{"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-03-04T10:52:42Z","publisher":"Springer Nature","day":"01","has_accepted_license":"1","abstract":[{"text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.","lang":"eng"}],"citation":{"apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s41468-020-00058-8\">https://doi.org/10.1007/s41468-020-00058-8</a>.","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. <i>Journal of Applied and Computational Topology</i>. 2020;4(4):455-480. doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>","ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:<a href=\"https://doi.org/10.1007/s41468-020-00058-8\">10.1007/s41468-020-00058-8</a>.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480."},"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s41468-020-00058-8","date_published":"2020-12-01T00:00:00Z","quality_controlled":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["500"],"oa":1,"title":"Čech-Delaunay gradient flow and homology inference for self-maps","intvolume":"         4","department":[{"_id":"HeEd"}],"author":[{"full_name":"Bauer, U.","last_name":"Bauer","first_name":"U."},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"last_name":"Mrozek","full_name":"Mrozek, M.","first_name":"M."}],"publication":"Journal of Applied and Computational Topology","acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","page":"455-480","_id":"15064","status":"public","month":"12","file":[{"checksum":"eed1168b6e66cd55272c19bb7fca8a1c","content_type":"application/pdf","file_id":"15065","success":1,"date_updated":"2024-03-04T10:52:42Z","date_created":"2024-03-04T10:52:42Z","creator":"dernst","access_level":"open_access","file_size":851190,"relation":"main_file","file_name":"2020_JourApplCompTopology_Bauer.pdf"}],"publication_status":"published","oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"issue":"4","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"year":"2020","volume":4,"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z"}