[{"volume":15,"issue":"5","ec_funded":1,"publication_status":"published","file":[{"checksum":"3566f3a8b0c1bc550e62914a88c584ff","file_id":"4670","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:08:10Z","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","creator":"system","date_updated":"2020-07-14T12:45:26Z","file_size":1317546}],"language":[{}],"scopus_import":1,"month":"10","intvolume":" 15","abstract":[{"lang":"eng"}],"oa_version":"Published Version","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:26Z","date_updated":"2021-01-12T06:54:53Z","creator":{"id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","login":"dernst"},"ddc":[],"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","pubrep_id":"486","_id":"2035","uri_base":"https://research-explorer.ista.ac.at","page":"1213 - 1244","date_published":"2015-10-01T00:00:00Z","date_created":"2018-12-11T11:55:20Z","has_accepted_license":"1","day":"01","dc":{"subject":["ddc:000"],"rights":["info:eu-repo/semantics/openAccess"],"language":["eng"],"creator":["Edelsbrunner, Herbert","Jablonski, Grzegorz","Mrozek, Marian"],"title":["The persistent homology of a self-map"],"identifier":["https://research-explorer.ista.ac.at/record/2035","https://research-explorer.ista.ac.at/download/2035/4670"],"description":["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"],"source":["Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-014-9223-y","info:eu-repo/grantAgreement/EC/FP7/318493"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"publisher":["Springer"],"date":["2015"]},"publication":"Foundations of Computational Mathematics","quality_controlled":"1","oa":1,"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.","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-3536-9866","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz"},{"last_name":"Mrozek","first_name":"Marian"}],"publist_id":"5022","dini_type":"doc-type:article","citation":{"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.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y.","apa":"Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}]}]