital objects in rhombic dodecahedron grid","intvolume":" 4","file":[{"creator":"dernst","file_size":3668725,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","success":1,"checksum":"4a1043fa0548a725d464017fe2483ce0","date_updated":"2021-03-22T08:56:37Z","date_created":"2021-03-22T08:56:37Z","file_id":"9272","relation":"main_file"}],"oa_version":"Published Version","month":"11","publication_identifier":{"issn":["2353-3390"]},"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"doi":"10.1515/mathm-2020-0106","language":[{"iso":"eng"}],"file_date_updated":"2021-03-22T08:56:37Z","ec_funded":1,"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","year":"2020","publication_status":"published","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"author":[{"first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"last_name":"Largeteau-Skapin","first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"full_name":"Andres, Eric","first_name":"Eric","last_name":"Andres"}],"date_updated":"2021-03-22T09:01:50Z","date_created":"2021-03-16T08:55:19Z","volume":4},{"page":"359-371","citation":{"chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In 28th International Symposium on Graph Drawing and Network Visualization, 12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","ista":"Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.","apa":"Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic edges. In 28th International Symposium on Graph Drawing and Network Visualization (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in 28th International Symposium on Graph Drawing and Network Visualization, Virtual, Online, 2020, vol. 12590, pp. 359–371.","ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th International Symposium on Graph Drawing and Network Visualization. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28"},"publication":"28th International Symposium on Graph Drawing and Network Visualization","date_published":"2020-09-20T00:00:00Z","series_title":"LNCS","scopus_import":"1","article_processing_charge":"No","day":"20","intvolume":" 12590","status":"public","title":"Crossings between non-homotopic edges","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9299","oa_version":"Preprint","type":"conference","abstract":[{"text":"We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ .","lang":"eng"}],"project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.14908"}],"external_id":{"arxiv":["2006.14908"]},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-68766-3_28","conference":{"name":"GD: Graph Drawing and Network Visualization","end_date":"2020-09-18","location":"Virtual, Online","start_date":"2020-09-16"},"publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"month":"09","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2020","acknowledgement":"Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908.","volume":12590,"date_created":"2021-03-28T22:01:44Z","date_updated":"2021-04-06T11:32:32Z","author":[{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach"},{"full_name":"Tardos, Gábor","last_name":"Tardos","first_name":"Gábor"},{"full_name":"Tóth, Géza","first_name":"Géza","last_name":"Tóth"}]},{"type":"journal_article","abstract":[{"lang":"eng","text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"issue":"2","_id":"9630","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","title":"Topological data analysis in information space","ddc":["510","000"],"status":"public","intvolume":" 11","file":[{"file_size":1449234,"content_type":"application/pdf","creator":"asandaue","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","access_level":"open_access","date_created":"2021-08-11T11:55:11Z","date_updated":"2021-08-11T11:55:11Z","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","success":1,"relation":"main_file","file_id":"9882"}],"oa_version":"Published Version","scopus_import":"1","day":"14","article_processing_charge":"Yes","has_accepted_license":"1","publication":"Journal of Computational Geometry","citation":{"mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020."},"article_type":"original","page":"162-182","date_published":"2020-12-14T00:00:00Z","file_date_updated":"2021-08-11T11:55:11Z","license":"https://creativecommons.org/licenses/by/3.0/","year":"2020","acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","publication_status":"published","publisher":"Carleton University","department":[{"_id":"HeEd"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","last_name":"Virk","first_name":"Ziga"},{"first_name":"Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"date_updated":"2021-08-11T12:26:34Z","date_created":"2021-07-04T22:01:26Z","volume":11,"month":"12","publication_identifier":{"eissn":["1920180X"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"}],"doi":"10.20382/jocg.v11i2a7","language":[{"iso":"eng"}]},{"scopus_import":"1","day":"09","article_processing_charge":"No","article_type":"original","publication":"European Journal of Mathematics","citation":{"ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics.","apa":"Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” European Journal of Mathematics. Springer Nature, 2020.","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” European Journal of Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s40879-020-00426-9.","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020)."},"date_published":"2020-09-09T00:00:00Z","type":"journal_article","abstract":[{"text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.","lang":"eng"}],"status":"public","title":"Billiards in ellipses revisited","_id":"8538","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Preprint","month":"09","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2001.02934","open_access":"1"}],"external_id":{"arxiv":["2001.02934"]},"language":[{"iso":"eng"}],"doi":"10.1007/s40879-020-00426-9","ec_funded":1,"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2020","acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","date_created":"2020-09-20T22:01:38Z","date_updated":"2021-12-02T15:10:17Z","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"full_name":"Schwartz, Richard","first_name":"Richard","last_name":"Schwartz"},{"full_name":"Tabachnikov, Serge","first_name":"Serge","last_name":"Tabachnikov"}]},{"file":[{"checksum":"38cbfa4f5d484d267a35d44d210df044","date_updated":"2020-07-14T12:48:06Z","date_created":"2020-06-17T10:13:34Z","file_id":"7969","relation":"main_file","creator":"dernst","file_size":1009739,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf"}],"oa_version":"Published Version","_id":"7952","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 164","ddc":["510"],"status":"public","title":"The topological correctness of PL-approximations of isomanifolds","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary. ","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"date_published":"2020-06-01T00:00:00Z","citation":{"chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.20.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.20.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ista":"Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations of isomanifolds. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.20"},"publication":"36th International Symposium on Computational Geometry","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":"1","related_material":{"record":[{"relation":"later_version","status":"public","id":"9649"}]},"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"volume":164,"date_created":"2020-06-09T07:24:11Z","date_updated":"2023-08-02T06:49:16Z","year":"2020","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:48:06Z","article_number":"20:1-20:18","doi":"10.4230/LIPIcs.SoCG.2020.20","conference":{"end_date":"2020-06-26","location":"Zürich, Switzerland","start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"month":"06"},{"date_published":"2020-06-21T00:00:00Z","publication":"Geometric Aspects of Functional Analysis","citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","apa":"Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1","ista":"Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1"},"page":"1-27","day":"21","article_processing_charge":"No","scopus_import":"1","series_title":"LNM","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"74","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","status":"public","intvolume":" 2256","abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"type":"book_chapter","doi":"10.1007/978-3-030-36020-7_1","language":[{"iso":"eng"}],"external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"oa":1,"quality_controlled":"1","isi":1,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"month":"06","publication_identifier":{"eissn":["16179692"],"isbn":["9783030360191"],"issn":["00758434"],"eisbn":["9783030360207"]},"author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"date_updated":"2023-08-17T13:48:31Z","date_created":"2018-12-11T11:44:29Z","volume":2256,"year":"2020","publication_status":"published","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Springer Nature","editor":[{"last_name":"Klartag","first_name":"Bo'az","full_name":"Klartag, Bo'az"},{"last_name":"Milman","first_name":"Emanuel","full_name":"Milman, Emanuel"}],"ec_funded":1},{"month":"02","publication_identifier":{"eissn":["10957219"],"issn":["0040585X"]},"language":[{"iso":"eng"}],"doi":"10.1137/S0040585X97T989726","quality_controlled":"1","isi":1,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"oa":1,"ec_funded":1,"date_created":"2020-03-01T23:00:39Z","date_updated":"2023-08-18T06:45:48Z","volume":64,"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"SIAM","year":"2020","day":"13","article_processing_charge":"No","scopus_import":"1","date_published":"2020-02-13T00:00:00Z","article_type":"original","page":"595-614","publication":"Theory of Probability and its Applications","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:10.1137/S0040585X97T989726.","apa":"Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726"},"abstract":[{"text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$.","lang":"eng"}],"issue":"4","type":"journal_article","oa_version":"Preprint","status":"public","title":"Weighted Poisson–Delaunay mosaics","intvolume":" 64","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7554"},{"citation":{"ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020.","apa":"Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00188-x","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x."