{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T10:45:50Z","timestamp":1750848350035,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T00:00:00Z","timestamp":1567814400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T00:00:00Z","timestamp":1567814400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["Toposys project FP7-ICT-318493-STREP"],"award-info":[{"award-number":["Toposys project FP7-ICT-318493-STREP"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000782","name":"European Science Foundation","doi-asserted-by":"crossref","award":["ESF Short Visit grant"],"award-info":[{"award-number":["ESF Short Visit grant"]}],"id":[{"id":"10.13039\/501100000782","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["FP7 Integrated Project IQmulus","FP7-ICT-2011318787"],"award-info":[{"award-number":["FP7 Integrated Project IQmulus","FP7-ICT-2011318787"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["H2020 Project Gravitate","H2020 - RE- FLECTIVE - 7 - 2014 - 665155"],"award-info":[{"award-number":["H2020 Project Gravitate","H2020 - RE- FLECTIVE - 7 - 2014 - 665155"]}],"id":[{"id":"10.13039\/100010663","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":[[2019,12]]},"DOI":"10.1007\/s41468-019-00041-y","type":"journal-article","created":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T14:22:50Z","timestamp":1568211770000},"page":"381-422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On the geometrical properties of the coherent matching distance in 2D persistent homology"],"prefix":"10.1007","volume":"3","author":[{"given":"Andrea","family":"Cerri","sequence":"first","affiliation":[]},{"given":"Marc","family":"Ethier","sequence":"additional","affiliation":[]},{"given":"Patrizio","family":"Frosini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,7]]},"reference":[{"issue":"2","key":"41_CR1","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10851-008-0096-z","volume":"32","author":"S Biasotti","year":"2008","unstructured":"Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., Landi, C.: Multidimensional size functions for shape comparison. J. Math. Imaging Vis. 32(2), 161\u2013179 (2008)","journal-title":"J. Math. Imaging Vis."},{"issue":"14","key":"41_CR2","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1016\/j.patrec.2011.07.014","volume":"32","author":"S Biasotti","year":"2011","unstructured":"Biasotti, S., Cerri, A., Frosini, P., Giorgi, D.: A new algorithm for computing the 2-dimensional matching distance between size functions. Pattern Recogn. Lett. 32(14), 1735\u20131746 (2011)","journal-title":"Pattern Recogn. Lett."},{"key":"41_CR3","unstructured":"Bjerkevik, H.B.: Stability of higher-dimensional interval decomposable persistence modules. ArXiv e-prints (2016). \n                    arXiv:1609.02086"},{"key":"41_CR4","unstructured":"Bjerkevik, H.B., Botnan, M.B.: Computational complexity of the interleaving distance. In: Speckmann, B., T\u00f3th, C.D.(eds.) 34th International Symposium on Computational Geometry (SoCG 2018), Leibniz International Proceedings in Informatics (LIPIcs), pp. 13:1\u201313:15. Dagstuhl, Germany (2018). Schloss Dagstuhl\u2013Leibniz-Zentrum fuer Informatik"},{"key":"41_CR5","unstructured":"Bjerkevik, H.B., Botnan, M.B., Kerber, M.: Computing the interleaving distance is NP-hard. CoRR (2018). \n                    arXiv:1811.09165"},{"issue":"6","key":"41_CR6","doi-asserted-by":"publisher","first-page":"3133","DOI":"10.2140\/agt.2018.18.3133","volume":"18","author":"MB Botnan","year":"2018","unstructured":"Botnan, M.B., Lesnick, M.: Algebraic stability of zigzag persistence modules. Algebr. Geom. Topol. 18(6), 3133\u20133204 (2018)","journal-title":"Algebr. Geom. Topol."