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A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","page":"18-33","date_created":"2024-01-28T23:01:43Z","date_published":"2024-01-06T00:00:00Z","doi":"10.1007/978-3-031-49275-4_2","year":"2024","publication":"31st International Symposium on Graph Drawing and Network Visualization","day":"06","article_processing_charge":"No","external_id":{"arxiv":["2202.12175"]},"author":[{"full_name":"De Nooijer, Phoebe","last_name":"De Nooijer","first_name":"Phoebe"},{"full_name":"Terziadis, Soeren","last_name":"Terziadis","first_name":"Soeren"},{"last_name":"Weinberger","full_name":"Weinberger, Alexandra","first_name":"Alexandra"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová"},{"first_name":"Tamara","last_name":"Mchedlidze","full_name":"Mchedlidze, Tamara"},{"full_name":"Löffler, Maarten","last_name":"Löffler","first_name":"Maarten"},{"first_name":"Günter","full_name":"Rote, Günter","last_name":"Rote"}],"title":"Removing popular faces in curve arrangements","citation":{"mla":"De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.","ama":"De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve arrangements. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2","apa":"De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T., Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49275-4_2","ieee":"P. De Nooijer et al., “Removing popular faces in curve arrangements,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.","short":"P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M. Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 18–33.","chicago":"De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve Arrangements.” In 31st International Symposium on Graph Drawing and Network Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.","ista":"De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14466, 18–33."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2202.12175"}],"alternative_title":["LNCS"],"scopus_import":"1","intvolume":" 14466","month":"01","abstract":[{"text":"A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate possibilities to eliminate the popular faces in an arrangement by inserting a single additional curve. This turns out to be NP-hard; however, it becomes tractable when the number of popular faces is small: We present a probabilistic FPT-approach in the number of popular faces.","lang":"eng"}],"oa_version":"Preprint","volume":14466,"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031492747"]},"language":[{"iso":"eng"}],"conference":{"start_date":"2023-09-20","location":"Isola delle Femmine, Palermo, Italy","end_date":"2023-09-22","name":"GD: Graph Drawing and Network Visualization"},"type":"conference","status":"public","_id":"14888","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2024-01-29T09:45:06Z"},{"status":"public","type":"conference","conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2023-09-20","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy"},"_id":"15012","department":[{"_id":"HeEd"}],"date_updated":"2024-02-20T09:13:07Z","month":"01","intvolume":" 14465","alternative_title":["LNCS"],"scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.","lang":"eng"}],"volume":14465,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["16113349"],"isbn":["9783031492716"],"issn":["03029743"]},"publication_status":"published","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"title":"Decomposition of geometric graphs into star-forests","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"},{"last_name":"Schnider","full_name":"Schnider, Patrick","first_name":"Patrick"}],"external_id":{"arxiv":["2306.13201"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Pach, J., Saghafian, M., & Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In 31st International Symposium on Graph Drawing and Network Visualization (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. https://doi.org/10.1007/978-3-031-49272-3_23","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: 31st International Symposium on Graph Drawing and Network Visualization. Vol 14465. Springer Nature; 2024:339-346. doi:10.1007/978-3-031-49272-3_23","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in 31st International Symposium on Graph Drawing and Network Visualization, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346.","short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” 31st International Symposium on Graph Drawing and Network Visualization, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:10.1007/978-3-031-49272-3_23.","ista":"Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.","chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In 31st International Symposium on Graph Drawing and Network Visualization, 14465:339–46. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49272-3_23."},"quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31.","date_published":"2024-01-01T00:00:00Z","doi":"10.1007/978-3-031-49272-3_23","date_created":"2024-02-18T23:01:03Z","page":"339-346","day":"01","publication":"31st International Symposium on Graph Drawing and Network Visualization","year":"2024"},{"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"type":"dissertation","status":"public","_id":"15094","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"file_date_updated":"2024-03-14T14:14:35Z","date_updated":"2024-03-20T09:36:57Z","supervisor":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"ddc":["514","500","516"],"alternative_title":["ISTA Thesis"],"month":"03","abstract":[{"text":"Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","related_material":{"record":[{"status":"public","id":"11660","relation":"part_of_dissertation"},{"status":"public","id":"11658","relation":"part_of_dissertation"},{"id":"13182","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"15090"},{"id":"15091","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"15093","relation":"part_of_dissertation"}]},"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663 - 337X"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2024-03-14T08:55:07Z","file_name":"Thesis Sebastiano.pdf","date_updated":"2024-03-14T08:55:07Z","file_size":4106872,"creator":"scultrer","file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"},{"content_type":"application/zip","relation":"source_file","access_level":"closed","file_id":"15113","checksum":"bcbd213490f5a7e68855a092bbce93f1","file_size":4746234,"date_updated":"2024-03-14T14:14:35Z","creator":"scultrer","file_name":"Thesis (1).zip","date_created":"2024-03-14T08:56:24Z"}],"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"article_processing_charge":"No","author":[{"orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano"}],"title":"Persistence and Morse theory for discrete geometric structures","citation":{"mla":"Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094.","ieee":"S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.","ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:10.15479/at:ista:15094","apa":"Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094","chicago":"Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094.","ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"publisher":"Institute of Science and Technology Austria","page":"108","date_created":"2024-03-08T15:28:10Z","date_published":"2024-03-08T00:00:00Z","doi":"10.15479/at:ista:15094","year":"2024","has_accepted_license":"1","day":"08"},{"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422","name":"Wittgenstein Award - Monika Henzinger"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775 "}],"title":"Dynamically maintaining the persistent homology of time series","editor":[{"first_name":"David P.","last_name":"Woodruff","full_name":"Woodruff, David P."}],"author":[{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"last_name":"Ost","full_name":"Ost, Lara","first_name":"Lara"}],"external_id":{"arxiv":["2311.01115"]},"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorigthms, 243–295.","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika H Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11.","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11","apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M. H., & Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11","ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. H. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria, VA, USA, 2024, pp. 243–295.","short":"S. Cultrera di Montesano, H. Edelsbrunner, M.H. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11."},"publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","oa":1,"acknowledgement":"The first and second authors are funded by the European Research Council under the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35.","date_published":"2024-01-04T00:00:00Z","doi":"10.1137/1.9781611977912.11","date_created":"2024-03-08T10:27:39Z","page":"243 - 295","day":"04","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","year":"2024","status":"public","type":"conference","conference":{"start_date":"2024-01-07","location":"Alexandria, VA, USA","end_date":"2024-01-10","name":"SODA: Symposium on Discrete Algorigthms"},"_id":"15093","department":[{"_id":"HeEd"},{"_id":"MoHe"}],"date_updated":"2024-03-20T09:36:56Z","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2311.01115"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right."}],"related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["9781611977912"]},"publication_status":"published"},{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_updated":"2024-03-20T09:36:56Z","citation":{"ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” arXiv. .","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). Chromatic alpha complexes. arXiv.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv.","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” ArXiv, 2212.03128.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” ArXiv, n.d."},"title":"Chromatic alpha complexes","department":[{"_id":"HeEd"}],"author":[{"last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano"},{"first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","last_name":"Draganov"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"}],"article_processing_charge":"No","external_id":{"arxiv":["2212.03128"]},"article_number":"2212.03128","_id":"15091","status":"public","type":"preprint","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)"},"day":"07","publication":"arXiv","language":[{"iso":"eng"}],"year":"2024","publication_status":"submitted","related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"date_published":"2024-02-07T00:00:00Z","date_created":"2024-03-08T10:13:59Z","oa_version":"Preprint","abstract":[{"text":"Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided.","lang":"eng"}],"month":"02","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03128"}]},{"status":"public","conference":{"name":"STOC: Symposium on Theory of Computing","end_date":"2023-06-23","location":"Orlando, FL, United States","start_date":"2023-06-20"},"type":"conference","_id":"13048","department":[{"_id":"HeEd"}],"date_updated":"2023-05-22T08:15:19Z","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/2303.04014","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"In this paper we introduce a pruning of the medial axis called the (λ,α)-medial axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff sense under weak assumptions. More formally we prove that if K and K′ are close in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is 1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲ dH(K,K′)1/2. These quantified stability results provide guarantees for practical computations of medial axes from approximations. Moreover, they provide key ingredients for studying the computability of the medial axis in the context of computable analysis.","lang":"eng"}],"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["9781450399135"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"title":"Hausdorff and Gromov-Hausdorff stable subsets of the medial axis","article_processing_charge":"No","external_id":{"arxiv":["2303.04014"]},"author":[{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 1768–76. Association for Computing Machinery, 2023. https://doi.org/10.1145/3564246.3585113.","ista":"Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 1768–1776.","mla":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–76, doi:10.1145/3564246.3585113.","apa":"Lieutier, A., & Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (pp. 1768–1776). Orlando, FL, United States: Association for Computing Machinery. https://doi.org/10.1145/3564246.3585113","ama":"Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In: Proceedings of the 55th Annual ACM Symposium on Theory of Computing. Association for Computing Machinery; 2023:1768-1776. doi:10.1145/3564246.3585113","short":"A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776.","ieee":"A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets of the medial axis,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Orlando, FL, United States, 2023, pp. 1768–1776."},"oa":1,"quality_controlled":"1","publisher":"Association for Computing Machinery","acknowledgement":"We are greatly indebted to Erin Chambers for posing a number of questions that eventually led to this paper. We would also like to thank the other organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted to Tatiana Ezubova for helping with the search for and translation of Russian literature. The second author thanks all members of the Edelsbrunner and Datashape groups for the atmosphere in which the research was conducted.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. The Austrian science fund (FWF) M-3073.","date_created":"2023-05-22T08:02:02Z","doi":"10.1145/3564246.3585113","date_published":"2023-06-02T00:00:00Z","page":"1768-1776","publication":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","day":"02","year":"2023"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2023-01-20T10:02:48Z","date_updated":"2023-06-27T12:53:43Z","ddc":["510"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"12086","volume":85,"ec_funded":1,"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"71685ca5121f4c837f40c3f8eb50c915","file_id":"12322","success":1,"creator":"dernst","date_updated":"2023-01-20T10:02:48Z","file_size":911017,"date_created":"2023-01-20T10:02:48Z","file_name":"2023_Algorithmica_Edelsbrunner.pdf"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"01","intvolume":" 85","abstract":[{"text":"We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.","lang":"eng"}],"oa_version":"Published Version","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Osang","full_name":"Osang, Georg F","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000846967100001"]},"title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023. https://doi.org/10.1007/s00453-022-01027-6.","ista":"Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature, 2023, pp. 277–95, doi:10.1007/s00453-022-01027-6.","ieee":"H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp. 277–295, 2023.","short":"H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.","ama":"Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6","apa":"Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6"},"user_id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"page":"277-295","doi":"10.1007/s00453-022-01027-6","date_published":"2023-01-01T00:00:00Z","date_created":"2022-09-11T22:01:57Z","isi":1,"has_accepted_license":"1","year":"2023","day":"01","publication":"Algorithmica","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35."},{"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"citation":{"apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local criteria for triangulating general manifolds. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 2023;69:156-191. doi:10.1007/s00454-022-00431-7","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational Geometry 69 (2023) 156–191.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” Discrete & Computational Geometry, vol. 69. Springer Nature, pp. 156–191, 2023.","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry, vol. 69, Springer Nature, 2023, pp. 156–91, doi:10.1007/s00454-022-00431-7.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000862193600001"]},"article_processing_charge":"No","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"full_name":"Dyer, Ramsay","last_name":"Dyer","first_name":"Ramsay"},{"full_name":"Ghosh, Arijit","last_name":"Ghosh","first_name":"Arijit"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"title":"Local criteria for triangulating general manifolds","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2023","has_accepted_license":"1","isi":1,"publication":"Discrete & Computational Geometry","day":"01","page":"156-191","date_created":"2023-01-16T10:04:06Z","date_published":"2023-01-01T00:00:00Z","doi":"10.1007/s00454-022-00431-7","_id":"12287","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"status":"public","date_updated":"2023-08-01T12:47:32Z","ddc":["510"],"file_date_updated":"2023-02-02T11:01:10Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 69","month":"01","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"file_size":582850,"date_updated":"2023-02-02T11:01:10Z","creator":"dernst","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","date_created":"2023-02-02T11:01:10Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"46352e0ee71e460848f88685ca852681","file_id":"12488"}],"ec_funded":1,"volume":69},{"_id":"12548","status":"public","type":"conference","conference":{"name":"ICDMW: Conference on Data Mining Workshops","location":"Orlando, FL, United States","end_date":"2022-12-01","start_date":"2022-11-28"},"ddc":["600"],"date_updated":"2023-08-01T13:15:48Z","department":[{"_id":"HeEd"}],"file_date_updated":"2023-02-14T07:58:26Z","oa_version":"Submitted Version","abstract":[{"text":"The limited exchange between human communities is a key factor in preventing the spread of COVID-19. This paper introduces a digital framework that combines an integration of real mobility data at the country scale with a series of modeling techniques and visual capabilities that highlight mobility patterns before and during the pandemic. The findings not only significantly exhibit mobility trends and different degrees of similarities at regional and local levels but also provide potential insight into the emergence of a pandemic on human behavior patterns and their likely socio-economic impacts.","lang":"eng"}],"month":"02","file":[{"creator":"fkarimip","file_size":1183339,"date_updated":"2023-02-14T07:58:26Z","file_name":"Visual Analysis_Mobility_COVID19 - SocDM2022.pdf","date_created":"2023-02-14T07:58:26Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12549","checksum":"c253bee25e6dfe484f96662daa119cb6"}],"language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["9798350346091"],"eissn":["2375-9259"]},"publication_status":"published","article_number":"00093","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Forghani, Mohammad, Christophe Claramunt, Farid Karimipour, and Georg Heiler. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers, 2023. https://doi.org/10.1109/icdmw58026.2022.00093.","ista":"Forghani M, Claramunt C, Karimipour F, Heiler G. 2023. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. 2022 IEEE International Conference on Data Mining Workshops. ICDMW: Conference on Data Mining Workshops, 00093.","mla":"Forghani, Mohammad, et al. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2022 IEEE International Conference on Data Mining Workshops, 00093, Institute of Electrical and Electronics Engineers, 2023, doi:10.1109/icdmw58026.2022.00093.","ama":"Forghani M, Claramunt C, Karimipour F, Heiler G. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In: 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers; 2023. doi:10.1109/icdmw58026.2022.00093","apa":"Forghani, M., Claramunt, C., Karimipour, F., & Heiler, G. (2023). Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In 2022 IEEE International Conference on Data Mining Workshops. Orlando, FL, United States: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/icdmw58026.2022.00093","ieee":"M. Forghani, C. Claramunt, F. Karimipour, and G. Heiler, “Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic,” in 2022 IEEE International Conference on Data Mining Workshops, Orlando, FL, United States, 2023.","short":"M. Forghani, C. Claramunt, F. Karimipour, G. Heiler, in:, 2022 IEEE International Conference on Data Mining Workshops, Institute of Electrical and Electronics Engineers, 2023."},"title":"Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic","author":[{"first_name":"Mohammad","full_name":"Forghani, Mohammad","last_name":"Forghani"},{"first_name":"Christophe","full_name":"Claramunt, Christophe","last_name":"Claramunt"},{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","last_name":"Karimipour","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid"},{"first_name":"Georg","full_name":"Heiler, Georg","last_name":"Heiler"}],"article_processing_charge":"No","external_id":{"isi":["000971492200145"]},"quality_controlled":"1","publisher":"Institute of Electrical and Electronics Engineers","oa":1,"day":"08","publication":"2022 IEEE International Conference on Data Mining Workshops","has_accepted_license":"1","isi":1,"year":"2023","date_published":"2023-02-08T00:00:00Z","doi":"10.1109/icdmw58026.2022.00093","date_created":"2023-02-14T07:56:21Z"},{"citation":{"chicago":"Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling. American Chemical Society, 2023. https://doi.org/10.1021/acs.jcim.2c01346.","ista":"Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 63(3), 973–985.","mla":"Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85, doi:10.1021/acs.jcim.2c01346.","ama":"Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 2023;63(3):973-985. doi:10.1021/acs.jcim.2c01346","apa":"Koehl, P., Akopyan, A., & Edelsbrunner, H. (2023). Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. American Chemical Society. https://doi.org/10.1021/acs.jcim.2c01346","short":"P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.","ieee":"P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives,” Journal of Chemical Information and Modeling, vol. 63, no. 3. American Chemical Society, pp. 973–985, 2023."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"isi":["000920370700001"],"pmid":["36638318"]},"author":[{"first_name":"Patrice","full_name":"Koehl, Patrice","last_name":"Koehl"},{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"title":"Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"year":"2023","has_accepted_license":"1","isi":1,"publication":"Journal of Chemical Information and Modeling","day":"13","page":"973-985","date_created":"2023-02-12T23:00:59Z","doi":"10.1021/acs.jcim.2c01346","date_published":"2023-02-13T00:00:00Z","acknowledgement":"P.K. acknowledges support from the University of California Multicampus Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant No.1760485). H.E. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.\r\nOpen Access is funded by the Austrian Science Fund (FWF).","oa":1,"quality_controlled":"1","publisher":"American Chemical Society","date_updated":"2023-08-16T12:22:07Z","ddc":["510","540"],"file_date_updated":"2023-08-16T12:21:13Z","department":[{"_id":"HeEd"}],"_id":"12544","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1549-960X"],"issn":["1549-9596"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"14070","checksum":"7d20562269edff1e31b9d6019d4983b0","file_size":8069223,"date_updated":"2023-08-16T12:21:13Z","creator":"dernst","file_name":"2023_JCIM_Koehl.pdf","date_created":"2023-08-16T12:21:13Z"}],"ec_funded":1,"volume":63,"issue":"3","abstract":[{"lang":"eng","text":"Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software."