{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:38:36Z","timestamp":1773232716733,"version":"3.50.1"},"publisher-location":"Cham","reference-count":17,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032039200","type":"print"},{"value":"9783032039217","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T00:00:00Z","timestamp":1760918400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T00:00:00Z","timestamp":1760918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-03921-7_3","type":"book-chapter","created":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T22:02:49Z","timestamp":1760911369000},"page":"22-31","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Confidence Bands for\u00a0Multiparameter Persistence Landscapes"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8340-4235","authenticated-orcid":false,"given":"In\u00e9s","family":"Garc\u00eda-Redondo","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6774-8150","authenticated-orcid":false,"given":"Anthea","family":"Monod","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9162-0390","authenticated-orcid":false,"given":"Qiquan","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,20]]},"reference":[{"issue":"3","key":"3_CR1","first-page":"77","volume":"16","author":"P Bubenik","year":"2015","unstructured":"Bubenik, P.: Statistical topological data analysis using persistence landscapes. J. Mach. Learn. Res. 16(3), 77\u2013102 (2015)","journal-title":"J. Mach. Learn. Res."},{"issue":"12","key":"3_CR2","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1002\/mma.2704","volume":"36","author":"A Cerri","year":"2013","unstructured":"Cerri, A., Fabio, B.D., Ferri, M., Frosini, P., Landi, C.: Betti numbers in multidimensional persistent homology are stable functions. Math. Methods Appl. Sci. 36(12), 1543\u20131557 (2013)","journal-title":"Math. Methods Appl. Sci."},{"key":"3_CR3","doi-asserted-by":"publisher","unstructured":"Chach\u00f3lski, W., Corbet, R., Sattelberger, A.L.: The shift-dimension of multipersistence modules. J. Appl. Comput. Topol. 8(3), 643\u2013667 (2024). https:\/\/doi.org\/10.1007\/s41468-024-00169-6, http:\/\/dx.doi.org\/10.1007\/s41468-024-00169-6","DOI":"10.1007\/s41468-024-00169-6"},{"key":"3_CR4","doi-asserted-by":"publisher","unstructured":"Chazal, F., Fasy, B.T., Lecci, F., Rinaldo, A., Singh, A., Wasserman, L.: On the bootstrap for persistence diagrams and landscapes (2014). https:\/\/doi.org\/10.48550\/arXiv.1311.0376","DOI":"10.48550\/arXiv.1311.0376"},{"key":"3_CR5","doi-asserted-by":"publisher","unstructured":"Chazal, F., Fasy, B.T., Lecci, F., Rinaldo, A., Wasserman, L.: Stochastic convergence of persistence landscapes and silhouettes. In: Proceedings of the Thirtieth Annual Symposium on Computational Geometry. pp. 474\u2013483. SOCG\u201914, Association for Computing Machinery, New York, NY, USA (2014). https:\/\/doi.org\/10.1145\/2582112.2582128","DOI":"10.1145\/2582112.2582128"},{"key":"3_CR6","volume":"2","author":"R Corbet","year":"2019","unstructured":"Corbet, R., Fugacci, U., Kerber, M., Landi, C., Wang, B.: A kernel for multi-parameter persistent homology. Comput. Graphics: X 2, 100005 (2019)","journal-title":"Comput. Graphics: X"},{"key":"3_CR7","doi-asserted-by":"publisher","unstructured":"Efron, B.: Bootstrap methods: another look at the jackknife. In: Kotz, S., Johnson, N.L. (eds.) Breakthroughs in Statistics: Methodology and Distribution, pp. 569\u2013593. Springer, New York, NY (1992). https:\/\/doi.org\/10.1007\/978-1-4612-4380-9_41","DOI":"10.1007\/978-1-4612-4380-9_41"},{"key":"3_CR8","doi-asserted-by":"crossref","unstructured":"Efron, B., Tibshirani, R.J.: An introduction to the bootstrap. Chapman and Hall\/CRC (1994)","DOI":"10.1201\/9780429246593"},{"key":"3_CR9","unstructured":"G\u00e4fvert, O., Chach\u00f3lski, W.: Stable invariants for multiparameter persistence (2021). https:\/\/arxiv.org\/abs\/1703.03632"},{"issue":"5","key":"3_CR10","doi-asserted-by":"publisher","first-page":"2740","DOI":"10.1214\/17-AAP1371","volume":"28","author":"Y Hiraoka","year":"2018","unstructured":"Hiraoka, Y., Shirai, T., Trinh, K.D.: Limit theorems for persistence diagrams. Ann. Appl. Probab. 28(5), 2740\u20132780 (2018)","journal-title":"Ann. Appl. Probab."},{"key":"3_CR11","doi-asserted-by":"publisher","unstructured":"Kosorok, M.R.: Introduction to Empirical Processes and Semiparametric Inference. Springer Series in Statistics, Springer, New York, NY (2008).https:\/\/doi.org\/10.1007\/978-0-387-74978-5","DOI":"10.1007\/978-0-387-74978-5"},{"key":"3_CR12","unstructured":"Lesnick, M., Wright, M.: Interactive visualization of 2-d persistence modules (2015). https:\/\/arxiv.org\/abs\/1512.00180"},{"key":"3_CR13","doi-asserted-by":"publisher","unstructured":"Loiseaux, D., Schreiber, H.: Multipers: multiparameter persistence for machine learning. J. Open Source Softw. 9(103), 6773 (2024). https:\/\/doi.org\/10.21105\/joss.06773","DOI":"10.21105\/joss.06773"},{"key":"3_CR14","first-page":"68316","volume":"36","author":"D Loiseaux","year":"2023","unstructured":"Loiseaux, D., Scoccola, L., Carri\u00e8re, M., Botnan, M.B., Oudot, S.: Stable vectorization of multiparameter persistent homology using signed barcodes as measures. Adv. Neural. Inf. Process. Syst. 36, 68316\u201368342 (2023)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"1","key":"3_CR15","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1137\/22M1489150","volume":"8","author":"S Oudot","year":"2024","unstructured":"Oudot, S., Scoccola, L.: On the stability of multigraded betti numbers and hilbert functions. SIAM J. Appl. Algebra Geometry 8(1), 54\u201388 (2024)","journal-title":"SIAM J. Appl. Algebra Geometry"},{"issue":"61","key":"3_CR16","first-page":"1","volume":"21","author":"O Vipond","year":"2020","unstructured":"Vipond, O.: Multiparameter persistence landscapes. J. Mach. Learn. Res. 21(61), 1\u201338 (2020)","journal-title":"J. Mach. Learn. Res."},{"key":"3_CR17","unstructured":"Xin, C., Mukherjee, S., Samaga, S.N., Dey, T.K.: Gril: A $$2 $$-parameter persistence based vectorization for machine learning. In: Topological, Algebraic and Geometric Learning Workshops 2023, pp. 313\u2013333. PMLR (2023)"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-03921-7_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T16:09:12Z","timestamp":1773158952000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-03921-7_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,20]]},"ISBN":["9783032039200","9783032039217"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-03921-7_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,20]]},"assertion":[{"value":"20 October 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors declare no competing interests that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"GSI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Geometric Science of Information","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Saint-Malo","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 October 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 October 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conference-gsi.org\/gsi-2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}