{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Induced matchings of barcodes and the algebraic stability of persistence","date_created":"2018-12-11T11:56:01Z","language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:55:38Z","author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Lesnick","first_name":"Michael","full_name":"Lesnick, Michael"}],"doi":"10.1145/2582112.2582168","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","year":"2014","day":"01","_id":"2153","page":"355 - 364","month":"06","publication":"Proceedings of the Annual Symposium on Computational Geometry","citation":{"ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 355–64, doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>.","apa":"Bauer, U., &#38; Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 355–364). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:355-364. doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 355–64. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>.","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 355–364.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364."},"publisher":"ACM","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.3681"}],"publication_status":"published","type":"conference","publist_id":"4853","conference":{"location":"Kyoto, Japan","end_date":"2014-06-11","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"oa_version":"Submitted Version","date_published":"2014-06-01T00:00:00Z","status":"public","oa":1,"abstract":[{"lang":"eng","text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s)."}],"ec_funded":1,"department":[{"_id":"HeEd"}]}