}],"oa_version":"Published Version","pmid":1,"scopus_import":"1","intvolume":" 63","month":"02"},{"_id":"12764","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","ddc":["510"],"date_updated":"2023-10-04T11:46:48Z","department":[{"_id":"HeEd"}],"file_date_updated":"2023-10-04T11:46:24Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique."}],"intvolume":" 70","month":"07","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"creator":"dernst","date_updated":"2023-10-04T11:46:24Z","file_size":1026683,"date_created":"2023-10-04T11:46:24Z","file_name":"2023_DiscreteGeometry_Kourimska.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"14396","checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","success":1}],"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"volume":70,"project":[{"call_identifier":"FWF","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2","ama":"Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2","ieee":"H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.","short":"H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.","mla":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2.","ista":"Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153.","chicago":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2."},"title":"Discrete yamabe problem for polyhedral surfaces","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000948148000001"]},"author":[{"full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","last_name":"Kourimska","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E"}],"acknowledgement":"Open access funding provided by the Austrian Science Fund (FWF). This research was supported by the FWF grant, Project number I4245-N35, and by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","publication":"Discrete and Computational Geometry","day":"01","year":"2023","has_accepted_license":"1","isi":1,"date_created":"2023-03-26T22:01:09Z","date_published":"2023-07-01T00:00:00Z","doi":"10.1007/s00454-023-00484-2","page":"123-153"},{"date_updated":"2023-10-04T12:03:40Z","ddc":["000"],"file_date_updated":"2023-03-07T14:40:14Z","department":[{"_id":"HeEd"}],"_id":"12709","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2023-03-07T14:40:14Z","file_size":1359323,"date_created":"2023-03-07T14:40:14Z","file_name":"2023_DisCompGeo_Corbet.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"12715","checksum":"71ce7e59f7ee4620acc704fecca620c2","success":1}],"volume":70,"related_material":{"record":[{"status":"public","id":"9605","relation":"earlier_version"}]},"abstract":[{"text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 70","month":"09","citation":{"ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8","apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the multicover bifiltration. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00476-8","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 376–405, 2023.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405.","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000936496800001"],"arxiv":["2103.07823"]},"author":[{"first_name":"René","last_name":"Corbet","full_name":"Corbet, René"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116"}],"title":"Computing the multicover bifiltration","year":"2023","has_accepted_license":"1","isi":1,"publication":"Discrete and Computational Geometry","day":"01","page":"376-405","date_created":"2023-03-05T23:01:06Z","doi":"10.1007/s00454-022-00476-8","date_published":"2023-09-01T00:00:00Z","acknowledgement":"We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology.","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"page":"619-641","doi":"10.1007/s41468-023-00116-x","date_published":"2023-09-01T00:00:00Z","date_created":"2023-03-26T22:01:08Z","year":"2023","day":"01","publication":"Journal of Applied and Computational Topology","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu for encouragement. We further acknowledge the anonymous reviewers whose comments helped improve the exposition.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). The first author is further supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. The second author is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073.","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel","first_name":"Jean Daniel"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"article_processing_charge":"No","title":"The reach of subsets of manifolds","citation":{"ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641.","chicago":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x.","ama":"Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x","apa":"Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x","ieee":"J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,” Journal of Applied and Computational Topology, vol. 7. Springer Nature, pp. 619–641, 2023.","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","mla":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"volume":7,"ec_funded":1,"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1"}],"month":"09","intvolume":" 7","abstract":[{"text":"Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert showed that sets of positive reach in Euclidean space and Riemannian manifolds are very similar. In this paper we introduce a slight variant of Kleinjohann’s and Bangert’s extension and quantify the similarity between sets of positive reach in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we bound the local feature size (a local version of the reach) of its lifting to the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated by the importance of the reach and local feature size to manifold learning, topological inference, and triangulating manifolds and the fact that intrinsic approaches circumvent the curse of dimensionality.","lang":"eng"}],"oa_version":"Submitted Version","department":[{"_id":"HeEd"}],"date_updated":"2023-10-04T12:07:18Z","article_type":"original","type":"journal_article","status":"public","_id":"12763"},{"_id":"12960","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-10-10T07:34:35Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M^ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1","open_access":"1"}],"scopus_import":"1","intvolume":" 52","month":"04","publication_status":"published","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","id":"9441","status":"public"}]},"issue":"2","volume":52,"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"citation":{"ista":"Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 52(2), 452–486.","chicago":"Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918.","ieee":"J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","ama":"Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918","apa":"Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918","mla":"Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:10.1137/21M1412918."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"isi":["001013183000012"]},"author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"last_name":"Kachanovich","full_name":"Kachanovich, Siargey","first_name":"Siargey"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","acknowledgement":"The authors have received funding from the European Research Council under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations of Geometric Un-derstanding in Higher Dimensions). The first author was supported by the French government,through the 3IA C\\^ote d'Azur Investments in the Future project managed by the National ResearchAgency (ANR) with the reference ANR-19-P3IA-0002. The third author was supported by the Eu-ropean Union's Horizon 2020 research and innovation programme under the Marie Sk\\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science Fund) grant M 3073.","oa":1,"publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","year":"2023","isi":1,"publication":"SIAM Journal on Computing","day":"30","page":"452-486","date_created":"2023-05-14T22:01:00Z","date_published":"2023-04-30T00:00:00Z","doi":"10.1137/21M1412918"},{"acknowledgement":"The first author has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.","publisher":"Elsevier","quality_controlled":"1","publication":"Pattern Recognition","day":"01","year":"2023","isi":1,"date_created":"2023-06-18T22:00:45Z","date_published":"2023-10-01T00:00:00Z","doi":"10.1016/j.patcog.2023.109693","article_number":"109693","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693.","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” Pattern Recognition, vol. 142, no. 10. Elsevier, 2023.","ama":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10). doi:10.1016/j.patcog.2023.109693","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. Elsevier. https://doi.org/10.1016/j.patcog.2023.109693","chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.","ista":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693."},"title":"Discrete analytical objects in the body-centered cubic grid","external_id":{"isi":["001013526000001"]},"article_processing_charge":"No","author":[{"last_name":"Čomić","full_name":"Čomić, Lidija","first_name":"Lidija"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"first_name":"Eric","full_name":"Andres, Eric","last_name":"Andres"}],"oa_version":"None","abstract":[{"lang":"eng","text":"We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line."}],"intvolume":" 142","month":"10","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0031-3203"]},"volume":142,"issue":"10","_id":"13134","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-10-10T07:37:16Z","department":[{"_id":"HeEd"}]},{"_id":"14557","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-11-20T09:24:48Z","department":[{"_id":"HeEd"}],"oa_version":"None","abstract":[{"text":"Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem.","lang":"eng"}],"intvolume":" 46","month":"11","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1607-3606"],"eissn":["1727-933X"]},"issue":"S1","volume":46,"project":[{"_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I04245","name":"Algebraic Footprints of Geometric Features in Homology"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor & Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731.","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.","mla":"Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor & Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731.","apa":"Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731","ama":"Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221. doi:10.2989/16073606.2023.2247731","ieee":"D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no. S1. Taylor & Francis, pp. 191–221, 2023.","short":"D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221."},"title":"Epimorphisms and closure operators of categories of semilattices","article_processing_charge":"No","author":[{"first_name":"D.","last_name":"Dikranjan","full_name":"Dikranjan, D."},{"first_name":"A.","last_name":"Giordano Bruno","full_name":"Giordano Bruno, A."},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","last_name":"Zava","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888"}],"acknowledgement":"The first and second named authors are members of GNSAGA – INdAM.\r\nThe third named author was supported by the FWF Grant, Project number I4245–N35","publisher":"Taylor & Francis","quality_controlled":"1","publication":"Quaestiones Mathematicae","day":"01","year":"2023","date_created":"2023-11-19T23:00:55Z","doi":"10.2989/16073606.2023.2247731","date_published":"2023-11-01T00:00:00Z","page":"191-221"},{"date_updated":"2023-12-13T12:25:06Z","department":[{"_id":"HeEd"}],"_id":"14345","article_type":"original","type":"journal_article","status":"public","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"epub_ahead","language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1007/s00454-023-00566-1","open_access":"1"}],"month":"09","citation":{"apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2023). On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00566-1","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” Discrete and Computational Geometry. Springer Nature, 2023.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00566-1.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00566-1."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Alexey","last_name":"Garber","full_name":"Garber, Alexey"},{"first_name":"Mohadese","last_name":"Ghafari","full_name":"Ghafari, Mohadese"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"]},"title":"On angles in higher order Brillouin tessellations and related tilings in the plane","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"isi":1,"year":"2023","day":"07","publication":"Discrete and Computational Geometry","doi":"10.1007/s00454-023-00566-1","date_published":"2023-09-07T00:00:00Z","date_created":"2023-09-17T22:01:10Z","acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","publisher":"Springer Nature","quality_controlled":"1","oa":1},{"volume":34,"issue":"7","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0129-0541"],"eissn":["1793-6373"]},"intvolume":" 34","month":"10","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2205.11637","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"Given a triangle Δ, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ, every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2023-12-13T13:04:55Z","status":"public","article_type":"original","type":"journal_article","_id":"14464","date_created":"2023-10-29T23:01:18Z","doi":"10.1142/S012905412342008X","date_published":"2023-10-05T00:00:00Z","page":"737-760","publication":"International Journal of Foundations of Computer Science","day":"05","year":"2023","isi":1,"oa":1,"publisher":"World Scientific Publishing","quality_controlled":"1","title":"Optimal embedded and enclosing isosceles triangles","external_id":{"arxiv":["2205.11637"],"isi":["001080874400001"]},"article_processing_charge":"No","author":[{"last_name":"Ambrus","full_name":"Ambrus, Áron","first_name":"Áron"},{"last_name":"Csikós","full_name":"Csikós, Mónika","first_name":"Mónika"},{"first_name":"Gergely","last_name":"Kiss","full_name":"Kiss, Gergely"},{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Gábor","full_name":"Somlai, Gábor","last_name":"Somlai"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 34(7), 737–760.","chicago":"Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science. World Scientific Publishing, 2023. https://doi.org/10.1142/S012905412342008X.","apa":"Ambrus, Á., Csikós, M., Kiss, G., Pach, J., & Somlai, G. (2023). Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. World Scientific Publishing. https://doi.org/10.1142/S012905412342008X","ama":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 2023;34(7):737-760. doi:10.1142/S012905412342008X","short":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal of Foundations of Computer Science 34 (2023) 737–760.","ieee":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and enclosing isosceles triangles,” International Journal of Foundations of Computer Science, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.","mla":"Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science, vol. 34, no. 7, World Scientific Publishing, 2023, pp. 737–60, doi:10.1142/S012905412342008X."}},{"doi":"10.46298/DMTCS.8383","date_published":"2023-01-18T00:00:00Z","date_created":"2023-04-16T22:01:08Z","has_accepted_license":"1","year":"2023","day":"18","publication":"Discrete Mathematics and Theoretical Computer Science","quality_controlled":"1","publisher":"EPI Sciences","oa":1,"acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n","author":[{"first_name":"Ahmad","full_name":"Biniaz, Ahmad","last_name":"Biniaz"},{"first_name":"Kshitij","full_name":"Jain, Kshitij","last_name":"Jain"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Tillmann","last_name":"Miltzow","full_name":"Miltzow, Tillmann"},{"full_name":"Mondal, Debajyoti","last_name":"Mondal","first_name":"Debajyoti"},{"full_name":"Naredla, Anurag Murty","last_name":"Naredla","first_name":"Anurag Murty"},{"first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"article_processing_charge":"No","external_id":{"arxiv":["1903.06981"]},"title":"Token swapping on trees","citation":{"ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","ieee":"A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_number":"9","volume":24,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7950"}]},"issue":"2","publication_identifier":{"issn":["1462-7264"],"eissn":["1365-8050"]},"publication_status":"published","file":[{"file_name":"2022_DMTCS_Biniaz.pdf","date_created":"2023-04-17T08:10:28Z","file_size":2072197,"date_updated":"2023-04-17T08:10:28Z","creator":"dernst","success":1,"file_id":"12844","checksum":"439102ea4f6e2aeefd7107dfb9ccf532","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"01","intvolume":" 24","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"oa_version":"Published Version","file_date_updated":"2023-04-17T08:10:28Z","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"date_updated":"2024-01-04T12:42:09Z","ddc":["000"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"12833"},{"file":[{"checksum":"465c28ef0b151b4b1fb47977ed5581ab","file_id":"14740","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2024-01-08T10:09:14Z","file_name":"2023_IEEEToP_Ali.pdf","creator":"dernst","date_updated":"2024-01-08T10:09:14Z","file_size":2370988}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0162-8828"],"eissn":["1939-3539"]},"publication_status":"published","issue":"12","volume":45,"oa_version":"Published Version","abstract":[{"text":"Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.","lang":"eng"}],"month":"12","intvolume":" 45","ddc":["000"],"date_updated":"2024-01-08T10:11:46Z","department":[{"_id":"HeEd"}],"file_date_updated":"2024-01-08T10:09:14Z","_id":"14739","status":"public","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","has_accepted_license":"1","year":"2023","date_published":"2023-12-01T00:00:00Z","doi":"10.1109/tpami.2023.3308391","date_created":"2024-01-08T09:59:46Z","page":"14069-14080","acknowledgement":"The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions.","quality_controlled":"1","publisher":"IEEE","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391","apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391","ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","short":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.","ista":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.","chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391."},"title":"A survey of vectorization methods in topological data analysis","author":[{"last_name":"Ali","full_name":"Ali, Dashti","first_name":"Dashti"},{"full_name":"Asaad, Aras","last_name":"Asaad","first_name":"Aras"},{"first_name":"Maria-Jose","last_name":"Jimenez","full_name":"Jimenez, Maria-Jose"},{"first_name":"Vidit","full_name":"Nanda, Vidit","last_name":"Nanda"},{"last_name":"Paluzo-Hidalgo","full_name":"Paluzo-Hidalgo, Eduardo","first_name":"Eduardo"},{"orcid":"0000-0003-2449-1433","full_name":"Soriano Trigueros, Manuel","last_name":"Soriano Trigueros","first_name":"Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8"}],"article_processing_charge":"Yes (in subscription journal)"},{"citation":{"mla":"Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier, 2023, doi:10.1016/j.jcta.2023.105776.","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023).","ieee":"L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol. 199, no. 10. Elsevier, 2023.","ama":"Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10). doi:10.1016/j.jcta.2023.105776","apa":"Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776","chicago":"Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.","ista":"Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2206.13592"]},"article_processing_charge":"Yes (in subscription journal)","author":[{"last_name":"Fang","full_name":"Fang, Lixing","first_name":"Lixing"},{"first_name":"Hao","last_name":"Huang","full_name":"Huang, Hao"},{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"first_name":"Gábor","full_name":"Tardos, Gábor","last_name":"Tardos"},{"first_name":"Junchi","last_name":"Zuo","full_name":"Zuo, Junchi"}],"title":"Successive vertex orderings of fully regular graphs","article_number":"105776","year":"2023","has_accepted_license":"1","publication":"Journal of Combinatorial Theory. Series A","day":"01","date_created":"2023-06-25T22:00:45Z","date_published":"2023-10-01T00:00:00Z","doi":"10.1016/j.jcta.2023.105776","oa":1,"quality_controlled":"1","publisher":"Elsevier","date_updated":"2024-01-30T12:03:51Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2024-01-30T12:03:10Z","_id":"13165","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"9eebc213b4182a66063a99083ff5bd04","file_id":"14902","success":1,"creator":"dernst","date_updated":"2024-01-30T12:03:10Z","file_size":352555,"date_created":"2024-01-30T12:03:10Z","file_name":"2023_JourCombinatiorialTheory_Fang.pdf"}],"issue":"10","volume":199,"abstract":[{"lang":"eng","text":"A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph.\r\nAs an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph.\r\nAs another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 199","month":"10"},{"quality_controlled":"1","publisher":"Elsevier","oa":1,"doi":"10.1016/j.tcs.2023.114129","date_published":"2023-10-25T00:00:00Z","date_created":"2023-09-24T22:01:11Z","day":"25","publication":"Theoretical Computer Science","isi":1,"year":"2023","article_number":"114129","title":"Weakly weighted generalised quasi-metric spaces and semilattices","author":[{"first_name":"Ilaria","last_name":"Castellano","full_name":"Castellano, Ilaria"},{"last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna","first_name":"Anna"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","last_name":"Zava","orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò"}],"external_id":{"arxiv":["2212.08424"],"isi":["001076934000001"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier, 2023, doi:10.1016/j.tcs.2023.114129.","apa":"Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2023.114129","ama":"Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129","short":"I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023).","ieee":"I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” Theoretical Computer Science, vol. 977. Elsevier, 2023.","chicago":"Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science. Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129."},"month":"10","intvolume":" 977","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.08424 "}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy."}],"volume":977,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0304-3975"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"14362","department":[{"_id":"HeEd"}],"date_updated":"2024-01-30T13:22:04Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology, Springer Nature, 2023, doi:10.1007/s41468-023-00126-9.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2023). Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 2023. doi:10.1007/s41468-023-00126-9","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023).","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” Journal of Applied and Computational Topology. Springer Nature, 2023.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology."},"title":"Geometric characterization of the persistence of 1D maps","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"article_processing_charge":"Yes (via OA deal)","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"day":"17","publication":"Journal of Applied and Computational Topology","has_accepted_license":"1","year":"2023","doi":"10.1007/s41468-023-00126-9","date_published":"2023-06-17T00:00:00Z","date_created":"2023-07-02T22:00:44Z","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"ddc":["000"],"date_updated":"2024-03-20T09:36:56Z","file_date_updated":"2023-07-03T09:41:05Z","department":[{"_id":"HeEd"}],"_id":"13182","status":"public","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)"},"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"13185","checksum":"697249d5d1c61dea4410b9f021b70fce","success":1,"date_updated":"2023-07-03T09:41:05Z","file_size":487355,"creator":"alisjak","date_created":"2023-07-03T09:41:05Z","file_name":"2023_Journal of Applied and Computational Topology_Biswas.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"epub_ahead","related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"ec_funded":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram."}],"month":"06","scopus_import":"1"},{"ddc":["500"],"date_updated":"2024-02-26T23:30:04Z","supervisor":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"file_date_updated":"2024-02-26T23:30:03Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"14226","status":"public","type":"dissertation","language":[{"iso":"eng"}],"file":[{"file_id":"14227","checksum":"453caf851d75c3478c10ed09bd242a91","access_level":"closed","relation":"source_file","content_type":"application/x-zip-compressed","embargo_to":"open_access","date_created":"2023-08-24T13:02:49Z","file_name":"documents-export-2023-08-24.zip","creator":"cchlebak","date_updated":"2024-02-26T23:30:03Z","file_size":15501411},{"date_created":"2023-08-24T13:03:42Z","file_name":"thesis_pdf_a.pdf","date_updated":"2024-02-26T23:30:03Z","file_size":6854783,"creator":"cchlebak","checksum":"7349d29963d6695e555e171748648d9a","file_id":"14228","embargo":"2024-02-25","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","degree_awarded":"MS","publication_identifier":{"issn":["2791-4585"]},"oa_version":"Published Version","abstract":[{"text":"We introduce the notion of a Faustian interchange in a 1-parameter family of smooth\r\nfunctions to generalize the medial axis to critical points of index larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating such\r\ngeneralized medial axes.","lang":"eng"}],"month":"08","alternative_title":["ISTA Master's Thesis"],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"chicago":"Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.","ista":"Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute of Science and Technology Austria.","mla":"Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.","short":"E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute of Science and Technology Austria, 2023.","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","ama":"Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226","apa":"Stephenson, E. R. (2023). Generalizing medial axes with homology switches. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226"},"title":"Generalizing medial axes with homology switches","article_processing_charge":"No","author":[{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"}],"day":"24","year":"2023","has_accepted_license":"1","date_created":"2023-08-24T13:01:18Z","date_published":"2023-08-24T00:00:00Z","doi":"10.15479/at:ista:14226","page":"43","oa":1,"publisher":"Institute of Science and Technology Austria"},{"date_updated":"2023-02-21T09:50:52Z","ddc":["510"],"file_date_updated":"2022-06-07T07:58:30Z","department":[{"_id":"HeEd"}],"series_title":"LIPIcs","_id":"11428","type":"conference","conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Berlin, Germany","end_date":"2022-06-10","start_date":"2022-06-07"},"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)"},"status":"public","publication_identifier":{"isbn":["978-3-95977-227-3"],"issn":["1868-8969"]},"publication_status":"published","file":[{"checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","file_id":"11437","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2022-06-07T07:58:30Z","file_name":"2022_LIPICs_Chambers.pdf","creator":"dernst","date_updated":"2022-06-07T07:58:30Z","file_size":17580705}],"language":[{"iso":"eng"}],"volume":224,"ec_funded":1,"abstract":[{"lang":"eng","text":"The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible."}],"oa_version":"Published Version","scopus_import":"1","month":"06","intvolume":" 224","citation":{"ista":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary tale: Burning the medial axis is unstable. 38th International Symposium on Computational Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.","chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.","short":"E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in 38th International Symposium on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber (Eds.), 38th International Symposium on Computational Geometry (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2022.66","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66","mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Erin","last_name":"Chambers","full_name":"Chambers, Erin"},{"last_name":"Fillmore","full_name":"Fillmore, Christopher D","first_name":"Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","editor":[{"full_name":"Goaoc, Xavier","last_name":"Goaoc","first_name":"Xavier"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"}],"title":"A cautionary tale: Burning the medial axis is unstable","project":[{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"},{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","year":"2022","day":"01","publication":"38th International Symposium on Computational Geometry","page":"66:1-66:9","date_published":"2022-06-01T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2022.66","date_created":"2022-06-01T14:18:04Z","acknowledgement":"Partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics” and the European Research Council (ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported in part by the National Science Foundation through grants DBI-1759807, CCF-1907612, and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing code to generate the examples.","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1},{"language":[{"iso":"eng"}],"day":"01","year":"2022","publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031062445"],"eissn":["1611-3349"],"eisbn":["9783031062452"]},"date_created":"2022-06-02T05:40:53Z","volume":13238,"date_published":"2022-05-01T00:00:00Z","doi":"10.1007/978-3-031-06245-2","page":"153","oa_version":"None","abstract":[{"lang":"eng","text":"This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks."}],"intvolume":" 13238","month":"05","place":"Cham","edition":"1","publisher":"Springer Nature","alternative_title":["LNCS"],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2022-06-02T05:56:22Z","citation":{"chicago":"Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2.","ista":"Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.","mla":"Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2.","short":"F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022.","ieee":"F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.","ama":"Karimipour F, Storandt S, eds. Web and Wireless Geographical Information Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2","apa":"Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2"},"title":"Web and Wireless Geographical Information Systems","department":[{"_id":"HeEd"}],"editor":[{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","last_name":"Karimipour","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid"},{"full_name":"Storandt, Sabine","last_name":"Storandt","first_name":"Sabine"}],"article_processing_charge":"No","_id":"11429","status":"public","type":"book_editor"},{"doi":"10.1007/978-3-030-95519-9_1","date_published":"2022-01-27T00:00:00Z","date_created":"2022-06-07T08:21:11Z","page":"1-26","day":"27","publication":"Research in Computational Topology 2","year":"2022","publisher":"Springer Nature","quality_controlled":"1","oa":1,"edition":"1","acknowledgement":"This project started during the Women in Computational Topology workshop held in Canberra in July of 2019. All authors are very grateful for its organisation and the financial support for the workshop from the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics. AG is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860. VR was supported by Australian Research Council Future Fellowship FT140100604 during the early stages of this project.","title":"The persistent homology of dual digital image constructions","editor":[{"first_name":"Ellen","last_name":"Gasparovic","full_name":"Gasparovic, Ellen"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"},{"first_name":"Katharine","last_name":"Turner","full_name":"Turner, Katharine"}],"author":[{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"last_name":"Garin","full_name":"Garin, Adélie","first_name":"Adélie"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"first_name":"Kelly","full_name":"Maggs, Kelly","last_name":"Maggs"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"external_id":{"arxiv":["2102.11397"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” Research in Computational Topology 2, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.","short":"B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.","ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in Research in Computational Topology 2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1","ama":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:10.1007/978-3-030-95519-9_1","chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In Research in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.","ista":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology of dual digital image constructions. In: Research in Computational Topology 2. Association for Women in Mathematics Series, vol. 30, 1–26."},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"volume":30,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"publication_status":"published","month":"01","place":"Cham","intvolume":" 30","scopus_import":"1","alternative_title":["Association for Women in Mathematics Series"],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2022-06-07T08:32:42Z","status":"public","type":"book_chapter","series_title":"AWMS","_id":"11440"},{"citation":{"ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750","apa":"Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750.","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Shipman, Barbara A.","last_name":"Shipman","first_name":"Barbara A."},{"full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","last_name":"Stephenson","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Tangible topology through the lens of limits","quality_controlled":"1","publisher":"Taylor & Francis","year":"2022","day":"28","publication":"PRIMUS","page":"593-609","date_published":"2022-05-28T00:00:00Z","doi":"10.1080/10511970.2021.1872750","date_created":"2023-01-16T10:07:21Z","_id":"12307","type":"journal_article","article_type":"original","status":"public","keyword":["Education","General Mathematics"],"date_updated":"2023-01-30T13:02:30Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"abstract":[{"lang":"eng","text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences."}],"oa_version":"None","scopus_import":"1","month":"05","intvolume":" 32","publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":32,"issue":"5"},{"abstract":[{"lang":"eng","text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 26","month":"06","publication_status":"published","publication_identifier":{"issn":["1526-1719"]},"language":[{"iso":"eng"}],"file":[{"checksum":"dc6e255e3558faff924fd9e370886c11","file_id":"11940","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2022-08-22T06:42:42Z","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","date_updated":"2022-08-22T06:42:42Z","file_size":694538,"creator":"dernst"}],"ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9296"}]},"volume":26,"issue":"2","_id":"11938","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2023-02-23T13:54:21Z","ddc":["000"],"file_date_updated":"2022-08-22T06:42:42Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","oa":1,"publisher":"Brown University","quality_controlled":"1","year":"2022","has_accepted_license":"1","publication":"Journal of Graph Algorithms and Applications","day":"01","page":"225-240","date_created":"2022-08-21T22:01:56Z","date_published":"2022-06-01T00:00:00Z","doi":"10.7155/jgaa.00591","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","grant_number":"S11407"}],"citation":{"ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["2101.03928"]},"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Daniel","full_name":"Perz, Daniel","last_name":"Perz"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"last_name":"Tkadlec","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef"},{"first_name":"Birgit","full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber"}],"title":"On compatible matchings"},{"ddc":["516"],"date_updated":"2023-08-02T06:49:17Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-07-14T06:44:36Z","_id":"9649","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"file":[{"file_id":"9650","checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf","date_created":"2021-07-14T06:44:36Z","file_size":1455699,"date_updated":"2021-07-14T06:44:36Z","creator":"mwintrae"}],"publication_status":"published","publication_identifier":{"eissn":["1615-3383"]},"ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7952"}]},"volume":22,"oa_version":"Published Version","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 : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently\r\nfine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.","lang":"eng"}],"intvolume":" 22","month":"0","scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . Springer Nature. https://doi.org/10.1007/s10208-021-09520-0","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012. doi:10.1007/s10208-021-09520-0","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22 (2022) 967–1012.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer Nature, pp. 967–1012, 2022.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics , vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0.","ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics . Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0."},"title":"The topological correctness of PL approximations of isomanifolds","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000673039600001"]},"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"}],"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"publication":"Foundations of Computational Mathematics ","day":"01","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2021-07-14T06:44:53Z","doi":"10.1007/s10208-021-09520-0","date_published":"2022-01-01T00:00:00Z","page":"967-1012","acknowledgement":"First and foremost, we acknowledge Siargey Kachanovich for discussions. We thank Herbert Edelsbrunner and all members of his group, all former and current members of the Datashape team (formerly known as Geometrica), and André Lieutier for encouragement. We further thank the reviewers of Foundations of Computational Mathematics and the reviewers and program committee of the Symposium on Computational Geometry for their feedback, which improved the exposition.\r\nThis work was funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). This work was also supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411.","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"month":"03","intvolume":" 309","scopus_import":"1","oa_version":"None","abstract":[{"text":"Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces.","lang":"eng"}],"volume":309,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0166-8641"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"10413","department":[{"_id":"HeEd"}],"date_updated":"2023-08-02T13:33:24Z","quality_controlled":"1","publisher":"Elsevier","acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","doi":"10.1016/j.topol.2021.107916","date_published":"2022-03-15T00:00:00Z","date_created":"2021-12-05T23:01:44Z","day":"15","publication":"Topology and its Applications","isi":1,"year":"2022","article_number":"107916","title":"Generalized quasi-metric semilattices","author":[{"last_name":"Dikranjan","full_name":"Dikranjan, Dikran","first_name":"Dikran"},{"first_name":"Anna","last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna"},{"full_name":"Künzi, Hans Peter","last_name":"Künzi","first_name":"Hans Peter"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","last_name":"Zava"},{"first_name":"Daniele","full_name":"Toller, Daniele","last_name":"Toller"}],"external_id":{"isi":["000791838800012"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D. (2022). Generalized quasi-metric semilattices. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2021.107916","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916","ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier, 2022.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916.","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916."}},{"date_published":"2022-04-01T00:00:00Z","doi":"10.1007/s00454-022-00371-2","date_created":"2022-02-20T23:01:34Z","page":"811-842","day":"01","publication":"Discrete and Computational Geometry","has_accepted_license":"1","isi":1,"year":"2022","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"external_id":{"isi":["000752175300002"]},"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00371-2.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842, 2022.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00371-2","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2","mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry, vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2."},"volume":67,"file":[{"date_updated":"2022-08-02T06:07:55Z","file_size":2518111,"creator":"dernst","date_created":"2022-08-02T06:07:55Z","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"11718","checksum":"9383d3b70561bacee905e335dc922680","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","month":"04","intvolume":" 67","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function."}],"department":[{"_id":"HeEd"}],"file_date_updated":"2022-08-02T06:07:55Z","ddc":["510"],"date_updated":"2023-08-02T14:31:25Z","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10773"},{"status":"public","type":"conference","conference":{"name":"Big Data: International Conference on Big Data","location":"Orlando, FL, United States; Virtuell","end_date":"2021-12-18","start_date":"2021-12-15"},"_id":"10828","department":[{"_id":"HeEd"}],"date_updated":"2023-08-02T14:44:21Z","month":"01","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown."}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9781665439022"]},"publication_status":"published","title":"The impact of changes in resolution on the persistent homology of images","author":[{"last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sarah","last_name":"Tymochko","full_name":"Tymochko, Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"first_name":"Adélie","last_name":"Garin","full_name":"Garin, Adélie"},{"first_name":"Hoa","full_name":"Bui, Hoa","last_name":"Bui"},{"last_name":"Bleile","full_name":"Bleile, Bea","first_name":"Bea"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"}],"external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The impact of changes in resolution on the persistent homology of images. 2021 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3824–3834.","chicago":"Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent Homology of Images.” In 2021 IEEE International Conference on Big Data, 3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483.","ama":"Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: 2021 IEEE International Conference on Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483","apa":"Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483","short":"T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins, in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.","ieee":"T. Heiss et al., “The impact of changes in resolution on the persistent homology of images,” in 2021 IEEE International Conference on Big Data, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.","mla":"Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483."},"quality_controlled":"1","publisher":"IEEE","oa":1,"doi":"10.1109/BigData52589.2021.9671483","date_published":"2022-01-13T00:00:00Z","date_created":"2022-03-06T23:01:53Z","page":"3824-3834","day":"13","publication":"2021 IEEE International Conference on Big Data","isi":1,"year":"2022"},{"publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579.","date_published":"2022-11-01T00:00:00Z","doi":"10.1016/j.jalgebra.2022.06.017","date_created":"2022-07-08T11:40:07Z","page":"145-179","day":"01","publication":"Journal of Algebra","isi":1,"has_accepted_license":"1","year":"2022","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"title":"Contravariant pairings between standard Whittaker modules and Verma modules","author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000861841100004"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Brown, A., & Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017."},"month":"11","intvolume":" 609","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N ."}],"issue":"11","volume":609,"ec_funded":1,"file":[{"file_name":"2022_JournalAlgebra_Brown.pdf","date_created":"2023-02-02T07:32:48Z","file_size":582962,"date_updated":"2023-02-02T07:32:48Z","creator":"dernst","success":1,"checksum":"82abaee3d7837f703e499a9ecbb25b7c","file_id":"12473","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","status":"public","keyword":["Algebra and Number Theory"],"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)"},"_id":"11545","file_date_updated":"2023-02-02T07:32:48Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-08-03T11:56:30Z"},{"publication":"International Journal of Molecular Sciences","day":"01","year":"2022","isi":1,"has_accepted_license":"1","date_created":"2022-02-13T23:01:35Z","date_published":"2022-02-01T00:00:00Z","doi":"10.3390/ijms23031763","acknowledgement":"This work was partially supported by grants from National Institutes of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary Research Program (to B.C., H.V.K. and Z.P.). ","oa":1,"publisher":"MDPI","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 23(3), 1763.","chicago":"Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi, Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.","short":"Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B. Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022).","ieee":"Y. Chang et al., “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” International Journal of Molecular Sciences, vol. 23, no. 3. MDPI, 2022.","apa":"Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V., … Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763","ama":"Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3). doi:10.3390/ijms23031763","mla":"Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23, no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763."},"title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","article_processing_charge":"Yes","external_id":{"isi":["000754773500001"]},"author":[{"full_name":"Chang, Yan","last_name":"Chang","first_name":"Yan"},{"first_name":"Marah","last_name":"Funk","full_name":"Funk, Marah"},{"first_name":"Souvik","full_name":"Roy, Souvik","last_name":"Roy"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"},{"first_name":"Sangyong","last_name":"Choi","full_name":"Choi, Sangyong"},{"first_name":"Hristo V.","last_name":"Kojouharov","full_name":"Kojouharov, Hristo V."