--- _id: '3377' 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. 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. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: Edelsbrunner H, Morozov D, Patel A. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 2011;11(3):345-361. doi:10.1007/s10208-011-9090-8 apa: Edelsbrunner, H., Morozov, D., & Patel, A. (2011). Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-011-9090-8 chicago: Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-011-9090-8. ieee: H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 345–361, 2011. ista: Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 11(3), 345–361. mla: Edelsbrunner, Herbert, et al. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:10.1007/s10208-011-9090-8. short: H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361. date_created: 2018-12-11T12:02:59Z date_published: 2011-06-01T00:00:00Z date_updated: 2021-01-12T07:43:04Z day: '01' department: - _id: HeEd doi: 10.1007/s10208-011-9090-8 intvolume: ' 11' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/0911.2142 month: '06' oa: 1 oa_version: Submitted Version page: 345 - 361 publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '3230' quality_controlled: '1' scopus_import: 1 status: public title: Quantifying transversality by measuring the robustness of intersections type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2011' ...