{"id":"https://openalex.org/W2046346696","doi":"https://doi.org/10.1137/s089547980139087x","title":"The Distance of Potentially Stable Sign Patterns to the Unstable Matrices","display_name":"The Distance of Potentially Stable Sign Patterns to the Unstable Matrices","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2046346696","doi":"https://doi.org/10.1137/s089547980139087x","mag":"2046346696"},"language":"en","primary_location":{"id":"doi:10.1137/s089547980139087x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089547980139087x","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","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/A5100306465","display_name":"Lin Qing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qing Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064094814","display_name":"D.D. Olesky","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. D. Olesky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110087820","display_name":"P. van den Driessche","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. van den Driessche","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.16827059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"24","issue":"2","first_page":"356","last_page":"367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9957000017166138,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9930999875068665,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8411535024642944},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.7761518955230713},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6930533647537231},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6559742093086243},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5802431106567383},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"Distance matrix","score":0.5217557549476624},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.4756578803062439},{"id":"https://openalex.org/keywords/distance-matrices-in-phylogeny","display_name":"Distance matrices in phylogeny","score":0.47398868203163147},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.47326162457466125},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.4380704462528229},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22249865531921387},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.19270798563957214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07452422380447388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8411535024642944},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.7761518955230713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6930533647537231},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6559742093086243},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5802431106567383},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.5217557549476624},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4756578803062439},{"id":"https://openalex.org/C5349765","wikidata":"https://www.wikidata.org/wiki/Q5282866","display_name":"Distance matrices in phylogeny","level":2,"score":0.47398868203163147},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.47326162457466125},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4380704462528229},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22249865531921387},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.19270798563957214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07452422380447388},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s089547980139087x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s089547980139087x","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/18683","is_oa":false,"landing_page_url":"https://hdl.handle.net/1828/18683","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Thesis"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W594391557","https://openalex.org/W626808453","https://openalex.org/W1606198627","https://openalex.org/W1968741513","https://openalex.org/W1988732861","https://openalex.org/W2021437094","https://openalex.org/W2021501770","https://openalex.org/W2035180740","https://openalex.org/W2036513250","https://openalex.org/W2040552465","https://openalex.org/W2047917018"],"related_works":["https://openalex.org/W2001076853","https://openalex.org/W1872375678","https://openalex.org/W4387171312","https://openalex.org/W4388316203","https://openalex.org/W4206923957","https://openalex.org/W4285790638","https://openalex.org/W4235784610","https://openalex.org/W2952169863","https://openalex.org/W2967856490","https://openalex.org/W4236196889"],"abstract_inverted_index":{"A":[0,16],"measure":[1],"$\\delta_{us}(A)$":[2],"of":[3,41,84,105],"the":[4,8,71,128,131],"relative":[5,68],"distance":[6,69,129],"to":[7,21,50,70,97,126,130],"unstable":[9,72,132],"matrices":[10,133],"for":[11,103,114,134],"a":[12,22,47,81,109],"stable":[13,24,57,63,88,138],"n-by-n":[14],"matrix":[15,64,100,110],"is":[17,28,36,46,74,92,101,111],"defined":[18],"and":[19,34,52,60,79,94,120],"extended":[20],"potentially":[23,56,87,137],"sign":[25,58,90,139],"pattern.":[26],"It":[27],"shown":[29],"that":[30],"$\\delta_{us}(A)":[31],"\\in":[32],"(0,1]$":[33],"$|\\delta_{us}(A)-\\delta_{us}(B)|$":[35],"bounded":[37],"above":[38],"in":[39],"terms":[40],"||A-B||2.":[42],"For":[43,77],"n=2,":[44],"there":[45],"unique":[48],"(up":[49],"permutation":[51],"signature":[53],"similarity)":[54],"minimally":[55,86],"pattern,":[59],"an":[61,95,98],"optimal":[62,99],"(i.e.,":[65],"having":[66],"maximal":[67],"matrices)":[73],"determined":[75],"analytically.":[76],"n=3":[78],"4":[80],"complete":[82],"list":[83],"all":[85],"tree":[89],"patterns":[91],"given":[93],"approximation":[96],"found":[102],"each":[104],"these":[106,121],"patterns.":[107,140],"Such":[108],"also":[112],"computed":[113],"some":[115],"rooted":[116],"trees":[117],"with":[118],"n=5,":[119],"results":[122],"can":[123],"be":[124],"applied":[125],"estimate":[127],"more":[135],"general":[136]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}