{"isi":1,"date_updated":"2025-09-30T08:53:52Z","quality_controlled":"1","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"},{"last_name":"Patel","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","full_name":"Patel, Amit","first_name":"Amit"}],"department":[{"_id":"HeEd"}],"issue":"3","oa_version":"Submitted Version","date_created":"2018-12-11T12:02:59Z","publication_status":"published","article_processing_charge":"No","intvolume":"        11","title":"Quantifying transversality by measuring the robustness of intersections","abstract":[{"lang":"eng","text":"By definition, transverse intersections are stable under in- finitesimal perturbations. Using persistent homology, we ex- tend this notion to sizeable perturbations. Specifically, we assign to each homology class of the intersection its robust- ness, the magnitude of a perturbation necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for con- tours of smooth mappings."}],"external_id":{"arxiv":["0911.2142"],"isi":["000290038800004"]},"arxiv":1,"date_published":"2011-06-01T00:00:00Z","_id":"3377","publisher":"Springer","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0911.2142"}],"citation":{"ieee":"H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” <i>Foundations of Computational Mathematics</i>, vol. 11, no. 3. Springer, pp. 345–361, 2011.","apa":"Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2011). Quantifying transversality by measuring the robustness of intersections. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-011-9090-8\">https://doi.org/10.1007/s10208-011-9090-8</a>","mla":"Edelsbrunner, Herbert, et al. “Quantifying Transversality by Measuring the Robustness of Intersections.” <i>Foundations of Computational Mathematics</i>, vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:<a href=\"https://doi.org/10.1007/s10208-011-9090-8\">10.1007/s10208-011-9090-8</a>.","ama":"Edelsbrunner H, Morozov D, Patel A. Quantifying transversality by measuring the robustness of intersections. <i>Foundations of Computational Mathematics</i>. 2011;11(3):345-361. doi:<a href=\"https://doi.org/10.1007/s10208-011-9090-8\">10.1007/s10208-011-9090-8</a>","ista":"Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 11(3), 345–361.","chicago":"Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality by Measuring the Robustness of Intersections.” <i>Foundations of Computational Mathematics</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s10208-011-9090-8\">https://doi.org/10.1007/s10208-011-9090-8</a>.","short":"H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361."},"corr_author":"1","page":"345 - 361","type":"journal_article","publication":"Foundations of Computational Mathematics","oa":1,"volume":11,"status":"public","publist_id":"3230","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","acknowledgement":"This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057.","day":"01","scopus_import":"1","year":"2011","language":[{"iso":"eng"}],"month":"06","doi":"10.1007/s10208-011-9090-8"}