},"publication":"Discrete and Computational Geometry","page":"759-775","article_type":"original","date_published":"2020-03-20T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"20","_id":"7666","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 64","status":"public","title":"Tri-partitions and bases of an ordered complex","ddc":["510"],"oa_version":"Published Version","file":[{"file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","access_level":"open_access","content_type":"application/pdf","file_size":701673,"creator":"dernst","relation":"main_file","file_id":"8786","date_updated":"2020-11-20T13:22:21Z","date_created":"2020-11-20T13:22:21Z","checksum":"f8cc96e497f00c38340b5dafe0cb91d7","success":1}],"type":"journal_article","abstract":[{"text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups.","lang":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000520918800001"]},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00454-020-00188-x","language":[{"iso":"eng"}],"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"month":"03","acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina"}],"volume":64,"date_created":"2020-04-19T22:00:56Z","date_updated":"2023-08-21T06:13:48Z","ec_funded":1,"file_date_updated":"2020-11-20T13:22:21Z"},{"scopus_import":"1","article_processing_charge":"No","day":"05","page":"888-917","article_type":"original","citation":{"apa":"Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” Discrete and Computational Geometry, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","ista":"Pach J, Reed B, Yuditsky Y. 2020. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 63(4), 888–917.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z."},"publication":"Discrete and Computational Geometry","date_published":"2020-06-05T00:00:00Z","type":"journal_article","issue":"4","abstract":[{"text":"A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.","lang":"eng"}],"intvolume":" 63","title":"Almost all string graphs are intersection graphs of plane convex sets","status":"public","_id":"7962","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"month":"06","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00213-z","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2020","volume":63,"date_created":"2020-06-14T22:00:51Z","date_updated":"2023-08-21T08:49:18Z","author":[{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Reed, Bruce","last_name":"Reed","first_name":"Bruce"},{"full_name":"Yuditsky, Yelena","first_name":"Yelena","last_name":"Yuditsky"}]},{"_id":"8323","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 64","title":"A farewell to Ricky Pollack","status":"public","oa_version":"None","type":"journal_article","citation":{"ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5","chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","mla":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5."},"publication":"Discrete and Computational Geometry","page":"571-574","article_type":"letter_note","date_published":"2020-10-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","year":"2020","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","author":[{"full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","first_name":"János"}],"volume":64,"date_updated":"2023-08-22T09:05:04Z","date_created":"2020-08-30T22:01:12Z","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"external_id":{"isi":["000561483500001"]},"isi":1,"doi":"10.1007/s00454-020-00237-5","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"10"},{"abstract":[{"text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.","lang":"eng"}],"type":"conference","article_number":"9158054","oa_version":"None","date_updated":"2023-08-22T09:33:34Z","date_created":"2020-09-28T08:59:27Z","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"last_name":"Graff","first_name":"Beata","full_name":"Graff, Beata"},{"full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866"},{"first_name":"Krzysztof","last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof"}],"publisher":"IEEE","department":[{"_id":"HeEd"}],"status":"public","title":"The application of persistent homology in the analysis of heart rate variability","publication_status":"published","_id":"8580","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2020","publication_identifier":{"isbn":["9781728157511"]},"article_processing_charge":"No","month":"08","day":"01","scopus_import":"1","language":[{"iso":"eng"}],"doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","conference":{"start_date":"2020-07-15","location":"Pisa, Italy","end_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"quality_controlled":"1","isi":1,"external_id":{"isi":["000621172600045"]},"citation":{"ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.","apa":"Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054.","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054."},"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, "},{"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"month":"02","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rny037","isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.07513"}],"external_id":{"arxiv":["1702.07513"],"isi":["000522852700002"]},"oa":1,"volume":2020,"date_updated":"2023-08-24T14:19:55Z","date_created":"2022-03-18T11:39:30Z","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"publisher":"Oxford University Press","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","year":"2020","article_processing_charge":"No","day":"01","keyword":["General Mathematics"],"scopus_import":"1","date_published":"2020-02-01T00:00:00Z","page":"669-697","article_type":"original","citation":{"short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697."},"publication":"International Mathematics Research Notices","issue":"3","abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 2020","title":"Waist of balls in hyperbolic and spherical spaces","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10867"},{"date_published":"2020-02-10T00:00:00Z","citation":{"short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","mla":"Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460.","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria."},"page":"155","has_accepted_license":"1","article_processing_charge":"No","day":"10","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"7461","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","date_updated":"2020-07-14T12:47:58Z","date_created":"2020-02-06T14:43:54Z","access_level":"open_access","file_name":"thesis_ist-final_noack.pdf","content_type":"application/pdf","file_size":76195184,"creator":"koelsboe"},{"checksum":"7a52383c812b0be64d3826546509e5a4","date_updated":"2020-07-14T12:47:58Z","date_created":"2020-02-06T14:52:45Z","file_id":"7462","relation":"source_file","creator":"koelsboe","file_size":122103715,"content_type":"application/x-zip-compressed","access_level":"closed","file_name":"latex-files.zip","description":"latex source files, figures"}],"_id":"7460","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["514"],"title":"The hole system of triangulated shapes","status":"public","abstract":[{"lang":"eng","text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"doi":"10.15479/AT:ISTA:7460","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"oa":1,"publication_identifier":{"issn":["2663-337X"]},"month":"02","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"6608"}]},"author":[{"orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina","full_name":"Ölsböck, Katharina"}],"date_updated":"2023-09-07T13:15:30Z","date_created":"2020-02-06T14:56:53Z","year":"2020","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publication_status":"published","file_date_updated":"2020-07-14T12:47:58Z","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/"},{"oa":1,"tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"doi":"10.15479/AT:ISTA:7944","supervisor":[{"full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"year":"2020","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"author":[{"full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"7950"},{"status":"public","relation":"part_of_dissertation","id":"5986"}]},"date_created":"2020-06-08T00:49:46Z","date_updated":"2023-09-07T13:17:37Z","file_date_updated":"2020-07-14T12:48:05Z","license":"https://creativecommons.org/licenses/by-sa/4.0/","citation":{"mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020."},"page":"160","date_published":"2020-06-09T00:00:00Z","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"day":"09","article_processing_charge":"No","has_accepted_license":"1","_id":"7944","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["516","514"],"title":"Reconfiguration problems","status":"public","file":[{"access_level":"open_access","file_name":"THESIS_Zuzka_Masarova.pdf","creator":"zmasarov","content_type":"application/pdf","file_size":13661779,"file_id":"7945","relation":"main_file","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","date_updated":"2020-07-14T12:48:05Z","date_created":"2020-06-08T00:34:00Z"},{"file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","access_level":"closed","creator":"zmasarov","content_type":"application/zip","file_size":32184006,"file_id":"7946","relation":"source_file","date_created":"2020-06-08T00:35:30Z","date_updated":"2020-07-14T12:48:05Z","checksum":"45341a35b8f5529c74010b7af43ac188"}],"oa_version":"Published Version","type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"lang":"eng","text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars."}]},{"file_date_updated":"2020-10-27T14:31:52Z","ec_funded":1,"article_number":"75","date_updated":"2023-09-07T13:29:00Z","date_created":"2020-10-25T23:01:18Z","volume":173,"author":[{"first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"},{"full_name":"Rouxel-Labbé, Mael","last_name":"Rouxel-Labbé","first_name":"Mael"},{"full_name":"Teillaud, Monique","last_name":"Teillaud","first_name":"Monique"}],"related_material":{"record":[{"id":"9056","status":"public","relation":"dissertation_contains"}]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2020","month":"08","publication_identifier":{"issn":["18688969"],"isbn":["9783959771627"]},"language":[{"iso":"eng"}],"conference":{"end_date":"2020-09-09","start_date":"2020-09-07","location":"Virtual, Online; Pisa, Italy","name":"ESA: Annual European Symposium on Algorithms"},"doi":"10.4230/LIPIcs.ESA.2020.75","quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"oa":1,"abstract":[{"text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","oa_version":"Published Version","file":[{"creator":"cziletti","content_type":"application/pdf","file_size":733291,"file_name":"2020_LIPIcs_Osang.pdf","access_level":"open_access","date_created":"2020-10-27T14:31:52Z","date_updated":"2020-10-27T14:31:52Z","success":1,"checksum":"fe0f7c49a99ed870c671b911e10d5496","file_id":"8712","relation":"main_file"}],"ddc":["000"],"status":"public","title":"Generalizing CGAL periodic Delaunay triangulations","intvolume":" 173","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8703","day":"26","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2020-08-26T00:00:00Z","publication":"28th Annual European Symposium on Algorithms","citation":{"chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75.","mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75.","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173.","apa":"Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75","ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75"}},{"year":"2020","acknowledgement":"The authors are greatly indebted to Dror Atariah, Günther Rote and John Sullivan for discussion and suggestions. The authors also thank Jean-Daniel Boissonnat, Ramsay Dyer, David de Laat and Rien van de Weijgaert for discussion. This work has been supported in part by the European Union’s Seventh Framework Programme for Research of the\r\nEuropean Commission, under FET-Open grant number 255827 (CGL Computational Geometry Learning) and ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions), the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement number 754411,and the Austrian Science Fund (FWF): Z00342 N31.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Akadémiai Kiadó","author":[{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs"}],"date_updated":"2023-10-10T13:05:27Z","date_created":"2020-07-24T07:09:18Z","volume":57,"file_date_updated":"2020-07-24T07:09:06Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","external_id":{"isi":["000570978400005"]},"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)"},"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"doi":"10.1556/012.2020.57.2.1454","language":[{"iso":"eng"}],"month":"07","publication_identifier":{"issn":["0081-6906"],"eissn":["1588-2896"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8163","title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","status":"public","ddc":["510"],"intvolume":" 57","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","creator":"mwintrae","content_type":"application/pdf","file_size":1476072,"file_id":"8164","relation":"main_file","date_updated":"2020-07-24T07:09:06Z","date_created":"2020-07-24T07:09:06Z"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces."}],"issue":"2","publication":"Studia Scientiarum Mathematicarum Hungarica","citation":{"chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","ista":"Vegter G, Wintraecken M. 2020. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 57(2), 193–199.","apa":"Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454"},"article_type":"original","page":"193-199","date_published":"2020-07-24T00:00:00Z","scopus_import":"1","day":"24","has_accepted_license":"1","article_processing_charge":"No"},{"publication_identifier":{"issn":["2544-7297"]},"month":"06","doi":"10.1515/cmb-2020-0100","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","ec_funded":1,"file_date_updated":"2021-02-19T13:56:24Z","author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"volume":8,"date_updated":"2023-10-17T12:34:51Z","date_created":"2021-02-17T15:13:01Z","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of the weighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations and for his continued encouragement. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis 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). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","publisher":"De Gruyter","department":[{"_id":"HeEd"}],"publication_status":"published","article_processing_charge":"No","has_accepted_license":"1","day":"20","date_published":"2020-06-20T00:00:00Z","citation":{"ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100."},"publication":"Computational and Mathematical Biophysics","page":"51-67","article_type":"original","issue":"1","abstract":[{"text":"Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_name":"2020_CompMathBiophysics_Akopyan2.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":562359,"file_id":"9171","relation":"main_file","date_updated":"2021-02-19T13:56:24Z","date_created":"2021-02-19T13:56:24Z","success":1,"checksum":"cea41de9937d07a3b927d71ee8b4e432"}],"_id":"9157","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 8","ddc":["510"],"title":"The weighted mean curvature derivative of a space-filling diagram","status":"public"},{"language":[{"iso":"eng"}],"doi":"10.1515/cmb-2020-0101","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1908.06777"]},"publication_identifier":{"issn":["2544-7297"]},"month":"07","volume":8,"date_created":"2021-02-17T15:12:44Z","date_updated":"2023-10-17T12:35:10Z","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"publisher":"De Gruyter","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2020","acknowledgement":"The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis 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). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","ec_funded":1,"file_date_updated":"2021-02-19T13:33:19Z","date_published":"2020-07-21T00:00:00Z","page":"74-88","article_type":"original","citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101"},"publication":"Computational and Mathematical Biophysics","article_processing_charge":"No","has_accepted_license":"1","day":"21","oa_version":"Published Version","file":[{"success":1,"checksum":"ca43a7440834eab6bbea29c59b56ef3a","date_created":"2021-02-19T13:33:19Z","date_updated":"2021-02-19T13:33:19Z","file_id":"9170","relation":"main_file","creator":"dernst","file_size":707452,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_CompMathBiophysics_Akopyan.pdf"}],"intvolume":" 8","ddc":["510"],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","status":"public","_id":"9156","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","abstract":[{"lang":"eng","text":"The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy."}],"type":"journal_article"},{"type":"journal_article","abstract":[{"text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.","lang":"eng"}],"issue":"4","_id":"15064","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Čech-Delaunay gradient flow and homology inference for self-maps","ddc":["500"],"status":"public","intvolume":" 4","oa_version":"Published Version","file":[{"date_updated":"2024-03-04T10:52:42Z","date_created":"2024-03-04T10:52:42Z","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","success":1,"relation":"main_file","file_id":"15065","file_size":851190,"content_type":"application/pdf","creator":"dernst","file_name":"2020_JourApplCompTopology_Bauer.pdf","access_level":"open_access"}],"scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publication":"Journal of Applied and Computational Topology","citation":{"chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8"},"article_type":"original","page":"455-480","date_published":"2020-12-01T00:00:00Z","file_date_updated":"2024-03-04T10:52:42Z","year":"2020","acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"full_name":"Bauer, U.","first_name":"U.","last_name":"Bauer"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz"},{"last_name":"Mrozek","first_name":"M.","full_name":"Mrozek, M."}],"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z","volume":4,"month":"12","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1007/s41468-020-00058-8","language":[{"iso":"eng"}]},{"year":"2019","department":[{"_id":"HeEd"}],"publisher":"Carleton University","publication_status":"published","author":[{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"volume":10,"date_updated":"2021-01-12T08:07:50Z","date_created":"2019-06-03T09:35:33Z","ec_funded":1,"file_date_updated":"2020-07-14T12:47:32Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.20382/jocg.v10i1a9","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1920-180X"]},"month":"07","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6515","intvolume":" 10","title":"Simplices modelled on spaces of constant curvature","ddc":["510"],"status":"public","file":[{"file_size":2170882,"content_type":"application/pdf","creator":"mwintrae","file_name":"mainJournalFinal.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:32Z","date_created":"2019-06-03T09:30:01Z","checksum":"57b4df2f16a74eb499734ec8ee240178","relation":"main_file","file_id":"6516"}],"oa_version":"Published Version","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature."}],"citation":{"ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9","apa":"Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . Carleton University. https://doi.org/10.20382/jocg.v10i1a9","ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton University, pp. 223–256, 2019.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","mla":"Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry , vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.","chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton University, 2019. https://doi.org/10.20382/jocg.v10i1a9."},"publication":"Journal of Computational Geometry ","page":"223–256","date_published":"2019-07-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01"},{"has_accepted_license":"1","day":"01","month":"08","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2019-08-01T00:00:00Z","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10"},"page":"275-279","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"citation":{"short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279."},"publication":"The 31st Canadian Conference in Computational Geometry","ec_funded":1,"abstract":[{"lang":"eng","text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space."