},{"full_name":"Chen, Benito","last_name":"Chen","first_name":"Benito"},{"full_name":"Pan, Zui","last_name":"Pan","first_name":"Zui"}],"article_number":"1763","language":[{"iso":"eng"}],"file":[{"file_size":24416183,"date_updated":"2022-02-14T07:46:30Z","creator":"dernst","file_name":"2022_IJMS_Chang.pdf","date_created":"2022-02-14T07:46:30Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"10756","checksum":"8890ad20c54e90dc58ad5ea97c902998"}],"publication_status":"published","publication_identifier":{"eissn":["14220067"],"issn":["16616596"]},"volume":23,"issue":"3","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs."}],"intvolume":" 23","month":"02","scopus_import":"1","ddc":["510","576"],"date_updated":"2023-08-09T10:17:07Z","department":[{"_id":"HeEd"}],"file_date_updated":"2022-02-14T07:46:30Z","_id":"10754","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original"},{"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0","apa":"Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics. Springer Nature, 2022. https://doi.org/10.1007/s40879-020-00405-0.","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"external_id":{"arxiv":["1912.12685"]},"article_processing_charge":"Yes (via OA deal)","title":"When different norms lead to same billiard trajectories?","acknowledgement":"AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"European Journal of Mathematics","page":"1309 - 1312","date_published":"2022-12-01T00:00:00Z","doi":"10.1007/s40879-020-00405-0","date_created":"2020-05-03T22:00:48Z","_id":"7791","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2024-02-22T15:58:42Z","ddc":["510"],"file_date_updated":"2020-07-14T12:48:03Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law."}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 8","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"7796","checksum":"f53e71fd03744075adcd0b8fc1b8423d","creator":"dernst","file_size":263926,"date_updated":"2020-07-14T12:48:03Z","file_name":"2020_EuropMathematics_Akopyan.pdf","date_created":"2020-05-04T10:33:42Z"}],"language":[{"iso":"eng"}],"issue":"4","volume":8,"ec_funded":1},{"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"has_accepted_license":"1","year":"2022","day":"25","publication":"LIPIcs","date_published":"2022-07-25T00:00:00Z","date_created":"2022-07-27T09:31:15Z","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).","ieee":"R. Biswas, S. Cultrera di Montesano, H. 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I: Geometric characterization of critical point pairs","abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. ","lang":"eng"}],"oa_version":"Submitted Version","alternative_title":["LIPIcs"],"month":"07","publication_status":"submitted","file":[{"file_id":"11661","checksum":"95903f9d1649e8e437a967b6f2f64730","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"window 1.pdf","date_created":"2022-07-27T09:30:30Z","file_size":564836,"date_updated":"2022-07-27T09:30:30Z","creator":"scultrer"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"ec_funded":1,"_id":"11660","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2024-03-20T09:36:56Z","ddc":["510"],"file_date_updated":"2022-07-27T09:30:30Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}]},{"month":"07","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements."}],"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"file_id":"11659","checksum":"b2f511e8b1cae5f1892b0cdec341acac","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2022-07-27T09:25:53Z","file_name":"D-S-E.pdf","date_updated":"2022-07-27T09:25:53Z","file_size":639266,"creator":"scultrer"}],"publication_status":"submitted","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"11658","file_date_updated":"2022-07-27T09:25:53Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2024-03-20T09:36:56Z","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. 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Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik, n.d.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics, Schloss Dagstuhl - Leibniz Zentrum für Informatik."}},{"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03121"}],"month":"12","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"oa_version":"Preprint","date_published":"2022-12-06T00:00:00Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"date_created":"2024-03-08T09:54:20Z","ec_funded":1,"publication_status":"submitted","year":"2022","day":"06","publication":"arXiv","language":[{"iso":"eng"}],"type":"preprint","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":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"status":"public","_id":"15090","article_number":"2212.03121","author":[{"last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano"},{"first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","last_name":"Draganov"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"}],"external_id":{"arxiv":["2212.03121"]},"article_processing_charge":"No","title":"On the size of chromatic Delaunay mosaics","department":[{"_id":"HeEd"}],"date_updated":"2024-03-20T09:36:56Z","citation":{"mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, 2212.03121.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. .","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, n.d.","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"publication":"Journal of Ambient Intelligence and Humanized Computing","day":"01","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2021-11-02T09:28:55Z","doi":"10.1007/s12652-021-03569-z","date_published":"2022-05-01T00:00:00Z","page":"2621–2635","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing. Springer Nature, 2022. https://doi.org/10.1007/s12652-021-03569-z.","ista":"Goudarzi S, Sharif M, Karimipour F. 2022. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 13, 2621–2635.","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:10.1007/s12652-021-03569-z.","apa":"Goudarzi, S., Sharif, M., & Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z","ama":"Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","ieee":"S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” Journal of Ambient Intelligence and Humanized Computing, vol. 13. Springer Nature, pp. 2621–2635, 2022."},"title":"A context-aware dimension reduction framework for trajectory and health signal analyses","external_id":{"isi":["000712198000001"]},"article_processing_charge":"No","author":[{"first_name":"Samira","full_name":"Goudarzi, Samira","last_name":"Goudarzi"},{"full_name":"Sharif, Mohammad","last_name":"Sharif","first_name":"Mohammad"},{"first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","last_name":"Karimipour"}],"project":[{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"file":[{"file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","date_created":"2021-11-12T19:38:05Z","file_size":1634958,"date_updated":"2022-12-20T23:30:08Z","creator":"fkarimip","embargo":"2022-11-12","checksum":"0a8961416a9bb2be5a1cebda65468bcf","file_id":"10279","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","publication_identifier":{"eissn":["1868-5145"],"issn":["1868-5137"]},"volume":13,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"It is practical to collect a huge amount of movement data and environmental context information along with the health signals of individuals because there is the emergence of new generations of positioning and tracking technologies and rapid advancements of health sensors. The study of the relations between these datasets and their sequence similarity analysis is of interest to many applications such as health monitoring and recommender systems. However, entering all movement parameters and health signals can lead to the complexity of the problem and an increase in its computational load. In this situation, dimension reduction techniques can be used to avoid consideration of simultaneous dependent parameters in the process of similarity measurement of the trajectories. The present study provides a framework, named CaDRAW, to use spatial–temporal data and movement parameters along with independent context information in the process of measuring the similarity of trajectories. In this regard, the omission of dependent movement characteristic signals is conducted by using an unsupervised feature selection dimension reduction technique. To evaluate the effectiveness of the proposed framework, it was applied to a real contextualized movement and related health signal datasets of individuals. The results indicated the capability of the proposed framework in measuring the similarity and in decreasing the characteristic signals in such a way that the similarity results -before and after reduction of dependent characteristic signals- have small differences. The mean differences between the obtained results before and after reducing the dimension were 0.029 and 0.023 for the round path, respectively."}],"intvolume":" 13","month":"05","scopus_import":"1","ddc":["000"],"date_updated":"2023-08-02T13:31:48Z","department":[{"_id":"HeEd"}],"file_date_updated":"2022-12-20T23:30:08Z","_id":"10208","keyword":["general computer science"],"status":"public","article_type":"original","type":"journal_article"},{"month":"10","intvolume":" 68","scopus_import":"1","alternative_title":["Early Career"],"main_file_link":[{"url":"http://www.ams.org/notices/","open_access":"1"}],"oa_version":"Published Version","volume":68,"issue":"9","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0002-9920"],"eissn":["1088-9477"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"letter_note","_id":"10071","department":[{"_id":"HeEd"}],"date_updated":"2021-12-03T07:31:26Z","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"date_published":"2021-10-01T00:00:00Z","doi":"10.1090/noti2349","date_created":"2021-10-03T22:01:22Z","page":"1511-1514","day":"01","publication":"Notices of the American Mathematical Society","year":"2021","title":"How to tutorial-a-thon","author":[{"full_name":"Adams, Henry","last_name":"Adams","first_name":"Henry"},{"id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","full_name":"Kourimska, Hana","last_name":"Kourimska"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Percival, Sarah","last_name":"Percival","first_name":"Sarah"},{"first_name":"Lori","full_name":"Ziegelmeier, Lori","last_name":"Ziegelmeier"}],"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:10.1090/noti2349.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021.","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021). How to tutorial-a-thon. Notices of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/noti2349","ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.","ista":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon. Notices of the American Mathematical Society. 68(9), 1511–1514."}},{"file":[{"date_created":"2021-11-29T08:41:00Z","file_name":"2021_ACL_Ilharco.pdf","creator":"cchlebak","date_updated":"2021-11-29T08:41:00Z","file_size":1227703,"file_id":"10368","checksum":"b14052a025a6ecf675bdfe51db98c0d7","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9-781-9540-8557-2"]},"publication_status":"published","month":"08","scopus_import":"1","main_file_link":[{"url":"https://aclanthology.org/2021.acl-tutorials.6/","open_access":"1"}],"oa_version":"Published Version","abstract":[{"text":"How information is created, shared and consumed has changed rapidly in recent decades, in part thanks to new social platforms and technologies on the web. With ever-larger amounts of unstructured and limited labels, organizing and reconciling information from different sources and modalities is a central challenge in machine learning. This cutting-edge tutorial aims to introduce the multimodal entailment task, which can be useful for detecting semantic alignments when a single modality alone does not suffice for a whole content understanding. Starting with a brief overview of natural language processing, computer vision, structured data and neural graph learning, we lay the foundations for the multimodal sections to follow. We then discuss recent multimodal learning literature covering visual, audio and language streams, and explore case studies focusing on tasks which require fine-grained understanding of visual and linguistic semantics question answering, veracity and hatred classification. Finally, we introduce a new dataset for recognizing multimodal entailment, exploring it in a hands-on collaborative section. Overall, this tutorial gives an overview of multimodal learning, introduces a multimodal entailment dataset, and encourages future research in the topic.","lang":"eng"}],"file_date_updated":"2021-11-29T08:41:00Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2022-01-26T14:26:36Z","status":"public","type":"conference","conference":{"end_date":"2021-08-06","location":"Bangkok, Thailand","start_date":"2021-08-01","name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10367","doi":"10.18653/v1/2021.acl-tutorials.6","date_published":"2021-08-01T00:00:00Z","date_created":"2021-11-28T23:01:30Z","page":"29-30","day":"01","publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","has_accepted_license":"1","year":"2021","quality_controlled":"1","publisher":"Association for Computational Linguistics","oa":1,"acknowledgement":"We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn, Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina, Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell, John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar, Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao, Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes.","title":"Recognizing multimodal entailment","author":[{"last_name":"Ilharco","full_name":"Ilharco, Cesar","first_name":"Cesar"},{"full_name":"Shirazi, Afsaneh","last_name":"Shirazi","first_name":"Afsaneh"},{"last_name":"Gopalan","full_name":"Gopalan, Arjun","first_name":"Arjun"},{"last_name":"Nagrani","full_name":"Nagrani, Arsha","first_name":"Arsha"},{"full_name":"Bratanič, Blaž","last_name":"Bratanič","first_name":"Blaž"},{"first_name":"Chris","last_name":"Bregler","full_name":"Bregler, Chris"},{"last_name":"Liu","full_name":"Liu, Christina","first_name":"Christina"},{"last_name":"Ferreira","full_name":"Ferreira, Felipe","first_name":"Felipe"},{"last_name":"Barcik","full_name":"Barcik, Gabriek","first_name":"Gabriek"},{"first_name":"Gabriel","full_name":"Ilharco, Gabriel","last_name":"Ilharco"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F","last_name":"Osang"},{"last_name":"Bulian","full_name":"Bulian, Jannis","first_name":"Jannis"},{"first_name":"Jared","last_name":"Frank","full_name":"Frank, Jared"},{"first_name":"Lucas","full_name":"Smaira, Lucas","last_name":"Smaira"},{"first_name":"Qin","full_name":"Cao, Qin","last_name":"Cao"},{"first_name":"Ricardo","full_name":"Marino, Ricardo","last_name":"Marino"},{"full_name":"Patel, Roma","last_name":"Patel","first_name":"Roma"},{"last_name":"Leung","full_name":"Leung, Thomas","first_name":"Thomas"},{"first_name":"Vaiva","full_name":"Imbrasaite, Vaiva","last_name":"Imbrasaite"}],"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"chicago":"Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30. Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6.","ista":"Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C, Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q, Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment. 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing, 29–30.","mla":"Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6.","apa":"Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6","ama":"Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6","short":"C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler, C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L. Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30.","ieee":"C. Ilharco et al., “Recognizing multimodal entailment,” in 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok, Thailand, 2021, pp. 29–30."}},{"department":[{"_id":"HeEd"}],"file_date_updated":"2022-01-10T08:33:22Z","date_updated":"2022-01-10T08:36:55Z","ddc":["500"],"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)"},"status":"public","_id":"10608","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"publication_status":"published","file":[{"checksum":"c435dcfa1ad3aadc5cdd7366bc7f4e98","file_id":"10610","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2022-01-10T08:33:22Z","file_name":"2021_EuJournalMath_Weighill.pdf","date_updated":"2022-01-10T08:33:22Z","file_size":384908,"creator":"cchlebak"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"12","abstract":[{"lang":"eng","text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property."}],"oa_version":"Published Version","author":[{"last_name":"Weighill","full_name":"Weighill, Thomas","first_name":"Thomas"},{"first_name":"Takamitsu","full_name":"Yamauchi, Takamitsu","last_name":"Yamauchi"},{"last_name":"Zava","full_name":"Zava, Nicolò","first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"article_processing_charge":"Yes (via OA deal)","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","citation":{"chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.","ista":"Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics.","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021, doi:10.1007/s40879-021-00515-3.","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3","apa":"Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-021-00515-3","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” European Journal of Mathematics. Springer Nature, 2021."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2021-12-30T00:00:00Z","doi":"10.1007/s40879-021-00515-3","date_created":"2022-01-09T23:01:27Z","has_accepted_license":"1","year":"2021","day":"30","publication":"European Journal of Mathematics","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria)."},{"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"date_updated":"2023-02-21T16:33:44Z","status":"public","type":"conference","conference":{"name":"WALCOM: Algorithms and Computation","start_date":"2021-02-28","end_date":"2021-03-02","location":"Yangon, Myanmar"},"_id":"9296","related_material":{"record":[{"relation":"later_version","id":"11938","status":"public"}]},"volume":12635,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783030682101"],"eissn":["16113349"],"issn":["03029743"]},"publication_status":"published","month":"02","intvolume":" 12635","alternative_title":["LNCS"],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge."}],"title":"On compatible matchings","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"first_name":"Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","full_name":"Arroyo Guevara, Alan M","orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"last_name":"Parada","full_name":"Parada, Irene","first_name":"Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"last_name":"Pilz","full_name":"Pilz, Alexander","first_name":"Alexander"},{"full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef"},{"first_name":"Birgit","full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber"}],"external_id":{"arxiv":["2101.03928"]},"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","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.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","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 et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233."},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"name":"Game Theory","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_published":"2021-02-16T00:00:00Z","doi":"10.1007/978-3-030-68211-8_18","date_created":"2021-03-28T22:01:41Z","page":"221-233","day":"16","publication":"15th International Conference on Algorithms and Computation","year":"2021","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE)."},{"date_published":"2021-04-01T00:00:00Z","doi":"10.1007/s00022-021-00577-4","date_created":"2021-06-06T22:01:29Z","has_accepted_license":"1","year":"2021","day":"01","publication":"Journal of Geometry","quality_controlled":"1","publisher":"Springer Nature","oa":1,"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Osang, Georg F","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","title":"A step in the Delaunay mosaic of order k","citation":{"mla":"Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.","ieee":"H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.","short":"H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).","apa":"Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4","ama":"Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4.","ista":"Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"15","volume":112,"issue":"1","publication_identifier":{"eissn":["14208997"],"issn":["00472468"]},"publication_status":"published","file":[{"date_created":"2021-06-11T13:16:26Z","file_name":"2021_Geometry_Edelsbrunner.pdf","date_updated":"2021-06-11T13:16:26Z","file_size":694706,"creator":"kschuh","file_id":"9544","checksum":"e52a832f1def52a2b23d21bcc09e646f","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"04","intvolume":" 112","abstract":[{"text":"Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.","lang":"eng"}],"oa_version":"Published Version","file_date_updated":"2021-06-11T13:16:26Z","department":[{"_id":"HeEd"}],"date_updated":"2022-05-12T11:41:45Z","ddc":["510"],"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)"},"status":"public","_id":"9465"},{"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32."},"title":"The density fingerprint of a periodic point set","article_processing_charge":"No","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":" Kurlin , Vitaliy","last_name":" Kurlin ","first_name":"Vitaliy"},{"last_name":"Smith","full_name":"Smith, Philip","first_name":"Philip"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"_id":"25C5A090-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00312","name":"The Wittgenstein Prize"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"publication":"37th International Symposium on Computational Geometry (SoCG 2021)","day":"02","year":"2021","has_accepted_license":"1","date_created":"2021-04-22T08:09:58Z","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.32","page":"32:1-32:16","acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","ddc":["004","516"],"date_updated":"2023-02-23T13:55:40Z","file_date_updated":"2021-04-22T08:08:14Z","department":[{"_id":"HeEd"}],"_id":"9345","status":"public","conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Virtual","name":"SoCG: Symposium on Computational Geometry"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","language":[{"iso":"eng"}],"file":[{"file_name":"df_socg_final_version.pdf","date_created":"2021-04-22T08:08:14Z","creator":"mwintrae","file_size":3117435,"date_updated":"2021-04-22T08:08:14Z","success":1,"checksum":"1787baef1523d6d93753b90d0c109a6d","file_id":"9346","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["1868-8969"]},"ec_funded":1,"volume":189,"oa_version":"Published Version","abstract":[{"text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction.","lang":"eng"}],"intvolume":" 189","month":"06","alternative_title":["LIPIcs"]},{"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16"},"title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","article_processing_charge":"No","author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"article_number":"16","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"}],"publication":"Leibniz International Proceedings in Informatics","day":"02","year":"2021","has_accepted_license":"1","date_created":"2021-06-27T22:01:48Z","doi":"10.4230/LIPIcs.SoCG.2021.16","date_published":"2021-06-02T00:00:00Z","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ddc":["516"],"date_updated":"2023-02-23T14:02:28Z","file_date_updated":"2021-06-28T13:11:39Z","department":[{"_id":"HeEd"}],"_id":"9604","status":"public","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)"},"conference":{"end_date":"2021-06-11","location":"Online","start_date":"2021-06-07","name":"SoCG: International Symposium on Computational Geometry"},"type":"conference","language":[{"iso":"eng"}],"file":[{"creator":"asandaue","date_updated":"2021-06-28T13:11:39Z","file_size":727817,"date_created":"2021-06-28T13:11:39Z","file_name":"2021_LIPIcs_Biswas.