[{"publication_identifier":{"eissn":["1879-081X"],"issn":["0925-7721"]},"related_material":{"record":[{"relation":"shorter_version","status":"public","id":"6989"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"article_number":"101700","article_type":"original","citation":{"ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. 2021;93. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>","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.","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.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>.","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).","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. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” <i>Computational Geometry: Theory and Applications</i>, vol. 93. Elsevier, 2021.","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>, vol. 93, 101700, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>."},"type":"journal_article","project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"quality_controlled":"1","year":"2021","day":"01","date_published":"2021-02-01T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"_id":"8317","article_processing_charge":"No","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"first_name":"Hugo A.","full_name":"Akitaya, Hugo A.","last_name":"Akitaya"},{"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","full_name":"Demaine, Martin L.","first_name":"Martin L."},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"last_name":"Kleist","full_name":"Kleist, Linda","first_name":"Linda"},{"first_name":"Irina","last_name":"Kostitsyna","full_name":"Kostitsyna, Irina"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"full_name":"Schmidt, Christiane","last_name":"Schmidt","first_name":"Christiane"}],"publisher":"Elsevier","volume":93,"status":"public","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.","arxiv":1,"publication":"Computational Geometry: Theory and Applications","date_created":"2020-08-30T22:01:09Z","corr_author":"1","isi":1,"month":"02","intvolume":"        93","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2026-04-16T09:14:31Z","scopus_import":"1","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"title":"Folding polyominoes with holes into a cube","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"}],"doi":"10.1016/j.comgeo.2020.101700"},{"citation":{"mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” <i>15th International Conference on Algorithms and Computation</i>, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:<a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">10.1007/978-3-030-68211-8_18</a>.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In <i>15th International Conference on Algorithms and Computation</i>, 12635:221–33. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">https://doi.org/10.1007/978-3-030-68211-8_18</a>.","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.","ieee":"O. Aichholzer <i>et al.</i>, “On compatible matchings,” in <i>15th International Conference on Algorithms and Computation</i>, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In <i>15th International Conference on Algorithms and Computation</i> (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">https://doi.org/10.1007/978-3-030-68211-8_18</a>","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.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: <i>15th International Conference on Algorithms and Computation</i>. Vol 12635. Springer Nature; 2021:221-233. doi:<a href=\"https://doi.org/10.1007/978-3-030-68211-8_18\">10.1007/978-3-030-68211-8_18</a>"},"type":"conference","quality_controlled":"1","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"},{"_id":"2584A770-B435-11E9-9278-68D0E5697425","name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","grant_number":"P 23499-N23"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF","grant_number":"S11407"}],"publication_identifier":{"issn":["0302-9743"],"eisbn":["9783030682118"],"isbn":["9783030682101"],"eissn":["1611-3349"]},"main_file_link":[{"url":"https://arxiv.org/abs/2101.03928","open_access":"1"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"11938"}]},"status":"public","ec_funded":1,"volume":12635,"arxiv":1,"conference":{"end_date":"2021-03-02","location":"Yangon, Myanmar","name":"WALCOM: Algorithms and Computation","start_date":"2021-02-28"},"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).","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"day":"16","year":"2021","date_published":"2021-02-16T00:00:00Z","publisher":"Springer Nature","alternative_title":["LNCS"],"author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M","last_name":"Arroyo Guevara","full_name":"Arroyo Guevara, Alan M"},{"full_name":"Masárová, Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Irene","full_name":"Parada, Irene","last_name":"Parada"},{"full_name":"Perz, Daniel","last_name":"Perz","first_name":"Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","last_name":"Tkadlec"},{"first_name":"Birgit","full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber"}],"_id":"9296","article_processing_charge":"No","intvolume":"     12635","oa":1,"publication":"15th International Conference on Algorithms and Computation","page":"221-233","date_created":"2021-03-28T22:01:41Z","isi":1,"month":"02","title":"On