}],"file_date_updated":"2020-07-14T12:47:34Z","type":"conference","file":[{"relation":"main_file","file_id":"6629","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-12T08:32:46Z","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_name":"IntrinsicExtrinsicCCCG2019.pdf","access_level":"open_access","file_size":321176,"content_type":"application/pdf","creator":"mwintrae"}],"oa_version":"Submitted Version","date_created":"2019-07-12T08:34:57Z","date_updated":"2021-01-12T08:08:16Z","author":[{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"department":[{"_id":"HeEd"}],"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","publication_status":"published","ddc":["004"],"status":"public","year":"2019","_id":"6628","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"day":"01","has_accepted_license":"1","scopus_import":1,"date_published":"2019-06-01T00:00:00Z","publication":"35th International Symposium on Computational Geometry","citation":{"ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31","ista":"Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31."},"page":"31:1-31:14","abstract":[{"lang":"eng","text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"access_level":"open_access","file_name":"2019_LIPICS_Edelsbrunner.pdf","content_type":"application/pdf","file_size":1355179,"creator":"dernst","relation":"main_file","file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4","date_created":"2019-07-24T06:40:01Z","date_updated":"2020-07-14T12:47:35Z"}],"oa_version":"Published Version","_id":"6648","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Topological data analysis in information space","status":"public","ddc":["510"],"intvolume":" 129","month":"06","publication_identifier":{"isbn":["9783959771047"]},"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18"},"doi":"10.4230/LIPICS.SOCG.2019.31","language":[{"iso":"eng"}],"external_id":{"arxiv":["1903.08510"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"file_date_updated":"2020-07-14T12:47:35Z","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Virk","first_name":"Ziga","full_name":"Virk, Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert"}],"date_updated":"2021-01-12T08:08:23Z","date_created":"2019-07-17T10:36:09Z","volume":129,"year":"2019","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}]},{"scopus_import":"1","day":"01","month":"08","article_processing_charge":"No","quality_controlled":"1","page":"164-170","publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","oa":1,"main_file_link":[{"open_access":"1","url":"https://cccg.ca/proceedings/2019/proceedings.pdf"}],"external_id":{"arxiv":["1910.09917"]},"citation":{"ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” in Proceedings of the 31st Canadian Conference on Computational Geometry, Edmonton, Canada, 2019, pp. 164–170.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.","chicago":"Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In Proceedings of the 31st Canadian Conference on Computational Geometry, 164–70. Canadian Conference on Computational Geometry, 2019.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170."},"language":[{"iso":"eng"}],"conference":{"start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10","name":"CCCG: Canadian Conference in Computational Geometry"},"date_published":"2019-08-01T00:00:00Z","type":"conference","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. ","lang":"eng"}],"publication_status":"published","status":"public","title":"Folding polyominoes with holes into a cube","department":[{"_id":"HeEd"}],"publisher":"Canadian Conference on Computational Geometry","_id":"6989","year":"2019","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","date_created":"2019-11-04T16:46:11Z","date_updated":"2023-08-04T10:57:42Z","oa_version":"Published Version","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"full_name":"Akitaya, Hugo A","last_name":"Akitaya","first_name":"Hugo A"},{"first_name":"Kenneth C","last_name":"Cheung","full_name":"Cheung, Kenneth C"},{"full_name":"Demaine, Erik D","last_name":"Demaine","first_name":"Erik D"},{"last_name":"Demaine","first_name":"Martin L","full_name":"Demaine, Martin L"},{"first_name":"Sandor P","last_name":"Fekete","full_name":"Fekete, Sandor P"},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"full_name":"Kostitsyna, Irina","first_name":"Irina","last_name":"Kostitsyna"},{"full_name":"Löffler, Maarten","first_name":"Maarten","last_name":"Löffler"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana"},{"last_name":"Mundilova","first_name":"Klara","full_name":"Mundilova, Klara"},{"full_name":"Schmidt, Christiane","first_name":"Christiane","last_name":"Schmidt"}],"related_material":{"record":[{"id":"8317","status":"public","relation":"extended_version"}]}},{"_id":"6671","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 3","title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","ddc":["000"],"status":"public","file":[{"checksum":"a5b244db9f751221409cf09c97ee0935","date_updated":"2020-07-14T12:47:36Z","date_created":"2019-07-31T08:09:56Z","file_id":"6741","relation":"main_file","creator":"dernst","file_size":2215157,"content_type":"application/pdf","access_level":"open_access","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf"}],"oa_version":"Published Version","type":"journal_article","issue":"1-2","abstract":[{"text":"In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.","lang":"eng"}],"citation":{"ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8","ista":"Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 3(1–2), 29–58.","apa":"Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8","ieee":"J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” Journal of Applied and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.","mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8."},"publication":"Journal of Applied and Computational Topology","page":"29–58","article_type":"original","date_published":"2019-06-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","year":"2019","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"last_name":"Lieutier","first_name":"André","full_name":"Lieutier, André"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"volume":3,"date_created":"2019-07-24T08:37:29Z","date_updated":"2023-08-22T12:37:47Z","ec_funded":1,"file_date_updated":"2020-07-14T12:47:36Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","doi":"10.1007/s41468-019-00029-8","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"month":"06"},{"type":"journal_article","abstract":[{"text":"We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. ","lang":"eng"}],"intvolume":" 147","title":"Two circles and only a straightedge","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6050","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","page":"91-102","citation":{"mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240"},"publication":"Proceedings of the American Mathematical Society","date_published":"2019-01-01T00:00:00Z","publisher":"AMS","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2019","volume":147,"date_created":"2019-02-24T22:59:19Z","date_updated":"2023-08-24T14:48:59Z","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"last_name":"Fedorov","first_name":"Roman","full_name":"Fedorov, Roman"}],"month":"01","quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1090/proc/14240"},{"language":[{"iso":"eng"}],"doi":"10.12775/TMNA.2019.008","isi":1,"quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"month":"06","date_updated":"2023-08-29T06:32:48Z","date_created":"2019-07-14T21:59:19Z","volume":53,"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Hubard, Alfredo","first_name":"Alfredo","last_name":"Hubard"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"publication_status":"published","publisher":"Akademicka Platforma Czasopism","department":[{"_id":"HeEd"}],"year":"2019","ec_funded":1,"date_published":"2019-06-01T00:00:00Z","page":"457-490","publication":"Topological Methods in Nonlinear Analysis","citation":{"chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","apa":"Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008"},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","title":"Lower and upper bounds for the waists of different spaces","status":"public","intvolume":" 53","_id":"6634","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.","lang":"eng"}],"issue":"2","type":"journal_article"},{"publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"month":"07","doi":"10.1051/0004-6361/201834916","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"project":[{"grant_number":"M62909-18-1-2038","_id":"265683E4-B435-11E9-9278-68D0E5697425","name":"Toward Computational Information Topology"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"file_date_updated":"2020-07-14T12:47:39Z","article_number":"A163","author":[{"full_name":"Pranav, Pratyush","first_name":"Pratyush","last_name":"Pranav"},{"first_name":"Robert J.","last_name":"Adler","full_name":"Adler, Robert J."},{"full_name":"Buchert, Thomas","last_name":"Buchert","first_name":"Thomas"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Bernard J.T.","last_name":"Jones","full_name":"Jones, Bernard J.T."},{"full_name":"Schwartzman, Armin","first_name":"Armin","last_name":"Schwartzman"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert","first_name":"Rien"}],"volume":627,"date_created":"2019-08-04T21:59:18Z","date_updated":"2023-08-29T07:01:48Z","year":"2019","publisher":"EDP Sciences","department":[{"_id":"HeEd"}],"publication_status":"published","has_accepted_license":"1","article_processing_charge":"No","day":"17","scopus_import":"1","date_published":"2019-07-17T00:00:00Z","citation":{"apa":"Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916","chicago":"Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916."},"publication":"Astronomy and Astrophysics","article_type":"original","abstract":[{"lang":"eng","text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models."