{"id":"https://openalex.org/W1554433915","doi":"https://doi.org/10.1007/s10444-016-9478-8","title":"Optimal configurations of lines and a statistical application","display_name":"Optimal configurations of lines and a statistical application","publication_year":2016,"publication_date":"2016-08-11","ids":{"openalex":"https://openalex.org/W1554433915","doi":"https://doi.org/10.1007/s10444-016-9478-8","mag":"1554433915"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-016-9478-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-016-9478-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10444-016-9478-8.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10444-016-9478-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030279456","display_name":"Fran\u00e7ois Bachoc","orcid":"https://orcid.org/0000-0001-5336-5714"},"institutions":[{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]},{"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/I134560555","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]},{"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","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Bachoc","raw_affiliation_strings":["Toulouse Mathematics Institute, University Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France","Toulouse Mathematics Institute, University Paul Sabatier, Toulouse Cedex 9, France 31062#TAB#"],"affiliations":[{"raw_affiliation_string":"Toulouse Mathematics Institute, University Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555"]},{"raw_affiliation_string":"Toulouse Mathematics Institute, University Paul Sabatier, Toulouse Cedex 9, France 31062#TAB#","institution_ids":["https://openalex.org/I4210098964","https://openalex.org/I134560555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029839615","display_name":"Martin Ehler","orcid":"https://orcid.org/0000-0002-3247-6279"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Martin Ehler","raw_affiliation_strings":["Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria","Department of Mathematics, University of Vienna, Vienna, Austria A-1090#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Vienna, Austria A-1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009720755","display_name":"Manuel Gr\u00e4f","orcid":"https://orcid.org/0000-0002-9258-9689"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Manuel Gr\u00e4f","raw_affiliation_strings":["Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria","Department of Mathematics, University of Vienna, Vienna, Austria A-1090#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Mathematics, University of Vienna, Vienna, Austria A-1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030279456"],"corresponding_institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964","https://openalex.org/I84500057"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00212372,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"1","first_page":"113","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6314078569412231},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.6280859708786011},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5124099850654602},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44982922077178955},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.42829880118370056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40357282757759094},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3697623610496521},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34453627467155457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34302058815956116},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3202970623970032},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17243963479995728}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6314078569412231},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.6280859708786011},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5124099850654602},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44982922077178955},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.42829880118370056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40357282757759094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3697623610496521},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34453627467155457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34302058815956116},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3202970623970032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17243963479995728},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10444-016-9478-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-016-9478-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10444-016-9478-8.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.00444","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.00444","pdf_url":"https://arxiv.org/pdf/1503.00444","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":"","raw_type":"text"},{"id":"mag:1554433915","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1503.00444.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:info:fedora/oai:univie.ac.at:o:475257","is_oa":true,"landing_page_url":"https://phaidra.univie.ac.at/o:475257","pdf_url":null,"source":{"id":"https://openalex.org/S4306401993","display_name":"Phaidra (Universit\u00e4t Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129774422","host_organization_name":"University of Vienna","host_organization_lineage":["https://openalex.org/I129774422"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1019-7168","raw_type":"article"},{"id":"doi:10.48550/arxiv.1503.00444","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.00444","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10444-016-9478-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-016-9478-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10444-016-9478-8.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2916271932","display_name":null,"funder_award_id":"VRG12-009","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"}],"funders":[{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1554433915.pdf","grobid_xml":"https://content.openalex.org/works/W1554433915.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1605351220","https://openalex.org/W1879145692","https://openalex.org/W1916127968","https://openalex.org/W2009462809","https://openalex.org/W2018529115","https://openalex.org/W2029734006","https://openalex.org/W2035469609","https://openalex.org/W2047569290","https://openalex.org/W2055815775","https://openalex.org/W2060002743","https://openalex.org/W2084196626","https://openalex.org/W2087255259","https://openalex.org/W2130853073","https://openalex.org/W2152345982","https://openalex.org/W6814994134"],"related_works":["https://openalex.org/W59837522","https://openalex.org/W2999105568","https://openalex.org/W2106560786","https://openalex.org/W2754529490","https://openalex.org/W1568343651","https://openalex.org/W2050900474","https://openalex.org/W2752549241","https://openalex.org/W87396886","https://openalex.org/W1728329879","https://openalex.org/W2018490654","https://openalex.org/W2964029738","https://openalex.org/W2797218201","https://openalex.org/W2558887336","https://openalex.org/W125908803","https://openalex.org/W2086413511","https://openalex.org/W2950708571","https://openalex.org/W936536805","https://openalex.org/W2093047512","https://openalex.org/W3081445885","https://openalex.org/W2909270161"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,51,63,70],"construction":[3],"of":[4,13,38,44,65],"confidence":[5],"intervals":[6],"in":[7,19],"statistics,":[8],"we":[9,28],"study":[10],"optimal":[11],"configurations":[12,43],"2":[14,45],"d":[15,46],"\u2212":[16,47],"1":[17,48],"lines":[18,49],"real":[20],"projective":[21],"space":[22],"\u211d\u2119":[23],"d\u22121.":[24],"For":[25],"small":[26],"d,":[27],"determine":[29],"line":[30],"sets":[31],"that":[32,56],"numerically":[33],"minimize":[34],"a":[35,66],"wide":[36],"variety":[37],"potential":[39],"functions":[40],"among":[41],"all":[42],"through":[50],"origin.":[52],"Numerical":[53],"experiments":[54],"verify":[55],"our":[57],"findings":[58],"enable":[59],"to":[60],"assess":[61],"efficiently":[62],"tightness":[64],"bound":[67],"arising":[68],"from":[69],"statistical":[71],"literature.":[72]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
