{"id":"https://openalex.org/W2173753796","doi":"https://doi.org/10.1007/s10208-017-9370-z","title":"Structure and Stability of the One-Dimensional Mapper","display_name":"Structure and Stability of the One-Dimensional Mapper","publication_year":2017,"publication_date":"2017-10-30","ids":{"openalex":"https://openalex.org/W2173753796","doi":"https://doi.org/10.1007/s10208-017-9370-z","mag":"2173753796"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-017-9370-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-017-9370-z","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.05823","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Mathieu Carri\u00e8re","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mathieu Carri\u00e8re","raw_affiliation_strings":["Inria Saclay, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alan Turing, Ecole Polytechnique, 91120, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria Saclay, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alan Turing, Ecole Polytechnique, 91120, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210126360","https://openalex.org/I4210139461"]}]},{"author_position":"last","author":{"id":null,"display_name":"Steve Oudot","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Steve Oudot","raw_affiliation_strings":["Inria Saclay, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alan Turing, Ecole Polytechnique, 91120, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria Saclay, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alan Turing, Ecole Polytechnique, 91120, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210126360","https://openalex.org/I4210139461"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210126360","https://openalex.org/I4210139461"],"apc_list":{"value":2290,"currency":"USD","value_usd":2290},"apc_paid":null,"fwci":2.4343,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.89736015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"6","first_page":"1333","last_page":"1396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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":1.0,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6474000215530396},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5616000294685364},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5235000252723694},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.40130001306533813},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3939000070095062},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.38449999690055847},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.35600000619888306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7483999729156494},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6474000215530396},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5616000294685364},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5235000252723694},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3343999981880188},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33000001311302185},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2824999988079071},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2703000009059906},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C155673373","wikidata":"https://www.wikidata.org/wiki/Q1648886","display_name":"Structural stability","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2531000077724457}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10208-017-9370-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-017-9370-z","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.05823","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.05823","pdf_url":"https://arxiv.org/pdf/1511.05823","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,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01633101v2","is_oa":false,"landing_page_url":"https://hal.science/hal-01633101","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of Computational Mathematics, 2017, pp.1-64. &#x27E8;10.1007/s10208-017-9370-z&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.05823","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.05823","pdf_url":"https://arxiv.org/pdf/1511.05823","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,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1680409093","display_name":"Topological Data Analysis: Statistical Methods and Inference","funder_award_id":"ANR-13-BS01-0008","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1481615578","https://openalex.org/W1499561838","https://openalex.org/W1823996076","https://openalex.org/W1963491718","https://openalex.org/W2037613900","https://openalex.org/W2056761334","https://openalex.org/W2071164857","https://openalex.org/W2075608792","https://openalex.org/W2079527407","https://openalex.org/W2089472251","https://openalex.org/W2089763657","https://openalex.org/W2091677960","https://openalex.org/W2092052904","https://openalex.org/W2135830218","https://openalex.org/W2151335375","https://openalex.org/W2154187696","https://openalex.org/W2158407067","https://openalex.org/W2335396666","https://openalex.org/W2962902468","https://openalex.org/W3013843370","https://openalex.org/W4243672683","https://openalex.org/W4244087459","https://openalex.org/W4251358505"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-09-02T07:38:04.252551","created_date":"2016-06-24T00:00:00"}
