{"id":"https://openalex.org/W2087040380","doi":"https://doi.org/10.1137/0614060","title":"Compartmental Modeling and Second-Moment Analysis of State Space Systems","display_name":"Compartmental Modeling and Second-Moment Analysis of State Space Systems","publication_year":1993,"publication_date":"1993-07-01","ids":{"openalex":"https://openalex.org/W2087040380","doi":"https://doi.org/10.1137/0614060","mag":"2087040380"},"language":"en","primary_location":{"id":"doi:10.1137/0614060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614060","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/A5009770702","display_name":"Dennis S. Bernstein","orcid":"https://orcid.org/0000-0003-0399-3039"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I4210135154","display_name":"Sun Nuclear (United States)","ror":"https://ror.org/043kws463","country_code":"US","type":"company","lineage":["https://openalex.org/I4210135154"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dennis S. Bernstein","raw_affiliation_strings":["Harris Corporation, Mail Stop 22/4847, Melbourne, Florida 32902","Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harris Corporation, Mail Stop 22/4847, Melbourne, Florida 32902","institution_ids":["https://openalex.org/I4210135154"]},{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114255781","display_name":"David C. Hyland","orcid":"https://orcid.org/0000-0001-9726-3509"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I4210135154","display_name":"Sun Nuclear (United States)","ror":"https://ror.org/043kws463","country_code":"US","type":"company","lineage":["https://openalex.org/I4210135154"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David C. Hyland","raw_affiliation_strings":["Harris Corporation, Mail Stop 22/4847, Melbourne, Florida 32902","Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harris Corporation, Mail Stop 22/4847, Melbourne, Florida 32902","institution_ids":["https://openalex.org/I4210135154"]},{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":95,"citation_normalized_percentile":{"value":0.22669063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"3","first_page":"880","last_page":"901"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9947999715805054,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8379614353179932},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6964206695556641},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5768983960151672},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5369422435760498},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.533892810344696},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5161491632461548},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4676624834537506},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4599240720272064},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4564902186393738},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.44395118951797485},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4400462508201599},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43157389760017395},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.41658106446266174},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4073488414287567},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.245748370885849},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09050297737121582}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8379614353179932},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6964206695556641},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5768983960151672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5369422435760498},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.533892810344696},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5161491632461548},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4676624834537506},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4599240720272064},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4564902186393738},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.44395118951797485},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4400462508201599},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43157389760017395},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.41658106446266174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4073488414287567},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.245748370885849},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09050297737121582},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0614060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0614060","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W213501209","https://openalex.org/W239577987","https://openalex.org/W852592595","https://openalex.org/W1484199093","https://openalex.org/W1488435683","https://openalex.org/W1500921805","https://openalex.org/W1503543307","https://openalex.org/W1526841806","https://openalex.org/W1529274881","https://openalex.org/W1530239534","https://openalex.org/W1539689348","https://openalex.org/W1584477029","https://openalex.org/W1952568655","https://openalex.org/W1965640670","https://openalex.org/W1972447015","https://openalex.org/W1982848188","https://openalex.org/W1984050667","https://openalex.org/W1985991529","https://openalex.org/W1987442494","https://openalex.org/W1989779205","https://openalex.org/W1990656395","https://openalex.org/W1991579213","https://openalex.org/W1996851673","https://openalex.org/W1998388140","https://openalex.org/W2003137566","https://openalex.org/W2005789397","https://openalex.org/W2006101270","https://openalex.org/W2007876331","https://openalex.org/W2015464381","https://openalex.org/W2019001673","https://openalex.org/W2020564215","https://openalex.org/W2022587566","https://openalex.org/W2022656677","https://openalex.org/W2034168406","https://openalex.org/W2034883606","https://openalex.org/W2036033309","https://openalex.org/W2038525572","https://openalex.org/W2043596157","https://openalex.org/W2046559445","https://openalex.org/W2050852065","https://openalex.org/W2056732290","https://openalex.org/W2060018371","https://openalex.org/W2064251523","https://openalex.org/W2069970818","https://openalex.org/W2070401957","https://openalex.org/W2075920047","https://openalex.org/W2076467525","https://openalex.org/W2080476921","https://openalex.org/W2081837399","https://openalex.org/W2095477585","https://openalex.org/W2095590702","https://openalex.org/W2102615935","https://openalex.org/W2144716010","https://openalex.org/W2146240297","https://openalex.org/W2148533644","https://openalex.org/W2148835469","https://openalex.org/W2153411247","https://openalex.org/W2153624328","https://openalex.org/W2163433943","https://openalex.org/W2164301889","https://openalex.org/W2168830285","https://openalex.org/W2322982587","https://openalex.org/W2419507668","https://openalex.org/W2476238858","https://openalex.org/W2527383467","https://openalex.org/W2567294192","https://openalex.org/W2797638056","https://openalex.org/W4231122727","https://openalex.org/W4297582748","https://openalex.org/W4298691646"],"related_works":["https://openalex.org/W2330333053","https://openalex.org/W2348046789","https://openalex.org/W2323013444","https://openalex.org/W2161606278","https://openalex.org/W1561236277","https://openalex.org/W60641320","https://openalex.org/W2349620591","https://openalex.org/W351236607","https://openalex.org/W2105685401","https://openalex.org/W2018396125"],"abstract_inverted_index":{"Compartmental":[0],"models":[1,19],"involve":[2],"nonnegative":[3],"state":[4,38,48,106],"variables":[5,107],"that":[6,79],"exchange":[7],"mass,":[8],"energy,":[9],"or":[10],"other":[11],"quantities":[12],"in":[13,22,101],"accordance":[14],"with":[15,51],"conservation":[16],"laws.":[17],"Such":[18],"are":[20,95],"widespread":[21],"biology":[23],"and":[24,41,67],"economics.":[25],"In":[26],"this":[27],"paper":[28,113],"a":[29,62,109,129],"connection":[30],"is":[31,59,72],"made":[32],"between":[33],"arbitrary":[34,47],"(not":[35],"necessarily":[36],"nonnegative)":[37],"space":[39,49],"systems":[40],"compartmental":[42,110,131],"models.":[43],"Specifically,":[44],"for":[45],"an":[46,77],"model":[50],"additive":[52],"white":[53],"noise,":[54],"the":[55,81,84,88,105,120,124],"nonnegative-definite":[56],"second-moment":[57,89],"matrix":[58,70],"characterized":[60],"by":[61],"Lyapunov":[63],"differential":[64],"equation.":[65],"Kronecker":[66],"Hadamard":[68],"(Schur)":[69],"algebra":[71],"then":[73],"used":[74],"to":[75],"derive":[76],"equation":[78],"characterizes":[80],"dynamics":[82],"of":[83,87,108,123],"diagonal":[85,93,125],"elements":[86,94,126],"matrix.":[90],"Since":[91],"these":[92],"nonnegative,":[96],"they":[97],"can":[98],"be":[99],"viewed,":[100],"certain":[102],"cases,":[103],"as":[104],"model.":[111,132],"This":[112],"examines":[114],"weak":[115],"coupling":[116],"conditions":[117],"under":[118],"which":[119],"steady-state":[121,130],"values":[122],"actually":[127],"satisfy":[128]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}