[{"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","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2202.12175","open_access":"1"}],"alternative_title":["LNCS"],"scopus_import":"1","intvolume":" 14466","month":"01","publication_status":"published","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031492747"],"issn":["0302-9743"]},"language":[{"iso":"eng"}],"volume":14466,"_id":"14888","conference":{"end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20","name":"GD: Graph Drawing and Network Visualization"},"type":"conference","status":"public","date_updated":"2024-01-29T09:45:06Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"acknowledgement":"This work was initiated at the 16th European Research Week on Geometric Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF): W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]. A preliminary version of this work has been presented at the 38th European Workshop on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper, which includes appendices but is otherwise identical, is available as a technical report [10].","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2024","publication":"31st International Symposium on Graph Drawing and Network Visualization","day":"06","page":"18-33","date_created":"2024-01-28T23:01:43Z","doi":"10.1007/978-3-031-49275-4_2","date_published":"2024-01-06T00:00:00Z","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","article_processing_charge":"No","external_id":{"arxiv":["2202.12175"]},"author":[{"first_name":"Phoebe","full_name":"De Nooijer, Phoebe","last_name":"De Nooijer"},{"first_name":"Soeren","full_name":"Terziadis, Soeren","last_name":"Terziadis"},{"first_name":"Alexandra","last_name":"Weinberger","full_name":"Weinberger, Alexandra"},{"last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana"},{"first_name":"Tamara","full_name":"Mchedlidze, Tamara","last_name":"Mchedlidze"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"first_name":"Günter","last_name":"Rote","full_name":"Rote, Günter"}],"title":"Removing popular faces in curve arrangements"},{"date_updated":"2024-02-20T09:13:07Z","department":[{"_id":"HeEd"}],"_id":"15012","type":"conference","conference":{"end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy","start_date":"2023-09-20","name":"GD: Graph Drawing and Network Visualization"},"status":"public","publication_identifier":{"eissn":["16113349"],"isbn":["9783031492716"],"issn":["03029743"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":14465,"ec_funded":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","scopus_import":"1","alternative_title":["LNCS"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.13201"}],"month":"01","intvolume":" 14465","citation":{"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.","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.","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","full_name":"Pach, János","last_name":"Pach"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","full_name":"Saghafian, Morteza"},{"last_name":"Schnider","full_name":"Schnider, Patrick","first_name":"Patrick"}],"article_processing_charge":"No","external_id":{"arxiv":["2306.13201"]},"title":"Decomposition of geometric graphs into star-forests","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"year":"2024","day":"01","publication":"31st International Symposium on Graph Drawing and Network Visualization","page":"339-346","doi":"10.1007/978-3-031-49272-3_23","date_published":"2024-01-01T00:00:00Z","date_created":"2024-02-18T23:01:03Z","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.","quality_controlled":"1","publisher":"Springer Nature","oa":1},{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria.","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.","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","ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 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.","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."},"title":"Persistence and Morse theory for discrete geometric structures","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"}],"article_processing_charge":"No","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","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"day":"08","has_accepted_license":"1","year":"2024","doi":"10.15479/at:ista:15094","date_published":"2024-03-08T00:00:00Z","date_created":"2024-03-08T15:28:10Z","page":"108","publisher":"Institute of Science and Technology Austria","oa":1,"ddc":["514","500","516"],"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"date_updated":"2024-03-20T09:36:57Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"file_date_updated":"2024-03-14T14:14:35Z","_id":"15094","status":"public","type":"dissertation","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)"},"file":[{"file_name":"Thesis Sebastiano.pdf","date_created":"2024-03-14T08:55:07Z","file_size":4106872,"date_updated":"2024-03-14T08:55:07Z","creator":"scultrer","success":1,"file_id":"15112","checksum":"1e468bfa42a7dcf04d89f4dadc621c87","content_type":"application/pdf","relation":"main_file","access_level":"open_access"},{"file_name":"Thesis (1).zip","date_created":"2024-03-14T08:56:24Z","file_size":4746234,"date_updated":"2024-03-14T14:14:35Z","creator":"scultrer","checksum":"bcbd213490f5a7e68855a092bbce93f1","file_id":"15113","content_type":"application/zip","relation":"source_file","access_level":"closed"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663 - 337X"]},"degree_awarded":"PhD","publication_status":"published","related_material":{"record":[{"relation":"part_of_dissertation","id":"11660","status":"public"},{"status":"public","id":"11658","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"13182"},{"status":"public","id":"15090","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"15091","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"15093"}]},"ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","oa_version":"Published Version","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"}],"month":"03","alternative_title":["ISTA Thesis"]},{"title":"Dynamically maintaining the persistent homology of time series","editor":[{"last_name":"Woodruff","full_name":"Woodruff, David P.","first_name":"David P."