}],"type":"journal_article","oa_version":"Published Version","file":[{"checksum":"83b9209ed9eefbdcefd89019c5a97805","date_updated":"2020-07-14T12:47:39Z","date_created":"2019-08-05T08:08:59Z","file_id":"6766","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":14420451,"access_level":"open_access","file_name":"2019_AstronomyAstrophysics_Pranav.pdf"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6756","intvolume":" 627","ddc":["520","530"],"status":"public","title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background"},{"month":"10","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"doi":"10.1112/blms.12276","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"ec_funded":1,"author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"full_name":"Izmestiev, Ivan","last_name":"Izmestiev","first_name":"Ivan"}],"date_updated":"2023-08-29T07:08:34Z","date_created":"2019-08-11T21:59:23Z","volume":51,"year":"2019","publication_status":"published","publisher":"London Mathematical Society","department":[{"_id":"HeEd"}],"day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2019-10-01T00:00:00Z","publication":"Bulletin of the London Mathematical Society","citation":{"chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","apa":"Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276","ista":"Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276"},"article_type":"original","page":"765-775","abstract":[{"text":"The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry.","lang":"eng"}],"issue":"5","type":"journal_article","oa_version":"Preprint","_id":"6793","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"The Regge symmetry, confocal conics, and the Schläfli formula","intvolume":" 51"},{"status":"public","title":"Arakawa-Suzuki functors for Whittaker modules","intvolume":" 538","_id":"6828","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group ."}],"article_type":"original","page":"261-289","publication":"Journal of Algebra","citation":{"ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027."},"date_published":"2019-11-15T00:00:00Z","day":"15","article_processing_charge":"No","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","year":"2019","date_created":"2019-08-22T07:54:13Z","date_updated":"2023-08-29T07:11:47Z","volume":538,"author":[{"full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","first_name":"Adam"}],"isi":1,"quality_controlled":"1","external_id":{"arxiv":["1805.04676"],"isi":["000487176300011"]},"main_file_link":[{"url":"https://arxiv.org/abs/1805.04676","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2019.07.027","month":"11","publication_identifier":{"issn":["0021-8693"]}},{"scopus_import":"1","month":"11","day":"28","article_processing_charge":"No","publication_identifier":{"isbn":["9781538670248"]},"quality_controlled":"1","isi":1,"publication":"2019 IEEE Intelligent Transportation Systems Conference","external_id":{"isi":["000521238102050"]},"citation":{"ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514."},"language":[{"iso":"eng"}],"conference":{"end_date":"2019-10-30","start_date":"2019-10-27","location":"Auckland, New Zealand","name":"ITSC: Intelligent Transportation Systems Conference"},"date_published":"2019-11-28T00:00:00Z","doi":"10.1109/ITSC.2019.8917514","article_number":"8917514","type":"conference","abstract":[{"text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next.","lang":"eng"}],"publication_status":"published","title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","status":"public","publisher":"IEEE","department":[{"_id":"HeEd"}],"year":"2019","_id":"7216","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2019-12-29T23:00:47Z","date_updated":"2023-09-06T14:50:28Z","oa_version":"None","author":[{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116"},{"first_name":"James","last_name":"Cook","full_name":"Cook, James"},{"full_name":"Fabrikant, Alex","first_name":"Alex","last_name":"Fabrikant"},{"first_name":"Marco","last_name":"Gruteser","full_name":"Gruteser, Marco"}]},{"oa_version":"Published Version","file":[{"creator":"dernst","file_size":599339,"content_type":"application/pdf","access_level":"open_access","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","date_updated":"2020-07-14T12:47:10Z","date_created":"2019-02-06T10:10:46Z","file_id":"5932","relation":"main_file"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"5678","intvolume":" 62","ddc":["516"],"title":"Poisson–Delaunay Mosaics of Order k","status":"public","issue":"4","abstract":[{"lang":"eng","text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold."}],"type":"journal_article","date_published":"2019-12-01T00:00:00Z","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2"},"publication":"Discrete and Computational Geometry","page":"865–878","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Nikitenko","first_name":"Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"}],"volume":62,"date_created":"2018-12-16T22:59:20Z","date_updated":"2023-09-07T12:07:12Z","year":"2019","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:47:10Z","doi":"10.1007/s00454-018-0049-2","language":[{"iso":"eng"}],"external_id":{"isi":["000494042900008"],"arxiv":["1709.09380"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"month":"12"},{"type":"journal_article","abstract":[{"lang":"eng","text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram."}],"_id":"6608","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","ddc":["000"],"title":"Holes and dependences in an ordered complex","intvolume":" 73","oa_version":"Published Version","file":[{"file_name":"Elsevier_2019_Edelsbrunner.pdf","access_level":"open_access","creator":"kschuh","content_type":"application/pdf","file_size":2665013,"file_id":"6624","relation":"main_file","date_created":"2019-07-08T15:24:26Z","date_updated":"2020-07-14T12:47:34Z","checksum":"7c99be505dc7533257d42eb1830cef04"}],"scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1","publication":"Computer Aided Geometric Design","citation":{"ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003."},"page":"1-15","date_published":"2019-08-01T00:00:00Z","file_date_updated":"2020-07-14T12:47:34Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","year":"2019","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","first_name":"Katharina","full_name":"Ölsböck, Katharina"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7460"}]},"date_updated":"2023-09-07T13:15:29Z","date_created":"2019-07-07T21:59:20Z","volume":73,"month":"08","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"external_id":{"isi":["000485207800001"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"doi":"10.1016/j.cagd.2019.06.003","language":[{"iso":"eng"}]},{"article_processing_charge":"No","day":"16","month":"03","citation":{"chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv."},"external_id":{"arxiv":["1903.06981"]},"main_file_link":[{"url":"https://arxiv.org/abs/1903.06981","open_access":"1"}],"oa":1,"publication":"arXiv","date_published":"2019-03-16T00:00:00Z","language":[{"iso":"eng"}],"type":"preprint","article_number":"1903.06981","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"_id":"7950","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"publication_status":"submitted","status":"public","title":"Token swapping on trees","related_material":{"record":[{"id":"7944","status":"public","relation":"dissertation_contains"},{"id":"12833","status":"public","relation":"later_version"}]},"author":[{"full_name":"Biniaz, Ahmad","first_name":"Ahmad","last_name":"Biniaz"},{"full_name":"Jain, Kshitij","first_name":"Kshitij","last_name":"Jain"},{"last_name":"Lubiw","first_name":"Anna","full_name":"Lubiw, Anna"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana"},{"first_name":"Tillmann","last_name":"Miltzow","full_name":"Miltzow, Tillmann"},{"full_name":"Mondal, Debajyoti","last_name":"Mondal","first_name":"Debajyoti"},{"first_name":"Anurag Murty","last_name":"Naredla","full_name":"Naredla, Anurag Murty"},{"orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","first_name":"Josef","full_name":"Tkadlec, Josef"},{"full_name":"Turcotte, Alexi","last_name":"Turcotte","first_name":"Alexi"}],"oa_version":"Preprint","date_updated":"2024-01-04T12:42:08Z","date_created":"2020-06-08T12:25:25Z"},{"day":"11","has_accepted_license":"1","scopus_import":1,"date_published":"2018-06-11T00:00:00Z","page":"35:1 - 35:13","citation":{"short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35.","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13."},"abstract":[{"lang":"eng","text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex."}],"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"type":"conference","file":[{"access_level":"open_access","file_name":"2018_LIPIcs_Edelsbrunner.pdf","file_size":489080,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5724","checksum":"7509403803b3ac1aee94bbc2ad293d21","date_created":"2018-12-17T16:31:31Z","date_updated":"2020-07-14T12:45:20Z"}],"oa_version":"Published Version","title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","status":"public","ddc":["000"],"intvolume":" 99","_id":"188","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"06","language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","start_date":"2018-06-11","location":"Budapest, Hungary"},"doi":"10.4230/LIPIcs.SoCG.2018.35","quality_controlled":"1","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"file_date_updated":"2020-07-14T12:45:20Z","publist_id":"7733","date_created":"2018-12-11T11:45:05Z","date_updated":"2021-01-12T06:53:48Z","volume":99,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Virk","first_name":"Ziga","full_name":"Virk, Ziga"},{"last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund","year":"2018"},{"publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"year":"2018","date_updated":"2023-09-07T12:25:32Z","date_created":"2018-12-11T11:45:10Z","author":[{"full_name":"Iglesias Ham, Mabel","first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2020-07-14T12:45:24Z","publist_id":"7712","oa":1,"supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:th_1026","month":"06","publication_identifier":{"issn":["2663-337X"]},"ddc":["514","516"],"status":"public","title":"Multiple covers with balls","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"201","oa_version":"Published Version","file":[{"content_type":"application/zip","file_size":11827713,"creator":"kschuh","file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip","access_level":"closed","date_created":"2019-02-05T07:43:31Z","date_updated":"2020-07-14T12:45:24Z","checksum":"dd699303623e96d1478a6ae07210dd05","relation":"source_file","file_id":"5918"},{"checksum":"ba163849a190d2b41d66fef0e4983294","date_created":"2019-02-05T07:43:45Z","date_updated":"2020-07-14T12:45:24Z","relation":"main_file","file_id":"5919","file_size":4783846,"content_type":"application/pdf","creator":"kschuh","access_level":"open_access","file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf"}],"pubrep_id":"1026","alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"lang":"eng","text":"We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications."}],"page":"171","citation":{"ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026."},"date_published":"2018-06-11T00:00:00Z","day":"11","article_processing_charge":"No","has_accepted_license":"1"},{"month":"06","language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11"},"doi":"10.4230/LIPIcs.SoCG.2018.34","quality_controlled":"1","project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"file_date_updated":"2020-07-14T12:45:19Z","publist_id":"7732","article_number":"34","date_created":"2018-12-11T11:45:05Z","date_updated":"2023-09-07T13:29:00Z","volume":99,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F"}],"related_material":{"record":[{"id":"9317","status":"public","relation":"later_version"},{"id":"9056","status":"public","relation":"dissertation_contains"}]},"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"acknowledgement":"This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","day":"11","has_accepted_license":"1","scopus_import":1,"date_published":"2018-06-11T00:00:00Z","citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34.","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34.","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","apa":"Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34","ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34"},"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 from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. ","lang":"eng"}],"alternative_title":["LIPIcs"],"type":"conference","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","file_size":528018,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5738","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","date_created":"2018-12-18T09:27:22Z","date_updated":"2020-07-14T12:45:19Z"}],"ddc":["516"],"status":"public","title":"The multi-cover persistence of Euclidean balls","intvolume":" 99","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"187"},{"month":"06","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000431418800004"]},"language":[{"iso":"eng"}],"doi":"10.1007/s10711-017-0265-6","ec_funded":1,"publist_id":"7014","file_date_updated":"2020-07-14T12:47:44Z","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","volume":194,"date_updated":"2023-09-08T11:40:29Z","date_created":"2018-12-11T11:47:57Z","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","page":"55 - 64","article_type":"original","citation":{"chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64.","ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 2018;194(1):55-64. doi:10.1007/s10711-017-0265-6"},"publication":"Geometriae Dedicata","date_published":"2018-06-01T00:00:00Z","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them."}],"intvolume":" 194","status":"public","ddc":["510"],"title":"3-Webs generated by confocal conics and circles","_id":"692","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","file":[{"file_name":"2018_Springer_Akopyan.pdf","access_level":"open_access","file_size":1140860,"content_type":"application/pdf","creator":"kschuh","relation":"main_file","file_id":"7222","date_updated":"2020-07-14T12:47:44Z","date_created":"2020-01-03T11:35:08Z","checksum":"1febcfc1266486053a069e3425ea3713"}]},{"page":"2242 - 2257","publication":"SIAM Journal on Discrete Mathematics","citation":{"mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018."},"date_published":"2018-09-06T00:00:00Z","scopus_import":"1","day":"06","article_processing_charge":"No","title":"Counting blanks in polygonal arrangements","status":"public","intvolume":" 32","_id":"58","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks."}],"issue":"3","quality_controlled":"1","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"external_id":{"arxiv":["1604.00960"],"isi":["000450810500036"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"language":[{"iso":"eng"}],"doi":"10.1137/16M110407X","month":"09","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Society for Industrial and Applied Mathematics ","year":"2018","date_created":"2018-12-11T11:44:24Z","date_updated":"2023-09-11T12:48:39Z","volume":32,"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Erel","last_name":"Segal Halevi","full_name":"Segal Halevi, Erel"}],"ec_funded":1,"publist_id":"7996"},{"month":"04","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"oa":1,"external_id":{"isi":["000423197800019"]},"language":[{"iso":"eng"}],"doi":"10.1090/tran/7292","publist_id":"7363","ec_funded":1,"publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","volume":370,"date_created":"2018-12-11T11:46:35Z","date_updated":"2023-09-11T14:19:12Z","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"first_name":"Alexander","last_name":"Bobenko","full_name":"Bobenko, Alexander"}],"scopus_import":"1","article_processing_charge":"No","day":"01","page":"2825 - 2854","citation":{"chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society. American Mathematical Society, 2018. https://doi.org/10.1090/tran/7292.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292.","apa":"Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7292","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions of the American Mathematical Society, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292"},"publication":"Transactions of the American Mathematical Society","date_published":"2018-04-01T00:00:00Z","type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem."}],"intvolume":" 370","status":"public","title":"Incircular nets and confocal conics","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"458","oa_version":"Preprint"},{"volume":40,"date_updated":"2023-09-13T08:49:16Z","date_created":"2018-12-11T11:44:40Z","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Petrunin","first_name":"Anton","full_name":"Petrunin, Anton"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","publist_id":"7948","language":[{"iso":"eng"}],"doi":"10.1007/s00283-018-9795-5","quality_controlled":"1","isi":1,"oa":1,"external_id":{"arxiv":["1702.05172"],"isi":["000444141200005"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.05172"}],"month":"09","oa_version":"Preprint","intvolume":" 40","title":"Long geodesics on convex surfaces","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"106","issue":"3","abstract":[{"lang":"eng","text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below."}],"type":"journal_article","date_published":"2018-09-01T00:00:00Z","page":"26 - 31","citation":{"chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31.","apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5"},"publication":"Mathematical Intelligencer","article_processing_charge":"No","day":"01","scopus_import":"1"},{"month":"03","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000415778300010"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2017.06.014","ec_funded":1,"publist_id":"7289","file_date_updated":"2020-07-14T12:46:38Z","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","year":"2018","volume":68,"date_updated":"2023-09-13T08:59:00Z","date_created":"2018-12-11T11:46:59Z","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Iglesias Ham, Mabel","first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"01","page":"119 - 133","citation":{"chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014"},"publication":"Computational Geometry: Theory and Applications","date_published":"2018-03-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"intvolume":" 68","title":"Multiple covers with balls I: Inclusion–exclusion","status":"public","ddc":["000"],"_id":"530","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","file":[{"creator":"dernst","file_size":708357,"content_type":"application/pdf","file_name":"2018_Edelsbrunner.pdf","access_level":"open_access","date_created":"2019-02-12T06:47:52Z","date_updated":"2020-07-14T12:46:38Z","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_id":"5953","relation":"main_file"}]},{"abstract":[{"text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF.","lang":"eng"}],"type":"conference","oa_version":"Submitted Version","status":"public","title":"On the memory hardness of data independent password hashing functions","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"193","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2018-06-01T00:00:00Z","page":"51 - 65","publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","citation":{"mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534"},"ec_funded":1,"publist_id":"7723","date_updated":"2023-09-13T09:13:12Z","date_created":"2018-12-11T11:45:07Z","author":[{"full_name":"Alwen, Joel F","last_name":"Alwen","first_name":"Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gazi, Peter","first_name":"Peter","last_name":"Gazi"},{"full_name":"Kamath Hosdurg, Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","first_name":"Chethan","last_name":"Kamath Hosdurg"},{"id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","last_name":"Klein","first_name":"Karen","full_name":"Klein, Karen"},{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","last_name":"Pietrzak"},{"full_name":"Reyzin, Lenoid","first_name":"Lenoid","last_name":"Reyzin"},{"full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek"},{"full_name":"Rybar, Michal","first_name":"Michal","last_name":"Rybar","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","publisher":"ACM","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"year":"2018","acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","month":"06","language":[{"iso":"eng"}],"conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","end_date":"2018-06-08","location":"Incheon, Republic of Korea","start_date":"2018-06-04"},"doi":"10.1145/3196494.3196534","isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160"},{"_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815","call_identifier":"H2020","name":"Teaching Old Crypto New