{"id":"https://openalex.org/W1511369121","doi":"https://doi.org/10.1109/acc.2015.7172022","title":"Model reduction for a class of singularly perturbed stochastic differential equations","display_name":"Model reduction for a class of singularly perturbed stochastic differential equations","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1511369121","doi":"https://doi.org/10.1109/acc.2015.7172022","mag":"1511369121"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7172022","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7172022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/109532","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039414641","display_name":"Narmada Herath","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Narmada Herath","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044539045","display_name":"Abdullah Hamadeh","orcid":"https://orcid.org/0000-0002-9419-1797"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abdullah Hamadeh","raw_affiliation_strings":["Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA","Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036095256","display_name":"Domitilla Del Vecchio","orcid":"https://orcid.org/0000-0001-6472-8576"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Domitilla Del Vecchio","raw_affiliation_strings":["Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, US","Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, US","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3555,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79911776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"43","issue":null,"first_page":"4404","last_page":"4410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9538999795913696,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.7306190133094788},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7291294932365417},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.682304859161377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6040757298469543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5231512784957886},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.47578465938568115},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4675295352935791},{"id":"https://openalex.org/keywords/method-of-matched-asymptotic-expansions","display_name":"Method of matched asymptotic expansions","score":0.46690043807029724},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43380531668663025},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4239163100719452},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4110947251319885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4008373022079468},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.34998607635498047},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16985023021697998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15978726744651794}],"concepts":[{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.7306190133094788},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7291294932365417},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.682304859161377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6040757298469543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5231512784957886},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.47578465938568115},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4675295352935791},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.46690043807029724},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43380531668663025},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4239163100719452},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4110947251319885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4008373022079468},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34998607635498047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16985023021697998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15978726744651794},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2015.7172022","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7172022","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/109532","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/109532","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT Web Domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/109532","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/109532","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT Web Domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W627107180","https://openalex.org/W1251317174","https://openalex.org/W1515224583","https://openalex.org/W1980396134","https://openalex.org/W2046451925","https://openalex.org/W2077139816","https://openalex.org/W2102787760","https://openalex.org/W2138358136","https://openalex.org/W2145137020","https://openalex.org/W2146823966","https://openalex.org/W2166499263","https://openalex.org/W2171658369","https://openalex.org/W2186962916","https://openalex.org/W2320575569","https://openalex.org/W2402624661","https://openalex.org/W2500486994","https://openalex.org/W2799664482"],"related_works":["https://openalex.org/W2092584480","https://openalex.org/W2383715914","https://openalex.org/W2724386038","https://openalex.org/W2080853821","https://openalex.org/W2370449520","https://openalex.org/W2095085140","https://openalex.org/W2371765427","https://openalex.org/W1994025175","https://openalex.org/W2332818190","https://openalex.org/W2386800263"],"abstract_inverted_index":{"A":[0],"class":[1,111],"of":[2,28,38,66,79,83,95,112,121],"singularly":[3,85],"perturbed":[4,86],"stochastic":[5,93],"differential":[6],"equations":[7,90],"(SDE)":[8],"with":[9,41,98,134],"linear":[10,99],"drift":[11],"and":[12,63,75,105,136],"nonlinear":[13],"diffusion":[14],"terms":[15],"is":[16],"considered.":[17],"We":[18,116],"prove":[19],"that,":[20],"on":[21,124],"a":[22,39,125,129],"finite":[23],"time":[24],"interval,":[25],"the":[26,29,45,61,67,73,80,84,92,110,119],"trajectories":[27],"slow":[30,81,106,137],"variables":[31,70,82],"can":[32],"be":[33],"well":[34,130],"approximated":[35],"by":[36],"those":[37],"system":[40,133],"reduced":[42,68],"dimension":[43],"as":[44],"singular":[46],"perturbation":[47],"parameter":[48,58],"becomes":[49,59],"small.":[50],"In":[51],"particular,":[52],"we":[53],"show":[54],"that":[55],"when":[56],"this":[57],"small":[60],"first":[62,74],"second":[64,76],"moments":[65],"system's":[69],"closely":[71],"approximate":[72],"moments,":[77],"respectively,":[78],"system.":[87],"Chemical":[88],"Langevin":[89],"describing":[91],"dynamics":[94],"molecular":[96],"systems":[97],"propensity":[100],"functions":[101],"including":[102],"both":[103],"fast":[104,135],"reactions":[107],"fall":[108],"within":[109],"SDEs":[113],"considered":[114],"here.":[115],"therefore":[117],"illustrate":[118],"goodness":[120],"our":[122],"approximation":[123],"simulation":[126],"example":[127],"modeling":[128],"known":[131],"biomolecular":[132],"processes.":[138]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