}],"author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H"},{"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":{"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","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","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.","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.","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.","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."},"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422","name":"Wittgenstein Award - Monika Henzinger"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775 ","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"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","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.","department":[{"_id":"HeEd"},{"_id":"MoHe"}],"date_updated":"2024-03-20T09:36:56Z","status":"public","type":"conference","conference":{"name":"SODA: Symposium on Discrete Algorigthms","location":"Alexandria, VA, USA","end_date":"2024-01-10","start_date":"2024-01-07"},"_id":"15093","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["9781611977912"]},"publication_status":"published","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/2311.01115","open_access":"1"}],"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."}]},{"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)"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"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.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” arXiv. .","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."},"date_updated":"2024-03-20T09:36:56Z","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"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"external_id":{"arxiv":["2212.03128"]},"article_processing_charge":"No","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"month":"02","main_file_link":[{"url":"https://arxiv.org/abs/2212.03128","open_access":"1"}],"oa":1,"day":"07","publication":"arXiv","language":[{"iso":"eng"}],"year":"2024","publication_status":"submitted","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"date_published":"2024-02-07T00:00:00Z","date_created":"2024-03-08T10:13:59Z"},{"department":[{"_id":"HeEd"}],"date_updated":"2023-05-22T08:15:19Z","status":"public","type":"conference","conference":{"name":"STOC: Symposium on Theory of Computing","start_date":"2023-06-20","location":"Orlando, FL, United States","end_date":"2023-06-23"},"_id":"13048","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9781450399135"]},"publication_status":"published","month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.04014"}],"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"}],"title":"Hausdorff and Gromov-Hausdorff stable subsets of the medial axis","author":[{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"external_id":{"arxiv":["2303.04014"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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."},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"date_published":"2023-06-02T00:00:00Z","doi":"10.1145/3564246.3585113","date_created":"2023-05-22T08:02:02Z","page":"1768-1776","day":"02","publication":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","year":"2023","quality_controlled":"1","publisher":"Association for Computing Machinery","oa":1,"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."},{"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"}],"volume":85,"ec_funded":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","month":"01","intvolume":" 85","date_updated":"2023-06-27T12:53:43Z","ddc":["510"],"file_date_updated":"2023-01-20T10:02:48Z","department":[{"_id":"HeEd"}],"_id":"12086","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","isi":1,"has_accepted_license":"1","year":"2023","day":"01","publication":"Algorithmica","page":"277-295","doi":"10.1007/s00453-022-01027-6","date_published":"2023-01-01T00:00:00Z","date_created":"2022-09-11T22:01:57Z","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.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"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.","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","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","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."},"user_id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Osang","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000846967100001"]},"title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}]},{"day":"01","publication":"Discrete & Computational Geometry","has_accepted_license":"1","isi":1,"year":"2023","date_published":"2023-01-01T00:00:00Z","doi":"10.1007/s00454-022-00431-7","date_created":"2023-01-16T10:04:06Z","page":"156-191","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).","publisher":"Springer Nature","quality_controlled":"1","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","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","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."},"title":"Local criteria for triangulating general manifolds","author":[{"first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat"},{"last_name":"Dyer","full_name":"Dyer, Ramsay","first_name":"Ramsay"},{"last_name":"Ghosh","full_name":"Ghosh, Arijit","first_name":"Arijit"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"article_processing_charge":"No","external_id":{"isi":["000862193600001"]},"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"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"46352e0ee71e460848f88685ca852681","file_id":"12488","success":1,"creator":"dernst","date_updated":"2023-02-02T11:01:10Z","file_size":582850,"date_created":"2023-02-02T11:01:10Z","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","volume":69,"ec_funded":1,"oa_version":"Published Version","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."