compatible matchings","abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["2101.03928"],"isi":["001435069600018"]},"doi":"10.1007/978-3-030-68211-8_18","oa_version":"Preprint","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2026-04-16T09:18:21Z"},{"publication":"Discrete Geometry and Mathematical Morphology","page":"152-163","date_created":"2021-08-08T22:01:29Z","isi":1,"month":"05","intvolume":"     12708","oa_version":"None","language":[{"iso":"eng"}],"date_updated":"2026-04-16T09:26:30Z","publication_status":"published","scopus_import":"1","external_id":{"isi":["001286400400010"]},"abstract":[{"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.","lang":"eng"}],"title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","doi":"10.1007/978-3-030-76657-3_10","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783030766566"],"issn":["0302-9743"]},"citation":{"mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” <i>Discrete Geometry and Mathematical Morphology</i>, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., &#38; Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In <i>Discrete Geometry and Mathematical Morphology</i> (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>","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 <i>Discrete Geometry and Mathematical Morphology</i>, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","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 <i>Discrete Geometry and Mathematical Morphology</i>, 12708:152–63. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: <i>Discrete Geometry and Mathematical Morphology</i>. Vol 12708. Springer Nature; 2021:152-163. doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>","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."},"type":"conference","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","year":"2021","day":"16","date_published":"2021-05-16T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"_id":"9824","article_processing_charge":"No","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"full_name":"Andres, Eric","last_name":"Andres","first_name":"Eric"}],"publisher":"Springer Nature","alternative_title":["LNCS"],"volume":12708,"ec_funded":1,"status":"public","conference":{"name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","start_date":"2021-05-24","end_date":"2021-05-27","location":"Uppsala, Sweden"},"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)."},{"type":"journal_article","quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>.","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. 2020;4(4):455-480. doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>","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.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>."},"issue":"4","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"has_accepted_license":"1","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.","file_date_updated":"2024-03-04T10:52:42Z","volume":4,"file":[{"success":1,"creator":"dernst","file_name":"2020_JourApplCompTopology_Bauer.pdf","content_type":"application/pdf","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","relation":"main_file","file_id":"15065","date_updated":"2024-03-04T10:52:42Z","access_level":"open_access","date_created":"2024-03-04T10:52:42Z","file_size":851190}],"license":"https://creativecommons.org/licenses/by/4.0/","status":"public","_id":"15064","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Bauer","full_name":"Bauer, U.","first_name":"U."},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"first_name":"M.","full_name":"Mrozek, M.","last_name":"Mrozek"}],"publisher":"Springer Nature","day":"01","year":"2020","date_published":"2020-12-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"oa":1,"intvolume":"         4","ddc":["500"],"month":"12","page":"455-480","publication":"Journal of Applied and Computational Topology","date_created":"2024-03-04T10:47:49Z","doi":"10.1007/s41468-020-00058-8","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"}],"title":"Čech-Delaunay gradient flow and homology inference for self-maps","date_updated":"2024-03-04T10:54:04Z","publication_status":"published","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}]},{"oa_version":"Preprint","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2023-08-24T14:19:55Z","title":"Waist of balls in hyperbolic and spherical spaces","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":{"arxiv":["1702.07513"],"isi":["000522852700002"]},"doi":"10.1093/imrn/rny037","page":"669-697","publication":"International Mathematics Research Notices","date_created":"2022-03-18T11:39:30Z","isi":1,"month":"02","intvolume":"      2020","oa":1,"department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","year":"2020","date_published":"2020-02-01T00:00:00Z","publisher":"Oxford University Press","_id":"10867","article_processing_charge":"No","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"status":"public","volume":2020,"arxiv":1,"acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"keyword":["General Mathematics"],"issue":"3","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"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>","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.