Tricks"}],"oa":1,"external_id":{"isi":["000516620100005"]},"main_file_link":[{"url":"https://eprint.iacr.org/2016/783","open_access":"1"}]},{"month":"03","publication_identifier":{"issn":["08954801"]},"oa":1,"external_id":{"isi":["000428958900038"]},"main_file_link":[{"open_access":"1","url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf"}],"isi":1,"quality_controlled":"1","project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"doi":"10.1137/16M1097201","language":[{"iso":"eng"}],"publist_id":"7553","acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Society for Industrial and Applied Mathematics ","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"date_updated":"2023-09-13T09:34:38Z","date_created":"2018-12-11T11:45:46Z","volume":32,"scopus_import":"1","day":"29","article_processing_charge":"No","publication":"SIAM J Discrete Math","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201"},"article_type":"original","page":"750 - 782","date_published":"2018-03-29T00:00:00Z","type":"journal_article","abstract":[{"text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice.","lang":"eng"}],"issue":"1","_id":"312","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"On the optimality of the FCC lattice for soft sphere packing","intvolume":" 32","oa_version":"Submitted Version"},{"doi":"10.1016/j.crma.2018.03.005","language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000430402700009"],"arxiv":["1805.01652"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.01652"}],"quality_controlled":"1","isi":1,"month":"04","publication_identifier":{"issn":["1631073X"]},"author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"}],"date_created":"2018-12-11T11:46:19Z","date_updated":"2023-09-13T09:34:12Z","volume":356,"year":"2018","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publist_id":"7420","date_published":"2018-04-01T00:00:00Z","publication":"Comptes Rendus Mathematique","citation":{"ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005","mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005."},"article_type":"original","page":"412-414","day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"409","status":"public","title":"On the number of non-hexagons in a planar tiling","intvolume":" 356","abstract":[{"text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons.","lang":"eng"}],"issue":"4","type":"journal_article"},{"date_published":"2018-10-01T00:00:00Z","page":"3215 - 3238","article_type":"original","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238.","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389"},"publication":"Annals of Applied Probability","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Preprint","intvolume":" 28","status":"public","title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"87","issue":"5","abstract":[{"lang":"eng","text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1214/18-AAP1389","project":[{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1705.02870"],"isi":["000442893500018"]},"main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"month":"10","volume":28,"date_updated":"2023-09-15T12:10:35Z","date_created":"2018-12-11T11:44:33Z","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"}],"department":[{"_id":"HeEd"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2018","publist_id":"7967"},{"day":"31","article_processing_charge":"No","has_accepted_license":"1","date_published":"2018-05-31T00:00:00Z","publication":"Forum of Mathematics, Sigma","citation":{"chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7"},"abstract":[{"lang":"eng","text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle."}],"type":"journal_article","file":[{"content_type":"application/pdf","file_size":249246,"creator":"dernst","access_level":"open_access","file_name":"2018_ForumMahtematics_Akopyan.pdf","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","date_updated":"2020-07-14T12:47:28Z","date_created":"2019-04-30T06:14:58Z","relation":"main_file","file_id":"6356"}],"oa_version":"Published Version","_id":"6355","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","ddc":["510"],"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","intvolume":" 6","month":"05","publication_identifier":{"issn":["2050-5094"]},"doi":"10.1017/fms.2018.7","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2020-07-14T12:47:28Z","ec_funded":1,"article_number":"e7","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"date_updated":"2023-09-19T14:50:12Z","date_created":"2019-04-30T06:09:57Z","volume":6,"year":"2018","publication_status":"published","publisher":"Cambridge University Press","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}]},{"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000432205500011"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00454-017-9883-x","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"06","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","volume":59,"date_created":"2018-12-11T11:49:57Z","date_updated":"2023-09-20T12:08:51Z","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"},{"first_name":"Mikhail","last_name":"Grigorev","full_name":"Grigorev, Mikhail"}],"publist_id":"6324","ec_funded":1,"file_date_updated":"2019-01-18T09:27:36Z","page":"1001-1009","article_type":"original","citation":{"short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009."},"publication":"Discrete & Computational Geometry","date_published":"2018-06-01T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","intvolume":" 59","status":"public","title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","ddc":["516","000"],"_id":"1064","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"access_level":"open_access","file_name":"2018_DiscreteComp_Akopyan.pdf","file_size":482518,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5844","success":1,"date_updated":"2019-01-18T09:27:36Z","date_created":"2019-01-18T09:27:36Z"}],"oa_version":"Published Version","type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets."}]},{"article_processing_charge":"No","day":"13","month":"09","language":[{"iso":"eng"}],"date_published":"2018-09-13T00:00:00Z","doi":"10.48550/arXiv.1804.03057","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"external_id":{"arxiv":["1804.03057"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"citation":{"chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057"},"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization."}],"type":"preprint","article_number":"1804.03057","oa_version":"Preprint","date_updated":"2023-12-18T10:51:02Z","date_created":"2018-12-11T11:44:30Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","first_name":"Sergey","full_name":"Avvakumov, Sergey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"arXiv","publication_status":"published","status":"public","title":"Convex fair partitions into arbitrary number of pieces","_id":"75","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2018"},{"month":"04","doi":"10.1142/S0218195916600050","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","publist_id":"7338","file_date_updated":"2020-07-14T12:46:35Z","related_material":{"record":[{"id":"10892","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"volume":26,"date_created":"2018-12-11T11:46:43Z","date_updated":"2023-02-21T16:06:22Z","year":"2017","acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","publisher":"World Scientific Publishing","department":[{"_id":"HeEd"}],"publication_status":"published","has_accepted_license":"1","day":"13","scopus_import":1,"date_published":"2017-04-13T00:00:00Z","citation":{"ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050."},"publication":"International Journal of Computational Geometry and Applications","page":"211 - 229","issue":"3-4","abstract":[{"lang":"eng","text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"type":"journal_article","pubrep_id":"949","file":[{"file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","access_level":"open_access","creator":"system","file_size":769296,"content_type":"application/pdf","file_id":"4758","relation":"main_file","date_updated":"2020-07-14T12:46:35Z","date_created":"2018-12-12T10:09:34Z","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e"}],"oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"481","intvolume":" 26","ddc":["004","514","516"],"title":"Planar matchings for weighted straight skeletons","status":"public"},{"abstract":[{"text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.","lang":"eng"}],"publist_id":"7299","type":"journal_article","author":[{"full_name":"Austin, Kyle","first_name":"Kyle","last_name":"Austin"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"}],"date_updated":"2021-01-12T08:01:21Z","date_created":"2018-12-11T11:46:56Z","oa_version":"Submitted Version","volume":215,"year":"2017","_id":"521","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","status":"public","title":"Higson compactification and dimension raising","department":[{"_id":"HeEd"}],"intvolume":" 215","publisher":"Elsevier","day":"01","month":"01","publication_identifier":{"issn":["01668641"]},"doi":"10.1016/j.topol.2016.10.005","date_published":"2017-01-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Topology and its Applications","main_file_link":[{"url":"https://arxiv.org/abs/1608.03954v1","open_access":"1"}],"citation":{"short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57."},"oa":1,"quality_controlled":"1","page":"45 - 57"},{"ec_funded":1,"publist_id":"7246","year":"2017","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"International Press","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek","first_name":"Peter","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek"}],"date_updated":"2021-01-12T08:03:12Z","date_created":"2018-12-11T11:47:14Z","volume":19,"month":"01","publication_identifier":{"issn":["15320073"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1507.04310","open_access":"1"}],"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"grant_number":"701309","_id":"2590DB08-B435-11E9-9278-68D0E5697425","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020"}],"doi":"10.4310/HHA.2017.v19.n2.a16","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).","lang":"eng"}],"issue":"2","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"568","title":"Persistence of zero sets","status":"public","intvolume":" 19","oa_version":"Submitted Version","scopus_import":1,"day":"01","publication":"Homology, Homotopy and Applications","citation":{"ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16."