{"id":"https://openalex.org/W2901511573","doi":"https://doi.org/10.1137/19m1286219","title":"Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks with Delays","display_name":"Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks with Delays","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2901511573","doi":"https://doi.org/10.1137/19m1286219","mag":"2901511573"},"language":"en","primary_location":{"id":"doi:10.1137/19m1286219","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1286219","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.biorxiv.org/content/biorxiv/early/2019/10/01/481085.full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000665137","display_name":"Corentin Briat","orcid":"https://orcid.org/0000-0003-1822-2683"},"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":true,"raw_author_name":"Corentin Briat","raw_affiliation_strings":["D-BSSE, ETH-Z\u00fcrich, Switzerland (, )"],"raw_orcid":"https://orcid.org/0000-0003-1822-2683","affiliations":[{"raw_affiliation_string":"D-BSSE, ETH-Z\u00fcrich, Switzerland (, )","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018485369","display_name":"Mustafa Khammash","orcid":"https://orcid.org/0000-0002-4855-9220"},"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":true,"raw_author_name":"Mustafa Khammash","raw_affiliation_strings":["D-BSSE, ETH-Z\u00fcrich, Switzerland, (.)","ETH Z\u00fcrich"],"raw_orcid":"https://orcid.org/0000-0002-4855-9220","affiliations":[{"raw_affiliation_string":"D-BSSE, ETH-Z\u00fcrich, Switzerland, (.)","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000665137","https://openalex.org/A5018485369"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.2237,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.47221443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"3","first_page":"1575","last_page":"1608"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9761999845504761,"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/ergodicity","display_name":"Ergodicity","score":0.8258143663406372},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6231892108917236},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5469933748245239},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5283635258674622},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49907946586608887},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.48506680130958557},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4685325026512146},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4641137719154358},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.44501742720603943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.413130521774292},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4054802656173706},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3751872181892395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1539718210697174},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1335926353931427},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11367678642272949}],"concepts":[{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.8258143663406372},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6231892108917236},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5469933748245239},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5283635258674622},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49907946586608887},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.48506680130958557},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4685325026512146},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4641137719154358},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.44501742720603943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.413130521774292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4054802656173706},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3751872181892395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1539718210697174},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1335926353931427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11367678642272949},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/19m1286219","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1286219","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":"doi:10.1101/481085","is_oa":true,"landing_page_url":"https://doi.org/10.1101/481085","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2019/10/01/481085.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},{"id":"pmh:oai:arXiv.org:1811.09188","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1811.09188","pdf_url":"https://arxiv.org/pdf/1811.09188","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/447608","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/447608","pdf_url":"https://www.research-collection.ethz.ch/bitstream/20.500.11850/447608/4/paper8-ergodicity.pdf","source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 19 (3)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1811.09188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.09188","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.3929/ethz-b-000447608","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000447608","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2901511573","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1101/481085","is_oa":true,"landing_page_url":"https://doi.org/10.1101/481085","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2019/10/01/481085.