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9611","checksum":"22b11a719018b22ecba2471b51f2eb40","success":1}],"publication_status":"published","publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"ec_funded":1,"volume":189,"oa_version":"Published Version","abstract":[{"text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation.","lang":"eng"}],"intvolume":" 189","month":"06","scopus_import":"1","alternative_title":["LIPIcs"]},{"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","author":[{"full_name":"Čomić, Lidija","last_name":"Čomić","first_name":"Lidija"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","citation":{"chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","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.","mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","quality_controlled":"1","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).","page":"152-163","date_created":"2021-08-08T22:01:29Z","doi":"10.1007/978-3-030-76657-3_10","date_published":"2021-05-16T00:00:00Z","year":"2021","publication":"Discrete Geometry and Mathematical Morphology","day":"16","conference":{"name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","end_date":"2021-05-27","location":"Uppsala, Sweden","start_date":"2021-05-24"},"type":"conference","status":"public","_id":"9824","department":[{"_id":"HeEd"}],"date_updated":"2022-05-31T06:58:21Z","scopus_import":"1","alternative_title":["LNCS"],"intvolume":" 12708","month":"05","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"}],"oa_version":"None","ec_funded":1,"volume":12708,"publication_status":"published","publication_identifier":{"issn":["03029743"],"eissn":["16113349"],"isbn":["9783030766566"]},"language":[{"iso":"eng"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","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.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700."},"title":"Folding polyominoes with holes into a cube","article_processing_charge":"No","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"full_name":"Akitaya, Hugo A.","last_name":"Akitaya","first_name":"Hugo A."},{"full_name":"Cheung, Kenneth C.","last_name":"Cheung","first_name":"Kenneth C."},{"first_name":"Erik D.","full_name":"Demaine, Erik D.","last_name":"Demaine"},{"first_name":"Martin L.","last_name":"Demaine","full_name":"Demaine, Martin L."},{"first_name":"Sándor P.","last_name":"Fekete","full_name":"Fekete, Sándor P."},{"first_name":"Linda","full_name":"Kleist, Linda","last_name":"Kleist"},{"last_name":"Kostitsyna","full_name":"Kostitsyna, Irina","first_name":"Irina"},{"first_name":"Maarten","full_name":"Löffler, Maarten","last_name":"Löffler"},{"full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"article_number":"101700","project":[{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"publication":"Computational Geometry: Theory and Applications","day":"01","year":"2021","isi":1,"date_created":"2020-08-30T22:01:09Z","date_published":"2021-02-01T00:00:00Z","doi":"10.1016/j.comgeo.2020.101700","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.","oa":1,"publisher":"Elsevier","quality_controlled":"1","date_updated":"2023-08-04T10:57:42Z","department":[{"_id":"HeEd"}],"_id":"8317","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["09257721"]},"related_material":{"record":[{"id":"6989","status":"public","relation":"shorter_version"}]},"volume":93,"oa_version":"Preprint","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"}],"intvolume":" 93","month":"02","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"scopus_import":"1"},{"_id":"8773","status":"public","keyword":["Applied Mathematics","General Mathematics"],"type":"journal_article","article_type":"original","date_updated":"2023-08-04T11:11:47Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"month":"01","intvolume":" 149","main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"publication_status":"published","volume":149,"issue":"1","ec_funded":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52."},"title":"Contravariant forms on Whittaker modules","author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","last_name":"Brown","full_name":"Brown, Adam"},{"last_name":"Romanov","full_name":"Romanov, Anna","first_name":"Anna"}],"article_processing_charge":"No","external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"day":"01","publication":"Proceedings of the American Mathematical Society","isi":1,"year":"2021","date_published":"2021-01-01T00:00:00Z","doi":"10.1090/proc/15205","date_created":"2020-11-19T10:17:40Z","page":"37-52"},{"oa":1,"quality_controlled":"1","publisher":"IEEE","year":"2021","isi":1,"publication":"2020 IEEE International Conference on Big Data","day":"19","page":"3123-3132","date_created":"2021-03-21T11:34:07Z","date_published":"2021-03-19T00:00:00Z","doi":"10.1109/bigdata50022.2020.9378374","citation":{"chicago":"Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani, Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374.","ista":"Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F. 2021. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. 2020 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3123–3132.","mla":"Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374.","ama":"Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374","apa":"Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., & Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In 2020 IEEE International Conference on Big Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374","short":"G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour, in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132.","ieee":"G. Heiler et al., “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in 2020 IEEE International Conference on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["2008.10064"],"isi":["000662554703032"]},"article_processing_charge":"No","author":[{"first_name":"Georg","full_name":"Heiler, Georg","last_name":"Heiler"},{"last_name":"Reisch","full_name":"Reisch, Tobias","first_name":"Tobias"},{"last_name":"Hurt","full_name":"Hurt, Jan","first_name":"Jan"},{"first_name":"Mohammad","last_name":"Forghani","full_name":"Forghani, Mohammad"},{"first_name":"Aida","full_name":"Omani, Aida","last_name":"Omani"},{"first_name":"Allan","last_name":"Hanbury","full_name":"Hanbury, Allan"},{"orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid","last_name":"Karimipour","first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425"}],"title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","abstract":[{"text":"In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2008.10064","open_access":"1"}],"scopus_import":"1","month":"03","publication_status":"published","publication_identifier":{"isbn":["9781728162515"]},"language":[{"iso":"eng"}],"_id":"9253","conference":{"name":"Big Data: International Conference on Big Data","end_date":"2020-12-13","location":"Atlanta, GA, United States","start_date":"2020-12-10"},"type":"conference","status":"public","date_updated":"2023-08-07T14:00:13Z","department":[{"_id":"HeEd"}]},{"file_date_updated":"2021-12-01T10:56:53Z","department":[{"_id":"HeEd"}],"ddc":["516"],"date_updated":"2023-08-07T14:35:44Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"9317","ec_funded":1,"volume":65,"related_material":{"record":[{"relation":"earlier_version","id":"187","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2021-12-01T10:56:53Z","file_size":677704,"date_created":"2021-12-01T10:56:53Z","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"10394","checksum":"59b4e1e827e494209bcb4aae22e1d347","success":1}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"intvolume":" 65","month":"03","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers."}],"title":"The multi-cover persistence of Euclidean balls","external_id":{"isi":["000635460400001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1296–1313, 2021.","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","apa":"Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00281-9","ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9.","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00281-9."},"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"date_created":"2021-04-11T22:01:15Z","doi":"10.1007/s00454-021-00281-9","date_published":"2021-03-31T00:00:00Z","page":"1296–1313","publication":"Discrete and Computational Geometry","day":"31","year":"2021","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria)."},{"author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"last_name":"Tomon","full_name":"Tomon, István","first_name":"István"}],"external_id":{"isi":["000702280800002"]},"article_processing_charge":"No","title":"Erdős-Hajnal-type results for monotone paths","citation":{"mla":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp. 21–37, doi:10.1016/j.jctb.2021.05.004.","ieee":"J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021.","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","ama":"Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004","apa":"Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004","chicago":"Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004.","ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"page":"21-37","doi":"10.1016/j.jctb.2021.05.004","date_published":"2021-06-09T00:00:00Z","date_created":"2021-06-27T22:01:47Z","isi":1,"has_accepted_license":"1","year":"2021","day":"09","publication":"Journal of Combinatorial Theory. Series B","publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"We would like to thank the anonymous referees for their useful comments and suggestions. János Pach is partially supported by Austrian Science Fund (FWF) grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially supported by Swiss National Science Foundation grant no. 200021_196965, and thanks the support of MIPT Moscow. Both authors are partially supported by The Russian Government in the framework of MegaGrant no. 075-15-2019-1926.","file_date_updated":"2021-06-28T13:33:23Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-10T13:38:00Z","ddc":["510"],"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)"},"status":"public","_id":"9602","volume":151,"publication_identifier":{"issn":["0095-8956"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"15fbc9064cd9d1c777ac0043b78c8f12","file_id":"9612","file_size":418168,"date_updated":"2021-06-28T13:33:23Z","creator":"asandaue","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","date_created":"2021-06-28T13:33:23Z"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"06","intvolume":" 151","abstract":[{"text":"An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees.","lang":"eng"}],"oa_version":"Published Version"},{"file_date_updated":"2021-08-09T09:25:41Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-10T14:21:42Z","ddc":["006"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"9821","issue":"7","volume":16,"publication_status":"published","publication_identifier":{"eissn":["19326203"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2021-08-09T09:25:41Z","file_size":2706919,"creator":"asandaue","date_created":"2021-08-09T09:25:41Z","file_name":"2021_PLoSONE_Graff.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"9832","checksum":"0277aa155d5db1febd2cb384768bba5f","success":1}],"scopus_import":"1","intvolume":" 16","month":"07","abstract":[{"text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.","lang":"eng"}],"oa_version":"Published Version","pmid":1,"article_processing_charge":"Yes","external_id":{"pmid":["34292957"],"isi":["000678124900050"]},"author":[{"last_name":"Graff","full_name":"Graff, Grzegorz","first_name":"Grzegorz"},{"last_name":"Graff","full_name":"Graff, Beata","first_name":"Beata"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz"},{"first_name":"Dariusz","last_name":"Gąsecki","full_name":"Gąsecki, Dariusz"},{"last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof"}],"title":"Persistent homology as a new method of the assessment of heart rate variability","citation":{"mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:10.1371/journal.pone.0253851.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851","ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 2021;16(7). doi:10.1371/journal.pone.0253851","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science, 2021. https://doi.org/10.1371/journal.pone.0253851.","ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"e0253851","date_created":"2021-08-08T22:01:28Z","doi":"10.1371/journal.pone.0253851","date_published":"2021-07-01T00:00:00Z","year":"2021","isi":1,"has_accepted_license":"1","publication":"PLoS ONE","day":"01","oa":1,"quality_controlled":"1","publisher":"Public Library of Science","acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper."},{"month":"10","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density."}],"ec_funded":1,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"14053","checksum":"3514382e3a1eb87fa6c61ad622874415","file_size":1966019,"date_updated":"2023-08-14T11:55:10Z","creator":"dernst","file_name":"2023_ExperimentalMath_Akopyan.pdf","date_created":"2023-08-14T11:55:10Z"}],"publication_status":"published","publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"10222","file_date_updated":"2023-08-14T11:55:10Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-08-14T11:57:07Z","oa":1,"quality_controlled":"1","publisher":"Taylor and Francis","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and for directing us to relevant references. We also thank to Anton Mellit for a useful discussion on Bessel functions.","date_created":"2021-11-07T23:01:25Z","date_published":"2021-10-25T00:00:00Z","doi":"10.1080/10586458.2021.1980459","page":"1-15","publication":"Experimental Mathematics","day":"25","year":"2021","has_accepted_license":"1","isi":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"The Wittgenstein Prize","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"title":"The beauty of random polytopes inscribed in the 2-sphere","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2007.07783"],"isi":["000710893500001"]},"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15.","chicago":"Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics. Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459.","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","ieee":"A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis, pp. 1–15, 2021.","ama":"Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459","apa":"Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2021.1980459","mla":"Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459."}},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434."},"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","external_id":{"isi":["000597770300001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"publication":"Discrete & Computational Geometry","day":"01","year":"2021","has_accepted_license":"1","isi":1,"date_created":"2020-12-12T11:07:02Z","date_published":"2021-07-01T00:00:00Z","doi":"10.1007/s00454-020-00250-8","page":"386-434","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","ddc":["516"],"date_updated":"2023-09-05T15:02:40Z","file_date_updated":"2021-08-06T09:52:29Z","department":[{"_id":"HeEd"}],"_id":"8940","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"file":[{"creator":"kschuh","file_size":983307,"date_updated":"2021-08-06T09:52:29Z","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","date_created":"2021-08-06T09:52:29Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"9795","checksum":"c848986091e56699dc12de85adb1e39c"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"ec_funded":1,"volume":66,"issue":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric."}],"intvolume":" 66","month":"07"},{"citation":{"chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.","ista":"Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140.","mla":"Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.","ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x","apa":"Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x","short":"A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140.","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam"},{"full_name":"Bobrowski, Omer","last_name":"Bobrowski","first_name":"Omer"},{"last_name":"Munch","full_name":"Munch, Elizabeth","first_name":"Elizabeth"},{"last_name":"Wang","full_name":"Wang, Bei","first_name":"Bei"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1909.03488"]},"title":"Probabilistic convergence and stability of random mapper graphs","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"has_accepted_license":"1","year":"2021","day":"01","publication":"Journal of Applied and Computational Topology","page":"99-140","doi":"10.1007/s41468-020-00063-x","date_published":"2021-03-01T00:00:00Z","date_created":"2021-02-11T14:41:02Z","acknowledgement":"AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","quality_controlled":"1","oa":1,"date_updated":"2023-09-05T15:37:56Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-02-11T14:43:59Z","_id":"9111","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"3f02e9d47c428484733da0f588a3c069","file_id":"9112","file_size":2090265,"date_updated":"2021-02-11T14:43:59Z","creator":"dernst","file_name":"2020_JourApplCompTopology_Brown.pdf","date_created":"2021-02-11T14:43:59Z"}],"language":[{"iso":"eng"}],"issue":"1","volume":5,"ec_funded":1,"abstract":[{"lang":"eng","text":"We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data."}],"oa_version":"Published Version","scopus_import":"1","month":"03","intvolume":" 5"},{"oa":1,"publisher":"Institute of Science and Technology Austria","day":"01","year":"2021","has_accepted_license":"1","date_created":"2021-02-02T14:11:06Z","date_published":"2021-02-01T00:00:00Z","doi":"10.15479/AT:ISTA:9056","page":"134","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021."},"title":"Multi-cover persistence and Delaunay mosaics","article_processing_charge":"No","author":[{"orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"oa_version":"Published Version","abstract":[{"text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.","lang":"eng"}],"month":"02","place":"Klosterneuburg","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"date_updated":"2021-02-03T10:37:28Z","file_size":13446994,"creator":"patrickd","date_created":"2021-02-02T14:09:25Z","file_name":"thesis_source.zip","content_type":"application/zip","access_level":"closed","relation":"source_file","checksum":"bcf27986147cab0533b6abadd74e7629","file_id":"9063"},{"success":1,"file_id":"9064","checksum":"9cc8af266579a464385bbe2aff6af606","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"thesis_pdfA2b.pdf","date_created":"2021-02-02T14:09:18Z","file_size":5210329,"date_updated":"2021-02-02T14:09:18Z","creator":"patrickd"}],"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"187"},{"relation":"part_of_dissertation","status":"public","id":"8703"}]},"_id":"9056","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","ddc":["006","514","516"],"date_updated":"2023-09-07T13:29:01Z","supervisor":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"file_date_updated":"2021-02-03T10:37:28Z"},{"month":"10","intvolume":" 17","scopus_import":"1","oa_version":"Submitted Version","pmid":1,"abstract":[{"lang":"eng","text":"Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals."}],"issue":"40","volume":17,"ec_funded":1,"file":[{"date_updated":"2023-10-03T09:21:42Z","file_size":4678788,"creator":"dernst","date_created":"2023-10-03T09:21:42Z","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"14385","checksum":"b4da0c420530295e61b153960f6cb350","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1744-683X"],"eissn":["1744-6848"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"10204","department":[{"_id":"HeEd"}],"file_date_updated":"2023-10-03T09:21:42Z","ddc":["540"],"date_updated":"2023-10-03T09:24:27Z","quality_controlled":"1","publisher":"Royal Society of Chemistry ","oa":1,"acknowledgement":"MS acknowledges the support by Australian Research Council funding through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour and N. Francois for their input and valuable discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant no. 788183 and from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","doi":"10.1039/d1sm00774b","date_published":"2021-10-20T00:00:00Z","date_created":"2021-10-31T23:01:30Z","page":"9107-9115","day":"20","publication":"Soft Matter","isi":1,"has_accepted_license":"1","year":"2021","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","author":[{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Saadatfar, Mohammad","last_name":"Saadatfar","first_name":"Mohammad"}],"external_id":{"isi":["000700090000001"],"pmid":["34569592"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b.","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115.","ieee":"G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” Soft Matter, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021.","apa":"Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b","ama":"Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115. doi:10.1039/d1sm00774b","chicago":"Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b.","ista":"Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115."}},{"author":[{"first_name":"René","full_name":"Corbet, René","last_name":"Corbet"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"last_name":"Lesnick","full_name":"Lesnick, Michael","first_name":"Michael"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang"}],"external_id":{"arxiv":["2103.07823"]},"article_processing_charge":"No","title":"Computing the multicover bifiltration","citation":{"chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27.","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing the multicover bifiltration. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27"},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","article_number":"27","doi":"10.4230/LIPIcs.SoCG.2021.27","date_published":"2021-06-02T00:00:00Z","date_created":"2021-06-27T22:01:49Z","has_accepted_license":"1","year":"2021","day":"02","publication":"Leibniz International Proceedings in Informatics","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","file_date_updated":"2021-06-28T12:40:47Z","department":[{"_id":"HeEd"}],"date_updated":"2023-10-04T12:03:39Z","ddc":["516"],"type":"conference","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)"},"conference":{"name":"SoCG: International Symposium on Computational Geometry","start_date":"2021-06-07","end_date":"2021-06-11","location":"Online"},"status":"public","_id":"9605","volume":189,"related_material":{"record":[{"id":"12709","status":"public","relation":"later_version"}],"link":[{"url":"https://arxiv.org/abs/2103.07823","relation":"extended_version"}]},"publication_identifier":{"issn":["18688969"],"isbn":["9783959771849"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"0de217501e7ba8b267d58deed0d51761","file_id":"9610","file_size":"1367983","date_updated":"2021-06-28T12:40:47Z","creator":"cziletti","file_name":"2021_LIPIcs_Corbet.pdf","date_created":"2021-06-28T12:40:47Z"}],"language":[{"iso":"eng"}],"scopus_import":"1","alternative_title":["LIPIcs"],"month":"06","intvolume":" 189","abstract":[{"text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. ","lang":"eng"}],"oa_version":"Published Version"},{"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:17:1-17:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.17.