},{"issue":"8","key":"41_CR7","doi-asserted-by":"publisher","first-page":"3003","DOI":"10.1090\/S0002-9939-10-10312-8","volume":"138","author":"F Cagliari","year":"2010","unstructured":"Cagliari, F., Di Fabio, B., Ferri, M.: One-dimensional reduction of multidimensional persistent homology. Proc. Am. Math. Soc. 138(8), 3003\u20133017 (2010)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"41_CR8","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00454-009-9176-0","volume":"42","author":"G Carlsson","year":"2009","unstructured":"Carlsson, G., Zomorodian, A.: The theory of multidimensional persistence. Discrete Comput. Geom. 42(1), 71\u201393 (2009)","journal-title":"Discrete Comput. Geom."},{"key":"41_CR9","doi-asserted-by":"crossref","unstructured":"Carlsson, G., Singh, G., Zomorodian, A.: Computing multidimensional persistence. In: Dong, Y., Du, D.-Z., Ibarra, O.H. (eds) ISAAC, volume 5878 of Lecture Notes in Computer Science, pp. 730\u2013739. Springer (2009)","DOI":"10.1007\/978-3-642-10631-6_74"},{"issue":"4","key":"41_CR10","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1002\/mma.3093","volume":"38","author":"A Cerri","year":"2015","unstructured":"Cerri, A., Frosini, P.: Necessary conditions for discontinuities of multidimensional persistent Betti numbers. Math. Methods Appl. Sci. 38(4), 617\u2013629 (2015)","journal-title":"Math. Methods Appl. Sci."},{"key":"41_CR11","doi-asserted-by":"publisher","DOI":"10.4208\/jcm.1809-m2018-0043","author":"A Cerri","year":"2019","unstructured":"Cerri, A., Frosini, P.: A new approximation algorithm for the matching distance in multidimensional persistence. J. Comput. Math. (2019). \n                    https:\/\/doi.org\/10.4208\/jcm.1809-m2018-0043\n                    \n                  . (To appear)","journal-title":"J. Comput. Math."},{"issue":"2","key":"41_CR12","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s10208-015-9244-1","volume":"16","author":"A Cerri","year":"2016","unstructured":"Cerri, A., Landi, C.: Hausdorff stability of persistence spaces. Found. Comput. Math. 16(2), 343\u2013367 (2016)","journal-title":"Found. Comput. Math."},{"issue":"12","key":"41_CR13","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1002\/mma.2704","volume":"36","author":"A Cerri","year":"2013","unstructured":"Cerri, A., Di Fabio, B., Ferri, M., Frosini, P., Landi, C.: Betti numbers in multidimensional persistent homology are stable functions. Math. Methods Appl. Sci. 36(12), 1543\u20131557 (2013a)","journal-title":"Math. Methods Appl. Sci."},{"key":"41_CR14","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1007\/978-3-642-37067-0_17","volume-title":"Discrete Geometry for Computer Imagery","author":"Andrea Cerri","year":"2013","unstructured":"Cerri, A., Ethier, M., Frosini, P.: A study of monodromy in the computation of multidimensional persistence. In: Proceedings of the 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 20\u201322 Mar 2013. Lecture Notes in Computer Science, vol. 7749, pp. 192\u2013202 (2013b)"},{"key":"41_CR15","doi-asserted-by":"crossref","unstructured":"Cerri, A., Ethier, M., Frosini, P.: The coherent matching distance in 2d persistent homology. In: Bac, A., Mari, J.-L. (eds.) Proceedings of the 6th International Workshop on Computational Topology in Image Context, Marseille, France, 15\u201317 June 2016. Lecture Notes in Computer Science, vol. 9667, pp. 216\u2013227. Springer International Publishing Switzerland (2016)","DOI":"10.1007\/978-3-319-39441-1_20"},{"issue":"1","key":"41_CR16","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.L.: Stability of persistence diagrams. Discrete Comput. Geom. 37(1), 103\u2013120 (2007)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"41_CR17","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/s10440-008-9332-1","volume":"109","author":"M d\u2019Amico","year":"2010","unstructured":"d\u2019Amico, M., Frosini, P., Landi, C.: Natural pseudo-distance and optimal matching between reduced size functions. Acta Appl. Math. 109(2), 527\u2013554 (2010)","journal-title":"Acta Appl. Math."