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","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>.","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>","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>."},"article_type":"original","type":"journal_article","quality_controlled":"1"},{"publisher":"Springer Nature","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"orcid":"0000-0002-4672-8297","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","last_name":"Ölsböck","full_name":"Ölsböck, Katharina"}],"_id":"7666","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2020-03-20T00:00:00Z","year":"2020","day":"20","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).","status":"public","ec_funded":1,"file":[{"file_size":701673,"date_created":"2020-11-20T13:22:21Z","date_updated":"2020-11-20T13:22:21Z","access_level":"open_access","relation":"main_file","file_id":"8786","creator":"dernst","success":1,"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","content_type":"application/pdf","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf"}],"volume":64,"file_date_updated":"2020-11-20T13:22:21Z","has_accepted_license":"1","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"quality_controlled":"1","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"type":"journal_article","citation":{"mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 759–75, doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. 2020;64:759-775. doi:<a href=\"https://doi.org/10.1007/s00454-020-00188-x\">10.1007/s00454-020-00188-x</a>","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.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 759–775, 2020.","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00188-x\">https://doi.org/10.1007/s00454-020-00188-x</a>"},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:48:36Z","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1007/s00454-020-00188-x","title":"Tri-partitions and bases of an ordered complex","abstract":[{"lang":"eng","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."}],"external_id":{"isi":["000520918800001"]},"month":"03","ddc":["510"],"isi":1,"corr_author":"1","date_created":"2020-04-19T22:00:56Z","page":"759-775","publication":"Discrete and Computational Geometry","oa":1,"intvolume":"        64"},{"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"quality_controlled":"1","type":"conference","citation":{"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.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: <i>36th International Symposium on Computational Geometry</i>. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in <i>36th International Symposium on Computational Geometry</i>, Zürich, Switzerland, 2020, vol. 164.","apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In <i>36th International Symposium on Computational Geometry</i> (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” In <i>36th International Symposium on Computational Geometry</i>, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” <i>36th International Symposium on Computational Geometry</i>, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2020.20\">10.4230/LIPIcs.SoCG.2020.20</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"20:1-20:18","related_material":{"record":[{"status":"public","relation":"later_version","id":"9649"}]},"has_accepted_license":"1","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"conference":{"location":"Zürich, Switzerland","end_date":"2020-06-26","start_date":"2020-06-22","name":"SoCG: Symposium on Computational Geometry"},"status":"public","ec_funded":1,"file":[{"relation":"main_file","file_id":"7969","creator":"dernst","content_type":"application/pdf","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","checksum":"38cbfa4f5d484d267a35d44d210df044","file_size":1009739,"date_created":"2020-06-17T10:13:34Z","date_updated":"2020-07-14T12:48:06Z","access_level":"open_access"}],"file_date_updated":"2020-07-14T12:48:06Z","volume":164,"alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"7952","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_published":"2020-06-01T00:00:00Z","year":"2020","day":"01","oa":1,"intvolume":"       164","month":"06","ddc":["510"],"corr_author":"1","date_created":"2020-06-09T07:24:11Z","publication":"36th International Symposium on Computational Geometry","doi":"10.4230/LIPIcs.SoCG.2020.20","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"}],"title":"The topological correctness of PL-approximations of isomanifolds","scopus_import":"1","publication_status":"published","date_updated":"2025-04-22T13:45:17Z","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"publication_status":"published","date_updated":"2025-04-15T07:16:56Z","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Preprint","doi":"10.1007/s00454-020-00213-z","external_id":{"arxiv":["1803.06710"],"isi":["000538229000001"]},"title":"Almost all string graphs are intersection graphs of plane convex sets","abstract":[{"lang":"eng","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."