{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T23:00:14Z","timestamp":1740178814955,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-18-1-0307"],"award-info":[{"award-number":["W911NF-18-1-0307"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1764406"],"award-info":[{"award-number":["1764406"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["594594"],"award-info":[{"award-number":["594594"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Appl. and Comput. Topology"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s41468-023-00157-2","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T08:02:37Z","timestamp":1705996957000},"page":"347-399","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Topological and metric properties of spaces of generalized persistence diagrams"],"prefix":"10.1007","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5262-2133","authenticated-orcid":false,"given":"Peter","family":"Bubenik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9896-872X","authenticated-orcid":false,"given":"Iryna","family":"Hartsock","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"issue":"12","key":"157_CR1","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1016\/j.topol.2008.02.011","volume":"155","author":"G Bell","year":"2008","unstructured":"Bell, G., Dranishnikov, A.: Asymptotic dimension. Topol. Appl. 155(12), 1265\u20131296 (2008)","journal-title":"Topol. Appl."},{"key":"157_CR2","volume-title":"Wiley Series in Probability and Statistics: Probability and Statistics","author":"P Billingsley","year":"1999","unstructured":"Billingsley, P.: Convergence of probability measures. In: Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edn. Wiley, New York (1999)","edition":"2"},{"issue":"1","key":"157_CR3","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/s00454-021-00298-0","volume":"66","author":"HB Bjerkevik","year":"2021","unstructured":"Bjerkevik, H.B.: On the stability of interval decomposable persistence modules. Discret. Comput. Geom. 66(1), 92\u2013121 (2021)","journal-title":"Discret. Comput. Geom."},{"issue":"4","key":"157_CR4","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1007\/s10208-014-9201-4","volume":"14","author":"AJ Blumberg","year":"2014","unstructured":"Blumberg, A.J., Gal, I., Mandell, M.A., Pancia, M.: Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces. Found. Comput. Math. 14(4), 745\u2013789 (2014)","journal-title":"Found. Comput. Math."},{"issue":"6","key":"157_CR5","doi-asserted-by":"publisher","first-page":"3133","DOI":"10.2140\/agt.2018.18.3133","volume":"18","author":"M Botnan","year":"2018","unstructured":"Botnan, M., Lesnick, M.: Algebraic stability of zigzag persistence modules. Algebr. Geom. Topol. 18(6), 3133\u20133204 (2018)","journal-title":"Algebr. Geom. Topol."},{"key":"157_CR6","volume-title":"Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","author":"MR Bridson","year":"1999","unstructured":"Bridson, M.R., Haefliger, A.: Metric spaces of non-positive curvature. In: Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319. Springer, Berlin (1999)"},{"key":"157_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2022.101882","volume":"105\u2013106","author":"P Bubenik","year":"2022","unstructured":"Bubenik, P., Elchesen, A.: Universality of persistence diagrams and the bottleneck and Wasserstein distances. Comput. Geom. 105\u2013106, 101882 (2022a)","journal-title":"Comput. Geom."},{"issue":"4","key":"157_CR8","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s41468-022-00091-9","volume":"6","author":"P Bubenik","year":"2022","unstructured":"Bubenik, P., Elchesen, A.: Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces. J. Appl. Comput. Topol. 6(4), 429\u2013474 (2022b)","journal-title":"J. Appl. Comput. Topol."},{"issue":"3","key":"157_CR9","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s41468-018-0022-4","volume":"2","author":"P Bubenik","year":"2018","unstructured":"Bubenik, P., Vergili, T.: Topological spaces of persistence modules and their properties. J. Appl. Comput. Topol. 2(3), 233\u2013269 (2018)","journal-title":"J. Appl. Comput. Topol."},{"issue":"3","key":"157_CR10","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s41468-020-00056-w","volume":"4","author":"P Bubenik","year":"2020","unstructured":"Bubenik, P., Wagner, A.: Embeddings of persistence diagrams into Hilbert spaces. J. Appl. Comput. Topol. 4(3), 339\u2013351 (2020)","journal-title":"J. Appl. Comput. Topol."