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational GeometryLeibniz International Proceedings in Informatics (LIPIcs), LIPIcs, vol. 189, 17:1-17:16.","mla":"Boissonnat, Jean-Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter-Freudenthal-Kuhn Triangulations.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 17:1-17:16, doi:10.4230/LIPIcs.SoCG.2021.17.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:17:1-17:16. doi:10.4230/LIPIcs.SoCG.2021.17","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 17:1-17:16). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.17","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 17:1-17:16.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2021, p. 17:1-17:16."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"last_name":"Kachanovich","full_name":"Kachanovich, Siargey","first_name":"Siargey"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"No","title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations","acknowledgement":"We thank Dominique Attali, Guilherme de Fonseca, Arijit Ghosh, Vincent Pilaud and Aurélien Alvarez for their comments and suggestions. We also acknowledge the reviewers.","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"has_accepted_license":"1","year":"2021","day":"02","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","page":"17:1-17:16","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.17","date_created":"2021-06-02T10:10:55Z","_id":"9441","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","type":"conference","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)"},"conference":{"start_date":"2021-06-07","location":"Virtual","end_date":"2021-06-11","name":"SoCG: Symposium on Computational Geometry"},"status":"public","date_updated":"2023-10-10T07:34:34Z","ddc":["005","516","514"],"file_date_updated":"2021-06-02T10:22:33Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"oa_version":"Published Version","alternative_title":["LIPIcs"],"month":"06","place":"Dagstuhl, Germany","intvolume":" 189","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-184-9"]},"publication_status":"published","file":[{"checksum":"c322aa48d5d35a35877896cc565705b6","file_id":"9442","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2021-06-02T10:22:33Z","file_name":"LIPIcs-SoCG-2021-17.pdf","creator":"mwintrae","date_updated":"2021-06-02T10:22:33Z","file_size":1972902}],"language":[{"iso":"eng"}],"volume":189,"related_material":{"record":[{"relation":"later_version","id":"12960","status":"public"}]},"ec_funded":1},{"status":"public","type":"journal_article","article_type":"original","_id":"8338","department":[{"_id":"HeEd"}],"date_updated":"2024-03-07T14:51:11Z","intvolume":" 66","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1908.00856","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory."}],"ec_funded":1,"volume":66,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","external_id":{"isi":["000564488500002"],"arxiv":["1908.00856"]},"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":"Alexander I.","last_name":"Bobenko","full_name":"Bobenko, Alexander I."},{"first_name":"Wolfgang K.","last_name":"Schief","full_name":"Schief, Wolfgang K."},{"last_name":"Techter","full_name":"Techter, Jan","first_name":"Jan"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 938–76, doi:10.1007/s00454-020-00240-w.","ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 2021;66:938-976. doi:10.1007/s00454-020-00240-w","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., & Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00240-w","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 938–976, 2021.","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00240-w.","ista":"Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 66, 938–976."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by the Australian Research Council (DP1401000851). A.V.A. was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha).","date_created":"2020-09-06T22:01:13Z","date_published":"2021-10-01T00:00:00Z","doi":"10.1007/s00454-020-00240-w","page":"938-976","publication":"Discrete and Computational Geometry","day":"01","year":"2021","isi":1},{"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"title":"Local conditions for triangulating submanifolds of Euclidean space","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000558119300001"]},"author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"full_name":"Dyer, Ramsay","last_name":"Dyer","first_name":"Ramsay"},{"first_name":"Arijit","last_name":"Ghosh","full_name":"Ghosh, Arijit"},{"first_name":"Andre","full_name":"Lieutier, Andre","last_name":"Lieutier"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry, vol. 66, Springer Nature, 2021, pp. 666–86, doi:10.1007/s00454-020-00233-9.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” Discrete and Computational Geometry, vol. 66. Springer Nature, pp. 666–686, 2021.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00233-9","ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 2021;66:666-686. doi:10.1007/s00454-020-00233-9","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00233-9.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 66, 666–686."},"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India.\r\nThis work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","date_created":"2020-08-11T07:11:51Z","date_published":"2021-09-01T00:00:00Z","doi":"10.1007/s00454-020-00233-9","page":"666-686","publication":"Discrete and Computational Geometry","day":"01","year":"2021","has_accepted_license":"1","isi":1,"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"8248","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2024-03-07T14:54:59Z","intvolume":" 66","month":"09","main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic."}],"ec_funded":1,"volume":66,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]}},{"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1712.07734"],"isi":["000536324700001"]},"author":[{"full_name":"Brown, Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam"},{"last_name":"Wang","full_name":"Wang, Bei","first_name":"Bei"}],"title":"Sheaf-theoretic stratification learning from geometric and topological perspectives","citation":{"mla":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1166–98, doi:10.1007/s00454-020-00206-y.","short":"A. Brown, B. Wang, Discrete and Computational Geometry 65 (2021) 1166–1198.","ieee":"A. Brown and B. Wang, “Sheaf-theoretic stratification learning from geometric and topological perspectives,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1166–1198, 2021.","ama":"Brown A, Wang B. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 2021;65:1166-1198. doi:10.1007/s00454-020-00206-y","apa":"Brown, A., & Wang, B. (2021). Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00206-y","chicago":"Brown, Adam, and Bei Wang. “Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00206-y.","ista":"Brown A, Wang B. 2021. Sheaf-theoretic stratification learning from geometric and topological perspectives. Discrete and Computational Geometry. 65, 1166–1198."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). This work was partially supported by NSF IIS-1513616 and NSF ABI-1661375. The authors would like to thank the anonymous referees for their insightful comments.","page":"1166-1198","date_created":"2020-05-30T10:26:04Z","doi":"10.1007/s00454-020-00206-y","date_published":"2021-06-01T00:00:00Z","year":"2021","has_accepted_license":"1","isi":1,"publication":"Discrete and Computational Geometry","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"7905","file_date_updated":"2020-11-25T09:06:41Z","department":[{"_id":"HeEd"}],"date_updated":"2024-03-07T15:01:58Z","ddc":["510"],"scopus_import":"1","intvolume":" 65","month":"06","abstract":[{"lang":"eng","text":"We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms."}],"oa_version":"Published Version","volume":65,"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2020_DiscreteCompGeometry_Brown.pdf","date_created":"2020-11-25T09:06:41Z","file_size":1013730,"date_updated":"2020-11-25T09:06:41Z","creator":"dernst","success":1,"checksum":"487a84ea5841b75f04f66d7ebd71b67e","file_id":"8803","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}]},{"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, vol. 14, Springer Nature, 2020, pp. 141–76, doi:10.1007/s11786-020-00461-5.","short":"A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science 14 (2020) 141–176.","ieee":"A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” Mathematics in Computer Science, vol. 14. Springer Nature, pp. 141–176, 2020.","ama":"Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. Mathematics in Computer Science. 2020;14:141-176. doi:10.1007/s11786-020-00461-5","apa":"Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations have good quality. Mathematics in Computer Science. Springer Nature. https://doi.org/10.1007/s11786-020-00461-5","chicago":"Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science. Springer Nature, 2020. https://doi.org/10.1007/s11786-020-00461-5.","ista":"Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science. 14, 141–176."},"title":"Coxeter triangulations have good quality","author":[{"last_name":"Choudhary","full_name":"Choudhary, Aruni","first_name":"Aruni"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","quality_controlled":"1","oa":1,"day":"01","publication":"Mathematics in Computer Science","has_accepted_license":"1","year":"2020","doi":"10.1007/s11786-020-00461-5","date_published":"2020-03-01T00:00:00Z","date_created":"2020-03-05T13:30:18Z","page":"141-176","_id":"7567","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2021-01-12T08:14:13Z","file_date_updated":"2020-11-20T10:18:02Z","department":[{"_id":"HeEd"}],"oa_version":"Published Version","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."}],"month":"03","intvolume":" 14","scopus_import":"1","file":[{"file_name":"2020_MathCompScie_Choudhary.pdf","date_created":"2020-11-20T10:18:02Z","creator":"dernst","file_size":872275,"date_updated":"2020-11-20T10:18:02Z","success":1,"file_id":"8783","checksum":"1d145f3ab50ccee735983cb89236e609","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1661-8270"],"eissn":["1661-8289"]},"publication_status":"published","volume":14,"ec_funded":1},{"volume":15,"ec_funded":1,"file":[{"file_size":2207071,"date_updated":"2020-10-08T08:56:14Z","creator":"dernst","file_name":"2020-B-01-PoissonExperimentalSurvey.pdf","date_created":"2020-10-08T08:56:14Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"7b5e0de10675d787a2ddb2091370b8d8","file_id":"8628"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["21978549"],"isbn":["9783030434076"],"issn":["21932808"]},"publication_status":"published","month":"06","intvolume":" 15","scopus_import":"1","alternative_title":["Abel Symposia"],"oa_version":"Submitted Version","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"}],"file_date_updated":"2020-10-08T08:56:14Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2021-01-12T08:17:06Z","status":"public","type":"conference","_id":"8135","doi":"10.1007/978-3-030-43408-3_8","date_published":"2020-06-22T00:00:00Z","date_created":"2020-07-19T22:00:59Z","page":"181-218","day":"22","publication":"Topological Data Analysis","has_accepted_license":"1","year":"2020","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant 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).","title":"Radius functions on Poisson–Delaunay mosaics and related complexes experimentally","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ölsböck","full_name":"Ölsböck, Katharina","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Synak, Peter","last_name":"Synak","first_name":"Peter","id":"331776E2-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Edelsbrunner, Herbert, Anton Nikitenko, Katharina Ölsböck, and Peter Synak. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” In Topological Data Analysis, 15:181–218. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-43408-3_8.","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.","mla":"Edelsbrunner, Herbert, et al. “Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally.” Topological Data Analysis, vol. 15, Springer Nature, 2020, pp. 181–218, doi:10.1007/978-3-030-43408-3_8.","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 Topological Data Analysis, 2020, vol. 15, pp. 181–218.","apa":"Edelsbrunner, H., Nikitenko, A., Ölsböck, K., & Synak, P. (2020). 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I 02979-N35. ","quality_controlled":"1","publisher":"De Gruyter","oa":1,"citation":{"mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:10.1515/mathm-2020-0106.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. 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In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.","lang":"eng"}],"oa_version":"Published Version","month":"11","intvolume":" 4","date_updated":"2021-03-22T09:01:50Z","ddc":["510"],"file_date_updated":"2021-03-22T08:56:37Z","department":[{"_id":"HeEd"}],"_id":"9249","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public"},{"volume":12590,"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783030687656"],"eissn":["1611-3349"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2006.14908","open_access":"1"}],"scopus_import":"1","intvolume":" 12590","month":"09","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⟶∞ ."}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2021-04-06T11:32:32Z","conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2020-09-16","location":"Virtual, Online","end_date":"2020-09-18"},"type":"conference","status":"public","_id":"9299","series_title":"LNCS","page":"359-371","date_created":"2021-03-28T22:01:44Z","doi":"10.1007/978-3-030-68766-3_28","date_published":"2020-09-20T00:00:00Z","year":"2020","publication":"28th International Symposium on Graph Drawing and Network Visualization","day":"20","oa":1,"quality_controlled":"1","publisher":"Springer Nature","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.","article_processing_charge":"No","external_id":{"arxiv":["2006.14908"]},"author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","last_name":"Pach"},{"first_name":"Gábor","full_name":"Tardos, Gábor","last_name":"Tardos"},{"first_name":"Géza","full_name":"Tóth, Géza","last_name":"Tóth"}],"title":"Crossings between non-homotopic edges","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.","chicago":"Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In 28th International Symposium on Graph Drawing and Network Visualization, 12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28.","ieee":"J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in 28th International Symposium on Graph Drawing and Network Visualization, Virtual, Online, 2020, vol. 12590, pp. 359–371.","short":"J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371.","ama":"Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th International Symposium on Graph Drawing and Network Visualization. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28","apa":"Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic edges. In 28th International Symposium on Graph Drawing and Network Visualization (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28","mla":"Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}]},{"citation":{"ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","article_processing_charge":"Yes","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Virk, Ziga","last_name":"Virk","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert"}],"title":"Topological data analysis in information space","project":[{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"}],"year":"2020","has_accepted_license":"1","publication":"Journal of Computational Geometry","day":"14","page":"162-182","date_created":"2021-07-04T22:01:26Z","date_published":"2020-12-14T00:00:00Z","doi":"10.20382/jocg.v11i2a7","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).","oa":1,"quality_controlled":"1","publisher":"Carleton University","date_updated":"2021-08-11T12:26:34Z","ddc":["510","000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-08-11T11:55:11Z","_id":"9630","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"eissn":["1920180X"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","date_created":"2021-08-11T11:55:11Z","creator":"asandaue","file_size":1449234,"date_updated":"2021-08-11T11:55:11Z","success":1,"checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_id":"9882","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"license":"https://creativecommons.org/licenses/by/3.0/","issue":"2","volume":11,"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."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 11","month":"12"},{"type":"journal_article","article_type":"original","status":"public","_id":"8538","department":[{"_id":"HeEd"}],"date_updated":"2021-12-02T15:10:17Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"month":"09","abstract":[{"lang":"eng","text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods."}],"oa_version":"Preprint","ec_funded":1,"publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Schwartz","full_name":"Schwartz, Richard","first_name":"Richard"},{"full_name":"Tabachnikov, Serge","last_name":"Tabachnikov","first_name":"Serge"}],"article_processing_charge":"No","external_id":{"arxiv":["2001.02934"]},"title":"Billiards in ellipses revisited","citation":{"chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” European Journal of Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s40879-020-00426-9.","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2020. Billiards in ellipses revisited. European Journal of Mathematics.","mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” European Journal of Mathematics, Springer Nature, 2020, doi:10.1007/s40879-020-00426-9.","apa":"Akopyan, A., Schwartz, R., & Tabachnikov, S. (2020). Billiards in ellipses revisited. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00426-9","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. European Journal of Mathematics. 2020. doi:10.1007/s40879-020-00426-9","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” European Journal of Mathematics. Springer Nature, 2020.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics (2020)."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","date_published":"2020-09-09T00:00:00Z","doi":"10.1007/s40879-020-00426-9","date_created":"2020-09-20T22:01:38Z","year":"2020","day":"09","publication":"European Journal of Mathematics"},{"abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: 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. "}],"oa_version":"Published Version","alternative_title":["LIPIcs"],"scopus_import":"1","intvolume":" 164","month":"06","publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-143-6"]},"language":[{"iso":"eng"}],"file":[{"file_size":1009739,"date_updated":"2020-07-14T12:48:06Z","creator":"dernst","file_name":"2020_LIPIcsSoCG_Boissonnat.pdf","date_created":"2020-06-17T10:13:34Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"7969","checksum":"38cbfa4f5d484d267a35d44d210df044"}],"ec_funded":1,"related_material":{"record":[{"relation":"later_version","id":"9649","status":"public"}]},"volume":164,"_id":"7952","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2020-06-22","end_date":"2020-06-26","location":"Zürich, Switzerland"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","status":"public","date_updated":"2023-08-02T06:49:16Z","ddc":["510"],"file_date_updated":"2020-07-14T12:48:06Z","department":[{"_id":"HeEd"}],"oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","year":"2020","has_accepted_license":"1","publication":"36th International Symposium on Computational Geometry","day":"01","date_created":"2020-06-09T07:24:11Z","doi":"10.4230/LIPIcs.SoCG.2020.20","date_published":"2020-06-01T00:00:00Z","article_number":"20:1-20:18","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL-Approximations of Isomanifolds.” 36th International Symposium on Computational Geometry, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.20.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations of isomanifolds,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164.","short":"J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2020). The topological correctness of PL-approximations of isomanifolds. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.20","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations of isomanifolds. In: 36th International Symposium on Computational Geometry. Vol 164. 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SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"title":"The topological correctness of PL-approximations of isomanifolds"},{"year":"2020","isi":1,"publication":"Geometric Aspects of Functional Analysis","day":"21","page":"1-27","date_created":"2018-12-11T11:44:29Z","doi":"10.1007/978-3-030-36020-7_1","date_published":"2020-06-21T00:00:00Z","oa":1,"publisher":"Springer Nature","quality_controlled":"1","citation":{"ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in Geometric Aspects of Functional Analysis, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. Geometric Aspects of Functional Analysis. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:10.1007/978-3-030-36020-7_1","apa":"Akopyan, A., & Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag & E. Milman (Eds.), Geometric Aspects of Functional Analysis (Vol. 2256, pp. 1–27). Springer Nature. https://doi.org/10.1007/978-3-030-36020-7_1","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:10.1007/978-3-030-36020-7_1.","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.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In Geometric Aspects of Functional Analysis, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-36020-7_1."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"article_processing_charge":"No","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"editor":[{"first_name":"Bo'az","last_name":"Klartag","full_name":"Klartag, Bo'az"},{"first_name":"Emanuel","full_name":"Milman, Emanuel","last_name":"Milman"}],"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication_status":"published","publication_identifier":{"eisbn":["9783030360207"],"eissn":["16179692"],"isbn":["9783030360191"],"issn":["00758434"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":2256,"abstract":[{"lang":"eng","text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the waist of radially symmetric Gaussian measures. In particular, it turns our possible to extend Gromov’s original result to the case of not necessarily radially symmetric Gaussian measure. We also provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe use a simpler form of Gromov’s pancake argument to produce some estimates of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.07350"}],"scopus_import":"1","intvolume":" 2256","month":"06","date_updated":"2023-08-17T13:48:31Z","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"series_title":"LNM","_id":"74","type":"book_chapter","status":"public"},{"month":"02","intvolume":" 64","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.08735"}],"oa_version":"Preprint","abstract":[{"text":"Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$.","lang":"eng"}],"issue":"4","volume":64,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0040585X"],"eissn":["10957219"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"7554","department":[{"_id":"HeEd"}],"date_updated":"2023-08-18T06:45:48Z","publisher":"SIAM","quality_controlled":"1","oa":1,"doi":"10.1137/S0040585X97T989726","date_published":"2020-02-13T00:00:00Z","date_created":"2020-03-01T23:00:39Z","page":"595-614","day":"13","publication":"Theory of Probability and its Applications","isi":1,"year":"2020","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"title":"Weighted Poisson–Delaunay mosaics","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000551393100007"],"arxiv":["1705.08735"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications, vol. 64, no. 4, SIAM, 2020, pp. 595–614, doi:10.1137/S0040585X97T989726.","short":"H. Edelsbrunner, A. Nikitenko, Theory of Probability and Its Applications 64 (2020) 595–614.","ieee":"H. Edelsbrunner and A. Nikitenko, “Weighted Poisson–Delaunay mosaics,” Theory of Probability and its Applications, vol. 64, no. 4. SIAM, pp. 595–614, 2020.","apa":"Edelsbrunner, H., & Nikitenko, A. (2020). Weighted Poisson–Delaunay mosaics. Theory of Probability and Its Applications. SIAM. https://doi.org/10.1137/S0040585X97T989726","ama":"Edelsbrunner H, Nikitenko A. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 2020;64(4):595-614. doi:10.1137/S0040585X97T989726","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Weighted Poisson–Delaunay Mosaics.” Theory of Probability and Its Applications. SIAM, 2020. https://doi.org/10.1137/S0040585X97T989726.","ista":"Edelsbrunner H, Nikitenko A. 2020. Weighted Poisson–Delaunay mosaics. Theory of Probability and its Applications. 64(4), 595–614."}},{"scopus_import":"1","month":"03","intvolume":" 64","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."}],"oa_version":"Published Version","volume":64,"ec_funded":1,"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"publication_status":"published","file":[{"file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","date_created":"2020-11-20T13:22:21Z","creator":"dernst","file_size":701673,"date_updated":"2020-11-20T13:22:21Z","success":1,"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","file_id":"8786","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"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)"},"status":"public","_id":"7666","department":[{"_id":"HeEd"}],"file_date_updated":"2020-11-20T13:22:21Z","date_updated":"2023-08-21T06:13:48Z","ddc":["510"],"publisher":"Springer Nature","quality_controlled":"1","oa":1,"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).","page":"759-775","doi":"10.1007/s00454-020-00188-x","date_published":"2020-03-20T00:00:00Z","date_created":"2020-04-19T22:00:56Z","has_accepted_license":"1","isi":1,"year":"2020","day":"20","publication":"Discrete and Computational Geometry","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","last_name":"Ölsböck"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000520918800001"]},"title":"Tri-partitions and bases of an ordered complex","citation":{"ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x.","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020.","short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x","apa":"Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 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We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.","lang":"eng"}],"department":[{"_id":"HeEd"}],"date_updated":"2023-08-21T08:49:18Z","status":"public","article_type":"original","type":"journal_article","_id":"7962","date_created":"2020-06-14T22:00:51Z","date_published":"2020-06-05T00:00:00Z","doi":"10.1007/s00454-020-00213-z","page":"888-917","publication":"Discrete and Computational Geometry","day":"05","year":"2020","isi":1,"oa":1,"publisher":"Springer Nature","quality_controlled":"1","title":"Almost all string graphs are intersection graphs of plane convex sets","external_id":{"isi":["000538229000001"],"arxiv":["1803.06710"]},"article_processing_charge":"No","author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","full_name":"Pach, János"},{"first_name":"Bruce","full_name":"Reed, Bruce","last_name":"Reed"},{"first_name":"Yelena","last_name":"Yuditsky","full_name":"Yuditsky, Yelena"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Pach, János, Bruce Reed, and Yelena Yuditsky. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00213-z.","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.","mla":"Pach, János, et al. “Almost All String Graphs Are Intersection Graphs of Plane Convex Sets.” Discrete and Computational Geometry, vol. 63, no. 4, Springer Nature, 2020, pp. 888–917, doi:10.1007/s00454-020-00213-z.","short":"J. Pach, B. Reed, Y. Yuditsky, Discrete and Computational Geometry 63 (2020) 888–917.","ieee":"J. Pach, B. Reed, and Y. Yuditsky, “Almost all string graphs are intersection graphs of plane convex sets,” Discrete and Computational Geometry, vol. 63, no. 4. Springer Nature, pp. 888–917, 2020.","ama":"Pach J, Reed B, Yuditsky Y. Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. 2020;63(4):888-917. doi:10.1007/s00454-020-00213-z","apa":"Pach, J., Reed, B., & Yuditsky, Y. (2020). Almost all string graphs are intersection graphs of plane convex sets. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00213-z"},"project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}]},{"oa":1,"publisher":"Springer Nature","date_created":"2020-08-30T22:01:12Z","doi":"10.1007/s00454-020-00237-5","date_published":"2020-10-01T00:00:00Z","page":"571-574","publication":"Discrete and Computational Geometry","day":"01","year":"2020","isi":1,"title":"A farewell to Ricky Pollack","external_id":{"isi":["000561483500001"]},"article_processing_charge":"No","author":[{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 571–74, doi:10.1007/s00454-020-00237-5.","apa":"Pach, J. (2020). A farewell to Ricky Pollack. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00237-5","ama":"Pach J. A farewell to Ricky Pollack. Discrete and Computational Geometry. 2020;64:571-574. doi:10.1007/s00454-020-00237-5","short":"J. Pach, Discrete and Computational Geometry 64 (2020) 571–574.","ieee":"J. Pach, “A farewell to Ricky Pollack,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 571–574, 2020.","chicago":"Pach, János. “A Farewell to Ricky Pollack.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00237-5.","ista":"Pach J. 2020. A farewell to Ricky Pollack. Discrete and Computational Geometry. 64, 571–574."},"intvolume":" 64","month":"10","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-020-00237-5"}],"scopus_import":"1","oa_version":"None","volume":64,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"status":"public","article_type":"letter_note","type":"journal_article","_id":"8323","department":[{"_id":"HeEd"}],"date_updated":"2023-08-22T09:05:04Z"},{"publication_identifier":{"isbn":["9781728157511"]},"isi":1,"year":"2020","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","date_created":"2020-09-28T08:59:27Z","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."}],"oa_version":"None","quality_controlled":"1","publisher":"IEEE","scopus_import":"1","month":"08","date_updated":"2023-08-22T09:33:34Z","citation":{"mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.","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 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.","ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054","apa":"Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054","chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.","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, . 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Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"article_processing_charge":"No","external_id":{"arxiv":["1702.07513"],"isi":["000522852700002"]},"title":"Waist of balls in hyperbolic and spherical spaces","acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","publisher":"Oxford University Press","quality_controlled":"1","oa":1,"isi":1,"year":"2020","day":"01","publication":"International Mathematics Research Notices","page":"669-697","date_published":"2020-02-01T00:00:00Z","doi":"10.1093/imrn/rny037","date_created":"2022-03-18T11:39:30Z","_id":"10867","article_type":"original","type":"journal_article","status":"public","keyword":["General Mathematics"],"date_updated":"2023-08-24T14:19:55Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"month":"02","intvolume":" 2020","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":2020},{"date_updated":"2023-09-07T13:15:30Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"ddc":["514"],"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"file_date_updated":"2020-07-14T12:47:58Z","_id":"7460","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"type":"dissertation","keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"status":"public","publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"7461","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","creator":"koelsboe","date_updated":"2020-07-14T12:47:58Z","file_size":76195184,"date_created":"2020-02-06T14:43:54Z","file_name":"thesis_ist-final_noack.pdf"},{"file_size":122103715,"date_updated":"2020-07-14T12:47:58Z","creator":"koelsboe","file_name":"latex-files.zip","date_created":"2020-02-06T14:52:45Z","description":"latex source files, figures","content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed","checksum":"7a52383c812b0be64d3826546509e5a4","file_id":"7462"}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"6608","status":"public"}]},"abstract":[{"text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.","lang":"eng"}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"02","citation":{"ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7460.","short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:10.15479/AT:ISTA:7460","apa":"Ölsböck, K. (2020). The hole system of triangulated shapes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7460","mla":"Ölsböck, Katharina. The Hole System of Triangulated Shapes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7460."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","author":[{"last_name":"Ölsböck","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87"}],"title":"The hole system of triangulated shapes","year":"2020","has_accepted_license":"1","day":"10","page":"155","date_created":"2020-02-06T14:56:53Z","doi":"10.15479/AT:ISTA:7460","date_published":"2020-02-10T00:00:00Z","oa":1,"publisher":"Institute of Science and Technology Austria"},{"has_accepted_license":"1","year":"2020","day":"09","page":"160","date_published":"2020-06-09T00:00:00Z","doi":"10.15479/AT:ISTA:7944","date_created":"2020-06-08T00:49:46Z","publisher":"Institute of Science and Technology Austria","oa":1,"citation":{"ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","apa":"Masárová, Z. (2020). Reconfiguration problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7944","short":"Z. Masárová, Reconfiguration Problems, Institute of Science and Technology Austria, 2020.","ieee":"Z. Masárová, “Reconfiguration problems,” Institute of Science and Technology Austria, 2020.","mla":"Masárová, Zuzana. Reconfiguration Problems. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7944.","ista":"Masárová Z. 2020. Reconfiguration problems. Institute of Science and Technology Austria.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"}],"article_processing_charge":"No","title":"Reconfiguration problems","publication_identifier":{"isbn":["978-3-99078-005-3"],"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"creator":"zmasarov","date_updated":"2020-07-14T12:48:05Z","file_size":13661779,"date_created":"2020-06-08T00:34:00Z","file_name":"THESIS_Zuzka_Masarova.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"7945","checksum":"df688bc5a82b50baee0b99d25fc7b7f0"},{"file_id":"7946","checksum":"45341a35b8f5529c74010b7af43ac188","content_type":"application/zip","access_level":"closed","relation":"source_file","date_created":"2020-06-08T00:35:30Z","file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","date_updated":"2020-07-14T12:48:05Z","file_size":32184006,"creator":"zmasarov"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"id":"7950","status":"public","relation":"part_of_dissertation"},{"id":"5986","status":"public","relation":"part_of_dissertation"}]},"license":"https://creativecommons.org/licenses/by-sa/4.0/","abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"06","supervisor":[{"last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_updated":"2023-09-07T13:17:37Z","ddc":["516","514"],"file_date_updated":"2020-07-14T12:48:05Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"_id":"7944","type":"dissertation","tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)"},"status":"public","keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"]},{"date_updated":"2023-09-07T13:29:00Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-10-27T14:31:52Z","_id":"8703","conference":{"location":"Virtual, Online; Pisa, Italy","end_date":"2020-09-09","start_date":"2020-09-07","name":"ESA: Annual European Symposium on Algorithms"},"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"type":"conference","status":"public","publication_status":"published","publication_identifier":{"isbn":["9783959771627"],"issn":["18688969"]},"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"8712","checksum":"fe0f7c49a99ed870c671b911e10d5496","creator":"cziletti","file_size":733291,"date_updated":"2020-10-27T14:31:52Z","file_name":"2020_LIPIcs_Osang.pdf","date_created":"2020-10-27T14:31:52Z"}],"ec_funded":1,"volume":173,"related_material":{"record":[{"relation":"dissertation_contains","id":"9056","status":"public"}]},"abstract":[{"text":"Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","alternative_title":["LIPIcs"],"intvolume":" 173","month":"08","citation":{"ista":"Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75.","chicago":"Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75.","ama":"Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75","apa":"Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75","ieee":"G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173.","short":"G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","mla":"Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Rouxel-Labbé","full_name":"Rouxel-Labbé, Mael","first_name":"Mael"},{"first_name":"Monique","full_name":"Teillaud, Monique","last_name":"Teillaud"}],"title":"Generalizing CGAL periodic Delaunay triangulations","article_number":"75","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"year":"2020","has_accepted_license":"1","publication":"28th Annual European Symposium on Algorithms","day":"26","date_created":"2020-10-25T23:01:18Z","date_published":"2020-08-26T00:00:00Z","doi":"10.4230/LIPIcs.ESA.2020.75","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1"},{"title":"Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes","article_processing_charge":"No","external_id":{"isi":["000570978400005"]},"author":[{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Vegter, G., & Wintraecken, M. (2020). Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó. https://doi.org/10.1556/012.2020.57.2.1454","ama":"Vegter G, Wintraecken M. Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes. Studia Scientiarum Mathematicarum Hungarica. 2020;57(2):193-199. doi:10.1556/012.2020.57.2.1454","ieee":"G. Vegter and M. Wintraecken, “Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2. Akadémiai Kiadó, pp. 193–199, 2020.","short":"G. Vegter, M. Wintraecken, Studia Scientiarum Mathematicarum Hungarica 57 (2020) 193–199.","mla":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 2, Akadémiai Kiadó, 2020, pp. 193–99, doi:10.1556/012.2020.57.2.1454.","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.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “Refutation of a Claim Made by Fejes Tóth on the Accuracy of Surface Meshes.” Studia Scientiarum Mathematicarum Hungarica. Akadémiai Kiadó, 2020. https://doi.org/10.1556/012.2020.57.2.1454."},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"date_created":"2020-07-24T07:09:18Z","doi":"10.1556/012.2020.57.2.1454","date_published":"2020-07-24T00:00:00Z","page":"193-199","publication":"Studia Scientiarum Mathematicarum Hungarica","day":"24","year":"2020","has_accepted_license":"1","isi":1,"oa":1,"publisher":"Akadémiai Kiadó","quality_controlled":"1","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.","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-24T07:09:06Z","ddc":["510"],"date_updated":"2023-10-10T13:05:27Z","status":"public","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)"},"type":"journal_article","article_type":"original","_id":"8163","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","issue":"2","volume":57,"language":[{"iso":"eng"}],"file":[{"date_created":"2020-07-24T07:09:06Z","file_name":"57-2-05_4214-1454Vegter-Wintraecken_OpenAccess_CC-BY-NC.pdf","creator":"mwintrae","date_updated":"2020-07-24T07:09:06Z","file_size":1476072,"file_id":"8164","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1588-2896"],"issn":["0081-6906"]},"intvolume":" 57","month":"07","scopus_import":"1","oa_version":"Published Version","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."}]},{"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).","quality_controlled":"1","publisher":"De Gruyter","oa":1,"has_accepted_license":"1","year":"2020","day":"20","publication":"Computational and Mathematical Biophysics","page":"51-67","date_published":"2020-06-20T00:00:00Z","doi":"10.1515/cmb-2020-0100","date_created":"2021-02-17T15:13:01Z","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0100.","ista":"Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:10.1515/cmb-2020-0100.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 51–67, 2020.","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 51–67.","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0100","ama":"Akopyan A, Edelsbrunner H. The weighted mean curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):51-67. doi:10.1515/cmb-2020-0100"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"The weighted mean curvature derivative of a space-filling diagram","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"}],"oa_version":"Published Version","month":"06","intvolume":" 8","publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9171","checksum":"cea41de9937d07a3b927d71ee8b4e432","success":1,"creator":"dernst","date_updated":"2021-02-19T13:56:24Z","file_size":562359,"date_created":"2021-02-19T13:56:24Z","file_name":"2020_CompMathBiophysics_Akopyan2.pdf"}],"language":[{"iso":"eng"}],"volume":8,"issue":"1","ec_funded":1,"_id":"9157","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-10-17T12:34:51Z","ddc":["510"],"file_date_updated":"2021-02-19T13:56:24Z","department":[{"_id":"HeEd"}]},{"citation":{"ista":"Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.","chicago":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.","ama":"Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101","apa":"Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101","short":"A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88.","ieee":"A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.","mla":"Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"external_id":{"arxiv":["1908.06777"]},"article_processing_charge":"No","title":"The weighted Gaussian curvature derivative of a space-filling diagram","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"has_accepted_license":"1","year":"2020","day":"21","publication":"Computational and Mathematical Biophysics","page":"74-88","date_published":"2020-07-21T00:00:00Z","doi":"10.1515/cmb-2020-0101","date_created":"2021-02-17T15:12:44Z","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).","quality_controlled":"1","publisher":"De Gruyter","oa":1,"date_updated":"2023-10-17T12:35:10Z","ddc":["510"],"file_date_updated":"2021-02-19T13:33:19Z","department":[{"_id":"HeEd"}],"_id":"9156","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"issn":["2544-7297"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9170","checksum":"ca43a7440834eab6bbea29c59b56ef3a","file_size":707452,"date_updated":"2021-02-19T13:33:19Z","creator":"dernst","file_name":"2020_CompMathBiophysics_Akopyan.pdf","date_created":"2021-02-19T13:33:19Z"}],"language":[{"iso":"eng"}],"issue":"1","volume":8,"ec_funded":1,"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","month":"07","intvolume":" 8"},{"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"15065","checksum":"eed1168b6e66cd55272c19bb7fca8a1c","success":1,"creator":"dernst","date_updated":"2024-03-04T10:52:42Z","file_size":851190,"date_created":"2024-03-04T10:52:42Z","file_name":"2020_JourApplCompTopology_Bauer.pdf"}],"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"issue":"4","volume":4,"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"intvolume":" 4","month":"12","scopus_import":"1","ddc":["500"],"date_updated":"2024-03-04T10:54:04Z","department":[{"_id":"HeEd"}],"file_date_updated":"2024-03-04T10:52:42Z","_id":"15064","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","publication":"Journal of Applied and Computational Topology","day":"01","year":"2020","has_accepted_license":"1","date_created":"2024-03-04T10:47:49Z","doi":"10.1007/s41468-020-00058-8","date_published":"2020-12-01T00:00:00Z","page":"455-480","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.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8.","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.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8"},"title":"Čech-Delaunay gradient flow and homology inference for self-maps","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"U.","last_name":"Bauer","full_name":"Bauer, 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","last_name":"Jablonski","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz"},{"full_name":"Mrozek, M.","last_name":"Mrozek","first_name":"M."}]},{"citation":{"chicago":"Dyer, Ramsay, Gert Vegter, and Mathijs Wintraecken. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry . Carleton University, 2019. https://doi.org/10.20382/jocg.v10i1a9.","ista":"Dyer R, Vegter G, Wintraecken M. 2019. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 10(1), 223–256.","mla":"Dyer, Ramsay, et al. “Simplices Modelled on Spaces of Constant Curvature.” Journal of Computational Geometry , vol. 10, no. 1, Carleton University, 2019, pp. 223–256, doi:10.20382/jocg.v10i1a9.","ieee":"R. Dyer, G. Vegter, and M. Wintraecken, “Simplices modelled on spaces of constant curvature,” Journal of Computational Geometry , vol. 10, no. 1. Carleton University, pp. 223–256, 2019.","short":"R. Dyer, G. Vegter, M. Wintraecken, Journal of Computational Geometry 10 (2019) 223–256.","apa":"Dyer, R., Vegter, G., & Wintraecken, M. (2019). Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . Carleton University. https://doi.org/10.20382/jocg.v10i1a9","ama":"Dyer R, Vegter G, Wintraecken M. Simplices modelled on spaces of constant curvature. Journal of Computational Geometry . 2019;10(1):223–256. doi:10.20382/jocg.v10i1a9"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Dyer, Ramsay","last_name":"Dyer","first_name":"Ramsay"},{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"title":"Simplices modelled on spaces of constant curvature","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"year":"2019","has_accepted_license":"1","publication":"Journal of Computational Geometry ","day":"01","page":"223–256","date_created":"2019-06-03T09:35:33Z","doi":"10.20382/jocg.v10i1a9","date_published":"2019-07-01T00:00:00Z","oa":1,"publisher":"Carleton University","quality_controlled":"1","date_updated":"2021-01-12T08:07:50Z","ddc":["510"],"file_date_updated":"2020-07-14T12:47:32Z","department":[{"_id":"HeEd"}],"_id":"6515","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["1920-180X"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2019-06-03T09:30:01Z","file_name":"mainJournalFinal.pdf","date_updated":"2020-07-14T12:47:32Z","file_size":2170882,"creator":"mwintrae","file_id":"6516","checksum":"57b4df2f16a74eb499734ec8ee240178","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"ec_funded":1,"volume":10,"issue":"1","abstract":[{"text":"We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"intvolume":" 10","month":"07"},{"ddc":["004"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:08:16Z","citation":{"ieee":"G. Vegter and M. Wintraecken, “The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds,” in The 31st Canadian Conference in Computational Geometry, Edmonton, Canada, 2019, pp. 275–279.","short":"G. Vegter, M. Wintraecken, in:, The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–279.","ama":"Vegter G, Wintraecken M. