{"oa_version":"Published Version","issue":"5","scopus_import":1,"quality_controlled":"1","title":"The persistent homology of a self-map","language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:45:26Z","file_id":"4670","creator":"system","checksum":"3566f3a8b0c1bc550e62914a88c584ff","date_created":"2018-12-12T10:08:10Z","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","relation":"main_file","access_level":"open_access","file_size":1317546,"content_type":"application/pdf"}],"pubrep_id":"486","intvolume":"        15","publist_id":"5022","date_published":"2015-10-01T00:00:00Z","day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Springer","year":"2015","ec_funded":1,"abstract":[{"lang":"eng","text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n"}],"publication_status":"published","publication":"Foundations of Computational Mathematics","_id":"2035","doi":"10.1007/s10208-014-9223-y","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mrozek","first_name":"Marian","full_name":"Mrozek, Marian"}],"has_accepted_license":"1","type":"journal_article","date_updated":"2021-01-12T06:54:53Z","volume":15,"oa":1,"file_date_updated":"2020-07-14T12:45:26Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"status":"public","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"page":"1213 - 1244","month":"10","date_created":"2018-12-11T11:55:20Z","citation":{"ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. 2015;15(5):1213-1244. doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>.","apa":"Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2015). The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>."},"department":[{"_id":"HeEd"}],"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639."}