{"id":"https://openalex.org/W2606436810","doi":"https://doi.org/10.1007/s10208-019-09417-z","title":"Operator Scaling: Theory and Applications","display_name":"Operator Scaling: Theory and Applications","publication_year":2019,"publication_date":"2019-05-06","ids":{"openalex":"https://openalex.org/W2606436810","doi":"https://doi.org/10.1007/s10208-019-09417-z","mag":"2606436810"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-019-09417-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-019-09417-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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.03730","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027551258","display_name":"Ankit Garg","orcid":"https://orcid.org/0000-0002-3343-0061"},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]},{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB","IN"],"is_corresponding":true,"raw_author_name":"Ankit Garg","raw_affiliation_strings":["Microsoft Research India, Bengaluru, India","(Microsoft)"],"affiliations":[{"raw_affiliation_string":"Microsoft Research India, Bengaluru, India","institution_ids":["https://openalex.org/I4210124949"]},{"raw_affiliation_string":"(Microsoft)","institution_ids":["https://openalex.org/I4210164937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022317936","display_name":"Leonid Gurvits","orcid":"https://orcid.org/0000-0002-0694-2459"},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonid Gurvits","raw_affiliation_strings":["Department of Computer Science, The City College of New York, New York, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The City College of New York, New York, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101874933","display_name":"Rafael Oliveira","orcid":"https://orcid.org/0000-0001-8917-8689"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]},{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rafael Oliveira","raw_affiliation_strings":["Simons Institute, Berkeley, USA","Princeton University"],"affiliations":[{"raw_affiliation_string":"Simons Institute, Berkeley, USA","institution_ids":["https://openalex.org/I4210107338"]},{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039043184","display_name":"Avi Wigderson","orcid":"https://orcid.org/0000-0002-1539-1417"},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Avi Wigderson","raw_affiliation_strings":["Institute for Advanced Study, Princeton, USA","Institute for Advanced Study, Princeton, (USA)"],"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study, Princeton, USA","institution_ids":["https://openalex.org/I40036882"]},{"raw_affiliation_string":"Institute for Advanced Study, Princeton, (USA)","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027551258"],"corresponding_institution_ids":["https://openalex.org/I4210124949","https://openalex.org/I4210164937"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68438734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"20","issue":"2","first_page":"223","last_page":"290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.5766546726226807},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5308904051780701},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.48806464672088623},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.43848133087158203},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42656978964805603},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.4115538001060486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39266178011894226},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35816317796707153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3514149785041809},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15433093905448914},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12223869562149048}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5766546726226807},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5308904051780701},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.48806464672088623},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.43848133087158203},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42656978964805603},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.4115538001060486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39266178011894226},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35816317796707153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3514149785041809},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15433093905448914},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12223869562149048},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10208-019-09417-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-019-09417-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:1511.03730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.03730","pdf_url":"https://arxiv.org/pdf/1511.03730","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:2606436810","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1511.03730","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.1511.03730","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.03730","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":"pmh:oai:arXiv.org:1511.03730","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.03730","pdf_url":"https://arxiv.org/pdf/1511.03730","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1943969787","display_name":null,"funder_award_id":"CCF-1412958","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3089858946","display_name":null,"funder_award_id":"CCF-1523816","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5226981347","display_name":null,"funder_award_id":"CCF-1149888","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8047500120","display_name":"AF:  Small:  New Techniques for Private Information Retrieval and Locally Decodable Codes","funder_award_id":"1523816","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8233928647","display_name":null,"funder_award_id":"1149888","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8513554395","display_name":null,"funder_award_id":"1451191","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G882115978","display_name":"AF: Large: Theory of Computation - Pushing the State-of-the-Art","funder_award_id":"1412958","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/F4320309292","display_name":"Princeton University","ror":"https://ror.org/00hx57361"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2606436810.pdf","grobid_xml":"https://content.openalex.org/works/W2606436810.grobid-xml"},"referenced_works_count":81,"referenced_works":["https://openalex.org/W15553240","https://openalex.org/W71789597","https://openalex.org/W181977719","https://openalex.org/W201320490","https://openalex.org/W644150847","https://openalex.org/W1529220174","https://openalex.org/W1535255862","https://openalex.org/W1666394328","https://openalex.org/W1863071953","https://openalex.org/W1966991151","https://openalex.org/W1967348711","https://openalex.org/W1967971164","https://openalex.org/W1968380471","https://openalex.org/W1974934818","https://openalex.org/W1984314155","https://openalex.org/W1987465321","https://openalex.org/W1990283121","https://openalex.org/W1991584875","https://openalex.org/W2000141173","https://openalex.org/W2003979730","https://openalex.org/W2006912660","https://openalex.org/W2015555828","https://openalex.org/W2016183859","https://openalex.org/W2016949650","https://openalex.org/W2026036943","https://openalex.org/W2027044307","https://openalex.org/W2033637560","https://openalex.org/W2033766285","https://openalex.org/W2037417588","https://openalex.org/W2050735826","https://openalex.org/W2052125266","https://openalex.org/W2052526078","https://openalex.org/W2060462816","https://openalex.org/W2061853206","https://openalex.org/W2066144963","https://openalex.org/W2073240615","https://openalex.org/W2073412179","https://openalex.org/W2074392054","https://openalex.org/W2074897640","https://openalex.org/W2076795871","https://openalex.org/W2082002555","https://openalex.org/W2089368046","https://openalex.org/W2092082049","https://openalex.org/W2107547393","https://openalex.org/W2109995168","https://openalex.org/W2116102644","https://openalex.org/W2121894367","https://openalex.org/W2125251485","https://openalex.org/W2132646786","https://openalex.org/W2133353165","https://openalex.org/W2136276291","https://openalex.org/W2142326730","https://openalex.org/W2142920747","https://openalex.org/W2148231801","https://openalex.org/W2158111726","https://openalex.org/W2162960148","https://openalex.org/W2170546552","https://openalex.org/W2171597564","https://openalex.org/W2177482211","https://openalex.org/W2200115418","https://openalex.org/W2258857078","https://openalex.org/W2282196733","https://openalex.org/W2318517541","https://openalex.org/W2319466955","https://openalex.org/W2330662384","https://openalex.org/W2333555861","https://openalex.org/W2399980850","https://openalex.org/W2574511727","https://openalex.org/W2592548894","https://openalex.org/W2792881463","https://openalex.org/W2911280162","https://openalex.org/W2949623309","https://openalex.org/W2950616565","https://openalex.org/W2962745033","https://openalex.org/W2962789909","https://openalex.org/W2962817959","https://openalex.org/W4250950881","https://openalex.org/W4256666875","https://openalex.org/W4299838326","https://openalex.org/W6607317244","https://openalex.org/W6780146607"],"related_works":["https://openalex.org/W2473128238","https://openalex.org/W2951834959","https://openalex.org/W1966991151","https://openalex.org/W2956865288","https://openalex.org/W1514995304","https://openalex.org/W3126681082","https://openalex.org/W2950357695","https://openalex.org/W2294074214","https://openalex.org/W1798002591","https://openalex.org/W2253408331","https://openalex.org/W2021193487","https://openalex.org/W2939109135","https://openalex.org/W1827476544","https://openalex.org/W2119127687","https://openalex.org/W1992256491","https://openalex.org/W2884952491","https://openalex.org/W2052427582","https://openalex.org/W2726560500","https://openalex.org/W2767521804","https://openalex.org/W2981665229"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
