{"id":"https://openalex.org/W2504602122","doi":"https://doi.org/10.1007/978-3-319-33507-0_28","title":"Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve","display_name":"Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2504602122","doi":"https://doi.org/10.1007/978-3-319-33507-0_28","mag":"2504602122"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-33507-0_28","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-33507-0_28","pdf_url":null,"source":{"id":"https://openalex.org/S4210180650","display_name":"Springer proceedings in mathematics & statistics","issn_l":"2194-1009","issn":["2194-1009","2194-1017"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Springer Proceedings in Mathematics &amp; Statistics","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049569993","display_name":"Colas Schretter","orcid":"https://orcid.org/0000-0002-3938-3227"},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]},{"id":"https://openalex.org/I39327780","display_name":"iMinds","ror":"https://ror.org/03baec336","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I39327780"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Colas Schretter","raw_affiliation_strings":["ETRO Department, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium","IMinds, Gaston Crommenlaan 8, Box 102, 9050, Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETRO Department, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium","institution_ids":["https://openalex.org/I13469542"]},{"raw_affiliation_string":"IMinds, Gaston Crommenlaan 8, Box 102, 9050, Ghent, Belgium","institution_ids":["https://openalex.org/I39327780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058665232","display_name":"Zhijian He","orcid":"https://orcid.org/0000-0002-0730-5953"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhijian He","raw_affiliation_strings":["Tsinghua University, Haidian Dist., Beijing, 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University, Haidian Dist., Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021474812","display_name":"Mathieu Gerber","orcid":"https://orcid.org/0000-0001-6774-2330"},"institutions":[{"id":"https://openalex.org/I97565354","display_name":"University of Lausanne","ror":"https://ror.org/019whta54","country_code":"CH","type":"education","lineage":["https://openalex.org/I97565354"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mathieu Gerber","raw_affiliation_strings":["Universit\u00e9 de Lausanne, 1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lausanne, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I97565354"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059273710","display_name":"ChopinNicolas","orcid":null},"institutions":[{"id":"https://openalex.org/I84009706","display_name":"ENSAE Paris","ror":"https://ror.org/01fz7mn40","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210108488","https://openalex.org/I4210145102","https://openalex.org/I84009706"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Chopin","raw_affiliation_strings":["Centre de Recherche En \u00c9conomie Et Statistique, ENSAE, 92245, Malakoff, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Recherche En \u00c9conomie Et Statistique, ENSAE, 92245, Malakoff, France","institution_ids":["https://openalex.org/I84009706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086124758","display_name":"Harald Niederreiter","orcid":"https://orcid.org/0000-0001-6224-9969"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Harald Niederreiter","raw_affiliation_strings":["RICAM, Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RICAM, Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5049569993"],"corresponding_institution_ids":["https://openalex.org/I13469542","https://openalex.org/I39327780"],"apc_list":null,"apc_paid":null,"fwci":6.3464,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.96289063,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"531","last_page":"544"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/fibonacci-number","display_name":"Fibonacci number","score":0.8699098229408264},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"Golden ratio","score":0.775031328201294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6618714332580566},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6280936002731323},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.4893884062767029},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.47897031903266907},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40448492765426636},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3480069637298584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2920273244380951},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.2801303267478943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12883532047271729}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8699098229408264},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.775031328201294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6618714332580566},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6280936002731323},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4893884062767029},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.47897031903266907},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40448492765426636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3480069637298584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2920273244380951},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2801303267478943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12883532047271729},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-319-33507-0_28","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-33507-0_28","pdf_url":null,"source":{"id":"https://openalex.org/S4210180650","display_name":"Springer proceedings in mathematics & statistics","issn_l":"2194-1009","issn":["2194-1009","2194-1017"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Springer Proceedings in Mathematics &amp; Statistics","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-02391228v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02391228","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":"Monte Carlo and Quasi-Monte Carlo Methods, pp.531-544, 2016, &#x27E8;10.1007/978-3-319-33507-0_28&#x27E9;","raw_type":"Book sections"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/6e3e2772-4900-47fe-a41d-5c709e353b5e","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/6e3e2772-4900-47fe-a41d-5c709e353b5e","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Schretter, C, He, Z, Gerber, M, Chopin, N & Niederreiter, H 2016, Van der Corput and Golden Ratio sequences along the Hilbert space filling curve. in Monte Carlo and Quasi-Monte Carlo Methods : MCQMC, Leuven, Belgium, April 2014. Springer Proceedings in Mathematics & Statistics, Springer International Publishing AG. < http://link.springer.com/chapter/10.1007/978-3-319-33507-0_28 >","raw_type":"bookPart"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W74732468","https://openalex.org/W314363935","https://openalex.org/W981517633","https://openalex.org/W1933639893","https://openalex.org/W1966612958","https://openalex.org/W1976544585","https://openalex.org/W2005503189","https://openalex.org/W2010306732","https://openalex.org/W2032709962","https://openalex.org/W2043419861","https://openalex.org/W2077542803","https://openalex.org/W2100668339","https://openalex.org/W2151135734","https://openalex.org/W2153750152","https://openalex.org/W2887152882","https://openalex.org/W2963545926","https://openalex.org/W2997027240","https://openalex.org/W3099473245","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W4210464319","https://openalex.org/W4287828559","https://openalex.org/W3012096978","https://openalex.org/W3131374234","https://openalex.org/W4302325333","https://openalex.org/W2284786951","https://openalex.org/W3185543273","https://openalex.org/W2783128811","https://openalex.org/W3203770208","https://openalex.org/W4282570110"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2025-10-10T00:00:00"}