[{"year":"2020","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","keyword":["General Mathematics"],"date_created":"2022-03-18T11:39:30Z","citation":{"apa":"Akopyan, A., &#38; Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2020. <a href=\"https://doi.org/10.1093/imrn/rny037\">https://doi.org/10.1093/imrn/rny037</a>.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. <i>International Mathematics Research Notices</i>. 2020;2020(3):669-697. doi:<a href=\"https://doi.org/10.1093/imrn/rny037\">10.1093/imrn/rny037</a>","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” <i>International Mathematics Research Notices</i>, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020."},"article_type":"original","_id":"10867","doi":"10.1093/imrn/rny037","publication_status":"published","abstract":[{"lang":"eng","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."}],"external_id":{"isi":["000522852700002"],"arxiv":["1702.07513"]},"date_published":"2020-02-01T00:00:00Z","publisher":"Oxford University Press","volume":2020,"quality_controlled":"1","page":"669-697","department":[{"_id":"HeEd"}],"issue":"3","article_processing_charge":"No","oa":1,"date_updated":"2023-08-24T14:19:55Z","title":"Waist of balls in hyperbolic and spherical spaces","isi":1,"scopus_import":"1","intvolume":"      2020","language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","arxiv":1,"author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"month":"02","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"day":"01","type":"journal_article","status":"public"},{"publication_status":"published","external_id":{"arxiv":["1910.09917"]},"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"}],"publisher":"Canadian Conference on Computational Geometry","date_published":"2019-08-01T00:00:00Z","department":[{"_id":"HeEd"}],"page":"164-170","quality_controlled":"1","acknowledgement":"This research was performed in part at the 33rd BellairsWinter  Workshop  on  Computational  Geometry.    Wethank all other participants for a fruitful atmosphere.","year":"2019","citation":{"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 <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i> (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","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.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","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 <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, 164–70. Canadian Conference on Computational Geometry, 2019.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2019:164-170.","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” in <i>Proceedings of the 31st Canadian Conference on Computational Geometry</i>, Edmonton, Canada, 2019, pp. 164–170.","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."},"date_created":"2019-11-04T16:46:11Z","related_material":{"record":[{"id":"8317","relation":"extended_version","status":"public"}]},"_id":"6989","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"last_name":"Akitaya","full_name":"Akitaya, Hugo A","first_name":"Hugo A"},{"last_name":"Cheung","first_name":"Kenneth C","full_name":"Cheung, Kenneth C"},{"first_name":"Erik D","full_name":"Demaine, Erik D","last_name":"Demaine"},{"first_name":"Martin L","full_name":"Demaine, Martin L","last_name":"Demaine"},{"last_name":"Fekete","first_name":"Sandor P","full_name":"Fekete, Sandor P"},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"last_name":"Kostitsyna","full_name":"Kostitsyna, Irina","first_name":"Irina"},{"full_name":"Löffler, Maarten","first_name":"Maarten","last_name":"Löffler"},{"first_name":"Zuzana","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"full_name":"Schmidt, Christiane","first_name":"Christiane","last_name":"Schmidt"}],"arxiv":1,"conference":{"name":"CCCG: Canadian Conference in Computational Geometry","start_date":"2019-08-08","location":"Edmonton, Canada","end_date":"2019-08-10"},"month":"08","main_file_link":[{"url":"https://cccg.ca/proceedings/2019/proceedings.pdf","open_access":"1"}],"day":"01","oa_version":"Published Version","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","type":"conference","status":"public","oa":1,"date_updated":"2023-08-04T10:57:42Z","article_processing_charge":"No","title":"Folding polyominoes with holes into a cube","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry"},{"quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","type":"conference","date_published":"2019-11-28T00:00:00Z","publisher":"IEEE","publication_status":"published","author":[{"first_name":"Georg F","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"James","full_name":"Cook, James","last_name":"Cook"},{"last_name":"Fabrikant","full_name":"Fabrikant, Alex","first_name":"Alex"},{"last_name":"Gruteser","full_name":"Gruteser, Marco","first_name":"Marco"}],"abstract":[{"lang":"eng","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."