{"id":"https://openalex.org/W4294973985","doi":"https://doi.org/10.1007/s00224-023-10142-y","title":"Arithmetical Hierarchy of the Besicovitch-Stability of Noisy Tilings","display_name":"Arithmetical Hierarchy of the Besicovitch-Stability of Noisy Tilings","publication_year":2023,"publication_date":"2023-08-29","ids":{"openalex":"https://openalex.org/W4294973985","doi":"https://doi.org/10.1007/s00224-023-10142-y"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-023-10142-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-023-10142-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2209.01949","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005823280","display_name":"L\u00e9o Gayral","orcid":"https://orcid.org/0009-0003-1994-7413"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"L\u00e9o Gayral","raw_affiliation_strings":["IMT, Universit\u00e9 Toulouse III - Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 9, F-31062, France","IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMT, Universit\u00e9 Toulouse III - Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 9, F-31062, France","institution_ids":["https://openalex.org/I134560555"]},{"raw_affiliation_string":"IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555","https://openalex.org/I196454796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009309137","display_name":"Mathieu Sablik","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mathieu Sablik","raw_affiliation_strings":["IMT, Universit\u00e9 Toulouse III - Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 9, F-31062, France","IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMT, Universit\u00e9 Toulouse III - Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 9, F-31062, France","institution_ids":["https://openalex.org/I134560555"]},{"raw_affiliation_string":"IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555","https://openalex.org/I196454796"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005823280"],"corresponding_institution_ids":["https://openalex.org/I134560555","https://openalex.org/I196454796","https://openalex.org/I84500057"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.1859,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48530146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"67","issue":"6","first_page":"1209","last_page":"1240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","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/T12162","display_name":"Cellular Automata and Applications","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/T11567","display_name":"semigroups and automata theory","score":0.9994000196456909,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8239707350730896},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6825047135353088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6818196773529053},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.659612238407135},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.64576655626297},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5932210683822632},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.5551879405975342},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5476001501083374},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5271826982498169},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5108787417411804},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.4975629150867462},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.48297372460365295},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4568638503551483},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.30288201570510864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20555365085601807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1525309681892395},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.08882677555084229}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8239707350730896},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6825047135353088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6818196773529053},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.659612238407135},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.64576655626297},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5932210683822632},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.5551879405975342},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5476001501083374},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5271826982498169},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5108787417411804},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.4975629150867462},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.48297372460365295},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4568638503551483},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.30288201570510864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20555365085601807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1525309681892395},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.08882677555084229},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00224-023-10142-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-023-10142-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2209.01949","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.01949","pdf_url":"https://arxiv.org/pdf/2209.01949","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03771115v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03771115","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":"Theory of Computing Systems, 2023, 67 (6), pp.1209-1240. ⟨10.1007/s00224-023-10142-y⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2209.01949","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2209.01949","pdf_url":"https://arxiv.org/pdf/2209.01949","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W567294561","https://openalex.org/W1483888214","https://openalex.org/W1509579779","https://openalex.org/W1570408932","https://openalex.org/W1990043417","https://openalex.org/W1990125233","https://openalex.org/W2005248179","https://openalex.org/W2013126736","https://openalex.org/W2017025480","https://openalex.org/W2037469541","https://openalex.org/W2052038522","https://openalex.org/W2052399269","https://openalex.org/W2080896750","https://openalex.org/W2117302073","https://openalex.org/W2117832390","https://openalex.org/W2133245254","https://openalex.org/W2402515172","https://openalex.org/W2476570889","https://openalex.org/W2497732645","https://openalex.org/W2514471596","https://openalex.org/W2767752761","https://openalex.org/W2941392041","https://openalex.org/W2951481180","https://openalex.org/W2963223424","https://openalex.org/W3098115869","https://openalex.org/W3100759919","https://openalex.org/W3104237022","https://openalex.org/W3128735723","https://openalex.org/W3144756211","https://openalex.org/W3172548798","https://openalex.org/W4205976284","https://openalex.org/W4221016121","https://openalex.org/W4230422011","https://openalex.org/W4232277851","https://openalex.org/W4243563333","https://openalex.org/W4319736507","https://openalex.org/W6948181216"],"related_works":["https://openalex.org/W2120230527","https://openalex.org/W1536365843","https://openalex.org/W2125797022","https://openalex.org/W1490819493","https://openalex.org/W2100222222","https://openalex.org/W2048854384","https://openalex.org/W1637457106","https://openalex.org/W91167006","https://openalex.org/W4287108996","https://openalex.org/W62699086"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}