}],"month":"06","isi":1,"date_created":"2020-06-14T22:00:51Z","page":"888-917","publication":"Discrete and Computational Geometry","oa":1,"intvolume":"        63","_id":"7962","article_processing_charge":"No","author":[{"full_name":"Pach, János","last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János"},{"first_name":"Bruce","last_name":"Reed","full_name":"Reed, Bruce"},{"last_name":"Yuditsky","full_name":"Yuditsky, Yelena","first_name":"Yelena"}],"publisher":"Springer Nature","date_published":"2020-06-05T00:00:00Z","year":"2020","day":"05","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"arxiv":1,"volume":63,"status":"public","issue":"4","main_file_link":[{"url":"https://arxiv.org/abs/1803.06710","open_access":"1"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"quality_controlled":"1","project":[{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"}],"type":"journal_article","article_type":"original","citation":{"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. <i>Discrete and Computational Geometry</i>. 2020;63(4):888-917. doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>","apa":"Pach, J., Reed, B., &#38; Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00213-z\">https://doi.org/10.1007/s00454-020-00213-z</a>.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” <i>Discrete and Computational Geometry</i>, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:<a href=\"https://doi.org/10.1007/s00454-020-00213-z\">10.1007/s00454-020-00213-z</a>."}},{"date_created":"2020-07-24T07:09:18Z","page":"193-199","publication":"Studia Scientiarum Mathematicarum Hungarica","month":"07","ddc":["510"],"isi":1,"corr_author":"1","intvolume":"        57","oa":1,"language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","publication_status":"published","date_updated":"2025-04-15T07:16:57Z","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."}],"title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","external_id":{"isi":["000570978400005"]},"doi":"10.1556/012.2020.57.2.1454","has_accepted_license":"1","publication_identifier":{"issn":["0081-6906"],"eissn":["1588-2896"]},"issue":"2","citation":{"short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó, 2020. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>.","apa":"Vegter, G., &#38; Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. <i>Studia Scientiarum Mathematicarum Hungarica</i>. Akadémiai Kiadó. <a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">https://doi.org/10.1556/012.2020.57.2.1454</a>","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” <i>Studia Scientiarum Mathematicarum Hungarica</i>, 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. <i>Studia Scientiarum Mathematicarum Hungarica</i>. 2020;57(2):193-199. doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>","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.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” <i>Studia Scientiarum Mathematicarum Hungarica</i>, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:<a href=\"https://doi.org/10.1556/012.2020.57.2.1454\">10.1556/012.2020.57.2.1454</a>."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"article_type":"original","quality_controlled":"1","project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_published":"2020-07-24T00:00:00Z","year":"2020","day":"24","publisher":"Akadémiai Kiadó","_id":"8163","article_processing_charge":"No","author":[{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"ec_funded":1,"status":"public","file":[{"file_size":1476072,"date_created":"2020-07-24T07:09:06Z","date_updated":"2020-07-24T07:09:06Z","access_level":"open_access","relation":"main_file","file_id":"8164","creator":"mwintrae","content_type":"application/pdf","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf"}],"license":"https://creativecommons.org/licenses/by-nc/4.0/","volume":57,"file_date_updated":"2020-07-24T07:09:06Z","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."},{"corr_author":"1","month":"10","isi":1,"date_created":"2020-08-30T22:01:12Z","publication":"Discrete and Computational Geometry","page":"571-574","oa":1,"intvolume":"        64","date_updated":"2024-10-09T20:59:55Z","publication_status":"published","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"None","doi":"10.1007/s00454-020-00237-5","external_id":{"isi":["000561483500001"]},"title":"A farewell to Ricky Pollack","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"type":"journal_article","article_type":"letter_note","citation":{"mla":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>, vol. 64, Springer Nature, 2020, pp. 571–74, doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>.","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","ieee":"J. Pach, “A farewell to Ricky Pollack,” <i>Discrete and Computational Geometry</i>, vol. 64. Springer Nature, pp. 571–574, 2020.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00237-5\">https://doi.org/10.1007/s00454-020-00237-5</a>","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574.","ama":"Pach J. A farewell to Ricky Pollack. <i>Discrete and Computational Geometry</i>. 