},"page":"313 - 342","date_published":"2017-01-01T00:00:00Z"},{"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2017","date_updated":"2022-01-28T07:48:24Z","date_created":"2019-01-08T20:42:56Z","volume":10256,"author":[{"last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"}],"place":"Cham","extern":"1","quality_controlled":"1","language":[{"iso":"eng"}],"conference":{"name":"IWCIA: International Workshop on Combinatorial Image Analysis","end_date":"2017-06-21","location":"Plovdiv, Bulgaria","start_date":"2017-06-19"},"doi":"10.1007/978-3-319-59108-7_8","month":"05","publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"title":"Construction of persistent Voronoi diagram on 3D digital plane","status":"public","intvolume":" 10256","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"5803","oa_version":"None","alternative_title":["LNCS"],"type":"book_chapter","abstract":[{"lang":"eng","text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept."}],"page":"93-104","publication":"Combinatorial image analysis","citation":{"chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8"},"date_published":"2017-05-17T00:00:00Z","day":"17","article_processing_charge":"No"},{"publication_identifier":{"issn":["18688969"]},"month":"06","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.4230/LIPIcs.SoCG.2017.39","conference":{"name":"Symposium on Computational Geometry, SoCG","start_date":"2017-07-04","location":"Brisbane, Australia","end_date":"2017-07-07"},"language":[{"iso":"eng"}],"publist_id":"7021","file_date_updated":"2020-07-14T12:47:42Z","year":"2017","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"volume":77,"date_updated":"2021-01-12T08:09:26Z","date_created":"2018-12-11T11:47:56Z","scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39."},"page":"391-3916","date_published":"2017-06-01T00:00:00Z","type":"conference","alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. "}],"_id":"688","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 77","ddc":["514","516"],"title":"Topological data analysis with Bregman divergences","status":"public","pubrep_id":"895","file":[{"relation":"main_file","file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","date_updated":"2020-07-14T12:47:42Z","date_created":"2018-12-12T10:11:03Z","access_level":"open_access","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","file_size":990546,"content_type":"application/pdf","creator":"system"}],"oa_version":"Published Version"},{"oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"707","status":"public","title":"A tight estimate for the waist of the ball ","intvolume":" 49","abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"issue":"4","type":"journal_article","date_published":"2017-08-01T00:00:00Z","publication":"Bulletin of the London Mathematical Society","citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:10.1112/blms.12062.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062.","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017."},"page":"690 - 693","day":"01","scopus_import":1,"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"date_updated":"2021-01-12T08:11:41Z","date_created":"2018-12-11T11:48:02Z","volume":49,"year":"2017","publication_status":"published","publisher":"Wiley-Blackwell","department":[{"_id":"HeEd"}],"ec_funded":1,"publist_id":"6982","doi":"10.1112/blms.12062","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1608.06279","open_access":"1"}],"quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"month":"08","publication_identifier":{"issn":["00246093"]}},{"external_id":{"arxiv":["1607.05915"]},"main_file_link":[{"url":"https://arxiv.org/abs/1607.05915","open_access":"1"}],"oa":1,"quality_controlled":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"doi":"10.1017/apr.2017.20","language":[{"iso":"eng"}],"month":"09","publication_identifier":{"issn":["00018678"]},"year":"2017","publication_status":"published","publisher":"Cambridge University Press","department":[{"_id":"HeEd"}],"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","last_name":"Nikitenko"},{"full_name":"Reitzner, Matthias","last_name":"Reitzner","first_name":"Matthias"}],"related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"date_created":"2018-12-11T11:48:07Z","date_updated":"2023-09-07T12:07:12Z","volume":49,"ec_funded":1,"publist_id":"6962","publication":"Advances in Applied Probability","citation":{"short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.","ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","apa":"Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767."},"page":"745 - 767","date_published":"2017-09-01T00:00:00Z","scopus_import":1,"day":"01","_id":"718","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","intvolume":" 49","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.","lang":"eng"}],"issue":"3"},{"author":[{"orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton","full_name":"Nikitenko, Anton"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"718"},{"relation":"part_of_dissertation","status":"public","id":"5678"},{"id":"87","status":"public","relation":"part_of_dissertation"}]},"date_updated":"2023-09-15T12:10:34Z","date_created":"2019-04-09T15:04:32Z","year":"2017","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Institute of Science and Technology Austria","file_date_updated":"2020-07-14T12:47:26Z","doi":"10.15479/AT:ISTA:th_873","degree_awarded":"PhD","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"month":"10","publication_identifier":{"issn":["2663-337X"]},"pubrep_id":"873","oa_version":"Published Version","file":[{"date_created":"2019-04-09T14:54:51Z","date_updated":"2020-07-14T12:47:26Z","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_id":"6289","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":2324870,"file_name":"2017_Thesis_Nikitenko.pdf","access_level":"open_access"},{"file_name":"2017_Thesis_Nikitenko_source.zip","access_level":"closed","creator":"dernst","content_type":"application/zip","file_size":2863219,"file_id":"6290","relation":"source_file","date_updated":"2020-07-14T12:47:26Z","date_created":"2019-04-09T14:54:51Z","checksum":"99b7ad76e317efd447af60f91e29b49b"}],"_id":"6287","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Discrete Morse theory for random complexes ","status":"public","ddc":["514","516","519"],"abstract":[{"text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's.","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2017-10-27T00:00:00Z","citation":{"chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria.","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873"},"page":"86","day":"27","article_processing_charge":"No","has_accepted_license":"1"},{"article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2017-01-01T00:00:00Z","citation":{"ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008."},"publication":"Journal of Symbolic Computation","page":"76 - 90","article_type":"original","abstract":[{"lang":"eng","text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology."}],"type":"journal_article","oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1433","intvolume":" 78","title":"Phat - Persistent homology algorithms toolbox","status":"public","publication_identifier":{"issn":[" 07477171"]},"month":"01","doi":"10.1016/j.jsc.2016.03.008","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://doi.org/10.1016/j.jsc.2016.03.008","open_access":"1"}],"external_id":{"isi":["000384396000005"]},"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","isi":1,"publist_id":"5765","ec_funded":1,"related_material":{"record":[{"id":"10894","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Bauer, Ulrich","last_name":"Bauer","first_name":"Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"volume":78,"date_created":"2018-12-11T11:51:59Z","date_updated":"2023-09-20T09:42:40Z","year":"2017","department":[{"_id":"HeEd"}],"publisher":"Academic Press","publication_status":"published"},{"date_published":"2017-02-21T00:00:00Z","page":"627 - 644","citation":{"ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026."},"publication":"Advances in Mathematics","article_processing_charge":"No","day":"21","scopus_import":"1","oa_version":"Submitted Version","intvolume":" 308","title":"Algebraic vertices of non-convex polyhedra","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1180","abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2016.12.026","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1508.07594","open_access":"1"}],"external_id":{"isi":["000409292900015"]},"oa":1,"publication_identifier":{"issn":["00018708"]},"month":"02","volume":308,"date_created":"2018-12-11T11:50:34Z","date_updated":"2023-09-20T11:21:27Z","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bárány","first_name":"Imre","full_name":"Bárány, Imre"},{"full_name":"Robins, Sinai","last_name":"Robins","first_name":"Sinai"}],"department":[{"_id":"HeEd"}],"publisher":"Academic Press","publication_status":"published","year":"2017","ec_funded":1,"publist_id":"6173"},{"ec_funded":1,"publist_id":"6182","date_updated":"2023-09-20T11:23:53Z","date_created":"2018-12-11T11:50:32Z","volume":37,"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","acknowledgement":"This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.","year":"2017","month":"10","publication_identifier":{"issn":["02099683"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00493-016-3308-y","isi":1,"quality_controlled":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"external_id":{"isi":["000418056000005"]},"abstract":[{"text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.","lang":"eng"}],"issue":"5","type":"journal_article","oa_version":"Submitted Version","status":"public","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","intvolume":" 37","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1173","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2017-10-01T00:00:00Z","page":"887 - 910","publication":"Combinatorica","citation":{"ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y","ieee":"H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” Combinatorica, vol. 37, no. 5. Springer, pp. 887–910, 2017.","ista":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","mla":"Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y.","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y."}}]