{"id":"https://openalex.org/W4415016709","doi":"https://doi.org/10.1007/s41468-026-00254-y","title":"Gromov\u2013Wasserstein bound between Reeb and Mapper graphs","display_name":"Gromov\u2013Wasserstein bound between Reeb and Mapper graphs","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W4415016709","doi":"https://doi.org/10.1007/s41468-026-00254-y"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-026-00254-y","doi":"https://doi.org/10.1007/s41468-026-00254-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s41468-026-00254-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.02810","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093952498","display_name":"Ziyad Oulhaj","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ziyad Oulhaj","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Nantes Universit\u00e9, \u00c9cole Centrale Nantes, Nantes, France","LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Nantes Universit\u00e9, \u00c9cole Centrale Nantes, Nantes, France","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I4210153365","https://openalex.org/I97188460"]},{"raw_affiliation_string":"LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","institution_ids":["https://openalex.org/I4210153365"]},{"raw_affiliation_string":"Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I97188460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037161705","display_name":"Mathieu Carri\u00e8re","orcid":"https://orcid.org/0000-0002-4747-9915","observed_orcids":["https://orcid.org/0000-0002-4747-9915"]},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210106545","display_name":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/01nzkaw91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210106545"]},{"id":"https://openalex.org/I4405261415","display_name":"DATASHAPE: Comprendre la forme des donn\u00e9es","ror":"https://ror.org/059213d70","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210106545","https://openalex.org/I4210126360","https://openalex.org/I4405256294","https://openalex.org/I4405261415"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mathieu Carri\u00e8re","raw_affiliation_strings":["DataShape, Centre Inria d\u2019Universit\u00e9 C\u00f4te d\u2019Azur, Sophia Antipolis, Biot, France","DATASHAPE - Understanding the Shape of Data (Inria Saclay\r\n1, rue Honor\u00e9 d\u2019Estienne d\u2019Orves\r\n91120 Palaiseau\r\n\r\nInria d'Universit\u00e9 C\u00f4te d'Azur\r\n2004 route des lucioles\r\n06902 Sophia Antipolis - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DataShape, Centre Inria d\u2019Universit\u00e9 C\u00f4te d\u2019Azur, Sophia Antipolis, Biot, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I4210106545","https://openalex.org/I4405261415"]},{"raw_affiliation_string":"DATASHAPE - Understanding the Shape of Data (Inria Saclay\r\n1, rue Honor\u00e9 d\u2019Estienne d\u2019Orves\r\n91120 Palaiseau\r\n\r\nInria d'Universit\u00e9 C\u00f4te d'Azur\r\n2004 route des lucioles\r\n06902 Sophia Antipolis - France)","institution_ids":["https://openalex.org/I4210106545","https://openalex.org/I4405261415"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022113367","display_name":"Bertrand Michel","orcid":"https://orcid.org/0000-0002-5901-4146","observed_orcids":["https://orcid.org/0000-0002-5901-4146"]},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bertrand Michel","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Nantes Universit\u00e9, \u00c9cole Centrale Nantes, Nantes, France","LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray, CNRS UMR 6629, Nantes Universit\u00e9, \u00c9cole Centrale Nantes, Nantes, France","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I4210153365","https://openalex.org/I97188460"]},{"raw_affiliation_string":"LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","institution_ids":["https://openalex.org/I4210153365"]},{"raw_affiliation_string":"Nantes Univ - ECN - NANTES UNIVERSIT\u00c9 - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I97188460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5093952498"],"corresponding_institution_ids":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I4210153365","https://openalex.org/I97188460"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02761748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"10","issue":"4","first_page":"23","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reeb-graph","display_name":"Reeb graph","score":0.8230000138282776},{"id":"https://openalex.org/keywords/metric-measure-spaces","display_name":"metric measure spaces","score":0.9760000109672546},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.5569999814033508},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.8799999952316284},{"id":"https://openalex.org/keywords/probability-measures","display_name":"probability measures","score":0.6200000047683716},{"id":"https://openalex.org/keywords/data-visualization","display_name":"data visualization","score":0.44699999690055847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6029000282287598},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5357999801635742},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49399998784065247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41769999265670776},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3652999997138977},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3391000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31869998574256897},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s41468-026-00254-y","doi":"https://doi.org/10.1007/s41468-026-00254-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s41468-026-00254-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2506.02810","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.02810","pdf_url":"https://arxiv.org/pdf/2506.02810","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05097643v1","doi":null,"is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05097643","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied and Computational Topology, 2026, 10 (4), pp.23. &#x27E8;10.1007/s41468-026-00254-y&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2506.02810","doi":"https://doi.org/10.48550/arxiv.2506.02810","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.02810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.02810","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.02810","pdf_url":"https://arxiv.org/pdf/2506.02810","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8408888918","display_name":"Geometry in Data: Statistical Inference & Clustering","funder_award_id":"ANR-22-CE40-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415016709.pdf","grobid_xml":"https://content.openalex.org/works/W4415016709.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1499561838","https://openalex.org/W2000354818","https://openalex.org/W2014739666","https://openalex.org/W2020756904","https://openalex.org/W2027842533","https://openalex.org/W2121888429","https://openalex.org/W2157878484","https://openalex.org/W2173753796","https://openalex.org/W2217946182","https://openalex.org/W2335518360","https://openalex.org/W2612349766","https://openalex.org/W2640923064","https://openalex.org/W2727413762","https://openalex.org/W2781831736","https://openalex.org/W2830596730","https://openalex.org/W2895344618","https://openalex.org/W2902335845","https://openalex.org/W2952114199","https://openalex.org/W2962902468","https://openalex.org/W3040283615","https://openalex.org/W3100400426","https://openalex.org/W3111781256","https://openalex.org/W3122771322","https://openalex.org/W3184455115","https://openalex.org/W3214990680","https://openalex.org/W4213199372","https://openalex.org/W4248500611","https://openalex.org/W4322631077","https://openalex.org/W4403142246","https://openalex.org/W4403322200","https://openalex.org/W4404308518","https://openalex.org/W4409474691","https://openalex.org/W4414297648","https://openalex.org/W4415702410"],"related_works":["https://openalex.org/W3111781256","https://openalex.org/W3122771322","https://openalex.org/W4417182602","https://openalex.org/W2217946182","https://openalex.org/W2995406249","https://openalex.org/W7167926006","https://openalex.org/W2963212950","https://openalex.org/W2963606893","https://openalex.org/W7099861945","https://openalex.org/W2890370060"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-10T00:00:00"}
