[{"dini_type":"doc-type:conferenceObject","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.","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 355–364.","apa":"Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In Proceedings of the Annual Symposium on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publist_id":"4853","author":[{"orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"last_name":"Lesnick","first_name":"Michael"}],"project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"day":"01","dc":{"title":["Induced matchings of barcodes and the algebraic stability of persistence"],"language":["eng"],"rights":["info:eu-repo/semantics/openAccess"],"creator":["Bauer, Ulrich","Lesnick, Michael"],"date":["2014"],"type":["info:eu-repo/semantics/conferenceObject","doc-type:conferenceObject","text","http://purl.org/coar/resource_type/c_5794"],"publisher":["ACM"],"source":["Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:355-364. doi:10.1145/2582112.2582168"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1145/2582112.2582168","info:eu-repo/grantAgreement/EC/FP7/318493"],"identifier":["https://research-explorer.ista.ac.at/record/2153"],"description":["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)."]},"publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"355 - 364","uri_base":"https://research-explorer.ista.ac.at","date_published":"2014-06-01T00:00:00Z","date_created":"2018-12-11T11:56:01Z","quality_controlled":"1","oa":1,"date_updated":"2021-01-12T06:55:38Z","creator":{"id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","login":"apreinsp"},"department":[{"_id":"HeEd","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"_id":"2153","type":"conference","conference":{"start_date":"2014-06-08","location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry"},"status":"public","publication_status":"published","language":[{}],"ec_funded":1,"abstract":[{"lang":"eng"}],"oa_version":"Submitted Version","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1311.3681","open_access":"1"}],"month":"06"}]