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"None","day":"28","external_id":{"isi":["000521238102050"]},"month":"11","publication_identifier":{"isbn":["9781538670248"]},"conference":{"location":"Auckland, New Zealand","end_date":"2019-10-30","name":"ITSC: Intelligent Transportation Systems Conference","start_date":"2019-10-27"},"language":[{"iso":"eng"}],"_id":"7216","doi":"10.1109/ITSC.2019.8917514","publication":"2019 IEEE Intelligent Transportation Systems Conference","date_created":"2019-12-29T23:00:47Z","citation":{"apa":"Osang, G. F., Cook, J., Fabrikant, A., &#38; Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In <i>2019 IEEE Intelligent Transportation Systems Conference</i>. Auckland, New Zealand: IEEE. <a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">https://doi.org/10.1109/ITSC.2019.8917514</a>","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” <i>2019 IEEE Intelligent Transportation Systems Conference</i>, 8917514, IEEE, 2019, doi:<a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">10.1109/ITSC.2019.8917514</a>.","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 <i>2019 IEEE Intelligent Transportation Systems Conference</i>. IEEE, 2019. <a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">https://doi.org/10.1109/ITSC.2019.8917514</a>.","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: <i>2019 IEEE Intelligent Transportation Systems Conference</i>. IEEE; 2019. doi:<a href=\"https://doi.org/10.1109/ITSC.2019.8917514\">10.1109/ITSC.2019.8917514</a>","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 <i>2019 IEEE Intelligent Transportation Systems Conference</i>, Auckland, New Zealand, 2019.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019."},"title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","article_processing_charge":"No","year":"2019","date_updated":"2023-09-06T14:50:28Z","scopus_import":"1","article_number":"8917514","isi":1},{"department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"date_published":"2019-03-16T00:00:00Z","status":"public","type":"preprint","arxiv":1,"author":[{"full_name":"Biniaz, Ahmad","first_name":"Ahmad","last_name":"Biniaz"},{"first_name":"Kshitij","full_name":"Jain, Kshitij","last_name":"Jain"},{"first_name":"Anna","full_name":"Lubiw, Anna","last_name":"Lubiw"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","orcid":"0000-0002-6660-1322","first_name":"Zuzana","full_name":"Masárová, Zuzana"},{"last_name":"Miltzow","first_name":"Tillmann","full_name":"Miltzow, Tillmann"},{"last_name":"Mondal","first_name":"Debajyoti","full_name":"Mondal, Debajyoti"},{"full_name":"Naredla, Anurag Murty","first_name":"Anurag Murty","last_name":"Naredla"},{"last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","first_name":"Josef"},{"first_name":"Alexi","full_name":"Turcotte, Alexi","last_name":"Turcotte"}],"publication_status":"submitted","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"oa_version":"Preprint","day":"16","external_id":{"arxiv":["1903.06981"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"month":"03","language":[{"iso":"eng"}],"_id":"7950","publication":"arXiv","title":"Token swapping on trees","date_created":"2020-06-08T12:25:25Z","citation":{"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.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” <i>ArXiv</i>, 1903.06981.","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.” <i>ArXiv</i>, n.d.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. <i>arXiv</i>.","ieee":"A. Biniaz <i>et al.</i>, “Token swapping on trees,” <i>arXiv</i>. .","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. <i>arXiv</i>."},"article_processing_charge":"No","year":"2019","oa":1,"date_updated":"2024-01-04T12:42:08Z","article_number":"1903.06981","related_material":{"record":[{"id":"7944","relation":"dissertation_contains","status":"public"},{"relation":"later_version","id":"12833","status":"public"}]}},{"page":"865–878","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":62,"publisher":"Springer","date_published":"2019-12-01T00:00:00Z","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"abstract":[{"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.","lang":"eng"}],"ddc":["516"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","doi":"10.1007/s00454-018-0049-2","file_date_updated":"2020-07-14T12:47:10Z","_id":"5678","article_type":"original","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"6287","status":"public"}]},"citation":{"apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4. Springer, pp. 865–878, 2019.","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. 2019;62(4):865–878. doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878."},"date_created":"2018-12-16T22:59:20Z","year":"2019","type":"journal_article","status":"public","oa_version":"Published Version","day":"01","file":[{"file_id":"5932","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","date_updated":"2020-07-14T12:47:10Z","date_created":"2019-02-06T10:10:46Z","creator":"dernst","content_type":"application/pdf","file_size":599339,"relation":"main_file","access_level":"open_access"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"12","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","orcid":"0000-0002-0659-3201"}],"arxiv":1,"publication":"Discrete and Computational Geometry","language":[{"iso":"eng"}],"intvolume":"        62","has_accepted_license":"1","scopus_import":"1","isi":1,"title":"Poisson–Delaunay Mosaics of Order k","oa":1,"date_updated":"2023-09-07T12:07:12Z","article_processing_charge":"Yes (via OA deal)","issue":"4"},{"title":"Two circles and only a straightedge","date_updated":"2023-08-24T14:48:59Z","oa":1,"article_processing_charge":"No","scopus_import":"1","intvolume":"       147","isi":1,"language":[{"iso":"eng"}],"publication":"Proceedings of the American Mathematical Society","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Fedorov","full_name":"Fedorov, Roman","first_name":"Roman"}],"arxiv":1,"day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"01","type":"journal_article","status":"public","date_created":"2019-02-24T22:59:19Z","citation":{"ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” <i>Proceedings of the American Mathematical Society</i>, vol. 147. AMS, pp. 91–102, 2019.","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. 