{"id":"https://openalex.org/W2531373463","doi":"https://doi.org/10.1137/15m1031965","title":"Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks","display_name":"Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2531373463","doi":"https://doi.org/10.1137/15m1031965","mag":"2531373463","pmid":"https://pubmed.ncbi.nlm.nih.gov/28936130"},"language":"en","primary_location":{"id":"doi:10.1137/15m1031965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1031965","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5603244","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080477542","display_name":"Marcella Gomez","orcid":"https://orcid.org/0000-0001-9709-5015"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marcella M. Gomez","raw_affiliation_strings":["Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA","Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014853663","display_name":"Mehdi Sadeghpour","orcid":"https://orcid.org/0000-0003-3946-960X"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mehdi Sadeghpour","raw_affiliation_strings":["Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053287366","display_name":"Matthew R. Bennett","orcid":"https://orcid.org/0000-0002-4975-8854"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew R. Bennett","raw_affiliation_strings":["Department of BioSciences and Department of Bioengineering, Rice University, Houston, TX 77005, USA","Departments of Computing and Mathematical Sciences and Bioengineering, Rice University, Houston, TX 77005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of BioSciences and Department of Bioengineering, Rice University, Houston, TX 77005, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Departments of Computing and Mathematical Sciences and Bioengineering, Rice University, Houston, TX 77005","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043415749","display_name":"G\u00e1bor Orosz","orcid":"https://orcid.org/0000-0002-9000-3736"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G\u00e1bor Orosz","raw_affiliation_strings":["Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068600217","display_name":"Richard M. Murray","orcid":"https://orcid.org/0000-0002-5785-7481"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard M. Murray","raw_affiliation_strings":["Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA","Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2828,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.80919923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"1844","last_page":"1873"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":1.0,"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":1.0,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.9739999771118164,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7359488010406494},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6226224899291992},{"id":"https://openalex.org/keywords/stochastic-dynamics","display_name":"Stochastic dynamics","score":0.5998974442481995},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5728352665901184},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.571251630783081},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5172761082649231},{"id":"https://openalex.org/keywords/gene-regulatory-network","display_name":"Gene regulatory network","score":0.509650707244873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4991326332092285},{"id":"https://openalex.org/keywords/genetic-network","display_name":"Genetic network","score":0.42762523889541626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37154585123062134},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36713290214538574},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3645637035369873},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12854522466659546},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.0762433111667633},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07354786992073059},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06796666979789734}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7359488010406494},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6226224899291992},{"id":"https://openalex.org/C2984125019","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic dynamics","level":2,"score":0.5998974442481995},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5728352665901184},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.571251630783081},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5172761082649231},{"id":"https://openalex.org/C67339327","wikidata":"https://www.wikidata.org/wiki/Q1502576","display_name":"Gene regulatory network","level":4,"score":0.509650707244873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4991326332092285},{"id":"https://openalex.org/C2986044853","wikidata":"https://www.wikidata.org/wiki/Q1502576","display_name":"Genetic network","level":3,"score":0.42762523889541626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37154585123062134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36713290214538574},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3645637035369873},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12854522466659546},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0762433111667633},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07354786992073059},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06796666979789734},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C150194340","wikidata":"https://www.wikidata.org/wiki/Q26972","display_name":"Gene expression","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1031965","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1031965","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmid:28936130","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28936130","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on applied dynamical systems","raw_type":null},{"id":"pmh:oai:authors.library.caltech.edu:73975","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170202-073327562","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:5603244","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5603244","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Appl Dyn Syst","raw_type":"Text"},{"id":"pmh:oai:scholarship.rice.edu:1911/94278","is_oa":false,"landing_page_url":"http://hdl.handle.net/1911/94278","pdf_url":null,"source":{"id":"https://openalex.org/S4306401268","display_name":"Rice Digital Scholarship Archive (Rice University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74775410","host_organization_name":"Rice University","host_organization_lineage":["https://openalex.org/I74775410"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:5603244","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5603244","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Appl Dyn Syst","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3289633681","display_name":null,"funder_award_id":"C-1729","funder_id":"https://openalex.org/F4320306196","funder_display_name":"Welch Foundation"},{"id":"https://openalex.org/G426254373","display_name":null,"funder_award_id":"R01 GM104974","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306196","display_name":"Welch Foundation","ror":"https://ror.org/00np6vq88"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1946177469","https://openalex.org/W1964947431","https://openalex.org/W1968856189","https://openalex.org/W1969101909","https://openalex.org/W1979881360","https://openalex.org/W1987006270","https://openalex.org/W1992044377","https://openalex.org/W2007769474","https://openalex.org/W2008597963","https://openalex.org/W2015707942","https://openalex.org/W2017090803","https://openalex.org/W2037785621","https://openalex.org/W2038176510","https://openalex.org/W2048017269","https://openalex.org/W2057917329","https://openalex.org/W2061269613","https://openalex.org/W2069500900","https://openalex.org/W2070743199","https://openalex.org/W2071579490","https://openalex.org/W2073045768","https://openalex.org/W2080232351","https://openalex.org/W2084907740","https://openalex.org/W2087290699","https://openalex.org/W2088925327","https://openalex.org/W2092227167","https://openalex.org/W2095230945","https://openalex.org/W2101703936","https://openalex.org/W2106043531","https://openalex.org/W2113282439","https://openalex.org/W2116633469","https://openalex.org/W2122125075","https://openalex.org/W2124760969","https://openalex.org/W2131406112","https://openalex.org/W2132828256","https://openalex.org/W2134459671","https://openalex.org/W2147495945","https://openalex.org/W2150453753","https://openalex.org/W2151265887","https://openalex.org/W2151821327","https://openalex.org/W2155418451","https://openalex.org/W2168727894","https://openalex.org/W2169137022","https://openalex.org/W2186962916","https://openalex.org/W2540877599","https://openalex.org/W3105845768","https://openalex.org/W3139820272"],"related_works":["https://openalex.org/W4380053183","https://openalex.org/W1530164014","https://openalex.org/W2146909165","https://openalex.org/W3091282642","https://openalex.org/W1988143233","https://openalex.org/W1968640374","https://openalex.org/W2125300189","https://openalex.org/W2062901238","https://openalex.org/W2562553847","https://openalex.org/W33244840"],"abstract_inverted_index":{"The":[0,55,67],"dynamics":[1,20,41],"of":[2,31,33,53,90],"systems":[3],"with":[4],"stochastically":[5],"varying":[6],"time":[7],"delays":[8],"are":[9,57,63,70],"investigated":[10],"in":[11,83],"this":[12],"paper.":[13],"It":[14],"is":[15,79],"shown":[16],"that":[17,62,81],"the":[18,29,34,38,84,88],"mean":[19],"can":[21,42,86],"be":[22,43],"used":[23,44],"to":[24,45,72],"derive":[25,46],"necessary":[26],"conditions":[27,48],"for":[28,49],"stability":[30,52,60,89],"equilibria":[32],"stochastic":[35],"system.":[36],"Moreover,":[37],"second":[39],"moment":[40],"sufficient":[47],"almost":[50],"sure":[51],"equilibria.":[54],"results":[56],"summarized":[58],"using":[59],"charts":[61],"obtained":[64],"via":[65],"semi-discretization.":[66],"theoretical":[68],"methods":[69],"applied":[71],"simple":[73],"gene":[74],"regulatory":[75],"networks":[76],"where":[77],"it":[78],"demonstrated":[80],"stochasticity":[82],"delay":[85],"improve":[87],"steady":[91],"protein":[92],"production.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}