2020;64:571-574. doi:<a href=\"https://doi.org/10.1007/s00454-020-00237-5\">10.1007/s00454-020-00237-5</a>"},"author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","full_name":"Pach, János"}],"_id":"8323","article_processing_charge":"No","publisher":"Springer Nature","date_published":"2020-10-01T00:00:00Z","day":"01","year":"2020","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":64,"status":"public"},{"oa_version":"None","day":"01","year":"2020","date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"date_updated":"2023-08-22T09:33:34Z","_id":"8580","author":[{"first_name":"Grzegorz","last_name":"Graff","full_name":"Graff, Grzegorz"},{"full_name":"Graff, Beata","last_name":"Graff","first_name":"Beata"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz","first_name":"Krzysztof"}],"article_processing_charge":"No","publication_status":"published","scopus_import":"1","publisher":"IEEE","external_id":{"isi":["000621172600045"]},"title":"The application of persistent homology in the analysis of heart rate variability","status":"public","abstract":[{"lang":"eng","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."}],"doi":"10.1109/ESGCO49734.2020.9158054","conference":{"start_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations","location":"Pisa, Italy","end_date":"2020-07-15"},"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","date_created":"2020-09-28T08:59:27Z","publication_identifier":{"isbn":["9781728157511"]},"isi":1,"article_number":"9158054","month":"08","citation":{"mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, 9158054, IEEE, 2020, doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>.","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE, 2020. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>.","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.","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>, Pisa, Italy, 2020.","apa":"Graff, G., Graff, B., Jablonski, G., &#38; Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. Pisa, Italy: IEEE. <a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">https://doi.org/10.1109/ESGCO49734.2020.9158054</a>","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.","ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: <i>11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, </i>. IEEE; 2020. doi:<a href=\"https://doi.org/10.1109/ESGCO49734.2020.9158054\">10.1109/ESGCO49734.2020.9158054</a>"},"type":"conference","quality_controlled":"1"},{"ec_funded":1,"status":"public","file":[{"access_level":"open_access","date_updated":"2021-02-19T13:33:19Z","date_created":"2021-02-19T13:33:19Z","file_size":707452,"file_name":"2020_CompMathBiophysics_Akopyan.pdf","checksum":"ca43a7440834eab6bbea29c59b56ef3a","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"9170","relation":"main_file"}],"file_date_updated":"2021-02-19T13:33:19Z","volume":8,"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).","arxiv":1,"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2020-07-21T00:00:00Z","day":"21","year":"2020","publisher":"De Gruyter","article_processing_charge":"No","_id":"9156","author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"citation":{"mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0101\">https://doi.org/10.1515/cmb-2020-0101</a>","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):74-88. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0101\">10.1515/cmb-2020-0101</a>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35"}],"quality_controlled":"1","type":"journal_article","has_accepted_license":"1","publication_identifier":{"issn":["2544-7297"]},"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."}],"title":"The weighted Gaussian curvature derivative of a space-filling diagram","external_id":{"arxiv":["1908.06777"]},"doi":"10.1515/cmb-2020-0101","language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","date_updated":"2025-04-14T07:48:34Z","publication_status":"published","intvolume":"         8","oa":1,"date_created":"2021-02-17T15:12:44Z","page":"74-88","publication":"Computational and Mathematical Biophysics","month":"07","ddc":["510"],"corr_author":"1"},{"doi":"10.1515/cmb-2020-0100","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"}],"title":"The weighted mean curvature derivative of a space-filling diagram","publication_status":"published","date_updated":"2025-04-14T07:48:35Z","language":[{"iso":"eng"}],"oa_version":"Published Version","oa":1,"intvolume":"         8","corr_author":"1","month":"06","ddc":["510"],"date_created":"2021-02-17T15:13:01Z","page":"51-67","publication":"Computational and Mathematical Biophysics","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).","file_date_updated":"2021-02-19T13:56:24Z","volume":8,"status":"public","ec_funded":1,"file":[{"file_id":"9171","relation":"main_file","checksum":"cea41de9937d07a3b927d71ee8b4e432","content_type":"application/pdf","file_name":"2020_CompMathBiophysics_Akopyan2.pdf","creator":"dernst","success":1,"file_size":562359,"date_created":"2021-02-19T13:56:24Z","access_level":"open_access","date_updated":"2021-02-19T13:56:24Z"}],"_id":"9157","article_processing_charge":"No","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"publisher":"De Gruyter","date_published":"2020-06-20T00:00:00Z","year":"2020","day":"20","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>.","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):51-67. doi:<a href=\"https://doi.org/10.1515/cmb-2020-0100\">10.1515/cmb-2020-0100</a>","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","apa":"Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>. De Gruyter. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/cmb-2020-0100\">https://doi.org/10.1515/cmb-2020-0100</a>."