2019;147:91-102. doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>","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.” <i>Proceedings of the American Mathematical Society</i>. AMS, 2019. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” <i>Proceedings of the American Mathematical Society</i>, vol. 147, AMS, 2019, pp. 91–102, doi:<a href=\"https://doi.org/10.1090/proc/14240\">10.1090/proc/14240</a>.","apa":"Akopyan, A., &#38; Fedorov, R. (2019). Two circles and only a straightedge. <i>Proceedings of the American Mathematical Society</i>. AMS. <a href=\"https://doi.org/10.1090/proc/14240\">https://doi.org/10.1090/proc/14240</a>"},"year":"2019","_id":"6050","doi":"10.1090/proc/14240","publication_status":"published","external_id":{"isi":["000450363900008"],"arxiv":["1709.02562"]},"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"}],"page":"91-102","department":[{"_id":"HeEd"}],"volume":147,"quality_controlled":"1","publisher":"AMS","date_published":"2019-01-01T00:00:00Z"},{"status":"public","type":"journal_article","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"date_updated":"2020-07-14T12:47:32Z","date_created":"2019-06-03T09:30:01Z","file_id":"6516","checksum":"57b4df2f16a74eb499734ec8ee240178","file_name":"mainJournalFinal.pdf","relation":"main_file","content_type":"application/pdf","file_size":2170882,"access_level":"open_access","creator":"mwintrae"}],"oa_version":"Published Version","day":"01","publication_identifier":{"issn":["1920-180X"]},"month":"07","author":[{"last_name":"Dyer","full_name":"Dyer, Ramsay","first_name":"Ramsay"},{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken"}],"publication":"Journal of Computational Geometry ","language":[{"iso":"eng"}],"scopus_import":1,"has_accepted_license":"1","intvolume":"        10","title":"Simplices modelled on spaces of constant curvature","issue":"1","oa":1,"date_updated":"2021-01-12T08:07:50Z","volume":10,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"223–256","date_published":"2019-07-01T00:00:00Z","publisher":"Carleton University","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"abstract":[{"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.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"publication_status":"published","doi":"10.20382/jocg.v10i1a9","_id":"6515","file_date_updated":"2020-07-14T12:47:32Z","ec_funded":1,"citation":{"ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” <i>Journal of Computational Geometry </i>, vol. 10, no. 1. Carleton University, pp. 223–256, 2019.","ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. <i>Journal of Computational Geometry </i>. 2019;10(1):223–256. doi:<a href=\"https://doi.org/10.20382/jocg.v10i1a9\">10.20382/jocg.v10i1a9</a>","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.” <i>Journal of Computational Geometry </i>, vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:<a href=\"https://doi.org/10.20382/jocg.v10i1a9\">10.20382/jocg.v10i1a9</a>.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” <i>Journal of Computational Geometry </i>. Carleton University, 2019. <a href=\"https://doi.org/10.20382/jocg.v10i1a9\">https://doi.org/10.20382/jocg.v10i1a9</a>.","apa":"Dyer, R., Vegter, G., &#38; Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. <i>Journal of Computational Geometry </i>. Carleton University. <a href=\"https://doi.org/10.20382/jocg.v10i1a9\">https://doi.org/10.20382/jocg.v10i1a9</a>"},"date_created":"2019-06-03T09:35:33Z","year":"2019"},{"month":"08","oa_version":"Published Version","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_size":2665013,"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"kschuh","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-08T15:24:26Z","file_id":"6624","file_name":"Elsevier_2019_Edelsbrunner.pdf","checksum":"7c99be505dc7533257d42eb1830cef04"}],"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"full_name":"Ölsböck, Katharina","first_name":"Katharina","orcid":"0000-0002-4672-8297","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"status":"public","type":"journal_article","isi":1,"scopus_import":"1","intvolume":"        73","has_accepted_license":"1","oa":1,"date_updated":"2023-09-07T13:15:29Z","article_processing_charge":"No","title":"Holes and dependences in an ordered complex","publication":"Computer Aided Geometric Design","language":[{"iso":"eng"}],"ddc":["000"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"external_id":{"isi":["000485207800001"]},"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."