{"id":"https://openalex.org/W2965813887","doi":"https://doi.org/10.1007/s10107-020-01558-2","title":"A tight degree 4 sum-of-squares lower bound for the Sherrington\u2013Kirkpatrick Hamiltonian","display_name":"A tight degree 4 sum-of-squares lower bound for the Sherrington\u2013Kirkpatrick Hamiltonian","publication_year":2020,"publication_date":"2020-11-05","ids":{"openalex":"https://openalex.org/W2965813887","doi":"https://doi.org/10.1007/s10107-020-01558-2","mag":"2965813887"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01558-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01558-2","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.11686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Dmitriy Kunisky","orcid":"https://orcid.org/0000-0002-0854-4067"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dmitriy Kunisky","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, 10012, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-0854-4067","affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, 10012, NY, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":null,"display_name":"Afonso S. Bandeira","orcid":"https://orcid.org/0000-0002-7331-7557"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Afonso S. Bandeira","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich, Zurich, 8092, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-7331-7557","affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, Zurich, 8092, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4335,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6683509,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"190","issue":"1-2","first_page":"721","last_page":"759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3562000095844269,"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":0.3562000095844269,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.18639999628067017,"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/T12303","display_name":"Tensor decomposition and applications","score":0.11060000211000443,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7432000041007996},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6456999778747559},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6284000277519226},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4916999936103821},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4788999855518341},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4677000045776367},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.3765000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8763999938964844},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7432000041007996},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6456999778747559},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6284000277519226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5874999761581421},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4916999936103821},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4788999855518341},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3855000138282776},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3425999879837036},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.32179999351501465},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2906000018119812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28790000081062317},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.28450000286102295}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-020-01558-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01558-2","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1907.11686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.11686","pdf_url":"https://arxiv.org/pdf/1907.11686","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.4230/lipics.icalp.2021.90","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2021.90","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.11686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.11686","pdf_url":"https://arxiv.org/pdf/1907.11686","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2485349017","display_name":null,"funder_award_id":"CCF-2008920","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5550787473","display_name":null,"funder_award_id":"DMS-1719545","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6452663133","display_name":null,"funder_award_id":"DMS-1712730","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6591094171","display_name":"AF: SMALL: Further Investigation of the Sum of Squares Hierarchy","funder_award_id":"2008920","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/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W653291882","https://openalex.org/W1489953262","https://openalex.org/W1497040579","https://openalex.org/W1560153690","https://openalex.org/W1739872454","https://openalex.org/W1967344706","https://openalex.org/W2022820481","https://openalex.org/W2039292332","https://openalex.org/W2047265165","https://openalex.org/W2081131431","https://openalex.org/W2094235750","https://openalex.org/W2095058792","https://openalex.org/W2140874510","https://openalex.org/W2156085019","https://openalex.org/W2165281529","https://openalex.org/W2168417806","https://openalex.org/W2216459995","https://openalex.org/W2306186691","https://openalex.org/W2401610261","https://openalex.org/W2770109286","https://openalex.org/W2943555824","https://openalex.org/W2963349778","https://openalex.org/W2964013189","https://openalex.org/W2971940014","https://openalex.org/W3011822549","https://openalex.org/W3034256405","https://openalex.org/W3099419577","https://openalex.org/W4210422269","https://openalex.org/W4240189201","https://openalex.org/W6600379903","https://openalex.org/W6650821145"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-08-13T00:00:00"}