},"issue":"1","has_accepted_license":"1","publication_identifier":{"issn":["2544-7297"]}},{"oa_version":"Published Version","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2025-04-14T07:48:35Z","abstract":[{"lang":"eng","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."}],"title":"Digital objects in rhombic dodecahedron grid","doi":"10.1515/mathm-2020-0106","publication":"Mathematical Morphology - Theory and Applications","page":"143-158","date_created":"2021-03-16T08:55:19Z","corr_author":"1","ddc":["510"],"month":"11","intvolume":"         4","oa":1,"day":"17","year":"2020","date_published":"2020-11-17T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"full_name":"Andres, Eric","last_name":"Andres","first_name":"Eric"}],"_id":"9249","article_processing_charge":"No","publisher":"De Gruyter","file_date_updated":"2021-03-22T08:56:37Z","volume":4,"file":[{"creator":"dernst","success":1,"checksum":"4a1043fa0548a725d464017fe2483ce0","content_type":"application/pdf","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","relation":"main_file","file_id":"9272","date_updated":"2021-03-22T08:56:37Z","access_level":"open_access","file_size":3668725,"date_created":"2021-03-22T08:56:37Z"}],"status":"public","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. ","publication_identifier":{"issn":["2353-3390"]},"has_accepted_license":"1","issue":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","citation":{"apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2020). Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. 2020;4(1):143-158. doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>."},"type":"journal_article","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1"},{"volume":12590,"status":"public","conference":{"end_date":"2020-09-18","location":"Virtual, Online","name":"GD: Graph Drawing and Network Visualization","start_date":"2020-09-16"},"arxiv":1,"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.","date_published":"2020-09-20T00:00:00Z","day":"20","year":"2020","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"_id":"9299","article_processing_charge":"No","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"last_name":"Tardos","full_name":"Tardos, Gábor","first_name":"Gábor"},{"full_name":"Tóth, Géza","last_name":"Tóth","first_name":"Géza"}],"publisher":"Springer Nature","citation":{"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.","ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: <i>28th International Symposium on Graph Drawing and Network Visualization</i>. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In <i>28th International Symposium on Graph Drawing and Network Visualization</i>, 12590:359–71. LNCS. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","apa":"Pach, J., Tardos, G., &#38; Tóth, G. (2020). Crossings between non-homotopic edges. In <i>28th International Symposium on Graph Drawing and Network Visualization</i> (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">https://doi.org/10.1007/978-3-030-68766-3_28</a>","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in <i>28th International Symposium on Graph Drawing and Network Visualization</i>, Virtual, Online, 2020, vol. 12590, pp. 359–371.","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” <i>28th International Symposium on Graph Drawing and Network Visualization</i>, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:<a href=\"https://doi.org/10.1007/978-3-030-68766-3_28\">10.1007/978-3-030-68766-3_28</a>."},"project":[{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","type":"conference","publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"external_id":{"arxiv":["2006.14908"]},"abstract":[{"lang":"eng","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⟶∞ ."}],"title":"Crossings between non-homotopic edges","doi":"10.1007/978-3-030-68766-3_28","language":[{"iso":"eng"}],"oa_version":"Preprint","date_updated":"2025-04-15T07:16:52Z","series_title":"LNCS","publication_status":"published","scopus_import":"1","intvolume":"     12590","oa":1,"date_created":"2021-03-28T22:01:44Z","page":"359-371","publication":"28th International Symposium on Graph Drawing and Network Visualization","month":"09"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"date_published":"2020-06-21T00:00:00Z","day":"21","year":"2020","publisher":"Springer Nature","_id":"74","article_processing_charge":"No","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"ec_funded":1,"status":"public","volume":2256,"arxiv":1,"publication_identifier":{"issn":["0075-8434"],"isbn":["9783030360191"],"eisbn":["9783030360207"],"eissn":["1617-9692"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>.","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. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in <i>Geometric Aspects of Functional Analysis</i>, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag &#38; E. Milman (Eds.), <i>Geometric Aspects of Functional Analysis</i> (Vol. 2256, pp. 1–27). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>."