}],"publication_status":"published","publisher":"Elsevier","date_published":"2019-08-01T00:00:00Z","page":"1-15","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":73,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"ec_funded":1,"related_material":{"record":[{"id":"7460","relation":"dissertation_contains","status":"public"}]},"year":"2019","citation":{"chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>.","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>, vol. 73, Elsevier, 2019, pp. 1–15, doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” <i>Computer Aided Geometric Design</i>, vol. 73. Elsevier, pp. 1–15, 2019.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. 2019;73:1-15. doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2019). Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>"},"date_created":"2019-07-07T21:59:20Z","doi":"10.1016/j.cagd.2019.06.003","file_date_updated":"2020-07-14T12:47:34Z","_id":"6608"},{"author":[{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"full_name":"Wintraecken, Mathijs","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","orcid":"0000-0002-7472-2220"}],"publication_status":"published","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"ddc":["004"],"month":"08","oa_version":"Submitted Version","day":"01","file":[{"file_id":"6629","checksum":"ceabd152cfa55170d57763f9c6c60a53","file_name":"IntrinsicExtrinsicCCCG2019.pdf","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-12T08:32:46Z","creator":"mwintrae","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":321176}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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."}],"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"date_published":"2019-08-01T00:00:00Z","type":"conference","status":"public","department":[{"_id":"HeEd"}],"page":"275-279","quality_controlled":"1","oa":1,"date_updated":"2021-01-12T08:08:16Z","year":"2019","date_created":"2019-07-12T08:34:57Z","citation":{"ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: <i>The 31st Canadian Conference in Computational Geometry</i>. ; 2019:275-279.","ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in <i>The 31st Canadian Conference in Computational Geometry</i>, Edmonton, Canada, 2019, pp. 275–279.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 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.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” <i>The 31st Canadian Conference in Computational Geometry</i>, 2019, pp. 275–79.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In <i>The 31st Canadian Conference in Computational Geometry</i>, 275–79, 2019.","apa":"Vegter, G., &#38; Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In <i>The 31st Canadian Conference in Computational Geometry</i> (pp. 275–279). Edmonton, Canada."},"title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","ec_funded":1,"has_accepted_license":"1","scopus_import":1,"file_date_updated":"2020-07-14T12:47:34Z","_id":"6628","language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry"},{"publication":"Topological Methods in Nonlinear Analysis","language":[{"iso":"eng"}],"scopus_import":"1","intvolume":"        53","isi":1,"title":"Lower and upper bounds for the waists of different spaces","date_updated":"2023-08-29T06:32:48Z","oa":1,"issue":"2","article_processing_charge":"No","type":"journal_article","status":"public","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"06","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Hubard","full_name":"Hubard, Alfredo","first_name":"Alfredo"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"arxiv":1,"doi":"10.12775/TMNA.2019.008","_id":"6634","ec_funded":1,"citation":{"apa":"Akopyan, A., Hubard, A., &#38; Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. <i>Topological Methods in Nonlinear Analysis</i>. 2019;53(2):457-490. doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","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.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>. Akademicka Platforma Czasopism, 2019. <a href=\"https://doi.org/10.12775/TMNA.2019.008\">https://doi.org/10.12775/TMNA.2019.008</a>.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:<a href=\"https://doi.org/10.12775/TMNA.2019.008\">10.12775/TMNA.2019.008</a>."},"date_created":"2019-07-14T21:59:19Z","year":"2019","page":"457-490","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":53,"publisher":"Akademicka Platforma Czasopism","date_published":"2019-06-01T00:00:00Z","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"external_id":{"isi":["000472541600004"],"arxiv":["1612.06926"]},"abstract":[{"lang":"eng","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."}],"publication_status":"published"},{"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"first_name":"Hubert","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"arxiv":1,"conference":{"start_date":"2019-06-18","name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21","location":"Portland, OR, United States"},"month":"06","publication_identifier":{"isbn":["9783959771047"]},"day":"01","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2019_LIPICS_Edelsbrunner.pdf","file_id":"6666","checksum":"8ec8720730d4c789bf7b06540f1c29f4","date_created":"2019-07-24T06:40:01Z","date_updated":"2020-07-14T12:47:35Z","creator":"dernst","relation":"main_file","file_size":1355179,"content_type":"application/pdf","access_level":"open_access"}],"alternative_title":["LIPIcs"],"type":"conference","status":"public","date_updated":"2021-01-12T08:08:23Z","oa":1,"title":"Topological data analysis in information space","intvolume":"       129","scopus_import":1,"has_accepted_license":"1","language":[{"iso":"eng"}],"publication":"35th International Symposium on Computational Geometry","publication_status":"published","ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["1903.08510"]},"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."