},{"key":"157_CR11","volume-title":"A Course in Metric Geometry","author":"D Burago","year":"2001","unstructured":"Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry, vol. 33. American Mathematical Soc, Providence (2001)"},{"issue":"2(284)","key":"157_CR12","first-page":"3","volume":"47","author":"Yu Burago","year":"1992","unstructured":"Burago, Yu., Gromov, M., Perel\u2019man, G., Aleksandrov, A.D.: Spaces with curvatures bounded below. Uspekhi Mat. Nauk 47(2(284)), 3\u201351, 222 (1992)","journal-title":"Uspekhi Mat. Nauk"},{"key":"157_CR13","volume-title":"Topological Data Analysis with Applications","author":"G Carlsson","year":"2022","unstructured":"Carlsson, G., Vejdemo-Johansson, M.: Topological Data Analysis with Applications. Cambridge University Press, Cambridge (2022)"},{"key":"157_CR14","unstructured":"Che, M., Galaz-Garc\u00eda, F., Guijarro, L., Solis, I.M.: Metric geometry of spaces of persistence diagrams (2021). arXiv:2109.14697v2"},{"key":"157_CR15","unstructured":"Chowdhury, S.: Geodesics in persistence diagram space (2019). arXiv:1905.10820"},{"issue":"2","key":"157_CR16","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00454-019-00165-z","volume":"63","author":"J Cochoy","year":"2020","unstructured":"Cochoy, J., Oudot, S.: Decomposition of exact pfd persistence bimodules. Discret. Comput. Geom. 63(2), 255\u2013293 (2020)","journal-title":"Discret. Comput. Geom."},{"issue":"1","key":"157_CR17","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s00454-006-1276-5","volume":"37","author":"D Cohen-Steiner","year":"2007","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discret. Comput. Geom. 37(1), 103\u2013120 (2007)","journal-title":"Discret. Comput. Geom."},{"issue":"2","key":"157_CR18","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10208-010-9060-6","volume":"10","author":"D Cohen-Steiner","year":"2010","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J., Mileyko, Y.: Lipschitz functions have $$L_p$$-stable persistence. Found. Comput. Math. 10(2), 127\u2013139 (2010)","journal-title":"Found. Comput. Math."},{"issue":"6","key":"157_CR19","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1016\/j.cag.2004.08.015","volume":"28","author":"A Collins","year":"2004","unstructured":"Collins, A., Zomorodian, A., Carlsson, G., Guibas, L.J.: A barcode shape descriptor for curve point cloud data. Comput. Graph. 28(6), 881\u2013894 (2004)","journal-title":"Comput. Graph."},{"key":"157_CR20","doi-asserted-by":"publisher","DOI":"10.1017\/9781009099950","volume-title":"Computational Topology for Data Analysis","author":"TK Dey","year":"2022","unstructured":"Dey, T.K., Wang, Y.: Computational Topology for Data Analysis. Cambridge University Press, Cambridge, UK (2022)"},{"issue":"6","key":"157_CR21","doi-asserted-by":"publisher","first-page":"2383","DOI":"10.1090\/proc\/13491","volume":"145","author":"D Kasprowski","year":"2017","unstructured":"Kasprowski, D.: The asymptotic dimension of quotients by finite groups. Proc. Am. Math. Soc. 145(6), 2383\u20132389 (2017)","journal-title":"Proc. Am. Math. Soc."},{"issue":"4","key":"157_CR22","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s41468-021-00075-1","volume":"5","author":"W Kim","year":"2021","unstructured":"Kim, W., M\u00e9moli, F.: Generalized persistence diagrams for persistence modules over posets. J. Appl. Comput. Topol. 5(4), 533\u2013581 (2021)","journal-title":"J. Appl. Comput. Topol."},{"key":"157_CR23","doi-asserted-by":"publisher","DOI":"10.1090\/noti2761","author":"W Kim","year":"2023","unstructured":"Kim, W., Memoli, F.: Persistence over posets. Not. Am. Math. Soc. (2023). https:\/\/doi.org\/10.1090\/noti2761","journal-title":"Not. Am. Math. Soc."},{"issue":"2","key":"157_CR24","first-page":"185","volume":"5","author":"O Kuchaiev","year":"2008","unstructured":"Kuchaiev, O., Protasov, I.: Coarse rays. Ukr. Mat. Visn. 5(2), 185\u2013192 (2008)","journal-title":"Ukr. Mat. Visn."},{"issue":"4","key":"157_CR25","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1216\/RMJ-1980-10-4-717","volume":"10","author":"RA McCoy","year":"1980","unstructured":"McCoy, R.A.: Countability properties of function spaces. Rocky Mt. J. Math. 10(4), 717\u2013730 (1980)","journal-title":"Rocky Mt. J. Math."},{"issue":"12","key":"157_CR26","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/12\/124007","volume":"27","author":"Y Mileyko","year":"2011","unstructured":"Mileyko, Y., Mukherjee, S., Harer, J.: Probability measures on the space of persistence diagrams. Inverse Probl. 27(12), 124007 (2011)","journal-title":"Inverse Probl."},{"issue":"6","key":"157_CR27","doi-asserted-by":"publisher","first-page":"2693","DOI":"10.1090\/proc\/15363","volume":"149","author":"A Mitra","year":"2021","unstructured":"Mitra, A., Virk, \u017d: The space of persistence diagrams on $$n$$ points coarsely embeds into Hilbert space. Proc. Am. Math. Soc. 149(6), 2693\u20132703 (2021)","journal-title":"Proc. Am. Math. Soc."