}],"month":"01","intvolume":" 69","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-01T12:47:32Z","department":[{"_id":"HeEd"}],"file_date_updated":"2023-02-02T11:01:10Z","_id":"12287","status":"public","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"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)"}},{"article_number":"00093","external_id":{"isi":["000971492200145"]},"article_processing_charge":"No","author":[{"full_name":"Forghani, Mohammad","last_name":"Forghani","first_name":"Mohammad"},{"full_name":"Claramunt, Christophe","last_name":"Claramunt","first_name":"Christophe"},{"last_name":"Karimipour","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid"},{"last_name":"Heiler","full_name":"Heiler, Georg","first_name":"Georg"}],"title":"Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic","citation":{"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.","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","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","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Institute of Electrical and Electronics Engineers","quality_controlled":"1","date_created":"2023-02-14T07:56:21Z","date_published":"2023-02-08T00:00:00Z","doi":"10.1109/icdmw58026.2022.00093","year":"2023","isi":1,"has_accepted_license":"1","publication":"2022 IEEE International Conference on Data Mining Workshops","day":"08","conference":{"name":"ICDMW: Conference on Data Mining Workshops","start_date":"2022-11-28","end_date":"2022-12-01","location":"Orlando, FL, United States"},"type":"conference","status":"public","_id":"12548","department":[{"_id":"HeEd"}],"file_date_updated":"2023-02-14T07:58:26Z","date_updated":"2023-08-01T13:15:48Z","ddc":["600"],"month":"02","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"}],"oa_version":"Submitted Version","publication_status":"published","publication_identifier":{"eisbn":["9798350346091"],"eissn":["2375-9259"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"c253bee25e6dfe484f96662daa119cb6","file_id":"12549","success":1,"creator":"fkarimip","date_updated":"2023-02-14T07:58:26Z","file_size":1183339,"date_created":"2023-02-14T07:58:26Z","file_name":"Visual Analysis_Mobility_COVID19 - SocDM2022.pdf"}]},{"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"title":"Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives","author":[{"first_name":"Patrice","full_name":"Koehl, Patrice","last_name":"Koehl"},{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000920370700001"],"pmid":["36638318"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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","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","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.","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.","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.","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."},"quality_controlled":"1","publisher":"American Chemical Society","oa":1,"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).","doi":"10.1021/acs.jcim.2c01346","date_published":"2023-02-13T00:00:00Z","date_created":"2023-02-12T23:00:59Z","page":"973-985","day":"13","publication":"Journal of Chemical Information and Modeling","isi":1,"has_accepted_license":"1","year":"2023","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)"},"_id":"12544","file_date_updated":"2023-08-16T12:21:13Z","department":[{"_id":"HeEd"}],"ddc":["510","540"],"date_updated":"2023-08-16T12:22:07Z","month":"02","intvolume":" 63","scopus_import":"1","pmid":1,"oa_version":"Published Version","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."}],"volume":63,"issue":"3","ec_funded":1,"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"14070","checksum":"7d20562269edff1e31b9d6019d4983b0","success":1,"date_updated":"2023-08-16T12:21:13Z","file_size":8069223,"creator":"dernst","date_created":"2023-08-16T12:21:13Z","file_name":"2023_JCIM_Koehl.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1549-9596"],"eissn":["1549-960X"]},"publication_status":"published"},{"month":"07","intvolume":" 70","scopus_import":"1","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."}],"volume":70,"file":[{"date_updated":"2023-10-04T11:46:24Z","file_size":1026683,"creator":"dernst","date_created":"2023-10-04T11:46:24Z","file_name":"2023_DiscreteGeometry_Kourimska.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"14396","checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","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)"},"_id":"12764","file_date_updated":"2023-10-04T11:46:24Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-10-04T11:46:48Z","quality_controlled":"1","publisher":"Springer Nature","oa":1,"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.","doi":"10.1007/s00454-023-00484-2","date_published":"2023-07-01T00:00:00Z","date_created":"2023-03-26T22:01:09Z","page":"123-153","day":"01","publication":"Discrete and Computational Geometry","isi":1,"has_accepted_license":"1","year":"2023","project":[{"call_identifier":"FWF","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245"}],"title":"Discrete yamabe problem for polyhedral surfaces","author":[{"full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","last_name":"Kourimska","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana"}],"external_id":{"isi":["000948148000001"]},"article_processing_charge":"Yes (via OA deal)","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","short":"H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.","ieee":"H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.","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."}},{"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.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2023","day":"01","publication":"Discrete and Computational Geometry","page":"376-405","doi":"10.1007/s00454-022-00476-8","date_published":"2023-09-01T00:00:00Z","date_created":"2023-03-05T23:01:06Z","citation":{"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.","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.","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","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"René","full_name":"Corbet, René","last_name":"Corbet"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"},{"first_name":"Michael","full_name":"Lesnick, Michael","last_name":"Lesnick"},{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000936496800001"],"arxiv":["2103.07823"]},"title":"Computing the multicover bifiltration","abstract":[{"lang":"eng","text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness."}],"oa_version":"Published Version","scopus_import":"1","month":"09","intvolume":" 70","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"12715","checksum":"71ce7e59f7ee4620acc704fecca620c2","file_size":1359323,"date_updated":"2023-03-07T14:40:14Z","creator":"cchlebak","file_name":"2023_DisCompGeo_Corbet.pdf","date_created":"2023-03-07T14:40:14Z"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"earlier_version","id":"9605","status":"public"}]},"volume":70,"_id":"12709","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":"2023-10-04T12:03:40Z","ddc":["000"],"file_date_updated":"2023-03-07T14:40:14Z","department":[{"_id":"HeEd"}]},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"ec_funded":1,"volume":7,"oa_version":"Submitted Version","abstract":[{"lang":"eng","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."}],"intvolume":" 7","month":"09","main_file_link":[{"url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1","open_access":"1"}],"scopus_import":"1","date_updated":"2023-10-04T12:07:18Z","department":[{"_id":"HeEd"}],"_id":"12763","status":"public","type":"journal_article","article_type":"original","publication":"Journal of Applied and Computational Topology","day":"01","year":"2023","date_created":"2023-03-26T22:01:08Z","date_published":"2023-09-01T00:00:00Z","doi":"10.1007/s41468-023-00116-x","page":"619-641","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.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","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.","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.","ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641."},"title":"The reach of subsets of manifolds","article_processing_charge":"No","author":[{"full_name":"Boissonnat, Jean Daniel","last_name":"Boissonnat","first_name":"Jean Daniel"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}]},{"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","publication":"SIAM Journal on Computing","day":"30","year":"2023","isi":1,"date_created":"2023-05-14T22:01:00Z","date_published":"2023-04-30T00:00:00Z","doi":"10.1137/21M1412918","page":"452-486","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","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.","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","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.","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."},"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","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","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","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. "}],"intvolume":" 52","month":"04","main_file_link":[{"open_access":"1","url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"ec_funded":1,"issue":"2","related_material":{"record":[{"status":"public","id":"9441","relation":"earlier_version"}]},"volume":52,"_id":"12960","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-10-10T07:34:35Z","department":[{"_id":"HeEd"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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","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.","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.","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."},"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"},{"first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin"},{"first_name":"Rita","full_name":"Zrour, Rita","last_name":"Zrour"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"article_number":"109693","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"}],"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","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","date_updated":"2023-10-10T07:37:16Z","department":[{"_id":"HeEd"}],"_id":"13134","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0031-3203"]},"issue":"10","volume":142,"oa_version":"None","abstract":[{"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.","lang":"eng"}],"intvolume":" 142","month":"10","scopus_import":"1"},{"date_updated":"2023-11-20T09:24:48Z","department":[{"_id":"HeEd"}],"_id":"14557","status":"public","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1727-933X"],"issn":["1607-3606"]},"publication_status":"published","volume":46,"issue":"S1","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"}],"month":"11","intvolume":" 46","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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","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","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.","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.","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.","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."},"title":"Epimorphisms and closure operators of categories of semilattices","author":[{"full_name":"Dikranjan, D.","last_name":"Dikranjan","first_name":"D."},{"last_name":"Giordano Bruno","full_name":"Giordano Bruno, A.","first_name":"A."},{"last_name":"Zava","orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò"}],"article_processing_charge":"No","project":[{"_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245"}],"day":"01","publication":"Quaestiones Mathematicae","year":"2023","doi":"10.2989/16073606.2023.2247731","date_published":"2023-11-01T00:00:00Z","date_created":"2023-11-19T23:00:55Z","page":"191-221","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"},{"language":[{"iso":"eng"}],"publication_status":"epub_ahead","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"ec_funded":1,"oa_version":"Published Version","abstract":[{"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)).","lang":"eng"}],"month":"09","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-023-00566-1"}],"scopus_import":"1","date_updated":"2023-12-13T12:25:06Z","department":[{"_id":"HeEd"}],"_id":"14345","status":"public","type":"journal_article","article_type":"original","publication":"Discrete and Computational Geometry","day":"07","year":"2023","isi":1,"date_created":"2023-09-17T22:01:10Z","date_published":"2023-09-07T00:00:00Z","doi":"10.1007/s00454-023-00566-1","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.