}],"project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_published":"2019-06-01T00:00:00Z","page":"31:1-31:14","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":129,"year":"2019","citation":{"apa":"Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2019). Topological data analysis in information space. In <i>35th International Symposium on Computational Geometry</i> (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">https://doi.org/10.4230/LIPICS.SOCG.2019.31</a>","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: <i>35th International Symposium on Computational Geometry</i>. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">10.4230/LIPICS.SOCG.2019.31</a>","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in <i>35th International Symposium on Computational Geometry</i>, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","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.” <i>35th International Symposium on Computational Geometry</i>, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">10.4230/LIPICS.SOCG.2019.31</a>.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In <i>35th International Symposium on Computational Geometry</i>, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2019.31\">https://doi.org/10.4230/LIPICS.SOCG.2019.31</a>.","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."},"date_created":"2019-07-17T10:36:09Z","file_date_updated":"2020-07-14T12:47:35Z","_id":"6648","doi":"10.4230/LIPICS.SOCG.2019.31"},{"author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"month":"06","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"file":[{"date_updated":"2020-07-14T12:47:36Z","date_created":"2019-07-31T08:09:56Z","file_id":"6741","checksum":"a5b244db9f751221409cf09c97ee0935","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","access_level":"open_access","relation":"main_file","file_size":2215157,"content_type":"application/pdf","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Published Version","status":"public","type":"journal_article","article_processing_charge":"Yes (via OA deal)","issue":"1-2","date_updated":"2023-08-22T12:37:47Z","oa":1,"title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","has_accepted_license":"1","intvolume":"         3","language":[{"iso":"eng"}],"publication":"Journal of Applied and Computational Topology","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["000"],"abstract":[{"lang":"eng","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."}],"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"date_published":"2019-06-01T00:00:00Z","publisher":"Springer Nature","volume":3,"quality_controlled":"1","page":"29–58","department":[{"_id":"HeEd"}],"year":"2019","citation":{"short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. <i>Journal of Applied and Computational Topology</i>. 2019;3(1-2):29–58. doi:<a href=\"https://doi.org/10.1007/s41468-019-00029-8\">10.1007/s41468-019-00029-8</a>","ieee":"J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” <i>Journal of Applied and Computational Topology</i>, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.","chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s41468-019-00029-8\">https://doi.org/10.1007/s41468-019-00029-8</a>.","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.","mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” <i>Journal of Applied and Computational Topology</i>, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:<a href=\"https://doi.org/10.1007/s41468-019-00029-8\">10.1007/s41468-019-00029-8</a>.","apa":"Boissonnat, J.-D., Lieutier, A., &#38; Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-019-00029-8\">https://doi.org/10.1007/s41468-019-00029-8</a>"},"date_created":"2019-07-24T08:37:29Z","ec_funded":1,"_id":"6671","article_type":"original","file_date_updated":"2020-07-14T12:47:36Z","doi":"10.1007/s41468-019-00029-8"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["520","530"],"abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["1812.07678"],"isi":["000475839300003"]},"publication_status":"published","date_published":"2019-07-17T00:00:00Z","publisher":"EDP Sciences","volume":627,"quality_controlled":"1","department":[{"_id":"HeEd"}],"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"}],"article_number":"A163","year":"2019","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. <i>Astronomy and Astrophysics</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/0004-6361/201834916\">https://doi.org/10.1051/0004-6361/201834916</a>","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).","ieee":"P. Pranav <i>et al.</i>, “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” <i>Astronomy and Astrophysics</i>, vol. 627. EDP Sciences, 2019.