{"oa_version":"Submitted Version","page":"355 - 364","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"ec_funded":1,"status":"public","publisher":"ACM","quality_controlled":"1","language":[{"iso":"eng"}],"publist_id":"4853","year":"2014","oa":1,"abstract":[{"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).","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.3681"}],"title":"Induced matchings of barcodes and the algebraic stability of persistence","doi":"10.1145/2582112.2582168","author":[{"full_name":"Bauer, Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"first_name":"Michael","full_name":"Lesnick, Michael","last_name":"Lesnick"}],"month":"06","date_updated":"2021-01-12T06:55:38Z","_id":"2153","project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"}],"scopus_import":1,"date_published":"2014-06-01T00:00:00Z","publication":"Proceedings of the Annual Symposium on Computational Geometry","day":"01","publication_status":"published","date_created":"2018-12-11T11:56:01Z","citation":{"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>.","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>","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.","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>","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","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>."},"type":"conference","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2014-06-08","end_date":"2014-06-11","location":"Kyoto, Japan"}}