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In: The 31st Canadian Conference in Computational Geometry. ; 2019:275-279.","apa":"Vegter, G., & Wintraecken, M. (2019). The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. In The 31st Canadian Conference in Computational Geometry (pp. 275–279). Edmonton, Canada.","mla":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” The 31st Canadian Conference in Computational Geometry, 2019, pp. 275–79.","ista":"Vegter G, Wintraecken M. 2019. The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds. The 31st Canadian Conference in Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 275–279.","chicago":"Vegter, Gert, and Mathijs Wintraecken. “The Extrinsic Nature of the Hausdorff Distance of Optimal Triangulations of Manifolds.” In The 31st Canadian Conference in Computational Geometry, 275–79, 2019."},"file_date_updated":"2020-07-14T12:47:34Z","title":"The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds","department":[{"_id":"HeEd"}],"author":[{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"_id":"6628","status":"public","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"type":"conference","conference":{"end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08","name":"CCCG: Canadian Conference in Computational Geometry"},"day":"01","file":[{"file_id":"6629","checksum":"ceabd152cfa55170d57763f9c6c60a53","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"IntrinsicExtrinsicCCCG2019.pdf","date_created":"2019-07-12T08:32:46Z","creator":"mwintrae","file_size":321176,"date_updated":"2020-07-14T12:47:34Z"}],"language":[{"iso":"eng"}],"publication":"The 31st Canadian Conference in Computational Geometry","has_accepted_license":"1","publication_status":"published","year":"2019","date_published":"2019-08-01T00:00:00Z","date_created":"2019-07-12T08:34:57Z","ec_funded":1,"page":"275-279","oa_version":"Submitted Version","abstract":[{"text":"Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space.","lang":"eng"}],"month":"08","scopus_import":1,"quality_controlled":"1","oa":1},{"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"has_accepted_license":"1","year":"2019","day":"01","publication":"35th International Symposium on Computational Geometry","page":"31:1-31:14","doi":"10.4230/LIPICS.SOCG.2019.31","date_published":"2019-06-01T00:00:00Z","date_created":"2019-07-17T10:36:09Z","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"citation":{"ista":"Edelsbrunner H, Virk Z, Wagner H. 2019. Topological data analysis in information space. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 31:1-31:14.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” In 35th International Symposium on Computational Geometry, 129:31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.31.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2019). Topological data analysis in information space. In 35th International Symposium on Computational Geometry (Vol. 129, p. 31:1-31:14). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.31","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:31:1-31:14. doi:10.4230/LIPICS.SOCG.2019.31","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 31:1-31:14.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 31:1-31:14, doi:10.4230/LIPICS.SOCG.2019.31."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"external_id":{"arxiv":["1903.08510"]},"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\r\nneeded for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context."}],"oa_version":"Published Version","scopus_import":1,"alternative_title":["LIPIcs"],"month":"06","intvolume":" 129","publication_identifier":{"isbn":["9783959771047"]},"publication_status":"published","file":[{"file_name":"2019_LIPICS_Edelsbrunner.pdf","date_created":"2019-07-24T06:40:01Z","creator":"dernst","file_size":1355179,"date_updated":"2020-07-14T12:47:35Z","checksum":"8ec8720730d4c789bf7b06540f1c29f4","file_id":"6666","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":129,"_id":"6648","type":"conference","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)"},"conference":{"name":"SoCG 2019: Symposium on Computational Geometry","end_date":"2019-06-21","location":"Portland, OR, United States","start_date":"2019-06-18"},"status":"public","date_updated":"2021-01-12T08:08:23Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:35Z"},{"date_created":"2019-11-04T16:46:11Z","related_material":{"record":[{"id":"8317","status":"public","relation":"extended_version"}]},"date_published":"2019-08-01T00:00:00Z","page":"164-170","language":[{"iso":"eng"}],"publication":"Proceedings of the 31st Canadian Conference on Computational Geometry","day":"01","year":"2019","publication_status":"published","month":"08","oa":1,"main_file_link":[{"open_access":"1","url":"https://cccg.ca/proceedings/2019/proceedings.pdf"}],"quality_controlled":"1","publisher":"Canadian Conference on Computational Geometry","scopus_import":"1","acknowledgement":"This research was performed in part at the 33rd BellairsWinter Workshop on Computational Geometry. Wethank all other participants for a fruitful atmosphere.","oa_version":"Published Version","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with hole(s) to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability. ","lang":"eng"}],"title":"Folding polyominoes with holes into a cube","department":[{"_id":"HeEd"}],"article_processing_charge":"No","external_id":{"arxiv":["1910.09917"]},"author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"last_name":"Akitaya","full_name":"Akitaya, Hugo A","first_name":"Hugo A"},{"first_name":"Kenneth C","last_name":"Cheung","full_name":"Cheung, Kenneth C"},{"last_name":"Demaine","full_name":"Demaine, Erik D","first_name":"Erik D"},{"full_name":"Demaine, Martin L","last_name":"Demaine","first_name":"Martin L"},{"first_name":"Sandor P","last_name":"Fekete","full_name":"Fekete, Sandor P"},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"full_name":"Kostitsyna, Irina","last_name":"Kostitsyna","first_name":"Irina"},{"first_name":"Maarten","full_name":"Löffler, Maarten","last_name":"Löffler"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mundilova","full_name":"Mundilova, Klara","first_name":"Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","date_updated":"2023-08-04T10:57:42Z","citation":{"mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–70.","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” in Proceedings of the 31st Canadian Conference on Computational Geometry, Edmonton, Canada, 2019, pp. 164–170.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, in:, Proceedings of the 31st Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2019, pp. 164–170.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. In: Proceedings of the 31st Canadian Conference on Computational Geometry. Canadian Conference on Computational Geometry; 2019:164-170.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2019). Folding polyominoes with holes into a cube. In Proceedings of the 31st Canadian Conference on Computational Geometry (pp. 164–170). Edmonton, Canada: Canadian Conference on Computational Geometry.","chicago":"Aichholzer, Oswin, Hugo A Akitaya, Kenneth C Cheung, Erik D Demaine, Martin L Demaine, Sandor P Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” In Proceedings of the 31st Canadian Conference on Computational Geometry, 164–70. Canadian Conference on Computational Geometry, 2019.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2019. Folding polyominoes with holes into a cube. Proceedings of the 31st Canadian Conference on Computational Geometry. CCCG: Canadian Conference in Computational Geometry, 164–170."},"status":"public","conference":{"name":"CCCG: Canadian Conference in Computational Geometry","end_date":"2019-08-10","location":"Edmonton, Canada","start_date":"2019-08-08"},"type":"conference","_id":"6989"},{"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"first_name":"André","full_name":"Lieutier, André","last_name":"Lieutier"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"title":"The reach, metric distortion, geodesic convexity and the variation of tangent spaces","citation":{"chicago":"Boissonnat, Jean-Daniel, André Lieutier, and Mathijs Wintraecken. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology. Springer Nature, 2019. https://doi.org/10.1007/s41468-019-00029-8.","ista":"Boissonnat J-D, Lieutier A, Wintraecken M. 2019. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 3(1–2), 29–58.","mla":"Boissonnat, Jean-Daniel, et al. “The Reach, Metric Distortion, Geodesic Convexity and the Variation of Tangent Spaces.” Journal of Applied and Computational Topology, vol. 3, no. 1–2, Springer Nature, 2019, pp. 29–58, doi:10.1007/s41468-019-00029-8.","ieee":"J.-D. Boissonnat, A. Lieutier, and M. Wintraecken, “The reach, metric distortion, geodesic convexity and the variation of tangent spaces,” Journal of Applied and Computational Topology, vol. 3, no. 1–2. Springer Nature, pp. 29–58, 2019.","short":"J.-D. Boissonnat, A. Lieutier, M. Wintraecken, Journal of Applied and Computational Topology 3 (2019) 29–58.","ama":"Boissonnat J-D, Lieutier A, Wintraecken M. The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. 2019;3(1-2):29–58. doi:10.1007/s41468-019-00029-8","apa":"Boissonnat, J.-D., Lieutier, A., & Wintraecken, M. (2019). The reach, metric distortion, geodesic convexity and the variation of tangent spaces. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-019-00029-8"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"29–58","date_created":"2019-07-24T08:37:29Z","date_published":"2019-06-01T00:00:00Z","doi":"10.1007/s41468-019-00029-8","year":"2019","has_accepted_license":"1","publication":"Journal of Applied and Computational Topology","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","file_date_updated":"2020-07-14T12:47:36Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-22T12:37:47Z","ddc":["000"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"6671","ec_funded":1,"issue":"1-2","volume":3,"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"6741","checksum":"a5b244db9f751221409cf09c97ee0935","creator":"dernst","file_size":2215157,"date_updated":"2020-07-14T12:47:36Z","file_name":"2019_JournAppliedComputTopol_Boissonnat.pdf","date_created":"2019-07-31T08:09:56Z"}],"intvolume":" 3","month":"06","abstract":[{"text":"In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.","lang":"eng"}],"oa_version":"Published Version"},{"_id":"6050","status":"public","type":"journal_article","date_updated":"2023-08-24T14:48:59Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. "}],"month":"01","intvolume":" 147","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1709.02562","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":147,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240.","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102."},"title":"Two circles and only a straightedge","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"last_name":"Fedorov","full_name":"Fedorov, Roman","first_name":"Roman"}],"article_processing_charge":"No","external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"quality_controlled":"1","publisher":"AMS","oa":1,"day":"01","publication":"Proceedings of the American Mathematical Society","isi":1,"year":"2019","doi":"10.1090/proc/14240","date_published":"2019-01-01T00:00:00Z","date_created":"2019-02-24T22:59:19Z","page":"91-102"},{"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"external_id":{"isi":["000472541600004"],"arxiv":["1612.06926"]},"article_processing_charge":"No","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Alfredo","last_name":"Hubard","full_name":"Hubard, Alfredo"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"}],"title":"Lower and upper bounds for the waists of different spaces","citation":{"ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008","apa":"Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Akademicka Platforma Czasopism","page":"457-490","date_created":"2019-07-14T21:59:19Z","doi":"10.12775/TMNA.2019.008","date_published":"2019-06-01T00:00:00Z","year":"2019","isi":1,"publication":"Topological Methods in Nonlinear Analysis","day":"01","type":"journal_article","status":"public","_id":"6634","department":[{"_id":"HeEd"}],"date_updated":"2023-08-29T06:32:48Z","main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"scopus_import":"1","intvolume":" 53","month":"06","abstract":[{"lang":"eng","text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure."}],"oa_version":"Preprint","ec_funded":1,"volume":53,"issue":"2","publication_status":"published","language":[{"iso":"eng"}]},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"6756","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:39Z","date_updated":"2023-08-29T07:01:48Z","ddc":["520","530"],"scopus_import":"1","intvolume":" 627","month":"07","abstract":[{"text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models.","lang":"eng"}],"oa_version":"Published Version","volume":627,"publication_status":"published","publication_identifier":{"eissn":["14320746"],"issn":["00046361"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"6766","checksum":"83b9209ed9eefbdcefd89019c5a97805","date_updated":"2020-07-14T12:47:39Z","file_size":14420451,"creator":"dernst","date_created":"2019-08-05T08:08:59Z","file_name":"2019_AstronomyAstrophysics_Pranav.pdf"}],"project":[{"grant_number":"M62909-18-1-2038","name":"Toward Computational Information Topology","_id":"265683E4-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"article_number":"A163","external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"article_processing_charge":"No","author":[{"first_name":"Pratyush","full_name":"Pranav, Pratyush","last_name":"Pranav"},{"first_name":"Robert J.","full_name":"Adler, Robert J.","last_name":"Adler"},{"first_name":"Thomas","full_name":"Buchert, Thomas","last_name":"Buchert"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Jones, Bernard J.T.","last_name":"Jones","first_name":"Bernard J.T."},{"first_name":"Armin","last_name":"Schwartzman","full_name":"Schwartzman, Armin"},{"full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"},{"last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien","first_name":"Rien"}],"title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","citation":{"mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916","apa":"Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).","chicago":"Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.","ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"EDP Sciences","date_created":"2019-08-04T21:59:18Z","doi":"10.1051/0004-6361/201834916","date_published":"2019-07-17T00:00:00Z","year":"2019","isi":1,"has_accepted_license":"1","publication":"Astronomy and Astrophysics","day":"17"},{"quality_controlled":"1","publisher":"London Mathematical Society","oa":1,"isi":1,"year":"2019","day":"01","publication":"Bulletin of the London Mathematical Society","page":"765-775","date_published":"2019-10-01T00:00:00Z","doi":"10.1112/blms.12276","date_created":"2019-08-11T21:59:23Z","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276.","ista":"Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276","apa":"Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Izmestiev","full_name":"Izmestiev, Ivan","first_name":"Ivan"}],"external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"article_processing_charge":"No","title":"The Regge symmetry, confocal conics, and the Schläfli formula","abstract":[{"text":"The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"month":"10","intvolume":" 51","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":51,"issue":"5","ec_funded":1,"_id":"6793","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-08-29T07:08:34Z","department":[{"_id":"HeEd"}]},{"volume":538,"publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1805.04676","open_access":"1"}],"month":"11","intvolume":" 538","abstract":[{"lang":"eng","text":"In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group ."}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-08-29T07:11:47Z","article_type":"original","type":"journal_article","status":"public","_id":"6828","page":"261-289","doi":"10.1016/j.jalgebra.2019.07.027","date_published":"2019-11-15T00:00:00Z","date_created":"2019-08-22T07:54:13Z","isi":1,"year":"2019","day":"15","publication":"Journal of Algebra","publisher":"Elsevier","quality_controlled":"1","oa":1,"author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam","last_name":"Brown"}],"external_id":{"arxiv":["1805.04676"],"isi":["000487176300011"]},"article_processing_charge":"No","title":"Arakawa-Suzuki functors for Whittaker modules","citation":{"chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"department":[{"_id":"HeEd"}],"title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","external_id":{"isi":["000521238102050"]},"article_processing_charge":"No","author":[{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116"},{"full_name":"Cook, James","last_name":"Cook","first_name":"James"},{"full_name":"Fabrikant, Alex","last_name":"Fabrikant","first_name":"Alex"},{"first_name":"Marco","last_name":"Gruteser","full_name":"Gruteser, Marco"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-06T14:50:28Z","citation":{"ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.","chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514."},"status":"public","conference":{"name":"ITSC: Intelligent Transportation Systems Conference","start_date":"2019-10-27","location":"Auckland, New Zealand","end_date":"2019-10-30"},"type":"conference","article_number":"8917514","_id":"7216","date_created":"2019-12-29T23:00:47Z","doi":"10.1109/ITSC.2019.8917514","date_published":"2019-11-28T00:00:00Z","publication":"2019 IEEE Intelligent Transportation Systems Conference","language":[{"iso":"eng"}],"day":"28","year":"2019","publication_status":"published","publication_identifier":{"isbn":["9781538670248"]},"isi":1,"month":"11","quality_controlled":"1","publisher":"IEEE","scopus_import":"1","oa_version":"None","abstract":[{"text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next.","lang":"eng"}]},{"oa":1,"publisher":"Springer","quality_controlled":"1","publication":"Discrete and Computational Geometry","day":"01","year":"2019","has_accepted_license":"1","isi":1,"date_created":"2018-12-16T22:59:20Z","date_published":"2019-12-01T00:00:00Z","doi":"10.1007/s00454-018-0049-2","page":"865–878","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2."},"title":"Poisson–Delaunay Mosaics of Order k","external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"}],"oa_version":"Published Version","abstract":[{"text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.","lang":"eng"}],"intvolume":" 62","month":"12","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:47:10Z","file_size":599339,"creator":"dernst","date_created":"2019-02-06T10:10:46Z","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","file_id":"5932"}],"publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"ec_funded":1,"volume":62,"issue":"4","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"_id":"5678","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["516"],"date_updated":"2023-09-07T12:07:12Z","file_date_updated":"2020-07-14T12:47:10Z","department":[{"_id":"HeEd"}]},{"date_updated":"2023-09-07T13:15:29Z","ddc":["000"],"file_date_updated":"2020-07-14T12:47:34Z","department":[{"_id":"HeEd"}],"_id":"6608","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"file":[{"file_size":2665013,"date_updated":"2020-07-14T12:47:34Z","creator":"kschuh","file_name":"Elsevier_2019_Edelsbrunner.pdf","date_created":"2019-07-08T15:24:26Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"6624","checksum":"7c99be505dc7533257d42eb1830cef04"}],"ec_funded":1,"volume":73,"related_material":{"record":[{"relation":"dissertation_contains","id":"7460","status":"public"}]},"abstract":[{"text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 73","month":"08","citation":{"ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003","apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000485207800001"]},"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","last_name":"Ölsböck"}],"title":"Holes and dependences in an ordered complex","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"year":"2019","has_accepted_license":"1","isi":1,"publication":"Computer Aided Geometric Design","day":"01","page":"1-15","date_created":"2019-07-07T21:59:20Z","date_published":"2019-08-01T00:00:00Z","doi":"10.1016/j.cagd.2019.06.003","oa":1,"publisher":"Elsevier","quality_controlled":"1"},{"date_created":"2020-06-08T12:25:25Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7944"},{"id":"12833","status":"public","relation":"later_version"}]},"date_published":"2019-03-16T00:00:00Z","publication_status":"submitted","year":"2019","language":[{"iso":"eng"}],"publication":"arXiv","day":"16","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.06981"}],"month":"03","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"oa_version":"Preprint","external_id":{"arxiv":["1903.06981"]},"article_processing_charge":"No","author":[{"first_name":"Ahmad","last_name":"Biniaz","full_name":"Biniaz, Ahmad"},{"first_name":"Kshitij","full_name":"Jain, Kshitij","last_name":"Jain"},{"last_name":"Lubiw","full_name":"Lubiw, Anna","first_name":"Anna"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová"},{"last_name":"Miltzow","full_name":"Miltzow, Tillmann","first_name":"Tillmann"},{"last_name":"Mondal","full_name":"Mondal, Debajyoti","first_name":"Debajyoti"},{"full_name":"Naredla, Anurag Murty","last_name":"Naredla","first_name":"Anurag Murty"},{"first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","last_name":"Tkadlec"},{"last_name":"Turcotte","full_name":"Turcotte, Alexi","first_name":"Alexi"}],"title":"Token swapping on trees","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"date_updated":"2024-01-04T12:42:08Z","citation":{"short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.).","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"preprint","status":"public","_id":"7950","article_number":"1903.06981"},{"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","oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","day":"11","year":"2018","has_accepted_license":"1","date_created":"2018-12-11T11:45:05Z","date_published":"2018-06-11T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2018.35","page":"35:1 - 35:13","project":[{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35."},"title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert","last_name":"Wagner"}],"publist_id":"7733","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex."}],"intvolume":" 99","month":"06","alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"scopus_import":1,"language":[{"iso":"eng"}],"file":[{"file_name":"2018_LIPIcs_Edelsbrunner.pdf","date_created":"2018-12-17T16:31:31Z","file_size":489080,"date_updated":"2020-07-14T12:45:20Z","creator":"dernst","file_id":"5724","checksum":"7509403803b3ac1aee94bbc2ad293d21","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","volume":99,"_id":"188","status":"public","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)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2018-06-11","end_date":"2018-06-14","location":"Budapest, Hungary"},"type":"conference","ddc":["000"],"date_updated":"2021-01-12T06:53:48Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:20Z"}]