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. <i>Astronomy and Astrophysics</i>. 2019;627. doi:<a href=\"https://doi.org/10.1051/0004-6361/201834916\">10.1051/0004-6361/201834916</a>","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.” <i>Astronomy and Astrophysics</i>. EDP Sciences, 2019. <a href=\"https://doi.org/10.1051/0004-6361/201834916\">https://doi.org/10.1051/0004-6361/201834916</a>.","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” <i>Astronomy and Astrophysics</i>, vol. 627, A163, EDP Sciences, 2019, doi:<a href=\"https://doi.org/10.1051/0004-6361/201834916\">10.1051/0004-6361/201834916</a>.","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."},"date_created":"2019-08-04T21:59:18Z","doi":"10.1051/0004-6361/201834916","article_type":"original","_id":"6756","file_date_updated":"2020-07-14T12:47:39Z","publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"date_created":"2019-08-05T08:08:59Z","date_updated":"2020-07-14T12:47:39Z","file_name":"2019_AstronomyAstrophysics_Pranav.pdf","file_id":"6766","checksum":"83b9209ed9eefbdcefd89019c5a97805","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":14420451,"creator":"dernst"}],"oa_version":"Published Version","day":"17","arxiv":1,"author":[{"first_name":"Pratyush","full_name":"Pranav, Pratyush","last_name":"Pranav"},{"first_name":"Robert J.","full_name":"Adler, Robert J.","last_name":"Adler"},{"last_name":"Buchert","first_name":"Thomas","full_name":"Buchert, Thomas"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jones, Bernard J.T.","first_name":"Bernard J.T.","last_name":"Jones"},{"full_name":"Schwartzman, Armin","first_name":"Armin","last_name":"Schwartzman"},{"last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert","first_name":"Hubert"},{"full_name":"Van De Weygaert, Rien","first_name":"Rien","last_name":"Van De Weygaert"}],"type":"journal_article","status":"public","isi":1,"scopus_import":"1","has_accepted_license":"1","intvolume":"       627","article_processing_charge":"No","date_updated":"2023-08-29T07:01:48Z","oa":1,"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","publication":"Astronomy and Astrophysics","language":[{"iso":"eng"}]},{"publication":"Bulletin of the London Mathematical Society","language":[{"iso":"eng"}],"isi":1,"intvolume":"        51","scopus_import":"1","oa":1,"date_updated":"2023-08-29T07:08:34Z","article_processing_charge":"No","issue":"5","title":"The Regge symmetry, confocal conics, and the Schläfli formula","type":"journal_article","status":"public","publication_identifier":{"eissn":["14692120"],"issn":["00246093"]},"month":"10","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.04929"}],"day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"first_name":"Ivan","full_name":"Izmestiev, Ivan","last_name":"Izmestiev"}],"arxiv":1,"doi":"10.1112/blms.12276","article_type":"original","_id":"6793","ec_funded":1,"year":"2019","date_created":"2019-08-11T21:59:23Z","citation":{"apa":"Akopyan, A., &#38; Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>","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.","chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society, 2019. <a href=\"https://doi.org/10.1112/blms.12276\">https://doi.org/10.1112/blms.12276</a>.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. <i>Bulletin of the London Mathematical Society</i>. 2019;51(5):765-775. doi:<a href=\"https://doi.org/10.1112/blms.12276\">10.1112/blms.12276</a>","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” <i>Bulletin of the London Mathematical Society</i>, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019."},"publisher":"London Mathematical Society","date_published":"2019-10-01T00:00:00Z","page":"765-775","department":[{"_id":"HeEd"}],"volume":51,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"external_id":{"isi":["000478560200001"],"arxiv":["1903.04929"]},"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"}],"publication_status":"published"},{"date_created":"2019-08-22T07:54:13Z","citation":{"apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. 2019;538:261-289. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” <i>Journal of Algebra</i>, vol. 538. Elsevier, pp. 261–289, 2019.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>, vol. 538, Elsevier, 2019, pp. 261–89, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289."},"year":"2019","_id":"6828","article_type":"original","doi":"10.1016/j.jalgebra.2019.07.027","publication_status":"published","abstract":[{"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 .","lang":"eng"}],"external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"volume":538,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"261-289","date_published":"2019-11-15T00:00:00Z","publisher":"Elsevier","title":"Arakawa-Suzuki functors for Whittaker modules","article_processing_charge":"No","oa":1,"date_updated":"2023-08-29T07:11:47Z","intvolume":"       538","isi":1,"language":[{"iso":"eng"}],"publication":"Journal of Algebra","arxiv":1,"author":[{"full_name":"Brown, Adam","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"oa_version":"Preprint","day":"15","month":"11","publication_identifier":{"issn":["0021-8693"]},"status":"public","type":"journal_article"},{"month":"10","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02870"}],"arxiv":1,"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","first_name":"Anton"}],"type":"journal_article","status":"public","isi":1,"scopus_import":"1","intvolume":"        28","issue":"5","article_processing_charge":"No","date_updated":"2023-09-15T12:10:35Z","oa":1,"title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","publication":"Annals of Applied Probability","language":[{"iso":"eng"}],"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."