{"day":"28","extern":1,"_id":"3964","publication":"Foundations of Computational Mathematics","volume":10,"publication_status":"published","intvolume":"        10","citation":{"apa":"Cohen Steiner, D., Edelsbrunner, H., Harer, J., &#38; Mileyko, Y. (2010). Lipschitz functions have L_p-stable persistence. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-010-9060-6\">https://doi.org/10.1007/s10208-010-9060-6</a>","chicago":"Cohen Steiner, David, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko. “Lipschitz Functions Have L_p-Stable Persistence.” <i>Foundations of Computational Mathematics</i>. Springer, 2010. <a href=\"https://doi.org/10.1007/s10208-010-9060-6\">https://doi.org/10.1007/s10208-010-9060-6</a>.","ista":"Cohen Steiner D, Edelsbrunner H, Harer J, Mileyko Y. 2010. Lipschitz functions have L_p-stable persistence. Foundations of Computational Mathematics. 10(2), 127–139.","short":"D. Cohen Steiner, H. Edelsbrunner, J. Harer, Y. Mileyko, Foundations of Computational Mathematics 10 (2010) 127–139.","mla":"Cohen Steiner, David, et al. “Lipschitz Functions Have L_p-Stable Persistence.” <i>Foundations of Computational Mathematics</i>, vol. 10, no. 2, Springer, 2010, pp. 127–39, doi:<a href=\"https://doi.org/10.1007/s10208-010-9060-6\">10.1007/s10208-010-9060-6</a>.","ieee":"D. Cohen Steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko, “Lipschitz functions have L_p-stable persistence,” <i>Foundations of Computational Mathematics</i>, vol. 10, no. 2. Springer, pp. 127–139, 2010.","ama":"Cohen Steiner D, Edelsbrunner H, Harer J, Mileyko Y. Lipschitz functions have L_p-stable persistence. <i>Foundations of Computational Mathematics</i>. 2010;10(2):127-139. doi:<a href=\"https://doi.org/10.1007/s10208-010-9060-6\">10.1007/s10208-010-9060-6</a>"},"title":"Lipschitz functions have L_p-stable persistence","quality_controlled":0,"date_created":"2018-12-11T12:06:09Z","status":"public","date_updated":"2021-01-12T07:53:31Z","date_published":"2010-01-28T00:00:00Z","publisher":"Springer","month":"01","type":"journal_article","publist_id":"2163","doi":"10.1007/s10208-010-9060-6","issue":"2","abstract":[{"lang":"eng","text":"We prove two stability results for Lipschitz functions on triangulable, compact metric spaces and consider applications of both to problems in systems biology. Given two functions, the first result is formulated in terms of the Wasserstein distance between their persistence diagrams and the second in terms of their total persistence."}],"author":[{"last_name":"Cohen Steiner","first_name":"David","full_name":"Cohen-Steiner, David"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"John","last_name":"Harer","full_name":"Harer, John"},{"full_name":"Mileyko, Yuriy","first_name":"Yuriy","last_name":"Mileyko"}],"year":"2010","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 and by CNRS under grant PICS-3416.","page":"127 - 139"}