{"id":"https://openalex.org/W2763062829","doi":"https://doi.org/10.1145/3188745.3188794","title":"The Paulsen problem, continuous operator scaling, and smoothed analysis","display_name":"The Paulsen problem, continuous operator scaling, and smoothed analysis","publication_year":2018,"publication_date":"2018-06-20","ids":{"openalex":"https://openalex.org/W2763062829","doi":"https://doi.org/10.1145/3188745.3188794","mag":"2763062829"},"language":"en","primary_location":{"id":"doi:10.1145/3188745.3188794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188794","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046446942","display_name":"Tsz Chiu Kwok","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Tsz Chiu Kwok","raw_affiliation_strings":["University of Waterloo, Canada","University of Waterloo , Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008440961","display_name":"Lap Chi Lau","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lap Chi Lau","raw_affiliation_strings":["University of Waterloo, Canada","University of Waterloo , Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024980585","display_name":"Yin Tat Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yin Tat Lee","raw_affiliation_strings":["University of Washington, USA","University of Washington , USA "],"affiliations":[{"raw_affiliation_string":"University of Washington, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington , USA ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020684035","display_name":"Akshay Ramachandran","orcid":"https://orcid.org/0000-0001-7347-9735"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Akshay Ramachandran","raw_affiliation_strings":["University of Waterloo, Canada","University of Waterloo , Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046446942"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.4875,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64594564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"182","last_page":"189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.7472407817840576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6965369582176208},{"id":"https://openalex.org/keywords/parsevals-theorem","display_name":"Parseval's theorem","score":0.6489270925521851},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6174414157867432},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5770382881164551},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5289701819419861},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5070545673370361},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3805912435054779},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3078979253768921},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.14166873693466187},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1357869803905487},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.10372930765151978}],"concepts":[{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.7472407817840576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6965369582176208},{"id":"https://openalex.org/C89451469","wikidata":"https://www.wikidata.org/wiki/Q1443036","display_name":"Parseval's theorem","level":5,"score":0.6489270925521851},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6174414157867432},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5770382881164551},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5289701819419861},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5070545673370361},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3805912435054779},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3078979253768921},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.14166873693466187},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1357869803905487},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.10372930765151978},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3188745.3188794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188794","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1710.02587","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.02587","pdf_url":"https://arxiv.org/pdf/1710.02587","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:2763062829","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1710.02587","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":"doi:10.48550/arxiv.1710.02587","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.02587","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:10.1145/3188745.3188794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188794","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1906418360","display_name":null,"funder_award_id":"1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6275837611","display_name":null,"funder_award_id":"2950-120719","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G80067104","display_name":null,"funder_award_id":"2950-120715","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G874486094","display_name":null,"funder_award_id":"CCF-1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2763062829.pdf","grobid_xml":"https://content.openalex.org/works/W2763062829.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W634207668","https://openalex.org/W1488435683","https://openalex.org/W1560153690","https://openalex.org/W1571821595","https://openalex.org/W1670485642","https://openalex.org/W1770596155","https://openalex.org/W1966245736","https://openalex.org/W1966991151","https://openalex.org/W1972334901","https://openalex.org/W1980621453","https://openalex.org/W1982562599","https://openalex.org/W1990283121","https://openalex.org/W1993000235","https://openalex.org/W1993677524","https://openalex.org/W1996415070","https://openalex.org/W2010693285","https://openalex.org/W2034025033","https://openalex.org/W2052125266","https://openalex.org/W2072565885","https://openalex.org/W2075014089","https://openalex.org/W2086869478","https://openalex.org/W2094235750","https://openalex.org/W2094366212","https://openalex.org/W2094600024","https://openalex.org/W2107808918","https://openalex.org/W2119337797","https://openalex.org/W2131172946","https://openalex.org/W2132702454","https://openalex.org/W2143355494","https://openalex.org/W2157491291","https://openalex.org/W2162960148","https://openalex.org/W2163296328","https://openalex.org/W2172004671","https://openalex.org/W2232865852","https://openalex.org/W2261415748","https://openalex.org/W2487688054","https://openalex.org/W2543706324","https://openalex.org/W2592938513","https://openalex.org/W2605569246","https://openalex.org/W2606394847","https://openalex.org/W2606436810","https://openalex.org/W2610466503","https://openalex.org/W2610680804","https://openalex.org/W2610857016","https://openalex.org/W2950633396","https://openalex.org/W2951834959","https://openalex.org/W2962719003","https://openalex.org/W2962763948","https://openalex.org/W2963422302","https://openalex.org/W2963595145","https://openalex.org/W2964063683","https://openalex.org/W2965497096","https://openalex.org/W3036945217","https://openalex.org/W3102478671","https://openalex.org/W4229706427","https://openalex.org/W4250334485","https://openalex.org/W4292170079","https://openalex.org/W6736828128","https://openalex.org/W6785711600"],"related_works":["https://openalex.org/W2942057781","https://openalex.org/W2766533971","https://openalex.org/W3036852563","https://openalex.org/W2621572195","https://openalex.org/W2952539829","https://openalex.org/W2914000446","https://openalex.org/W2962790878","https://openalex.org/W2889902862","https://openalex.org/W2971497379","https://openalex.org/W2606176578","https://openalex.org/W2201865757","https://openalex.org/W2922161739","https://openalex.org/W3178716795","https://openalex.org/W2952868803","https://openalex.org/W2489279134","https://openalex.org/W3160895500","https://openalex.org/W2183261441","https://openalex.org/W2951276273","https://openalex.org/W2947505063","https://openalex.org/W1532694742"],"abstract_inverted_index":{"The":[0,114],"Paulsen":[1],"problem":[2,7],"is":[3,30,67,80,98,118],"a":[4,34],"basic":[5],"open":[6,116],"in":[8],"operator":[9],"theory:":[10],"Given":[11,54],"vectors":[12,37,130],"u1,":[13,55],"\u2026,":[14,39,56],"un":[15],"\u2208":[16,41],"\u211dd":[17,42],"that":[18,43,90],"are":[19,104],"\u0454-nearly":[20,96,105],"satisfying":[21],"the":[22,26,46,50,58,62,78,82,91,120,127],"Parseval\u2019s":[23,47],"condition":[24,48],"and":[25,49,102],"equal":[27,51],"norm":[28,52],"condition,":[29],"it":[31],"close":[32],"to":[33],"set":[35,63,83],"of":[36,64,84,94,126,129],"v1,":[38],"vn":[40],"exactly":[44],"satisfy":[45],"condition?":[53],"un,":[57],"squared":[59,92,108,121],"distance":[60,93,109,122],"(to":[61],"exact":[65,85],"solutions)":[66],"defined":[68],"as":[69],"infv":[70],"\u2211i=1n":[71],"||":[72],"ui":[73],"\u2212":[74],"vi":[75],"||22":[76],"where":[77],"infimum":[79],"over":[81],"solutions.":[86],"Previous":[87],"results":[88],"show":[89],"any":[95],"solution":[97],"at":[99,110],"most":[100],"O(poly(d,n,\u0454))":[101],"there":[103],"solutions":[106],"with":[107],"least":[111],"\u03a9(d":[112],"\u0454).":[113],"fundamental":[115],"question":[117],"whether":[119],"can":[123],"be":[124],"independent":[125],"number":[128],"n.":[131]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}