}],"external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"publication_status":"published","date_published":"2018-10-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","volume":28,"quality_controlled":"1","page":"3215 - 3238","department":[{"_id":"HeEd"}],"project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"related_material":{"record":[{"id":"6287","relation":"dissertation_contains","status":"public"}]},"year":"2018","date_created":"2018-12-11T11:44:33Z","publist_id":"7967","citation":{"apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AAP1389\">https://doi.org/10.1214/18-AAP1389</a>","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. <i>Annals of Applied Probability</i>. 2018;28(5):3215-3238. doi:<a href=\"https://doi.org/10.1214/18-AAP1389\">10.1214/18-AAP1389</a>","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” <i>Annals of Applied Probability</i>, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","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.” <i>Annals of Applied Probability</i>, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:<a href=\"https://doi.org/10.1214/18-AAP1389\">10.1214/18-AAP1389</a>.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2018. <a href=\"https://doi.org/10.1214/18-AAP1389\">https://doi.org/10.1214/18-AAP1389</a>.","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."},"doi":"10.1214/18-AAP1389","_id":"87","article_type":"original"},{"author":[{"orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy"}],"month":"06","day":"01","oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"file_name":"2018_Springer_Akopyan.pdf","file_id":"7222","checksum":"1febcfc1266486053a069e3425ea3713","date_updated":"2020-07-14T12:47:44Z","date_created":"2020-01-03T11:35:08Z","creator":"kschuh","file_size":1140860,"relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"type":"journal_article","status":"public","oa":1,"date_updated":"2023-09-08T11:40:29Z","issue":"1","article_processing_charge":"Yes (via OA deal)","title":"3-Webs generated by confocal conics and circles","isi":1,"intvolume":"       194","scopus_import":"1","has_accepted_license":"1","language":[{"iso":"eng"}],"publication":"Geometriae Dedicata","publication_status":"published","ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["000431418800004"]},"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."}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"publisher":"Springer","date_published":"2018-06-01T00:00:00Z","department":[{"_id":"HeEd"}],"page":"55 - 64","quality_controlled":"1","volume":194,"year":"2018","publist_id":"7014","citation":{"apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. <i>Geometriae Dedicata</i>. Springer. <a href=\"https://doi.org/10.1007/s10711-017-0265-6\">https://doi.org/10.1007/s10711-017-0265-6</a>","chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” <i>Geometriae Dedicata</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s10711-017-0265-6\">https://doi.org/10.1007/s10711-017-0265-6</a>.","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” <i>Geometriae Dedicata</i>, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:<a href=\"https://doi.org/10.1007/s10711-017-0265-6\">10.1007/s10711-017-0265-6</a>.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64.","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. <i>Geometriae Dedicata</i>. 2018;194(1):55-64. doi:<a href=\"https://doi.org/10.1007/s10711-017-0265-6\">10.1007/s10711-017-0265-6</a>","ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” <i>Geometriae Dedicata</i>, vol. 194, no. 1. Springer, pp. 55–64, 2018.","short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64."},"date_created":"2018-12-11T11:47:57Z","ec_funded":1,"file_date_updated":"2020-07-14T12:47:44Z","_id":"692","article_type":"original","doi":"10.1007/s10711-017-0265-6"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"oa_version":"Preprint","day":"13","external_id":{"arxiv":["1804.03057"]},"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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"09","publication_status":"published","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"first_name":"Sergey","full_name":"Avvakumov, Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"arxiv":1,"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"arXiv","date_published":"2018-09-13T00:00:00Z","status":"public","type":"preprint","project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"ec_funded":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"8156"}]},"article_number":"1804.03057","date_created":"2018-12-11T11:44:30Z","title":"Convex fair partitions into arbitrary number of pieces","citation":{"ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","mla":"Akopyan, Arseniy, et al. <i>Convex Fair Partitions into Arbitrary Number of Pieces</i>. 