},"project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","type":"book_chapter","language":[{"iso":"eng"}],"oa_version":"Preprint","scopus_import":"1","series_title":"LNM","publication_status":"published","date_updated":"2025-07-10T11:54:33Z","abstract":[{"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.","lang":"eng"}],"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"doi":"10.1007/978-3-030-36020-7_1","date_created":"2018-12-11T11:44:29Z","page":"1-27","publication":"Geometric Aspects of Functional Analysis","month":"06","editor":[{"full_name":"Klartag, Bo'az","last_name":"Klartag","first_name":"Bo'az"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"isi":1,"intvolume":"      2256","oa":1},{"intvolume":"        64","oa":1,"date_created":"2020-03-01T23:00:39Z","page":"595-614","publication":"Theory of Probability and its Applications","month":"02","isi":1,"external_id":{"arxiv":["1705.08735"],"isi":["000551393100007"]},"title":"Weighted Poisson–Delaunay mosaics","abstract":[{"lang":"eng","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 ${R}^n$."}],"doi":"10.1137/S0040585X97T989726","language":[{"iso":"eng"}],"oa_version":"Preprint","publication_status":"published","date_updated":"2025-07-10T11:54:44Z","scopus_import":"1","article_type":"original","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:<a href=\"https://doi.org/10.1137/S0040585X97T989726\">10.1137/S0040585X97T989726</a>.","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. <i>Theory of Probability and its Applications</i>. 2020;64(4):595-614. doi:<a href=\"https://doi.org/10.1137/S0040585X97T989726\">10.1137/S0040585X97T989726</a>","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614.","apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. <i>Theory of Probability and Its Applications</i>. SIAM. <a href=\"https://doi.org/10.1137/S0040585X97T989726\">https://doi.org/10.1137/S0040585X97T989726</a>","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” <i>Theory of Probability and its Applications</i>, vol. 64, no. 4. SIAM, pp. 595–614, 2020.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” <i>Theory of Probability and Its Applications</i>. SIAM, 2020. <a href=\"https://doi.org/10.1137/S0040585X97T989726\">https://doi.org/10.1137/S0040585X97T989726</a>.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614."},"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"type":"journal_article","publication_identifier":{"issn":["0040-585X"],"eissn":["1095-7219"]},"issue":"4","main_file_link":[{"url":"https://arxiv.org/abs/1705.08735","open_access":"1"}],"volume":64,"status":"public","ec_funded":1,"arxiv":1,"date_published":"2020-02-13T00:00:00Z","year":"2020","day":"13","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","_id":"7554","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"publisher":"SIAM"},{"intvolume":"        14","oa":1,"date_created":"2020-03-05T13:30:18Z","publication":"Mathematics in Computer Science","page":"141-176","month":"03","ddc":["510"],"corr_author":"1","title":"Coxeter triangulations have good quality","abstract":[{"lang":"eng","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."}],"doi":"10.1007/s11786-020-00461-5","language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:44:03Z","citation":{"mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>, vol. 14, Springer Nature, 2020, pp. 141–76, doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>.","apa":"Choudhary, A., Kachanovich, S., &#38; Wintraecken, M. (2020). Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” <i>Mathematics in Computer Science</i>, vol. 14. Springer Nature, pp. 141–176, 2020.","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” <i>Mathematics in Computer Science</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11786-020-00461-5\">https://doi.org/10.1007/s11786-020-00461-5</a>.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. <i>Mathematics in Computer Science</i>. 2020;14:141-176. doi:<a href=\"https://doi.org/10.1007/s11786-020-00461-5\">10.1007/s11786-020-00461-5</a>","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176."},"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","type":"journal_article","has_accepted_license":"1","publication_identifier":{"issn":["1661-8270"],"eissn":["1661-8289"]},"ec_funded":1,"status":"public","file":[{"date_created":"2020-11-20T10:18:02Z","file_size":872275,"access_level":"open_access","date_updated":"2020-11-20T10:18:02Z","file_id":"8783","relation":"main_file","content_type":"application/pdf","checksum":"1d145f3ab50ccee735983cb89236e609","file_name":"2020_MathCompScie_Choudhary.pdf","creator":"dernst","success":1}],"file_date_updated":"2020-11-20T10:18:02Z","volume":14,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_published":"2020-03-01T00:00:00Z","day":"01","year":"2020","publisher":"Springer Nature","author":[{"full_name":"Choudhary, Aruni","last_name":"Choudhary","first_name":"Aruni"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220"}],"_id":"7567","article_processing_charge":"Yes (via OA deal)"},{"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","department":[{"_id":"HeEd"}],"date_published":"2020-12-14T00:00:00Z","day":"14","year":"2020","publisher":"Carleton University","_id":"9630","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk"},{"full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","orcid":"0009-0009-9111-8429"}],"article_processing_charge":"Yes","status":"public","license":"https://creativecommons.org/licenses/by/3.0/","file":[{"file_id":"9882","relation":"main_file","content_type":"application/pdf","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","success":1,"creator":"asandaue","file_size":1449234,"date_created":"2021-08-11T11:55:11Z","access_level":"open_access","date_updated":"2021-08-11T11:55:11Z"}],"volume":11,"file_date_updated":"2021-08-11T11:55:11Z","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).","has_accepted_license":"1","publication_identifier":{"eissn":["1920-180X"]},"issue":"2","citation":{"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.” <i>Journal of Computational Geometry</i>. Carleton University, 2020. <a href=\"https://doi.org/10.20382/jocg.v11i2a7\">https://doi.org/10.20382/jocg.v11i2a7</a>.