},{"key":"157_CR28","volume-title":"Featured Titles for Topology","author":"J Munkres","year":"2000","unstructured":"Munkres, J.: Topology. In: Featured Titles for Topology. Prentice Hall, Incorporated, Hoboken (2000)"},{"issue":"4","key":"157_CR29","first-page":"571","volume":"12","author":"S-I Ohta","year":"2012","unstructured":"Ohta, S.-I.: Barycenters in alexandrov spaces of curvature bounded below. Adv. Geom. 12(4), 571\u2013587 (2012)","journal-title":"Adv. Geom."},{"issue":"4","key":"157_CR30","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1007\/s10208-022-09567-7","volume":"23","author":"JA Perea","year":"2022","unstructured":"Perea, J.A., Munch, E., Khasawneh, F.A.: Approximating continuous functions on persistence diagrams using template functions. Found. Comput. Math. 23(4), 1215\u20131272 (2022)","journal-title":"Found. Comput. Math."},{"key":"157_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/9781316671665","volume-title":"Topological Data Analysis for Genomics and Evolution: Topology in Biology","author":"R Rabadan","year":"2019","unstructured":"Rabadan, R., Blumberg, A.J.: Topological Data Analysis for Genomics and Evolution: Topology in Biology. Cambridge University Press, Cambridge (2019)"},{"key":"157_CR32","series-title":"University Lecture Series","doi-asserted-by":"crossref","DOI":"10.1090\/ulect\/031","volume-title":"Lectures on Coarse Geometry","author":"J Roe","year":"2003","unstructured":"Roe, J.: Lectures on Coarse Geometry. University Lecture Series, vol. 31. American Mathematical Society, Providence, RI (2003)"},{"key":"157_CR33","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond","author":"B Scholkopf","year":"2001","unstructured":"Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, MA, USA (2001)"},{"issue":"1","key":"157_CR34","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s41468-017-0003-z","volume":"1","author":"J Skryzalin","year":"2017","unstructured":"Skryzalin, J., Carlsson, G.: Numeric invariants from multidimensional persistence. J. Appl. Comput. Topol. 1(1), 89\u2013119 (2017)","journal-title":"J. Appl. Comput. Topol."},{"key":"157_CR35","volume-title":"Information Science and Statistics","author":"I Steinwart","year":"2008","unstructured":"Steinwart, I., Christmann, A.: Support vector machines. In: Information Science and Statistics. Springer, New York (2008)"},{"issue":"1","key":"157_CR36","doi-asserted-by":"publisher","first-page":"255","DOI":"10.4310\/HHA.2020.v22.n1.a15","volume":"22","author":"K Turner","year":"2020","unstructured":"Turner, K.: Medians of populations of persistence diagrams. Homol. Homotopy Appl. 22(1), 255\u2013282 (2020)","journal-title":"Homol. Homotopy Appl."},{"issue":"1","key":"157_CR37","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/s00454-014-9604-7","volume":"52","author":"K Turner","year":"2014","unstructured":"Turner, K., Mileyko, Y., Mukherjee, S., Harer, J.: Fr\u00e9chet means for distributions of persistence diagrams. Discret. Comput. Geom. 52(1), 44\u201370 (2014)","journal-title":"Discret. Comput. Geom."},{"issue":"6","key":"157_CR38","doi-asserted-by":"publisher","first-page":"2673","DOI":"10.1090\/proc\/15451","volume":"149","author":"A Wagner","year":"2021","unstructured":"Wagner, A.: Nonembeddability of persistence diagrams with $$p>2$$ Wasserstein metric. Proc. Am. Math. Soc. 149(6), 2673\u20132677 (2021)","journal-title":"Proc. Am. Math. Soc."},{"key":"157_CR39","volume-title":"Addison\u2013Wesley Series in Mathematics","author":"S Willard","year":"2004","unstructured":"Willard, S.: General topology. In: Addison\u2013Wesley Series in Mathematics. Dover Publications, Mineola (2004)"}],"container-title":["Journal of Applied and Computational Topology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-023-00157-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41468-023-00157-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-023-00157-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T20:50:24Z","timestamp":1719953424000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41468-023-00157-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,23]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["157"],"URL":"https:\/\/doi.org\/10.1007\/s41468-023-00157-2","relation":{},"ISSN":["2367-1726","2367-1734"],"issn-type":[{"type":"print","value":"2367-1726"},{"type":"electronic","value":"2367-1734"}],"subject":[],"published":{"date-parts":[[2024,1,23]]},"assertion":[{"value":"27 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 September 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}