1804.03057, arXiv, 2018, doi:<a href=\"https://doi.org/10.48550/arXiv.1804.03057\">10.48550/arXiv.1804.03057</a>.","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","apa":"Akopyan, A., Avvakumov, S., &#38; Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. <a href=\"https://doi.org/10.48550/arXiv.1804.03057\">https://doi.org/10.48550/arXiv.1804.03057</a>"},"date_updated":"2023-12-18T10:51:02Z","oa":1,"year":"2018","article_processing_charge":"No","doi":"10.48550/arXiv.1804.03057","_id":"75","language":[{"iso":"eng"}]},{"has_accepted_license":"1","scopus_import":1,"intvolume":"        99","date_updated":"2023-09-07T13:29:00Z","oa":1,"title":"The multi-cover persistence of Euclidean balls","language":[{"iso":"eng"}],"month":"06","conference":{"end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11","name":"SoCG: Symposium on Computational Geometry"},"file":[{"relation":"main_file","file_size":528018,"access_level":"open_access","content_type":"application/pdf","creator":"dernst","date_created":"2018-12-18T09:27:22Z","date_updated":"2020-07-14T12:45:19Z","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","file_id":"5738","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"11","oa_version":"Published Version","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"first_name":"Georg F","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","orcid":"0000-0002-8882-5116"}],"status":"public","type":"conference","alternative_title":["LIPIcs"],"article_number":"34","related_material":{"record":[{"id":"9317","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"9056"}]},"year":"2018","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).","date_created":"2018-12-11T11:45:05Z","citation":{"ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">https://doi.org/10.4230/LIPIcs.SoCG.2018.34</a>.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. <i>The Multi-Cover Persistence of Euclidean Balls</i>. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">10.4230/LIPIcs.SoCG.2018.34</a>.","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.","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">10.4230/LIPIcs.SoCG.2018.34</a>","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","apa":"Edelsbrunner, H., &#38; 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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.34\">https://doi.org/10.4230/LIPIcs.SoCG.2018.34</a>"},"publist_id":"7732","doi":"10.4230/LIPIcs.SoCG.2018.34","_id":"187","file_date_updated":"2020-07-14T12:45:19Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["516"],"abstract":[{"lang":"eng","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. "}],"publication_status":"published","date_published":"2018-06-11T00:00:00Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","volume":99,"department":[{"_id":"HeEd"}],"project":[{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}]},{"alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"status":"public","type":"conference","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Virk, Ziga","first_name":"Ziga","last_name":"Virk"},{"full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"conference":{"end_date":"2018-06-14","location":"Budapest, Hungary","start_date":"2018-06-11","name":"SoCG: Symposium on Computational Geometry"},"month":"06","day":"11","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2018-12-17T16:31:31Z","date_updated":"2020-07-14T12:45:20Z","file_id":"5724","checksum":"7509403803b3ac1aee94bbc2ad293d21","file_name":"2018_LIPIcs_Edelsbrunner.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_size":489080,"creator":"dernst"}],"language":[{"iso":"eng"}],"oa":1,"date_updated":"2021-01-12T06:53:48Z","title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","intvolume":"        99","scopus_import":1,"has_accepted_license":"1","project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_published":"2018-06-11T00:00:00Z","page":"35:1 - 35:13","department":[{"_id":"HeEd"}],"volume":99,"quality_controlled":"1","publication_status":"published","ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2020-07-14T12:45:20Z","_id":"188","doi":"10.4230/LIPIcs.SoCG.2018.35","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","date_created":"2018-12-11T11:45:05Z","publist_id":"7733","citation":{"short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","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.","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:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">10.4230/LIPIcs.SoCG.2018.35</a>","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.","mla":"Edelsbrunner, Herbert, et al. <i>Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry</i>. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">10.4230/LIPIcs.SoCG.2018.35</a>.","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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">https://doi.org/10.4230/LIPIcs.SoCG.2018.35</a>.","apa":"Edelsbrunner, H., Virk, Z., &#38; 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. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2018.35\">https://doi.org/10.4230/LIPIcs.SoCG.2018.35</a>"}}]