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3677077610","display_name":null,"funder_award_id":"743269","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2901511573.pdf","grobid_xml":"https://content.openalex.org/works/W2901511573.grobid-xml"},"referenced_works_count":72,"referenced_works":["https://openalex.org/W85072216","https://openalex.org/W138967515","https://openalex.org/W172803389","https://openalex.org/W636382642","https://openalex.org/W1506119886","https://openalex.org/W1570713732","https://openalex.org/W1752953962","https://openalex.org/W1965738187","https://openalex.org/W1967642584","https://openalex.org/W1969101909","https://openalex.org/W1974631391","https://openalex.org/W1981626449","https://openalex.org/W1982975329","https://openalex.org/W2011963508","https://openalex.org/W2013502724","https://openalex.org/W2019582172","https://openalex.org/W2021290840","https://openalex.org/W2034311030","https://openalex.org/W2036546758","https://openalex.org/W2041903808","https://openalex.org/W2042942320","https://openalex.org/W2046455140","https://openalex.org/W2060662954","https://openalex.org/W2062404235","https://openalex.org/W2078358623","https://openalex.org/W2080739873","https://openalex.org/W2081827062","https://openalex.org/W2082256594","https://openalex.org/W2091727980","https://openalex.org/W2094631910","https://openalex.org/W2099531989","https://openalex.org/W2125744693","https://openalex.org/W2127535453","https://openalex.org/W2128005148","https://openalex.org/W2132828256","https://openalex.org/W2134459671","https://openalex.org/W2136771204","https://openalex.org/W2161686043","https://openalex.org/W2165716201","https://openalex.org/W2168403922","https://openalex.org/W2200864842","https://openalex.org/W2203446876","https://openalex.org/W2247294682","https://openalex.org/W2296319761","https://openalex.org/W2301167765","https://openalex.org/W2313836003","https://openalex.org/W2467963231","https://openalex.org/W2480970951","https://openalex.org/W2512902587","https://openalex.org/W2515256404","https://openalex.org/W2516171867","https://openalex.org/W2525143841","https://openalex.org/W2593643352","https://openalex.org/W2593688179","https://openalex.org/W2607621829","https://openalex.org/W2612673814","https://openalex.org/W2739921102","https://openalex.org/W2801991624","https://openalex.org/W2808037978","https://openalex.org/W2889646832","https://openalex.org/W2892928034","https://openalex.org/W2952738056","https://openalex.org/W2962815097","https://openalex.org/W2962855705","https://openalex.org/W2963578887","https://openalex.org/W2964216632","https://openalex.org/W3100321237","https://openalex.org/W3104465214","https://openalex.org/W3105441398","https://openalex.org/W3106372989","https://openalex.org/W4247230948","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W1877700460","https://openalex.org/W2489716993","https://openalex.org/W2602832211","https://openalex.org/W315832763","https://openalex.org/W2087724359","https://openalex.org/W1572956868","https://openalex.org/W647375504","https://openalex.org/W1986596303","https://openalex.org/W2137445034","https://openalex.org/W2099883625","https://openalex.org/W160211812","https://openalex.org/W2054824313","https://openalex.org/W3112582141","https://openalex.org/W2764331377","https://openalex.org/W2549307219","https://openalex.org/W2377353405","https://openalex.org/W2952302511","https://openalex.org/W1987409993","https://openalex.org/W212409559","https://openalex.org/W2952365402"],"abstract_inverted_index":{"Abstract":[0],"Delays":[1],"are":[2,114,182,192,217],"important":[3],"phenomena":[4],"arising":[5],"in":[6,49,53,116,241],"a":[7,35,82,104,135,275,284],"wide":[8],"variety":[9],"of":[10,18,37,119,209,226,235,251,268,274,278,308],"real":[11],"world":[12],"systems,":[13],"including":[14],"biological":[15],"ones,":[16],"because":[17],"diffusion/propagation":[19],"effects":[20],"or":[21],"as":[22,81,178,212,214],"simplifying":[23],"modeling":[24],"elements.":[25],"We":[26,61,229],"propose":[27],"here":[28,63],"to":[29,69,99,185,202,205,256],"consider":[30,186],"delayed":[31,78,163,279,285],"stochastic":[32,164,280],"reaction":[33,79,83,148,159,165,210,281],"networks,":[34,160],"class":[36,277],"networks":[38,211],"that":[39,56,64,161,198,232,294,301],"has":[40],"been":[41],"relatively":[42],"few":[43],"studied":[44],"until":[45],"now.":[46],"The":[47,260],"difficulty":[48],"analyzing":[50],"them":[51],"resides":[52],"the":[54,67,76,100,117,139,162,173,206,215,224,233,242,249,252,257,266,269,272,302,306],"fact":[55],"their":[57,132,227],"state-space":[58,140],"is":[59,108,167,176,263,289,292],"infinite-dimensional.":[60],"demonstrate":[62,197],"by":[65,92,265],"restricting":[66],"delays":[68,199,216,237],"be":[70,90],"phase-type":[71,112,218],"distributed,":[72,219],"one":[73],"can":[74,89,123],"represent":[75],"associated":[77],"network":[80,84,102,149,166,175,282,304],"with":[85],"finite-dimensional":[86],"state-space.":[87],"This":[88],"achieved":[91],"suitably":[93],"adding":[94],"chemical":[95],"species":[96],"and":[97,129,170,220,310],"reactions":[98,181],"delay-free":[101,174,258,303],"following":[103],"simple":[105],"algorithm":[106],"which":[107],"fully":[109],"characterized.":[110],"Since":[111],"distributions":[113],"dense":[115],"set":[118],"probability":[120],"distributions,":[121],"they":[122],"approximate":[124],"any":[125],"distribution":[126],"arbitrarily":[127],"closely":[128],"this":[130,221,295],"makes":[131],"consideration":[133],"only":[134,171],"bit":[136],"restrictive.":[137],"As":[138],"remains":[141],"finite-dimensional,":[142],"usual":[143],"tools":[144],"developed":[145],"for":[146,156],"non-delayed":[147],"directly":[150],"apply.":[151],"In":[152],"particular,":[153],"we":[154],"prove,":[155],"unimolecular":[157],"mass-action":[158],"ergodic":[168,177],"if":[169,172],"well.":[179],"Bimolecular":[180],"more":[183],"difficult":[184],"but":[187,245],"slightly":[188],"stronger":[189],"analogous":[190],"results":[191,196],"nevertheless":[193],"obtained.":[194],"These":[195],"have":[200],"little":[201],"no":[203],"harm":[204],"ergodicity":[207,309],"property":[208],"long":[213],"holds":[222],"regardless":[223],"complexity":[225],"distribution.":[228],"also":[230],"prove":[231],"presence":[234,267],"those":[236],"adds":[238],"convolution":[239],"terms":[240],"moment":[243],"equation":[244],"does":[246],"not":[247],"change":[248],"value":[250],"stationary":[253],"means":[254],"compared":[255],"case.":[259],"covariance,":[261],"however,":[262],"influenced":[264],"delays.":[270],"Finally,":[271],"control":[273],"certain":[276],"using":[283],"antithetic":[286],"integral":[287],"controller":[288,296],"considered.":[290],"It":[291],"proven":[293],"achieves":[297],"its":[298],"goal":[299],"provided":[300],"satisfy":[305],"conditions":[307],"output-controllability.":[311]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2022-08-01T00:00:00"}