},{"key":"41_CR18","unstructured":"Dey, T.K., Xin, C.: Computing bottleneck distance for 2-D interval decomposable modules. In: Speckmann, B., T\u00f3th, C.D. (eds.) 34th International Symposium on Computational Geometry (SoCG 2018), Leibniz International Proceedings in Informatics (LIPIcs), pp. 32:1\u201332:15. Dagstuhl, Germany (2018). Schloss Dagstuhl\u2013Leibniz-Zentrum fuer Informatik"},{"key":"41_CR19","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Harer, J.: Jacobi sets of multiple Morse functions. In: Foundations of Computational Mathematics: Minneapolis, 2002, volume 312 of London Mathematical Society Lecture Note Series, pp. 37\u201357. Cambridge University Press, Cambridge (2004)","DOI":"10.1017\/CBO9781139106962.003"},{"key":"41_CR20","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Morozov, D.: Persistent homology: theory and practice. In: European Congress of Mathematics, pp. 31\u201350. European Mathematical Society, Z\u00fcrich (2013)","DOI":"10.4171\/120-1\/3"},{"issue":"4","key":"41_CR21","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28(4), 511\u2013533 (2002)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"41_CR22","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s002000100078","volume":"12","author":"P Frosini","year":"2001","unstructured":"Frosini, P., Landi, C.: Size functions and formal series. Appl. Algebra Eng. Commun. Comput. 12(4), 327\u2013349 (2001)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"3","key":"41_CR23","doi-asserted-by":"crossref","first-page":"455","DOI":"10.36045\/bbms\/1103065863","volume":"6","author":"P Frosini","year":"1999","unstructured":"Frosini, P., Mulazzani, M.: Size homotopy groups for computation of natural size distances. Bull. Belg. Math. Soc. Simon Stevin 6(3), 455\u2013464 (1999)","journal-title":"Bull. Belg. Math. Soc. Simon Stevin"},{"key":"41_CR24","unstructured":"Kerber, M., Lesnick, M., Oudot, S.: Exact computation of the matching distance on 2-parameter persistence modules. In: Barequet, G., Wang, Y. (eds.) 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), pp. 46:1\u201346:15. Dagstuhl, Germany (2019). Schloss Dagstuhl\u2013Leibniz-Zentrum fuer Informatik"},{"issue":"3","key":"41_CR25","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/s10208-015-9255-y","volume":"15","author":"M Lesnick","year":"2015","unstructured":"Lesnick, M.: The theory of the interleaving distance on multidimensional persistence modules. Found. Comput. Math. 15(3), 613\u2013650 (2015)","journal-title":"Found. Comput. Math."},{"key":"41_CR26","unstructured":"Lesnick, M., Wright, M.: Interactive visualization of 2-D persistence modules. ArXiv e-prints (2015). \n                    arXiv:1512.00180"},{"issue":"3","key":"41_CR27","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0040-9383(75)90002-6","volume":"14","author":"YH Wan","year":"1975","unstructured":"Wan, Y.H.: Morse theory for two functions. Topology 14(3), 217\u2013228 (1975)","journal-title":"Topology"}],"container-title":["Journal of Applied and Computational Topology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-019-00041-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s41468-019-00041-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s41468-019-00041-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,5]],"date-time":"2020-09-05T23:24:45Z","timestamp":1599348285000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s41468-019-00041-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,7]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["41"],"URL":"https:\/\/doi.org\/10.1007\/s41468-019-00041-y","relation":{},"ISSN":["2367-1726","2367-1734"],"issn-type":[{"type":"print","value":"2367-1726"},{"type":"electronic","value":"2367-1734"}],"subject":[],"published":{"date-parts":[[2019,9,7]]},"assertion":[{"value":"9 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}