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","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","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","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)."},"title":"On angles in higher order Brillouin tessellations and related tilings in the plane","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"]},"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Alexey","full_name":"Garber, Alexey","last_name":"Garber"},{"last_name":"Ghafari","full_name":"Ghafari, Mohadese","first_name":"Mohadese"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}]},{"article_type":"original","type":"journal_article","status":"public","_id":"14464","department":[{"_id":"HeEd"}],"date_updated":"2023-12-13T13:04:55Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2205.11637"}],"month":"10","intvolume":" 34","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","issue":"7","volume":34,"publication_identifier":{"eissn":["1793-6373"],"issn":["0129-0541"]},"publication_status":"published","language":[{"iso":"eng"}],"author":[{"first_name":"Áron","last_name":"Ambrus","full_name":"Ambrus, Áron"},{"first_name":"Mónika","full_name":"Csikós, Mónika","last_name":"Csikós"},{"full_name":"Kiss, Gergely","last_name":"Kiss","first_name":"Gergely"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Somlai, Gábor","last_name":"Somlai","first_name":"Gábor"}],"external_id":{"isi":["001080874400001"],"arxiv":["2205.11637"]},"article_processing_charge":"No","title":"Optimal embedded and enclosing isosceles triangles","citation":{"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.","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.","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.","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.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"World Scientific Publishing","quality_controlled":"1","oa":1,"page":"737-760","date_published":"2023-10-05T00:00:00Z","doi":"10.1142/S012905412342008X","date_created":"2023-10-29T23:01:18Z","isi":1,"year":"2023","day":"05","publication":"International Journal of Foundations of Computer Science"},{"article_number":"9","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","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.","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."},"title":"Token swapping on trees","author":[{"first_name":"Ahmad","full_name":"Biniaz, Ahmad","last_name":"Biniaz"},{"full_name":"Jain, Kshitij","last_name":"Jain","first_name":"Kshitij"},{"first_name":"Anna","full_name":"Lubiw, Anna","last_name":"Lubiw"},{"orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"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"},{"full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Turcotte, Alexi","last_name":"Turcotte","first_name":"Alexi"}],"article_processing_charge":"No","external_id":{"arxiv":["1903.06981"]},"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","quality_controlled":"1","publisher":"EPI Sciences","oa":1,"day":"18","publication":"Discrete Mathematics and Theoretical Computer Science","has_accepted_license":"1","year":"2023","doi":"10.46298/DMTCS.8383","date_published":"2023-01-18T00:00:00Z","date_created":"2023-04-16T22:01:08Z","_id":"12833","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)"},"ddc":["000"],"date_updated":"2024-01-04T12:42:09Z","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"file_date_updated":"2023-04-17T08:10:28Z","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"month":"01","intvolume":" 24","scopus_import":"1","file":[{"success":1,"file_id":"12844","checksum":"439102ea4f6e2aeefd7107dfb9ccf532","content_type":"application/pdf","relation":"main_file","access_level":"open_access","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"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1365-8050"],"issn":["1462-7264"]},"publication_status":"published","volume":24,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7950"}]},"issue":"2"},{"date_published":"2023-12-01T00:00:00Z","doi":"10.1109/tpami.2023.3308391","date_created":"2024-01-08T09:59:46Z","page":"14069-14080","day":"01","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","has_accepted_license":"1","year":"2023","quality_controlled":"1","publisher":"IEEE","oa":1,"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.","title":"A survey of vectorization methods in topological data analysis","author":[{"last_name":"Ali","full_name":"Ali, Dashti","first_name":"Dashti"},{"last_name":"Asaad","full_name":"Asaad, Aras","first_name":"Aras"},{"first_name":"Maria-Jose","last_name":"Jimenez","full_name":"Jimenez, Maria-Jose"},{"first_name":"Vidit","last_name":"Nanda","full_name":"Nanda, Vidit"},{"first_name":"Eduardo","last_name":"Paluzo-Hidalgo","full_name":"Paluzo-Hidalgo, Eduardo"},{"full_name":"Soriano Trigueros, Manuel","orcid":"0000-0003-2449-1433","last_name":"Soriano Trigueros","first_name":"Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8"}],"article_processing_charge":"Yes (in subscription journal)","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."},"issue":"12","volume":45,"file":[{"file_size":2370988,"date_updated":"2024-01-08T10:09:14Z","creator":"dernst","file_name":"2023_IEEEToP_Ali.pdf","date_created":"2024-01-08T10:09:14Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"14740","checksum":"465c28ef0b151b4b1fb47977ed5581ab"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"publication_status":"published","month":"12","intvolume":" 45","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"file_date_updated":"2024-01-08T10:09:14Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2024-01-08T10:11:46Z","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)"},"_id":"14739"}]