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” <i>Journal of Computational Geometry</i>, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","apa":"Edelsbrunner, H., Virk, Z., &#38; Wagner, H. (2020). Topological data analysis in information space. <i>Journal of Computational Geometry</i>. Carleton University. <a href=\"https://doi.org/10.20382/jocg.v11i2a7\">https://doi.org/10.20382/jocg.v11i2a7</a>","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. <i>Journal of Computational Geometry</i>. 2020;11(2):162-182. doi:<a href=\"https://doi.org/10.20382/jocg.v11i2a7\">10.20382/jocg.v11i2a7</a>","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” <i>Journal of Computational Geometry</i>, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:<a href=\"https://doi.org/10.20382/jocg.v11i2a7\">10.20382/jocg.v11i2a7</a>."},"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"article_type":"original","project":[{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"quality_controlled":"1","type":"journal_article","language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","date_updated":"2026-04-02T14:35:31Z","publication_status":"published","title":"Topological data analysis in information space","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."}],"doi":"10.20382/jocg.v11i2a7","date_created":"2021-07-04T22:01:26Z","page":"162-182","publication":"Journal of Computational Geometry","month":"12","ddc":["510","000"],"corr_author":"1","intvolume":"        11","oa":1},{"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19630"}]},"has_accepted_license":"1","publication_identifier":{"eissn":["2197-8549"],"isbn":["9783030434076"],"issn":["2193-2808"]},"quality_controlled":"1","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales","_id":"2533E772-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"638176"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"type":"conference","citation":{"chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In <i>Topological Data Analysis</i>, 15:181–218. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">https://doi.org/10.1007/978-3-030-43408-3_8</a>.","short":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, P. Synak, in:, Topological Data Analysis, Springer Nature, 2020, pp. 181–218.","ieee":"H. Edelsbrunner, A. Nikitenko, K. Ölsböck, and P. Synak, “Radius functions on Poisson–Delaunay mosaics and related complexes experimentally,” in <i>Topological Data Analysis</i>, 2020, vol. 15, pp. 181–218.","apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., &#38; Synak, P. (2020). Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In <i>Topological Data Analysis</i> (Vol. 15, pp. 181–218). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">https://doi.org/10.1007/978-3-030-43408-3_8</a>","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.","ama":"Edelsbrunner H, Nikitenko A, Ölsböck K, Synak P. Radius functions on Poisson–Delaunay mosaics and related complexes experimentally. In: <i>Topological Data Analysis</i>. Vol 15. Springer Nature; 2020:181-218. doi:<a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">10.1007/978-3-030-43408-3_8</a>","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” <i>Topological Data Analysis</i>, vol. 15, Springer Nature, 2020, pp. 181–218, doi:<a href=\"https://doi.org/10.1007/978-3-030-43408-3_8\">10.1007/978-3-030-43408-3_8</a>."},"alternative_title":["Abel Symposia"],"publisher":"Springer Nature","_id":"8135","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ölsböck, Katharina","last_name":"Ölsböck","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297"},{"first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87","full_name":"Synak, Peter","last_name":"Synak"}],"article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"HeEd"}],"date_published":"2020-06-22T00:00:00Z","day":"22","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).","ec_funded":1,"status":"public","file":[{"access_level":"open_access","date_updated":"2020-10-08T08:56:14Z","date_created":"2020-10-08T08:56:14Z","file_size":2207071,"content_type":"application/pdf","checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","creator":"dernst","success":1,"file_id":"8628","relation":"main_file"}],"file_date_updated":"2020-10-08T08:56:14Z","volume":15,"month":"06","ddc":["510"],"isi":1,"date_created":"2020-07-19T22:00:59Z","page":"181-218","publication":"Topological Data Analysis","oa":1,"intvolume":"        15","scopus_import":"1","date_updated":"2026-04-07T12:35:47Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Submitted Version","doi":"10.1007/978-3-030-43408-3_8","title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","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"}],"external_id":{"isi":["001321861000008"]}}]